{"text_format":"1","workbook":"xlsx","n_sheets":28,"sheets":["Introduction","Index","Help","Power_function","Log_function","Exponential_function","Ln_function","Growth","Simple_interest","Compound_interest","Continuous_interest","IRR","Inflation","Yield_curves_Discount_factors","Forward_interest_rates","Annuities","Bond_fundamentals","Floating_rate_notes","Swap_fundamentals","Swap_Cross_Currency","Sensitivity","Gradient_and_curvature","Frequency_distribution","Variance_and_correlation","Interpolation_and_extrapolation","Asset_evolution","Multi_asset","__ans__"],"not_rendered":{"charts":35,"images":4,"macros":1,"external_links":0,"defined_names":92,"comments":0,"pivot_tables":0},"unopened":[],"bounds":{"document_bytes":16777216,"sheet_cells":100000,"rows_first":2000,"rows_last":500,"rows_between":2000,"halvings":0,"cell_chars":16384,"cell_head_chars":4096},"cells_cut":0,"cells_raw":0,"read":"whole","date_system":"1900"}

{"sheet":"Introduction","index":0,"n_rows":28,"n_cols":3,"rows_kept":28,"cut":false,"hidden":false,"merged":[[19,2,19,6],[22,1,22,7],[24,2,24,6],[26,2,26,8],[27,2,27,8],[15,1,17,7],[2,1,3,7],[5,1,6,7],[8,2,8,6],[10,1,11,7],[13,2,13,6]]}
[" "]
[null,"About this spreadsheet"]
[null,"This spreadsheet lets you test - and possibly improve - your financial mathematics skills."]
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[null,"You might find the following resource useful:  It contains background notes about the financial mathematics concepts referred to in this spreadsheet."]
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[null,null,"Background notes"]
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[null,"If you do well then you can choose to post your score on our \"leader-board\".  The leader board is at the following address:"]
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[null,null,"Leader board"]
[" ","Index"]
[null,"This spreadsheet has an index page that shows a summary of which topics you have mastered.  To go to the index page click on the following link."]
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[null,null,"Index"]
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[null,"Help"]
[null,"For help click on the following link."]
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[null,null,"Help"]
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[null,null,"Copyright (c) 2020 Tykoh Group Pty Ltd.  All rights reserved."]
[null,null,"www.tykoh.com"]

{"sheet":"Index","index":1,"n_rows":145,"n_cols":9,"rows_kept":145,"cut":false,"hidden":false,"merged":[[143,3,143,9],[144,3,144,9]]}
[null,"Financial mathematics competition",null,null,null,null,null,null,"Help"]
[null,"[-]","Power and logarithm functions",null,null,null,null,null,1262]
[null,null,null,"[-]","Power function"]
[null,null,null,null,null,{"$f":"Power_function!$A$2","v":2},"Used in annual compounding"]
[null,null,null,null,null,{"$f":"Power_function!$A$14","v":1},"Determining interest rate to double investment in ten years"]
[null,null,null,null,null,{"$f":"Power_function!$A$21","v":7},"Compounding value vs compounding frequency"]
[null,null,null,"[-]","Log function"]
[null,null,null,null,null,{"$f":"Log_function!$A$2","v":1},"Time to compound annually to a given value"]
[null,null,null,null,null,{"$f":"Log_function!$A$9","v":1},"Time to compound semi-annually to a given value"]
[null,"[-]","Exponential and ln functions"]
[null,null,null,"[-]","Exponential function"]
[null,null,null,null,null,{"$f":"Exponential_function!$A$2","v":2},"Exponential function - Used with continuously compounding interest rate."]
[null,null,null,null,null,{"$f":"Exponential_function!$A$13","v":1},"Exponential function - Converting continuous rate to quarterly compounding."]
[null,null,null,null,null,{"$f":"Exponential_function!$A$20","v":8},"Exponential function - Showing e^x is approximately 1+x if x is small."]
[null,null,null,"[-]","Ln function"]
[null,null,null,null,null,{"$f":"Ln_function!$A$2","v":1},"Ln function - Converting from periodic interest rate to continuous compounding"]
[null,"[-]","Measures of growth"]
[null,null,null,"[-]","Growth"]
[null,null,null,null,null,{"$f":"Growth!$A$8","v":8},"Calculating arithmetic and compound average growth rate - when growth is constant"]
[null,null,null,null,null,{"$f":"Growth!$A$31","v":8},"Calculating arithmetic and compound average growth rate - when growth varies"]
[null,null,null,null,null,{"$f":"Growth!$A$58","v":3},"Calculating quarterly, semi and p.a. growth given monthly growth"]
[null,null,null,null,null,{"$f":"Growth!$A$69","v":1},"Calculating effective growth rate given the nominal growth rate"]
[null,null,null,null,null,{"$f":"Growth!$A$76","v":1},"Calculating yearly effective growth rate given nominal continuously compounding rate"]
[null,null,null,null,null,{"$f":"Growth!$A$82","v":1},"Calculating nominal growth rate given the effective growth rate"]
[null,null,null,null,null,{"$f":"Growth!$A$90","v":1},"Calculating nominal compounding rate given yearly effective rate."]
[null,null,null,null,null,{"$f":"Growth!$A$96","v":3},"Showing that 10% growth followed by -10% growth has a different result than has zero growth."]
[null,"[-]","Present and future value; interest rates: simple, compounding, continuous; compounding conversion."]
[null,null,null,"[-]","Simple interest"]
[null,null,null,null,null,{"$f":"Simple_interest!$A$2","v":1},"Future value of an investment earning simple interest."]
[null,null,null,null,null,{"$f":"Simple_interest!$A$9","v":1},"Present value of an investment earning simple interest."]
[null,null,null,null,null,{"$f":"Simple_interest!$A$16","v":1},"Simple interest rate as a function of present value, future value and investment term."]
[null,null,null,null,null,{"$f":"Simple_interest!$A$23","v":1},"Investment term as a function of present value, future value and interest rate."]
[null,null,null,"[-]","Compound interest"]
[null,null,null,null,null,{"$f":"Compound_interest!$A$2","v":1},"Future value of an investment earning compound interest."]
[null,null,null,null,null,{"$f":"Compound_interest!$A$9","v":1},"Present value of an investment earning compound interest."]
[null,null,null,null,null,{"$f":"Compound_interest!$A$16","v":1},"Compound interest rate as a function of present value, future value and investment term."]
[null,null,null,null,null,{"$f":"Compound_interest!$A$23","v":1},"Investment term as a function of present value, future value and interest rate."]
[null,null,null,"[-]","Continuous interest"]
[null,null,null,null,null,{"$f":"Continuous_interest!$A$2","v":1},"Future value of an investment earning continuous interest"]
[null,null,null,null,null,{"$f":"Continuous_interest!$A$9","v":1},"Present value of an investment earning continuous interest"]
[null,null,null,null,null,{"$f":"Continuous_interest!$A$16","v":1},"Continuous interest rate as a function of present value, future value and investment term."]
[null,null,null,null,null,{"$f":"Continuous_interest!$A$23","v":1},"Investment term as a function of present value, future value and interest rate."]
[null,"[-]","Internal rate of return, real and nominal rates"]
[null,null,null,"[-]","IRR"]
[null,null,null,null,null,{"$f":"IRR!$A$2","v":1},"Calculate IRR of a yearly series of cash flows."]
[null,null,null,null,null,{"$f":"IRR!$A$9","v":1},"Calculate nominal yearly IRR for a semi-annual series of cash flows"]
[null,null,null,null,null,{"$f":"IRR!$A$16","v":11},"Demonstration that certain cash flows can have more than one IRR"]
[null,null,null,"[-]","Inflation"]
[null,null,null,null,null,{"$f":"Inflation!$A$2","v":13},"Calculating present value on nominal and inflation-adjusted bases"]
[null,null,null,null,null,{"$f":"Inflation!$A$28","v":4},"Calculating IRR on nominal and inflation-adjusted bases"]
[null,"[-]","Yield / Zero-Coupon curve, discount factors, forward interest rates"]
[null,null,null,"[-]","Yield curves Discount factors"]
[null,null,null,null,null,{"$f":"Yield_curves_Discount_factors!$A$2","v":5},"Calculating discount factors from points on a yield curve"]
[null,null,null,null,null,{"$f":"Yield_curves_Discount_factors!$A$11","v":6},"Using discount factors to calculate the value of a series of future cash flows."]
[null,null,null,null,null,{"$f":"Yield_curves_Discount_factors!$A$20","v":5},"Generating a yield curve equivalent to a set of discount factors."]
[null,null,null,"[-]","Forward interest rates"]
[null,null,null,null,null,{"$f":"Forward_interest_rates!$A$2","v":3},"Calculating forward interest rate implied by zero coupon yield curve"]
[null,null,null,null,null,{"$f":"Forward_interest_rates!$A$27","v":9},"Calculating implied forward curve from yield curve."]
[null,null,null,null,null,{"$f":"Forward_interest_rates!$A$58","v":8},"Calculating zero curve from forward curve"]
[null,"[-]","Bond fundamentals and sensitivities"]
[null,null,null,"[-]","Annuities"]
[null,null,null,null,null,{"$f":"Annuities!$A$2","v":12},"Value of a growing annuity"]
[null,null,null,null,null,{"$f":"Annuities!$A$18","v":1},"Present value of a basis point (PVBP)"]
[null,null,null,"[-]","Bond fundamentals"]
[null,null,null,null,null,{"$f":"Bond_fundamentals!$A$2","v":5},"Present value of a bond - calculating from future cash flows and a discount rate."]
[null,null,null,null,null,{"$f":"Bond_fundamentals!$A$21","v":12},"Using present value and yield to generate future cash flows."]
[null,null,null,null,null,{"$f":"Bond_fundamentals!$A$41","v":23},"Calculating yield to maturity of a bond."]
[null,null,null,null,null,{"$f":"Bond_fundamentals!$A$83","v":16},"Calculating yield to maturity of an annuity"]
[null,null,null,"[-]","Floating rate notes"]
[null,null,null,null,null,{"$f":"Floating_rate_notes!$A$2","v":13},"Valuing a floating rate note from first principles."]
[null,"[-]","Swap fundamentals"]
[null,null,null,"[-]","Swap fundamentals"]
[null,null,null,null,null,{"$f":"Swap_fundamentals!$A$6","v":32},"Valuing the fixed and floating legs of a fixed-to-float interest rate swap"]
[null,null,null,null,null,{"$f":"Swap_fundamentals!$A$24","v":23},"Calculating fixed coupon rate that makes swap value zero."]
[null,null,null,"[-]","Swap Cross Currency"]
[null,null,null,null,null,{"$f":"Swap_Cross_Currency!$A$21","v":1},"Converting USD quarterly swap rate to semi."]
[null,null,null,null,null,{"$f":"Swap_Cross_Currency!$A$28","v":1},"Calculating USD PVBP"]
[null,null,null,null,null,{"$f":"Swap_Cross_Currency!$A$38","v":1},"Calculating the margin above the USD semi swap rate we want to receive"]
[null,null,null,null,null,{"$f":"Swap_Cross_Currency!$A$43","v":1},"Calculating AUD PVBP"]
[null,null,null,null,null,{"$f":"Swap_Cross_Currency!$A$47","v":1},"Calculating AUD margin"]
[null,null,null,null,null,{"$f":"Swap_Cross_Currency!$A$51","v":101},"Modelling swap cash flows"]
[null,"[-]","Sensitivity, rate of change, curvature"]
[null,null,null,"[-]","Sensitivity"]
[null,null,null,null,null,{"$f":"Sensitivity!$A$9","v":5},"Calculating sensitivity of fixed-interest investment's value to time"]
[null,null,null,null,null,{"$f":"Sensitivity!$A$28","v":25},"Calculating sensitivity of forward price to its drivers."]
[null,null,null,null,null,{"$f":"Sensitivity!$A$60","v":16},"Calculating sensitivity of annuity to its drivers"]
[null,null,null,"[-]","Gradient and curvature"]
[null,null,null,null,null,{"$f":"Gradient_and_curvature!$A$6","v":4},"Gradient of e^(ax)"]
[null,null,null,null,null,{"$f":"Gradient_and_curvature!$A$19","v":4},"Gradient of x^n"]
[null,null,null,null,null,{"$f":"Gradient_and_curvature!$A$30","v":4},"Gradient of a^x"]
[null,null,null,null,null,{"$f":"Gradient_and_curvature!$A$41","v":4},"Gradient of ln(x)"]
[null,null,null,null,null,{"$f":"Gradient_and_curvature!$A$51","v":4},"Calculating gradient of the product of two functions"]
[null,null,null,null,null,{"$f":"Gradient_and_curvature!$A$68","v":4},"Calculating the gradient of a function of a function"]
[null,null,null,null,null,{"$f":"Gradient_and_curvature!$A$83","v":8},"Calculating gradient of a piecewise-linear curve."]
[null,null,null,null,null,{"$f":"Gradient_and_curvature!$A$114","v":7},"Calculating curvature"]
[null,null,null,null,null,{"$f":"Gradient_and_curvature!$A$135","v":1},"Using gradient and curvature in interpolating and extrapolating"]
[null,"[-]","Mean, standard deviation, distributions"]
[null,null,null,"[-]","Frequency distribution"]
[null,null,null,null,null,{"$f":"Frequency_distribution!$A$2","v":12},"Calculating a frequency distribution from a sample set"]
[null,null,null,null,null,{"$f":"Frequency_distribution!$A$27","v":1},"Calculating a mean from a frequency distribution."]
[null,null,null,null,null,{"$f":"Frequency_distribution!$A$33","v":2},"Calculating a mode from a frequency distribution."]
[null,null,null,null,null,{"$f":"Frequency_distribution!$A$40","v":24},"Calculating a cumulative frequency distribution."]
[null,null,null,null,null,{"$f":"Frequency_distribution!$A$63","v":1},"Calculating lowest return in upper quartile."]
[null,null,null,null,null,{"$f":"Frequency_distribution!$A$69","v":52},"Calculating standard deviation."]
[null,null,null,null,null,{"$f":"Frequency_distribution!$A$101","v":24},"Generating a normal distribution"]
[null,null,null,null,null,{"$f":"Frequency_distribution!$A$130","v":15},"Calculating percentage of outcomes less than N standard deviations above mean"]
[null,null,null,null,null,{"$f":"Frequency_distribution!$A$162","v":11},"Calculating percentage of outcomes within N standard deviations of the mean"]
[null,null,null,null,null,{"$f":"Frequency_distribution!$A$183","v":15},"Calculating number of standard deviations above mean below which a given percentage of samples occur."]
[null,null,null,null,null,{"$f":"Frequency_distribution!$A$213","v":64},"Generating samples from a normal distribution."]
[null,null,null,"[-]","Variance and correlation"]
[null,null,null,null,null,{"$f":"Variance_and_correlation!$A$2","v":3},"Calculating sample variance"]
[null,null,null,null,null,{"$f":"Variance_and_correlation!$A$25","v":3},"Calculating population variance"]
[null,null,null,null,null,{"$f":"Variance_and_correlation!$A$35","v":12},"Calculating population covariance"]
[null,null,null,null,null,{"$f":"Variance_and_correlation!$A$58","v":9},"Calculating population correlation"]
[null,null,null,null,null,{"$f":"Variance_and_correlation!$A$68","v":9},"Calculating correlation matrix from covariance matrix"]
[null,null,null,null,null,{"$f":"Variance_and_correlation!$A$83","v":9},"Calculating covariance matrix from correlation matrix and standard deviation"]
[null,null,null,null,null,{"$f":"Variance_and_correlation!$A$98","v":20},"Calculating volatility"]
[null,null,null,null,null,{"$f":"Variance_and_correlation!$A$137","v":39},"Calculating correlation of log returns"]
[null,"[-]","Interpolation, extrapolation and curve fitting"]
[null,null,null,"[-]","Interpolation and extrapolation"]
[null,null,null,null,null,{"$f":"Interpolation_and_extrapolation!$A$7","v":2},"Linear interpolation"]
[null,null,null,null,null,{"$f":"Interpolation_and_extrapolation!$A$27","v":47},"Cubic spline interpolation"]
[null,null,null,null,null,{"$f":"Interpolation_and_extrapolation!$A$142","v":15},"TREND function to perform linear interpolation / extrapolation"]
[null,null,null,null,null,{"$f":"Interpolation_and_extrapolation!$A$172","v":15},"GROWTH function to perform linear interpolation / extrapolation"]
[null,null,null,null,null,{"$f":"Interpolation_and_extrapolation!$A$198","v":39},"Fitting to a logarithmic curve"]
[null,null,null,null,null,{"$f":"Interpolation_and_extrapolation!$A$224","v":39},"Fitting to a square-root curve"]
[null,"[-]","Asset evolution"]
[null,null,null,"[-]","Asset evolution"]
[null,null,null,null,null,{"$f":"Asset_evolution!$A$2","v":8},"Calculating asset price distribution in one period's time."]
[null,null,null,null,null,{"$f":"Asset_evolution!$A$20","v":8},"Calculating asset price distribution in two period's time."]
[null,null,null,null,null,{"$f":"Asset_evolution!$A$37","v":45},"Calculating asset price distribution \"N\" periods into the future. "]
[null,null,null,null,null,{"$f":"Asset_evolution!$A$80","v":64},"Calculating probability distribution of long-term return."]
[null,null,null,null,null,{"$f":"Asset_evolution!$A$114","v":42},"Calculating probability distribution of logarithm of asset price in \"N\" period's time."]
[null,null,null,null,null,{"$f":"Asset_evolution!$A$146","v":64},"Calculating distribution of compound average growth rates over \"N\" periods."]
[null,null,null,null,null,{"$f":"Asset_evolution!$A$175","v":38},"Matching volatility and growth rate when evolving an asset's price."]
[null,null,null,null,null,{"$f":"Asset_evolution!$A$252","v":43},"Calculating asset price distribution by using continuous log-normal distribution."]
[null,null,null,null,null,{"$f":"Asset_evolution!$A$305","v":7},"Calculating confidence intervals on an asset's future price."]
[null,null,null,null,null,{"$f":"Asset_evolution!$A$335","v":2},"Calculating confidence intervals on an asset's future price (alternate formula)"]
[null,null,null,"[-]","Multi asset"]
[null,null,null,null,null,{"$f":"Multi_asset!$A$2","v":1},"Calculating return of a portfolio of assets"]
[null,null,null,null,null,{"$f":"Multi_asset!$A$14","v":1},"Calculating volatility of a portfolio of assets"]
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[null,null,null,"Copyright (c) 2020 Tykoh Group Pty Ltd.  All rights reserved."]
[null,null,null,"www.tykoh.com"]

{"sheet":"Help","index":2,"n_rows":74,"n_cols":4,"rows_kept":74,"cut":false,"hidden":false,"merged":[[72,3,72,9],[73,3,73,9],[2,1,3,8],[51,1,52,8],[54,1,55,8],[57,1,59,8],[66,1,69,8],[5,1,6,8],[33,1,36,8],[18,1,19,8],[61,1,64,8]]}
[null,"Help"," "]
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[null,"This spreadsheet contains a set of questions which you can answer.  The questions are in tabs to the right of this - Help - tab."]
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[null,"To answer questions you need to put formulas into cells that have a colored background (outlined in red border below)."]
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[null,"When a formula is correct a corresponding blue marker on the left will turn yellow:"]
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[null,"On the Index page is a summary of questions you have answered correctly.  Markers on that page indicate whether questions have been completed correctly.  A marker that looks like \"-\" means all parts of the question has been completed correctly.  A marker that looks like \"x\" means the answer isn't complete. "]
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[null,"Macros"]
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[null,"If you have macros enabled then the functions described below will be available to you."]
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[null,"1.  Clicking in the '[+]' and '[-]'  markers on the Index page will expand or collapse the corresponding index section."]
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[null,"2.  You can check your progress through the questions (e.g. 35%). To do that, right-mouse-click on any tab and select the \"Tykoh check progress\" menu item on the pop-up menu."]
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[null,"3. You can load model answers.  To do that, right-mouse-click on the tab you want the answers for.  Then select the \"Tykoh load answers\" menu item on the pop-up menu.  The answers that are loadable are changed from time-to time so all, none or a subset may be available."]
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[null,"4. You can add your name to a live \"leader-board\" if your percentage progress is sufficiently high relative to others who have answered the questions.  You will be given that opportunity when you choose the \"Tykoh check progress\" option mentioned above."]
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[null,null,null,"Copyright (c) 2020 Tykoh Group Pty Ltd.  All rights reserved."]
[null,null,null,"www.tykoh.com"]

{"sheet":"Power_function","index":3,"n_rows":92,"n_cols":12,"rows_kept":92,"cut":false,"hidden":false,"merged":[[91,3,91,9],[0,3,0,9],[26,3,29,10],[15,3,16,10],[3,3,4,10],[22,3,24,10],[90,3,90,9]]}
[null,null,null,"Click here to see what your answer should look like."]
[{"$f":"SUM($A$3:$A$13)","v":2},null,1,"Used in annual compounding",null,null,null,null,null,"Power_and_log","Power_function"]
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[null,null,null,"$100 earns 5% interest compounding annually.  How much is the compounded value in four years?"]
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[{"$f":"IF(OR(NOT(ISNUMBER($I$7)),ISERROR($I$7)),1,IF(AND(LEN($I$7)>0,ABS((1-($I$7* 2.05547511577606+ 0.0334240198135376)/ 249.877709014341))<0.00005),0,1))","v":1},null,null,"Compounded value in four years:"]
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[null,null,null,"How much is the compounded value in four and a half years?"]
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[{"$f":"IF(OR(NOT(ISNUMBER($I$11)),ISERROR($I$11)),1,IF(AND(LEN($I$11)>0,ABS((1-($I$11* 0.795186161994934+-0.210437536239624)/ 98.8318493341835))<0.00005),0,1))","v":1},null,null,"Compounded value in four and a half years:"]
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[null,null,null,null,null,null,null,null,null,null,null,"Index"]
[{"$f":"SUM($A$15:$A$20)","v":1},null,2,"Determining interest rate to double investment in ten years"]
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[null,null,null,"What nominal interest rate (semi-annual compounding) is required to double an investment in ten years?"]
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[{"$f":"IF(OR(NOT(ISNUMBER($H$19)),ISERROR($H$19)),1,IF(AND(LEN($H$19)>0,ABS((1-($H$19*-1.98051989078522+ 0.274740099906921)/ 0.135054333677173))<0.00005),0,1))","v":1},null,null,"Rate required:"]
[null,null,null,null,null,null,null,null,null,null,null,"Index"]
[{"$f":"SUM($A$22:$A$91)","v":7},null,{"$f":"C14+1","v":3},"Compounding value vs compounding frequency"]
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[null,null,null,"Continuous compounding formulae usually contain \"e\" - which is approximately 2.71828.  This example shows that when the compounding frequency is increased the result converges to \"e\"."]
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[null,null,null,"An investment of $1 earns a nominal annual interest rate of 100%.  The investment is for a term of one year. Interest compounds \"n\" times per year.  The value of the investment at the end of one year is \"v\".  Complete the following table showing v as a function of n.\n"]
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[null,null,null,"n","v"]
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[{"$f":"IF(OR(NOT(ISNUMBER($E$34)),ISERROR($E$34)),1,IF(AND(LEN($E$34)>0,ABS((1-($E$34*-4.85982358455657+ 0.26072359085083)/-9.45892357826233))<0.00005),0,1))","v":1},null,null,1]
[{"$f":"IF(OR(NOT(ISNUMBER($E$35)),ISERROR($E$35)),1,IF(AND(LEN($E$35)>0,ABS((1-($E$35* 3.14490020275116+ 0.209037899971008)/ 7.28506335616112))<0.00005),0,1))","v":1},null,null,2]
[{"$f":"IF(OR(NOT(ISNUMBER($E$36)),ISERROR($E$36)),1,IF(AND(LEN($E$36)>0,ABS((1-($E$36*-4.54647243022919+-0.0859673023223877)/-11.1857535089366))<0.00005),0,1))","v":1},null,null,4]
[{"$f":"IF(OR(NOT(ISNUMBER($E$37)),ISERROR($E$37)),1,IF(AND(LEN($E$37)>0,ABS((1-($E$37* 3.62619340419769+ 0.290480017662048)/ 9.76585135201057))<0.00005),0,1))","v":1},null,null,12]
[{"$f":"IF(OR(NOT(ISNUMBER($E$38)),ISERROR($E$38)),1,IF(AND(LEN($E$38)>0,ABS((1-($E$38*-1.26463830471039+ 0.461953163146973)/-2.97099285533929))<0.00005),0,1))","v":1},null,null,365]
[{"$f":"IF(OR(NOT(ISNUMBER($E$39)),ISERROR($E$39)),1,IF(AND(LEN($E$39)>0,ABS((1-($E$39* 3.71445834636688+-0.443763136863709)/ 9.65267668767217))<0.00005),0,1))","v":1},null,null,10000]
[{"$f":"IF(OR(NOT(ISNUMBER($E$40)),ISERROR($E$40)),1,IF(AND(LEN($E$40)>0,ABS((1-($E$40* 4.49556648731232+-0.135981321334839)/ 12.0842292589204))<0.00005),0,1))","v":1},null,null,1000000]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[null,null,null,"Copyright (c) 2020 Tykoh Group Pty Ltd.  All rights reserved.",null,null,null,null,null,null,null,"Index"]
[null,null,null,"www.tykoh.com"]

{"sheet":"Log_function","index":4,"n_rows":17,"n_cols":12,"rows_kept":17,"cut":false,"hidden":false,"merged":[[3,3,4,8],[10,3,11,8],[15,3,15,9],[16,3,16,9],[0,3,0,9]]}
[null,null,null,"Click here to see what your answer should look like."]
[{"$f":"SUM($A$3:$A$8)","v":1},null,1,"Time to compound annually to a given value",null,null,null,null,null,"Power_and_log","Log_function"]
[]
[null,null,null,"$100 compounds annually at 6%.  How long will it take to compound to a value of $120?"]
[]
[]
[{"$f":"IF(OR(NOT(ISNUMBER($G$7)),ISERROR($G$7)),1,IF(AND(LEN($G$7)>0,ABS((1-($G$7* 0.248684287071228+ 0.267111659049988)/ 1.04523686902565))<0.00005),0,1))","v":1},null,null,"Time to compound (years):"]
[null,null,null,null,null,null,null,null,null,null,null,"Index"]
[{"$f":"SUM($A$10:$A$16)","v":1},null,{"$f":"C2+1","v":2},"Time to compound semi-annually to a given value"]
[]
[null,null,null,"$100 compounds semi-annually at a nominal annual rate of 6%. How long will it take to compound to a value of $120?"]
[]
[]
[{"$f":"IF(OR(NOT(ISNUMBER($G$14)),ISERROR($G$14)),1,IF(AND(LEN($G$14)>0,ABS((1-($G$14*-4.46495473384857+ 0.0924582481384277)/-13.6776785022889))<0.00005),0,1))","v":1},null,null,"Time to compound (years):"]
[]
[null,null,null,"Copyright (c) 2020 Tykoh Group Pty Ltd.  All rights reserved.",null,null,null,null,null,null,null,"Index"]
[null,null,null,"www.tykoh.com"]

{"sheet":"Exponential_function","index":5,"n_rows":34,"n_cols":13,"rows_kept":34,"cut":false,"hidden":false,"merged":[[3,4,4,11],[14,4,15,11],[32,5,32,11],[33,5,33,11],[0,4,0,10]]}
[null,null,null,null,"Click here to see what your answer should look like."]
[{"$f":"SUM($A$3:$B$12)","v":2},null,null,1,"Exponential function - Used with continuously compounding interest rate.",null,null,null,null,null,"Exponential_and_ln","Exponential_function"]
[]
[null,null,null,null,"What would $100 compound to if the nominal annual continuously compounding rate is 6% and the term is one year?"]
[]
[]
[{"$f":"IF(OR(NOT(ISNUMBER($G$7)),ISERROR($G$7)),1,IF(AND(LEN($G$7)>0,ABS((1-($G$7*-0.31299889087677+-0.201834559440613)/-33.4372006955523))<0.00005),0,1))","v":1},null,null,null,"Value in one year:"]
[]
[null,null,null,null,"What is the annual effective compounding rate?"]
[]
[{"$f":"IF(OR(NOT(ISNUMBER($G$11)),ISERROR($G$11)),1,IF(AND(LEN($G$11)>0,ABS((1-($G$11* 1.22696697711945+ 0.147821187973022)/ 0.223692588563288))<0.00005),0,1))","v":1},null,null,null,"Annual effective rate:"]
[null,null,null,null,null,null,null,null,null,null,null,null,"Index"]
[{"$f":"SUM($A$14:$B$19)","v":1},null,null,2,"Exponential function - Converting continuous rate to quarterly compounding."]
[]
[null,null,null,null,"What nominal quarterly compounding rate is equivalent to a continuously compounding rate of 7%?"]
[]
[]
[{"$f":"IF(OR(NOT(ISNUMBER($G$18)),ISERROR($G$18)),1,IF(AND(LEN($G$18)>0,ABS((1-($G$18*-2.36207067966461+-0.22065794467926)/-0.387458137081116))<0.00005),0,1))","v":1},null,null,null,"Quarterly rate:"]
[null,null,null,null,null,null,null,null,null,null,null,null,"Index"]
[{"$f":"SUM($A$21:$B$33)","v":8},null,null,{"$f":"D13+1","v":3},"Exponential function - Showing e^x is approximately 1+x if x is small."]
[]
[null,null,null,null,"Complete the following table"]
[]
[null,null,null,null,"x","ex","1+x"]
[]
[{"$f":"IF(OR(NOT(ISNUMBER($F$26)),ISERROR($F$26)),1,IF(AND(LEN($F$26)>0,ABS((1-($F$26* 3.29801619052887+ 0.324602127075195)/ 3.96947370819034))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($G$26)),ISERROR($G$26)),1,IF(AND(LEN($G$26)>0,ABS((1-($G$26* 0.891630053520203+ 0.486093163490295)/ 1.46688622236252))<0.00005),0,1))","v":1},null,null,0.1]
[{"$f":"IF(OR(NOT(ISNUMBER($F$27)),ISERROR($F$27)),1,IF(AND(LEN($F$27)>0,ABS((1-($F$27* 4.10964310169219+-0.273133993148804)/ 3.8778117083717))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($G$27)),ISERROR($G$27)),1,IF(AND(LEN($G$27)>0,ABS((1-($G$27* 1.95115506649017+ 0.480003237724304)/ 2.45066985487938))<0.00005),0,1))","v":1},null,null,0.01]
[{"$f":"IF(OR(NOT(ISNUMBER($F$28)),ISERROR($F$28)),1,IF(AND(LEN($F$28)>0,ABS((1-($F$28*-2.56068646907806+ 0.0338730812072754)/-2.52937535510999))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($G$28)),ISERROR($G$28)),1,IF(AND(LEN($G$28)>0,ABS((1-($G$28*-3.9363032579422+ 0.499414563179016)/-3.44082499802113))<0.00005),0,1))","v":1},null,null,1E-3]
[{"$f":"IF(OR(NOT(ISNUMBER($F$29)),ISERROR($F$29)),1,IF(AND(LEN($F$29)>0,ABS((1-($F$29* 1.76175892353058+-0.484296083450317)/ 1.2776390247817))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($G$29)),ISERROR($G$29)),1,IF(AND(LEN($G$29)>0,ABS((1-($G$29* 0.751838088035584+-0.399947762489319)/ 0.351965509355068))<0.00005),0,1))","v":1},null,null,1E-4]
[]
[]
[]
[null,null,null,null,null,"Copyright (c) 2020 Tykoh Group Pty Ltd.  All rights reserved.",null,null,null,null,null,null,"Index"]
[null,null,null,null,null,"www.tykoh.com"]

{"sheet":"Ln_function","index":6,"n_rows":11,"n_cols":12,"rows_kept":11,"cut":false,"hidden":false,"merged":[[3,3,4,9],[9,3,9,9],[10,3,10,9],[0,3,0,9]]}
[null,null,null,"Click here to see what your answer should look like."]
[{"$f":"SUM($A$3:$A$10)","v":1},null,1,"Ln function - Converting from periodic interest rate to continuous compounding",null,null,null,null,null,"Exponential_and_ln","Ln_function"]
[]
[null,null,null,"What continuously compounding rate is equivalent to an annually compounding rate of 6%?"]
[]
[]
[{"$f":"IF(OR(NOT(ISNUMBER($F$7)),ISERROR($F$7)),1,IF(AND(LEN($F$7)>0,ABS((1-($F$7*-3.96977365016937+ 0.298884391784668)/ 0.0675700156899686))<0.00005),0,1))","v":1},null,null,"Continuous rate:"]
[]
[]
[null,null,null,"Copyright (c) 2020 Tykoh Group Pty Ltd.  All rights reserved.",null,null,null,null,null,null,null,"Index"]
[null,null,null,"www.tykoh.com"]

{"sheet":"Growth","index":7,"n_rows":126,"n_cols":13,"rows_kept":126,"cut":false,"hidden":false,"merged":[[124,4,124,10],[125,4,125,10],[0,3,0,9],[59,3,59,11],[77,3,77,11],[110,3,113,11],[91,3,91,11],[2,3,5,11],[97,3,98,11],[83,3,85,11],[9,3,10,11],[32,3,33,11],[53,3,55,11],[70,3,71,11]]}
[null,null,null,"Click here to see what your answer should look like."]
[null,null,null,null,null,null,null,null,null,null,"Growth","Growth"]
[null,null,null,"Growth may seem a simple term but it encompasses some important and subtle concepts - For example,  a +10% growth followed by -10% growth leads to a different outcome than does zero growth.  In this section we review and apply various measures of growth and show how these measures relate to each other."]
[]
[]
[]
[]
[{"$f":"SUM($A$9:$A$30)","v":8},null,1,"Calculating arithmetic and compound average growth rate - when growth is constant"]
[]
[null,null,null,"Consider the investment shown below.  The value of the investment at the end of each year is listed.  Find the per annum (p.a.) growth rate in each year."]
[]
[]
[null,null,null,"Year","Value","Growth p.a."]
[null,null,null,0,50]
[{"$f":"IF(OR(NOT(ISNUMBER($F$15)),ISERROR($F$15)),1,IF(AND(LEN($F$15)>0,ABS((1-($F$15*-2.15519726276398+-0.454350829124451)/-0.50823076069355))<0.00005),0,1))","v":1},null,null,{"$f":"D14+1","v":1},{"$f":"E14*(1.025)","v":51.249999999999993}]
[{"$f":"IF(OR(NOT(ISNUMBER($F$16)),ISERROR($F$16)),1,IF(AND(LEN($F$16)>0,ABS((1-($F$16*-2.04227149486542+-0.117989301681519)/-0.169046089053154))<0.00005),0,1))","v":1},null,null,2,52.531249999999986]
[{"$f":"IF(OR(NOT(ISNUMBER($F$17)),ISERROR($F$17)),1,IF(AND(LEN($F$17)>0,ABS((1-($F$17*-1.99029505252838+ 0.448571085929871)/ 0.398813709616661))<0.00005),0,1))","v":1},null,null,3,53.844531249999982]
[{"$f":"IF(OR(NOT(ISNUMBER($F$18)),ISERROR($F$18)),1,IF(AND(LEN($F$18)>0,ABS((1-($F$18* 4.79829370975494+-0.098625659942627)/ 0.0213316828012462))<0.00005),0,1))","v":1},null,null,4,55.19064453124998]
[{"$f":"IF(OR(NOT(ISNUMBER($F$19)),ISERROR($F$19)),1,IF(AND(LEN($F$19)>0,ABS((1-($F$19*-2.21720039844513+-0.339558482170105)/-0.394988492131233))<0.00005),0,1))","v":1},null,null,5,56.570410644531222]
[{"$f":"IF(OR(NOT(ISNUMBER($F$20)),ISERROR($F$20)),1,IF(AND(LEN($F$20)>0,ABS((1-($F$20*-3.37178409099579+ 0.146587133407593)/ 0.0622925311326984))<0.00005),0,1))","v":1},null,null,6,57.984670910644496]
[]
[]
[null,null,null,"Determine the average (mean) yearly growth rate."]
[]
[{"$f":"IF(OR(NOT(ISNUMBER($F$25)),ISERROR($F$25)),1,IF(AND(LEN($F$25)>0,ABS((1-($F$25*-0.899267792701721+-0.0872331857681274)/-0.10971488058567))<0.00005),0,1))","v":1},null,null,"Mean growth rate:"]
[]
[null,null,null,"Calculate the compound average growth (CAGR) rate."]
[]
[{"$f":"IF(OR(NOT(ISNUMBER($F$29)),ISERROR($F$29)),1,IF(AND(LEN($F$29)>0,ABS((1-($F$29* 2.12730467319489+-0.173793792724609)/-0.120611175894737))<0.00005),0,1))","v":1},null,null,"CAGR"]
[null,null,null,null,null,null,null,null,null,null,null,null,"Index"]
[{"$f":"SUM($A$32:$A$57)","v":8},null,2,"Calculating arithmetic and compound average growth rate - when growth varies"]
[]
[null,null,null,"Consider the investment shown below.  The value of the investment at the end of each year is listed.  Find the p.a. growth rate in each year."]
[]
[]
[null,null,null,"Year","Value","Growth p.a."]
[null,null,null,0,50]
[{"$f":"IF(OR(NOT(ISNUMBER($F$38)),ISERROR($F$38)),1,IF(AND(LEN($F$38)>0,ABS((1-($F$38* 1.33178889751434+-0.292438864707947)/-0.292438864707947))<0.00005),0,1))","v":1},null,null,{"$f":"D37+1","v":1},50]
[{"$f":"IF(OR(NOT(ISNUMBER($F$39)),ISERROR($F$39)),1,IF(AND(LEN($F$39)>0,ABS((1-($F$39*-3.13986480236053+ 0.0833590030670166)/ 0.146156299114227))<0.00005),0,1))","v":1},null,null,2,49]
[{"$f":"IF(OR(NOT(ISNUMBER($F$40)),ISERROR($F$40)),1,IF(AND(LEN($F$40)>0,ABS((1-($F$40*-4.19285356998444+-0.042028546333313)/-0.298733866944605))<0.00005),0,1))","v":1},null,null,3,52]
[{"$f":"IF(OR(NOT(ISNUMBER($F$41)),ISERROR($F$41)),1,IF(AND(LEN($F$41)>0,ABS((1-($F$41* 4.05729830265045+-0.238631725311279)/-0.316656692669942))<0.00005),0,1))","v":1},null,null,4,51]
[{"$f":"IF(OR(NOT(ISNUMBER($F$42)),ISERROR($F$42)),1,IF(AND(LEN($F$42)>0,ABS((1-($F$42* 2.85212218761444+-0.121097445487976)/-0.00924951656191933))<0.00005),0,1))","v":1},null,null,5,53]
[{"$f":"IF(OR(NOT(ISNUMBER($F$43)),ISERROR($F$43)),1,IF(AND(LEN($F$43)>0,ABS((1-($F$43*-2.10334956645966+ 0.419377088546753)/ 0.340005406793558))<0.00005),0,1))","v":1},null,null,6,55]
[]
[]
[null,null,null,"Determine the average (mean) yearly growth rate."]
[]
[{"$f":"IF(OR(NOT(ISNUMBER($F$48)),ISERROR($F$48)),1,IF(AND(LEN($F$48)>0,ABS((1-($F$48* 1.31742417812347+ 0.127642035484314)/ 0.149367514222372))<0.00005),0,1))","v":1},null,null,"Mean growth rate:"]
[]
[null,null,null,"Calculate the compound average growth (CAGR) rate."]
[]
[{"$f":"IF(OR(NOT(ISNUMBER($F$52)),ISERROR($F$52)),1,IF(AND(LEN($F$52)>0,ABS((1-($F$52*-0.715436339378357+-0.402026176452637)/-0.413481648519039))<0.00005),0,1))","v":1},null,null,"CAGR"]
[]
[null,null,null,{"$f":"\"Note the difference between the average short term growth rate in cell \" & ADDRESS(ROW(F48),COLUMN(F48),4) & \" and the long term growth rate (CAGR) in cell \" & ADDRESS(ROW(F52),COLUMN(F52),4) &\". In this example you should find that the CAGR is less than the average arithmetic growth rate.  Can CAGR ever be greater?\"","v":"Note the difference between the average short term growth rate in cell F48 and the long term growth rate (CAGR) in cell F52. In this example you should find that the CAGR is less than the average arithmetic growth rate.  Can CAGR ever be greater?"}]
[]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,"Index"]
[{"$f":"SUM($A$59:$A$68)","v":3},null,3,"Calculating quarterly, semi and p.a. growth given monthly growth"]
[]
[null,null,null,"Monthly growth is 1%.  What is the growth in one quarter?  Six months?  One year?"]
[]
[null,null,null,"Period",null,"Growth"]
[]
[{"$f":"IF(OR(NOT(ISNUMBER($F$64)),ISERROR($F$64)),1,IF(AND(LEN($F$64)>0,ABS((1-($F$64* 0.610401034355164+ 0.194485306739807)/ 0.212981068481803))<0.00005),0,1))","v":1},null,null,"One quarter","[%]"]
[{"$f":"IF(OR(NOT(ISNUMBER($F$65)),ISERROR($F$65)),1,IF(AND(LEN($F$65)>0,ABS((1-($F$65* 4.13717567920685+ 0.334817171096802)/ 0.589336841944402))<0.00005),0,1))","v":1},null,null,"Six months","[%]"]
[{"$f":"IF(OR(NOT(ISNUMBER($F$66)),ISERROR($F$66)),1,IF(AND(LEN($F$66)>0,ABS((1-($F$66*-4.77370798587799+ 0.0433605909347534)/-0.562065068215448))<0.00005),0,1))","v":1},null,null,"One year","[%]"]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,"Index"]
[{"$f":"SUM($A$70:$A$75)","v":1},null,4,"Calculating effective growth rate given the nominal growth rate"]
[]
[null,null,null,"The nominal rate of growth p.a. is 10%.  Every six months the underlying increases by half of 10% (i.e. by 5%).  What is the effective yearly growth rate?"]
[]
[]
[{"$f":"IF(OR(NOT(ISNUMBER($F$74)),ISERROR($F$74)),1,IF(AND(LEN($F$74)>0,ABS((1-($F$74* 4.16163980960846+-0.0697388648986816)/ 0.356829215586186))<0.00005),0,1))","v":1},null,null,"Effective rate","[%]"]
[null,null,null,null,null,null,null,null,null,null,null,null,"Index"]
[{"$f":"SUM($A$77:$A$81)","v":1},null,5,"Calculating yearly effective growth rate given nominal continuously compounding rate"]
[]
[null,null,null,"The nominal continuously compounding rate is 10%.  What is the effective yearly growth rate?"]
[]
[{"$f":"IF(OR(NOT(ISNUMBER($F$80)),ISERROR($F$80)),1,IF(AND(LEN($F$80)>0,ABS((1-($F$80* 1.77947700023651+ 0.00245392322540283)/ 0.189603153034776))<0.00005),0,1))","v":1},null,null,"Effective rate","[%]"]
[null,null,null,null,null,null,null,null,null,null,null,null,"Index"]
[{"$f":"SUM($A$83:$A$89)","v":1},null,6,"Calculating nominal growth rate given the effective growth rate"]
[]
[null,null,null,"The nominal rate of growth p.a. is N (%).  Every quarter the underlying increases by one quarter of N.  In one year the underlying grows by 12%.  What is the nominal rate of growth on a quarterly basis (i.e, what is N)?"]
[]
[]
[]
[{"$f":"IF(OR(NOT(ISNUMBER($F$88)),ISERROR($F$88)),1,IF(AND(LEN($F$88)>0,ABS((1-($F$88* 0.137374997138977+-0.0370199680328369)/-0.0212287974369266))<0.00005),0,1))","v":1},null,null,"Nominal rate","[%]"]
[null,null,null,null,null,null,null,null,null,null,null,null,"Index"]
[{"$f":"SUM($A$91:$A$95)","v":1},null,7,"Calculating nominal compounding rate given yearly effective rate."]
[]
[null,null,null,"The yearly effective rate is 10%.  What is the equivalent continuously compounding nominal rate?"]
[]
[{"$f":"IF(OR(NOT(ISNUMBER($F$94)),ISERROR($F$94)),1,IF(AND(LEN($F$94)>0,ABS((1-($F$94*-1.46527349948883+-0.0951658487319946)/-0.234821329430787))<0.00005),0,1))","v":1},null,null,"Nominal rate","[%]"]
[null,null,null,null,null,null,null,null,null,null,null,null,"Index"]
[{"$f":"SUM($A$97:$A$125)","v":3},null,{"$f":"C90+1","v":8},"Showing that 10% growth followed by -10% growth has a different result than has zero growth."]
[]
[null,null,null,"An investment has an initial value of 100.  In the first year its value changes by +10% and in the second year by -10%.  What is the final value of the investment?"]
[]
[]
[{"$f":"IF(OR(NOT(ISNUMBER($F$101)),ISERROR($F$101)),1,IF(AND(LEN($F$101)>0,ABS((1-($F$101*-2.3026841878891+-0.444406509399414)/-228.41014111042))<0.00005),0,1))","v":1},null,null,"Final value"]
[]
[null,null,null,"What compound average growth rate (CAGR) is this equivalent to?"]
[]
[{"$f":"IF(OR(NOT(ISNUMBER($F$105)),ISERROR($F$105)),1,IF(AND(LEN($F$105)>0,ABS((1-($F$105*-2.56154835224152+ 0.479077935218811)/ 0.491917857438856))<0.00005),0,1))","v":1},null,null,"CAGR"]
[]
[null,null,null,"The CAGR you obtain above should be approximately equal to -(10%2)/2.  Confirm that is so."]
[]
[{"$f":"IF(OR(NOT(ISNUMBER($F$109)),ISERROR($F$109)),1,IF(AND(LEN($F$109)>0,ABS((1-($F$109*-4.39083755016327+-0.109708547592163)/-0.0877543598413467))<0.00005),0,1))","v":1},null,null,"-(10%)2/2"]
[]
[null,null,null,"If we think of the +10% and -10% growths as exhibiting volatility then we can see that volatility can \"feed through\" into growth by a factor of -s2/2.  That is why many formulae relating to the evolution of asset prices and formulae relating to option pricing contain that term in the \"growth\" part of the formula."]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[null,null,null,null,"Copyright (c) 2020 Tykoh Group Pty Ltd.  All rights reserved.",null,null,null,null,null,null,null,"Index"]
[null,null,null,null,"www.tykoh.com"]

{"sheet":"Simple_interest","index":8,"n_rows":32,"n_cols":12,"rows_kept":32,"cut":false,"hidden":false,"merged":[[30,3,30,9],[31,3,31,9],[0,3,0,9]]}
[null,null,null,"Click here to see what your answer should look like."]
[{"$f":"SUM($A$3:$A$8)","v":1},null,1,"Future value of an investment earning simple interest.",null,null,null,null,null,"Time_Value_Money","Simple_interest"]
[]
[null,null,null,"A $100 investment earns simple interest at the rate of 5% per annum (p.a.)"]
[null,null,null,"What is the investment's value after six months?"]
[]
[{"$f":"IF(OR(NOT(ISNUMBER($H$7)),ISERROR($H$7)),1,IF(AND(LEN($H$7)>0,ABS((1-($H$7*-1.35004580020905+-0.0101052522659302)/-138.389799773693))<0.00005),0,1))","v":1},null,null,"Investment value at six months",null,null,"[$]"]
[null,null,null,null,null,null,null,null,null,null,null,"Index"]
[{"$f":"SUM($A$10:$A$15)","v":1},null,2,"Present value of an investment earning simple interest."]
[]
[null,null,null,"An investment earning 6% per annum simple interest will have a value of $150 in three"]
[null,null,null,"months.  What is the inverstment's current value?"]
[]
[{"$f":"IF(OR(NOT(ISNUMBER($H$14)),ISERROR($H$14)),1,IF(AND(LEN($H$14)>0,ABS((1-($H$14*-3.44336926937103+-0.025540828704834)/-508.897846647084))<0.00005),0,1))","v":1},null,null,"Investment's current value ",null,null,"[$]"]
[null,null,null,null,null,null,null,null,null,null,null,"Index"]
[{"$f":"SUM($A$17:$A$22)","v":1},null,3,"Simple interest rate as a function of present value, future value and investment term."]
[]
[null,null,null,"An investment of $150 will have a value of $163 in one and a half years.  The"]
[null,null,null,"investment earns simple interest.  What is the per annum interest rate?"]
[]
[{"$f":"IF(OR(NOT(ISNUMBER($G$21)),ISERROR($G$21)),1,IF(AND(LEN($G$21)>0,ABS((1-($G$21*-2.42732346057892+ 0.128751873970032)/-0.0114934815300836))<0.00005),0,1))","v":1},null,null,"Interest rate",null,"[%]"]
[null,null,null,null,null,null,null,null,null,null,null,"Index"]
[{"$f":"SUM($A$24:$A$31)","v":1},null,{"$f":"C16+1","v":4},"Investment term as a function of present value, future value and interest rate."]
[]
[null,null,null,"An investment of $175 earns simple interest of 5.5%.  In how many years"]
[null,null,null,"will the investment be worth $185?"]
[]
[{"$f":"IF(OR(NOT(ISNUMBER($E$28)),ISERROR($E$28)),1,IF(AND(LEN($E$28)>0,ABS((1-($E$28* 0.42070209980011+-0.343697786331177)/ 0.0933953043702362))<0.00005),0,1))","v":1},null,null,"Years:"]
[]
[]
[null,null,null,"Copyright (c) 2020 Tykoh Group Pty Ltd.  All rights reserved.",null,null,null,null,null,null,null,"Index"]
[null,null,null,"www.tykoh.com"]

{"sheet":"Compound_interest","index":9,"n_rows":32,"n_cols":12,"rows_kept":32,"cut":false,"hidden":false,"merged":[[31,3,31,9],[0,3,0,9],[24,3,25,10],[3,3,4,10],[10,3,11,10],[17,3,18,10],[30,3,30,9]]}
[null,null,null,"Click here to see what your answer should look like."]
[{"$f":"SUM($A$3:$A$8)","v":1},null,1,"Future value of an investment earning compound interest.",null,null,null,null,null,"Time_Value_Money","Compound_interest"]
[]
[null,null,null,"A $100 investment earns compound interest at the rate of 5% per annum (p.a.)  What is the investment's value after six months?"]
[]
[]
[{"$f":"IF(OR(NOT(ISNUMBER($H$7)),ISERROR($H$7)),1,IF(AND(LEN($H$7)>0,ABS((1-($H$7* 4.38545167446136+ 0.154499411582947)/ 449.52957335859))<0.00005),0,1))","v":1},null,null,"Investment value at six months",null,null,"[$]"]
[null,null,null,null,null,null,null,null,null,null,null,"Index"]
[{"$f":"SUM($A$10:$A$15)","v":1},null,2,"Present value of an investment earning compound interest."]
[]
[null,null,null,"An investment earning 6% per annum compound interest will have a value of $150 in three months.  What is the inverstment's current value?"]
[]
[]
[{"$f":"IF(OR(NOT(ISNUMBER($H$14)),ISERROR($H$14)),1,IF(AND(LEN($H$14)>0,ABS((1-($H$14* 0.0608736276626587+-0.109528541564941)/ 8.88946574992785))<0.00005),0,1))","v":1},null,null,"Investment's current value ",null,null,"[$]"]
[null,null,null,null,null,null,null,null,null,null,null,"Index"]
[{"$f":"SUM($A$17:$A$22)","v":1},null,3,"Compound interest rate as a function of present value, future value and investment term."]
[]
[null,null,null,"An investment of $150 will have a value of $163 in one and a half years.  The investment earns compound interest.  What is the per annum interest rate?"]
[]
[]
[{"$f":"IF(OR(NOT(ISNUMBER($G$21)),ISERROR($G$21)),1,IF(AND(LEN($G$21)>0,ABS((1-($G$21*-3.9262467622757+ 0.283995270729065)/ 0.0603019967536721))<0.00005),0,1))","v":1},null,null,"Interest rate",null,"[%]"]
[null,null,null,null,null,null,null,null,null,null,null,"Index"]
[{"$f":"SUM($A$24:$A$31)","v":1},null,{"$f":"C16+1","v":4},"Investment term as a function of present value, future value and interest rate."]
[]
[null,null,null,"An investment of $175 earns compound interest of 5.5% p.a.  In how many years will the investment be worth $185?"]
[]
[]
[{"$f":"IF(OR(NOT(ISNUMBER($E$28)),ISERROR($E$28)),1,IF(AND(LEN($E$28)>0,ABS((1-($E$28*-0.403591990470886+ 0.253688097000122)/-0.165199194395767))<0.00005),0,1))","v":1},null,null,"Years:"]
[]
[]
[null,null,null,"Copyright (c) 2020 Tykoh Group Pty Ltd.  All rights reserved.",null,null,null,null,null,null,null,"Index"]
[null,null,null,"www.tykoh.com"]

{"sheet":"Continuous_interest","index":10,"n_rows":32,"n_cols":12,"rows_kept":32,"cut":false,"hidden":false,"merged":[[30,3,30,9],[31,3,31,9],[0,3,0,9]]}
[null,null,null,"Click here to see what your answer should look like."]
[{"$f":"SUM($A$3:$A$8)","v":1},null,1,"Future value of an investment earning continuous interest",null,null,null,null,null,"Time_Value_Money","Continuous_interest"]
[]
[null,null,null,"An investment of $100 earns a continuous interest rate of 5%.  What will the"]
[null,null,null,"investment compound to after nine months?"]
[]
[{"$f":"IF(OR(NOT(ISNUMBER($H$7)),ISERROR($H$7)),1,IF(AND(LEN($H$7)>0,ABS((1-($H$7* 0.9609454870224+ 0.332730174064636)/ 100.099243490894))<0.00005),0,1))","v":1},null,null,"Investment value at six months",null,null,"[$]"]
[null,null,null,null,null,null,null,null,null,null,null,"Index"]
[{"$f":"SUM($A$10:$A$15)","v":1},null,2,"Present value of an investment earning continuous interest"]
[]
[null,null,null,"An investment earning 6% per annum continuous interest will have a value of $150 in"]
[null,null,null,"three months.  What is the inverstment's current value?"]
[]
[{"$f":"IF(OR(NOT(ISNUMBER($H$14)),ISERROR($H$14)),1,IF(AND(LEN($H$14)>0,ABS((1-($H$14*-4.81241643428802+-0.289631366729736)/-711.404964530599))<0.00005),0,1))","v":1},null,null,"Investment's current value ",null,null,"[$]"]
[null,null,null,null,null,null,null,null,null,null,null,"Index"]
[{"$f":"SUM($A$17:$A$22)","v":1},null,3,"Continuous interest rate as a function of present value, future value and investment term."]
[]
[null,null,null,"An investment of $150 will have a value of $163 in one and a half years.  The"]
[null,null,null,"investment earns continuous interest.  What is the per annum interest rate?"]
[]
[{"$f":"IF(OR(NOT(ISNUMBER($H$21)),ISERROR($H$21)),1,IF(AND(LEN($H$21)>0,ABS((1-($H$21*-4.26046669483185+-0.394547343254089)/-0.630619537843536))<0.00005),0,1))","v":1},null,null,"Continuous interest rate",null,null,"[%]"]
[null,null,null,null,null,null,null,null,null,null,null,"Index"]
[{"$f":"SUM($A$24:$A$31)","v":1},null,{"$f":"C16+1","v":4},"Investment term as a function of present value, future value and interest rate."]
[]
[null,null,null,"An investment of $175 earns continuous interest of 5.5%.  In how many"]
[null,null,null,"years will the investment be worth $185?"]
[]
[{"$f":"IF(OR(NOT(ISNUMBER($E$28)),ISERROR($E$28)),1,IF(AND(LEN($E$28)>0,ABS((1-($E$28*-1.68305575847626+-0.371750116348267)/-2.07224389787141))<0.00005),0,1))","v":1},null,null,"Years:"]
[]
[]
[null,null,null,"Copyright (c) 2020 Tykoh Group Pty Ltd.  All rights reserved.",null,null,null,null,null,null,null,"Index"]
[null,null,null,"www.tykoh.com"]

{"sheet":"IRR","index":11,"n_rows":168,"n_cols":13,"rows_kept":168,"cut":false,"hidden":false,"merged":[[36,3,37,10],[41,3,42,10],[166,4,166,10],[167,4,167,10],[0,3,0,9]]}
[null,null,null,"Click here to see what your answer should look like."]
[{"$f":"SUM($A$3:$A$8)","v":1},null,1,"Calculate IRR of a yearly series of cash flows.",null,null,null,null,null,null,"IRR_and_Inflation","IRR"]
[]
[null,null,null,"Period","[yr]",0,1,{"$f":"G4+1","v":2},{"$f":"H4+1","v":3}]
[null,null,null,"Cash flow","[$ 000's]",-100,20,40,60]
[]
[{"$f":"IF(OR(NOT(ISNUMBER($F$7)),ISERROR($F$7)),1,IF(AND(LEN($F$7)>0,ABS((1-($F$7*-4.99758780002593+ 0.0367940664291382)/-0.373421111254846))<0.00005),0,1))","v":1},null,null,"IRR","[%]"]
[null,null,null,null,null,null,null,null,null,null,null,null,"Index"]
[{"$f":"SUM($A$10:$A$15)","v":1},null,2,"Calculate nominal yearly IRR for a semi-annual series of cash flows"]
[]
[null,null,null,"Period","[yr]",0,{"$f":"F11+0.5","v":0.5},{"$f":"G11+0.5","v":1},{"$f":"H11+0.5","v":1.5}]
[null,null,null,"Cash flow","[$ 000's]",-100,20,40,60]
[]
[{"$f":"IF(OR(NOT(ISNUMBER($F$14)),ISERROR($F$14)),1,IF(AND(LEN($F$14)>0,ABS((1-($F$14* 1.57054960727692+ 0.0440139770507813)/ 0.301843678895046))<0.00005),0,1))","v":1},null,null,"IRR","[%]"]
[null,null,null,null,null,null,null,null,null,null,null,null,"Index"]
[{"$f":"SUM($A$17:$A$167)","v":11},null,{"$f":"C9+1","v":3},"Demonstration that certain cash flows can have more than one IRR"]
[]
[null,null,null,"Period","[yr]",0,1,2]
[null,null,null,"Cashflow","[$ 000's]",{"$f":"4*H19/(5.6+0.16-4/100)","v":699.30069930069931},{"$f":"-2.4*F19","v":-1678.3216783216783},1000]
[]
[null,null,null,"Discount rate [%]","NPV[$ 000's]"]
[]
[{"$f":"IF(OR(NOT(ISNUMBER($E$23)),ISERROR($E$23)),1,IF(AND(LEN($E$23)>0,ABS((1-($E$23* 3.27411830425262+-0.418106436729431)/ 68.2696901559831))<0.00005),0,1))","v":1},null,null,0]
[{"$f":"IF(OR(NOT(ISNUMBER($E$24)),ISERROR($E$24)),1,IF(AND(LEN($E$24)>0,ABS((1-($E$24*-3.080775141716+ 0.178913354873657)/-24.247256837759))<0.00005),0,1))","v":1},null,null,{"$f":"D23+5%","v":0.05}]
[{"$f":"IF(OR(NOT(ISNUMBER($E$25)),ISERROR($E$25)),1,IF(AND(LEN($E$25)>0,ABS((1-($E$25*-0.457921624183655+-0.142976880073547)/-0.142976880073547))<0.00005),0,1))","v":1},null,null,0.1]
[{"$f":"IF(OR(NOT(ISNUMBER($E$26)),ISERROR($E$26)),1,IF(AND(LEN($E$26)>0,ABS((1-($E$26*-3.50018918514252+ 0.204395771026611)/ 14.085405666234))<0.00005),0,1))","v":1},null,null,0.15000000000000002]
[{"$f":"IF(OR(NOT(ISNUMBER($E$27)),ISERROR($E$27)),1,IF(AND(LEN($E$27)>0,ABS((1-($E$27* 4.28785979747772+ 0.0302125215530396)/-20.7927274428881))<0.00005),0,1))","v":1},null,null,0.2]
[{"$f":"IF(OR(NOT(ISNUMBER($E$28)),ISERROR($E$28)),1,IF(AND(LEN($E$28)>0,ABS((1-($E$28*-4.10358607769012+ 0.257729291915894)/ 14.0320042380084))<0.00005),0,1))","v":1},null,null,0.25]
[{"$f":"IF(OR(NOT(ISNUMBER($E$29)),ISERROR($E$29)),1,IF(AND(LEN($E$29)>0,ABS((1-($E$29*-0.981579422950745+-0.0381256341934204)/-0.0381256341934204))<0.00005),0,1))","v":1},null,null,0.3]
[{"$f":"IF(OR(NOT(ISNUMBER($E$30)),ISERROR($E$30)),1,IF(AND(LEN($E$30)>0,ABS((1-($E$30*-0.0783437490463257+-0.292372703552246)/-0.668132912701318))<0.00005),0,1))","v":1},null,null,0.35]
[{"$f":"IF(OR(NOT(ISNUMBER($E$31)),ISERROR($E$31)),1,IF(AND(LEN($E$31)>0,ABS((1-($E$31*-1.70264065265656+-0.404570937156677)/-18.6289250044096))<0.00005),0,1))","v":1},null,null,0.39999999999999997]
[]
[]
[]
[]
[]
[null,null,null,{"$f":"\"Generate the IRR for the cash flow in row \" & ROW(19:19) & \" using 0% as the second (optional, guess) parameter.\"","v":"Generate the IRR for the cash flow in row 19 using 0% as the second (optional, guess) parameter."}]
[]
[]
[{"$f":"IF(OR(NOT(ISNUMBER($F$40)),ISERROR($F$40)),1,IF(AND(LEN($F$40)>0,ABS((1-($F$40* 0.897925496101379+-0.330126523971558)/-0.240333974361422))<0.00005),0,1))","v":1},null,null,"IRR with 0% guess:"]
[]
[null,null,null,{"$f":"\"Generate the IRR for the cash flow in row \" & ROW(19:19) & \" using 50% as the second (optional, guess) parameter.\"","v":"Generate the IRR for the cash flow in row 19 using 50% as the second (optional, guess) parameter."}]
[]
[]
[{"$f":"IF(OR(NOT(ISNUMBER($F$45)),ISERROR($F$45)),1,IF(AND(LEN($F$45)>0,ABS((1-($F$45* 4.27616536617279+-0.402070164680481)/ 0.880779445171535))<0.00005),0,1))","v":1},null,null,"IRR with 50% guess:"]
[]
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[]
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[]
[]
[]
[]
[]
[]
[]
[]
[]
[null,null,null,null,"Copyright (c) 2020 Tykoh Group Pty Ltd.  All rights reserved.",null,null,null,null,null,null,null,"Index"]
[null,null,null,null,"www.tykoh.com"]

{"sheet":"Inflation","index":12,"n_rows":41,"n_cols":17,"rows_kept":41,"cut":false,"hidden":false,"merged":[[39,8,39,14],[40,8,40,14],[0,7,0,13],[30,7,30,8],[31,7,33,8],[36,7,36,15],[9,7,9,8],[21,7,21,8],[23,7,25,14],[29,7,29,8]]}
[null,null,null,null,null,null,null,"Click here to see what your answer should look like."]
[{"$f":"SUM($A$3:$E$27)","v":13},null,null,null,null,null,1,"Calculating present value on nominal and inflation-adjusted bases",null,null,null,null,null,null,"IRR_and_Inflation","Inflation"]
[]
[null,null,null,null,null,null,null,"Calculating NPV on a nominal basis"]
[]
[null,null,null,null,null,null,null,"Nominal discount rate",null,"[%]",4.4999999999999998E-2]
[]
[null,null,null,null,null,null,null,"Time",null,"[yrs]",null,1,{"$f":"L8+1","v":2},{"$f":"M8+1","v":3},{"$f":"N8+1","v":4},{"$f":"O8+1","v":5}]
[null,null,null,null,null,null,null,"Nominal cash flow",null,"[$ 000's]",null,-360,110,140,150,150]
[{"$f":"IF(OR(NOT(ISNUMBER($K$10)),ISERROR($K$10)),1,IF(AND(LEN($K$10)>0,ABS((1-($K$10*-0.561375021934509+-0.227053165435791)/-70.4360209899681))<0.00005),0,1))","v":1},null,null,null,null,null,null,"NPV using nominal values",null,"[$ 000's]"]
[]
[null,null,null,null,null,null,null,"Calculating NPV on a real (inflation-adjusted) basis"]
[]
[null,null,null,null,null,null,null,"Inflation rate",null,"[%]",1.2E-2]
[{"$f":"IF(OR(NOT(ISNUMBER($K$15)),ISERROR($K$15)),1,IF(AND(LEN($K$15)>0,ABS((1-($K$15* 3.72546851634979+ 0.250687718391418)/ 0.372170387402824))<0.00005),0,1))","v":1},null,null,null,null,null,null,"Real discount rate",null,"[%]",null,"<- Note - the exact value of this is not simply the "]
[null,null,null,null,null,null,null,null,null,null,null,"nominal discount rate less the inflation rate."]
[]
[null,null,null,null,null,null,null,"Time",null,"[yrs]",null,1,{"$f":"L18+1","v":2},{"$f":"M18+1","v":3},{"$f":"N18+1","v":4},{"$f":"O18+1","v":5}]
[{"$f":"IF(OR(NOT(ISNUMBER($L$19)),ISERROR($L$19)),1,IF(AND(LEN($L$19)>0,ABS((1-($L$19*-2.27057635784149+ 0.173646688461304)/-2.12417658567429))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($M$19)),ISERROR($M$19)),1,IF(AND(LEN($M$19)>0,ABS((1-($M$19*-2.43371069431305+-0.410103440284729)/-2.90257364560127))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($N$19)),ISERROR($N$19)),1,IF(AND(LEN($N$19)>0,ABS((1-($N$19*-4.69049394130707+-0.177282333374023)/-5.03866845512432))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($O$19)),ISERROR($O$19)),1,IF(AND(LEN($O$19)>0,ABS((1-($O$19* 2.90128886699677+-0.202741980552673)/ 2.8403355795108))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($P$19)),ISERROR($P$19)),1,IF(AND(LEN($P$19)>0,ABS((1-($P$19*-2.64717757701874+-0.0195252895355225)/-2.8293914752329))<0.00005),0,1))","v":1},null,null,"Inflation index",null,"[#]",1]
[{"$f":"IF(OR(NOT(ISNUMBER($L$20)),ISERROR($L$20)),1,IF(AND(LEN($L$20)>0,ABS((1-($L$20*-2.45398104190826+-0.159393429756165)/ 872.798289462512))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($M$20)),ISERROR($M$20)),1,IF(AND(LEN($M$20)>0,ABS((1-($M$20*-4.550661444664+-0.0175719261169434)/-488.789423260539))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($N$20)),ISERROR($N$20)),1,IF(AND(LEN($N$20)>0,ABS((1-($N$20*-2.93982803821564+ 0.364534497261047)/-396.743273007619))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($O$20)),ISERROR($O$20)),1,IF(AND(LEN($O$20)>0,ABS((1-($O$20* 0.886285901069641+ 0.254908323287964)/ 127.003472909459))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($P$20)),ISERROR($P$20)),1,IF(AND(LEN($P$20)>0,ABS((1-($P$20* 4.27883088588715+-0.168983101844788)/ 604.49460735475))<0.00005),0,1))","v":1},null,null,"Real cash flow",null,"[$ 000's]"]
[]
[{"$f":"IF(OR(NOT(ISNUMBER($K$22)),ISERROR($K$22)),1,IF(AND(LEN($K$22)>0,ABS((1-($K$22* 0.42941153049469+-0.419308662414551)/ 53.2855038960289))<0.00005),0,1))","v":1},null,null,null,null,null,null,"NPV using real values",null,"[$ 000's]"]
[]
[null,null,null,null,null,null,null,"Note that the NPV on a nominal basis is the same as the NPV on a real (inflation-adjusted) basis.  This is because NPV is relative to \"today\" and inflation has no effect relative to today."]
[]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Index"]
[{"$f":"SUM($A$29:$E$40)","v":4},null,null,null,null,null,{"$f":"G2+1","v":2},"Calculating IRR on nominal and inflation-adjusted bases"]
[]
[{"$f":"IF(OR(NOT(ISNUMBER($K$30)),ISERROR($K$30)),1,IF(AND(LEN($K$30)>0,ABS((1-($K$30* 1.34371936321259+-0.0899633169174194)/ 0.156318492365991))<0.00005),0,1))","v":1},null,null,null,null,null,null,"IRR of nominal cash flows",null,"[%]"]
[{"$f":"IF(OR(NOT(ISNUMBER($K$31)),ISERROR($K$31)),1,IF(AND(LEN($K$31)>0,ABS((1-($K$31* 4.60422813892365+-0.385376691818237)/ 0.393901044322077))<0.00005),0,1))","v":1},null,null,null,null,null,null,"IRR of real cash flows",null,"[%]"]
[null,null,null,null,null,null,null,"Difference between IRR on nominal and real bases"]
[{"$f":"IF(OR(NOT(ISNUMBER($K$33)),ISERROR($K$33)),1,IF(AND(LEN($K$33)>0,ABS((1-($K$33* 4.23445165157318+ 0.120209574699402)/ 0.179623299622021))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,null,"[%]"]
[]
[{"$f":"IF(OR(NOT(ISNUMBER($K$35)),ISERROR($K$35)),1,IF(AND(LEN($K$35)>0,ABS((1-($K$35*-1.52273595333099+-0.350754261016846)/-0.369027092456818))<0.00005),0,1))","v":1},null,null,null,null,null,null,"Inflation rate",null,"[%]"]
[]
[null,null,null,null,null,null,null,"Note that the IRR on a real basis does not equal the IRR on a nominal basis less inflation."]
[]
[]
[null,null,null,null,null,null,null,null,"Copyright (c) 2020 Tykoh Group Pty Ltd.  All rights reserved.",null,null,null,null,null,null,null,"Index"]
[null,null,null,null,null,null,null,null,"www.tykoh.com"]

{"sheet":"Yield_curves_Discount_factors","index":13,"n_rows":31,"n_cols":16,"rows_kept":31,"cut":false,"hidden":false,"merged":[[3,7,4,14],[21,7,22,14],[29,7,29,13],[30,7,30,13],[0,7,0,13]]}
[null,null,null,null,null,null,null,"Click here to see what your answer should look like."]
[{"$f":"SUM($A$3:$E$10)","v":5},null,null,null,null,null,1,"Calculating discount factors from points on a yield curve",null,null,null,null,null,"Yield_Curve","Yield_curves_and_discount_factors"]
[]
[null,null,null,null,null,null,null,"Consider the spot / zero-coupon yield curve shown below.  Yields are annual effective. Calculate discount factors corresponding to each point on the curve."]
[]
[]
[null,null,null,null,null,null,null,"Time",null,"[yrs]",0.25,{"$f":"K7+0.25","v":0.5},{"$f":"L7+0.25","v":0.75},{"$f":"M7+0.25","v":1},{"$f":"N7+0.25","v":1.25}]
[null,null,null,null,null,null,null,"Yield p.a.",null,"[%]",5.5E-2,5.7000000000000002E-2,5.7500000000000002E-2,5.8000000000000003E-2,5.8099999999999999E-2]
[{"$f":"IF(OR(NOT(ISNUMBER($K$9)),ISERROR($K$9)),1,IF(AND(LEN($K$9)>0,ABS((1-($K$9*-0.200217366218567+-0.280590891838074)/-0.478146166271858))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($L$9)),ISERROR($L$9)),1,IF(AND(LEN($L$9)>0,ABS((1-($L$9* 4.93731319904327+-0.369579553604126)/ 4.43276353832592))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($M$9)),ISERROR($M$9)),1,IF(AND(LEN($M$9)>0,ABS((1-($M$9*-4.71114218235016+-0.154608368873596)/-4.6722931960123))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($N$9)),ISERROR($N$9)),1,IF(AND(LEN($N$9)>0,ABS((1-($N$9* 0.476685166358948+ 0.422954559326172)/ 0.873507646621964))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($O$9)),ISERROR($O$9)),1,IF(AND(LEN($O$9)>0,ABS((1-($O$9* 0.382463335990906+-0.0935786962509155)/ 0.26281615052645))<0.00005),0,1))","v":1},null,null,"Discount factor",null,"[#]"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Index"]
[{"$f":"SUM($A$12:$E$19)","v":6},null,null,null,null,null,2,"Using discount factors to calculate the value of a series of future cash flows."]
[]
[null,null,null,null,null,null,null,"Use the discount factors above to value a security that has cash flows as shown below."]
[]
[null,null,null,null,null,null,null,"Time",null,"[yrs]",{"$f":"K7","v":0.25},{"$f":"L7","v":0.5},{"$f":"M7","v":0.75},{"$f":"N7","v":1},{"$f":"O7","v":1.25}]
[null,null,null,null,null,null,null,"Cash flows",null,"[$'000]",5,5,5,5,105]
[{"$f":"IF(OR(NOT(ISNUMBER($K$17)),ISERROR($K$17)),1,IF(AND(LEN($K$17)>0,ABS((1-($K$17* 3.47245514392853+ 0.326225519180298)/ 17.4576522748627))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($L$17)),ISERROR($L$17)),1,IF(AND(LEN($L$17)>0,ABS((1-($L$17* 1.72427594661713+ 0.221895098686218)/ 8.60759431098499))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($M$17)),ISERROR($M$17)),1,IF(AND(LEN($M$17)>0,ABS((1-($M$17* 4.96771395206451+-0.160193920135498)/ 23.6584100172345))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($N$17)),ISERROR($N$17)),1,IF(AND(LEN($N$17)>0,ABS((1-($N$17*-0.0478869676589966+-0.0870321989059448)/-0.313341119789672))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($O$17)),ISERROR($O$17)),1,IF(AND(LEN($O$17)>0,ABS((1-($O$17* 1.95281803607941+-0.320910692214966)/ 190.749168508161))<0.00005),0,1))","v":1},null,null,"Present value",null,"[$'000]"]
[{"$f":"IF(OR(NOT(ISNUMBER($K$18)),ISERROR($K$18)),1,IF(AND(LEN($K$18)>0,ABS((1-($K$18*-0.770817399024963+ 0.0431770086288452)/-90.2663084553178))<0.00005),0,1))","v":1},null,null,null,null,null,null,"Total value",null,"[$'000]"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Index"]
[{"$f":"SUM($A$21:$E$30)","v":5},null,null,null,null,null,{"$f":"G11+1","v":3},"Generating a yield curve equivalent to a set of discount factors."]
[]
[null,null,null,null,null,null,null,"Consider the discount factors shown below.  Calculate the equivalent spot / zero-coupon yields on an annual effective basis."]
[]
[]
[null,null,null,null,null,null,null,"Time",null,"[yrs]",{"$f":"K15","v":0.25},{"$f":"L15","v":0.5},{"$f":"M15","v":0.75},{"$f":"N15","v":1},{"$f":"O15","v":1.25}]
[null,null,null,null,null,null,null,"Discount factor",null,"[#]",{"$f":"K9","v":0},{"$f":"L9","v":0},{"$f":"M9","v":0},{"$f":"N9","v":0},{"$f":"O9","v":0}]
[{"$f":"IF(OR(NOT(ISNUMBER($K$27)),ISERROR($K$27)),1,IF(AND(LEN($K$27)>0,ABS((1-($K$27* 3.14663946628571+ 0.0409135818481445)/ 0.213978752493859))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($L$27)),ISERROR($L$27)),1,IF(AND(LEN($L$27)>0,ABS((1-($L$27*-0.724666714668274+ 0.00906813144683838)/-0.0322378712892532))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($M$27)),ISERROR($M$27)),1,IF(AND(LEN($M$27)>0,ABS((1-($M$27*-2.72218406200409+ 0.119187593460083)/-0.0373379901051524))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($N$27)),ISERROR($N$27)),1,IF(AND(LEN($N$27)>0,ABS((1-($N$27*-0.101695656776428+ 0.180819392204285)/ 0.174921044111252))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($O$27)),ISERROR($O$27)),1,IF(AND(LEN($O$27)>0,ABS((1-($O$27* 3.86600077152252+-0.1294846534729)/ 0.0951299913525583))<0.00005),0,1))","v":1},null,null,"Yield - annual effective)",null,"[%]"]
[]
[]
[null,null,null,null,null,null,null,"Copyright (c) 2020 Tykoh Group Pty Ltd.  All rights reserved.",null,null,null,null,null,null,null,"Index"]
[null,null,null,null,null,null,null,"www.tykoh.com"]

{"sheet":"Forward_interest_rates","index":14,"n_rows":86,"n_cols":16,"rows_kept":86,"cut":false,"hidden":false,"merged":[[84,7,84,13],[85,7,85,13],[0,7,0,13],[34,8,36,8],[8,7,9,13],[13,7,14,13],[18,7,20,14],[31,7,31,8]]}
[null,null,null,null,null,null,null,"Click here to see what your answer should look like."]
[{"$f":"SUM($A$3:$E$26)","v":3},null,null,null,null,null,1,"Calculating forward interest rate implied by zero coupon yield curve",null,null,null,null,null,"Yield_Curve","Forward_interest_rates"]
[]
[null,null,null,null,null,null,null,"Consider the zero coupon yield curve shown below.  "]
[]
[null,null,null,null,null,null,null,"Time",null,"[yrs]",1,{"$f":"K6+1","v":2},{"$f":"L6+1","v":3},{"$f":"M6+1","v":4},{"$f":"N6+1","v":5}]
[null,null,null,null,null,null,null,"Yield p.a.",null,"[%]",0.05,0.06,6.5000000000000002E-2,6.7500000000000004E-2,6.8750000000000006E-2]
[]
[null,null,null,null,null,null,null,"$100 is invested at time 0 for one year.  Call this investment \"A\".  How much will the investment be worth at the end of the year?"]
[]
[]
[{"$f":"IF(OR(NOT(ISNUMBER($L$12)),ISERROR($L$12)),1,IF(AND(LEN($L$12)>0,ABS((1-($L$12*-1.97502434253693+-0.207133173942566)/-207.58468914032))<0.00005),0,1))","v":1},null,null,null,null,null,null,"Investment in one year",null,null,"[$]"]
[]
[null,null,null,null,null,null,null,"$100 is invested at time 0 for two years.  Call this investment \"B\".  How much will the investment be worth in two years?"]
[]
[]
[{"$f":"IF(OR(NOT(ISNUMBER($L$17)),ISERROR($L$17)),1,IF(AND(LEN($L$17)>0,ABS((1-($L$17*-3.49688708782196+ 0.0298211574554443)/-392.88041203022))<0.00005),0,1))","v":1},null,null,null,null,null,null,"Investment in two years",null,null,"[$]"]
[]
[null,null,null,null,null,null,null,"Investment A is re-invested in one year for an additional year.  If, at maturity, the investment is worth the same as investment \"B\" then at what rate would the re-investment have been made?"]
[]
[]
[]
[{"$f":"IF(OR(NOT(ISNUMBER($K$23)),ISERROR($K$23)),1,IF(AND(LEN($K$23)>0,ABS((1-($K$23*-2.76738226413727+ 0.0845292806625366)/-0.109451038042705))<0.00005),0,1))","v":1},null,null,null,null,null,null,"Reinvestment rate",null,"[%]"]
[]
[null,null,null,null,null,null,null,"The rate you have obtained is the current implied forward rate from 1 year to 2 years."]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Index"]
[{"$f":"SUM($A$28:$E$57)","v":9},null,null,null,null,null,2,"Calculating implied forward curve from yield curve."]
[]
[null,null,null,null,null,null,null,"In a similar way to that used above calculate the complete one-year-ahead forward curve."]
[]
[null,null,null,null,null,null,null,"Time t",null,"[yrs]",{"$f":"K6","v":1},{"$f":"L6","v":2},{"$f":"M6","v":3},{"$f":"N6","v":4},{"$f":"O6","v":5}]
[{"$f":"IF(OR(NOT(ISNUMBER($K$32)),ISERROR($K$32)),1,IF(AND(LEN($K$32)>0,ABS((1-($K$32*-1.36541306972504+ 0.375974655151367)/-142.992397665977))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($L$32)),ISERROR($L$32)),1,IF(AND(LEN($L$32)>0,ABS((1-($L$32*-0.219858288764954+-0.309366583824158)/-25.0126439094543))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($M$32)),ISERROR($M$32)),1,IF(AND(LEN($M$32)>0,ABS((1-($M$32* 1.84062302112579+ 0.247415781021118)/ 222.585404594548))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($N$32)),ISERROR($N$32)),1,IF(AND(LEN($N$32)>0,ABS((1-($N$32* 1.13934934139252+ 0.282138705253601)/ 148.2367278784))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($O$32)),ISERROR($O$32)),1,IF(AND(LEN($O$32)>0,ABS((1-($O$32*-3.38256299495697+ 0.307779788970947)/-471.34948929535))<0.00005),0,1))","v":1},null,null,"Value of $100 invested for t",null,"[$]"]
[]
[]
[null,null,null,null,null,null,null,null,"Forward rate","From",0,{"$f":"K35+1","v":1},{"$f":"L35+1","v":2},{"$f":"M35+1","v":3},{"$f":"N35+1","v":4}]
[null,null,null,null,null,null,null,null,null,"To:",{"$f":"K35+1","v":1},{"$f":"L35+1","v":2},{"$f":"M35+1","v":3},{"$f":"N35+1","v":4},{"$f":"O35+1","v":5}]
[{"$f":"IF(OR(NOT(ISNUMBER($L$37)),ISERROR($L$37)),1,IF(AND(LEN($L$37)>0,ABS((1-($L$37*-2.97381699085236+ 0.456762433052063)/ 0.248312023026602))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($M$37)),ISERROR($M$37)),1,IF(AND(LEN($M$37)>0,ABS((1-($M$37*-4.34148967266083+-0.438477754592896)/-0.764397143904316))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($N$37)),ISERROR($N$37)),1,IF(AND(LEN($N$37)>0,ABS((1-($N$37* 2.93197572231293+-0.120395302772522)/ 0.0996062766402587))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($O$37)),ISERROR($O$37)),1,IF(AND(LEN($O$37)>0,ABS((1-($O$37*-0.364159941673279+-0.38045597076416)/-0.407318102917602))<0.00005),0,1))","v":1},null,null,null,null,null,"Value:",{"$f":"K7","v":0.05}]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Index"]
[{"$f":"SUM($A$59:$E$85)","v":8},null,null,null,null,null,{"$f":"G27+1","v":3},"Calculating zero curve from forward curve"]
[]
[null,null,null,null,null,null,null,"Term",null,"[yrs]",null,1,{"$f":"L60+1","v":2},{"$f":"M60+1","v":3},{"$f":"N60+1","v":4}]
[null,null,null,null,null,null,null,"Fwd rate",null,"[%]",null,{"$f":"K37","v":0.05},{"$f":"L37","v":0},{"$f":"M37","v":0},{"$f":"N37","v":0}]
[{"$f":"IF(OR(NOT(ISNUMBER($L$62)),ISERROR($L$62)),1,IF(AND(LEN($L$62)>0,ABS((1-($L$62*-3.84529888629913+-0.326226592063904)/-3.98841600758689))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($M$62)),ISERROR($M$62)),1,IF(AND(LEN($M$62)>0,ABS((1-($M$62*-4.51881110668182+ 0.214816331863403)/-3.80690946618023))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($N$62)),ISERROR($N$62)),1,IF(AND(LEN($N$62)>0,ABS((1-($N$62* 0.330223441123962+ 0.0610092878341675)/ 0.334384463660695))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($O$62)),ISERROR($O$62)),1,IF(AND(LEN($O$62)>0,ABS((1-($O$62*-2.83266484737396+-0.0319943428039551)/-2.21333582486122))<0.00005),0,1))","v":1},null,null,null,"Discount factor",null,"[#]",1]
[{"$f":"IF(OR(NOT(ISNUMBER($L$63)),ISERROR($L$63)),1,IF(AND(LEN($L$63)>0,ABS((1-($L$63* 2.46354758739471+ 0.252310872077942)/ 0.375488251447678))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($M$63)),ISERROR($M$63)),1,IF(AND(LEN($M$63)>0,ABS((1-($M$63*-1.01067721843719+ 0.403098821640015)/ 0.342458188533783))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($N$63)),ISERROR($N$63)),1,IF(AND(LEN($N$63)>0,ABS((1-($N$63* 2.46006906032562+-0.411440491676331)/-0.251536002755165))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($O$63)),ISERROR($O$63)),1,IF(AND(LEN($O$63)>0,ABS((1-($O$63* 1.34571135044098+ 0.213027954101563)/ 0.303863470256328))<0.00005),0,1))","v":1},null,null,null,"Zero rate",null,"[%]"]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[null,null,null,null,null,null,null,"Copyright (c) 2020 Tykoh Group Pty Ltd.  All rights reserved.",null,null,null,null,null,null,null,"Index"]
[null,null,null,null,null,null,null,"www.tykoh.com"]

{"sheet":"Annuities","index":15,"n_rows":54,"n_cols":18,"rows_kept":54,"cut":false,"hidden":false,"merged":[[52,9,52,15],[53,9,53,15],[0,8,0,14],[38,8,38,16],[3,8,5,16],[19,8,19,16],[26,8,28,16],[21,8,21,9],[22,8,22,9],[32,12,32,16],[24,8,24,9]]}
[null,null,null,null,null,null,null,null,"Click here to see what your answer should look like."]
[{"$f":"SUM($A$3:$F$17)","v":12},null,null,null,null,null,null,1,"Value of a growing annuity",null,null,null,null,null,null,"Bonds_and_FRNs","Annuities"]
[]
[null,null,null,null,null,null,null,null,{"$f":"\"An annuity of $\"  & K10 & \" will be received in one year's time.  Thereafter the annuity will grow at \" & TEXT(K8,\"0.0%\")&\" per year. The discount rate r (annual effective) is \"& TEXT(K9,\"0.0%\")& \" per year. Calculate the future and present values of the annuities and the total present value.\"","v":"An annuity of $100 will be received in one year's time.  Thereafter the annuity will grow at 2.0% per year. The discount rate r (annual effective) is 4.5% per year. Calculate the future and present values of the annuities and the total present value."}]
[]
[]
[]
[null,null,null,null,null,null,null,null,"g","[%]",0.02]
[null,null,null,null,null,null,null,null,"r","[%]",4.4999999999999998E-2]
[null,null,null,null,null,null,null,null,"C","[$]",100]
[]
[null,null,null,null,null,null,null,null,"Time","[yrs]",null,1,{"$f":"L12+1","v":2},{"$f":"M12+1","v":3},{"$f":"N12+1","v":4},{"$f":"O12+1","v":5},{"$f":"P12+1","v":6}]
[{"$f":"IF(OR(NOT(ISNUMBER($M$13)),ISERROR($M$13)),1,IF(AND(LEN($M$13)>0,ABS((1-($M$13*-4.84317600727081+-0.0688556432723999)/-494.072808384895))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($N$13)),ISERROR($N$13)),1,IF(AND(LEN($N$13)>0,ABS((1-($N$13*-0.980173945426941+-0.224704504013062)/-102.202001786232))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($O$13)),ISERROR($O$13)),1,IF(AND(LEN($O$13)>0,ABS((1-($O$13* 4.85373914241791+ 0.302587389945984)/ 515.385268174648))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($P$13)),ISERROR($P$13)),1,IF(AND(LEN($P$13)>0,ABS((1-($P$13* 1.96100771427155+-0.0824007987976074)/ 212.183380794764))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($Q$13)),ISERROR($Q$13)),1,IF(AND(LEN($Q$13)>0,ABS((1-($Q$13* 2.34488189220428+-0.222831606864929)/ 258.671076688539))<0.00005),0,1))","v":1},null,null,null,"Annuity","[$]",null,100]
[]
[{"$f":"IF(OR(NOT(ISNUMBER($L$15)),ISERROR($L$15)),1,IF(AND(LEN($L$15)>0,ABS((1-($L$15*-1.43413722515106+-0.0665428638458252)/-137.304554840024))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($M$15)),ISERROR($M$15)),1,IF(AND(LEN($M$15)>0,ABS((1-($M$15* 4.44971024990082+-0.378450036048889)/ 415.24431088049))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($N$15)),ISERROR($N$15)),1,IF(AND(LEN($N$15)>0,ABS((1-($N$15* 1.45951330661774+-0.152167320251465)/ 132.911512974771))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($O$15)),ISERROR($O$15)),1,IF(AND(LEN($O$15)>0,ABS((1-($O$15*-3.95567715167999+-0.314597487449646)/-352.325562899642))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($P$15)),ISERROR($P$15)),1,IF(AND(LEN($P$15)>0,ABS((1-($P$15*-4.22315299510956+-0.0672404766082764)/-366.889811113106))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($Q$15)),ISERROR($Q$15)),1,IF(AND(LEN($Q$15)>0,ABS((1-($Q$15* 4.59270894527435+ 0.0420292615890503)/ 389.420593836472))<0.00005),0,1))","v":1},null,null,"PV","[$]"]
[{"$f":"IF(OR(NOT(ISNUMBER($K$16)),ISERROR($K$16)),1,IF(AND(LEN($K$16)>0,ABS((1-($K$16*-0.0562328100204468+ 0.47296667098999)/-29.9432877598179))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,"Total PV","[$]"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Index"]
[{"$f":"SUM($A$19:$F$53)","v":1},null,null,null,null,null,null,{"$f":"H2+1","v":2},"Present value of a basis point (PVBP)"]
[]
[null,null,null,null,null,null,null,null,"The present value of a basis point (PVBP) is the present value of a one basis point p.a. annuity."]
[]
[null,null,null,null,null,null,null,null,"Nominal annual discount rate",null,"[%]",7.0000000000000007E-2]
[null,null,null,null,null,null,null,null,"Compounding periods per year",null,"[#]",2]
[null,null,null,null,null,null,null,null,"Number of years",null,"[#]",3]
[null,null,null,null,null,null,null,null,"Per-period discount rate",null,"[%]",{"$f":"L22/L23","v":3.5000000000000003E-2}]
[]
[null,null,null,null,null,null,null,null,"A formula can be used to calculate the PVBP.  Let C be the value (per annum) of each cash flow, r be the nominal annual discount rate, m be the number of compounding periods per year and n be the number of compounding periods.  Then the present value of the annuity is given by .."]
[]
[]
[]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,"A proof of this formula is available at the following link"]
[null,null,null,null,null,null,null,null,null,null,null,null,"Annuity formula"]
[]
[]
[]
[]
[]
[null,null,null,null,null,null,null,null,"Use the formula above to calculate the PVBP."]
[]
[{"$f":"IF(OR(NOT(ISNUMBER($K$41)),ISERROR($K$41)),1,IF(AND(LEN($K$41)>0,ABS((1-($K$41*-2.82200157642365+-0.12100875377655)/-7.63960126471249))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,"PVBP","[bps]"]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[null,null,null,null,null,null,null,null,null,"Copyright (c) 2020 Tykoh Group Pty Ltd.  All rights reserved.",null,null,null,null,null,null,null,"Index"]
[null,null,null,null,null,null,null,null,null,"www.tykoh.com"]

{"sheet":"Bond_fundamentals","index":16,"n_rows":196,"n_cols":16,"rows_kept":196,"cut":false,"hidden":false,"merged":[[194,7,194,13],[195,7,195,13],[0,7,0,13],[3,7,5,14],[22,7,26,14],[99,7,100,14],[102,7,103,8],[96,7,97,8],[91,7,93,14],[33,7,33,8],[17,7,18,14]]}
[null,null,null,null,null,null,null,"Click here to see what your answer should look like."]
[{"$f":"SUM($A$3:$E$20)","v":5},null,null,null,null,null,1,"Present value of a bond - calculating from future cash flows and a discount rate.",null,null,null,null,null,"Bonds_and_FRNs","Bond_fundamentals"]
[]
[null,null,null,null,null,null,null,"This exercise illustrates the fundamentals of bond valuation:  Taking the future coupon and principal payments and present-valuing them.  This method gives the total bond value (including accrued interest)."]
[]
[]
[]
[null,null,null,null,null,null,null,"A bond has cash flows as shown below.  The bond has a coupon rate of 6%."]
[]
[null,null,null,null,null,null,null,"Time of cash flow",null,"[yrs]",1,2,3,4]
[null,null,null,null,null,null,null,"Amount of cash flow",null,"[$ 000's]",6,6,6,106]
[]
[null,null,null,null,null,null,null,"Determine the present value of the invidual cashflows assuming the bond's yield is 4%."]
[]
[{"$f":"IF(OR(NOT(ISNUMBER($K$15)),ISERROR($K$15)),1,IF(AND(LEN($K$15)>0,ABS((1-($K$15*-1.04155719280243+-0.218496561050415)/-6.22748036567981))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($L$15)),ISERROR($L$15)),1,IF(AND(LEN($L$15)>0,ABS((1-($L$15* 0.0337117910385132+-0.361267685890198)/-0.174257010750517))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($M$15)),ISERROR($M$15)),1,IF(AND(LEN($M$15)>0,ABS((1-($M$15* 0.172558426856995+ 0.465364456176758)/ 1.38578733497986))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($N$15)),ISERROR($N$15)),1,IF(AND(LEN($N$15)>0,ABS((1-($N$15* 0.575010180473328+ 0.409204125404358)/ 52.5104420136605))<0.00005),0,1))","v":1},null,null,null,"Discounted value",null,"[$ 000's]"]
[{"$f":"IF(OR(NOT(ISNUMBER($K$16)),ISERROR($K$16)),1,IF(AND(LEN($K$16)>0,ABS((1-($K$16* 1.57256424427032+-0.0588853359222412)/ 168.614025971338))<0.00005),0,1))","v":1},null,null,null,null,null,null,"Total present value",null,"[$ 000's]"]
[]
[null,null,null,null,null,null,null,{"$f":"\"If we buy the above bond for the amount calculated in cell \" & ADDRESS(ROW(K16),COLUMN(K16),4) & \" then the implied yield is 4%.\"","v":"If we buy the above bond for the amount calculated in cell K16 then the implied yield is 4%."}]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Index"]
[{"$f":"SUM($A$22:$E$40)","v":12},null,null,null,null,null,2,"Using present value and yield to generate future cash flows."]
[]
[null,null,null,null,null,null,null,"The bond yield relates the present value of the bond to its future payments.  The yield is the fixed/constant discount rate that - applied to the future cash flows - gives the present value.  Another way of thinking about the yield is illustrated in this exercise:  If you sell a bond, deposit the sale proceeds into an account earning the yield, then you can exactly reproduce the coupon and principal payments the bond holder requires."]
[]
[]
[]
[]
[]
[null,null,null,null,null,null,null,{"$f":"\"If we earn 4% on investments and we start with the amount calculated in cell \" & ADDRESS(ROW(K16),COLUMN(K16),4) & \" above\"","v":"If we earn 4% on investments and we start with the amount calculated in cell K16 above"}]
[null,null,null,null,null,null,null,{"$f":"\"then we can reproduce the cash flows shown in cells \"&ADDRESS(ROW(K10),COLUMN(K10),4)&\":\"&ADDRESS(ROW(N11),COLUMN(N11),4)&\".\"","v":"then we can reproduce the cash flows shown in cells K10:N11."}]
[]
[{"$f":"IF(OR(NOT(ISNUMBER($K$32)),ISERROR($K$32)),1,IF(AND(LEN($K$32)>0,ABS((1-($K$32* 1.9299453496933+-0.435508847236633)/ 206.57002493795))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($L$32)),ISERROR($L$32)),1,IF(AND(LEN($L$32)>0,ABS((1-($L$32* 2.56092607975006+ 0.200514316558838)/ 270.506728292909))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($M$32)),ISERROR($M$32)),1,IF(AND(LEN($M$32)>0,ABS((1-($M$32*-0.0292903184890747+-0.344564318656921)/-3.38408479500099))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($N$32)),ISERROR($N$32)),1,IF(AND(LEN($N$32)>0,ABS((1-($N$32*-2.7626246213913+-0.173856019973755)/-281.749057815625))<0.00005),0,1))","v":1},null,null,null,"Opening balance",null,"[$ 000's]"]
[{"$f":"IF(OR(NOT(ISNUMBER($K$33)),ISERROR($K$33)),1,IF(AND(LEN($K$33)>0,ABS((1-($K$33* 2.84488618373871+-0.449737191200256)/ 11.7559386455072))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($L$33)),ISERROR($L$33)),1,IF(AND(LEN($L$33)>0,ABS((1-($L$33* 0.180159211158752+ 0.25702953338623)/ 1.01766303493643))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($M$33)),ISERROR($M$33)),1,IF(AND(LEN($M$33)>0,ABS((1-($M$33* 3.00669848918915+-0.174794554710388)/ 12.3056728427227))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($N$33)),ISERROR($N$33)),1,IF(AND(LEN($N$33)>0,ABS((1-($N$33* 4.72729027271271+ 0.304267168045044)/ 19.5770659721815))<0.00005),0,1))","v":1},null,null,null,"Interest earned",null,"[$ 000's]"]
[null,null,null,null,null,null,null,"Coupon / principal paid",null,"[$ 000's]",{"$f":"-K11","v":-6},{"$f":"-L11","v":-6},{"$f":"-M11","v":-6},{"$f":"-N11","v":-106}]
[{"$f":"IF(OR(NOT(ISNUMBER($K$35)),ISERROR($K$35)),1,IF(AND(LEN($K$35)>0,ABS((1-($K$35* 1.74826085567474+ 0.405129313468933)/ 184.934380929593))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($L$35)),ISERROR($L$35)),1,IF(AND(LEN($L$35)>0,ABS((1-($L$35* 3.75779688358307+-0.0833516120910645)/ 389.871458126596))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($M$35)),ISERROR($M$35)),1,IF(AND(LEN($M$35)>0,ABS((1-($M$35*-3.769171833992+ 0.454157948493958)/-383.711432823768))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($N$35)),ISERROR($N$35)),1,IF(AND(LEN($N$35)>0,ABS((1-($N$35* 2.97297298908234+ 0.196285009384155)/ 0.196285009384155))<0.00005),0,1))","v":1},null,null,null,"Closing balance",null,"[$ 000's]"]
[]
[null,null,null,null,null,null,null,"So if we can lend funds at a rate of 4% we can sell a bond for the amount calculated"]
[null,null,null,null,null,null,null,{"$f":"\"in cell \" & ADDRESS(ROW(K16),COLUMN(K16),4) & \" and can deliver to the bond holder the coupon and principal cashflows they\"","v":"in cell K16 and can deliver to the bond holder the coupon and principal cashflows they"}]
[null,null,null,null,null,null,null,"require."]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Index"]
[{"$f":"SUM($A$42:$E$82)","v":23},null,null,null,null,null,3,"Calculating yield to maturity of a bond."]
[]
[null,null,null,null,null,null,null,"Term",null,"[yrs]",null,1,2,3,4]
[null,null,null,null,null,null,null,"Zero rate",null,"[%]",null,0.05,6.0000000000000053E-2,6.4999999999999947E-2,6.7499999999999893E-2]
[{"$f":"IF(OR(NOT(ISNUMBER($L$45)),ISERROR($L$45)),1,IF(AND(LEN($L$45)>0,ABS((1-($L$45*-0.983954071998596+-0.483702301979065)/-0.532900005578995))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($M$45)),ISERROR($M$45)),1,IF(AND(LEN($M$45)>0,ABS((1-($M$45*-3.32237184047699+-0.335765838623047)/-0.568648283822196))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($N$45)),ISERROR($N$45)),1,IF(AND(LEN($N$45)>0,ABS((1-($N$45* 0.0972002744674683+-0.0939372777938843)/-0.0866403690174265))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($O$45)),ISERROR($O$45)),1,IF(AND(LEN($O$45)>0,ABS((1-($O$45*-3.93866240978241+-0.223876714706421)/-0.519415297898481))<0.00005),0,1))","v":1},null,null,null,"Fwd rate",null,"[%]"]
[{"$f":"IF(OR(NOT(ISNUMBER($L$46)),ISERROR($L$46)),1,IF(AND(LEN($L$46)>0,ABS((1-($L$46* 1.43046796321869+ 0.34909999370575)/ 1.71145043486641))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($M$46)),ISERROR($M$46)),1,IF(AND(LEN($M$46)>0,ABS((1-($M$46*-0.0203078985214233+-0.312224864959717)/-0.330298822347954))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($N$46)),ISERROR($N$46)),1,IF(AND(LEN($N$46)>0,ABS((1-($N$46* 3.96616637706757+-0.127185702323914)/ 3.15620153087099))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($O$46)),ISERROR($O$46)),1,IF(AND(LEN($O$46)>0,ABS((1-($O$46*-1.76445186138153+ 0.270832777023315)/-1.08791322566486))<0.00005),0,1))","v":1},null,null,null,"Discount factor",null,"[#]",1]
[null,null,null,null,null,null,null,"Cashflow",null,"[ 000's]",null,3,3,3,103]
[]
[{"$f":"IF(OR(NOT(ISNUMBER($L$49)),ISERROR($L$49)),1,IF(AND(LEN($L$49)>0,ABS((1-($L$49*-2.8199964761734+-0.0530067682266235)/-8.11013955729348))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($M$49)),ISERROR($M$49)),1,IF(AND(LEN($M$49)>0,ABS((1-($M$49*-2.63972222805023+ 0.378384590148926)/-6.66964556662457))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($N$49)),ISERROR($N$49)),1,IF(AND(LEN($N$49)>0,ABS((1-($N$49* 1.10432803630829+-0.12556779384613)/ 2.61708309188502))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($O$49)),ISERROR($O$49)),1,IF(AND(LEN($O$49)>0,ABS((1-($O$49*-1.10498130321503+ 0.360589265823364)/-87.2830937667885))<0.00005),0,1))","v":1},null,null,null,"Present value",null,"[ 000's]"]
[{"$f":"IF(OR(NOT(ISNUMBER($L$50)),ISERROR($L$50)),1,IF(AND(LEN($L$50)>0,ABS((1-($L$50* 0.859379172325134+ 0.431559443473816)/ 75.4790557867088))<0.00005),0,1))","v":1},null,null,null,null,null,null,"Total PV",null,"[ 000's]"]
[]
[{"$f":"IF(OR(NOT(ISNUMBER($L$52)),ISERROR($L$52)),1,IF(AND(LEN($L$52)>0,ABS((1-($L$52* 0.171924233436584+-0.169699192047119)/-0.158150321027873))<0.00005),0,1))","v":1},null,null,null,null,null,null,"YTM",null,"[%]",null,null,null,"<- Use RATE function"]
[]
[null,null,null,null,null,null,null,"Check of PV using YTM"]
[]
[{"$f":"IF(OR(NOT(ISNUMBER($L$56)),ISERROR($L$56)),1,IF(AND(LEN($L$56)>0,ABS((1-($L$56* 3.68453681468964+-0.240939021110535)/ 3.21167148173779))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($M$56)),ISERROR($M$56)),1,IF(AND(LEN($M$56)>0,ABS((1-($M$56*-2.4045866727829+-0.321306467056274)/-2.43270302864961))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($N$56)),ISERROR($N$56)),1,IF(AND(LEN($N$56)>0,ABS((1-($N$56*-1.53042852878571+-0.497494339942932)/-1.75673029068685))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($O$56)),ISERROR($O$56)),1,IF(AND(LEN($O$56)>0,ABS((1-($O$56* 2.42342054843903+ 0.340887069702148)/ 2.20936311540062))<0.00005),0,1))","v":1},null,null,null,"Discount factor using YTM",null,null,"[#]"]
[]
[{"$f":"IF(OR(NOT(ISNUMBER($L$58)),ISERROR($L$58)),1,IF(AND(LEN($L$58)>0,ABS((1-($L$58*-2.21410572528839+ 0.202970147132874)/-6.02124070976793))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($M$58)),ISERROR($M$58)),1,IF(AND(LEN($M$58)>0,ABS((1-($M$58*-0.951353907585144+ 0.311571359634399)/-2.19449597252245))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($N$58)),ISERROR($N$58)),1,IF(AND(LEN($N$58)>0,ABS((1-($N$58* 2.41780698299408+-0.0623360872268677)/ 5.90577562334387))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($O$58)),ISERROR($O$58)),1,IF(AND(LEN($O$58)>0,ABS((1-($O$58*-4.22019422054291+-0.0893683433532715)/-335.231024577531))<0.00005),0,1))","v":1},null,null,null,"Present value",null,null,"[ 000's]"]
[{"$f":"IF(OR(NOT(ISNUMBER($L$59)),ISERROR($L$59)),1,IF(AND(LEN($L$59)>0,ABS((1-($L$59*-1.60624802112579+ 0.210554242134094)/-140.059185092624))<0.00005),0,1))","v":1},null,null,null,null,null,null,"Total PV",null,null,"[ 000's]"]
[]
[null,null,null,null,null,null,null,{"$f":"\"The PV's in cell \" & ADDRESS(ROW(L50),COLUMN(L50),4)&\" and \" & ADDRESS(ROW(L59),COLUMN(L59),4)&\" should match.\"","v":"The PV's in cell L50 and L59 should match."}]
[]
[]
[]
[]
[]
[null,null,null,null,null,null,null,null,null,"YTM",{"$f":"$L$52","v":0},{"$f":"$L$52","v":0},{"$f":"$L$52","v":0},{"$f":"$L$52","v":0}]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Index"]
[{"$f":"SUM($A$84:$E$195)","v":16},null,null,null,null,null,{"$f":"G41+1","v":4},"Calculating yield to maturity of an annuity"]
[]
[null,null,null,null,null,null,null,{"$f":"\"Find individual and total PV's of annuities.  Use the interest rates in row \" & ROW(44:44) & \" above.\"","v":"Find individual and total PV's of annuities.  Use the interest rates in row 44 above."}]
[]
[null,null,null,null,null,null,null,"Term",null,"[yrs]",null,{"$f":"L43","v":1},{"$f":"M43","v":2},{"$f":"N43","v":3},{"$f":"O43","v":4}]
[null,null,null,null,null,null,null,"Cashflow",null,"[ 000's]",null,1,1,1,1]
[{"$f":"IF(OR(NOT(ISNUMBER($L$89)),ISERROR($L$89)),1,IF(AND(LEN($L$89)>0,ABS((1-($L$89*-1.87711894512177+ 0.298773527145386)/-1.48895880154201))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($M$89)),ISERROR($M$89)),1,IF(AND(LEN($M$89)>0,ABS((1-($M$89*-3.48243772983551+ 0.0929912328720093)/-3.00636594925287))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($N$89)),ISERROR($N$89)),1,IF(AND(LEN($N$89)>0,ABS((1-($N$89* 4.56236898899078+-0.256852149963379)/ 3.52010087404272))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($O$89)),ISERROR($O$89)),1,IF(AND(LEN($O$89)>0,ABS((1-($O$89* 4.39971148967743+-0.385667204856873)/ 3.00240505170202))<0.00005),0,1))","v":1},null,null,null,"Present value",null,"[ 000's]"]
[{"$f":"IF(OR(NOT(ISNUMBER($L$90)),ISERROR($L$90)),1,IF(AND(LEN($L$90)>0,ABS((1-($L$90* 4.84253227710724+ 0.132975816726685)/ 16.7927076481589))<0.00005),0,1))","v":1},null,null,null,null,null,null,"Total PV",null,"[ 000's]"]
[]
[null,null,null,null,null,null,null,{"$f":"\"Assemble a cash flow that alows you to use the IRR function to determine the yield to maturity.  The first cash flow is minus of PV in cell \" & ADDRESS(ROW(L90),COLUMN(L90),4) & \".  Subsequent values are the cash flows in row \" & ROW(88:88)&\".\"","v":"Assemble a cash flow that alows you to use the IRR function to determine the yield to maturity.  The first cash flow is minus of PV in cell L90.  Subsequent values are the cash flows in row 88."}]
[]
[]
[]
[{"$f":"IF(OR(NOT(ISNUMBER($K$96)),ISERROR($K$96)),1,IF(AND(LEN($K$96)>0,ABS((1-($K$96* 0.988563895225525+ 0.402569651603699)/-2.99838019245834))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($L$96)),ISERROR($L$96)),1,IF(AND(LEN($L$96)>0,ABS((1-($L$96* 0.7486492395401+-0.254826068878174)/ 0.493823170661926))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($M$96)),ISERROR($M$96)),1,IF(AND(LEN($M$96)>0,ABS((1-($M$96* 3.60162436962128+-0.425049662590027)/ 3.17657470703125))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($N$96)),ISERROR($N$96)),1,IF(AND(LEN($N$96)>0,ABS((1-($N$96*-0.611736178398132+ 0.259979009628296)/-0.351757168769836))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($O$96)),ISERROR($O$96)),1,IF(AND(LEN($O$96)>0,ABS((1-($O$96*-2.54321157932281+-0.121393799781799)/-2.66460537910461))<0.00005),0,1))","v":1},null,null,"IRR cash flows",null,"[ 000's]"]
[{"$f":"IF(OR(NOT(ISNUMBER($K$97)),ISERROR($K$97)),1,IF(AND(LEN($K$97)>0,ABS((1-($K$97*-1.02756440639496+ 0.0265731811523438)/-0.0383127916987964))<0.00005),0,1))","v":1},null,null,null,null,null,null,{"$f":"\"YTM [IRR of cashflows in row \" & ROW(96:96)&\"].\"","v":"YTM [IRR of cashflows in row 96]."},null,"[%]"]
[]
[]
[null,null,null,null,null,null,null,{"$f":"\"Check that discounting cash flows in row \" & ROW(88:88) & \" at YTM in cell \" & ADDRESS(ROW(K97),COLUMN(K97),4)&\" gives the same PV as in cell \" & ADDRESS(ROW(L90),COLUMN(L90),4)&\".\"","v":"Check that discounting cash flows in row 88 at YTM in cell K97 gives the same PV as in cell L90."}]
[]
[]
[{"$f":"IF(OR(NOT(ISNUMBER($L$103)),ISERROR($L$103)),1,IF(AND(LEN($L$103)>0,ABS((1-($L$103*-2.29640781879425+ 0.0811764001846313)/-2.07883652304625))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($M$103)),ISERROR($M$103)),1,IF(AND(LEN($M$103)>0,ABS((1-($M$103*-2.90301024913788+-0.42129111289978)/-2.98969450247456))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($N$103)),ISERROR($N$103)),1,IF(AND(LEN($N$103)>0,ABS((1-($N$103* 3.95446240901947+-0.388567090034485)/ 2.90229323213178))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($O$103)),ISERROR($O$103)),1,IF(AND(LEN($O$103)>0,ABS((1-($O$103* 1.52376711368561+ 0.400333881378174)/ 1.59307976617183))<0.00005),0,1))","v":1},null,null,null,{"$f":"\"Cashflow in row \" & ROW(88:88) & \" discounted at YTM. \"","v":"Cashflow in row 88 discounted at YTM. "},null,"[ 000's]"]
[]
[{"$f":"IF(OR(NOT(ISNUMBER($K$105)),ISERROR($K$105)),1,IF(AND(LEN($K$105)>0,ABS((1-($K$105*-2.68403351306915+ 0.449905514717102)/-8.78395726527531))<0.00005),0,1))","v":1},null,null,null,null,null,null,"Total PV"]
[]
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[null,null,null,null,null,null,null,null,null,"YTM",null,{"$f":"K97","v":0},{"$f":"L109","v":0},{"$f":"M109","v":0},{"$f":"N109","v":0}]
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[null,null,null,null,null,null,null,"Copyright (c) 2020 Tykoh Group Pty Ltd.  All rights reserved.",null,null,null,null,null,null,null,"Index"]
[null,null,null,null,null,null,null,"www.tykoh.com"]

{"sheet":"Floating_rate_notes","index":17,"n_rows":144,"n_cols":16,"rows_kept":144,"cut":false,"hidden":false,"merged":[[142,7,142,13],[143,7,143,13],[0,6,0,12],[19,6,19,7],[20,6,20,7],[3,6,5,14],[9,10,10,14],[11,10,13,14],[9,6,10,7],[11,6,12,7]]}
[null,null,null,null,null,null,"Click here to see what your answer should look like."]
[{"$f":"SUM($A$3:$D$143)","v":13},null,null,null,null,1,"Valuing a floating rate note from first principles.",null,null,null,null,null,null,"Bonds_and_FRNs","FRNs"]
[]
[null,null,null,null,null,null,{"$f":"\"Value a floating rate note immediately after a coupon has been paid.  The next coupon to be paid will have been rateset to the value shown in cell \" & ADDRESS(ROW(J14),COLUMN(J14),4)&\".  Following coupons (i.e. at times 0.5, 0.75 and 1.0 years) will 'float'.\"","v":"Value a floating rate note immediately after a coupon has been paid.  The next coupon to be paid will have been rateset to the value shown in cell J14.  Following coupons (i.e. at times 0.5, 0.75 and 1.0 years) will 'float'."}]
[]
[]
[]
[null,null,null,null,null,null,"Notional",null,"[$]",100]
[null,null,null,null,null,null,"Payments per year",null,"[#]",4]
[null,null,null,null,null,null,"Nominal interest margin p.a.",null,"[%]",0.01,"<- Need to add this to fwd rate when calculating FRN payment."]
[]
[null,null,null,null,null,null,"Nominal traded margin p.a.",null,"[%]",0.1,"<- Need to add this to fwd rate when discounting to present value."]
[]
[null,null,null,null,null,null,"Next coupon rate",null,"[%]",4.1000000000000002E-2]
[]
[null,null,null,null,null,null,"Term",null,"[yrs]",0,{"$f":"J16+1/ppy","v":0.25},{"$f":"K16+1/ppy","v":0.5},{"$f":"L16+1/ppy","v":0.75},{"$f":"M16+1/ppy","v":1}]
[null,null,null,null,null,null,"Fwd rate p.a.",null,"[%]",null,0.04,4.4999999999999998E-2,0.05,5.5E-2]
[{"$f":"IF(OR(NOT(ISNUMBER($K$18)),ISERROR($K$18)),1,IF(AND(LEN($K$18)>0,ABS((1-($K$18* 3.461874127388+-0.0587837696075439)/ 3.2860221505741))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($L$18)),ISERROR($L$18)),1,IF(AND(LEN($L$18)>0,ABS((1-($L$18*-0.0799375772476196+ 0.269506812095642)/ 0.194974243553023))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($M$18)),ISERROR($M$18)),1,IF(AND(LEN($M$18)>0,ABS((1-($M$18* 3.3489328622818+-0.117430686950684)/ 2.89220163525835))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($N$18)),ISERROR($N$18)),1,IF(AND(LEN($N$18)>0,ABS((1-($N$18*-3.04465115070343+-0.173842787742615)/-2.80795034183046))<0.00005),0,1))","v":1},null,null,"Discount factor",null,"[#]",1]
[{"$f":"IF(OR(NOT(ISNUMBER($K$19)),ISERROR($K$19)),1,IF(AND(LEN($K$19)>0,ABS((1-($K$19*-0.867668986320496+-0.347323179244995)/-1.45360113680363))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($L$19)),ISERROR($L$19)),1,IF(AND(LEN($L$19)>0,ABS((1-($L$19* 1.19831502437592+-0.400590062141418)/ 1.24709309637547))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($M$19)),ISERROR($M$19)),1,IF(AND(LEN($M$19)>0,ABS((1-($M$19*-2.94952809810638+ 0.192517757415771)/-4.23177438974381))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($N$19)),ISERROR($N$19)),1,IF(AND(LEN($N$19)>0,ABS((1-($N$19* 0.0445908308029175+-0.316923975944519)/ 4.21461920440196))<0.00005),0,1))","v":1},null,null,"FRN payment",null,"[$]"]
[{"$f":"IF(OR(NOT(ISNUMBER($K$20)),ISERROR($K$20)),1,IF(AND(LEN($K$20)>0,ABS((1-($K$20* 4.91402447223663+-0.0286085605621338)/ 6.0248998472656))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($L$20)),ISERROR($L$20)),1,IF(AND(LEN($L$20)>0,ABS((1-($L$20*-4.95980322360992+-0.0741506814956665)/-6.43276159852033))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($M$20)),ISERROR($M$20)),1,IF(AND(LEN($M$20)>0,ABS((1-($M$20*-2.11282670497894+ 0.252542495727539)/-2.59560278100329))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($N$20)),ISERROR($N$20)),1,IF(AND(LEN($N$20)>0,ABS((1-($N$20* 3.91279399394989+ 0.321931481361389)/ 344.341784729906))<0.00005),0,1))","v":1},null,null,"Present value of payment",null,"[$]"]
[{"$f":"IF(OR(NOT(ISNUMBER($J$21)),ISERROR($J$21)),1,IF(AND(LEN($J$21)>0,ABS((1-($J$21*-3.23113143444061+-0.39121413230896)/-296.956506909521))<0.00005),0,1))","v":1},null,null,null,null,null,"FRN value = Total PV",null,"[$]"]
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[null,null,null,null,null,null,null,"Copyright (c) 2020 Tykoh Group Pty Ltd.  All rights reserved.",null,null,null,null,null,null,null,"Index"]
[null,null,null,null,null,null,null,"www.tykoh.com"]

{"sheet":"Swap_fundamentals","index":18,"n_rows":78,"n_cols":18,"rows_kept":78,"cut":false,"hidden":false,"merged":[[76,9,76,15],[77,9,77,15],[0,8,0,14],[2,8,3,16],[18,8,18,9],[17,8,17,9],[33,8,33,9],[25,8,26,16]]}
[null,null,null,null,null,null,null,null,"Click here to see what your answer should look like."]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Swaps","Swap_fundamentals"]
[null,null,null,null,null,null,null,null,"In this section we show how to value the fixed and floating legs of a vanilla interest rate swap so as to make it \"fair\" - i.e. so the net present value is zero."]
[]
[]
[{"$f":"SUM($A$7:$F$23)","v":32},null,null,null,null,null,null,1,"Valuing the fixed and floating legs of a fixed-to-float interest rate swap"]
[]
[null,null,null,null,null,null,null,null,"Receive fixed, pay float, semi-annual payments.  [Represent inflows as positive and outflows as -ve.]"]
[]
[null,null,null,null,null,null,null,null,"Notional",null,"[$ 000's]",1000]
[null,null,null,null,null,null,null,null,"Fixed rate coupons",null,"[%]",0.08]
[]
[null,null,null,null,null,null,null,null,"Term",null,"[yrs]",0,0.5,{"$f":"M13+0.5","v":1},{"$f":"N13+0.5","v":1.5},{"$f":"O13+0.5","v":2}]
[null,null,null,null,null,null,null,null,"Fwd rate",null,"[%]",null,7.0000000000000007E-2,{"$f":"M14+0.2%","v":7.2000000000000008E-2},7.0999999999999994E-2,6.9000000000000006E-2]
[{"$f":"IF(OR(NOT(ISNUMBER($M$15)),ISERROR($M$15)),1,IF(AND(LEN($M$15)>0,ABS((1-($M$15*-4.89706575870514+-0.348343014717102)/-5.07980751588149))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($N$15)),ISERROR($N$15)),1,IF(AND(LEN($N$15)>0,ABS((1-($N$15*-1.22592389583588+-0.311868190765381)/-1.45517661953814))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($O$15)),ISERROR($O$15)),1,IF(AND(LEN($O$15)>0,ABS((1-($O$15* 4.79530990123749+ 0.37211811542511)/ 4.69095170730655))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($P$15)),ISERROR($P$15)),1,IF(AND(LEN($P$15)>0,ABS((1-($P$15* 0.815027356147766+ 0.229410886764526)/ 0.938974738458737))<0.00005),0,1))","v":1},null,null,null,null,"Discount factor",null,"[#]",1]
[{"$f":"IF(OR(NOT(ISNUMBER($L$16)),ISERROR($L$16)),1,IF(AND(LEN($L$16)>0,ABS((1-($L$16*-3.54999601840973+-0.242210030555725)/-3550.23822844028))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($M$16)),ISERROR($M$16)),1,IF(AND(LEN($M$16)>0,ABS((1-($M$16*-4.71753060817719+ 0.327898979187012)/ 165.441470265388))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($N$16)),ISERROR($N$16)),1,IF(AND(LEN($N$16)>0,ABS((1-($N$16* 2.83374011516571+ 0.291155457496643)/-101.723488688469))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($O$16)),ISERROR($O$16)),1,IF(AND(LEN($O$16)>0,ABS((1-($O$16*-1.67308509349822+-0.0490577220916748)/ 59.3454630970955))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($P$16)),ISERROR($P$16)),1,IF(AND(LEN($P$16)>0,ABS((1-($P$16* 0.551132559776306+ 0.303330302238464)/-569.84330278635))<0.00005),0,1))","v":1},null,null,null,"Floating cash flow",null,"[$ 000's]",null,null,null,null,null,"Total"]
[{"$f":"IF(OR(NOT(ISNUMBER($L$17)),ISERROR($L$17)),1,IF(AND(LEN($L$17)>0,ABS((1-($L$17* 0.639892220497131+-0.296417713165283)/-640.188638210297))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($M$17)),ISERROR($M$17)),1,IF(AND(LEN($M$17)>0,ABS((1-($M$17*-2.92406380176544+-0.135311961174011)/-117.097864031792))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($N$17)),ISERROR($N$17)),1,IF(AND(LEN($N$17)>0,ABS((1-($N$17* 0.735195279121399+-0.155819177627563)/ 29.2519919872284))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($O$17)),ISERROR($O$17)),1,IF(AND(LEN($O$17)>0,ABS((1-($O$17* 0.282296538352966+-0.0745149850845337)/ 11.2173465490341))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($P$17)),ISERROR($P$17)),1,IF(AND(LEN($P$17)>0,ABS((1-($P$17* 0.730133652687073+-0.449954986572266)/ 758.889043807983))<0.00005),0,1))","v":1},null,null,null,"Fixed cash flow",null,"[$ 000's]",null,null,null,null,null,"[$ 000's]"]
[{"$f":"IF(OR(NOT(ISNUMBER($L$18)),ISERROR($L$18)),1,IF(AND(LEN($L$18)>0,ABS((1-($L$18* 0.475999712944031+-0.293514609336853)/-476.293227553368))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($M$18)),ISERROR($M$18)),1,IF(AND(LEN($M$18)>0,ABS((1-($M$18* 4.62678253650665+ 0.43305230140686)/ 179.245903953838))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($N$18)),ISERROR($N$18)),1,IF(AND(LEN($N$18)>0,ABS((1-($N$18* 4.92572247982025+ 0.339586138725281)/ 184.090634571764))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($O$18)),ISERROR($O$18)),1,IF(AND(LEN($O$18)>0,ABS((1-($O$18*-0.906767249107361+ 0.305275440216064)/-32.3614504742211))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($P$18)),ISERROR($P$18)),1,IF(AND(LEN($P$18)>0,ABS((1-($P$18* 4.89428222179413+-0.241557955741882)/ 4431.16549496644))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($Q$18)),ISERROR($Q$18)),1,IF(AND(LEN($Q$18)>0,ABS((1-($Q$18*-3.25515925884247+ 0.194607496261597)/-56.4533989617533))<0.00005),0,1))","v":1},null,null,"Present value of fixed cash flow",null,"[$ 000's]"]
[{"$f":"IF(OR(NOT(ISNUMBER($L$19)),ISERROR($L$19)),1,IF(AND(LEN($L$19)>0,ABS((1-($L$19*-4.83011305332184+-0.160909295082092)/-4830.27396261692))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($M$19)),ISERROR($M$19)),1,IF(AND(LEN($M$19)>0,ABS((1-($M$19* 1.92547857761383+-0.389613151550293)/-65.5024152930808))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($N$19)),ISERROR($N$19)),1,IF(AND(LEN($N$19)>0,ABS((1-($N$19*-3.90261471271515+-0.209422469139099)/ 130.816755563936))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($O$19)),ISERROR($O$19)),1,IF(AND(LEN($O$19)>0,ABS((1-($O$19*-1.01121604442596+ 0.0590221881866455)/ 32.3902424533712))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($P$19)),ISERROR($P$19)),1,IF(AND(LEN($P$19)>0,ABS((1-($P$19*-1.8904834985733+-0.204419255256653)/ 1702.43499439952))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($Q$19)),ISERROR($Q$19)),1,IF(AND(LEN($Q$19)>0,ABS((1-($Q$19* 3.07941019535065+-0.190382480621338)/-0.190382480621338))<0.00005),0,1))","v":1},null,null,"Present value of floating cash flow",null,"[$ 000's]"]
[{"$f":"IF(OR(NOT(ISNUMBER($L$20)),ISERROR($L$20)),1,IF(AND(LEN($L$20)>0,ABS((1-($L$20*-1.2418395280838+-0.0989636182785034)/-0.0989636182785034))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($M$20)),ISERROR($M$20)),1,IF(AND(LEN($M$20)>0,ABS((1-($M$20* 3.41427624225616+-0.0904028415679932)/ 0.0745380397004206))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($N$20)),ISERROR($N$20)),1,IF(AND(LEN($N$20)>0,ABS((1-($N$20* 2.24558770656586+ 0.158763289451599)/ 0.263476125264082))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($O$20)),ISERROR($O$20)),1,IF(AND(LEN($O$20)>0,ABS((1-($O$20*-0.936183333396912+ 0.45033073425293)/ 0.408172666143601))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($P$20)),ISERROR($P$20)),1,IF(AND(LEN($P$20)>0,ABS((1-($P$20* 1.45570933818817+ 0.0160881280899048)/ 0.0794552480497874))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($Q$20)),ISERROR($Q$20)),1,IF(AND(LEN($Q$20)>0,ABS((1-($Q$20*-2.76676833629608+ 0.0827581882476807)/-0.424948157438203))<0.00005),0,1))","v":1},null,null,"PVBP",null,"[$ 000's]"]
[]
[null,null,null,null,null,null,null,null,"The present value of the floating leg should be zero.  Why is this so?"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Index"]
[{"$f":"SUM($A$25:$F$77)","v":23},null,null,null,null,null,null,2,"Calculating fixed coupon rate that makes swap value zero."]
[]
[null,null,null,null,null,null,null,null,"Continuing on from the preceding question: What fixed coupon rate is required in order to set the overall value of the swap (i.e. fixed leg + floating leg) to zero?"]
[]
[]
[{"$f":"IF(OR(NOT(ISNUMBER($N$29)),ISERROR($N$29)),1,IF(AND(LEN($N$29)>0,ABS((1-($N$29* 2.48532712459564+-0.0435296297073364)/ 0.131726726302404))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,"Fixed coupon rate to make swap zero value",null,null,null,"[%]"]
[]
[null,null,null,null,null,null,null,null,{"$f":"\"Using the fixed coupon rate calculated above in cell \" & ADDRESS(ROW(N29),COLUMN(N29),4) & \":\"","v":"Using the fixed coupon rate calculated above in cell N29:"}]
[]
[{"$f":"IF(OR(NOT(ISNUMBER($L$33)),ISERROR($L$33)),1,IF(AND(LEN($L$33)>0,ABS((1-($L$33* 4.04373705387115+-0.21698522567749)/-4043.95403909683))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($M$33)),ISERROR($M$33)),1,IF(AND(LEN($M$33)>0,ABS((1-($M$33* 1.67538344860077+ 0.390127301216125)/ 59.4611435901835))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($N$33)),ISERROR($N$33)),1,IF(AND(LEN($N$33)>0,ABS((1-($N$33*-2.1861857175827+-0.131943941116333)/-77.2129323213524))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($O$33)),ISERROR($O$33)),1,IF(AND(LEN($O$33)>0,ABS((1-($O$33*-4.85778868198395+-0.205340981483459)/-171.482259469303))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($P$33)),ISERROR($P$33)),1,IF(AND(LEN($P$33)>0,ABS((1-($P$33* 4.84046041965485+ 0.261282920837402)/ 5011.38765760487))<0.00005),0,1))","v":1},null,null,null,"Fixed payment",null,"[$ 000's]",null,null,null,null,null,"Total"]
[{"$f":"IF(OR(NOT(ISNUMBER($L$34)),ISERROR($L$34)),1,IF(AND(LEN($L$34)>0,ABS((1-($L$34* 0.808784365653992+ 0.105673432350159)/-808.678692221642))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($M$34)),ISERROR($M$34)),1,IF(AND(LEN($M$34)>0,ABS((1-($M$34*-2.3195618391037+ 0.00816655158996582)/-79.0097960281626))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($N$34)),ISERROR($N$34)),1,IF(AND(LEN($N$34)>0,ABS((1-($N$34* 2.93596684932709+ 0.35741126537323)/ 96.8982937589454))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($O$34)),ISERROR($O$34)),1,IF(AND(LEN($O$34)>0,ABS((1-($O$34*-4.06847417354584+ 0.0418734550476074)/-129.151898202353))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($P$34)),ISERROR($P$34)),1,IF(AND(LEN($P$34)>0,ABS((1-($P$34*-0.846236348152161+-0.426628947257996)/-763.137004046793))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($Q$34)),ISERROR($Q$34)),1,IF(AND(LEN($Q$34)>0,ABS((1-($Q$34*-0.48623263835907+ 0.198890447616577)/ 0.198890447616577))<0.00005),0,1))","v":1},null,null,"Present value of fixed payment",null,"[$ 000's]"]
[{"$f":"IF(OR(NOT(ISNUMBER($L$35)),ISERROR($L$35)),1,IF(AND(LEN($L$35)>0,ABS((1-($L$35*-0.00742971897125244+-0.0930658578872681)/-0.0930658578872681))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($M$35)),ISERROR($M$35)),1,IF(AND(LEN($M$35)>0,ABS((1-($M$35* 4.4507223367691+ 0.484649658203125)/ 1.63385693230063))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($N$35)),ISERROR($N$35)),1,IF(AND(LEN($N$35)>0,ABS((1-($N$35* 0.914422869682312+ 0.0319896936416626)/-0.646322869909342))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($O$35)),ISERROR($O$35)),1,IF(AND(LEN($O$35)>0,ABS((1-($O$35* 1.15071594715118+-0.410846471786499)/-0.689081633192658))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($P$35)),ISERROR($P$35)),1,IF(AND(LEN($P$35)>0,ABS((1-($P$35*-3.15575182437897+-0.216440320014954)/-2.60915316819179))<0.00005),0,1))","v":1},null,null,null,"Net cash flow"]
[{"$f":"IF(OR(NOT(ISNUMBER($L$36)),ISERROR($L$36)),1,IF(AND(LEN($L$36)>0,ABS((1-($L$36*-4.81191098690032+-0.347400188446045)/-0.347400188446045))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($M$36)),ISERROR($M$36)),1,IF(AND(LEN($M$36)>0,ABS((1-($M$36*-0.79888641834259+ 0.0484238862991333)/-0.150878525024982))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($N$36)),ISERROR($N$36)),1,IF(AND(LEN($N$36)>0,ABS((1-($N$36* 0.584447979927062+ 0.281006574630737)/-0.123316510596198))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($O$36)),ISERROR($O$36)),1,IF(AND(LEN($O$36)>0,ABS((1-($O$36*-4.57052290439606+-0.0942550897598267)/ 0.901057647020476))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($P$36)),ISERROR($P$36)),1,IF(AND(LEN($P$36)>0,ABS((1-($P$36*-4.41008508205414+-0.188162803649902)/-3.09924189152943))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($Q$36)),ISERROR($Q$36)),1,IF(AND(LEN($Q$36)>0,ABS((1-($Q$36* 1.03043735027313+ 0.0176931619644165)/ 0.0176931619644366))<0.00005),0,1))","v":1},null,null,"PV of net cash flow"]
[]
[]
[]
[null,null,null,null,null,null,null,null,null,null,null,{"$f":"N29","v":0},{"$f":"L40","v":0},{"$f":"M40","v":0},{"$f":"N40","v":0}]
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[null,null,null,null,null,null,null,null,null,"Copyright (c) 2020 Tykoh Group Pty Ltd.  All rights reserved.",null,null,null,null,null,null,null,"Index"]
[null,null,null,null,null,null,null,null,null,"www.tykoh.com"]

{"sheet":"Swap_Cross_Currency","index":19,"n_rows":94,"n_cols":25,"rows_kept":94,"cut":false,"hidden":false,"merged":[[92,14,92,20],[93,14,93,20],[0,11,0,17],[9,14,9,16],[10,14,10,16],[11,11,12,13],[12,14,12,16],[2,11,3,22],[11,14,11,16],[10,18,10,19],[5,11,7,22],[9,21,9,22],[9,18,9,19],[89,11,89,23],[52,22,52,23],[20,11,20,20],[11,20,11,23],[52,13,52,16],[52,17,52,20],[42,11,42,20],[22,11,23,22],[38,11,38,19],[50,11,50,18],[46,11,46,20],[29,11,31,22],[27,11,27,20],[37,11,37,20]]}
[null,null,null,null,null,null,null,null,null,null,null,"Click here to see what your answer should look like."]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Swaps","Swap_Cross_Currency"]
[null,null,null,null,null,null,null,null,null,null,null,"In this section we look at cross-currency fixed-for-floating swaps.  We deal with two currencies, two discount rates and two payment frequencies and calculate the margin needed on the floating leg to make the swap \"fair\"."]
[]
[]
[null,null,null,null,null,null,null,null,null,null,null,{"$f":"\"Company A issues three-year debt in USD at a fixed rate of \"&TEXT(P16,\"0.0%\")&\" p.a. semi against a market swap rate of \"&TEXT(P17,\"0.0%\")&\" p.a. quarterly.  Company A wants floating rate AUD debt.  AUD swap rates are \"&TEXT(P18,\"0.00%\")&\" p.a. quarterly.  What is the margin against BBSW that Company A will pay?\"","v":"Company A issues three-year debt in USD at a fixed rate of 4.5% p.a. semi against a market swap rate of 4.0% p.a. quarterly.  Company A wants floating rate AUD debt.  AUD swap rates are 6.00% p.a. quarterly.  What is the margin against BBSW that Company A will pay?"}]
[]
[]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,"Bank XYZ",null,"AUD BBSW + ?% quarterly",null,null,null,{"$f":"\"USD \" & TEXT(P16,\"0.0%\") & \" semi\"","v":"USD 4.5% semi"},null,null,"USD Bond Market"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,"<------------------------------------",null,null,"Company A","-------------------->"]
[null,null,null,null,null,null,null,null,null,null,null,{"$f":"\"Swap rate (AUD, 3-yr, qtly) = \" & TEXT(P18,\"0.0%\") & \" p.a.\"","v":"Swap rate (AUD, 3-yr, qtly) = 6.0% p.a."},null,null,{"$f":"\"USD \" & TEXT(P16,\"0.0%\") & \" semi\"","v":"USD 4.5% semi"},null,null,null,null,null,{"$f":"\"Swap rate (USD, 3-yr, qtly) = \" & TEXT(P17,\"0.0%\") & \" p.a.\"","v":"Swap rate (USD, 3-yr, qtly) = 4.0% p.a."}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,"------------------------------------>"]
[]
[]
[null,null,null,null,null,null,null,null,null,null,null,"USD bond coupon (semi)",null,null,null,4.4999999999999998E-2]
[null,null,null,null,null,null,null,null,null,null,null,"USD quarterly 3-yr swap rate:",null,null,null,0.04]
[null,null,null,null,null,null,null,null,null,null,null,"AUD quarterly 3-yr swap rate",null,null,null,0.06]
[null,null,null,null,null,null,null,null,null,null,null,"AUD / USD exchange rate:  ",null,null,null,0.9,{"$f":"\"(i.e. 1 AUD = \" & TEXT(P19,\"0.00\") &  \" USD)\"","v":"(i.e. 1 AUD = 0.90 USD)"}]
[]
[{"$f":"SUM($A$22:$I$27)","v":1},null,null,null,null,null,null,null,null,null,1,"Converting USD quarterly swap rate to semi."]
[]
[null,null,null,null,null,null,null,null,null,null,null,"Since Company A's obligation is to provide semi-annual payments into the USD Bond market we need to express rates and values on a semi-annual basis.  Begin by expressing the quarterly USD swap rate on a semi-annual basis."]
[]
[]
[{"$f":"IF(OR(NOT(ISNUMBER($P$26)),ISERROR($P$26)),1,IF(AND(LEN($P$26)>0,ABS((1-($P$26* 0.964377522468567+-0.170374631881714)/-0.131606655478477))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,null,null,null,"USD semi 3-yr swap rate:"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Index"]
[{"$f":"SUM($A$29:$I$37)","v":1},null,null,null,null,null,null,null,null,null,2,"Calculating USD PVBP"]
[]
[null,null,null,null,null,null,null,null,null,null,null,{"$f":"\"Company A has promised its USD bond holders \" & TEXT(P16,\"0.0%\") & \" coupons.  However, the market USD swap rate is less than this.  So Company A will need to pay a margin on top of BBSW to Bank XYZ in order to receive the full \" & TEXT(P16,\"0.0%\")&\".  Calculate the present value of a one basis point margin.\"","v":"Company A has promised its USD bond holders 4.5% coupons.  However, the market USD swap rate is less than this.  So Company A will need to pay a margin on top of BBSW to Bank XYZ in order to receive the full 4.5%.  Calculate the present value of a one basis point margin."}]
[]
[]
[]
[null,null,null,null,null,null,null,null,null,null,null,"[PVBP - the present value of a basis point is described in the Bonds and FRNs modules in the section on annuities.]"]
[]
[{"$f":"IF(OR(NOT(ISNUMBER($P$36)),ISERROR($P$36)),1,IF(AND(LEN($P$36)>0,ABS((1-($P$36* 4.09298360347748+ 0.270071864128113)/ 11.7294866787653))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,null,null,null,"USD semi PVBP"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Index"]
[{"$f":"SUM($A$39:$I$42)","v":1},null,null,null,null,null,null,null,null,null,3,"Calculating the margin above the USD semi swap rate we want to receive"]
[null,null,null,null,null,null,null,null,null,null,null,{"$f":"\"Calculate the margin above the USD semi swap rate (in cell \" & ADDRESS(ROW(P26),COLUMN(P26),4)&\") that we want to receive.\"","v":"Calculate the margin above the USD semi swap rate (in cell P26) that we want to receive."}]
[]
[{"$f":"IF(OR(NOT(ISNUMBER($P$41)),ISERROR($P$41)),1,IF(AND(LEN($P$41)>0,ABS((1-($P$41* 0.758739113807678+-0.0683999061584473)/-0.0647579584121704))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,null,null,null,"USD margin"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Index"]
[{"$f":"SUM($A$44:$I$46)","v":1},null,null,null,null,null,null,null,null,null,4,"Calculating AUD PVBP"]
[]
[{"$f":"IF(OR(NOT(ISNUMBER($P$45)),ISERROR($P$45)),1,IF(AND(LEN($P$45)>0,ABS((1-($P$45* 2.32524573802947+-0.337057948112488)/ 6.00359955064993))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,null,null,null,"AUD quarterly PVBP"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Index"]
[{"$f":"SUM($A$48:$I$50)","v":1},null,null,null,null,null,null,null,null,null,5,"Calculating AUD margin"]
[]
[{"$f":"IF(OR(NOT(ISNUMBER($P$49)),ISERROR($P$49)),1,IF(AND(LEN($P$49)>0,ABS((1-($P$49*-4.4038313627243+-0.256689310073853)/-0.278392767084488))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,null,null,null,"AUD margin"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Index"]
[{"$f":"SUM($A$52:$I$93)","v":101},null,null,null,null,null,null,null,null,null,{"$f":"K47+1","v":6},"Modelling swap cash flows"]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"AUD",null,null,null,"USD",null,null,null,"FX rate (base 1)","Net cashflow (in AUD)"]
[null,null,null,null,null,null,null,null,null,null,null,"Period","Yrs","BBSW","Discount factor","Floating payment","Present value","LIBOR","Discount factor","Fixed payment","Present value",null,"Net cashflow","PV of net cashflow"]
[{"$f":"IF(OR(NOT(ISNUMBER($Q$55)),ISERROR($Q$55)),1,IF(AND(LEN($Q$55)>0,ABS((1-($Q$55* 2.58574426174164+ 0.451247572898865)/ 259.025673747063))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($T$55)),ISERROR($T$55)),1,IF(AND(LEN($T$55)>0,ABS((1-($T$55*-1.54664933681488+ 0.18425178527832)/ 139.382692098618))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($U$55)),ISERROR($U$55)),1,IF(AND(LEN($U$55)>0,ABS((1-($U$55* 2.91464030742645+-0.46455991268158)/-262.782187581062))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($V$55)),ISERROR($V$55)),1,IF(AND(LEN($V$55)>0,ABS((1-($V$55* 2.94173538684845+-0.0165116786956787)/ 2.92522370815277))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($W$55)),ISERROR($W$55)),1,IF(AND(LEN($W$55)>0,ABS((1-($W$55*-2.93501436710358+ 0.102104067802429)/ 0.102104067802429))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($X$55)),ISERROR($X$55)),1,IF(AND(LEN($X$55)>0,ABS((1-($X$55* 4.08878862857819+ 0.4452805519104)/ 0.4452805519104))<0.00005),0,1))","v":1},null,null,null,null,null,0,0,null,1,100,null,null,1]
[{"$f":"IF(OR(NOT(ISNUMBER($O$56)),ISERROR($O$56)),1,IF(AND(LEN($O$56)>0,ABS((1-($O$56* 1.53397262096405+-0.485418200492859)/ 1.02588487434857))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($P$56)),ISERROR($P$56)),1,IF(AND(LEN($P$56)>0,ABS((1-($P$56* 1.61924183368683+ 0.464709043502808)/-2.16365694995761))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($Q$56)),ISERROR($Q$56)),1,IF(AND(LEN($Q$56)>0,ABS((1-($Q$56*-4.90581572055817+ 0.453598380088806)/ 8.29907463657738))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($V$56)),ISERROR($V$56)),1,IF(AND(LEN($V$56)>0,ABS((1-($V$56*-4.26365792751312+-0.206700325012207)/-4.4493550115031))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($W$56)),ISERROR($W$56)),1,IF(AND(LEN($W$56)>0,ABS((1-($W$56* 0.824844241142272+ 0.307886719703674)/-1.03100689594837))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($X$56)),ISERROR($X$56)),1,IF(AND(LEN($X$56)>0,ABS((1-($X$56*-4.59689795970917+-0.445351362228394)/ 6.90609758137272))<0.00005),0,1))","v":1},null,null,null,null,null,{"$f":"L55+1","v":1},{"$f":"M55+0.25","v":0.25},{"$f":"P18","v":0.06}]
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[{"$f":"IF(OR(NOT(ISNUMBER($O$58)),ISERROR($O$58)),1,IF(AND(LEN($O$58)>0,ABS((1-($O$58* 2.3083359003067+-0.307693004608154)/ 1.89980784411763))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($P$58)),ISERROR($P$58)),1,IF(AND(LEN($P$58)>0,ABS((1-($P$58* 2.73646056652069+-0.430148959159851)/-4.87199312712585))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($Q$58)),ISERROR($Q$58)),1,IF(AND(LEN($Q$58)>0,ABS((1-($Q$58*-2.51930415630341+ 0.450413465499878)/ 4.3611323675161))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($V$58)),ISERROR($V$58)),1,IF(AND(LEN($V$58)>0,ABS((1-($V$58* 3.19883286952972+-0.280530571937561)/ 2.87126139689735))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($W$58)),ISERROR($W$58)),1,IF(AND(LEN($W$58)>0,ABS((1-($W$58*-3.15775811672211+-0.263079643249512)/ 4.86261799925051))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($X$58)),ISERROR($X$58)),1,IF(AND(LEN($X$58)>0,ABS((1-($X$58* 4.25450503826141+-0.242495894432068)/-6.84676923325174))<0.00005),0,1))","v":1},null,null,null,null,null,3,0.75,0.06]
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[{"$f":"IF(OR(NOT(ISNUMBER($O$67)),ISERROR($O$67)),1,IF(AND(LEN($O$67)>0,ABS((1-($O$67* 0.443113446235657+ 0.0382506847381592)/ 0.408865197642384))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($P$67)),ISERROR($P$67)),1,IF(AND(LEN($P$67)>0,ABS((1-($P$67* 1.26684129238129+-0.41187059879303)/-129.15234651889))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($Q$67)),ISERROR($Q$67)),1,IF(AND(LEN($Q$67)>0,ABS((1-($Q$67* 2.11056768894196+-0.24201488494873)/-179.632612965109))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($S$67)),ISERROR($S$67)),1,IF(AND(LEN($S$67)>0,ABS((1-($S$67*-4.42431271076202+-0.224788069725037)/-4.15114095722157))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($T$67)),ISERROR($T$67)),1,IF(AND(LEN($T$67)>0,ABS((1-($T$67* 4.60600197315216+-0.173018217086792)/ 423.694313362241))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($U$67)),ISERROR($U$67)),1,IF(AND(LEN($U$67)>0,ABS((1-($U$67* 1.47697865962982+-0.13653290271759)/ 120.484643870855))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($V$67)),ISERROR($V$67)),1,IF(AND(LEN($V$67)>0,ABS((1-($V$67*-1.30093038082123+-0.173155307769775)/-1.39923312304463))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($W$67)),ISERROR($W$67)),1,IF(AND(LEN($W$67)>0,ABS((1-($W$67*-2.85240471363068+-0.287669062614441)/-19.8814007638599))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($X$67)),ISERROR($X$67)),1,IF(AND(LEN($X$67)>0,ABS((1-($X$67*-0.76831042766571+ 0.117498159408569)/-4.29668380561385))<0.00005),0,1))","v":1},null,null,12,3,0.06,null,null,null,{"$f":"$P$26","v":0}]
[{"$f":"IF(OR(NOT(ISNUMBER($Q$68)),ISERROR($Q$68)),1,IF(AND(LEN($Q$68)>0,ABS((1-($Q$68*-2.58519232273102+ 0.186122298240662)/ 3.66033601480149))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,null,null,null,null,null,"Total of AUD leg:"]
[{"$f":"IF(OR(NOT(ISNUMBER($Q$69)),ISERROR($Q$69)),1,IF(AND(LEN($Q$69)>0,ABS((1-($Q$69* 0.899296402931213+ 0.102811813354492)/ 1.3113671192192))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($U$69)),ISERROR($U$69)),1,IF(AND(LEN($U$69)>0,ABS((1-($U$69*-4.2124730348587+-0.455332159996033)/-5.55032193027305))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,null,null,null,null,{"$f":"\"Total of USD leg (in \" & ADDRESS(ROW(U69),COLUMN(U69),4) & \") in AUD:\"","v":"Total of USD leg (in U69) in AUD:"},null,null,null,null,null,"Total:"]
[{"$f":"IF(OR(NOT(ISNUMBER($Q$70)),ISERROR($Q$70)),1,IF(AND(LEN($Q$70)>0,ABS((1-($Q$70*-3.46790969371796+-0.253774404525757)/-0.253774404525537))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($X$70)),ISERROR($X$70)),1,IF(AND(LEN($X$70)>0,ABS((1-($X$70*-1.01244509220123+ 0.0839270353317261)/ 0.0839270353318223))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,null,null,null,null,"Total of AUD & USD legs:"]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[null,null,null,null,null,null,null,null,null,null,null,{"$f":"\"We can see that the net present value of the fixed and floating legs in cell \" & ADDRESS(ROW(X70),COLUMN(X70),4) & \" is zero as we would expect.\"","v":"We can see that the net present value of the fixed and floating legs in cell X70 is zero as we would expect."}]
[]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Copyright (c) 2020 Tykoh Group Pty Ltd.  All rights reserved.",null,null,null,null,null,null,null,null,null,"Index"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,"www.tykoh.com"]

{"sheet":"Sensitivity","index":20,"n_rows":148,"n_cols":18,"rows_kept":148,"cut":false,"hidden":false,"merged":[[146,9,146,15],[147,9,147,15],[0,7,0,13],[2,7,6,15],[10,7,11,15],[29,7,30,15],[61,7,63,16],[22,7,23,15]]}
[null,null,null,null,null,null,null,"Click here to see what your answer should look like."]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Sensitivity","Sensitivity"]
[null,null,null,null,null,null,null,"The sensitivity of an \"output\" to its \"inputs\" is often measured by varying the input by a small amount, determining the resultant change in output and then dividing the change in output by the change in input.  \"Inputs\" could be: Time elapsed, time to maturity, asset price, volatility, interest rate, yield, correlation, inflation rate, fx rate, default rate and so on.  \"Outputs\" could be value, rate of return, frequency, probability, duration and so on."]
[]
[]
[]
[]
[]
[{"$f":"SUM($A$10:$E$27)","v":5},null,null,null,null,null,1,"Calculating sensitivity of fixed-interest investment's value to time"]
[]
[null,null,null,null,null,null,null,"An investment of $100 earns 6% interest compounding semi-annually.  At what rate is the investment growing in value at time t = 1.5 years?"]
[]
[]
[{"$f":"IF(OR(NOT(ISNUMBER($M$14)),ISERROR($M$14)),1,IF(AND(LEN($M$14)>0,ABS((1-($M$14*-2.12371289730072+ 0.336374759674072)/-231.727467553198))<0.00005),0,1))","v":1},null,null,null,null,null,null,"Investment value at time 1.5 years:",null,null,null,"[$]"]
[{"$f":"IF(OR(NOT(ISNUMBER($M$15)),ISERROR($M$15)),1,IF(AND(LEN($M$15)>0,ABS((1-($M$15* 3.98083388805389+ 0.026617169380188)/ 435.025655971038))<0.00005),0,1))","v":1},null,null,null,null,null,null,"Investment value at time 1.5001 years:",null,null,null,"[$]"]
[]
[{"$f":"IF(OR(NOT(ISNUMBER($M$17)),ISERROR($M$17)),1,IF(AND(LEN($M$17)>0,ABS((1-($M$17*-1.12463176250458+-0.497285127639771)/-7.76236060196142))<0.00005),0,1))","v":1},null,null,null,null,null,null,"Rate of increase at time 1.5 years:",null,null,null,"[$ / yr]"]
[]
[null,null,null,null,null,null,null,"What continuously compounding rate is equivalent to the semi-annual rate given above?"]
[]
[{"$f":"IF(OR(NOT(ISNUMBER($M$21)),ISERROR($M$21)),1,IF(AND(LEN($M$21)>0,ABS((1-($M$21*-2.49130308628082+-0.337161660194397)/-0.484441530696645))<0.00005),0,1))","v":1},null,null,null,null,null,null,"Continuously compounding rate:",null,null,null,"[%]"]
[]
[null,null,null,null,null,null,null,{"$f":"\"From your knowledge of the slope of the exponential function what is the exact answer to the question above (whose approximate answer was calculated in cell \" & ADDRESS(ROW(M17),COLUMN(M17),4)&\"?\"","v":"From your knowledge of the slope of the exponential function what is the exact answer to the question above (whose approximate answer was calculated in cell M17?"}]
[]
[]
[{"$f":"IF(OR(NOT(ISNUMBER($M$26)),ISERROR($M$26)),1,IF(AND(LEN($M$26)>0,ABS((1-($M$26* 1.45133078098297+ 0.481146812438965)/ 9.85665695421618))<0.00005),0,1))","v":1},null,null,null,null,null,null,"Rate of increase at time 1.5 years:",null,null,null,"[$ / yr]"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Index"]
[{"$f":"SUM($A$29:$E$59)","v":25},null,null,null,null,null,2,"Calculating sensitivity of forward price to its drivers."]
[]
[null,null,null,null,null,null,null,"An asset has a spot price of S and yields a continuous return of d.  The interest rate (continuously compounding) is r.  The forward price, F, of the asset at time t is given by the following equation: "]
[]
[]
[null,null,null,null,null,null,null,"F = S * exp((r-d)*t)"]
[]
[null,null,null,null,null,null,null,"The current values of S, d, r and t are as shown below:"]
[]
[null,null,null,null,null,null,null,"Spot","[$]",100]
[null,null,null,null,null,null,null,"r","[%]",4.2999999999999997E-2]
[null,null,null,null,null,null,null,"d","[%[",1.2E-2]
[null,null,null,null,null,null,null,"t","[yrs]",1.5]
[]
[null,null,null,null,null,null,null,"Find the sensitivity of the forward price to S, r, d and t. "]
[]
[null,null,null,null,null,null,null,null,null,null,"Spot","r","d","t","Forward price"]
[]
[{"$f":"IF(OR(NOT(ISNUMBER($O$46)),ISERROR($O$46)),1,IF(AND(LEN($O$46)>0,ABS((1-($O$46*-1.88088238239288+-0.259301543235779)/-197.300178618099))<0.00005),0,1))","v":1},null,null,null,null,null,null,"Original values:",null,null,100,4.2999999999999997E-2,1.2E-2,1.5]
[{"$f":"IF(OR(NOT(ISNUMBER($K$47)),ISERROR($K$47)),1,IF(AND(LEN($K$47)>0,ABS((1-($K$47* 3.78593742847443+-0.370358228683472)/ 382.009322047234))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($L$47)),ISERROR($L$47)),1,IF(AND(LEN($L$47)>0,ABS((1-($L$47* 0.697960257530212+ 0.106938242912292)/ 0.136950533986092))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($M$47)),ISERROR($M$47)),1,IF(AND(LEN($M$47)>0,ABS((1-($M$47* 1.10196650028229+ 0.19386625289917)/ 0.207089850902557))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($N$47)),ISERROR($N$47)),1,IF(AND(LEN($N$47)>0,ABS((1-($N$47* 3.50022971630096+-0.402443766593933)/ 4.84790080785751))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($O$47)),ISERROR($O$47)),1,IF(AND(LEN($O$47)>0,ABS((1-($O$47*-1.05553805828094+ 0.32280707359314)/-111.36093679253))<0.00005),0,1))","v":1},null,null,"Increase original spot by 1%:"]
[{"$f":"IF(OR(NOT(ISNUMBER($K$48)),ISERROR($K$48)),1,IF(AND(LEN($K$48)>0,ABS((1-($K$48*-2.31867849826813+ 0.178433775901794)/-231.689416050911))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($L$48)),ISERROR($L$48)),1,IF(AND(LEN($L$48)>0,ABS((1-($L$48*-1.03801667690277+ 0.334396362304688)/ 0.279381478428841))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($M$48)),ISERROR($M$48)),1,IF(AND(LEN($M$48)>0,ABS((1-($M$48*-0.671728253364562+ 0.335960030555725)/ 0.32789929151535))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($N$48)),ISERROR($N$48)),1,IF(AND(LEN($N$48)>0,ABS((1-($N$48*-2.81214416027069+ 0.231136560440063)/-3.98707967996597))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($O$48)),ISERROR($O$48)),1,IF(AND(LEN($O$48)>0,ABS((1-($O$48* 3.99100720882416+-0.282343029975891)/ 424.133534743013))<0.00005),0,1))","v":1},null,null,"Add 1% to original r:"]
[{"$f":"IF(OR(NOT(ISNUMBER($K$49)),ISERROR($K$49)),1,IF(AND(LEN($K$49)>0,ABS((1-($K$49* 4.8214203119278+ 0.465725421905518)/ 482.607756614685))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($L$49)),ISERROR($L$49)),1,IF(AND(LEN($L$49)>0,ABS((1-($L$49* 3.71359527111053+ 0.0228043794631958)/ 0.182488976120949))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($M$49)),ISERROR($M$49)),1,IF(AND(LEN($M$49)>0,ABS((1-($M$49* 1.50928318500519+-0.0433189868927002)/-0.0101147568225861))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($N$49)),ISERROR($N$49)),1,IF(AND(LEN($N$49)>0,ABS((1-($N$49*-3.43450605869293+ 0.143064856529236)/-5.00869423151016))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($O$49)),ISERROR($O$49)),1,IF(AND(LEN($O$49)>0,ABS((1-($O$49* 1.12656652927399+ 0.35396671295166)/ 116.615787504028))<0.00005),0,1))","v":1},null,null,"Add 1% to original d:"]
[{"$f":"IF(OR(NOT(ISNUMBER($K$50)),ISERROR($K$50)),1,IF(AND(LEN($K$50)>0,ABS((1-($K$50*-1.32719814777374+-0.446891188621521)/-133.166705965996))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($L$50)),ISERROR($L$50)),1,IF(AND(LEN($L$50)>0,ABS((1-($L$50* 0.0581580400466919+-0.445383787155151)/-0.442882991433144))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($M$50)),ISERROR($M$50)),1,IF(AND(LEN($M$50)>0,ABS((1-($M$50*-1.2504917383194+-0.0487605333328247)/-0.0637664341926575))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($N$50)),ISERROR($N$50)),1,IF(AND(LEN($N$50)>0,ABS((1-($N$50*-2.0200389623642+ 0.468358516693115)/-2.58190031647682))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($O$50)),ISERROR($O$50)),1,IF(AND(LEN($O$50)>0,ABS((1-($O$50*-4.8712569475174+ 0.150017857551575)/-510.320145454365))<0.00005),0,1))","v":1},null,null,"Add 0.01 to original t:"]
[]
[]
[]
[{"$f":"IF(OR(NOT(ISNUMBER($K$54)),ISERROR($K$54)),1,IF(AND(LEN($K$54)>0,ABS((1-($K$54* 1.14014446735382+ 0.03324294090271)/ 1.22765609476317))<0.00005),0,1))","v":1},null,null,null,null,null,null,"Sensitivity to spot:",null,"[#]"]
[{"$f":"IF(OR(NOT(ISNUMBER($K$55)),ISERROR($K$55)),1,IF(AND(LEN($K$55)>0,ABS((1-($K$55*-4.70597326755524+ 0.216887831687927)/-744.852445456172))<0.00005),0,1))","v":1},null,null,null,null,null,null,"Sensitivity to r:",null,"[1/%]"]
[{"$f":"IF(OR(NOT(ISNUMBER($K$56)),ISERROR($K$56)),1,IF(AND(LEN($K$56)>0,ABS((1-($K$56*-1.85960710048676+ 0.481264114379883)/ 290.51866933807))<0.00005),0,1))","v":1},null,null,null,null,null,null,"Sensitivity to d:",null,"[1/%]"]
[{"$f":"IF(OR(NOT(ISNUMBER($K$57)),ISERROR($K$57)),1,IF(AND(LEN($K$57)>0,ABS((1-($K$57*-2.08947956562042+-0.135198950767517)/-6.92194865813086))<0.00005),0,1))","v":1},null,null,null,null,null,null,"Sensitivity to t:",null,"[1/yrs]"]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Index"]
[{"$f":"SUM($A$61:$E$147)","v":16},null,null,null,null,null,{"$f":"G28+1","v":3},"Calculating sensitivity of annuity to its drivers"]
[]
[null,null,null,null,null,null,null,"An investment generates a dividend that grows by g% per year in perpetuity.  The first dividend is D and is received in one year's time. Future dividends are discounted back to present value at a discount rate of r.  The present value, P, of the dividends generated by the investment is given by the formula P = D/(r-g)"]
[]
[]
[]
[null,null,null,null,null,null,null,"The current values of D, r and g are as shown below:"]
[]
[null,null,null,null,null,null,null,"D",1]
[null,null,null,null,null,null,null,"r",4.4999999999999998E-2]
[null,null,null,null,null,null,null,"g",1.4999999999999999E-2]
[]
[null,null,null,null,null,null,null,"Find the sensitivity of the present value, P,  to D, r and g."]
[]
[null,null,null,null,null,null,null,null,null,null,"D","r","g","P"]
[]
[{"$f":"IF(OR(NOT(ISNUMBER($N$76)),ISERROR($N$76)),1,IF(AND(LEN($N$76)>0,ABS((1-($N$76*-1.78284347057343+-0.146013021469116)/-59.57412870725))<0.00005),0,1))","v":1},null,null,null,null,null,null,"Original values:",null,null,1,{"$f":"I69","v":4.4999999999999998E-2},{"$f":"I70","v":1.4999999999999999E-2}]
[{"$f":"IF(OR(NOT(ISNUMBER($K$77)),ISERROR($K$77)),1,IF(AND(LEN($K$77)>0,ABS((1-($K$77*-2.64372408390045+ 0.0928419828414917)/-2.57731934189796))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($L$77)),ISERROR($L$77)),1,IF(AND(LEN($L$77)>0,ABS((1-($L$77* 2.02290117740631+-0.231828212738037)/-0.140797659754753))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($M$77)),ISERROR($M$77)),1,IF(AND(LEN($M$77)>0,ABS((1-($M$77* 0.753485560417175+ 0.0768529176712036)/ 0.0881552010774612))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($N$77)),ISERROR($N$77)),1,IF(AND(LEN($N$77)>0,ABS((1-($N$77* 4.90735828876495+ 0.43139910697937)/ 165.645794828733))<0.00005),0,1))","v":1},null,null,null,"Increase D by 1%"]
[{"$f":"IF(OR(NOT(ISNUMBER($K$78)),ISERROR($K$78)),1,IF(AND(LEN($K$78)>0,ABS((1-($K$78*-2.50026762485504+ 0.310058951377869)/-2.19020867347717))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($L$78)),ISERROR($L$78)),1,IF(AND(LEN($L$78)>0,ABS((1-($L$78* 2.698774933815+-0.0923051834106445)/ 0.0561274379491806))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($M$78)),ISERROR($M$78)),1,IF(AND(LEN($M$78)>0,ABS((1-($M$78* 1.2992399930954+-0.00630700588226318)/ 0.0131815940141678))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($N$78)),ISERROR($N$78)),1,IF(AND(LEN($N$78)>0,ABS((1-($N$78*-0.0148361921310425+-0.366844892501831)/-0.737749695777893))<0.00005),0,1))","v":1},null,null,null,"Add 1% to original r"]
[{"$f":"IF(OR(NOT(ISNUMBER($K$79)),ISERROR($K$79)),1,IF(AND(LEN($K$79)>0,ABS((1-($K$79* 4.69412267208099+-0.322379231452942)/ 4.37174344062805))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($L$79)),ISERROR($L$79)),1,IF(AND(LEN($L$79)>0,ABS((1-($L$79* 0.895553231239319+ 0.181571483612061)/ 0.22187137901783))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($M$79)),ISERROR($M$79)),1,IF(AND(LEN($M$79)>0,ABS((1-($M$79*-3.90436470508575+ 0.150965809822083)/ 0.0533566921949387))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($N$79)),ISERROR($N$79)),1,IF(AND(LEN($N$79)>0,ABS((1-($N$79* 2.38123714923859+ 0.28005576133728)/ 119.341913223267))<0.00005),0,1))","v":1},null,null,null,"Add 1% to original g"]
[]
[]
[{"$f":"IF(OR(NOT(ISNUMBER($L$82)),ISERROR($L$82)),1,IF(AND(LEN($L$82)>0,ABS((1-($L$82*-0.684576630592346+-0.41726553440094)/-23.236486554146))<0.00005),0,1))","v":1},null,null,null,null,null,null,"Sensitivity to D",null,null,"[#]"]
[{"$f":"IF(OR(NOT(ISNUMBER($L$83)),ISERROR($L$83)),1,IF(AND(LEN($L$83)>0,ABS((1-($L$83*-0.00297486782073975+ 0.0746650695800781)/ 2.5537215868632))<0.00005),0,1))","v":1},null,null,null,null,null,null,"Sensitivity to r",null,null,"[1/%]"]
[{"$f":"IF(OR(NOT(ISNUMBER($L$84)),ISERROR($L$84)),1,IF(AND(LEN($L$84)>0,ABS((1-($L$84*-4.40322697162628+-0.0875591039657593)/-7338.7991784811))<0.00005),0,1))","v":1},null,null,null,null,null,null,"Sensitivity to g",null,null,"[1/%]"]
[]
[null,null,null,null,null,null,null,null,null,null,null,{"$f":"K76/(L76-M76)","v":33.333333333333336}]
[null,null,null,null,null,null,null,null,null,null,0.5,16.666666666666668]
[null,null,null,null,null,null,null,null,null,null,{"$f":"K87+0.1","v":0.6},20]
[null,null,null,null,null,null,null,null,null,null,0.7,23.333333333333332]
[null,null,null,null,null,null,null,null,null,null,0.79999999999999993,26.666666666666664]
[null,null,null,null,null,null,null,null,null,null,0.89999999999999991,29.999999999999996]
[null,null,null,null,null,null,null,null,null,null,0.99999999999999989,33.333333333333329]
[null,null,null,null,null,null,null,null,null,null,1.0999999999999999,36.666666666666664]
[null,null,null,null,null,null,null,null,null,null,1.2,40]
[null,null,null,null,null,null,null,null,null,null,1.3,43.333333333333336]
[null,null,null,null,null,null,null,null,null,null,1.4000000000000001,46.666666666666671]
[null,null,null,null,null,null,null,null,null,null,1.5000000000000002,50.000000000000007]
[]
[]
[]
[]
[null,null,null,null,null,null,null,null,null,null,null,{"$f":"K76/(L76-M76)","v":33.333333333333336}]
[null,null,null,null,null,null,null,null,null,null,{"$f":"K104-$I$69*0.1","v":2.2500000000000006E-2},133.33333333333323]
[null,null,null,null,null,null,null,null,null,"r",{"$f":"K105-$I$69*0.1","v":2.7000000000000007E-2},83.333333333333286]
[null,null,null,null,null,null,null,null,null,null,{"$f":"K106-$I$69*0.1","v":3.1500000000000007E-2},60.606060606060581]
[null,null,null,null,null,null,null,null,null,null,{"$f":"K107-$I$69*0.1","v":3.6000000000000004E-2},47.619047619047606]
[null,null,null,null,null,null,null,null,null,null,{"$f":"K108-$I$69*0.1","v":4.0500000000000001E-2},39.2156862745098]
[null,null,null,null,null,null,null,null,null,null,{"$f":"I69","v":4.4999999999999998E-2},33.333333333333336]
[null,null,null,null,null,null,null,null,null,null,{"$f":"K108+$I$69*0.1","v":4.9499999999999995E-2},28.985507246376816]
[null,null,null,null,null,null,null,null,null,null,{"$f":"K109+$I$69*0.1","v":5.3999999999999992E-2},25.641025641025646]
[null,null,null,null,null,null,null,null,null,null,{"$f":"K110+$I$69*0.1","v":5.849999999999999E-2},22.988505747126442]
[null,null,null,null,null,null,null,null,null,null,{"$f":"K111+$I$69*0.1","v":6.2999999999999987E-2},20.833333333333339]
[null,null,null,null,null,null,null,null,null,null,{"$f":"K112+$I$69*0.1","v":6.7499999999999991E-2},19.047619047619051]
[]
[]
[]
[]
[null,null,null,null,null,null,null,null,null,"g",null,{"$f":"K76/(L76-M76)","v":33.333333333333336}]
[null,null,null,null,null,null,null,null,null,null,{"$f":"K120-0.1*$I$70","v":7.5000000000000015E-3},26.666666666666668]
[null,null,null,null,null,null,null,null,null,null,{"$f":"K121-0.1*$I$70","v":9.0000000000000011E-3},27.777777777777779]
[null,null,null,null,null,null,null,null,null,null,{"$f":"K122-0.1*$I$70","v":1.0500000000000001E-2},28.985507246376816]
[null,null,null,null,null,null,null,null,null,null,{"$f":"K123-0.1*$I$70","v":1.2E-2},30.303030303030301]
[null,null,null,null,null,null,null,null,null,null,{"$f":"K124-0.1*$I$70","v":1.35E-2},31.746031746031747]
[null,null,null,null,null,null,null,null,null,null,{"$f":"I70","v":1.4999999999999999E-2},33.333333333333336]
[null,null,null,null,null,null,null,null,null,null,{"$f":"K124+0.1*$I$70","v":1.6500000000000001E-2},35.087719298245617]
[null,null,null,null,null,null,null,null,null,null,{"$f":"K125+0.1*$I$70","v":1.8000000000000002E-2},37.037037037037045]
[null,null,null,null,null,null,null,null,null,null,{"$f":"K126+0.1*$I$70","v":1.9500000000000003E-2},39.215686274509814]
[null,null,null,null,null,null,null,null,null,null,{"$f":"K127+0.1*$I$70","v":2.1000000000000005E-2},41.666666666666679]
[null,null,null,null,null,null,null,null,null,null,{"$f":"K128+0.1*$I$70","v":2.2500000000000006E-2},44.444444444444457]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[null,null,null,null,null,null,null,null,null,"Copyright (c) 2020 Tykoh Group Pty Ltd.  All rights reserved.",null,null,null,null,null,null,null,"Index"]
[null,null,null,null,null,null,null,null,null,"www.tykoh.com"]

{"sheet":"Gradient_and_curvature","index":21,"n_rows":152,"n_cols":15,"rows_kept":152,"cut":false,"hidden":false,"merged":[[115,5,116,13],[118,5,118,13],[150,6,150,12],[151,6,151,12],[0,5,0,11],[2,5,3,13],[97,5,98,13],[42,5,43,13],[74,5,75,13],[7,5,8,13],[10,5,11,13],[20,5,22,13],[31,5,33,13],[14,10,14,13],[59,5,60,13],[136,5,139,13],[141,5,142,13]]}
[null,null,null,null,null,"Click here to see what your answer should look like."]
[null,null,null,null,null,null,null,null,null,null,null,null,"Sensitivity","Gradient_and_curvature"]
[null,null,null,null,null,"Gradient is a similar concept to sensitivity.  If Y is a function of X then the gradient of Y is the change in Y divided by the change in X."]
[]
[]
[{"$f":"SUM($A$7:$C$18)","v":4},null,null,null,1,"Gradient of e^(ax)"]
[]
[null,null,null,null,null,"Some common financial functions have gradients that can be expressed as formulae.  In this and following questions we look at some of those functions."]
[]
[]
[null,null,null,null,null,"Calculate the gradient of e2x when x is 1.5.  Show that the gradient is equal to 2.e2x.  We can conclude that, in general, the gradient of eax is a.eax."]
[]
[]
[null,null,null,null,null,"x","e2x","gradient","2.e2x"]
[{"$f":"IF(OR(NOT(ISNUMBER($G$15)),ISERROR($G$15)),1,IF(AND(LEN($G$15)>0,ABS((1-($G$15*-3.81750762462616+-0.353973150253296)/-77.0306634992325))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($H$15)),ISERROR($H$15)),1,IF(AND(LEN($H$15)>0,ABS((1-($H$15*-1.85413897037506+ 0.490732073783875)/-73.992766259101))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($I$15)),ISERROR($I$15)),1,IF(AND(LEN($I$15)>0,ABS((1-($I$15* 1.04322969913483+-0.225036144256592)/ 41.6826211384205))<0.00005),0,1))","v":1},null,null,1.5,null,null,null,null,{"$f":"\"Gradient is =(\" & ADDRESS(ROW(G16),COLUMN(G16),4)&\"-\"&ADDRESS(ROW(G15),COLUMN(G15),4)&\")/(\"& ADDRESS(ROW(F16),COLUMN(F16),4)&\"-\"&ADDRESS(ROW(F15),COLUMN(F15),4)&\")\"","v":"Gradient is =(G16-G15)/(F16-F15)"}]
[{"$f":"IF(OR(NOT(ISNUMBER($G$16)),ISERROR($G$16)),1,IF(AND(LEN($G$16)>0,ABS((1-($G$16*-0.836995244026184+-0.0299872159957886)/-16.8418223277561))<0.00005),0,1))","v":1},null,null,null,null,{"$f":"F15+0.00001","v":1.5000100000000001}]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Index"]
[{"$f":"SUM($A$20:$C$29)","v":4},null,null,null,2,"Gradient of x^n"]
[]
[null,null,null,null,null,"Calculate the gradient of x3 when x is 2.  Show that the gradient is equal to 3.x2.  We can conclude that, in general, the gradient of xn is n.x(n-1)."]
[]
[]
[]
[null,null,null,null,null,"x","x3","gradient","3.x2"]
[{"$f":"IF(OR(NOT(ISNUMBER($G$26)),ISERROR($G$26)),1,IF(AND(LEN($G$26)>0,ABS((1-($G$26*-4.36790645122528+-0.0418808460235596)/-34.9851324558258))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($H$26)),ISERROR($H$26)),1,IF(AND(LEN($H$26)>0,ABS((1-($H$26*-0.626087784767151+ 0.445070624351501)/-7.06802035823572))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($I$26)),ISERROR($I$26)),1,IF(AND(LEN($I$26)>0,ABS((1-($I$26*-2.26954400539398+-0.326418876647949)/-27.5609469413757))<0.00005),0,1))","v":1},null,null,2]
[{"$f":"IF(OR(NOT(ISNUMBER($G$27)),ISERROR($G$27)),1,IF(AND(LEN($G$27)>0,ABS((1-($G$27* 0.0609320402145386+-0.156298995018005)/ 0.331164638579688))<0.00005),0,1))","v":1},null,null,null,null,{"$f":"F26+0.00001","v":2.0000100000000001}]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Index"]
[{"$f":"SUM($A$31:$C$40)","v":4},null,null,null,3,"Gradient of a^x"]
[]
[null,null,null,null,null,"Calculate the gradient of 2x when x is 3.  Show that the gradient is equal to ln(2).2x.  We can conclude that, in general, the gradient of ax is ln(a).ax."]
[]
[]
[]
[null,null,null,null,null,"x","2x","gradient","ln(2).2x"]
[{"$f":"IF(OR(NOT(ISNUMBER($G$37)),ISERROR($G$37)),1,IF(AND(LEN($G$37)>0,ABS((1-($G$37* 0.129454731941223+-0.103491544723511)/ 0.932146310806274))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($H$37)),ISERROR($H$37)),1,IF(AND(LEN($H$37)>0,ABS((1-($H$37*-2.40569651126862+-0.432667851448059)/-13.7727281172063))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($I$37)),ISERROR($I$37)),1,IF(AND(LEN($I$37)>0,ABS((1-($I$37* 1.41124308109283+-0.135244846343994)/ 7.69034845560983))<0.00005),0,1))","v":1},null,null,3]
[{"$f":"IF(OR(NOT(ISNUMBER($G$38)),ISERROR($G$38)),1,IF(AND(LEN($G$38)>0,ABS((1-($G$38* 0.463406443595886+ 0.38165009021759)/ 4.08892733578333))<0.00005),0,1))","v":1},null,null,null,null,{"$f":"F37+0.00001","v":3.0000100000000001}]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Index"]
[{"$f":"SUM($A$42:$C$50)","v":4},null,null,null,4,"Gradient of ln(x)"]
[]
[null,null,null,null,null,"Calculating the gradient of ln(x) when x is 2.  Show the gradient is equal to 1/2.  We can conclude that, in general, the gradient of ln(x) is 1/x."]
[]
[]
[null,null,null,null,null,"x","ln(x)","gradient","1/x"]
[{"$f":"IF(OR(NOT(ISNUMBER($G$47)),ISERROR($G$47)),1,IF(AND(LEN($G$47)>0,ABS((1-($G$47*-0.769760012626647+ 0.0944955348968506)/-0.439061447563098))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($H$47)),ISERROR($H$47)),1,IF(AND(LEN($H$47)>0,ABS((1-($H$47*-1.19198858737946+-0.442776322364807)/-1.03876912608191))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($I$47)),ISERROR($I$47)),1,IF(AND(LEN($I$47)>0,ABS((1-($I$47*-3.90561997890472+-0.354150772094727)/-2.30696076154709))<0.00005),0,1))","v":1},null,null,2]
[{"$f":"IF(OR(NOT(ISNUMBER($G$48)),ISERROR($G$48)),1,IF(AND(LEN($G$48)>0,ABS((1-($G$48*-3.55047047138214+ 0.260129570960999)/-2.20088677824685))<0.00005),0,1))","v":1},null,null,null,null,{"$f":"F47+0.00001","v":2.0000100000000001}]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Index"]
[{"$f":"SUM($A$52:$C$67)","v":4},null,null,null,5,"Calculating gradient of the product of two functions"]
[]
[null,null,null,null,null,"Suppose f and g are functions of x.  Then the gradient of f x g is given by the following formula;"]
[]
[null,null,null,null,null,"      Gradient of f(x).g(x) = f ' (x).g(x) + f(x).g ' (x), where .."]
[]
[null,null,null,null,null,"       f ' (x) is the gradient of f(x) and g ' (x) is the gradient of g(x)"]
[]
[]
[null,null,null,null,null,"Calculate the gradient of 2x.x3 when x is 2.  Show that the gradient is the same as would be predicted by using the rule above.  The rule predicts the gradient should be 2x.x2(3+ln(2).x)"]
[]
[]
[null,null,null,null,null,"x","2x.x3","gradient","x2.2x(3+ln(2).x)"]
[{"$f":"IF(OR(NOT(ISNUMBER($G$64)),ISERROR($G$64)),1,IF(AND(LEN($G$64)>0,ABS((1-($G$64*-2.35363662242889+-0.361493825912476)/-75.6778657436371))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($H$64)),ISERROR($H$64)),1,IF(AND(LEN($H$64)>0,ABS((1-($H$64*-4.57773745059967+ 0.192577242851257)/-321.079259854433))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($I$64)),ISERROR($I$64)),1,IF(AND(LEN($I$64)>0,ABS((1-($I$64* 3.44490587711334+ 0.0173516273498535)/ 241.783291201286))<0.00005),0,1))","v":1},null,null,2]
[{"$f":"IF(OR(NOT(ISNUMBER($G$65)),ISERROR($G$65)),1,IF(AND(LEN($G$65)>0,ABS((1-($G$65* 3.00465285778046+ 0.483533978462219)/ 96.6345341336566))<0.00005),0,1))","v":1},null,null,null,null,{"$f":"F64+0.00001","v":2.0000100000000001}]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Index"]
[{"$f":"SUM($A$69:$C$82)","v":4},null,null,null,6,"Calculating the gradient of a function of a function"]
[]
[null,null,null,null,null,"g(x) is a function of x.  f is a function of g(X).  Then the gradient of f(g(x)) is given by a \"chain rule\":"]
[]
[null,null,null,null,null,"      Gradient of f(g(x)) = f ' (g(x)).g ' (x)"]
[]
[]
[null,null,null,null,null,"Calculate the gradient of 3ln(x) when x is 2.  Show that the gradient is the same as would be predicted by using the chain rule.  The rule predicts the gradient should be 3ln(x).ln(3)/x"]
[]
[]
[null,null,null,null,null,"x","3ln(x)","gradient","3ln(x).ln(3)/x"]
[{"$f":"IF(OR(NOT(ISNUMBER($G$79)),ISERROR($G$79)),1,IF(AND(LEN($G$79)>0,ABS((1-($G$79* 0.245988965034485+-0.431908845901489)/ 0.0948730945938507))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($H$79)),ISERROR($H$79)),1,IF(AND(LEN($H$79)>0,ABS((1-($H$79* 1.25053346157074+-0.170650124549866)/ 1.3003920819035))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($I$79)),ISERROR($I$79)),1,IF(AND(LEN($I$79)>0,ABS((1-($I$79*-2.21589028835297+ 0.182875633239746)/-2.42374580914283))<0.00005),0,1))","v":1},null,null,2]
[{"$f":"IF(OR(NOT(ISNUMBER($G$80)),ISERROR($G$80)),1,IF(AND(LEN($G$80)>0,ABS((1-($G$80*-0.979622006416321+-0.115617156028748)/-2.21347555426689))<0.00005),0,1))","v":1},null,null,null,null,{"$f":"F79+0.00001","v":2.0000100000000001}]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Index"]
[{"$f":"SUM($A$84:$C$113)","v":8},null,null,null,7,"Calculating gradient of a piecewise-linear curve."]
[]
[null,null,null,null,null,"x","y"]
[null,null,null,null,null,60,0]
[null,null,null,null,null,{"$f":"F86+10","v":70},0.04,null,"x","y"]
[null,null,null,null,null,80,0.43,null,{"$f":"F89","v":90},{"$f":"G89","v":2.12},null,{"$f":"F91","v":110},{"$f":"G91","v":12.79}]
[null,null,null,null,null,90,2.12,null,{"$f":"F90","v":100},{"$f":"J88","v":2.12},null,{"$f":"F93","v":130},{"$f":"M88","v":12.79}]
[null,null,null,null,null,100,6.19]
[null,null,null,null,null,110,12.79,null,{"$f":"I89","v":100},{"$f":"J89","v":2.12},null,{"$f":"L89","v":130},{"$f":"G93","v":30.6}]
[null,null,null,null,null,120,21.22,null,{"$f":"I91","v":100},{"$f":"G90","v":6.19},null,{"$f":"L91","v":130},{"$f":"M89","v":12.79}]
[null,null,null,null,null,130,30.6]
[null,null,null,null,null,140,40.369999999999997]
[]
[]
[]
[null,null,null,null,null,"The table and chart above show a piecewise-linear \"curve\".  Using that table calculate the gradients at the x values given in the table below."]
[]
[]
[null,null,null,null,null,"x","gradient"]
[{"$f":"IF(OR(NOT(ISNUMBER($G$102)),ISERROR($G$102)),1,IF(AND(LEN($G$102)>0,ABS((1-($G$102*-2.94646918773651+ 0.37592625617981)/ 0.364140379428864))<0.00005),0,1))","v":1},null,null,null,null,65]
[{"$f":"IF(OR(NOT(ISNUMBER($G$103)),ISERROR($G$103)),1,IF(AND(LEN($G$103)>0,ABS((1-($G$103*-3.48744928836823+-0.0983763933181763)/-0.234386915564537))<0.00005),0,1))","v":1},null,null,null,null,{"$f":"F102+10","v":75}]
[{"$f":"IF(OR(NOT(ISNUMBER($G$104)),ISERROR($G$104)),1,IF(AND(LEN($G$104)>0,ABS((1-($G$104* 1.08953058719635+ 0.0491595268249512)/ 0.233290196061134))<0.00005),0,1))","v":1},null,null,null,null,85]
[{"$f":"IF(OR(NOT(ISNUMBER($G$105)),ISERROR($G$105)),1,IF(AND(LEN($G$105)>0,ABS((1-($G$105* 2.29455649852753+-0.376679301261902)/ 0.557205193638802))<0.00005),0,1))","v":1},null,null,null,null,95]
[{"$f":"IF(OR(NOT(ISNUMBER($G$106)),ISERROR($G$106)),1,IF(AND(LEN($G$106)>0,ABS((1-($G$106*-1.75034701824188+-0.492187738418579)/-1.64741677045822))<0.00005),0,1))","v":1},null,null,null,null,105]
[{"$f":"IF(OR(NOT(ISNUMBER($G$107)),ISERROR($G$107)),1,IF(AND(LEN($G$107)>0,ABS((1-($G$107* 2.83429086208344+ 0.421605467796326)/ 2.81091266453266))<0.00005),0,1))","v":1},null,null,null,null,115]
[{"$f":"IF(OR(NOT(ISNUMBER($G$108)),ISERROR($G$108)),1,IF(AND(LEN($G$108)>0,ABS((1-($G$108*-2.00504243373871+-0.273933410644531)/-2.15466321349144))<0.00005),0,1))","v":1},null,null,null,null,125]
[{"$f":"IF(OR(NOT(ISNUMBER($G$109)),ISERROR($G$109)),1,IF(AND(LEN($G$109)>0,ABS((1-($G$109* 4.531289935112+-0.310882925987244)/ 4.11618734061718))<0.00005),0,1))","v":1},null,null,null,null,135]
[]
[]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Index"]
[{"$f":"SUM($A$115:$C$134)","v":7},null,null,null,8,"Calculating curvature"]
[]
[null,null,null,null,null,"Curvature is a second-order measure:  It is the gradient of the gradient.  In other words curvature measures how quickly the gradient of y changes as a function of x."]
[]
[]
[null,null,null,null,null,"Continuing with the above example - calculate the curvature of y(x) in the table below."]
[]
[null,null,null,null,null,"x","Curvature"]
[{"$f":"IF(OR(NOT(ISNUMBER($G$122)),ISERROR($G$122)),1,IF(AND(LEN($G$122)>0,ABS((1-($G$122*-0.828730463981628+-0.137325048446655)/-0.140225605070591))<0.00005),0,1))","v":1},null,null,null,null,70]
[{"$f":"IF(OR(NOT(ISNUMBER($G$123)),ISERROR($G$123)),1,IF(AND(LEN($G$123)>0,ABS((1-($G$123*-1.75201952457428+ 0.47962749004364)/ 0.456851236224175))<0.00005),0,1))","v":1},null,null,null,null,{"$f":"F122+10","v":80}]
[{"$f":"IF(OR(NOT(ISNUMBER($G$124)),ISERROR($G$124)),1,IF(AND(LEN($G$124)>0,ABS((1-($G$124* 0.790429711341858+ 0.0265851020812988)/ 0.045397329211235))<0.00005),0,1))","v":1},null,null,null,null,90]
[{"$f":"IF(OR(NOT(ISNUMBER($G$125)),ISERROR($G$125)),1,IF(AND(LEN($G$125)>0,ABS((1-($G$125*-3.6590701341629+ 0.398666501045227)/ 0.306092026650906))<0.00005),0,1))","v":1},null,null,null,null,100]
[{"$f":"IF(OR(NOT(ISNUMBER($G$126)),ISERROR($G$126)),1,IF(AND(LEN($G$126)>0,ABS((1-($G$126*-4.68845546245575+ 0.292565107345581)/ 0.206766372382641))<0.00005),0,1))","v":1},null,null,null,null,110]
[{"$f":"IF(OR(NOT(ISNUMBER($G$127)),ISERROR($G$127)),1,IF(AND(LEN($G$127)>0,ABS((1-($G$127* 2.19209611415863+-0.255853295326233)/-0.235028382241726))<0.00005),0,1))","v":1},null,null,null,null,120]
[{"$f":"IF(OR(NOT(ISNUMBER($G$128)),ISERROR($G$128)),1,IF(AND(LEN($G$128)>0,ABS((1-($G$128* 4.42223608493805+-0.0331716537475586)/-0.0159249330163005))<0.00005),0,1))","v":1},null,null,null,null,130]
[]
[]
[]
[]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Index"]
[{"$f":"SUM($A$136:$C$151)","v":1},null,null,null,{"$f":"E114+1","v":9},"Using gradient and curvature in interpolating and extrapolating"]
[]
[null,null,null,null,null,"Gradient and curvature can be used in interpolating and extrapolating.  Consider a function V(x).  Suppose the value of the function V(x), its gradient V'(x) and curvature V''(x) are all known at a particular value of x, say x1.  Then the value of V at a slightly different value of x - say x1+dx is given approximately by the following formula: V(x1+dx) = V(x) + V'(x).dx + 0.5 V''(x).dx2"]
[]
[]
[]
[]
[null,null,null,null,null,"Calculate the approximate value of V(x) when x is 2.1 by using the value of V(x) and its gradient and curvature at x = 2.0"]
[]
[]
[null,null,null,null,null,null,"value","gradient","curvature"]
[null,null,null,null,null,"x","V(x)","V'(x)","V''(x)"]
[null,null,null,null,null,2,{"$f":"EXP(0.4*F147)","v":2.2255409284924679},{"$f":"0.4*G147","v":0.89021637139698717},{"$f":"0.4*H147","v":0.3560865485587949}]
[{"$f":"IF(OR(NOT(ISNUMBER($G$148)),ISERROR($G$148)),1,IF(AND(LEN($G$148)>0,ABS((1-($G$148* 2.24007785320281+-0.10301148891449)/ 5.0858308756632))<0.00005),0,1))","v":1},null,null,null,null,2.1]
[]
[]
[null,null,null,null,null,null,"Copyright (c) 2020 Tykoh Group Pty Ltd.  All rights reserved.",null,null,null,null,null,null,null,"Index"]
[null,null,null,null,null,null,"www.tykoh.com"]

{"sheet":"Frequency_distribution","index":22,"n_rows":264,"n_cols":23,"rows_kept":264,"cut":false,"hidden":false,"merged":[[262,13,262,19],[263,13,263,19],[0,12,0,18],[238,12,238,20],[187,12,187,19],[184,12,185,20],[230,12,230,20],[214,12,218,20],[191,12,192,20],[220,12,222,20],[3,12,4,20],[70,12,73,20],[75,12,76,20],[102,12,104,20],[6,12,8,20],[41,12,43,20],[163,12,164,20],[106,12,109,20],[134,12,135,20],[131,12,132,20],[139,12,140,20]]}
[null,null,null,null,null,null,null,null,null,null,null,null,"Click here to see what your answer should look like."]
[{"$f":"SUM($A$3:$J$26)","v":12},null,null,null,null,null,null,null,null,null,null,1,"Calculating a frequency distribution from a sample set",null,null,null,null,null,null,null,"Frequency_distribution","Frequency_distribution"]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,"This question and the following ones relate to frequency distributions, mean and mode.  All of these are ways of reducing large data sets to represent them in a more concise but still useful form."]
[]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,"The table below shows the number of times a particular security has yielded a given return.  Calculate the frequency distribution of the returns.  The frequency distribtion is the list of the percentage of times each return has occurred."]
[]
[]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,"Return","Number of times","Frequency [%]"]
[]
[{"$f":"IF(OR(NOT(ISNUMBER($O$13)),ISERROR($O$13)),1,IF(AND(LEN($O$13)>0,ABS((1-($O$13*-2.68010795116425+ 0.10265851020813)/ 0.0664408351923968))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,null,null,null,null,-0.05,1]
[{"$f":"IF(OR(NOT(ISNUMBER($O$14)),ISERROR($O$14)),1,IF(AND(LEN($O$14)>0,ABS((1-($O$14* 0.511364340782166+-0.0382548570632935)/-0.0382548570632935))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,null,null,null,null,{"$f":"M13+1%","v":-0.04},0]
[{"$f":"IF(OR(NOT(ISNUMBER($O$15)),ISERROR($O$15)),1,IF(AND(LEN($O$15)>0,ABS((1-($O$15* 1.49291574954987+ 0.266034603118896)/ 0.326558214587134))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,null,null,null,null,-0.03,3]
[{"$f":"IF(OR(NOT(ISNUMBER($O$16)),ISERROR($O$16)),1,IF(AND(LEN($O$16)>0,ABS((1-($O$16*-4.34841454029083+-0.342772364616394)/-0.636584157879288))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,null,null,null,null,-1.9999999999999997E-2,5]
[{"$f":"IF(OR(NOT(ISNUMBER($O$17)),ISERROR($O$17)),1,IF(AND(LEN($O$17)>0,ABS((1-($O$17*-3.99802386760712+-0.448744058609009)/-0.989017554231592))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,null,null,null,null,-9.9999999999999967E-3,10]
[{"$f":"IF(OR(NOT(ISNUMBER($O$18)),ISERROR($O$18)),1,IF(AND(LEN($O$18)>0,ABS((1-($O$18* 0.456761717796326+ 0.457129836082459)/ 0.506509481249629))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,null,null,null,null,0,8]
[{"$f":"IF(OR(NOT(ISNUMBER($O$19)),ISERROR($O$19)),1,IF(AND(LEN($O$19)>0,ABS((1-($O$19*-2.73874223232269+-0.153432846069336)/-0.59755320806761))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,null,null,null,null,0.01,12]
[{"$f":"IF(OR(NOT(ISNUMBER($O$20)),ISERROR($O$20)),1,IF(AND(LEN($O$20)>0,ABS((1-($O$20* 3.90455424785614+-0.0193465948104858)/ 0.402767377930719))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,null,null,null,null,0.02,8]
[{"$f":"IF(OR(NOT(ISNUMBER($O$21)),ISERROR($O$21)),1,IF(AND(LEN($O$21)>0,ABS((1-($O$21*-2.68028914928436+ 0.349783182144165)/-0.121078425162547))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,null,null,null,null,0.03,13]
[{"$f":"IF(OR(NOT(ISNUMBER($O$22)),ISERROR($O$22)),1,IF(AND(LEN($O$22)>0,ABS((1-($O$22*-4.31448519229889+-0.366867184638977)/-0.891601870188842))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,null,null,null,null,0.04,9]
[{"$f":"IF(OR(NOT(ISNUMBER($O$23)),ISERROR($O$23)),1,IF(AND(LEN($O$23)>0,ABS((1-($O$23* 4.64230120182037+ 0.333914279937744)/ 0.522115680011543))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,null,null,null,null,0.05,3]
[{"$f":"IF(OR(NOT(ISNUMBER($O$24)),ISERROR($O$24)),1,IF(AND(LEN($O$24)>0,ABS((1-($O$24* 3.23433578014374+ 0.496660351753235)/ 0.58407483229766))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,null,null,null,null,6.0000000000000005E-2,2]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Index"]
[{"$f":"SUM($A$28:$J$32)","v":1},null,null,null,null,null,null,null,null,null,null,2,"Calculating a mean from a frequency distribution."]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,"Calculate the mean return."]
[]
[{"$f":"IF(OR(NOT(ISNUMBER($N$31)),ISERROR($N$31)),1,IF(AND(LEN($N$31)>0,ABS((1-($N$31*-2.60873973369598+ 0.162791013717651)/ 0.128947903658893))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,null,null,null,null,"Mean"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Index"]
[{"$f":"SUM($A$34:$J$39)","v":2},null,null,null,null,null,null,null,null,null,null,3,"Calculating a mode from a frequency distribution."]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,"Calculate the modal return (the return that occurred the most often)"]
[]
[{"$f":"IF(OR(NOT(ISNUMBER($R$37)),ISERROR($R$37)),1,IF(AND(LEN($R$37)>0,ABS((1-($R$37* 1.26110017299652+ 0.4707111120224)/ 16.8650133609772))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,null,null,null,null,"Number of times most frequent return has occurred:"]
[{"$f":"IF(OR(NOT(ISNUMBER($R$38)),ISERROR($R$38)),1,IF(AND(LEN($R$38)>0,ABS((1-($R$38*-0.792664885520935+-0.443310737609863)/-0.467090684175491))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,null,null,null,null,"Corresponding return:"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Index"]
[{"$f":"SUM($A$41:$J$62)","v":24},null,null,null,null,null,null,null,null,null,null,4,"Calculating a cumulative frequency distribution."]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"\"In cells \" & ADDRESS(ROW(O49),COLUMN(O49),4) & \":\" & ADDRESS(ROW(O60),COLUMN(O60),4) & \" show the number of times returns have been less than or equal to the return specified.  For example, the number in cell \" & ADDRESS(ROW(O51),COLUMN(O51),4) & \" should show the number of times returns were less than or equal to \" & TEXT(M51,\"0%\")&\". In cells \" & ADDRESS(ROW(P49),COLUMN(P49),4) & \":\" & ADDRESS(ROW(P60),COLUMN(P60),4) & \" show the cumulative frequency as a percentage.\"","v":"In cells O49:O60 show the number of times returns have been less than or equal to the return specified.  For example, the number in cell O51 should show the number of times returns were less than or equal to -3%. In cells P49:P60 show the cumulative frequency as a percentage."}]
[]
[]
[]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,"Return","Number of times","Cumulative frequency [number]","Cumulative frequency [%]"]
[]
[{"$f":"IF(OR(NOT(ISNUMBER($O$49)),ISERROR($O$49)),1,IF(AND(LEN($O$49)>0,ABS((1-($O$49* 3.78253161907196+-0.337231993675232)/ 3.44529962539673))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($P$49)),ISERROR($P$49)),1,IF(AND(LEN($P$49)>0,ABS((1-($P$49*-2.50896155834197+ 0.10795521736145)/ 0.0740503314379099))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,null,null,null,-0.05,1,null,null,null,null,null,0.75]
[{"$f":"IF(OR(NOT(ISNUMBER($O$50)),ISERROR($O$50)),1,IF(AND(LEN($O$50)>0,ABS((1-($O$50*-1.34675562381744+ 0.0289467573165894)/-1.31780886650085))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($P$50)),ISERROR($P$50)),1,IF(AND(LEN($P$50)>0,ABS((1-($P$50* 4.18389856815338+ 0.0466303825378418)/ 0.103169552377752))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,null,null,null,{"$f":"M49+1%","v":-0.04},0,null,null,null,null,null,0.75]
[{"$f":"IF(OR(NOT(ISNUMBER($O$51)),ISERROR($O$51)),1,IF(AND(LEN($O$51)>0,ABS((1-($O$51* 4.59699332714081+ 0.264620900154114)/ 18.6525942087173))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($P$51)),ISERROR($P$51)),1,IF(AND(LEN($P$51)>0,ABS((1-($P$51*-0.950290560722351+ 0.256076574325562)/ 0.204709516989218))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,null,null,null,-0.03,3,null,null,null,null,null,0.75]
[{"$f":"IF(OR(NOT(ISNUMBER($O$52)),ISERROR($O$52)),1,IF(AND(LEN($O$52)>0,ABS((1-($O$52* 0.737923979759216+-0.0549532175064087)/ 6.58636260032654))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($P$52)),ISERROR($P$52)),1,IF(AND(LEN($P$52)>0,ABS((1-($P$52*-4.54421937465668+-0.461399078369141)/-1.01407440771928))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,null,null,null,-1.9999999999999997E-2,5,null,null,null,null,null,0.75]
[{"$f":"IF(OR(NOT(ISNUMBER($O$53)),ISERROR($O$53)),1,IF(AND(LEN($O$53)>0,ABS((1-($O$53*-1.36817753314972+-0.084011435508728)/-26.0793845653534))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($P$53)),ISERROR($P$53)),1,IF(AND(LEN($P$53)>0,ABS((1-($P$53*-1.3458126783371+ 0.131080865859985)/-0.214465632631972))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,null,null,null,-9.9999999999999967E-3,10,null,null,null,null,null,0.75]
[{"$f":"IF(OR(NOT(ISNUMBER($O$54)),ISERROR($O$54)),1,IF(AND(LEN($O$54)>0,ABS((1-($O$54*-3.2026344537735+-0.0656567811965942)/-86.5367870330811))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($P$54)),ISERROR($P$54)),1,IF(AND(LEN($P$54)>0,ABS((1-($P$54*-3.43697965145111+ 0.470589160919189)/-0.78344395515081))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,null,null,null,0,8,null,null,null,null,null,0.75]
[{"$f":"IF(OR(NOT(ISNUMBER($O$55)),ISERROR($O$55)),1,IF(AND(LEN($O$55)>0,ABS((1-($O$55*-2.25262939929962+-0.441234469413757)/-88.2937810420989))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($P$55)),ISERROR($P$55)),1,IF(AND(LEN($P$55)>0,ABS((1-($P$55* 3.04763615131378+ 0.210018873214722)/ 1.81620549350171))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,null,null,null,0.01,12,null,null,null,null,null,0.75]
[{"$f":"IF(OR(NOT(ISNUMBER($O$56)),ISERROR($O$56)),1,IF(AND(LEN($O$56)>0,ABS((1-($O$56*-2.47995436191559+ 0.290293097496033)/-116.267561912537))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($P$56)),ISERROR($P$56)),1,IF(AND(LEN($P$56)>0,ABS((1-($P$56* 3.70190680027008+ 0.483708381652832)/ 2.83491945750005))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,null,null,null,0.02,8,null,null,null,null,null,0.75]
[{"$f":"IF(OR(NOT(ISNUMBER($O$57)),ISERROR($O$57)),1,IF(AND(LEN($O$57)>0,ABS((1-($O$57*-2.2897607088089+-0.0370286703109741)/-137.422671198845))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($P$57)),ISERROR($P$57)),1,IF(AND(LEN($P$57)>0,ABS((1-($P$57* 4.12946999073029+ 0.423066377639771)/ 3.77128528904271))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,null,null,null,0.03,13,null,null,null,null,null,0.75]
[{"$f":"IF(OR(NOT(ISNUMBER($O$58)),ISERROR($O$58)),1,IF(AND(LEN($O$58)>0,ABS((1-($O$58* 0.000690817832946777+ 0.384478449821472)/ 0.4321448802948))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($P$58)),ISERROR($P$58)),1,IF(AND(LEN($P$58)>0,ABS((1-($P$58* 0.724979043006896+-0.0778031349182129)/ 0.598190837615245))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,null,null,null,0.04,9,null,null,null,null,null,0.75]
[{"$f":"IF(OR(NOT(ISNUMBER($O$59)),ISERROR($O$59)),1,IF(AND(LEN($O$59)>0,ABS((1-($O$59* 3.19328010082245+ 0.226750493049622)/ 230.142917752266))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($P$59)),ISERROR($P$59)),1,IF(AND(LEN($P$59)>0,ABS((1-($P$59* 3.95535290241241+-0.346475839614868)/ 3.50197563300262))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,null,null,null,0.05,3,null,null,null,null,null,0.75]
[{"$f":"IF(OR(NOT(ISNUMBER($O$60)),ISERROR($O$60)),1,IF(AND(LEN($O$60)>0,ABS((1-($O$60* 2.74027764797211+ 0.166606307029724)/ 202.947152256966))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($P$60)),ISERROR($P$60)),1,IF(AND(LEN($P$60)>0,ABS((1-($P$60* 4.14102613925934+ 0.333417892456055)/ 4.47444403171539))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,null,null,null,6.0000000000000005E-2,2,null,null,null,null,null,0.75]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Index"]
[{"$f":"SUM($A$64:$J$68)","v":1},null,null,null,null,null,null,null,null,null,null,5,"Calculating lowest return in upper quartile."]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,"What is the lowest return in the upper quartile?"]
[]
[{"$f":"IF(OR(NOT(ISNUMBER($P$67)),ISERROR($P$67)),1,IF(AND(LEN($P$67)>0,ABS((1-($P$67* 2.77559459209442+ 0.27637255191803)/ 0.359640389680862))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,null,null,null,null,"Lowest return in upper quartile:"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Index"]
[{"$f":"SUM($A$70:$J$100)","v":52},null,null,null,null,null,null,null,null,null,null,6,"Calculating standard deviation."]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,"Both standard deviation and variance are measures of the \"spread\" of a distribution.  Standard deviation is the square root of variance.  Both standard deviation and variance can be calculated on \"sample\" or \"population\" terms.  \"Population\" means that the data you're working with comprises all the data, \"Sample\" means that there is more data and you're working with the sampled subset."]
[]
[]
[]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"\"Calculate the sample standard deviation of the frequency distribution described in cells \" & ADDRESS(ROW(M81),COLUMN(M81),4) & \":\" & ADDRESS(ROW(N92),COLUMN(N92),4) & \" below.\"","v":"Calculate the sample standard deviation of the frequency distribution described in cells M81:N92 below."}]
[]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,"Return","Number of times","Number of times x return","Return - mean return","(Return - mean return)2","Number of times x (Return - mean return)2"]
[]
[{"$f":"IF(OR(NOT(ISNUMBER($O$81)),ISERROR($O$81)),1,IF(AND(LEN($O$81)>0,ABS((1-($O$81*-0.262801051139832+ 0.237818002700806)/ 0.250958055257797))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($P$81)),ISERROR($P$81)),1,IF(AND(LEN($P$81)>0,ABS((1-($P$81* 0.646032691001892+-0.335491299629211)/-0.376173898819331))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($Q$81)),ISERROR($Q$81)),1,IF(AND(LEN($Q$81)>0,ABS((1-($Q$81*-1.8849128484726+-0.0321402549743652)/-0.0396150565544039))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($R$81)),ISERROR($R$81)),1,IF(AND(LEN($R$81)>0,ABS((1-($R$81* 3.94253432750702+ 0.36623203754425)/ 0.38186653324228))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,null,-0.05,1]
[{"$f":"IF(OR(NOT(ISNUMBER($O$82)),ISERROR($O$82)),1,IF(AND(LEN($O$82)>0,ABS((1-($O$82*-1.15682780742645+ 0.465498685836792)/ 0.465498685836792))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($P$82)),ISERROR($P$82)),1,IF(AND(LEN($P$82)>0,ABS((1-($P$82* 0.0314325094223022+ 0.484142661094666)/ 0.482477587622565))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($Q$82)),ISERROR($Q$82)),1,IF(AND(LEN($Q$82)>0,ABS((1-($Q$82*-0.531548857688904+ 0.279135704040527)/ 0.27764410572665))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($R$82)),ISERROR($R$82)),1,IF(AND(LEN($R$82)>0,ABS((1-($R$82*-1.91429913043976+-0.421151518821716)/-0.421151518821716))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,null,{"$f":"M81+1%","v":-0.04},0]
[{"$f":"IF(OR(NOT(ISNUMBER($O$83)),ISERROR($O$83)),1,IF(AND(LEN($O$83)>0,ABS((1-($O$83* 3.79768669605255+ 0.0792419910430908)/-0.262549811601639))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($P$83)),ISERROR($P$83)),1,IF(AND(LEN($P$83)>0,ABS((1-($P$83* 3.61620366573334+ 0.309590220451355)/ 0.15419119805903))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($Q$83)),ISERROR($Q$83)),1,IF(AND(LEN($Q$83)>0,ABS((1-($Q$83* 2.67865717411041+ 0.423984050750732)/ 0.428930663754289))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($R$83)),ISERROR($R$83)),1,IF(AND(LEN($R$83)>0,ABS((1-($R$83*-4.49705421924591+ 0.324866414070129)/ 0.299952602298744))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,null,-0.03,3]
[{"$f":"IF(OR(NOT(ISNUMBER($O$84)),ISERROR($O$84)),1,IF(AND(LEN($O$84)>0,ABS((1-($O$84*-2.71859347820281+-0.225151300430298)/ 0.0467080473899841))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($P$84)),ISERROR($P$84)),1,IF(AND(LEN($P$84)>0,ABS((1-($P$84*-4.473677277565+ 0.403058409690857)/ 0.550568849653811))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($Q$84)),ISERROR($Q$84)),1,IF(AND(LEN($Q$84)>0,ABS((1-($Q$84* 4.87949430942535+-0.23773193359375)/-0.232426864689332))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($R$84)),ISERROR($R$84)),1,IF(AND(LEN($R$84)>0,ABS((1-($R$84* 0.398370623588562+-0.156944632530212)/-0.154779056065095))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,null,-1.9999999999999997E-2,5]
[{"$f":"IF(OR(NOT(ISNUMBER($O$85)),ISERROR($O$85)),1,IF(AND(LEN($O$85)>0,ABS((1-($O$85*-2.86875426769257+-0.298755407333374)/-0.0118799805641175))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($P$85)),ISERROR($P$85)),1,IF(AND(LEN($P$85)>0,ABS((1-($P$85*-3.70598375797272+ 0.104879260063171)/ 0.190016724773355))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($Q$85)),ISERROR($Q$85)),1,IF(AND(LEN($Q$85)>0,ABS((1-($Q$85* 0.86100161075592+ 0.35697603225708)/ 0.357430432303662))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($R$85)),ISERROR($R$85)),1,IF(AND(LEN($R$85)>0,ABS((1-($R$85*-4.11767303943634+-0.299690127372742)/-0.321421455137481))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,null,-9.9999999999999967E-3,10]
[{"$f":"IF(OR(NOT(ISNUMBER($O$86)),ISERROR($O$86)),1,IF(AND(LEN($O$86)>0,ABS((1-($O$86* 1.34036839008331+-0.0395195484161377)/-0.0395195484161377))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($P$86)),ISERROR($P$86)),1,IF(AND(LEN($P$86)>0,ABS((1-($P$86*-2.14223921298981+ 0.333509802818298)/ 0.361301014230058))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($Q$86)),ISERROR($Q$86)),1,IF(AND(LEN($Q$86)>0,ABS((1-($Q$86*-1.93053185939789+ 0.474221229553223)/ 0.473896324848763))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($R$86)),ISERROR($R$86)),1,IF(AND(LEN($R$86)>0,ABS((1-($R$86*-1.02858364582062+ 0.291649460792542)/ 0.29026459200074))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,null,0,8]
[{"$f":"IF(OR(NOT(ISNUMBER($O$87)),ISERROR($O$87)),1,IF(AND(LEN($O$87)>0,ABS((1-($O$87* 3.05818855762482+ 0.107732057571411)/ 0.474714684486389))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($P$87)),ISERROR($P$87)),1,IF(AND(LEN($P$87)>0,ABS((1-($P$87*-1.43771708011627+ 0.0855320692062378)/ 0.0898063632282051))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($Q$87)),ISERROR($Q$87)),1,IF(AND(LEN($Q$87)>0,ABS((1-($Q$87* 1.60743296146393+ 0.0832419395446777)/ 0.0832561469506921))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($R$87)),ISERROR($R$87)),1,IF(AND(LEN($R$87)>0,ABS((1-($R$87*-4.41150963306427+ 0.340218663215637)/ 0.339750766065366))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,null,0.01,12]
[{"$f":"IF(OR(NOT(ISNUMBER($O$88)),ISERROR($O$88)),1,IF(AND(LEN($O$88)>0,ABS((1-($O$88*-4.40962970256805+-0.348699808120728)/-1.05424056053162))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($P$88)),ISERROR($P$88)),1,IF(AND(LEN($P$88)>0,ABS((1-($P$88*-1.84144079685211+-0.0643469095230103)/-0.0772867637711602))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($Q$88)),ISERROR($Q$88)),1,IF(AND(LEN($Q$88)>0,ABS((1-($Q$88*-0.76631486415863+ 0.356401443481445)/ 0.356363603536363))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($R$88)),ISERROR($R$88)),1,IF(AND(LEN($R$88)>0,ABS((1-($R$88*-4.4373494386673+ 0.397287011146545)/ 0.395534112259452))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,null,0.02,8]
[{"$f":"IF(OR(NOT(ISNUMBER($O$89)),ISERROR($O$89)),1,IF(AND(LEN($O$89)>0,ABS((1-($O$89*-2.6011723279953+-0.447389364242554)/-1.46184657216072))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($P$89)),ISERROR($P$89)),1,IF(AND(LEN($P$89)>0,ABS((1-($P$89* 2.80381619930267+-0.463295102119446)/-0.415554447915103))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($Q$89)),ISERROR($Q$89)),1,IF(AND(LEN($Q$89)>0,ABS((1-($Q$89*-3.63673627376556+ 0.169188022613525)/ 0.168133661308151))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($R$89)),ISERROR($R$89)),1,IF(AND(LEN($R$89)>0,ABS((1-($R$89*-2.3707515001297+ 0.342249035835266)/ 0.333313779067392))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,null,0.03,13]
[{"$f":"IF(OR(NOT(ISNUMBER($O$90)),ISERROR($O$90)),1,IF(AND(LEN($O$90)>0,ABS((1-($O$90*-2.89827525615692+-0.273785829544067)/-1.31716492176056))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($P$90)),ISERROR($P$90)),1,IF(AND(LEN($P$90)>0,ABS((1-($P$90* 0.0615304708480835+ 0.119644522666931)/ 0.121307508365528))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($Q$90)),ISERROR($Q$90)),1,IF(AND(LEN($Q$90)>0,ABS((1-($Q$90* 1.06745779514313+-0.399785041809082)/-0.399005306385311))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($R$90)),ISERROR($R$90)),1,IF(AND(LEN($R$90)>0,ABS((1-($R$90* 4.42988574504852+-0.117375731468201)/-0.0882530348243463))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,null,0.04,9]
[{"$f":"IF(OR(NOT(ISNUMBER($O$91)),ISERROR($O$91)),1,IF(AND(LEN($O$91)>0,ABS((1-($O$91*-1.52652442455292+-0.460213422775269)/-0.689192086458206))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($P$91)),ISERROR($P$91)),1,IF(AND(LEN($P$91)>0,ABS((1-($P$91* 3.90142858028412+-0.00644600391387939)/ 0.138012297572316))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($Q$91)),ISERROR($Q$91)),1,IF(AND(LEN($Q$91)>0,ABS((1-($Q$91*-0.926193594932556+ 0.431220531463623)/ 0.429950719368423))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($R$91)),ISERROR($R$91)),1,IF(AND(LEN($R$91)>0,ABS((1-($R$91*-2.48758614063263+ 0.054057240486145)/ 0.0438257932384751))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,null,0.05,3]
[{"$f":"IF(OR(NOT(ISNUMBER($O$92)),ISERROR($O$92)),1,IF(AND(LEN($O$92)>0,ABS((1-($O$92*-4.55525577068329+ 0.314128637313843)/-0.232502055168152))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($P$92)),ISERROR($P$92)),1,IF(AND(LEN($P$92)>0,ABS((1-($P$92*-0.300512909889221+ 0.0456403493881226)/ 0.0315081206527916))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($Q$92)),ISERROR($Q$92)),1,IF(AND(LEN($Q$92)>0,ABS((1-($Q$92*-1.23390138149261+-0.352931976318359)/-0.355660800147875))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($R$92)),ISERROR($R$92)),1,IF(AND(LEN($R$92)>0,ABS((1-($R$92* 2.33093440532684+-0.279682517051697)/-0.269372601776945))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,null,6.0000000000000005E-2,2]
[]
[]
[{"$f":"IF(OR(NOT(ISNUMBER($N$95)),ISERROR($N$95)),1,IF(AND(LEN($N$95)>0,ABS((1-($N$95*-2.89755523204803+-0.176833868026733)/-214.595921039581))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($R$95)),ISERROR($R$95)),1,IF(AND(LEN($R$95)>0,ABS((1-($R$95*-0.762067437171936+ 0.241235613822937)/ 0.210032041733329))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,null,null,null,"Total"]
[]
[{"$f":"IF(OR(NOT(ISNUMBER($O$97)),ISERROR($O$97)),1,IF(AND(LEN($O$97)>0,ABS((1-($O$97*-3.81562650203705+-0.0642542839050293)/-0.113754303390915))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,null,null,null,null,"Mean return"]
[]
[{"$f":"IF(OR(NOT(ISNUMBER($T$99)),ISERROR($T$99)),1,IF(AND(LEN($T$99)>0,ABS((1-($T$99* 3.24579894542694+ 0.0732995271682739)/ 0.150171077359787))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,null,null,null,null,{"$f":"\"Standard deviation = Square root of [total in column \" & CHAR(CODE(\"A\")+COLUMN(R:R)-1) & \" / (total in column \" & CHAR(CODE(\"A\")+COLUMN(N:N)-1) & \" - 1)]\"","v":"Standard deviation = Square root of [total in column R / (total in column N - 1)]"}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Index"]
[{"$f":"SUM($A$102:$J$129)","v":24},null,null,null,null,null,null,null,null,null,null,7,"Generating a normal distribution"]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,"We can generate a normal distribution by using the NORMDIST function.  In the question below we use the NORMDIST function to superimpose a normal curve on our actual frequency distribution.  This shows visually the extent to which the data set is \"Normal\"."]
[]
[]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"\"Cells \" & ADDRESS(ROW(N114),COLUMN(N114),4) & \":\" & ADDRESS(ROW(N127),COLUMN(N127),4) & \" calculate the cumulative normal distribution using the mean and standard deviation we calculated in cells \" & ADDRESS(ROW(O97),COLUMN(O97),4) & \" and \" & ADDRESS(ROW(T99),COLUMN(T99),4) & \" respectively. In cells \" & ADDRESS(ROW(O115),COLUMN(O115),4) & \":\" & ADDRESS(ROW(O126),COLUMN(O126),4) & \" calculate the increments in the cumulative distribution.  Scale these by the total number of samples in cell \" & ADDRESS(ROW(N95),COLUMN(N95),4) & \" to give the predicted number of normal samples in cells \" & ADDRESS(ROW(P115),COLUMN(P115),4) & \":\" & ADDRESS(ROW(P126),COLUMN(P126),4)&\".\"","v":"Cells N114:N127 calculate the cumulative normal distribution using the mean and standard deviation we calculated in cells O97 and T99 respectively. In cells O115:O126 calculate the increments in the cumulative distribution.  Scale these by the total number of samples in cell N95 to give the predicted number of normal samples in cells P115:P126."}]
[]
[]
[]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,"Return","Cumulative normal dist","Change in Cumulative normal dist","Frequency"]
[]
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[{"$f":"IF(OR(NOT(ISNUMBER($O$115)),ISERROR($O$115)),1,IF(AND(LEN($O$115)>0,ABS((1-($O$115* 2.68974125385284+-0.206050157546997)/-0.192240961682191))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($P$115)),ISERROR($P$115)),1,IF(AND(LEN($P$115)>0,ABS((1-($P$115*-4.29475843906403+ 0.123796820640564)/-1.50785822016164))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,null,null,null,{"$f":"M114+1%","v":-4.9999999999999996E-2},{"$error":"#NUM!"}]
[{"$f":"IF(OR(NOT(ISNUMBER($O$116)),ISERROR($O$116)),1,IF(AND(LEN($O$116)>0,ABS((1-($O$116* 0.0249201059341431+ 0.188366889953613)/ 0.188721184449868))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($P$116)),ISERROR($P$116)),1,IF(AND(LEN($P$116)>0,ABS((1-($P$116*-1.47639095783234+ 0.133022904396057)/-1.42024946983177))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,null,null,null,-3.9999999999999994E-2,{"$error":"#NUM!"}]
[{"$f":"IF(OR(NOT(ISNUMBER($O$117)),ISERROR($O$117)),1,IF(AND(LEN($O$117)>0,ABS((1-($O$117*-3.39395225048065+ 0.406655550003052)/ 0.294571514088053))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($P$117)),ISERROR($P$117)),1,IF(AND(LEN($P$117)>0,ABS((1-($P$117*-1.30385935306549+ 0.314906001091003)/-2.87149550815056))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,null,null,null,-2.9999999999999992E-2,{"$error":"#NUM!"}]
[{"$f":"IF(OR(NOT(ISNUMBER($O$118)),ISERROR($O$118)),1,IF(AND(LEN($O$118)>0,ABS((1-($O$118*-3.35972249507904+-0.000830173492431641)/-0.217026388879257))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($P$118)),ISERROR($P$118)),1,IF(AND(LEN($P$118)>0,ABS((1-($P$118*-4.66278374195099+ 0.247632145881653)/-21.9558798329685))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,null,null,null,-1.999999999999999E-2,{"$error":"#NUM!"}]
[{"$f":"IF(OR(NOT(ISNUMBER($O$119)),ISERROR($O$119)),1,IF(AND(LEN($O$119)>0,ABS((1-($O$119* 3.40702831745148+-0.205415964126587)/ 0.152947192338151))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($P$119)),ISERROR($P$119)),1,IF(AND(LEN($P$119)>0,ABS((1-($P$119*-0.788393616676331+ 0.0142701864242554)/-6.12225369967271))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,null,null,null,-9.9999999999999898E-3,{"$error":"#NUM!"}]
[{"$f":"IF(OR(NOT(ISNUMBER($O$120)),ISERROR($O$120)),1,IF(AND(LEN($O$120)>0,ABS((1-($O$120*-4.9607652425766+ 0.165517807006836)/-0.549975114651779))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($P$120)),ISERROR($P$120)),1,IF(AND(LEN($P$120)>0,ABS((1-($P$120* 4.76572215557098+-0.406603217124939)/ 50.4581691234706))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,null,null,null,0,{"$error":"#NUM!"}]
[{"$f":"IF(OR(NOT(ISNUMBER($O$121)),ISERROR($O$121)),1,IF(AND(LEN($O$121)>0,ABS((1-($O$121* 2.80459702014923+-0.455838918685913)/ 0.00947786100939974))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($P$121)),ISERROR($P$121)),1,IF(AND(LEN($P$121)>0,ABS((1-($P$121* 4.65886533260345+ 0.49972140789032)/ 57.6989434900527))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,null,null,null,0.01,{"$error":"#NUM!"}]
[{"$f":"IF(OR(NOT(ISNUMBER($O$122)),ISERROR($O$122)),1,IF(AND(LEN($O$122)>0,ABS((1-($O$122* 1.88683092594147+ 0.187899112701416)/ 0.489997349268604))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($P$122)),ISERROR($P$122)),1,IF(AND(LEN($P$122)>0,ABS((1-($P$122*-3.20552170276642+-0.325288653373718)/-38.3044740628079))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,null,null,null,0.02,{"$error":"#NUM!"}]
[{"$f":"IF(OR(NOT(ISNUMBER($O$123)),ISERROR($O$123)),1,IF(AND(LEN($O$123)>0,ABS((1-($O$123* 4.6669179201126+ 0.194937467575073)/ 0.799856122624022))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($P$123)),ISERROR($P$123)),1,IF(AND(LEN($P$123)>0,ABS((1-($P$123* 3.85139405727386+-0.372783303260803)/ 36.5688838370672))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,null,null,null,0.03,{"$error":"#NUM!"}]
[{"$f":"IF(OR(NOT(ISNUMBER($O$124)),ISERROR($O$124)),1,IF(AND(LEN($O$124)>0,ABS((1-($O$124*-3.49564492702484+-0.230072975158691)/-0.537793235191883))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($P$124)),ISERROR($P$124)),1,IF(AND(LEN($P$124)>0,ABS((1-($P$124*-4.6849137544632+-0.175904631614685)/-30.6943283431378))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,null,null,null,0.04,{"$error":"#NUM!"}]
[{"$f":"IF(OR(NOT(ISNUMBER($O$125)),ISERROR($O$125)),1,IF(AND(LEN($O$125)>0,ABS((1-($O$125* 4.01840507984161+-0.260411024093628)/-0.0588776389882595))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($P$125)),ISERROR($P$125)),1,IF(AND(LEN($P$125)>0,ABS((1-($P$125* 2.00891911983489+ 0.330838084220886)/ 7.78652147871319))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,null,null,null,0.05,{"$error":"#NUM!"}]
[{"$f":"IF(OR(NOT(ISNUMBER($O$126)),ISERROR($O$126)),1,IF(AND(LEN($O$126)>0,ABS((1-($O$126*-4.13065373897552+ 0.318339824676514)/ 0.219332363291754))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($P$126)),ISERROR($P$126)),1,IF(AND(LEN($P$126)>0,ABS((1-($P$126* 3.12539756298065+-0.297806620597839)/ 5.24571981810398))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,null,null,null,6.0000000000000005E-2,{"$error":"#NUM!"}]
[null,null,null,null,null,null,null,null,null,null,null,null,7.0000000000000007E-2,{"$error":"#NUM!"}]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Index"]
[{"$f":"SUM($A$131:$J$161)","v":15},null,null,null,null,null,null,null,null,null,null,8,"Calculating percentage of outcomes less than N standard deviations above mean"]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,"We can use the NORMSDIST function to give the proportion of values less than a given number of standard deviations above the mean."]
[]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,"An investment has normal returns.  What percentage of returns will be less than one standard deviation (s) above the mean?"]
[]
[]
[{"$f":"IF(OR(NOT(ISNUMBER($Q$138)),ISERROR($Q$138)),1,IF(AND(LEN($Q$138)>0,ABS((1-($Q$138*-3.96027743816376+ 0.123916387557983)/-3.20804222801488))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,null,null,null,null,"% returns < (mean + s):"]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,"Complete the table below showing the percentage of returns less than N standard deviations above the mean."]
[]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,"N","% returns"]
[]
[{"$f":"IF(OR(NOT(ISNUMBER($N$145)),ISERROR($N$145)),1,IF(AND(LEN($N$145)>0,ABS((1-($N$145*-4.24258291721343+ 0.122792601585388)/ 0.121805653428625))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,null,null,null,null,-3.5]
[{"$f":"IF(OR(NOT(ISNUMBER($N$146)),ISERROR($N$146)),1,IF(AND(LEN($N$146)>0,ABS((1-($N$146*-0.384406447410584+ 0.443000793457031)/ 0.442481883950326))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,null,null,null,null,{"$f":"M145+0.5","v":-3}]
[{"$f":"IF(OR(NOT(ISNUMBER($N$147)),ISERROR($N$147)),1,IF(AND(LEN($N$147)>0,ABS((1-($N$147*-3.07048618793488+-0.202225089073181)/-0.221291780687675))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,null,null,null,null,-2.5]
[{"$f":"IF(OR(NOT(ISNUMBER($N$148)),ISERROR($N$148)),1,IF(AND(LEN($N$148)>0,ABS((1-($N$148* 1.0677844285965+-0.253154516220093)/-0.228862279577311))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,null,null,null,null,-2]
[{"$f":"IF(OR(NOT(ISNUMBER($N$149)),ISERROR($N$149)),1,IF(AND(LEN($N$149)>0,ABS((1-($N$149*-1.87088549137115+-0.406587719917297)/-0.531576343490316))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,null,null,null,null,-1.5]
[{"$f":"IF(OR(NOT(ISNUMBER($N$150)),ISERROR($N$150)),1,IF(AND(LEN($N$150)>0,ABS((1-($N$150*-4.96686398983002+ 0.456898212432861)/-0.33112085511663))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,null,null,null,null,-1]
[{"$f":"IF(OR(NOT(ISNUMBER($N$151)),ISERROR($N$151)),1,IF(AND(LEN($N$151)>0,ABS((1-($N$151* 2.33778655529022+-0.0722655057907104)/ 0.649029404045238))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,null,null,null,null,-0.5]
[{"$f":"IF(OR(NOT(ISNUMBER($N$152)),ISERROR($N$152)),1,IF(AND(LEN($N$152)>0,ABS((1-($N$152*-0.404245257377625+-0.0395729541778564)/-0.241695582866669))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,null,null,null,null,0]
[{"$f":"IF(OR(NOT(ISNUMBER($N$153)),ISERROR($N$153)),1,IF(AND(LEN($N$153)>0,ABS((1-($N$153* 3.56248795986176+-0.0888458490371704)/ 2.37448084394788))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,null,null,null,null,0.5]
[{"$f":"IF(OR(NOT(ISNUMBER($N$154)),ISERROR($N$154)),1,IF(AND(LEN($N$154)>0,ABS((1-($N$154* 2.06826269626617+-0.123854637145996)/ 1.61626731584711))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,null,null,null,null,1]
[{"$f":"IF(OR(NOT(ISNUMBER($N$155)),ISERROR($N$155)),1,IF(AND(LEN($N$155)>0,ABS((1-($N$155*-1.13318264484406+-0.262908339500427)/-1.32038622331601))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,null,null,null,null,1.5]
[{"$f":"IF(OR(NOT(ISNUMBER($N$156)),ISERROR($N$156)),1,IF(AND(LEN($N$156)>0,ABS((1-($N$156*-2.72695243358612+-0.430163145065308)/-3.09507705097094))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,null,null,null,null,2]
[{"$f":"IF(OR(NOT(ISNUMBER($N$157)),ISERROR($N$157)),1,IF(AND(LEN($N$157)>0,ABS((1-($N$157* 2.90226399898529+ 0.322600245475769)/ 3.20684215634031))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,null,null,null,null,2.5]
[{"$f":"IF(OR(NOT(ISNUMBER($N$158)),ISERROR($N$158)),1,IF(AND(LEN($N$158)>0,ABS((1-($N$158*-1.67648732662201+-0.080019474029541)/-1.75424371370929))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,null,null,null,null,3]
[]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Index"]
[{"$f":"SUM($A$163:$J$182)","v":11},null,null,null,null,null,null,null,null,null,null,9,"Calculating percentage of outcomes within N standard deviations of the mean"]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,"Complete the table below showing the percentage of returns within N standard deviations from the mean."]
[]
[]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,"N","Percentage"]
[]
[{"$f":"IF(OR(NOT(ISNUMBER($N$170)),ISERROR($N$170)),1,IF(AND(LEN($N$170)>0,ABS((1-($N$170* 4.93945777416229+ 0.198990941047668)/ 0.198990941047668))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,null,null,null,null,0]
[{"$f":"IF(OR(NOT(ISNUMBER($N$171)),ISERROR($N$171)),1,IF(AND(LEN($N$171)>0,ABS((1-($N$171*-0.0946730375289917+ 0.333375692367554)/ 0.311049627371571))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,null,null,null,null,{"$f":"M170+0.3","v":0.3}]
[{"$f":"IF(OR(NOT(ISNUMBER($N$172)),ISERROR($N$172)),1,IF(AND(LEN($N$172)>0,ABS((1-($N$172*-1.60058081150055+-0.347542405128479)/-1.07019466109909))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,null,null,null,null,0.6]
[{"$f":"IF(OR(NOT(ISNUMBER($N$173)),ISERROR($N$173)),1,IF(AND(LEN($N$173)>0,ABS((1-($N$173* 4.05767500400543+ 0.0107669830322266)/ 2.57472964733035))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,null,null,null,null,0.89999999999999991]
[{"$f":"IF(OR(NOT(ISNUMBER($N$174)),ISERROR($N$174)),1,IF(AND(LEN($N$174)>0,ABS((1-($N$174* 2.88480937480927+ 0.114701867103577)/ 2.33560311508925))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,null,null,null,null,1.2]
[{"$f":"IF(OR(NOT(ISNUMBER($N$175)),ISERROR($N$175)),1,IF(AND(LEN($N$175)>0,ABS((1-($N$175*-1.54549300670624+ 0.462469339370728)/-0.876523542618238))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,null,null,null,null,1.5]
[{"$f":"IF(OR(NOT(ISNUMBER($N$176)),ISERROR($N$176)),1,IF(AND(LEN($N$176)>0,ABS((1-($N$176*-1.28881990909576+-0.196441769599915)/-1.39264625746987))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,null,null,null,null,1.8]
[{"$f":"IF(OR(NOT(ISNUMBER($N$177)),ISERROR($N$177)),1,IF(AND(LEN($N$177)>0,ABS((1-($N$177*-2.8142112493515+ 0.273993015289307)/-2.43966972744015))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,null,null,null,null,2.1]
[{"$f":"IF(OR(NOT(ISNUMBER($N$178)),ISERROR($N$178)),1,IF(AND(LEN($N$178)>0,ABS((1-($N$178* 3.93822371959686+-0.386381030082703)/ 3.48727522867318))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,null,null,null,null,2.4]
[{"$f":"IF(OR(NOT(ISNUMBER($N$179)),ISERROR($N$179)),1,IF(AND(LEN($N$179)>0,ABS((1-($N$179* 4.03875172138214+ 0.121668577194214)/ 4.13241580574632))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,null,null,null,null,2.6999999999999997]
[{"$f":"IF(OR(NOT(ISNUMBER($N$180)),ISERROR($N$180)),1,IF(AND(LEN($N$180)>0,ABS((1-($N$180* 3.90102326869965+ 0.256859183311462)/ 4.14735048474759))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,null,null,null,null,2.9999999999999996]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Index"]
[{"$f":"SUM($A$184:$J$212)","v":15},null,null,null,null,null,null,null,null,null,null,10,"Calculating number of standard deviations above mean below which a given percentage of samples occur."]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,"We can use the NORNMSINV function to give the number of standard deviations above the mean below which a certain proportion of outcomes will occur."]
[]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,"85% of returns occur less than N standard deviations above the mean.  What is N?"]
[]
[{"$f":"IF(OR(NOT(ISNUMBER($N$190)),ISERROR($N$190)),1,IF(AND(LEN($N$190)>0,ABS((1-($N$190*-1.72085702419281+ 0.0382719039916992)/-1.74528177442665))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,null,null,null,null,"N"]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,"Complete the following table which shows the number of standard deviations above the mean below which X% of samples occur."]
[]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,"X","Number Sd's"]
[]
[{"$f":"IF(OR(NOT(ISNUMBER($N$197)),ISERROR($N$197)),1,IF(AND(LEN($N$197)>0,ABS((1-($N$197* 3.24130237102509+-0.346738219261169)/-0.346738219261169))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,null,null,null,null,0.5]
[{"$f":"IF(OR(NOT(ISNUMBER($N$198)),ISERROR($N$198)),1,IF(AND(LEN($N$198)>0,ABS((1-($N$198* 2.93247520923615+-0.0713508129119873)/ 0.22316858265925))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,null,null,null,null,{"$f":"M197+4%","v":0.54}]
[{"$f":"IF(OR(NOT(ISNUMBER($N$199)),ISERROR($N$199)),1,IF(AND(LEN($N$199)>0,ABS((1-($N$199* 0.438675284385681+-0.428557515144348)/-0.339991835766182))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,null,null,null,null,0.58000000000000007]
[{"$f":"IF(OR(NOT(ISNUMBER($N$200)),ISERROR($N$200)),1,IF(AND(LEN($N$200)>0,ABS((1-($N$200*-4.43472325801849+ 0.335341930389404)/-1.01938082547281))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,null,null,null,null,0.62000000000000011]
[{"$f":"IF(OR(NOT(ISNUMBER($N$201)),ISERROR($N$201)),1,IF(AND(LEN($N$201)>0,ABS((1-($N$201* 4.84189689159393+-0.480725169181824)/ 1.51637877515762))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,null,null,null,null,0.66000000000000014]
[{"$f":"IF(OR(NOT(ISNUMBER($N$202)),ISERROR($N$202)),1,IF(AND(LEN($N$202)>0,ABS((1-($N$202* 1.56634151935577+ 0.454211950302124)/ 1.27560224612818))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,null,null,null,null,0.70000000000000018]
[{"$f":"IF(OR(NOT(ISNUMBER($N$203)),ISERROR($N$203)),1,IF(AND(LEN($N$203)>0,ABS((1-($N$203*-3.79988729953766+-0.115484833717346)/-2.5601248688858))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,null,null,null,null,0.74000000000000021]
[{"$f":"IF(OR(NOT(ISNUMBER($N$204)),ISERROR($N$204)),1,IF(AND(LEN($N$204)>0,ABS((1-($N$204*-0.0720208883285522+ 0.400066375732422)/ 0.344452334485273))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,null,null,null,null,0.78000000000000025]
[{"$f":"IF(OR(NOT(ISNUMBER($N$205)),ISERROR($N$205)),1,IF(AND(LEN($N$205)>0,ABS((1-($N$205*-3.30589115619659+ 0.325427651405334)/-2.70066969718534))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,null,null,null,null,0.82000000000000028]
[{"$f":"IF(OR(NOT(ISNUMBER($N$206)),ISERROR($N$206)),1,IF(AND(LEN($N$206)>0,ABS((1-($N$206* 1.52726471424103+-0.277717351913452)/ 1.37221625742536))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,null,null,null,null,0.86000000000000032]
[{"$f":"IF(OR(NOT(ISNUMBER($N$207)),ISERROR($N$207)),1,IF(AND(LEN($N$207)>0,ABS((1-($N$207*-4.53243792057037+ 0.411409258842468)/-5.39714365399822))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,null,null,null,null,0.90000000000000036]
[{"$f":"IF(OR(NOT(ISNUMBER($N$208)),ISERROR($N$208)),1,IF(AND(LEN($N$208)>0,ABS((1-($N$208*-0.0927108526229858+ 0.170433521270752)/ 0.0262891356799729))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,null,null,null,null,0.94000000000000039]
[{"$f":"IF(OR(NOT(ISNUMBER($N$209)),ISERROR($N$209)),1,IF(AND(LEN($N$209)>0,ABS((1-($N$209*-4.3417102098465+-0.486385226249695)/-9.40316784000104))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,null,null,null,null,0.98000000000000043]
[{"$f":"IF(OR(NOT(ISNUMBER($N$210)),ISERROR($N$210)),1,IF(AND(LEN($N$210)>0,ABS((1-($N$210* 4.55840885639191+-0.290087938308716)/ 16.6627097460588))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,null,null,null,null,{"$f":"99.99%","v":0.9998999999999999}]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Index"]
[{"$f":"SUM($A$214:$J$263)","v":64},null,null,null,null,null,null,null,null,null,null,{"$f":"L183+1","v":11},"Generating samples from a normal distribution."]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,"The RAND function can be used to generate samples drawn from a rectangular distribution.  The distribution can be \"mapped\" to another distribution.  For example, to generate samples drawn from a normal distribution you can pass the numbers generated by RAND to the NORMSINV function.  The NORMSINV function will then generate samples drawn from a normal distribution that has a mean of zero and standard deviation of 1."]
[]
[]
[]
[]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,"The samples below have been generated by using the =RAND() function.  That function generates numbers that are equally likely to fall anywhere in the range from 0 to 1.  In other words, the samples have a \"rectangular\" distribution.  "]
[]
[]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,0.22163257990557517,0.31503639542309814,0.55660031314753411,0.68568931885269091,0.77976897957253932,0.62185611647155969,0.26360245669676985,0.62208836731214423,3.8853111339498758E-2,0.25150063612337092]
[null,null,null,null,null,null,null,null,null,null,null,null,0.39083380421847219,0.39538602204330675,9.3602312550056688E-2,0.67331620487131438,0.94322019322285411,0.27044687577533777,0.56870816371981237,0.57439542862571513,0.41950002631301508,0.15044808374781216]
[null,null,null,null,null,null,null,null,null,null,null,null,0.10787924210021771,0.13205647438936818,0.10181217816117005,8.279515714182839E-2,0.2484960474213862,0.42350564268165591,0.91089798520285581,0.22877066136249891,0.98809307308722993,0.49207411857706873]
[null,null,null,null,null,null,null,null,null,null,null,null,2.377298642982506E-2,0.27034721628935032,0.76856000938886426,0.11445209300086523,0.10435548547698525,6.4237925354642122E-3,0.66853217864307335,0.94531970714242153,0.71875054547654216,0.22082798903692602]
[null,null,null,null,null,null,null,null,null,null,null,null,0.50039747432965775,0.42231072703518979,0.62628148739639045,0.32395317665280299,0.98592364515148923,0.60590037154417797,0.79558007375887296,0.72885035405033194,0.92804702830005326,0.20450224351227941]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,"Use the numbers above to generate normally distributed numbers."]
[]
[{"$f":"IF(OR(NOT(ISNUMBER($M$233)),ISERROR($M$233)),1,IF(AND(LEN($M$233)>0,ABS((1-($M$233* 3.92949998378754+-0.0544182062149048)/-3.06713111339557))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($N$233)),ISERROR($N$233)),1,IF(AND(LEN($N$233)>0,ABS((1-($N$233*-3.30050408840179+-0.212443351745605)/ 1.37715994396836))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($O$233)),ISERROR($O$233)),1,IF(AND(LEN($O$233)>0,ABS((1-($O$233* 2.50104129314423+ 0.353855729103088)/ 0.709892195135771))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($P$233)),ISERROR($P$233)),1,IF(AND(LEN($P$233)>0,ABS((1-($P$233*-2.44081199169159+-0.152724027633667)/-1.33326717940773))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($Q$233)),ISERROR($Q$233)),1,IF(AND(LEN($Q$233)>0,ABS((1-($Q$233* 3.68065297603607+ 0.358614802360535)/ 3.19791917114499))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($R$233)),ISERROR($R$233)),1,IF(AND(LEN($R$233)>0,ABS((1-($R$233*-0.842861533164978+ 0.0956740379333496)/-0.165915848523454))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($S$233)),ISERROR($S$233)),1,IF(AND(LEN($S$233)>0,ABS((1-($S$233*-3.10478508472443+ 0.444295048713684)/ 2.40738388868581))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($T$233)),ISERROR($T$233)),1,IF(AND(LEN($T$233)>0,ABS((1-($T$233*-2.41473376750946+-0.482324838638306)/-1.23323511562242))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($U$233)),ISERROR($U$233)),1,IF(AND(LEN($U$233)>0,ABS((1-($U$233*-1.77800238132477+ 0.100215315818787)/ 3.23688355736006))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($V$233)),ISERROR($V$233)),1,IF(AND(LEN($V$233)>0,ABS((1-($V$233*-1.21099412441254+ 0.142148971557617)/ 0.953242486146893))<0.00005),0,1))","v":1}]
[{"$f":"IF(OR(NOT(ISNUMBER($M$234)),ISERROR($M$234)),1,IF(AND(LEN($M$234)>0,ABS((1-($M$234* 2.41991221904755+ 0.211202263832092)/-0.459467967612676))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($N$234)),ISERROR($N$234)),1,IF(AND(LEN($N$234)>0,ABS((1-($N$234*-3.15144240856171+-0.442464590072632)/ 0.393638939198824))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($O$234)),ISERROR($O$234)),1,IF(AND(LEN($O$234)>0,ABS((1-($O$234*-2.53923952579498+-0.301784634590149)/ 3.04720258788833))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($P$234)),ISERROR($P$234)),1,IF(AND(LEN($P$234)>0,ABS((1-($P$234* 4.76013720035552+-0.322530269622803)/ 1.81519409479433))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($Q$234)),ISERROR($Q$234)),1,IF(AND(LEN($Q$234)>0,ABS((1-($Q$234* 1.56048476696014+ 0.408971905708313)/ 2.87827391187325))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($R$234)),ISERROR($R$234)),1,IF(AND(LEN($R$234)>0,ABS((1-($R$234*-2.28277385234833+-0.243592500686646)/ 1.15223702103942))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($S$234)),ISERROR($S$234)),1,IF(AND(LEN($S$234)>0,ABS((1-($S$234* 2.71041810512543+ 0.258571982383728)/ 0.727707950814031))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($T$234)),ISERROR($T$234)),1,IF(AND(LEN($T$234)>0,ABS((1-($T$234*-1.10817849636078+-0.34475040435791)/-0.552617950866479))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($U$234)),ISERROR($U$234)),1,IF(AND(LEN($U$234)>0,ABS((1-($U$234* 0.708534121513367+-0.379876494407654)/-0.52383128258687))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($V$234)),ISERROR($V$234)),1,IF(AND(LEN($V$234)>0,ABS((1-($V$234*-2.28431403636932+ 0.356967210769653)/ 2.7201209266718))<0.00005),0,1))","v":1}]
[{"$f":"IF(OR(NOT(ISNUMBER($M$235)),ISERROR($M$235)),1,IF(AND(LEN($M$235)>0,ABS((1-($M$235* 1.69069707393646+-0.0346328020095825)/-2.12752235587942))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($N$235)),ISERROR($N$235)),1,IF(AND(LEN($N$235)>0,ABS((1-($N$235* 0.661597847938538+-0.267773151397705)/-1.0065944247424))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($O$235)),ISERROR($O$235)),1,IF(AND(LEN($O$235)>0,ABS((1-($O$235*-4.83808815479279+-0.244698405265808)/ 5.90593022480758))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($P$235)),ISERROR($P$235)),1,IF(AND(LEN($P$235)>0,ABS((1-($P$235* 4.52460110187531+-0.444984674453735)/-6.71840291016718))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($Q$235)),ISERROR($Q$235)),1,IF(AND(LEN($Q$235)>0,ABS((1-($Q$235* 3.52757394313812+-0.419191956520081)/-2.81522626627586))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($R$235)),ISERROR($R$235)),1,IF(AND(LEN($R$235)>0,ABS((1-($R$235* 2.20325529575348+-0.231735229492188)/-0.656816319271346))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($S$235)),ISERROR($S$235)),1,IF(AND(LEN($S$235)>0,ABS((1-($S$235* 4.12471950054169+-0.44672429561615)/ 5.1064080391991))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($T$235)),ISERROR($T$235)),1,IF(AND(LEN($T$235)>0,ABS((1-($T$235* 0.980885624885559+-0.000522375106811523)/-0.729223768692973))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($U$235)),ISERROR($U$235)),1,IF(AND(LEN($U$235)>0,ABS((1-($U$235* 3.75327527523041+-0.0547734498977661)/ 8.42807606225295))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($V$235)),ISERROR($V$235)),1,IF(AND(LEN($V$235)>0,ABS((1-($V$235* 3.30683290958405+ 0.326351642608643)/ 0.260649682108116))<0.00005),0,1))","v":1}]
[{"$f":"IF(OR(NOT(ISNUMBER($M$236)),ISERROR($M$236)),1,IF(AND(LEN($M$236)>0,ABS((1-($M$236*-4.29269134998322+ 0.0809403657913208)/ 8.58649666366271))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($N$236)),ISERROR($N$236)),1,IF(AND(LEN($N$236)>0,ABS((1-($N$236* 0.077703595161438+ 0.292404890060425)/ 0.24486868908901))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($O$236)),ISERROR($O$236)),1,IF(AND(LEN($O$236)>0,ABS((1-($O$236*-0.693722367286682+ 0.477079749107361)/-0.0321907337424744))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($P$236)),ISERROR($P$236)),1,IF(AND(LEN($P$236)>0,ABS((1-($P$236*-3.58138024806976+ 0.172600746154785)/ 4.48166885147455))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($Q$236)),ISERROR($Q$236)),1,IF(AND(LEN($Q$236)>0,ABS((1-($Q$236* 1.92628085613251+ 0.233315110206604)/-2.18824690353211))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($R$236)),ISERROR($R$236)),1,IF(AND(LEN($R$236)>0,ABS((1-($R$236*-0.0355309247970581+ 0.488972902297974)/ 0.577372651291839))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($S$236)),ISERROR($S$236)),1,IF(AND(LEN($S$236)>0,ABS((1-($S$236* 3.53130757808685+-0.3270503282547)/ 1.21211836546225))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($T$236)),ISERROR($T$236)),1,IF(AND(LEN($T$236)>0,ABS((1-($T$236* 1.64115488529205+-0.22374963760376)/ 2.40386036696531))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($U$236)),ISERROR($U$236)),1,IF(AND(LEN($U$236)>0,ABS((1-($U$236* 3.70448768138886+ 0.2335444688797)/ 2.37893841981624))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($V$236)),ISERROR($V$236)),1,IF(AND(LEN($V$236)>0,ABS((1-($V$236*-1.05315387248993+-0.402517557144165)/ 0.407778873567895))<0.00005),0,1))","v":1}]
[{"$f":"IF(OR(NOT(ISNUMBER($M$237)),ISERROR($M$237)),1,IF(AND(LEN($M$237)>0,ABS((1-($M$237* 1.17934167385101+-0.392456650733948)/-0.391281648379391))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($N$237)),ISERROR($N$237)),1,IF(AND(LEN($N$237)>0,ABS((1-($N$237* 1.73322737216949+-0.190336227416992)/-0.530023796010547))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($O$237)),ISERROR($O$237)),1,IF(AND(LEN($O$237)>0,ABS((1-($O$237*-4.12896931171417+ 0.132897973060608)/-1.19671554721166))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($P$237)),ISERROR($P$237)),1,IF(AND(LEN($P$237)>0,ABS((1-($P$237* 0.486748814582825+ 0.0793592929840088)/-0.142925577165193))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($Q$237)),ISERROR($Q$237)),1,IF(AND(LEN($Q$237)>0,ABS((1-($Q$237* 3.4076064825058+ 0.433692812919617)/ 7.91390635390187))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($R$237)),ISERROR($R$237)),1,IF(AND(LEN($R$237)>0,ABS((1-($R$237*-2.89012372493744+-0.351670742034912)/-1.12810163529406))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($S$237)),ISERROR($S$237)),1,IF(AND(LEN($S$237)>0,ABS((1-($S$237* 2.16126143932343+ 0.310770153999329)/ 2.09583585931765))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($T$237)),ISERROR($T$237)),1,IF(AND(LEN($T$237)>0,ABS((1-($T$237*-1.7976588010788+ 0.349154233932495)/-0.746230656467671))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($U$237)),ISERROR($U$237)),1,IF(AND(LEN($U$237)>0,ABS((1-($U$237* 2.77957856655121+-0.117644906044006)/ 3.94442875160576))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($V$237)),ISERROR($V$237)),1,IF(AND(LEN($V$237)>0,ABS((1-($V$237* 0.842390656471252+-0.12913990020752)/-0.82465703801504))<0.00005),0,1))","v":1}]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,"Chart the frequency distribution of the normally distributed numbers.  Use the FREQUENCY function."]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,"Min number:",null,{"$f":"MIN(M233:V237)","v":0},null,"Rounded min:",null,{"$f":"ROUND(O241,1)","v":0},null,"Step size:",{"$f":"(S242-S241)/ROWS(intervals)","v":0}]
[null,null,null,null,null,null,null,null,null,null,null,null,"Max number:",null,{"$f":"MAX(M233:V237)","v":0},null,"Rounded max:",null,{"$f":"ROUND(O242,1)","v":0}]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,"Interval","Number"]
[]
[{"$f":"IF(OR(NOT(ISNUMBER($N$246)),ISERROR($N$246)),1,IF(AND(LEN($N$246)>0,ABS((1-($N$246* 0.216781497001648+-0.0253194570541382)/-0.0253194570541382))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,null,null,null,null,{"$f":"S241-V241","v":0}]
[{"$f":"IF(OR(NOT(ISNUMBER($N$247)),ISERROR($N$247)),1,IF(AND(LEN($N$247)>0,ABS((1-($N$247* 0.868037343025208+ 0.274543046951294)/ 0.274543046951294))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,null,null,null,null,{"$f":"M246+$V$241","v":0}]
[{"$f":"IF(OR(NOT(ISNUMBER($N$248)),ISERROR($N$248)),1,IF(AND(LEN($N$248)>0,ABS((1-($N$248*-1.73501551151276+-0.237387776374817)/-1.97240328788757))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,null,null,null,null,0]
[{"$f":"IF(OR(NOT(ISNUMBER($N$249)),ISERROR($N$249)),1,IF(AND(LEN($N$249)>0,ABS((1-($N$249* 3.65830957889557+-0.241005420684814)/ 3.41730415821075))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,null,null,null,null,0]
[{"$f":"IF(OR(NOT(ISNUMBER($N$250)),ISERROR($N$250)),1,IF(AND(LEN($N$250)>0,ABS((1-($N$250*-3.4145575761795+-0.339726328849792)/-3.7542839050293))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,null,null,null,null,0]
[{"$f":"IF(OR(NOT(ISNUMBER($N$251)),ISERROR($N$251)),1,IF(AND(LEN($N$251)>0,ABS((1-($N$251*-2.58549869060516+-0.323673486709595)/-15.8366656303406))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,null,null,null,null,0]
[{"$f":"IF(OR(NOT(ISNUMBER($N$252)),ISERROR($N$252)),1,IF(AND(LEN($N$252)>0,ABS((1-($N$252* 0.239800810813904+ 0.461671233177185)/ 1.1810736656189))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,null,null,null,null,0]
[{"$f":"IF(OR(NOT(ISNUMBER($N$253)),ISERROR($N$253)),1,IF(AND(LEN($N$253)>0,ABS((1-($N$253*-1.05857789516449+-0.202404022216797)/-10.7881829738617))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,null,null,null,null,0]
[{"$f":"IF(OR(NOT(ISNUMBER($N$254)),ISERROR($N$254)),1,IF(AND(LEN($N$254)>0,ABS((1-($N$254* 1.72134578227997+-0.268680930137634)/ 8.33804798126221))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,null,null,null,null,0]
[{"$f":"IF(OR(NOT(ISNUMBER($N$255)),ISERROR($N$255)),1,IF(AND(LEN($N$255)>0,ABS((1-($N$255* 1.92864716053009+-0.171569585800171)/ 9.47166621685028))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,null,null,null,null,0]
[{"$f":"IF(OR(NOT(ISNUMBER($N$256)),ISERROR($N$256)),1,IF(AND(LEN($N$256)>0,ABS((1-($N$256*-4.51374590396881+ 0.444864153862)/-35.6651030778885))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,null,null,null,null,0]
[{"$f":"IF(OR(NOT(ISNUMBER($N$257)),ISERROR($N$257)),1,IF(AND(LEN($N$257)>0,ABS((1-($N$257*-2.26823270320892+ 0.174652576446533)/-8.89827823638916))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,null,null,null,null,0]
[{"$f":"IF(OR(NOT(ISNUMBER($N$258)),ISERROR($N$258)),1,IF(AND(LEN($N$258)>0,ABS((1-($N$258* 4.98484313488007+-0.120288729667664)/-0.120288729667664))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,null,null,null,null,0]
[{"$f":"IF(OR(NOT(ISNUMBER($N$259)),ISERROR($N$259)),1,IF(AND(LEN($N$259)>0,ABS((1-($N$259*-1.34636104106903+-0.0420944690704346)/-5.42753863334656))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,null,null,null,null,0]
[]
[]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"Copyright (c) 2020 Tykoh Group Pty Ltd.  All rights reserved.",null,null,null,null,null,null,null,null,"Index"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"www.tykoh.com"]

{"sheet":"Variance_and_correlation","index":23,"n_rows":168,"n_cols":17,"rows_kept":168,"cut":false,"hidden":false,"merged":[[166,7,166,13],[167,7,167,13],[0,5,0,11],[3,5,5,13],[99,5,101,13],[129,5,130,13],[7,5,7,13],[26,5,28,13],[36,5,37,13],[45,6,45,8],[53,6,53,8],[51,5,51,13],[59,5,59,13],[138,5,138,13],[61,6,61,8],[69,5,71,13],[73,5,74,13],[76,6,76,8],[84,5,86,13],[91,6,91,8],[88,5,89,13]]}
[null,null,null,null,null,"Click here to see what your answer should look like."]
[{"$f":"SUM($A$3:$C$24)","v":3},null,null,null,1,"Calculating sample variance",null,null,null,null,null,null,null,null,"Frequency_distribution","Variance_and_correlation"]
[]
[null,null,null,null,null,"Variance is the square of the standard deviation.  One method of calculating standard deviation is shown in an earlier tab in this topic.  Another way - which can be used if you have individual samples - is to use the spreadsheet function STDEV."]
[]
[]
[]
[null,null,null,null,null,"Calculate the standard deviation and variance of the following set of samples:"]
[]
[null,null,null,null,null,0,-0.02,-0.05,-0.01,-0.03,-0.02,0.01,0.01]
[null,null,null,null,null,0,0.03,0.04,-0.02,0.03,0.02,-0.01,0.02]
[null,null,null,null,null,0.05,0.04,0.03,-0.03,-0.01,0,-0.01,0.04]
[null,null,null,null,null,0.01,-0.02,0.05,-0.02,0,0.01,0.01,0]
[null,null,null,null,null,0.02,-0.01,-0.01,-0.01,0,-0.01,0.06,0.03]
[null,null,null,null,null,0.03,0.04,0.03,0.04,-0.01,-0.03,0.03,0.04]
[null,null,null,null,null,0.01,0.03,0.01,0,0.01,0.06,0.03,0.02]
[null,null,null,null,null,0.01,0.02,0.01,0,0.05,0.02,0.04,0.01]
[null,null,null,null,null,0.02,0.03,0.04,0.03,0.02,0.03,0.04,0.03]
[null,null,null,null,null,-0.01,0.01]
[]
[{"$f":"IF(OR(NOT(ISNUMBER($J$21)),ISERROR($J$21)),1,IF(AND(LEN($J$21)>0,ABS((1-($J$21* 2.1928209066391+-0.244351983070374)/-0.192418531485764))<0.00005),0,1))","v":1},null,null,null,null,"Standard deviation:",null,null,"[%]"]
[{"$f":"IF(OR(NOT(ISNUMBER($J$22)),ISERROR($J$22)),1,IF(AND(LEN($J$22)>0,ABS((1-($J$22* 3.72563421726227+ 0.281277656555176)/ 0.283367377339756))<0.00005),0,1))","v":1},null,null,null,null,{"$f":"\"Variance (square of cell \" & ADDRESS(ROW(J21),COLUMN(J21),4)&\").\"","v":"Variance (square of cell J21)."},null,null,"[%]"]
[{"$f":"IF(OR(NOT(ISNUMBER($J$23)),ISERROR($J$23)),1,IF(AND(LEN($J$23)>0,ABS((1-($J$23*-0.357463955879211+-0.37453019618988)/-0.374730698927073))<0.00005),0,1))","v":1},null,null,null,null,"Variance (using VAR function)"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Index"]
[{"$f":"SUM($A$26:$C$34)","v":3},null,null,null,2,"Calculating population variance"]
[]
[null,null,null,null,null,"If your data encompasses the entire population you should use the STDEVP or VARP functions to calculate the population standard deviation and variance respectively.  Assume the data above comprises the entire population. Calculate the population standard deviation and variance."]
[]
[]
[]
[{"$f":"IF(OR(NOT(ISNUMBER($J$31)),ISERROR($J$31)),1,IF(AND(LEN($J$31)>0,ABS((1-($J$31*-3.01110923290253+-0.255072355270386)/-0.325902169877566))<0.00005),0,1))","v":1},null,null,null,null,"Standard deviation:",null,null,"[%]"]
[{"$f":"IF(OR(NOT(ISNUMBER($J$32)),ISERROR($J$32)),1,IF(AND(LEN($J$32)>0,ABS((1-($J$32* 4.95422780513763+-0.484395146369934)/-0.481653855235974))<0.00005),0,1))","v":1},null,null,null,null,{"$f":"\"Variance (square of cell \" & ADDRESS(ROW(J31),COLUMN(J31),4)&\").\"","v":"Variance (square of cell J31)."},null,null,"[%]"]
[{"$f":"IF(OR(NOT(ISNUMBER($J$33)),ISERROR($J$33)),1,IF(AND(LEN($J$33)>0,ABS((1-($J$33*-1.72443807125092+ 0.211709499359131)/ 0.21075532708815))<0.00005),0,1))","v":1},null,null,null,null,"Variance (using VARP function)"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Index"]
[{"$f":"SUM($A$36:$C$57)","v":12},null,null,null,3,"Calculating population covariance"]
[]
[null,null,null,null,null,"Consider the data for three series (X,Y & Z) below.  Calculate the (population) covariances between the series by using the COVAR function."]
[]
[]
[null,null,null,null,null,null,"X","Y","Z"]
[null,null,null,null,null,null,1.2,3,5]
[null,null,null,null,null,null,1.7,3.2,4.9000000000000004]
[null,null,null,null,null,null,2.1,3.1,5.5]
[null,null,null,null,null,null,2.2000000000000002,3.4,7]
[]
[null,null,null,null,null,null,"Covariance matrix"]
[null,null,null,null,null,null,"X","Y","Z"]
[{"$f":"IF(OR(NOT(ISNUMBER($G$48)),ISERROR($G$48)),1,IF(AND(LEN($G$48)>0,ABS((1-($G$48*-2.13272392749786+-0.183260798454285)/-0.513833007216454))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($H$48)),ISERROR($H$48)),1,IF(AND(LEN($H$48)>0,ABS((1-($H$48*-3.5099333524704+-0.177202463150024)/-0.326374630630016))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($I$48)),ISERROR($I$48)),1,IF(AND(LEN($I$48)>0,ABS((1-($I$48*-0.228548645973206+ 0.424441695213318)/ 0.369590020179749))<0.00005),0,1))","v":1},null,null,"X"]
[{"$f":"IF(OR(NOT(ISNUMBER($G$49)),ISERROR($G$49)),1,IF(AND(LEN($G$49)>0,ABS((1-($G$49*-4.60966050624847+ 0.263311386108398)/ 0.0674008145928383))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($H$49)),ISERROR($H$49)),1,IF(AND(LEN($H$49)>0,ABS((1-($H$49*-4.26183521747589+ 0.129788994789124)/ 0.0365613494068385))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($I$49)),ISERROR($I$49)),1,IF(AND(LEN($I$49)>0,ABS((1-($I$49* 1.86908066272736+ 0.277940988540649)/ 0.469521756470203))<0.00005),0,1))","v":1},null,null,"Y"]
[{"$f":"IF(OR(NOT(ISNUMBER($G$50)),ISERROR($G$50)),1,IF(AND(LEN($G$50)>0,ABS((1-($G$50*-0.94828188419342+ 0.259990572929382)/ 0.0324029207229614))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($H$50)),ISERROR($H$50)),1,IF(AND(LEN($H$50)>0,ABS((1-($H$50*-3.26499402523041+ 0.436571598052979)/ 0.101909710466862))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($I$50)),ISERROR($I$50)),1,IF(AND(LEN($I$50)>0,ABS((1-($I$50*-1.75944626331329+-0.430986285209656)/-1.67139590084553))<0.00005),0,1))","v":1},null,null,"Z"]
[]
[null,null,null,null,null,"Determine the (population) standard deviations of the X, Y and Z series."]
[]
[null,null,null,null,null,null,"Standard deviations"]
[null,null,null,null,null,null,"X","Y","Z"]
[{"$f":"IF(OR(NOT(ISNUMBER($G$56)),ISERROR($G$56)),1,IF(AND(LEN($G$56)>0,ABS((1-($G$56*-2.00590312480927+ 0.149908781051636)/-0.639816068911017))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($H$56)),ISERROR($H$56)),1,IF(AND(LEN($H$56)>0,ABS((1-($H$56*-3.39149534702301+ 0.378208518028259)/-0.123400408396722))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($I$56)),ISERROR($I$56)),1,IF(AND(LEN($I$56)>0,ABS((1-($I$56*-3.36914956569672+-0.0648965835571289)/-2.89377869513482))<0.00005),0,1))","v":1}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Index"]
[{"$f":"SUM($A$59:$C$67)","v":9},null,null,null,4,"Calculating population correlation"]
[]
[null,null,null,null,null,"Determine the correlations between the X, Y and Z series by using the CORREL function."]
[]
[null,null,null,null,null,null,"Correlation matrix"]
[null,null,null,null,null,null,"X","Y","Z"]
[{"$f":"IF(OR(NOT(ISNUMBER($G$64)),ISERROR($G$64)),1,IF(AND(LEN($G$64)>0,ABS((1-($G$64* 4.26604449748993+-0.0330671072006226)/ 4.23297739028931))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($H$64)),ISERROR($H$64)),1,IF(AND(LEN($H$64)>0,ABS((1-($H$64* 4.88952934741974+-0.0686233043670654)/ 3.5001265450672))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($I$64)),ISERROR($I$64)),1,IF(AND(LEN($I$64)>0,ABS((1-($I$64* 2.66153752803802+ 0.213177561759949)/ 2.14551704697932))<0.00005),0,1))","v":1},null,null,"X"]
[{"$f":"IF(OR(NOT(ISNUMBER($G$65)),ISERROR($G$65)),1,IF(AND(LEN($G$65)>0,ABS((1-($G$65*-2.94458806514739+-0.334354877471924)/-2.48353887197769))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($H$65)),ISERROR($H$65)),1,IF(AND(LEN($H$65)>0,ABS((1-($H$65* 1.61248862743378+ 0.484191060066223)/ 2.0966796875))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($I$65)),ISERROR($I$65)),1,IF(AND(LEN($I$65)>0,ABS((1-($I$65* 2.73604214191437+ 0.0681455135345459)/ 2.32642691786001))<0.00005),0,1))","v":1},null,null,"Y"]
[{"$f":"IF(OR(NOT(ISNUMBER($G$66)),ISERROR($G$66)),1,IF(AND(LEN($G$66)>0,ABS((1-($G$66*-1.16320669651031+-0.222895264625549)/-1.06741096484015))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($H$66)),ISERROR($H$66)),1,IF(AND(LEN($H$66)>0,ABS((1-($H$66* 2.64247953891754+-0.261940002441406)/ 1.91911646325786))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($I$66)),ISERROR($I$66)),1,IF(AND(LEN($I$66)>0,ABS((1-($I$66* 1.98398768901825+ 0.109557747840881)/ 2.09354543685913))<0.00005),0,1))","v":1},null,null,"Z"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Index"]
[{"$f":"SUM($A$69:$C$82)","v":9},null,null,null,5,"Calculating correlation matrix from covariance matrix"]
[]
[null,null,null,null,null,"The correlation between x and y - correl(x,y) - is equal to covar(x,y)/(sd(x)*sd(y)) where covar(x,y) is the covariance between x and y, and sd(x) and sd(y) are the standard deviations of x and y respectively."]
[]
[]
[]
[null,null,null,null,null,"Calculate the correlation matrix below by using the covariance and standard deviation matrices above."]
[]
[]
[null,null,null,null,null,null,"Correlation matrix"]
[null,null,null,null,null,null,"X","Y","Z"]
[{"$f":"IF(OR(NOT(ISNUMBER($G$79)),ISERROR($G$79)),1,IF(AND(LEN($G$79)>0,ABS((1-($G$79*-3.12945067882538+ 0.45914101600647)/-2.67030966281891))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($H$79)),ISERROR($H$79)),1,IF(AND(LEN($H$79)>0,ABS((1-($H$79* 3.16649854183197+ 0.160322070121765)/ 2.47147318333883))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($I$79)),ISERROR($I$79)),1,IF(AND(LEN($I$79)>0,ABS((1-($I$79*-4.31790769100189+-0.0346636772155762)/-3.16956725717972))<0.00005),0,1))","v":1},null,null,"X"]
[{"$f":"IF(OR(NOT(ISNUMBER($G$80)),ISERROR($G$80)),1,IF(AND(LEN($G$80)>0,ABS((1-($G$80*-4.00910675525665+ 0.159927487373352)/-2.76622309125816))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($H$80)),ISERROR($H$80)),1,IF(AND(LEN($H$80)>0,ABS((1-($H$80* 2.7862149477005+-0.0435860157012939)/ 2.74262893199921))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($I$80)),ISERROR($I$80)),1,IF(AND(LEN($I$80)>0,ABS((1-($I$80*-4.91087019443511+ 0.0312865972518921)/-4.02205990251708))<0.00005),0,1))","v":1},null,null,"Y"]
[{"$f":"IF(OR(NOT(ISNUMBER($G$81)),ISERROR($G$81)),1,IF(AND(LEN($G$81)>0,ABS((1-($G$81* 1.1205393075943+ 0.363587379455566)/ 1.17712554151221))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($H$81)),ISERROR($H$81)),1,IF(AND(LEN($H$81)>0,ABS((1-($H$81*-1.85019314289093+-0.219680190086365)/-1.74679730023351))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($I$81)),ISERROR($I$81)),1,IF(AND(LEN($I$81)>0,ABS((1-($I$81* 1.132453083992+-0.134859800338745)/ 0.997593283653256))<0.00005),0,1))","v":1},null,null,"Z"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Index"]
[{"$f":"SUM($A$84:$C$97)","v":9},null,null,null,6,"Calculating covariance matrix from correlation matrix and standard deviation"]
[]
[null,null,null,null,null,"The covariance between x and y - covar(x,y) - is equal to correl(x,y)*sd(x)*sd(y) where correl(x,y) is the correlation between x and y, and sd(x) and sd(y) are the standard deviations of x and y respectively."]
[]
[]
[]
[null,null,null,null,null,"Calculate the covariance matrix below by using the correlation and standard deviation matrices above."]
[]
[]
[null,null,null,null,null,null,"Covariance matrix"]
[null,null,null,null,null,null,"X","Y","Z"]
[{"$f":"IF(OR(NOT(ISNUMBER($G$94)),ISERROR($G$94)),1,IF(AND(LEN($G$94)>0,ABS((1-($G$94* 0.449413657188416+ 0.136580348014832)/ 0.206239464879036))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($H$94)),ISERROR($H$94)),1,IF(AND(LEN($H$94)>0,ABS((1-($H$94* 1.56035959720612+-0.347948551177979)/-0.281633268296719))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($I$94)),ISERROR($I$94)),1,IF(AND(LEN($I$94)>0,ABS((1-($I$94* 1.88358008861542+ 0.443879246711731)/ 0.895938467979431))<0.00005),0,1))","v":1},null,null,"X"]
[{"$f":"IF(OR(NOT(ISNUMBER($G$95)),ISERROR($G$95)),1,IF(AND(LEN($G$95)>0,ABS((1-($G$95* 2.71492779254913+ 0.443620443344116)/ 0.559004874527454))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($H$95)),ISERROR($H$95)),1,IF(AND(LEN($H$95)>0,ABS((1-($H$95*-3.50167334079742+-0.199089646339417)/-0.27568875066936))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($I$95)),ISERROR($I$95)),1,IF(AND(LEN($I$95)>0,ABS((1-($I$95* 2.26034224033356+-0.246908187866211)/-0.0152231082320215))<0.00005),0,1))","v":1},null,null,"Y"]
[{"$f":"IF(OR(NOT(ISNUMBER($G$96)),ISERROR($G$96)),1,IF(AND(LEN($G$96)>0,ABS((1-($G$96* 4.52131450176239+ 0.451875329017639)/ 1.53699080944061))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($H$96)),ISERROR($H$96)),1,IF(AND(LEN($H$96)>0,ABS((1-($H$96* 3.49555313587189+ 0.40328049659729)/ 0.761574693024158))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($I$96)),ISERROR($I$96)),1,IF(AND(LEN($I$96)>0,ABS((1-($I$96*-3.10690462589264+ 0.427108645439148)/-1.76325911581517))<0.00005),0,1))","v":1},null,null,"Z"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Index"]
[{"$f":"SUM($A$99:$C$136)","v":20},null,null,null,7,"Calculating volatility"]
[]
[null,null,null,null,null,"Volatility is the standard deviation of the \"log-returns\" of an asset.  The \"log-return\" r is given by r = ln(at+1/at) where at+1 is the price of the asset at time t+1 and at is the price at time t."]
[]
[]
[]
[null,null,null,null,null,"Calculate the volatility of the asset whose daily prices are shown below."]
[]
[null,null,null,null,null,"Day","Price","Log return"]
[null,null,null,null,null,1,100]
[{"$f":"IF(OR(NOT(ISNUMBER($H$108)),ISERROR($H$108)),1,IF(AND(LEN($H$108)>0,ABS((1-($H$108*-3.86447370052338+ 0.292196750640869)/ 0.265239674811444))<0.00005),0,1))","v":1},null,null,null,null,{"$f":"F107+1","v":2},100.7]
[{"$f":"IF(OR(NOT(ISNUMBER($H$109)),ISERROR($H$109)),1,IF(AND(LEN($H$109)>0,ABS((1-($H$109* 2.29836165904999+ 0.43370258808136)/ 0.445086274845224))<0.00005),0,1))","v":1},null,null,null,null,3,101.2]
[{"$f":"IF(OR(NOT(ISNUMBER($H$110)),ISERROR($H$110)),1,IF(AND(LEN($H$110)>0,ABS((1-($H$110*-0.407506823539734+ 0.408671140670776)/ 0.409074014478716))<0.00005),0,1))","v":1},null,null,null,null,4,101.1]
[{"$f":"IF(OR(NOT(ISNUMBER($H$111)),ISERROR($H$111)),1,IF(AND(LEN($H$111)>0,ABS((1-($H$111*-3.30280363559723+-0.0038677453994751)/ 0.0157918580969993))<0.00005),0,1))","v":1},null,null,null,null,5,100.5]
[{"$f":"IF(OR(NOT(ISNUMBER($H$112)),ISERROR($H$112)),1,IF(AND(LEN($H$112)>0,ABS((1-($H$112*-1.24279916286469+ 0.0979795455932617)/ 0.105421478984957))<0.00005),0,1))","v":1},null,null,null,null,6,99.9]
[{"$f":"IF(OR(NOT(ISNUMBER($H$113)),ISERROR($H$113)),1,IF(AND(LEN($H$113)>0,ABS((1-($H$113*-4.64367687702179+-0.153119444847107)/-0.153119444847107))<0.00005),0,1))","v":1},null,null,null,null,7,99.9]
[{"$f":"IF(OR(NOT(ISNUMBER($H$114)),ISERROR($H$114)),1,IF(AND(LEN($H$114)>0,ABS((1-($H$114* 2.28016197681427+-0.422531843185425)/-0.450087006043348))<0.00005),0,1))","v":1},null,null,null,null,8,98.7]
[{"$f":"IF(OR(NOT(ISNUMBER($H$115)),ISERROR($H$115)),1,IF(AND(LEN($H$115)>0,ABS((1-($H$115*-2.61964380741119+-0.432936787605286)/-0.454084380209976))<0.00005),0,1))","v":1},null,null,null,null,9,99.5]
[{"$f":"IF(OR(NOT(ISNUMBER($H$116)),ISERROR($H$116)),1,IF(AND(LEN($H$116)>0,ABS((1-($H$116* 3.35290491580963+-0.297821521759033)/-0.311327702824941))<0.00005),0,1))","v":1},null,null,null,null,10,99.1]
[{"$f":"IF(OR(NOT(ISNUMBER($H$117)),ISERROR($H$117)),1,IF(AND(LEN($H$117)>0,ABS((1-($H$117* 2.74305045604706+ 0.477053761482239)/ 0.44363547457571))<0.00005),0,1))","v":1},null,null,null,null,11,97.9]
[{"$f":"IF(OR(NOT(ISNUMBER($H$118)),ISERROR($H$118)),1,IF(AND(LEN($H$118)>0,ABS((1-($H$118* 2.9892235994339+-0.0195276737213135)/ 0.00782687649413395))<0.00005),0,1))","v":1},null,null,null,null,12,98.8]
[{"$f":"IF(OR(NOT(ISNUMBER($H$119)),ISERROR($H$119)),1,IF(AND(LEN($H$119)>0,ABS((1-($H$119* 1.81855142116547+-0.222891449928284)/-0.199119197416384))<0.00005),0,1))","v":1},null,null,null,null,13,100.1]
[{"$f":"IF(OR(NOT(ISNUMBER($H$120)),ISERROR($H$120)),1,IF(AND(LEN($H$120)>0,ABS((1-($H$120*-4.19357240200043+-0.160343170166016)/-0.130914471135683))<0.00005),0,1))","v":1},null,null,null,null,14,99.4]
[{"$f":"IF(OR(NOT(ISNUMBER($H$121)),ISERROR($H$121)),1,IF(AND(LEN($H$121)>0,ABS((1-($H$121*-2.58735477924347+-0.062008261680603)/-0.0879079251845606))<0.00005),0,1))","v":1},null,null,null,null,15,100.4]
[{"$f":"IF(OR(NOT(ISNUMBER($H$122)),ISERROR($H$122)),1,IF(AND(LEN($H$122)>0,ABS((1-($H$122*-1.69340789318085+ 0.14160943031311)/ 0.128169614583069))<0.00005),0,1))","v":1},null,null,null,null,16,101.2]
[{"$f":"IF(OR(NOT(ISNUMBER($H$123)),ISERROR($H$123)),1,IF(AND(LEN($H$123)>0,ABS((1-($H$123*-0.705991387367249+ 0.341600298881531)/ 0.333278103645923))<0.00005),0,1))","v":1},null,null,null,null,17,102.4]
[{"$f":"IF(OR(NOT(ISNUMBER($H$124)),ISERROR($H$124)),1,IF(AND(LEN($H$124)>0,ABS((1-($H$124*-0.342192053794861+-0.0515971183776855)/-0.0539283627972161))<0.00005),0,1))","v":1},null,null,null,null,18,103.1]
[{"$f":"IF(OR(NOT(ISNUMBER($H$125)),ISERROR($H$125)),1,IF(AND(LEN($H$125)>0,ABS((1-($H$125* 1.22545897960663+ 0.171589016914368)/ 0.175149675050209))<0.00005),0,1))","v":1},null,null,null,null,19,103.4]
[]
[]
[{"$f":"IF(OR(NOT(ISNUMBER($J$128)),ISERROR($J$128)),1,IF(AND(LEN($J$128)>0,ABS((1-($J$128* 4.97543156147003+-0.462069749832153)/-0.421683768346782))<0.00005),0,1))","v":1},null,null,null,null,"Standard deviation of log return:",null,null,"[%]",null,"<- Use STDEV"]
[]
[null,null,null,null,null,"The volatility above is the daily volatility. To convert to a yearly volatility multiply by the square root of the number of trading days in a year."]
[]
[]
[null,null,null,null,null,"Number of trading days in year:",null,null,"[#]",252]
[]
[{"$f":"IF(OR(NOT(ISNUMBER($J$135)),ISERROR($J$135)),1,IF(AND(LEN($J$135)>0,ABS((1-($J$135* 0.495204329490662+-0.446004509925842)/-0.382195120579447))<0.00005),0,1))","v":1},null,null,null,null,"Yearly volatility",null,null,"[%]"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Index"]
[{"$f":"SUM($A$138:$C$167)","v":39},null,null,null,{"$f":"E98+1","v":8},"Calculating correlation of log returns"]
[]
[null,null,null,null,null,"Calculate the correlation between the log returns of the two assets below."]
[]
[null,null,null,null,null,"Day","Asset 1 price","Asset 2 price","Asset 1 log return","Asset 2 log return"]
[null,null,null,null,null,1,1.1789000000000001,1.91]
[{"$f":"IF(OR(NOT(ISNUMBER($I$143)),ISERROR($I$143)),1,IF(AND(LEN($I$143)>0,ABS((1-($I$143* 1.10333502292633+-0.330470085144043)/-0.330376498900047))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($J$143)),ISERROR($J$143)),1,IF(AND(LEN($J$143)>0,ABS((1-($J$143*-0.0519067049026489+-0.0521348714828491)/-0.0517091806328142))<0.00005),0,1))","v":1},null,null,null,{"$f":"F142+1","v":2},1.179,1.8944000000000001]
[{"$f":"IF(OR(NOT(ISNUMBER($I$144)),ISERROR($I$144)),1,IF(AND(LEN($I$144)>0,ABS((1-($I$144* 4.89515602588654+ 0.0996105670928955)/ 0.0800573746294798))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($J$144)),ISERROR($J$144)),1,IF(AND(LEN($J$144)>0,ABS((1-($J$144* 2.5168651342392+-0.214123845100403)/-0.230652411898313))<0.00005),0,1))","v":1},null,null,null,3,1.1742999999999999,1.8819999999999999]
[{"$f":"IF(OR(NOT(ISNUMBER($I$145)),ISERROR($I$145)),1,IF(AND(LEN($I$145)>0,ABS((1-($I$145* 3.99554789066315+ 0.347276210784912)/ 0.309328903870284))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($J$145)),ISERROR($J$145)),1,IF(AND(LEN($J$145)>0,ABS((1-($J$145*-1.7466002702713+ 0.364964604377747)/ 0.397374162663417))<0.00005),0,1))","v":1},null,null,null,4,1.1632,1.8473999999999999]
[{"$f":"IF(OR(NOT(ISNUMBER($I$146)),ISERROR($I$146)),1,IF(AND(LEN($I$146)>0,ABS((1-($I$146* 0.121429562568665+-0.290048837661743)/-0.289767304051507))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($J$146)),ISERROR($J$146)),1,IF(AND(LEN($J$146)>0,ABS((1-($J$146* 3.85996758937836+-0.0130506753921509)/-0.027284845322941))<0.00005),0,1))","v":1},null,null,null,5,1.1658999999999999,1.8406]
[{"$f":"IF(OR(NOT(ISNUMBER($I$147)),ISERROR($I$147)),1,IF(AND(LEN($I$147)>0,ABS((1-($I$147* 4.84323561191559+-0.47099494934082)/-0.508526668507885))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($J$147)),ISERROR($J$147)),1,IF(AND(LEN($J$147)>0,ABS((1-($J$147* 4.72047984600067+ 0.349156975746155)/ 0.278878145175675))<0.00005),0,1))","v":1},null,null,null,6,1.1569,1.8133999999999999]
[{"$f":"IF(OR(NOT(ISNUMBER($I$148)),ISERROR($I$148)),1,IF(AND(LEN($I$148)>0,ABS((1-($I$148*-2.13383376598358+-0.294622182846069)/-0.285565228321936))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($J$148)),ISERROR($J$148)),1,IF(AND(LEN($J$148)>0,ABS((1-($J$148*-0.568261742591858+ 0.185047030448914)/ 0.18642752564386))<0.00005),0,1))","v":1},null,null,null,7,1.1519999999999999,1.8089999999999999]
[{"$f":"IF(OR(NOT(ISNUMBER($I$149)),ISERROR($I$149)),1,IF(AND(LEN($I$149)>0,ABS((1-($I$149*-2.18856275081635+ 0.46520471572876)/ 0.423057775646285))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($J$149)),ISERROR($J$149)),1,IF(AND(LEN($J$149)>0,ABS((1-($J$149*-3.16531479358673+ 0.154836773872375)/ 0.0634320658086116))<0.00005),0,1))","v":1},null,null,null,8,1.1744000000000001,1.8620000000000001]
[{"$f":"IF(OR(NOT(ISNUMBER($I$150)),ISERROR($I$150)),1,IF(AND(LEN($I$150)>0,ABS((1-($I$150*-4.5024698972702+ 0.375441312789917)/ 0.410465189926726))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($J$150)),ISERROR($J$150)),1,IF(AND(LEN($J$150)>0,ABS((1-($J$150*-4.45434629917145+-0.0138736963272095)/ 0.0504614204688376))<0.00005),0,1))","v":1},null,null,null,9,1.1653,1.8352999999999999]
[{"$f":"IF(OR(NOT(ISNUMBER($I$151)),ISERROR($I$151)),1,IF(AND(LEN($I$151)>0,ABS((1-($I$151*-0.278558135032654+-0.390511512756348)/-0.389865344706309))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($J$151)),ISERROR($J$151)),1,IF(AND(LEN($J$151)>0,ABS((1-($J$151*-4.01238262653351+-0.135476469993591)/-0.143120978004183))<0.00005),0,1))","v":1},null,null,null,10,1.1626000000000001,1.8388]
[{"$f":"IF(OR(NOT(ISNUMBER($I$152)),ISERROR($I$152)),1,IF(AND(LEN($I$152)>0,ABS((1-($I$152*-4.4600647687912+ 0.462817430496216)/ 0.468191465638448))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($J$152)),ISERROR($J$152)),1,IF(AND(LEN($J$152)>0,ABS((1-($J$152* 4.92144048213959+ 0.07426917552948)/ 0.0485080323968302))<0.00005),0,1))","v":1},null,null,null,11,1.1612,1.8291999999999999]
[{"$f":"IF(OR(NOT(ISNUMBER($I$153)),ISERROR($I$153)),1,IF(AND(LEN($I$153)>0,ABS((1-($I$153*-4.94921147823334+ 0.118594646453857)/ 0.116890079025873))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($J$153)),ISERROR($J$153)),1,IF(AND(LEN($J$153)>0,ABS((1-($J$153* 2.47712790966034+-0.111138224601746)/-0.110731993768628))<0.00005),0,1))","v":1},null,null,null,12,1.1616,1.8294999999999999]
[{"$f":"IF(OR(NOT(ISNUMBER($I$154)),ISERROR($I$154)),1,IF(AND(LEN($I$154)>0,ABS((1-($I$154* 0.67404568195343+-0.336693048477173)/-0.339076378368314))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($J$154)),ISERROR($J$154)),1,IF(AND(LEN($J$154)>0,ABS((1-($J$154* 1.68507516384125+-0.288317322731018)/-0.309729220764855))<0.00005),0,1))","v":1},null,null,null,13,1.1575,1.8064]
[{"$f":"IF(OR(NOT(ISNUMBER($I$155)),ISERROR($I$155)),1,IF(AND(LEN($I$155)>0,ABS((1-($I$155* 0.933266282081604+ 0.352386474609375)/ 0.35214455998874))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($J$155)),ISERROR($J$155)),1,IF(AND(LEN($J$155)>0,ABS((1-($J$155* 0.507318377494812+ 0.466621041297913)/ 0.469617217601131))<0.00005),0,1))","v":1},null,null,null,14,1.1572,1.8170999999999999]
[{"$f":"IF(OR(NOT(ISNUMBER($I$156)),ISERROR($I$156)),1,IF(AND(LEN($I$156)>0,ABS((1-($I$156*-1.26322448253632+ 0.125835657119751)/ 0.126381585855737))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($J$156)),ISERROR($J$156)),1,IF(AND(LEN($J$156)>0,ABS((1-($J$156*-3.63121569156647+ 0.238698840141296)/ 0.227923711488356))<0.00005),0,1))","v":1},null,null,null,15,1.1567000000000001,1.8225]
[{"$f":"IF(OR(NOT(ISNUMBER($I$157)),ISERROR($I$157)),1,IF(AND(LEN($I$157)>0,ABS((1-($I$157* 2.15891420841217+ 0.373852252960205)/ 0.377022876098698))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($J$157)),ISERROR($J$157)),1,IF(AND(LEN($J$157)>0,ABS((1-($J$157* 3.18854033946991+ 0.164695858955383)/ 0.180751155930407))<0.00005),0,1))","v":1},null,null,null,16,1.1584000000000001,1.8317000000000001]
[{"$f":"IF(OR(NOT(ISNUMBER($I$158)),ISERROR($I$158)),1,IF(AND(LEN($I$158)>0,ABS((1-($I$158*-2.27871119976044+-0.0475456714630127)/-0.0471522136014182))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($J$158)),ISERROR($J$158)),1,IF(AND(LEN($J$158)>0,ABS((1-($J$158* 0.911044478416443+-0.426225304603577)/-0.42255213348401))<0.00005),0,1))","v":1},null,null,null,17,1.1581999999999999,1.8391]
[{"$f":"IF(OR(NOT(ISNUMBER($I$159)),ISERROR($I$159)),1,IF(AND(LEN($I$159)>0,ABS((1-($I$159*-3.82597863674164+ 0.449105262756348)/ 0.46665337605524))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($J$159)),ISERROR($J$159)),1,IF(AND(LEN($J$159)>0,ABS((1-($J$159*-2.46260464191437+ 0.378105759620667)/ 0.388572381853935))<0.00005),0,1))","v":1},null,null,null,18,1.1529,1.8312999999999999]
[{"$f":"IF(OR(NOT(ISNUMBER($I$160)),ISERROR($I$160)),1,IF(AND(LEN($I$160)>0,ABS((1-($I$160* 0.776999592781067+-0.301661252975464)/-0.309722962815189))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($J$160)),ISERROR($J$160)),1,IF(AND(LEN($J$160)>0,ABS((1-($J$160* 3.65658223628998+-0.286507725715637)/-0.296705172874333))<0.00005),0,1))","v":1},null,null,null,19,1.141,1.8262]
[{"$f":"IF(OR(NOT(ISNUMBER($I$161)),ISERROR($I$161)),1,IF(AND(LEN($I$161)>0,ABS((1-($I$161*-1.91887319087982+-0.452616214752197)/-0.44823868341937))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($J$161)),ISERROR($J$161)),1,IF(AND(LEN($J$161)>0,ABS((1-($J$161*-0.52326500415802+-0.170004725456238)/-0.164966232884629))<0.00005),0,1))","v":1},null,null,null,20,1.1384000000000001,1.8087]
[]
[]
[{"$f":"IF(OR(NOT(ISNUMBER($H$164)),ISERROR($H$164)),1,IF(AND(LEN($H$164)>0,ABS((1-($H$164* 1.2095719575882+-0.128210306167603)/ 0.89901402621316))<0.00005),0,1))","v":1},null,null,null,null,"Correlation:","[%]"]
[]
[]
[null,null,null,null,null,null,null,"Copyright (c) 2020 Tykoh Group Pty Ltd.  All rights reserved.",null,null,null,null,null,null,null,null,"Index"]
[null,null,null,null,null,null,null,"www.tykoh.com"]

{"sheet":"Interpolation_and_extrapolation","index":24,"n_rows":248,"n_cols":20,"rows_kept":248,"cut":false,"hidden":false,"merged":[[246,10,246,16],[247,10,247,16],[0,8,0,14],[2,8,4,17],[8,8,10,17],[28,8,29,17],[33,8,34,17],[109,16,110,17],[38,8,38,10],[87,15,88,17],[59,8,59,17],[82,9,82,14],[54,8,55,17],[92,8,93,16],[105,8,106,16],[143,8,147,16],[149,8,151,16],[225,8,225,17],[118,8,118,16],[199,8,201,17],[203,8,203,17],[173,8,175,16],[177,8,177,16]]}
[null,null,null,null,null,null,null,null,"Click here to see what your answer should look like."]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Interpolation","Interpolation_and_extrapolation"]
[null,null,null,null,null,null,null,null,"Interpolation involves \"filling in the gaps\" between discrete data points.  In this section we review and apply various interpolation methods including two of the most used:  Linear and cubic spline interpolation.  We also look at \"curve fitting\" and at extrapolation."]
[]
[]
[]
[{"$f":"SUM($A$8:$F$26)","v":2},null,null,null,null,null,null,1,"Linear interpolation"]
[]
[null,null,null,null,null,null,null,null,{"$f":"\"Consider the two (x,y) data points defined in cells \" & ADDRESS(ROW(J13),COLUMN(J13),4) & \":\" & ADDRESS(ROW(J16),COLUMN(J16),4) &\".  Calculate by using linear interpolation the y value that corresponds to the x value in cell \" & ADDRESS(ROW(J18),COLUMN(J18),4)  &\".  Also calculate the x value that correponds to the y value in cell \" & ADDRESS(ROW(J21),COLUMN(J21),4)  &\".\"","v":"Consider the two (x,y) data points defined in cells J13:J16.  Calculate by using linear interpolation the y value that corresponds to the x value in cell J18.  Also calculate the x value that correponds to the y value in cell J21."}]
[]
[]
[]
[null,null,null,null,null,null,null,null,"x1",1.5]
[null,null,null,null,null,null,null,null,"x2",6]
[null,null,null,null,null,null,null,null,"y1",2]
[null,null,null,null,null,null,null,null,"y2",10,null,null,{"$f":"J18","v":3},{"$f":"M16","v":3},0,{"$f":"N17","v":0}]
[null,null,null,null,null,null,null,null,null,null,null,null,0,{"$f":"J19","v":0},{"$f":"J18","v":3},{"$f":"P16","v":0}]
[null,null,null,null,null,null,null,null,"x value to interpolate",3]
[{"$f":"IF(OR(NOT(ISNUMBER($J$19)),ISERROR($J$19)),1,IF(AND(LEN($J$19)>0,ABS((1-($J$19* 4.35637414455414+ 0.232558608055115)/ 20.5623046159744))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,"y at that x",null,null,null,{"$f":"J22","v":0},0,0,{"$f":"J21","v":7}]
[null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"M19","v":0},{"$f":"J21","v":7},{"$f":"M20","v":0},{"$f":"P19","v":7}]
[null,null,null,null,null,null,null,null,"y value to interpolate",7]
[{"$f":"IF(OR(NOT(ISNUMBER($J$22)),ISERROR($J$22)),1,IF(AND(LEN($J$22)>0,ABS((1-($J$22*-4.36098039150238+-0.15894889831543)/-18.9656768366694))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,"x at that y"]
[]
[]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Index"]
[{"$f":"SUM($A$28:$F$141)","v":47},null,null,null,null,null,null,2,"Cubic spline interpolation"]
[]
[null,null,null,null,null,null,null,null,"Cubic spline interpolation fits a curve (cubic) between data points.  In the method described below the leftmost and rightmost curve segments have zero curvature at the leftmost and rightmost points respectively."]
[]
[]
[null,null,null,null,null,null,null,null,"[For more information on this method see:",null,null,null,"http://www.scribd.com/doc/24255441/Cubic-Spline-Interpolation"]
[]
[null,null,null,null,null,null,null,null,{"$f":"\"Consider the table of (x,y) values shown below in cells \" & ADDRESS(ROW(J41),COLUMN(J41),4) & \":\" & ADDRESS(ROW(K48),COLUMN(K48),4) & \".  Use cubic spline interpolation to find the y value corresponding to the x value in cell \" &  ADDRESS(ROW(K50),COLUMN(K50),4) &\".\"","v":"Consider the table of (x,y) values shown below in cells J41:K48.  Use cubic spline interpolation to find the y value corresponding to the x value in cell K50."}]
[]
[]
[]
[]
[null,null,null,null,null,null,null,null,"Table to interpolate"]
[null,null,null,null,null,null,null,null,"i (interval)","xi","yi"]
[null,null,null,null,null,null,null,null,1,1,1]
[null,null,null,null,null,null,null,null,{"$f":"I41+1","v":2},{"$f":"J41+0.5","v":1.5},0]
[null,null,null,null,null,null,null,null,3,2,0.5,null,null,{"$f":"K50","v":3.25},0]
[null,null,null,null,null,null,null,null,4,2.5,0.8,null,null,{"$f":"N43","v":3.25},{"$f":"MAX(K41:K48)","v":1}]
[null,null,null,null,null,null,null,null,5,3,0.5]
[null,null,null,null,null,null,null,null,6,3.5,0.4]
[null,null,null,null,null,null,null,null,7,4,1]
[null,null,null,null,null,null,null,null,8,4.5,0.5]
[]
[null,null,null,null,null,null,null,null,"x value to interpolate",null,3.25]
[]
[]
[]
[]
[null,null,null,null,null,null,null,null,"Step 1 - Calculate \"hh\" - the interval between successive x values.  [x values are spaced evenly - so you can calculate the difference any two successive intrervals.]"]
[]
[]
[null,null,null,null,null,null,null,null,"hh",{"$f":"J42-J41","v":0.5}]
[]
[null,null,null,null,null,null,null,null,"Step 2 - Calculate which interval the interpolated x value is in"]
[]
[null,null,null,null,null,null,null,null,"i",{"$f":"FLOOR((x_to_interpolate-first_x)/hh,1)+1","v":5},"<- =FLOOR((x_to_interpolate-first_x)/hh,1)+1"]
[]
[null,null,null,null,null,null,null,null,"Step 3 - Calculate x's offset within the interval it is in"]
[]
[null,null,null,null,null,null,null,null,"dX",{"$f":"x_to_interpolate-first_x-(i-1)*hh","v":0.25},"<- =x_to_interpolate-first_x-(i-1)*hh"]
[]
[null,null,null,null,null,null,null,null,"Step 4 - Calculate a vector of curvatures of yi"]
[]
[null,null,null,null,null,null,null,null,"i","yi","Curvaturei"]
[null,null,null,null,null,null,null,null,{"$f":"I41","v":1},{"$f":"K41","v":1}]
[null,null,null,null,null,null,null,null,{"$f":"I71+1","v":2},0,{"$f":"6/(hh^2)*(J71-2*J72+J73)","v":36},"<- Copy and paste this formula down"]
[{"$f":"IF(OR(NOT(ISNUMBER($K$73)),ISERROR($K$73)),1,IF(AND(LEN($K$73)>0,ABS((1-($K$73*-1.16433918476105+ 0.0716339349746704)/ 5.6604620218277))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,3,0.5]
[{"$f":"IF(OR(NOT(ISNUMBER($K$74)),ISERROR($K$74)),1,IF(AND(LEN($K$74)>0,ABS((1-($K$74*-2.51908004283905+ 0.434232950210571)/ 36.7089855670929))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,4,0.8]
[{"$f":"IF(OR(NOT(ISNUMBER($K$75)),ISERROR($K$75)),1,IF(AND(LEN($K$75)>0,ABS((1-($K$75*-0.832353234291077+-0.216194272041321)/-4.21148979663849))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,5,0.5]
[{"$f":"IF(OR(NOT(ISNUMBER($K$76)),ISERROR($K$76)),1,IF(AND(LEN($K$76)>0,ABS((1-($K$76* 4.26273882389069+ 0.20559549331665)/ 71.8196077346802))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,6,0.4]
[{"$f":"IF(OR(NOT(ISNUMBER($K$77)),ISERROR($K$77)),1,IF(AND(LEN($K$77)>0,ABS((1-($K$77* 4.34952437877655+-0.0175837278366089)/-114.845027327538))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,7,1]
[null,null,null,null,null,null,null,null,8,0.5]
[]
[]
[null,null,null,null,null,null,null,null,"Step 5 - Generate an \"M\" matrix."]
[]
[null,null,null,null,null,null,null,null,"i","\"M\" matrix"]
[null,null,null,null,null,null,null,null,{"$f":"I71","v":1}]
[null,null,null,null,null,null,null,null,2,4,1,0,0,0,0]
[null,null,null,null,null,null,null,null,3,1,4,1,0,0,0]
[null,null,null,null,null,null,null,null,4,0,1,4,1,0,0]
[null,null,null,null,null,null,null,null,5,0,0,1,4,1,0,"<- Continue the pattern on the two rows below."]
[{"$f":"IF(OR(NOT(ISNUMBER($J$89)),ISERROR($J$89)),1,IF(AND(LEN($J$89)>0,ABS((1-($J$89*-1.79079234600067+ 0.300219297409058)/ 0.300219297409058))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($K$89)),ISERROR($K$89)),1,IF(AND(LEN($K$89)>0,ABS((1-($K$89*-4.34612333774567+-0.401809334754944)/-0.401809334754944))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($L$89)),ISERROR($L$89)),1,IF(AND(LEN($L$89)>0,ABS((1-($L$89* 2.02357351779938+-0.280369758605957)/-0.280369758605957))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($M$89)),ISERROR($M$89)),1,IF(AND(LEN($M$89)>0,ABS((1-($M$89*-1.34007275104523+ 0.269861817359924)/-1.0702109336853))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($N$89)),ISERROR($N$89)),1,IF(AND(LEN($N$89)>0,ABS((1-($N$89*-2.83115088939667+-0.162575483322144)/-11.4871790409088))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($O$89)),ISERROR($O$89)),1,IF(AND(LEN($O$89)>0,ABS((1-($O$89*-2.21520960330963+-0.0152045488357544)/-2.23041415214539))<0.00005),0,1))","v":1},null,null,6]
[{"$f":"IF(OR(NOT(ISNUMBER($J$90)),ISERROR($J$90)),1,IF(AND(LEN($J$90)>0,ABS((1-($J$90* 4.64906275272369+ 0.164893627166748)/ 0.164893627166748))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($K$90)),ISERROR($K$90)),1,IF(AND(LEN($K$90)>0,ABS((1-($K$90* 3.31472098827362+-0.03038489818573)/-0.03038489818573))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($L$90)),ISERROR($L$90)),1,IF(AND(LEN($L$90)>0,ABS((1-($L$90*-1.70949161052704+ 0.366649389266968)/ 0.366649389266968))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($M$90)),ISERROR($M$90)),1,IF(AND(LEN($M$90)>0,ABS((1-($M$90* 0.936364531517029+-0.169172883033752)/-0.169172883033752))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($N$90)),ISERROR($N$90)),1,IF(AND(LEN($N$90)>0,ABS((1-($N$90* 0.522995591163635+-0.473751068115234)/ 0.0492445230484009))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($O$90)),ISERROR($O$90)),1,IF(AND(LEN($O$90)>0,ABS((1-($O$90* 3.76800715923309+-0.0545543432235718)/ 15.0174742937088))<0.00005),0,1))","v":1},null,null,7]
[null,null,null,null,null,null,null,null,8]
[]
[null,null,null,null,null,null,null,null,{"$f":"\"Step 6 - Generate an 'M' vector in cells \" & ADDRESS(ROW(K98),COLUMN(K98),4)&\":\"&ADDRESS(ROW(K103),COLUMN(K103),4) &\" by multiplying the inverse of the 'M' matrix in \" & ADDRESS(ROW(J85),COLUMN(J85),4)&\":\"&ADDRESS(ROW(O90),COLUMN(O90),4) & \" by the y curvatures in cells \" & ADDRESS(ROW(K72),COLUMN(K72),4)&\":\"&ADDRESS(ROW(K77),COLUMN(K77),4)&\".\"","v":"Step 6 - Generate an 'M' vector in cells K98:K103 by multiplying the inverse of the 'M' matrix in J85:O90 by the y curvatures in cells K72:K77."}]
[]
[]
[null,null,null,null,null,null,null,null,"i","yi","Mi"]
[null,null,null,null,null,null,null,null,{"$f":"I84","v":1},{"$f":"J71","v":1},0]
[{"$f":"IF(OR(NOT(ISNUMBER($K$98)),ISERROR($K$98)),1,IF(AND(LEN($K$98)>0,ABS((1-($K$98* 0.661099553108215+-0.338180303573608)/ 6.08849767433004))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,2,0]
[{"$f":"IF(OR(NOT(ISNUMBER($K$99)),ISERROR($K$99)),1,IF(AND(LEN($K$99)>0,ABS((1-($K$99*-3.10917437076569+ 0.101617693901062)/ 9.07090752417998))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,3,0.5]
[{"$f":"IF(OR(NOT(ISNUMBER($K$100)),ISERROR($K$100)),1,IF(AND(LEN($K$100)>0,ABS((1-($K$100*-4.3145889043808+ 0.491684436798096)/ 13.3580820187798))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,4,0.8]
[{"$f":"IF(OR(NOT(ISNUMBER($K$101)),ISERROR($K$101)),1,IF(AND(LEN($K$101)>0,ABS((1-($K$101* 4.38013732433319+ 0.389248013496399)/ 2.19848096395268))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,5,0.5]
[{"$f":"IF(OR(NOT(ISNUMBER($K$102)),ISERROR($K$102)),1,IF(AND(LEN($K$102)>0,ABS((1-($K$102* 3.52378666400909+ 0.449986219406128)/ 22.0502779516556))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,6,0.4]
[{"$f":"IF(OR(NOT(ISNUMBER($K$103)),ISERROR($K$103)),1,IF(AND(LEN($K$103)>0,ABS((1-($K$103*-1.16334974765778+ 0.340624213218689)/ 9.8015230748302))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,7,1]
[null,null,null,null,null,null,null,null,8,0.5]
[]
[null,null,null,null,null,null,null,null,"Step 7 - Calculate the interpolated y values within each interval (in the step following we will choose only one of the intervals)"]
[]
[]
[null,null,null,null,null,null,null,null,"i","xi","yi","Mi","ai","bi","ci","y"]
[null,null,null,null,null,null,null,null,{"$f":"I97","v":1},{"$f":"J41","v":1},{"$f":"J97","v":1},0,{"$f":"(L111-L110)/(6*hh)","v":0},{"$f":"L110/2","v":0},{"$f":"(K111-K110)/hh-(L111+2*L110)*hh/6","v":-2},{"$f":"M110*dX^3+N110*dX^2+O110*dX+K110","v":0.5},"<- Copy and paste these formulae down"]
[{"$f":"IF(OR(NOT(ISNUMBER($M$111)),ISERROR($M$111)),1,IF(AND(LEN($M$111)>0,ABS((1-($M$111*-1.16740167140961+-0.0476865768432617)/ 4.85772642373465))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($N$111)),ISERROR($N$111)),1,IF(AND(LEN($N$111)>0,ABS((1-($N$111* 3.41771304607391+ 0.321041703224182)/ 16.9331699861198))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($O$111)),ISERROR($O$111)),1,IF(AND(LEN($O$111)>0,ABS((1-($O$111* 1.2779837846756+-0.0886752605438232)/-0.574054467805019))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($P$111)),ISERROR($P$111)),1,IF(AND(LEN($P$111)>0,ABS((1-($P$111*-3.63143503665924+ 0.169428706169128)/-0.350523929790875))<0.00005),0,1))","v":1},null,null,null,null,2,1.5,0,{"$f":"K98","v":0}]
[{"$f":"IF(OR(NOT(ISNUMBER($M$112)),ISERROR($M$112)),1,IF(AND(LEN($M$112)>0,ABS((1-($M$112*-3.68290364742279+-0.497625827789307)/-0.37819398157951))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($N$112)),ISERROR($N$112)),1,IF(AND(LEN($N$112)>0,ABS((1-($N$112*-1.94641411304474+ 0.0889712572097778)/ 2.89646132174164))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($O$112)),ISERROR($O$112)),1,IF(AND(LEN($O$112)>0,ABS((1-($O$112*-1.52064502239227+ 0.179136037826538)/-1.84226141275716))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($P$112)),ISERROR($P$112)),1,IF(AND(LEN($P$112)>0,ABS((1-($P$112* 0.487546324729919+-0.21226179599762)/ 0.149336457211551))<0.00005),0,1))","v":1},null,null,null,null,3,2,0.5,0]
[{"$f":"IF(OR(NOT(ISNUMBER($M$113)),ISERROR($M$113)),1,IF(AND(LEN($M$113)>0,ABS((1-($M$113*-2.85230576992035+-0.0607700347900391)/-3.28874534513892))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($N$113)),ISERROR($N$113)),1,IF(AND(LEN($N$113)>0,ABS((1-($N$113*-0.633142590522766+-0.130693793296814)/ 0.813343341675709))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($O$113)),ISERROR($O$113)),1,IF(AND(LEN($O$113)>0,ABS((1-($O$113* 4.83981430530548+-0.160154104232788)/-0.825192140001318))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($P$113)),ISERROR($P$113)),1,IF(AND(LEN($P$113)>0,ABS((1-($P$113*-1.3991791009903+ 0.473384737968445)/-0.492245909193872))<0.00005),0,1))","v":1},null,null,null,null,4,2.5,0.8,0]
[{"$f":"IF(OR(NOT(ISNUMBER($M$114)),ISERROR($M$114)),1,IF(AND(LEN($M$114)>0,ABS((1-($M$114*-2.01056897640228+-0.236630916595459)/-4.06797005293992))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($N$114)),ISERROR($N$114)),1,IF(AND(LEN($N$114)>0,ABS((1-($N$114*-2.65712082386017+ 0.166441082954407)/-0.382326020894696))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($O$114)),ISERROR($O$114)),1,IF(AND(LEN($O$114)>0,ABS((1-($O$114* 0.22752583026886+ 0.433005094528198)/ 0.255611544415452))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($P$114)),ISERROR($P$114)),1,IF(AND(LEN($P$114)>0,ABS((1-($P$114*-0.478134751319885+ 0.0823253393173218)/-0.0839541919429619))<0.00005),0,1))","v":1},null,null,null,null,5,3,0.5,0]
[{"$f":"IF(OR(NOT(ISNUMBER($M$115)),ISERROR($M$115)),1,IF(AND(LEN($M$115)>0,ABS((1-($M$115*-1.83640420436859+-0.321595191955566)/ 8.40886343569741))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($N$115)),ISERROR($N$115)),1,IF(AND(LEN($N$115)>0,ABS((1-($N$115*-4.12674725055695+ 0.31289541721344)/-12.3352801133496))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($O$115)),ISERROR($O$115)),1,IF(AND(LEN($O$115)>0,ABS((1-($O$115*-0.333096385002136+-0.0487105846405029)/-0.333862144731648))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($P$115)),ISERROR($P$115)),1,IF(AND(LEN($P$115)>0,ABS((1-($P$115*-1.52959406375885+-0.451357960700989)/-1.56993601738393))<0.00005),0,1))","v":1},null,null,null,null,6,3.5,0.4,0]
[{"$f":"IF(OR(NOT(ISNUMBER($M$116)),ISERROR($M$116)),1,IF(AND(LEN($M$116)>0,ABS((1-($M$116* 4.64772760868073+ 0.0910754203796387)/ 12.6902331344371))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($N$116)),ISERROR($N$116)),1,IF(AND(LEN($N$116)>0,ABS((1-($N$116*-2.2441703081131+-0.0306862592697144)/ 9.09462981873548))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($O$116)),ISERROR($O$116)),1,IF(AND(LEN($O$116)>0,ABS((1-($O$116*-1.66138827800751+ 0.340499639511108)/-0.249975218759784))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($P$116)),ISERROR($P$116)),1,IF(AND(LEN($P$116)>0,ABS((1-($P$116* 2.07241952419281+ 0.384541869163513)/ 2.2021983130635))<0.00005),0,1))","v":1},null,null,null,null,7,4,1,0]
[null,null,null,null,null,null,null,null,8,4.5,0.5,0]
[]
[null,null,null,null,null,null,null,null,"Step 8 - Choose the interpolated y value in the interval we calculated in step 2."]
[]
[null,null,null,null,null,null,null,null,"Interpolated y value:",null,{"$f":"CHOOSE(i,P110,P111,P112,P113,P114,P115,P116)","v":0}]
[]
[]
[]
[null,null,null,null,null,null,null,null,null,{"$f":"K121","v":0}]
[null,null,null,null,null,null,null,null,{"$f":"first_x","v":1},1]
[null,null,null,null,null,null,null,null,{"$f":"I126+0.25","v":1.25},0.5]
[null,null,null,null,null,null,null,null,1.5,0,null,null,null,{"$f":"x_to_interpolate","v":3.25},0]
[null,null,null,null,null,null,null,null,1.75,0,null,null,null,{"$f":"N128","v":3.25},{"$f":"K121","v":0}]
[null,null,null,null,null,null,null,null,2,0,null,null,null,0,{"$f":"O129","v":0}]
[null,null,null,null,null,null,null,null,2.25,0]
[null,null,null,null,null,null,null,null,2.5,0]
[null,null,null,null,null,null,null,null,2.75,0]
[null,null,null,null,null,null,null,null,3,0]
[null,null,null,null,null,null,null,null,3.25,0]
[null,null,null,null,null,null,null,null,3.5,0]
[null,null,null,null,null,null,null,null,3.75,0]
[null,null,null,null,null,null,null,null,4,0]
[null,null,null,null,null,null,null,null,4.25,0]
[null,null,null,null,null,null,null,null,{"$f":"I139+0.25-0.0001","v":4.4999000000000002},0]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Index"]
[{"$f":"SUM($A$143:$F$171)","v":15},null,null,null,null,null,null,3,"TREND function to perform linear interpolation / extrapolation"]
[]
[null,null,null,null,null,null,null,null,"The TREND function performs a \"least-squares\" straight-line fit to a set of data points.  Another such function is the GROWTH function - that function performs a fit to an exponential or growth curve.  Other types of curve can be fitted to by transforming them into straight lines, using TREND and then reversing the transformation.  Examples of these techniques are covered in this and the following questions."]
[]
[]
[]
[]
[]
[null,null,null,null,null,null,null,null,{"$f":"\"Consider the table of (x,y) values shown below in cells \" & ADDRESS(ROW(I158),COLUMN(I158),4) & \":\" & ADDRESS(ROW(J166),COLUMN(J166),4) & \".  Use the TREND function to perform a straight-line fit to those points and to calculate the y values corresponding to the x values in cells \" & ADDRESS(ROW(I155),COLUMN(I155),4) & \" to \" & ADDRESS(ROW(I169),COLUMN(I169),4) & \".\"","v":"Consider the table of (x,y) values shown below in cells I158:J166.  Use the TREND function to perform a straight-line fit to those points and to calculate the y values corresponding to the x values in cells I155 to I169."}]
[]
[]
[]
[null,null,null,null,null,null,null,null,"x","y","Interpolate"]
[{"$f":"IF(OR(NOT(ISNUMBER($K$155)),ISERROR($K$155)),1,IF(AND(LEN($K$155)>0,ABS((1-($K$155*-2.92438447475433+-0.388755798339844)/-1.99229328533014))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,0]
[{"$f":"IF(OR(NOT(ISNUMBER($K$156)),ISERROR($K$156)),1,IF(AND(LEN($K$156)>0,ABS((1-($K$156*-0.305288434028625+-0.375534415245056)/-0.566848500569662))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,{"$f":"I155+1","v":1}]
[{"$f":"IF(OR(NOT(ISNUMBER($K$157)),ISERROR($K$157)),1,IF(AND(LEN($K$157)>0,ABS((1-($K$157*-3.42043578624725+-0.000438451766967773)/-2.41184568107128))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,2]
[{"$f":"IF(OR(NOT(ISNUMBER($K$158)),ISERROR($K$158)),1,IF(AND(LEN($K$158)>0,ABS((1-($K$158* 3.3601325750351+ 0.180356860160828)/ 2.81246071060499))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,3,0.8]
[{"$f":"IF(OR(NOT(ISNUMBER($K$159)),ISERROR($K$159)),1,IF(AND(LEN($K$159)>0,ABS((1-($K$159* 2.73729860782623+-0.448100566864014)/ 1.91053840021292))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,4,0.85]
[{"$f":"IF(OR(NOT(ISNUMBER($K$160)),ISERROR($K$160)),1,IF(AND(LEN($K$160)>0,ABS((1-($K$160*-2.69975006580353+ 0.0952454805374146)/-2.4425195813179))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,5,0.95]
[{"$f":"IF(OR(NOT(ISNUMBER($K$161)),ISERROR($K$161)),1,IF(AND(LEN($K$161)>0,ABS((1-($K$161* 4.88292515277863+ 0.280525922775269)/ 5.2529713700215))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,6,1.05]
[{"$f":"IF(OR(NOT(ISNUMBER($K$162)),ISERROR($K$162)),1,IF(AND(LEN($K$162)>0,ABS((1-($K$162*-3.22797834873199+ 0.104544043540955)/-3.43547221223513))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,7,1.1000000000000001]
[{"$f":"IF(OR(NOT(ISNUMBER($K$163)),ISERROR($K$163)),1,IF(AND(LEN($K$163)>0,ABS((1-($K$163* 1.57906591892242+ 0.429154396057129)/ 2.28455685079098))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,8,1.08]
[{"$f":"IF(OR(NOT(ISNUMBER($K$164)),ISERROR($K$164)),1,IF(AND(LEN($K$164)>0,ABS((1-($K$164* 0.0890463590621948+ 0.0266729593276978)/ 0.138277729352315))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,9,1.2]
[{"$f":"IF(OR(NOT(ISNUMBER($K$165)),ISERROR($K$165)),1,IF(AND(LEN($K$165)>0,ABS((1-($K$165*-1.10189139842987+-0.0114314556121826)/-1.47878350118796))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,10,1.44]
[{"$f":"IF(OR(NOT(ISNUMBER($K$166)),ISERROR($K$166)),1,IF(AND(LEN($K$166)>0,ABS((1-($K$166* 3.15281331539154+ 0.403685450553894)/ 4.84915222525597))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,11,1.4]
[{"$f":"IF(OR(NOT(ISNUMBER($K$167)),ISERROR($K$167)),1,IF(AND(LEN($K$167)>0,ABS((1-($K$167* 1.20345652103424+ 0.462247371673584)/ 2.25339182714621))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,12]
[{"$f":"IF(OR(NOT(ISNUMBER($K$168)),ISERROR($K$168)),1,IF(AND(LEN($K$168)>0,ABS((1-($K$168*-3.51604759693146+ 0.391892552375793)/-5.11658201615016))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,13]
[{"$f":"IF(OR(NOT(ISNUMBER($K$169)),ISERROR($K$169)),1,IF(AND(LEN($K$169)>0,ABS((1-($K$169* 4.43077862262726+-0.118009805679321)/ 7.17062102854252))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,14]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Index"]
[{"$f":"SUM($A$173:$F$197)","v":15},null,null,null,null,null,null,4,"GROWTH function to perform linear interpolation / extrapolation"]
[]
[null,null,null,null,null,null,null,null,"The GROWTH function assumes the data points to be fitted are on an exponentially growing curve.  In this question we use the same data points as in the preceding question but now we assume the underlying function is exponential rather than linear."]
[]
[]
[]
[null,null,null,null,null,null,null,null,"Use the GROWTH function to fit an exponential curve to the (x,y) data points listed below."]
[]
[null,null,null,null,null,null,null,null,"x","y","Interpolate"]
[{"$f":"IF(OR(NOT(ISNUMBER($K$181)),ISERROR($K$181)),1,IF(AND(LEN($K$181)>0,ABS((1-($K$181* 4.7534841299057+-0.097511887550354)/ 2.99688109121839))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,0]
[{"$f":"IF(OR(NOT(ISNUMBER($K$182)),ISERROR($K$182)),1,IF(AND(LEN($K$182)>0,ABS((1-($K$182* 1.86925947666168+ 0.0735416412353516)/ 1.3811224974829))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,{"$f":"I181+1","v":1}]
[{"$f":"IF(OR(NOT(ISNUMBER($K$183)),ISERROR($K$183)),1,IF(AND(LEN($K$183)>0,ABS((1-($K$183*-1.18593037128448+-0.00782620906829834)/-0.899269452700342))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,2]
[{"$f":"IF(OR(NOT(ISNUMBER($K$184)),ISERROR($K$184)),1,IF(AND(LEN($K$184)>0,ABS((1-($K$184* 2.44284927845001+ 0.172216653823853)/ 2.14539673408034))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,3,0.8]
[{"$f":"IF(OR(NOT(ISNUMBER($K$185)),ISERROR($K$185)),1,IF(AND(LEN($K$185)>0,ABS((1-($K$185* 0.231260657310486+-0.49621593952179)/-0.295488220346314))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,4,0.85]
[{"$f":"IF(OR(NOT(ISNUMBER($K$186)),ISERROR($K$186)),1,IF(AND(LEN($K$186)>0,ABS((1-($K$186* 1.49151384830475+ 0.388525485992432)/ 1.77965776557262))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,5,0.95]
[{"$f":"IF(OR(NOT(ISNUMBER($K$187)),ISERROR($K$187)),1,IF(AND(LEN($K$187)>0,ABS((1-($K$187*-1.68525040149689+-0.0430887937545776)/-1.73213340803481))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,6,1.05]
[{"$f":"IF(OR(NOT(ISNUMBER($K$188)),ISERROR($K$188)),1,IF(AND(LEN($K$188)>0,ABS((1-($K$188* 4.05248463153839+ 0.0237987041473389)/ 4.38828970392244))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,7,1.1000000000000001]
[{"$f":"IF(OR(NOT(ISNUMBER($K$189)),ISERROR($K$189)),1,IF(AND(LEN($K$189)>0,ABS((1-($K$189*-0.350380539894104+-0.311469674110413)/-0.716966768945649))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,8,1.08]
[{"$f":"IF(OR(NOT(ISNUMBER($K$190)),ISERROR($K$190)),1,IF(AND(LEN($K$190)>0,ABS((1-($K$190* 0.64150869846344+-0.264187812805176)/ 0.5335971808566))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,9,1.2]
[{"$f":"IF(OR(NOT(ISNUMBER($K$191)),ISERROR($K$191)),1,IF(AND(LEN($K$191)>0,ABS((1-($K$191* 0.127593874931335+ 0.243624329566956)/ 0.414133870112616))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,10,1.44]
[{"$f":"IF(OR(NOT(ISNUMBER($K$192)),ISERROR($K$192)),1,IF(AND(LEN($K$192)>0,ABS((1-($K$192*-4.46590125560761+ 0.0544121265411377)/-6.35862150466557))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,11,1.4]
[{"$f":"IF(OR(NOT(ISNUMBER($K$193)),ISERROR($K$193)),1,IF(AND(LEN($K$193)>0,ABS((1-($K$193*-0.521712899208069+ 0.0158089399337769)/-0.789238586068558))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,12]
[{"$f":"IF(OR(NOT(ISNUMBER($K$194)),ISERROR($K$194)),1,IF(AND(LEN($K$194)>0,ABS((1-($K$194*-2.45321691036224+ 0.147140026092529)/-3.92067727007936))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,13]
[{"$f":"IF(OR(NOT(ISNUMBER($K$195)),ISERROR($K$195)),1,IF(AND(LEN($K$195)>0,ABS((1-($K$195*-1.69954597949982+ 0.137957692146301)/-2.89030782485328))<0.00005),0,1))","v":1},null,null,null,null,null,null,null,14]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Index"]
[{"$f":"SUM($A$199:$F$223)","v":39},null,null,null,null,null,null,5,"Fitting to a logarithmic curve"]
[]
[null,null,null,null,null,null,null,null,"You can fit points to an arbitrary underlying function by first transforming the function to a straight line, using the straight line interpolation function TREND and then reversing the original transformation.  The questions below illustrate that technique."]
[]
[]
[]
[null,null,null,null,null,null,null,null,"Fit a natural log curve to the (x,y) data points defined in the table below."]
[]
[null,null,null,null,null,null,null,null,"x","y","exp(y)","Interpolate","ln(Interpolate)"]
[{"$f":"IF(OR(NOT(ISNUMBER($L$207)),ISERROR($L$207)),1,IF(AND(LEN($L$207)>0,ABS((1-($L$207* 3.31835567951202+-0.165142297744751)/ 4.37359381572815))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($M$207)),ISERROR($M$207)),1,IF(AND(LEN($M$207)>0,ABS((1-($M$207*-2.40675985813141+-0.377173066139221)/-1.13092019601369))<0.00005),0,1))","v":1},null,null,null,null,null,null,0]
[{"$f":"IF(OR(NOT(ISNUMBER($L$208)),ISERROR($L$208)),1,IF(AND(LEN($L$208)>0,ABS((1-($L$208* 3.0911260843277+-0.142627716064453)/ 4.83324155057696))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($M$208)),ISERROR($M$208)),1,IF(AND(LEN($M$208)>0,ABS((1-($M$208* 0.787431597709656+-0.246319174766541)/ 0.1285491568206))<0.00005),0,1))","v":1},null,null,null,null,null,null,{"$f":"I207+1","v":1}]
[{"$f":"IF(OR(NOT(ISNUMBER($L$209)),ISERROR($L$209)),1,IF(AND(LEN($L$209)>0,ABS((1-($L$209*-1.00783050060272+ 0.389061212539673)/-1.47712590884864))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($M$209)),ISERROR($M$209)),1,IF(AND(LEN($M$209)>0,ABS((1-($M$209*-1.72329485416412+-0.275083661079407)/-1.33680109788529))<0.00005),0,1))","v":1},null,null,null,null,null,null,2]
[{"$f":"IF(OR(NOT(ISNUMBER($K$210)),ISERROR($K$210)),1,IF(AND(LEN($K$210)>0,ABS((1-($K$210*-4.18542325496674+-0.195502758026123)/-9.51033351501876))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($L$210)),ISERROR($L$210)),1,IF(AND(LEN($L$210)>0,ABS((1-($L$210* 4.44887816905975+-0.46731173992157)/ 8.84707276247765))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($M$210)),ISERROR($M$210)),1,IF(AND(LEN($M$210)>0,ABS((1-($M$210* 4.29870426654816+-0.305926561355591)/ 2.87042023179407))<0.00005),0,1))","v":1},null,null,null,null,null,3,0.8]
[{"$f":"IF(OR(NOT(ISNUMBER($K$211)),ISERROR($K$211)),1,IF(AND(LEN($K$211)>0,ABS((1-($K$211*-2.78284132480621+ 0.11553418636322)/-6.39533175862919))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($L$211)),ISERROR($L$211)),1,IF(AND(LEN($L$211)>0,ABS((1-($L$211*-3.08657586574554+ 0.12962818145752)/-7.07940417854028))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($M$211)),ISERROR($M$211)),1,IF(AND(LEN($M$211)>0,ABS((1-($M$211* 0.0513952970504761+-0.255000472068787)/-0.211403260510799))<0.00005),0,1))","v":1},null,null,null,null,null,4,0.85]
[{"$f":"IF(OR(NOT(ISNUMBER($K$212)),ISERROR($K$212)),1,IF(AND(LEN($K$212)>0,ABS((1-($K$212*-3.86262595653534+ 0.180070161819458)/-9.80755908431808))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($L$212)),ISERROR($L$212)),1,IF(AND(LEN($L$212)>0,ABS((1-($L$212*-3.49067270755768+-0.33373749256134)/-9.33118649129459))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($M$212)),ISERROR($M$212)),1,IF(AND(LEN($M$212)>0,ABS((1-($M$212*-4.75979268550873+-0.322996616363525)/-4.82979024230183))<0.00005),0,1))","v":1},null,null,null,null,null,5,0.95]
[{"$f":"IF(OR(NOT(ISNUMBER($K$213)),ISERROR($K$213)),1,IF(AND(LEN($K$213)>0,ABS((1-($K$213*-2.73216545581818+-0.0112408399581909)/-7.81881650951056))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($L$213)),ISERROR($L$213)),1,IF(AND(LEN($L$213)>0,ABS((1-($L$213* 1.56384289264679+ 0.230352163314819)/ 4.63965288734426))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($M$213)),ISERROR($M$213)),1,IF(AND(LEN($M$213)>0,ABS((1-($M$213*-0.345812439918518+-0.173191666603088)/-0.531650441894075))<0.00005),0,1))","v":1},null,null,null,null,null,6,1.05]
[{"$f":"IF(OR(NOT(ISNUMBER($K$214)),ISERROR($K$214)),1,IF(AND(LEN($K$214)>0,ABS((1-($K$214* 2.30371534824371+ 0.493986129760742)/ 7.41472950779843))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($L$214)),ISERROR($L$214)),1,IF(AND(LEN($L$214)>0,ABS((1-($L$214*-0.322702527046204+-0.309763312339783)/-1.29771375854005))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($M$214)),ISERROR($M$214)),1,IF(AND(LEN($M$214)>0,ABS((1-($M$214* 2.79002487659454+-0.318654775619507)/ 2.8031085531116))<0.00005),0,1))","v":1},null,null,null,null,null,7,1.1000000000000001]
[{"$f":"IF(OR(NOT(ISNUMBER($K$215)),ISERROR($K$215)),1,IF(AND(LEN($K$215)>0,ABS((1-($K$215*-3.44103395938873+ 0.125003695487976)/-10.0077386392461))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($L$215)),ISERROR($L$215)),1,IF(AND(LEN($L$215)>0,ABS((1-($L$215*-2.73101270198822+ 0.331064701080322)/-8.69069943405191))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($M$215)),ISERROR($M$215)),1,IF(AND(LEN($M$215)>0,ABS((1-($M$215*-0.234864354133606+-0.396173357963562)/-0.67682860500338))<0.00005),0,1))","v":1},null,null,null,null,null,8,1.08]
[{"$f":"IF(OR(NOT(ISNUMBER($K$216)),ISERROR($K$216)),1,IF(AND(LEN($K$216)>0,ABS((1-($K$216* 2.18408405780792+ 0.322600126266479)/ 7.57401456727367))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($L$216)),ISERROR($L$216)),1,IF(AND(LEN($L$216)>0,ABS((1-($L$216*-1.46286070346832+-0.333194375038147)/-5.51963609622087))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($M$216)),ISERROR($M$216)),1,IF(AND(LEN($M$216)>0,ABS((1-($M$216* 1.95731222629547+ 0.141852378845215)/ 2.6191323384921))<0.00005),0,1))","v":1},null,null,null,null,null,9,1.2]
[{"$f":"IF(OR(NOT(ISNUMBER($K$217)),ISERROR($K$217)),1,IF(AND(LEN($K$217)>0,ABS((1-($K$217* 3.92295062541962+ 0.312048554420471)/ 16.8696298494131))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($L$217)),ISERROR($L$217)),1,IF(AND(LEN($L$217)>0,ABS((1-($L$217*-2.72956550121307+ 0.396792650222778)/-9.94108443313029))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($M$217)),ISERROR($M$217)),1,IF(AND(LEN($M$217)>0,ABS((1-($M$217* 3.30843389034271+-0.363703846931458)/ 4.04204525108972))<0.00005),0,1))","v":1},null,null,null,null,null,10,1.44]
[{"$f":"IF(OR(NOT(ISNUMBER($K$218)),ISERROR($K$218)),1,IF(AND(LEN($K$218)>0,ABS((1-($K$218*-4.15377080440521+-0.41691255569458)/-17.261283783999))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($L$218)),ISERROR($L$218)),1,IF(AND(LEN($L$218)>0,ABS((1-($L$218*-2.55140602588654+-0.274453043937683)/-10.5549134140992))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($M$218)),ISERROR($M$218)),1,IF(AND(LEN($M$218)>0,ABS((1-($M$218*-4.27025973796844+ 0.0997235774993896)/-5.85131232433881))<0.00005),0,1))","v":1},null,null,null,null,null,11,1.4]
[{"$f":"IF(OR(NOT(ISNUMBER($L$219)),ISERROR($L$219)),1,IF(AND(LEN($L$219)>0,ABS((1-($L$219*-0.00117361545562744+-0.204317688941956)/-0.209330543032934))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($M$219)),ISERROR($M$219)),1,IF(AND(LEN($M$219)>0,ABS((1-($M$219* 1.06952726840973+-0.485366821289063)/ 1.06749726857419))<0.00005),0,1))","v":1},null,null,null,null,null,null,12]
[{"$f":"IF(OR(NOT(ISNUMBER($L$220)),ISERROR($L$220)),1,IF(AND(LEN($L$220)>0,ABS((1-($L$220*-0.453832745552063+-0.416908621788025)/-2.46517028162353))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($M$220)),ISERROR($M$220)),1,IF(AND(LEN($M$220)>0,ABS((1-($M$220* 0.398915410041809+ 0.0803186893463135)/ 0.681491398059433))<0.00005),0,1))","v":1},null,null,null,null,null,null,13]
[{"$f":"IF(OR(NOT(ISNUMBER($L$221)),ISERROR($L$221)),1,IF(AND(LEN($L$221)>0,ABS((1-($L$221* 4.14054334163666+-0.0147038698196411)/ 19.6744603434286))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($M$221)),ISERROR($M$221)),1,IF(AND(LEN($M$221)>0,ABS((1-($M$221*-2.5827544927597+ 0.499477863311768)/-3.52765992804659))<0.00005),0,1))","v":1},null,null,null,null,null,null,14]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Index"]
[{"$f":"SUM($A$225:$F$247)","v":39},null,null,null,null,null,null,{"$f":"H198+1","v":6},"Fitting to a square-root curve"]
[]
[null,null,null,null,null,null,null,null,"Fit a square root curve to the (x,y) data points defined in the table below."]
[]
[null,null,null,null,null,null,null,null,"x","y","y2","Interpolate","(Interpolate)1/2"]
[{"$f":"IF(OR(NOT(ISNUMBER($L$229)),ISERROR($L$229)),1,IF(AND(LEN($L$229)>0,ABS((1-($L$229*-1.67397797107697+-0.0484236478805542)/-0.0896574452592273))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($M$229)),ISERROR($M$229)),1,IF(AND(LEN($M$229)>0,ABS((1-($M$229* 4.27112400531769+-0.0593712329864502)/ 0.610966980537188))<0.00005),0,1))","v":1},null,null,null,null,null,null,0]
[{"$f":"IF(OR(NOT(ISNUMBER($L$230)),ISERROR($L$230)),1,IF(AND(LEN($L$230)>0,ABS((1-($L$230* 2.67206132411957+-0.376405358314514)/ 0.155786126653354))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($M$230)),ISERROR($M$230)),1,IF(AND(LEN($M$230)>0,ABS((1-($M$230*-2.66432702541351+ 0.30373477935791)/-0.885310191339173))<0.00005),0,1))","v":1},null,null,null,null,null,null,{"$f":"I229+1","v":1}]
[{"$f":"IF(OR(NOT(ISNUMBER($L$231)),ISERROR($L$231)),1,IF(AND(LEN($L$231)>0,ABS((1-($L$231*-4.19524013996124+-0.273978590965271)/-1.84176313815845))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($M$231)),ISERROR($M$231)),1,IF(AND(LEN($M$231)>0,ABS((1-($M$231*-4.50421988964081+-0.264170408248901)/-3.01766584506614))<0.00005),0,1))","v":1},null,null,null,null,null,null,2]
[{"$f":"IF(OR(NOT(ISNUMBER($K$232)),ISERROR($K$232)),1,IF(AND(LEN($K$232)>0,ABS((1-($K$232*-1.0618931055069+ 0.207159876823425)/-0.472451710700989))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($L$232)),ISERROR($L$232)),1,IF(AND(LEN($L$232)>0,ABS((1-($L$232* 0.927348732948303+ 0.396642208099365)/ 0.905053938225905))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($M$232)),ISERROR($M$232)),1,IF(AND(LEN($M$232)>0,ABS((1-($M$232* 2.90523231029511+ 0.129571080207825)/ 2.2807032992989))<0.00005),0,1))","v":1},null,null,null,null,null,3,0.8]
[{"$f":"IF(OR(NOT(ISNUMBER($K$233)),ISERROR($K$233)),1,IF(AND(LEN($K$233)>0,ABS((1-($K$233* 2.37854778766632+ 0.47422194480896)/ 2.19272272139788))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($L$233)),ISERROR($L$233)),1,IF(AND(LEN($L$233)>0,ABS((1-($L$233*-2.31034338474274+-0.189301133155823)/-1.85916855773197))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($M$233)),ISERROR($M$233)),1,IF(AND(LEN($M$233)>0,ABS((1-($M$233* 0.951061844825745+ 0.450563430786133)/ 1.25912200770568))<0.00005),0,1))","v":1},null,null,null,null,null,4,0.85]
[{"$f":"IF(OR(NOT(ISNUMBER($K$234)),ISERROR($K$234)),1,IF(AND(LEN($K$234)>0,ABS((1-($K$234* 4.45654094219208+ 0.213494896888733)/ 4.23552309721708))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($L$234)),ISERROR($L$234)),1,IF(AND(LEN($L$234)>0,ABS((1-($L$234*-1.61865890026093+-0.382768392562866)/-1.83521620290544))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($M$234)),ISERROR($M$234)),1,IF(AND(LEN($M$234)>0,ABS((1-($M$234* 0.0839370489120483+-0.412956357002258)/-0.333445525655073))<0.00005),0,1))","v":1},null,null,null,null,null,5,0.95]
[{"$f":"IF(OR(NOT(ISNUMBER($K$235)),ISERROR($K$235)),1,IF(AND(LEN($K$235)>0,ABS((1-($K$235*-2.17814862728119+-0.159013271331787)/-2.5604221329093))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($L$235)),ISERROR($L$235)),1,IF(AND(LEN($L$235)>0,ABS((1-($L$235* 4.19403731822968+ 0.357187390327454)/ 4.85257560995486))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($M$235)),ISERROR($M$235)),1,IF(AND(LEN($M$235)>0,ABS((1-($M$235*-2.87767589092255+-0.42059063911438)/-3.39985701140647))<0.00005),0,1))","v":1},null,null,null,null,null,6,1.05]
[{"$f":"IF(OR(NOT(ISNUMBER($K$236)),ISERROR($K$236)),1,IF(AND(LEN($K$236)>0,ABS((1-($K$236*-1.31557524204254+ 0.267151236534119)/-1.32469480633736))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($L$236)),ISERROR($L$236)),1,IF(AND(LEN($L$236)>0,ABS((1-($L$236* 4.6110063791275+ 0.146525382995605)/ 5.89363250053591))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($M$236)),ISERROR($M$236)),1,IF(AND(LEN($M$236)>0,ABS((1-($M$236*-0.240676999092102+-0.231831908226013)/-0.500528013975258))<0.00005),0,1))","v":1},null,null,null,null,null,7,1.1000000000000001]
[{"$f":"IF(OR(NOT(ISNUMBER($K$237)),ISERROR($K$237)),1,IF(AND(LEN($K$237)>0,ABS((1-($K$237*-2.62408912181854+ 0.228430986404419)/-2.83230656528473))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($L$237)),ISERROR($L$237)),1,IF(AND(LEN($L$237)>0,ABS((1-($L$237* 2.46084630489349+-0.339896321296692)/ 3.15678308162093))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($M$237)),ISERROR($M$237)),1,IF(AND(LEN($M$237)>0,ABS((1-($M$237* 2.04606592655182+-0.351082324981689)/ 2.08788108889793))<0.00005),0,1))","v":1},null,null,null,null,null,8,1.08]
[{"$f":"IF(OR(NOT(ISNUMBER($K$238)),ISERROR($K$238)),1,IF(AND(LEN($K$238)>0,ABS((1-($K$238*-2.29975044727325+-0.0179184675216675)/-3.32955911159515))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($L$238)),ISERROR($L$238)),1,IF(AND(LEN($L$238)>0,ABS((1-($L$238*-1.92723453044891+ 0.38509726524353)/-2.68973262144989))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($M$238)),ISERROR($M$238)),1,IF(AND(LEN($M$238)>0,ABS((1-($M$238* 1.78917825222015+ 0.15310800075531)/ 2.41304781451134))<0.00005),0,1))","v":1},null,null,null,null,null,9,1.2]
[{"$f":"IF(OR(NOT(ISNUMBER($K$239)),ISERROR($K$239)),1,IF(AND(LEN($K$239)>0,ABS((1-($K$239* 3.51081907749176+-0.166973114013672)/ 7.11306132507324))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($L$239)),ISERROR($L$239)),1,IF(AND(LEN($L$239)>0,ABS((1-($L$239*-1.52908146381378+ 0.362697243690491)/-2.3437752482805))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($M$239)),ISERROR($M$239)),1,IF(AND(LEN($M$239)>0,ABS((1-($M$239* 3.29980194568634+ 0.323333978652954)/ 4.71343355615565))<0.00005),0,1))","v":1},null,null,null,null,null,10,1.44]
[{"$f":"IF(OR(NOT(ISNUMBER($K$240)),ISERROR($K$240)),1,IF(AND(LEN($K$240)>0,ABS((1-($K$240* 3.45164716243744+ 0.211496233940125)/ 6.9767246723175))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($L$240)),ISERROR($L$240)),1,IF(AND(LEN($L$240)>0,ABS((1-($L$240* 0.0453048944473267+-0.113158702850342)/-0.0250617247568237))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($M$240)),ISERROR($M$240)),1,IF(AND(LEN($M$240)>0,ABS((1-($M$240* 1.43168151378632+-0.398090243339539)/ 1.59834101740384))<0.00005),0,1))","v":1},null,null,null,null,null,11,1.4]
[{"$f":"IF(OR(NOT(ISNUMBER($L$241)),ISERROR($L$241)),1,IF(AND(LEN($L$241)>0,ABS((1-($L$241*-2.69981563091278+ 0.27019190788269)/-5.45091240070595))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($M$241)),ISERROR($M$241)),1,IF(AND(LEN($M$241)>0,ABS((1-($M$241*-4.36327040195465+-0.121274590492249)/-6.47290190013265))<0.00005),0,1))","v":1},null,null,null,null,null,null,12]
[{"$f":"IF(OR(NOT(ISNUMBER($L$242)),ISERROR($L$242)),1,IF(AND(LEN($L$242)>0,ABS((1-($L$242*-4.65418756008148+ 0.201474189758301)/-10.4734117686007))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($M$242)),ISERROR($M$242)),1,IF(AND(LEN($M$242)>0,ABS((1-($M$242*-0.150859951972961+ 0.219738602638245)/-0.0087337462585815))<0.00005),0,1))","v":1},null,null,null,null,null,null,13]
[{"$f":"IF(OR(NOT(ISNUMBER($L$243)),ISERROR($L$243)),1,IF(AND(LEN($L$243)>0,ABS((1-($L$243*-0.526673197746277+-0.0941531658172607)/-1.39405927806497))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($M$243)),ISERROR($M$243)),1,IF(AND(LEN($M$243)>0,ABS((1-($M$243* 2.93915212154388+ 0.276377558708191)/ 4.89388334605476))<0.00005),0,1))","v":1},null,null,null,null,null,null,14]
[]
[]
[]
[null,null,null,null,null,null,null,null,null,null,"Copyright (c) 2020 Tykoh Group Pty Ltd.  All rights reserved.",null,null,null,null,null,null,null,null,"Index"]
[null,null,null,null,null,null,null,null,null,null,"www.tykoh.com"]

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[null,null,null,null,null,"Click here to see what your answer should look like."]
[{"$f":"SUM($A$3:$C$19)","v":8},null,null,null,1,"Calculating asset price distribution in one period's time.",null,null,null,null,null,null,null,"Asset_Evolution","Asset_evolution"]
[]
[null,null,null,null,null,"Assume that over a certain period an asset's value can change by +10% or by -10% and that each of these possibilities are equally likely.  The asset's current price is $100.  Calculate the probability distribution of the asset's price in one period's time.  The table below should be ranked in decreasing order of price."]
[]
[]
[]
[null,null,null,null,null,"Price in one period","Probability","Return"]
[{"$f":"IF(OR(NOT(ISNUMBER($F$9)),ISERROR($F$9)),1,IF(AND(LEN($F$9)>0,ABS((1-($F$9* 0.764880776405334+-0.128836154937744)/ 84.0080492496491))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($G$9)),ISERROR($G$9)),1,IF(AND(LEN($G$9)>0,ABS((1-($G$9*-4.10385429859161+ 0.0643283128738403)/-1.98759883642197))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($H$9)),ISERROR($H$9)),1,IF(AND(LEN($H$9)>0,ABS((1-($H$9*-0.625106692314147+-0.136400461196899)/-0.198911130428314))<0.00005),0,1))","v":1}]
[{"$f":"IF(OR(NOT(ISNUMBER($F$10)),ISERROR($F$10)),1,IF(AND(LEN($F$10)>0,ABS((1-($F$10* 1.35989129543304+ 0.104159712791443)/ 122.494376301765))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($G$10)),ISERROR($G$10)),1,IF(AND(LEN($G$10)>0,ABS((1-($G$10* 0.311298966407776+ 0.193273544311523)/ 0.348923027515411))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($H$10)),ISERROR($H$10)),1,IF(AND(LEN($H$10)>0,ABS((1-($H$10*-4.34819996356964+-0.188051581382751)/ 0.246768414974213))<0.00005),0,1))","v":1}]
[]
[null,null,null,null,null,"Calculate the expected or mean return over the period."]
[]
[{"$f":"IF(OR(NOT(ISNUMBER($I$14)),ISERROR($I$14)),1,IF(AND(LEN($I$14)>0,ABS((1-($I$14* 1.71679794788361+ 0.229875802993774)/ 0.229875802993774))<0.00005),0,1))","v":1},null,null,null,null,"Expected / mean return"]
[]
[null,null,null,null,null,"Calculate the volatility. [Use the STDEVP function.]"]
[]
[{"$f":"IF(OR(NOT(ISNUMBER($I$18)),ISERROR($I$18)),1,IF(AND(LEN($I$18)>0,ABS((1-($I$18* 3.30617368221283+ 0.139903903007507)/ 0.47052127122879))<0.00005),0,1))","v":1},null,null,null,null,"Volatility"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Index"]
[{"$f":"SUM($A$21:$C$36)","v":8},null,null,null,2,"Calculating asset price distribution in two period's time."]
[]
[null,null,null,null,null,"With the same asset as in the preceding question - what is its price probability distribution in two period's time?"]
[]
[null,null,null,null,null,"Price in two weeks","Probability"]
[{"$f":"IF(OR(NOT(ISNUMBER($F$25)),ISERROR($F$25)),1,IF(AND(LEN($F$25)>0,ABS((1-($F$25*-4.34989392757416+ 0.168291568756104)/-526.168873667716))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($G$25)),ISERROR($G$25)),1,IF(AND(LEN($G$25)>0,ABS((1-($G$25* 4.10145461559296+ 0.466993451118469)/ 1.49235710501671))<0.00005),0,1))","v":1}]
[{"$f":"IF(OR(NOT(ISNUMBER($F$26)),ISERROR($F$26)),1,IF(AND(LEN($F$26)>0,ABS((1-($F$26* 1.36720478534698+ 0.0442264080047607)/ 135.397500157356))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($G$26)),ISERROR($G$26)),1,IF(AND(LEN($G$26)>0,ABS((1-($G$26* 2.59147584438324+-0.260432839393616)/ 1.035305082798))<0.00005),0,1))","v":1}]
[{"$f":"IF(OR(NOT(ISNUMBER($F$27)),ISERROR($F$27)),1,IF(AND(LEN($F$27)>0,ABS((1-($F$27* 1.10259115695953+-0.000168800354003906)/ 89.3097149133682))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($G$27)),ISERROR($G$27)),1,IF(AND(LEN($G$27)>0,ABS((1-($G$27* 0.136711001396179+-0.138017058372498)/-0.103839308023453))<0.00005),0,1))","v":1}]
[]
[null,null,null,null,null,"What is the expected (mean, average) price in two period's time?"]
[]
[{"$f":"IF(OR(NOT(ISNUMBER($H$31)),ISERROR($H$31)),1,IF(AND(LEN($H$31)>0,ABS((1-($H$31*-1.64947211742401+-0.20067286491394)/-165.147884607315))<0.00005),0,1))","v":1},null,null,null,null,"Expected price"]
[]
[null,null,null,null,null,"What is the modal (most likely, highest probability) price in two period's time?"]
[]
[{"$f":"IF(OR(NOT(ISNUMBER($H$35)),ISERROR($H$35)),1,IF(AND(LEN($H$35)>0,ABS((1-($H$35*-0.564475655555725+ 0.337231516838074)/-55.5458583831787))<0.00005),0,1))","v":1},null,null,null,null,"Modal price"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Index"]
[{"$f":"SUM($A$38:$C$79)","v":45},null,null,null,3,"Calculating asset price distribution \"N\" periods into the future. "]
[]
[null,null,null,null,null,"Consider the same asset as in the preceding question.  What is its price distribution in 20 period's time?  [ Use the BINOMDIST function to calculate the probabilities]"]
[]
[]
[null,null,null,null,null,"Number of \"up\" moves in 20 periods","Price in 20 periods","Probability "]
[]
[{"$f":"IF(OR(NOT(ISNUMBER($G$44)),ISERROR($G$44)),1,IF(AND(LEN($G$44)>0,ABS((1-($G$44*-1.35370671749114+-0.405369281768799)/-911.111556614114))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($H$44)),ISERROR($H$44)),1,IF(AND(LEN($H$44)>0,ABS((1-($H$44* 1.55542075634003+ 0.157561421394348)/ 0.157562904759175))<0.00005),0,1))","v":1},null,null,null,20]
[{"$f":"IF(OR(NOT(ISNUMBER($G$45)),ISERROR($G$45)),1,IF(AND(LEN($G$45)>0,ABS((1-($G$45* 2.84743130207062+-0.0590212345123291)/ 1567.25775570634))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($H$45)),ISERROR($H$45)),1,IF(AND(LEN($H$45)>0,ABS((1-($H$45*-4.53570425510406+-0.0548959970474243)/-0.0549825087405225))<0.00005),0,1))","v":1},null,null,null,{"$f":"F44-1","v":19}]
[{"$f":"IF(OR(NOT(ISNUMBER($G$46)),ISERROR($G$46)),1,IF(AND(LEN($G$46)>0,ABS((1-($G$46* 2.91500151157379+ 0.0625534057617188)/ 1312.84311062323))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($H$46)),ISERROR($H$46)),1,IF(AND(LEN($H$46)>0,ABS((1-($H$46* 0.0616854429244995+ 0.342498421669006)/ 0.342509598955303))<0.00005),0,1))","v":1},null,null,null,18]
[{"$f":"IF(OR(NOT(ISNUMBER($G$47)),ISERROR($G$47)),1,IF(AND(LEN($G$47)>0,ABS((1-($G$47* 0.194829106330872+ 0.368107080459595)/ 72.1569600754813))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($H$47)),ISERROR($H$47)),1,IF(AND(LEN($H$47)>0,ABS((1-($H$47*-1.28998339176178+-0.34648334980011)/-0.347885805193528))<0.00005),0,1))","v":1},null,null,null,17]
[{"$f":"IF(OR(NOT(ISNUMBER($G$48)),ISERROR($G$48)),1,IF(AND(LEN($G$48)>0,ABS((1-($G$48*-3.80124509334564+ 0.216587543487549)/-1145.76825345177))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($H$48)),ISERROR($H$48)),1,IF(AND(LEN($H$48)>0,ABS((1-($H$48*-3.7341433763504+-0.266311526298523)/-0.283565330179613))<0.00005),0,1))","v":1},null,null,null,16]
[{"$f":"IF(OR(NOT(ISNUMBER($G$49)),ISERROR($G$49)),1,IF(AND(LEN($G$49)>0,ABS((1-($G$49*-4.11411464214325+-0.0672371387481689)/-1014.86432895566))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($H$49)),ISERROR($H$49)),1,IF(AND(LEN($H$49)>0,ABS((1-($H$49*-1.38883650302887+ 0.130926489830017)/ 0.110391477448502))<0.00005),0,1))","v":1},null,null,null,15]
[{"$f":"IF(OR(NOT(ISNUMBER($G$50)),ISERROR($G$50)),1,IF(AND(LEN($G$50)>0,ABS((1-($G$50* 3.44384253025055+ 0.0728464126586914)/ 695.0906569425))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($H$50)),ISERROR($H$50)),1,IF(AND(LEN($H$50)>0,ABS((1-($H$50* 4.68453586101531+ 0.47615110874176)/ 0.649312243435816))<0.00005),0,1))","v":1},null,null,null,14]
[{"$f":"IF(OR(NOT(ISNUMBER($G$51)),ISERROR($G$51)),1,IF(AND(LEN($G$51)>0,ABS((1-($G$51* 0.570014119148254+-0.0598781108856201)/ 94.0614585866655))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($H$51)),ISERROR($H$51)),1,IF(AND(LEN($H$51)>0,ABS((1-($H$51* 1.01246297359467+ 0.123915553092957)/ 0.19876575919443))<0.00005),0,1))","v":1},null,null,null,13]
[{"$f":"IF(OR(NOT(ISNUMBER($G$52)),ISERROR($G$52)),1,IF(AND(LEN($G$52)>0,ABS((1-($G$52*-2.74719655513763+ 0.350568294525146)/-370.793078421626))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($H$52)),ISERROR($H$52)),1,IF(AND(LEN($H$52)>0,ABS((1-($H$52*-1.25942528247833+ 0.043030858039856)/-0.10826938422565))<0.00005),0,1))","v":1},null,null,null,12]
[{"$f":"IF(OR(NOT(ISNUMBER($G$53)),ISERROR($G$53)),1,IF(AND(LEN($G$53)>0,ABS((1-($G$53*-4.94712054729462+-0.351515054702759)/-547.184388440159))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($H$53)),ISERROR($H$53)),1,IF(AND(LEN($H$53)>0,ABS((1-($H$53* 3.16489160060883+-0.0428091287612915)/ 0.464140480268725))<0.00005),0,1))","v":1},null,null,null,11]
[{"$f":"IF(OR(NOT(ISNUMBER($G$54)),ISERROR($G$54)),1,IF(AND(LEN($G$54)>0,ABS((1-($G$54* 2.88442671298981+-0.0278835296630859)/ 260.834498060792))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($H$54)),ISERROR($H$54)),1,IF(AND(LEN($H$54)>0,ABS((1-($H$54*-4.23692524433135+-0.264402747154236)/-1.01093648475808))<0.00005),0,1))","v":1},null,null,null,10]
[{"$f":"IF(OR(NOT(ISNUMBER($G$55)),ISERROR($G$55)),1,IF(AND(LEN($G$55)>0,ABS((1-($G$55*-4.70360457897186+-0.230722188949585)/-348.27345875589))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($H$55)),ISERROR($H$55)),1,IF(AND(LEN($H$55)>0,ABS((1-($H$55*-1.27432405948639+ 0.0335844755172729)/-0.170535654097875))<0.00005),0,1))","v":1},null,null,null,9]
[{"$f":"IF(OR(NOT(ISNUMBER($G$56)),ISERROR($G$56)),1,IF(AND(LEN($G$56)>0,ABS((1-($G$56* 3.25375139713287+-0.437020778656006)/ 196.549251657913))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($H$56)),ISERROR($H$56)),1,IF(AND(LEN($H$56)>0,ABS((1-($H$56* 1.98738753795624+ 0.183244824409485)/ 0.421998341709468))<0.00005),0,1))","v":1},null,null,null,8]
[{"$f":"IF(OR(NOT(ISNUMBER($G$57)),ISERROR($G$57)),1,IF(AND(LEN($G$57)>0,ABS((1-($G$57*-2.58127391338348+-0.0329487323760986)/-127.893187533796))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($H$57)),ISERROR($H$57)),1,IF(AND(LEN($H$57)>0,ABS((1-($H$57* 2.75829255580902+ 0.33405339717865)/ 0.537970746923747))<0.00005),0,1))","v":1},null,null,null,7]
[{"$f":"IF(OR(NOT(ISNUMBER($G$58)),ISERROR($G$58)),1,IF(AND(LEN($G$58)>0,ABS((1-($G$58* 3.93206655979156+-0.0482301712036133)/ 159.309121547191))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($H$58)),ISERROR($H$58)),1,IF(AND(LEN($H$58)>0,ABS((1-($H$58*-2.44488537311554+-0.156506896018982)/-0.246880657255133))<0.00005),0,1))","v":1},null,null,null,6]
[{"$f":"IF(OR(NOT(ISNUMBER($G$59)),ISERROR($G$59)),1,IF(AND(LEN($G$59)>0,ABS((1-($G$59* 2.69428551197052+ 0.3594810962677)/ 89.6992208740516))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($H$59)),ISERROR($H$59)),1,IF(AND(LEN($H$59)>0,ABS((1-($H$59*-3.26753199100494+-0.0823203325271606)/-0.130633297909299))<0.00005),0,1))","v":1},null,null,null,5]
[{"$f":"IF(OR(NOT(ISNUMBER($G$60)),ISERROR($G$60)),1,IF(AND(LEN($G$60)>0,ABS((1-($G$60*-1.85308873653412+-0.329773426055908)/-50.6041979422802))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($H$60)),ISERROR($H$60)),1,IF(AND(LEN($H$60)>0,ABS((1-($H$60* 1.51410758495331+-0.498013377189636)/-0.491017364264394))<0.00005),0,1))","v":1},null,null,null,4]
[{"$f":"IF(OR(NOT(ISNUMBER($G$61)),ISERROR($G$61)),1,IF(AND(LEN($G$61)>0,ABS((1-($G$61* 2.55373775959015+ 0.0173680782318115)/ 56.703524904741))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($H$61)),ISERROR($H$61)),1,IF(AND(LEN($H$61)>0,ABS((1-($H$61* 3.52417886257172+ 0.421670317649841)/ 0.42550176515897))<0.00005),0,1))","v":1},null,null,null,3]
[{"$f":"IF(OR(NOT(ISNUMBER($G$62)),ISERROR($G$62)),1,IF(AND(LEN($G$62)>0,ABS((1-($G$62* 1.78207457065582+ 0.453212738037109)/ 32.8182725013488))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($H$62)),ISERROR($H$62)),1,IF(AND(LEN($H$62)>0,ABS((1-($H$62*-3.18153202533722+-0.227505087852478)/-0.228081575474562))<0.00005),0,1))","v":1},null,null,null,2]
[{"$f":"IF(OR(NOT(ISNUMBER($G$63)),ISERROR($G$63)),1,IF(AND(LEN($G$63)>0,ABS((1-($G$63* 3.5839968919754+ 0.464637994766235)/ 53.7205699290223))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($H$63)),ISERROR($H$63)),1,IF(AND(LEN($H$63)>0,ABS((1-($H$63* 2.415651679039+-0.438642621040344)/-0.438596546141071))<0.00005),0,1))","v":1},null,null,null,1]
[{"$f":"IF(OR(NOT(ISNUMBER($G$64)),ISERROR($G$64)),1,IF(AND(LEN($G$64)>0,ABS((1-($G$64*-1.62240445613861+-0.261283397674561)/-19.985934014691))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($H$64)),ISERROR($H$64)),1,IF(AND(LEN($H$64)>0,ABS((1-($H$64*-4.67145264148712+-0.403087496757507)/-0.403091951801912))<0.00005),0,1))","v":1},null,null,null,0]
[]
[]
[null,null,null,null,null,"What is the expected (mean, average) price in twenty period's time?"]
[]
[{"$f":"IF(OR(NOT(ISNUMBER($H$69)),ISERROR($H$69)),1,IF(AND(LEN($H$69)>0,ABS((1-($H$69* 2.52822697162628+ 0.178341627120972)/ 253.001038789749))<0.00005),0,1))","v":1},null,null,null,null,"Expected price"]
[]
[null,null,null,null,null,"What is the modal (most likely, highest probability) price in 20 period's time?"]
[]
[{"$f":"IF(OR(NOT(ISNUMBER($H$73)),ISERROR($H$73)),1,IF(AND(LEN($H$73)>0,ABS((1-($H$73* 4.09536302089691+-0.369802117347717)/ 370.00748855796))<0.00005),0,1))","v":1},null,null,null,null,"Modal price"]
[]
[null,null,null,null,null,"What is the approximate probability that the asset's value in 20 period's time will be less than its current value?  [Add up the probabilities in the table above that correspond to an asset price of less than 100.]"]
[]
[]
[{"$f":"IF(OR(NOT(ISNUMBER($H$78)),ISERROR($H$78)),1,IF(AND(LEN($H$78)>0,ABS((1-($H$78* 4.12976324558258+ 0.167851448059082)/ 2.59655912551921))<0.00005),0,1))","v":1},null,null,null,null,"Probability:"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Index"]
[{"$f":"SUM($A$81:$C$113)","v":64},null,null,null,4,"Calculating probability distribution of long-term return."]
[]
[null,null,null,null,null,"Define the long-term return over \"N\" periods as being the percentage change in asset price over that interval.  Calculate the probability distribution of the long-term return of the asset above."]
[]
[]
[null,null,null,null,null,"Number of \"up\" moves in 20 periods","Price in 20 periods","Long-term return [%]","Probability "]
[]
[{"$f":"IF(OR(NOT(ISNUMBER($G$87)),ISERROR($G$87)),1,IF(AND(LEN($G$87)>0,ABS((1-($G$87* 2.8109472990036+-0.254741072654724)/ 1890.81004008771))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($H$87)),ISERROR($H$87)),1,IF(AND(LEN($H$87)>0,ABS((1-($H$87* 1.28584206104279+ 0.0886547565460205)/ 7.45331509600931))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($I$87)),ISERROR($I$87)),1,IF(AND(LEN($I$87)>0,ABS((1-($I$87*-4.34196054935455+-0.000226140022277832)/-0.000230280838536601))<0.00005),0,1))","v":1},null,null,{"$f":"F44","v":20}]
[{"$f":"IF(OR(NOT(ISNUMBER($G$88)),ISERROR($G$88)),1,IF(AND(LEN($G$88)>0,ABS((1-($G$88* 2.8911167383194+ 0.0848555564880371)/ 1591.4474864187))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($H$88)),ISERROR($H$88)),1,IF(AND(LEN($H$88)>0,ABS((1-($H$88* 3.93851935863495+ 0.315678715705872)/ 18.0560229089537))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($I$88)),ISERROR($I$88)),1,IF(AND(LEN($I$88)>0,ABS((1-($I$88* 1.91250622272491+ 0.0788781642913818)/ 0.0789146424526734))<0.00005),0,1))","v":1},null,null,19]
[{"$f":"IF(OR(NOT(ISNUMBER($G$89)),ISERROR($G$89)),1,IF(AND(LEN($G$89)>0,ABS((1-($G$89*-4.39534246921539+-0.380207657814026)/-1979.8372038166))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($H$89)),ISERROR($H$89)),1,IF(AND(LEN($H$89)>0,ABS((1-($H$89* 1.17044508457184+ 0.0370922088623047)/ 4.13778521535478))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($I$89)),ISERROR($I$89)),1,IF(AND(LEN($I$89)>0,ABS((1-($I$89*-2.70963490009308+ 0.23444139957428)/ 0.233950418824179))<0.00005),0,1))","v":1},null,null,18]
[{"$f":"IF(OR(NOT(ISNUMBER($G$90)),ISERROR($G$90)),1,IF(AND(LEN($G$90)>0,ABS((1-($G$90* 1.62013351917267+ 0.485437631607056)/ 597.457467276258))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($H$90)),ISERROR($H$90)),1,IF(AND(LEN($H$90)>0,ABS((1-($H$90*-1.15755617618561+-0.481914639472961)/-3.58961593588197))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($I$90)),ISERROR($I$90)),1,IF(AND(LEN($I$90)>0,ABS((1-($I$90* 3.1327873468399+ 0.275049686431885)/ 0.278455617499731))<0.00005),0,1))","v":1},null,null,17]
[{"$f":"IF(OR(NOT(ISNUMBER($G$91)),ISERROR($G$91)),1,IF(AND(LEN($G$91)>0,ABS((1-($G$91* 0.351836085319519+-0.2440584897995)/ 105.826139666355))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($H$91)),ISERROR($H$91)),1,IF(AND(LEN($H$91)>0,ABS((1-($H$91*-2.22311198711395+-0.402116060256958)/-4.88115711643736))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($I$91)),ISERROR($I$91)),1,IF(AND(LEN($I$91)>0,ABS((1-($I$91* 1.6848748922348+ 0.300609946250916)/ 0.308394998410108))<0.00005),0,1))","v":1},null,null,16]
[{"$f":"IF(OR(NOT(ISNUMBER($G$92)),ISERROR($G$92)),1,IF(AND(LEN($G$92)>0,ABS((1-($G$92*-4.4005674123764+ 0.252341270446777)/-1085.2018574724))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($H$92)),ISERROR($H$92)),1,IF(AND(LEN($H$92)>0,ABS((1-($H$92* 4.51453387737274+-0.0373014211654663)/ 6.5838190236275))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($I$92)),ISERROR($I$92)),1,IF(AND(LEN($I$92)>0,ABS((1-($I$92* 2.90718376636505+ 0.158892869949341)/ 0.201877810586666))<0.00005),0,1))","v":1},null,null,15]
[{"$f":"IF(OR(NOT(ISNUMBER($G$93)),ISERROR($G$93)),1,IF(AND(LEN($G$93)>0,ABS((1-($G$93*-3.14832270145416+-0.348551869392395)/-635.7261371061))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($H$93)),ISERROR($H$93)),1,IF(AND(LEN($H$93)>0,ABS((1-($H$93* 3.04791986942291+ 0.125705242156982)/ 3.22893361981317))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($I$93)),ISERROR($I$93)),1,IF(AND(LEN($I$93)>0,ABS((1-($I$93* 0.0763100385665894+ 0.265357136726379)/ 0.268177892775384))<0.00005),0,1))","v":1},null,null,14]
[{"$f":"IF(OR(NOT(ISNUMBER($G$94)),ISERROR($G$94)),1,IF(AND(LEN($G$94)>0,ABS((1-($G$94*-0.30831515789032+-0.135734796524048)/-51.0450610920116))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($H$94)),ISERROR($H$94)),1,IF(AND(LEN($H$94)>0,ABS((1-($H$94*-1.5311723947525+-0.167193055152893)/-1.16430877936561))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($I$94)),ISERROR($I$94)),1,IF(AND(LEN($I$94)>0,ABS((1-($I$94* 2.61203825473785+ 0.2550048828125)/ 0.448109822757033))<0.00005),0,1))","v":1},null,null,13]
[{"$f":"IF(OR(NOT(ISNUMBER($G$95)),ISERROR($G$95)),1,IF(AND(LEN($G$95)>0,ABS((1-($G$95* 1.24126613140106+-0.0973132848739624)/ 167.596562747363))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($H$95)),ISERROR($H$95)),1,IF(AND(LEN($H$95)>0,ABS((1-($H$95*-4.03269469738007+-0.137073278427124)/-1.5525108352881))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($I$95)),ISERROR($I$95)),1,IF(AND(LEN($I$95)>0,ABS((1-($I$95*-2.93144762516022+ 0.185018420219421)/-0.167149145451958))<0.00005),0,1))","v":1},null,null,12]
[{"$f":"IF(OR(NOT(ISNUMBER($G$96)),ISERROR($G$96)),1,IF(AND(LEN($G$96)>0,ABS((1-($G$96*-0.91817319393158+-0.29677152633667)/-101.787584435207))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($H$96)),ISERROR($H$96)),1,IF(AND(LEN($H$96)>0,ABS((1-($H$96* 1.11975371837616+ 0.441581845283508)/ 0.559554471858729))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($I$96)),ISERROR($I$96)),1,IF(AND(LEN($I$96)>0,ABS((1-($I$96*-0.272790789604187+ 0.256928205490112)/ 0.213232811906892))<0.00005),0,1))","v":1},null,null,11]
[{"$f":"IF(OR(NOT(ISNUMBER($G$97)),ISERROR($G$97)),1,IF(AND(LEN($G$97)>0,ABS((1-($G$97* 4.58932816982269+-0.373460412025452)/ 414.677152900036))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($H$97)),ISERROR($H$97)),1,IF(AND(LEN($H$97)>0,ABS((1-($H$97*-0.0964254140853882+-0.263510704040527)/-0.254290706029266))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($I$97)),ISERROR($I$97)),1,IF(AND(LEN($I$97)>0,ABS((1-($I$97*-3.27162563800812+ 0.277062058448792)/-0.299388734222248))<0.00005),0,1))","v":1},null,null,10]
[{"$f":"IF(OR(NOT(ISNUMBER($G$98)),ISERROR($G$98)),1,IF(AND(LEN($G$98)>0,ABS((1-($G$98* 4.12081062793732+-0.398554563522339)/ 304.520403597483))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($H$98)),ISERROR($H$98)),1,IF(AND(LEN($H$98)>0,ABS((1-($H$98*-0.624118447303771+ 0.153952479362488)/ 0.316255124137648))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($I$98)),ISERROR($I$98)),1,IF(AND(LEN($I$98)>0,ABS((1-($I$98* 0.179820656776428+ 0.324025630950928)/ 0.352829148780984))<0.00005),0,1))","v":1},null,null,9]
[{"$f":"IF(OR(NOT(ISNUMBER($G$99)),ISERROR($G$99)),1,IF(AND(LEN($G$99)>0,ABS((1-($G$99* 3.98997962474822+ 0.132271885871887)/ 241.690743153711))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($H$99)),ISERROR($H$99)),1,IF(AND(LEN($H$99)>0,ABS((1-($H$99* 2.45377361774445+ 0.404779195785522)/-0.563448480162027))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($I$99)),ISERROR($I$99)),1,IF(AND(LEN($I$99)>0,ABS((1-($I$99* 1.17918908596039+ 0.34196412563324)/ 0.483625244291716))<0.00005),0,1))","v":1},null,null,8]
[{"$f":"IF(OR(NOT(ISNUMBER($G$100)),ISERROR($G$100)),1,IF(AND(LEN($G$100)>0,ABS((1-($G$100*-2.33064591884613+-0.361799240112305)/-115.807487588085))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($H$100)),ISERROR($H$100)),1,IF(AND(LEN($H$100)>0,ABS((1-($H$100* 2.7336710691452+-0.441519141197205)/-1.82109975952588))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($I$100)),ISERROR($I$100)),1,IF(AND(LEN($I$100)>0,ABS((1-($I$100* 3.1880122423172+-0.371644735336304)/-0.135958710647174))<0.00005),0,1))","v":1},null,null,7]
[{"$f":"IF(OR(NOT(ISNUMBER($G$101)),ISERROR($G$101)),1,IF(AND(LEN($G$101)>0,ABS((1-($G$101*-3.84352266788483+-0.156593441963196)/-155.925470776586))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($H$101)),ISERROR($H$101)),1,IF(AND(LEN($H$101)>0,ABS((1-($H$101*-2.21278607845306+-0.445497035980225)/ 0.870499214478921))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($I$101)),ISERROR($I$101)),1,IF(AND(LEN($I$101)>0,ABS((1-($I$101* 1.6948002576828+ 0.435083508491516)/ 0.497730811107431))<0.00005),0,1))","v":1},null,null,6]
[{"$f":"IF(OR(NOT(ISNUMBER($G$102)),ISERROR($G$102)),1,IF(AND(LEN($G$102)>0,ABS((1-($G$102* 4.94169056415558+ 0.186724424362183)/ 164.048107007048))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($H$102)),ISERROR($H$102)),1,IF(AND(LEN($H$102)>0,ABS((1-($H$102* 1.87122285366058+-0.110763192176819)/-1.36150777035571))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($I$102)),ISERROR($I$102)),1,IF(AND(LEN($I$102)>0,ABS((1-($I$102*-1.39531075954437+ 0.151545524597168)/ 0.130914785369896))<0.00005),0,1))","v":1},null,null,5]
[{"$f":"IF(OR(NOT(ISNUMBER($G$103)),ISERROR($G$103)),1,IF(AND(LEN($G$103)>0,ABS((1-($G$103* 3.51496875286102+ 0.469599366188049)/ 95.8309427053686))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($H$103)),ISERROR($H$103)),1,IF(AND(LEN($H$103)>0,ABS((1-($H$103* 1.48922264575958+ 0.447562456130981)/-0.637633064450975))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($I$103)),ISERROR($I$103)),1,IF(AND(LEN($I$103)>0,ABS((1-($I$103* 2.29315221309662+-0.211463093757629)/-0.20086746456866))<0.00005),0,1))","v":1},null,null,4]
[{"$f":"IF(OR(NOT(ISNUMBER($G$104)),ISERROR($G$104)),1,IF(AND(LEN($G$104)>0,ABS((1-($G$104*-4.15068089962006+ 0.211066722869873)/-91.9229621252684))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($H$104)),ISERROR($H$104)),1,IF(AND(LEN($H$104)>0,ABS((1-($H$104*-0.257971882820129+-0.302327036857605)/-0.10161802118762))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($I$104)),ISERROR($I$104)),1,IF(AND(LEN($I$104)>0,ABS((1-($I$104*-3.23872745037079+-0.268329858779907)/-0.271850966733382))<0.00005),0,1))","v":1},null,null,3]
[{"$f":"IF(OR(NOT(ISNUMBER($G$105)),ISERROR($G$105)),1,IF(AND(LEN($G$105)>0,ABS((1-($G$105* 2.79824197292328+ 0.428513884544373)/ 51.2486480007841))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($H$105)),ISERROR($H$105)),1,IF(AND(LEN($H$105)>0,ABS((1-($H$105*-2.09510743618011+-0.282070159912109)/ 1.43253536855281))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($I$105)),ISERROR($I$105)),1,IF(AND(LEN($I$105)>0,ABS((1-($I$105*-4.16992008686066+-0.0169261693954468)/-0.0176817510762248))<0.00005),0,1))","v":1},null,null,2]
[{"$f":"IF(OR(NOT(ISNUMBER($G$106)),ISERROR($G$106)),1,IF(AND(LEN($G$106)>0,ABS((1-($G$106*-0.155245661735535+-0.187026739120483)/-2.49387929610449))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($H$106)),ISERROR($H$106)),1,IF(AND(LEN($H$106)>0,ABS((1-($H$106*-4.83128130435944+-0.225500226020813)/ 3.88788316699753))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($I$106)),ISERROR($I$106)),1,IF(AND(LEN($I$106)>0,ABS((1-($I$106* 0.811448693275452+ 0.360123157501221)/ 0.360138634656778))<0.00005),0,1))","v":1},null,null,1]
[{"$f":"IF(OR(NOT(ISNUMBER($G$107)),ISERROR($G$107)),1,IF(AND(LEN($G$107)>0,ABS((1-($G$107*-3.86052429676056+-0.482303500175476)/-47.4172663967514))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($H$107)),ISERROR($H$107)),1,IF(AND(LEN($H$107)>0,ABS((1-($H$107*-0.0171679258346558+ 0.418522596359253)/ 0.433603303204672))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($I$107)),ISERROR($I$107)),1,IF(AND(LEN($I$107)>0,ABS((1-($I$107* 2.59305894374847+ 0.369951605796814)/ 0.36995407873053))<0.00005),0,1))","v":1},null,null,0]
[]
[]
[null,null,null,null,null,"What is the expected long-term return?"]
[]
[{"$f":"IF(OR(NOT(ISNUMBER($I$112)),ISERROR($I$112)),1,IF(AND(LEN($I$112)>0,ABS((1-($I$112* 3.26527655124664+ 0.0287599563598633)/ 0.0287599563598672))<0.00005),0,1))","v":1},null,null,null,null,"Expected long-term return:"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Index"]
[{"$f":"SUM($A$115:$C$145)","v":42},null,null,null,5,"Calculating probability distribution of logarithm of asset price in \"N\" period's time."]
[]
[null,null,null,null,null,"The distribution above is log-normal (as long as time intervals are relatively short).  We can confirm the log-normal nature of the distribution by charting the distribution of the logarithm of the asset price:  It should be normal."]
[]
[]
[null,null,null,null,null,"In the table below calculate the natural log of the asset price and the probability of that occuring."]
[]
[null,null,null,null,null,"Number of \"up\" moves in 20 periods","Ln of price in 20 periods","Probability "]
[]
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[{"$f":"IF(OR(NOT(ISNUMBER($G$124)),ISERROR($G$124)),1,IF(AND(LEN($G$124)>0,ABS((1-($G$124* 4.66598927974701+-0.163548588752747)/ 29.2821243610473))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($H$124)),ISERROR($H$124)),1,IF(AND(LEN($H$124)>0,ABS((1-($H$124* 1.61891520023346+ 0.318078517913818)/ 0.318109396270756))<0.00005),0,1))","v":1},null,null,null,{"$f":"F123-1","v":19}]
[{"$f":"IF(OR(NOT(ISNUMBER($G$125)),ISERROR($G$125)),1,IF(AND(LEN($G$125)>0,ABS((1-($G$125* 1.39495551586151+-0.257189631462097)/ 8.26603375466549))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($H$125)),ISERROR($H$125)),1,IF(AND(LEN($H$125)>0,ABS((1-($H$125*-0.823318362236022+-0.123811960220337)/-0.123961143959832))<0.00005),0,1))","v":1},null,null,null,18]
[{"$f":"IF(OR(NOT(ISNUMBER($G$126)),ISERROR($G$126)),1,IF(AND(LEN($G$126)>0,ABS((1-($G$126* 2.38848626613617+ 0.373706221580505)/ 14.4881354733628))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($H$126)),ISERROR($H$126)),1,IF(AND(LEN($H$126)>0,ABS((1-($H$126* 4.8811537027359+ 0.0254421234130859)/ 0.0307488586627187))<0.00005),0,1))","v":1},null,null,null,17]
[{"$f":"IF(OR(NOT(ISNUMBER($G$127)),ISERROR($G$127)),1,IF(AND(LEN($G$127)>0,ABS((1-($G$127* 4.59299266338348+-0.042284369468689)/ 26.1776915120926))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($H$127)),ISERROR($H$127)),1,IF(AND(LEN($H$127)>0,ABS((1-($H$127* 2.50003159046173+ 0.448030710220337)/ 0.459582236343181))<0.00005),0,1))","v":1},null,null,null,16]
[{"$f":"IF(OR(NOT(ISNUMBER($G$128)),ISERROR($G$128)),1,IF(AND(LEN($G$128)>0,ABS((1-($G$128* 3.16777646541595+ 0.25954806804657)/ 17.7077251605107))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($H$128)),ISERROR($H$128)),1,IF(AND(LEN($H$128)>0,ABS((1-($H$128*-0.282968878746033+-0.348660945892334)/-0.352844857688979))<0.00005),0,1))","v":1},null,null,null,15]
[{"$f":"IF(OR(NOT(ISNUMBER($G$129)),ISERROR($G$129)),1,IF(AND(LEN($G$129)>0,ABS((1-($G$129*-1.48371994495392+ 0.470670819282532)/-7.40394965088176))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($H$129)),ISERROR($H$129)),1,IF(AND(LEN($H$129)>0,ABS((1-($H$129* 1.41313374042511+-0.0164272785186768)/ 0.03580838563812))<0.00005),0,1))","v":1},null,null,null,14]
[{"$f":"IF(OR(NOT(ISNUMBER($G$130)),ISERROR($G$130)),1,IF(AND(LEN($G$130)>0,ABS((1-($G$130*-4.18266355991364+ 0.349933981895447)/-21.0095858232005))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($H$130)),ISERROR($H$130)),1,IF(AND(LEN($H$130)>0,ABS((1-($H$130*-4.55216348171234+-0.100617408752441)/-0.437153542616215))<0.00005),0,1))","v":1},null,null,null,13]
[{"$f":"IF(OR(NOT(ISNUMBER($G$131)),ISERROR($G$131)),1,IF(AND(LEN($G$131)>0,ABS((1-($G$131*-2.9435807466507+-0.385804533958435)/-14.8270358684842))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($H$131)),ISERROR($H$131)),1,IF(AND(LEN($H$131)>0,ABS((1-($H$131* 0.940402150154114+ 0.475489854812622)/ 0.588464459280885))<0.00005),0,1))","v":1},null,null,null,12]
[{"$f":"IF(OR(NOT(ISNUMBER($G$132)),ISERROR($G$132)),1,IF(AND(LEN($G$132)>0,ABS((1-($G$132*-4.4431072473526+-0.421054005622864)/-21.3273732549277))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($H$132)),ISERROR($H$132)),1,IF(AND(LEN($H$132)>0,ABS((1-($H$132*-0.948891043663025+ 0.176311016082764)/ 0.0243184664786896))<0.00005),0,1))","v":1},null,null,null,11]
[{"$f":"IF(OR(NOT(ISNUMBER($G$133)),ISERROR($G$133)),1,IF(AND(LEN($G$133)>0,ABS((1-($G$133* 3.01126182079315+ 0.0489341020584106)/ 13.6136653349613))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($H$133)),ISERROR($H$133)),1,IF(AND(LEN($H$133)>0,ABS((1-($H$133*-3.73749911785126+-0.130417108535767)/-0.788953434961058))<0.00005),0,1))","v":1},null,null,null,10]
[{"$f":"IF(OR(NOT(ISNUMBER($G$134)),ISERROR($G$134)),1,IF(AND(LEN($G$134)>0,ABS((1-($G$134*-0.98757803440094+ 0.458791136741638)/-3.79174090335921))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($H$134)),ISERROR($H$134)),1,IF(AND(LEN($H$134)>0,ABS((1-($H$134* 0.160637497901917+ 0.0919876098632813)/ 0.117718385837179))<0.00005),0,1))","v":1},null,null,null,9]
[{"$f":"IF(OR(NOT(ISNUMBER($G$135)),ISERROR($G$135)),1,IF(AND(LEN($G$135)>0,ABS((1-($G$135* 3.08490931987762+ 0.263656258583069)/ 12.9220431402216))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($H$135)),ISERROR($H$135)),1,IF(AND(LEN($H$135)>0,ABS((1-($H$135*-2.283656001091+-0.435222387313843)/-0.709567924935754))<0.00005),0,1))","v":1},null,null,null,8]
[{"$f":"IF(OR(NOT(ISNUMBER($G$136)),ISERROR($G$136)),1,IF(AND(LEN($G$136)>0,ABS((1-($G$136*-0.783849358558655+-0.420198559761047)/-3.47929197522201))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($H$136)),ISERROR($H$136)),1,IF(AND(LEN($H$136)>0,ABS((1-($H$136*-3.93353879451752+-0.0405993461608887)/-0.331401278830526))<0.00005),0,1))","v":1},null,null,null,7]
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[{"$f":"IF(OR(NOT(ISNUMBER($G$138)),ISERROR($G$138)),1,IF(AND(LEN($G$138)>0,ABS((1-($G$138* 0.606555342674255+ 0.11043393611908)/ 2.2341742550246))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($H$138)),ISERROR($H$138)),1,IF(AND(LEN($H$138)>0,ABS((1-($H$138*-3.28513085842133+ 0.294663429260254)/ 0.246090251132046))<0.00005),0,1))","v":1},null,null,null,5]
[{"$f":"IF(OR(NOT(ISNUMBER($G$139)),ISERROR($G$139)),1,IF(AND(LEN($G$139)>0,ABS((1-($G$139* 1.93627536296844+ 0.128754258155823)/ 6.5197073123758))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($H$139)),ISERROR($H$139)),1,IF(AND(LEN($H$139)>0,ABS((1-($H$139*-3.85183036327362+-0.280199766159058)/-0.297997348890362))<0.00005),0,1))","v":1},null,null,null,4]
[{"$f":"IF(OR(NOT(ISNUMBER($G$140)),ISERROR($G$140)),1,IF(AND(LEN($G$140)>0,ABS((1-($G$140* 4.02836263179779+ 0.297270655632019)/ 12.7850818557669))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($H$140)),ISERROR($H$140)),1,IF(AND(LEN($H$140)>0,ABS((1-($H$140*-0.291599631309509+ 0.317014217376709)/ 0.316697193546588))<0.00005),0,1))","v":1},null,null,null,3]
[{"$f":"IF(OR(NOT(ISNUMBER($G$141)),ISERROR($G$141)),1,IF(AND(LEN($G$141)>0,ABS((1-($G$141*-1.34655296802521+ 0.397294163703918)/-3.50676855820578))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($H$141)),ISERROR($H$141)),1,IF(AND(LEN($H$141)>0,ABS((1-($H$141* 4.58123028278351+-0.256895303726196)/-0.256065193411132))<0.00005),0,1))","v":1},null,null,null,2]
[{"$f":"IF(OR(NOT(ISNUMBER($G$142)),ISERROR($G$142)),1,IF(AND(LEN($G$142)>0,ABS((1-($G$142* 1.73254907131195+-0.034981369972229)/ 4.64052851493909))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($H$142)),ISERROR($H$142)),1,IF(AND(LEN($H$142)>0,ABS((1-($H$142*-4.69415605068207+ 0.448816299438477)/ 0.448726765517222))<0.00005),0,1))","v":1},null,null,null,1]
[{"$f":"IF(OR(NOT(ISNUMBER($G$143)),ISERROR($G$143)),1,IF(AND(LEN($G$143)>0,ABS((1-($G$143*-4.63167011737823+-0.317854285240173)/-11.8875803826441))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($H$143)),ISERROR($H$143)),1,IF(AND(LEN($H$143)>0,ABS((1-($H$143* 2.05619156360626+ 0.194463968276978)/ 0.194465929214061))<0.00005),0,1))","v":1},null,null,null,0]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Index"]
[{"$f":"SUM($A$147:$C$174)","v":64},null,null,null,6,"Calculating distribution of compound average growth rates over \"N\" periods."]
[]
[null,null,null,null,null,"Number of \"up\" moves in 20 periods","Price in 20 periods","Probability","Per period CAGR [%]"]
[]
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[{"$f":"IF(OR(NOT(ISNUMBER($G$152)),ISERROR($G$152)),1,IF(AND(LEN($G$152)>0,ABS((1-($G$152*-2.36111462116241+-0.353513121604919)/-1063.68928009019))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($H$152)),ISERROR($H$152)),1,IF(AND(LEN($H$152)>0,ABS((1-($H$152* 3.76072227954865+ 0.492675065994263)/ 0.4933565018016))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($I$152)),ISERROR($I$152)),1,IF(AND(LEN($I$152)>0,ABS((1-($I$152*-0.857101082801819+ 0.272675395011902)/ 0.205696178861152))<0.00005),0,1))","v":1},null,null,18]
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[{"$f":"IF(OR(NOT(ISNUMBER($G$155)),ISERROR($G$155)),1,IF(AND(LEN($G$155)>0,ABS((1-($G$155* 2.08207428455353+ 0.368339776992798)/ 513.937628116266))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($H$155)),ISERROR($H$155)),1,IF(AND(LEN($H$155)>0,ABS((1-($H$155* 1.71084821224213+-0.149076581001282)/-0.123780378644369))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($I$155)),ISERROR($I$155)),1,IF(AND(LEN($I$155)>0,ABS((1-($I$155*-2.65313565731049+-0.248939037322998)/-0.371452712007782))<0.00005),0,1))","v":1},null,null,15]
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[{"$f":"IF(OR(NOT(ISNUMBER($G$157)),ISERROR($G$157)),1,IF(AND(LEN($G$157)>0,ABS((1-($G$157* 2.75235235691071+-0.215800285339355)/ 454.255543831864))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($H$157)),ISERROR($H$157)),1,IF(AND(LEN($H$157)>0,ABS((1-($H$157*-1.77325069904327+-0.0513566732406616)/-0.182451028051219))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($I$157)),ISERROR($I$157)),1,IF(AND(LEN($I$157)>0,ABS((1-($I$157* 0.340560078620911+-0.174635648727417)/-0.165987987312738))<0.00005),0,1))","v":1},null,null,13]
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[{"$f":"IF(OR(NOT(ISNUMBER($G$160)),ISERROR($G$160)),1,IF(AND(LEN($G$160)>0,ABS((1-($G$160*-2.44031727313995+-0.0182288885116577)/-220.716148804726))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($H$160)),ISERROR($H$160)),1,IF(AND(LEN($H$160)>0,ABS((1-($H$160* 4.35649216175079+ 0.117655038833618)/ 0.885256114803724))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($I$160)),ISERROR($I$160)),1,IF(AND(LEN($I$160)>0,ABS((1-($I$160*-3.71782839298248+ 0.364292025566101)/ 0.38292787421272))<0.00005),0,1))","v":1},null,null,10]
[{"$f":"IF(OR(NOT(ISNUMBER($G$161)),ISERROR($G$161)),1,IF(AND(LEN($G$161)>0,ABS((1-($G$161*-4.59716260433197+ 0.297159671783447)/-339.869413940286))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($H$161)),ISERROR($H$161)),1,IF(AND(LEN($H$161)>0,ABS((1-($H$161*-1.40521347522736+-0.388818621635437)/-0.613904505061328))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($I$161)),ISERROR($I$161)),1,IF(AND(LEN($I$161)>0,ABS((1-($I$161* 2.27594196796417+ 0.201292753219604)/ 0.167276780768889))<0.00005),0,1))","v":1},null,null,9]
[{"$f":"IF(OR(NOT(ISNUMBER($G$162)),ISERROR($G$162)),1,IF(AND(LEN($G$162)>0,ABS((1-($G$162* 4.98886048793793+-0.112460732460022)/ 301.919535962474))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($H$162)),ISERROR($H$162)),1,IF(AND(LEN($H$162)>0,ABS((1-($H$162* 0.647802948951721+-0.0590448379516602)/ 0.0187785506052478))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($I$162)),ISERROR($I$162)),1,IF(AND(LEN($I$162)>0,ABS((1-($I$162*-2.23763287067413+-0.183526396751404)/-0.128077755884236))<0.00005),0,1))","v":1},null,null,8]
[{"$f":"IF(OR(NOT(ISNUMBER($G$163)),ISERROR($G$163)),1,IF(AND(LEN($G$163)>0,ABS((1-($G$163* 2.45018303394318+-0.250881910324097)/ 121.115930888136))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($H$163)),ISERROR($H$163)),1,IF(AND(LEN($H$163)>0,ABS((1-($H$163*-4.44882929325104+ 0.119725108146667)/-0.209171649754353))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($I$163)),ISERROR($I$163)),1,IF(AND(LEN($I$163)>0,ABS((1-($I$163*-3.34413945674896+-0.253551959991455)/-0.138125567367901))<0.00005),0,1))","v":1},null,null,7]
[{"$f":"IF(OR(NOT(ISNUMBER($G$164)),ISERROR($G$164)),1,IF(AND(LEN($G$164)>0,ABS((1-($G$164* 0.360276103019714+-0.491707682609558)/ 14.1094301139207))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($H$164)),ISERROR($H$164)),1,IF(AND(LEN($H$164)>0,ABS((1-($H$164* 2.55987942218781+-0.0430681705474854)/ 0.0515562786140436))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($I$164)),ISERROR($I$164)),1,IF(AND(LEN($I$164)>0,ABS((1-($I$164*-2.90492117404938+-0.176943421363831)/-0.0486771987698456))<0.00005),0,1))","v":1},null,null,6]
[{"$f":"IF(OR(NOT(ISNUMBER($G$165)),ISERROR($G$165)),1,IF(AND(LEN($G$165)>0,ABS((1-($G$165*-4.43920075893402+-0.426498413085938)/-147.625835254877))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($H$165)),ISERROR($H$165)),1,IF(AND(LEN($H$165)>0,ABS((1-($H$165*-4.40738499164581+ 0.4254070520401)/ 0.360240486230396))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($I$165)),ISERROR($I$165)),1,IF(AND(LEN($I$165)>0,ABS((1-($I$165*-4.55805480480194+ 0.473659753799438)/ 0.718415246874826))<0.00005),0,1))","v":1},null,null,5]
[{"$f":"IF(OR(NOT(ISNUMBER($G$166)),ISERROR($G$166)),1,IF(AND(LEN($G$166)>0,ABS((1-($G$166*-4.84718859195709+-0.162134289741516)/-131.666693233869))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($H$166)),ISERROR($H$166)),1,IF(AND(LEN($H$166)>0,ABS((1-($H$166*-2.84734189510345+-0.0148959159851074)/-0.0280522074525606))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($I$166)),ISERROR($I$166)),1,IF(AND(LEN($I$166)>0,ABS((1-($I$166* 1.56973540782928+-0.365287661552429)/-0.464408043056781))<0.00005),0,1))","v":1},null,null,4]
[{"$f":"IF(OR(NOT(ISNUMBER($G$167)),ISERROR($G$167)),1,IF(AND(LEN($G$167)>0,ABS((1-($G$167* 4.08954441547394+-0.0986473560333252)/ 90.6783148492542))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($H$167)),ISERROR($H$167)),1,IF(AND(LEN($H$167)>0,ABS((1-($H$167*-3.33715498447418+-0.417390465736389)/-0.421018582994748))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($I$167)),ISERROR($I$167)),1,IF(AND(LEN($I$167)>0,ABS((1-($I$167* 3.87772619724274+-0.252631187438965)/-0.533757082115587))<0.00005),0,1))","v":1},null,null,3]
[{"$f":"IF(OR(NOT(ISNUMBER($G$168)),ISERROR($G$168)),1,IF(AND(LEN($G$168)>0,ABS((1-($G$168* 0.308238863945007+ 0.031227707862854)/ 5.62929269191351))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($H$168)),ISERROR($H$168)),1,IF(AND(LEN($H$168)>0,ABS((1-($H$168*-3.34790885448456+ 0.295186281204224)/ 0.294579646413467))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($I$168)),ISERROR($I$168)),1,IF(AND(LEN($I$168)>0,ABS((1-($I$168* 4.96990621089935+-0.44612991809845)/-0.852455583435363))<0.00005),0,1))","v":1},null,null,2]
[{"$f":"IF(OR(NOT(ISNUMBER($G$169)),ISERROR($G$169)),1,IF(AND(LEN($G$169)>0,ABS((1-($G$169*-4.16145741939545+ 0.32953405380249)/-61.5070968793445))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($H$169)),ISERROR($H$169)),1,IF(AND(LEN($H$169)>0,ABS((1-($H$169* 2.73097693920136+-0.16190230846405)/-0.161850219212738))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($I$169)),ISERROR($I$169)),1,IF(AND(LEN($I$169)>0,ABS((1-($I$169* 1.43524944782257+-0.336538553237915)/-0.46703769716614))<0.00005),0,1))","v":1},null,null,1]
[{"$f":"IF(OR(NOT(ISNUMBER($G$170)),ISERROR($G$170)),1,IF(AND(LEN($G$170)>0,ABS((1-($G$170* 4.82497155666351+-0.173645615577698)/ 58.4867444198025))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($H$170)),ISERROR($H$170)),1,IF(AND(LEN($H$170)>0,ABS((1-($H$170*-4.20610368251801+ 0.403963088989258)/ 0.403959077736204))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($I$170)),ISERROR($I$170)),1,IF(AND(LEN($I$170)>0,ABS((1-($I$170* 3.66705119609833+ 0.106591820716858)/-0.260113298892975))<0.00005),0,1))","v":1},null,null,0]
[]
[]
[{"$f":"IF(OR(NOT(ISNUMBER($I$173)),ISERROR($I$173)),1,IF(AND(LEN($I$173)>0,ABS((1-($I$173* 1.90093338489532+ 0.467603921890259)/ 0.458551459571738))<0.00005),0,1))","v":1},null,null,null,null,"Expected / mean CAGR"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Index"]
[{"$f":"SUM($A$176:$C$251)","v":38},null,null,null,7,"Matching volatility and growth rate when evolving an asset's price."]
[]
[null,null,null,null,null,"Up till now we have assumed the asset's up and down moves in each time step are +/- 10%.  If we want to match a particular real-world growth rate and volatility then we need to calculate the up and down moves.  There are various ways of doing this.  One is illustrated below."]
[]
[]
[]
[null,null,null,null,null,"An asset has a yearly return volatility of 30%.  Its growth rate is 20% p.a. (continuously compounding).  Its current price is 100.  What is its expected price in one month's time?"]
[]
[]
[{"$f":"IF(OR(NOT(ISNUMBER($I$184)),ISERROR($I$184)),1,IF(AND(LEN($I$184)>0,ABS((1-($I$184*-2.6147323846817+-0.447105526924133)/-266.314749627956))<0.00005),0,1))","v":1},null,null,null,null,"Expected price in one month:"]
[]
[null,null,null,null,null,"Assume that in each month the asset can change in price from S to S*u or to S*d.  Each possibility is equally likely.  u and d are defined this way:"]
[]
[]
[null,null,null,null,null,"u = egdt + s(dt)1/2"]
[null,null,null,null,null,"d = egdt - s(dt)1/2"]
[]
[null,null,null,null,null,"g is the growth rate, dt is the time interval (one month i.e. 1/12 years) and s is the volatility."]
[]
[null,null,null,null,null,"Calculate the \"u\" (up) and \"d\" (down) factors."]
[]
[{"$f":"IF(OR(NOT(ISNUMBER($G$196)),ISERROR($G$196)),1,IF(AND(LEN($G$196)>0,ABS((1-($G$196* 4.15882647037506+ 0.346144199371338)/ 4.93503021875425))<0.00005),0,1))","v":1},null,null,null,null,"u factor"]
[{"$f":"IF(OR(NOT(ISNUMBER($G$197)),ISERROR($G$197)),1,IF(AND(LEN($G$197)>0,ABS((1-($G$197*-3.14818680286407+ 0.216104626655579)/-2.71235066902118))<0.00005),0,1))","v":1},null,null,null,null,"d factor"]
[]
[null,null,null,null,null,"Determine the asset price in one month if the current asset price (100) is multiplied by the u (up) or d (down) factors."]
[]
[]
[null,null,null,null,null,null,null,"Price in one month.","Probability"]
[{"$f":"IF(OR(NOT(ISNUMBER($H$203)),ISERROR($H$203)),1,IF(AND(LEN($H$203)>0,ABS((1-($H$203* 1.6673070192337+ 0.122164487838745)/ 184.094300018911))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($I$203)),ISERROR($I$203)),1,IF(AND(LEN($I$203)>0,ABS((1-($I$203*-4.78572905063629+ 0.464447379112244)/-1.9284171462059))<0.00005),0,1))","v":1},null,null,null,"\"up\" price"]
[{"$f":"IF(OR(NOT(ISNUMBER($H$204)),ISERROR($H$204)),1,IF(AND(LEN($H$204)>0,ABS((1-($H$204* 4.00462210178375+-0.26530933380127)/ 372.24615632903))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($I$204)),ISERROR($I$204)),1,IF(AND(LEN($I$204)>0,ABS((1-($I$204*-0.0731354951858521+ 0.374155640602112)/ 0.337587893009186))<0.00005),0,1))","v":1},null,null,null,"\"down\" price"]
[]
[null,null,null,null,null,"Find the expected price (i.e. the mean or average) in one month's time."]
[]
[{"$f":"IF(OR(NOT(ISNUMBER($K$208)),ISERROR($K$208)),1,IF(AND(LEN($K$208)>0,ABS((1-($K$208*-0.491215586662292+ 0.494818925857544)/-49.4522928844045))<0.00005),0,1))","v":1},null,null,null,null,"Expected price (mean of \"up\" and \"down\" prices):"]
[]
[null,null,null,null,null,{"$f":"\"Find the growth rate (p.a.) that is implied by having an asset price now of 100 and an asset price in one month of that shown in cell \" & ADDRESS(ROW(K208),COLUMN(K208),4)&\".\"","v":"Find the growth rate (p.a.) that is implied by having an asset price now of 100 and an asset price in one month of that shown in cell K208."}]
[]
[]
[{"$f":"IF(OR(NOT(ISNUMBER($K$213)),ISERROR($K$213)),1,IF(AND(LEN($K$213)>0,ABS((1-($K$213*-2.71829187870026+ 0.370095133781433)/-0.173563241958616))<0.00005),0,1))","v":1},null,null,null,null,"Growth rate implied by expected price:"]
[]
[null,null,null,null,null,{"$f":"\"You should find that the implied growth rate in cell \" & ADDRESS(ROW(K213),COLUMN(K213),4) & \" matches the asset's assumed growth rate of 20%.\"","v":"You should find that the implied growth rate in cell K213 matches the asset's assumed growth rate of 20%."}]
[]
[]
[null,null,null,null,null,{"$f":"\"Find the one-month returns implied by the asset prices in cells \" & ADDRESS(ROW(H203),COLUMN(H203),4)&\":\"&ADDRESS(ROW(H204),COLUMN(H204),4)&\".\"","v":"Find the one-month returns implied by the asset prices in cells H203:H204."}]
[]
[{"$f":"IF(OR(NOT(ISNUMBER($K$220)),ISERROR($K$220)),1,IF(AND(LEN($K$220)>0,ABS((1-($K$220*-3.94117772579193+-0.148659229278564)/-0.556211967385715))<0.00005),0,1))","v":1},null,null,null,null,"One-month return implied by asset's \"up\" price in one month."]
[{"$f":"IF(OR(NOT(ISNUMBER($K$221)),ISERROR($K$221)),1,IF(AND(LEN($K$221)>0,ABS((1-($K$221*-0.559943318367004+ 0.116389393806458)/ 0.155471315238921))<0.00005),0,1))","v":1},null,null,null,null,"One-month return implied by asset's \"down\" price in one month."]
[]
[null,null,null,null,null,{"$f":"\"Find the yearly volatility implied by the returns in cells \" & ADDRESS(ROW(K220),COLUMN(K220),4)&\":\"&ADDRESS(ROW(K221),COLUMN(K221),4)&\".\"","v":"Find the yearly volatility implied by the returns in cells K220:K221."}]
[]
[{"$f":"IF(OR(NOT(ISNUMBER($K$225)),ISERROR($K$225)),1,IF(AND(LEN($K$225)>0,ABS((1-($K$225* 4.35602962970734+ 0.406368017196655)/ 1.71317690610886))<0.00005),0,1))","v":1},null,null,null,null,{"$f":"\"Yearly volatiliy implied by the one month returns in cells \" & ADDRESS(ROW(K220),COLUMN(K220),4)&\":\"& ADDRESS(ROW(K221),COLUMN(K221),4)&\".\"","v":"Yearly volatiliy implied by the one month returns in cells K220:K221."}]
[]
[null,null,null,null,null,{"$f":"\"You should find that the volatility in cell \" & ADDRESS(ROW(K225),COLUMN(K225),4) & \" matches the asset's known volatility of 30%.\"","v":"You should find that the volatility in cell K225 matches the asset's known volatility of 30%."}]
[]
[null,null,null,null,null,"We have confirmed that our \"up\" and \"down\" factors generate an expected return and volatility that matches the asset's assumed values."]
[]
[]
[null,null,null,null,null,"Calculate the probability distribution of the asset's price in one year."]
[]
[null,null,null,null,null,"Number of \"up\" moves in one year.","Price in one year.","Probability"]
[]
[{"$f":"IF(OR(NOT(ISNUMBER($G$236)),ISERROR($G$236)),1,IF(AND(LEN($G$236)>0,ABS((1-($G$236* 3.9635556936264+-0.342955231666565)/ 1290.64627224312))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($H$236)),ISERROR($H$236)),1,IF(AND(LEN($H$236)>0,ABS((1-($H$236* 3.70521605014801+ 0.180957794189453)/ 0.181862387951696))<0.00005),0,1))","v":1},null,null,null,12]
[{"$f":"IF(OR(NOT(ISNUMBER($G$237)),ISERROR($G$237)),1,IF(AND(LEN($G$237)>0,ABS((1-($G$237*-4.15450870990753+-0.193424582481384)/-1140.96570749049))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($H$237)),ISERROR($H$237)),1,IF(AND(LEN($H$237)>0,ABS((1-($H$237* 0.29595673084259+ 0.130737543106079)/ 0.13160460384097))<0.00005),0,1))","v":1},null,null,null,{"$f":"F236-1","v":11}]
[{"$f":"IF(OR(NOT(ISNUMBER($G$238)),ISERROR($G$238)),1,IF(AND(LEN($G$238)>0,ABS((1-($G$238* 2.04204022884369+-0.20937168598175)/ 472.49020567627))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($H$238)),ISERROR($H$238)),1,IF(AND(LEN($H$238)>0,ABS((1-($H$238*-2.01615750789642+-0.0884699821472168)/-0.120956895116251))<0.00005),0,1))","v":1},null,null,null,10]
[{"$f":"IF(OR(NOT(ISNUMBER($G$239)),ISERROR($G$239)),1,IF(AND(LEN($G$239)>0,ABS((1-($G$239*-1.49648010730743+ 0.136608242988586)/-291.897448969248))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($H$239)),ISERROR($H$239)),1,IF(AND(LEN($H$239)>0,ABS((1-($H$239* 1.57172977924347+-0.105021715164185)/-0.0206026352243499))<0.00005),0,1))","v":1},null,null,null,9]
[{"$f":"IF(OR(NOT(ISNUMBER($G$240)),ISERROR($G$240)),1,IF(AND(LEN($G$240)>0,ABS((1-($G$240*-0.294361710548401+-0.185697197914124)/-48.6124674585346))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($H$240)),ISERROR($H$240)),1,IF(AND(LEN($H$240)>0,ABS((1-($H$240* 2.59099066257477+ 0.434170722961426)/ 0.747290932427859))<0.00005),0,1))","v":1},null,null,null,8]
[{"$f":"IF(OR(NOT(ISNUMBER($G$241)),ISERROR($G$241)),1,IF(AND(LEN($G$241)>0,ABS((1-($G$241* 0.680744051933289+-0.37349259853363)/ 94.0390462529531))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($H$241)),ISERROR($H$241)),1,IF(AND(LEN($H$241)>0,ABS((1-($H$241*-2.41723716259003+ 0.379266023635864)/-0.0881294433493168))<0.00005),0,1))","v":1},null,null,null,7]
[{"$f":"IF(OR(NOT(ISNUMBER($G$242)),ISERROR($G$242)),1,IF(AND(LEN($G$242)>0,ABS((1-($G$242* 1.54907643795013+-0.150349736213684)/ 180.967103530494))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($H$242)),ISERROR($H$242)),1,IF(AND(LEN($H$242)>0,ABS((1-($H$242*-1.12080037593842+-0.156881809234619)/-0.409718612791039))<0.00005),0,1))","v":1},null,null,null,6]
[{"$f":"IF(OR(NOT(ISNUMBER($G$243)),ISERROR($G$243)),1,IF(AND(LEN($G$243)>0,ABS((1-($G$243* 4.55001533031464+ 0.124417424201965)/ 448.603248132198))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($H$243)),ISERROR($H$243)),1,IF(AND(LEN($H$243)>0,ABS((1-($H$243*-2.1152800321579+ 0.216901540756226)/-0.192107684211806))<0.00005),0,1))","v":1},null,null,null,5]
[{"$f":"IF(OR(NOT(ISNUMBER($G$244)),ISERROR($G$244)),1,IF(AND(LEN($G$244)>0,ABS((1-($G$244* 3.57333123683929+-0.403622269630432)/ 296.519485559788))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($H$244)),ISERROR($H$244)),1,IF(AND(LEN($H$244)>0,ABS((1-($H$244* 0.857258439064026+ 0.435735702514648)/ 0.539335050008958))<0.00005),0,1))","v":1},null,null,null,4]
[{"$f":"IF(OR(NOT(ISNUMBER($G$245)),ISERROR($G$245)),1,IF(AND(LEN($G$245)>0,ABS((1-($G$245*-3.80956470966339+ 0.306607842445374)/-266.555990473071))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($H$245)),ISERROR($H$245)),1,IF(AND(LEN($H$245)>0,ABS((1-($H$245*-2.81048476696014+ 0.494310617446899)/ 0.343356845784001))<0.00005),0,1))","v":1},null,null,null,3]
[{"$f":"IF(OR(NOT(ISNUMBER($G$246)),ISERROR($G$246)),1,IF(AND(LEN($G$246)>0,ABS((1-($G$246*-1.81437075138092+-0.167682766914368)/-107.314685055845))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($H$246)),ISERROR($H$246)),1,IF(AND(LEN($H$246)>0,ABS((1-($H$246* 0.190206170082092+ 0.212511539459229)/ 0.215576384973247))<0.00005),0,1))","v":1},null,null,null,2]
[{"$f":"IF(OR(NOT(ISNUMBER($G$247)),ISERROR($G$247)),1,IF(AND(LEN($G$247)>0,ABS((1-($G$247* 0.587355494499207+ 0.177473187446594)/ 29.4187719573926))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($H$247)),ISERROR($H$247)),1,IF(AND(LEN($H$247)>0,ABS((1-($H$247* 0.365312695503235+ 0.251044034957886)/ 0.252114286995493))<0.00005),0,1))","v":1},null,null,null,1]
[{"$f":"IF(OR(NOT(ISNUMBER($G$248)),ISERROR($G$248)),1,IF(AND(LEN($G$248)>0,ABS((1-($G$248*-0.80055296421051+-0.0865741968154907)/-33.6856495577764))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($H$248)),ISERROR($H$248)),1,IF(AND(LEN($H$248)>0,ABS((1-($H$248* 1.19933187961578+ 0.377058982849121)/ 0.377351788483793))<0.00005),0,1))","v":1},null,null,null,0]
[]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Index"]
[{"$f":"SUM($A$253:$C$304)","v":43},null,null,null,8,"Calculating asset price distribution by using continuous log-normal distribution."]
[]
[null,null,null,null,null,"We can save ourselves some work in calculating the future asset price if we know or assume that short-term asset returns are normally distributed (as they have been on this worksheet).  In this case the log of the future asset price is normally distributed.  The mean and standard deviation of the natural logarithm of the future asset price is given by the following formulae:"]
[]
[]
[]
[]
[null,null,null,null,null,"m = ln(S) + (g-s2/2)T"]
[null,null,null,null,null,"sd = s * T1/2"]
[]
[null,null,null,null,null,"where m is the mean of the log distribution, sd is its standard deviation, g is the continuously compounding short-term growth rate of the asset, s is the asset's yearly return volatility and T is the time (in years) at which we are calculating the asset price distribution."]
[]
[]
[]
[]
[null,null,null,null,null,"We'll calculate the distribution of asset prices for the case we considered above."]
[]
[null,null,null,null,null,"Calculate the mean m and standard deviation sd of the log of future asset prices using the two formulae above."]
[]
[{"$f":"IF(OR(NOT(ISNUMBER($G$271)),ISERROR($G$271)),1,IF(AND(LEN($G$271)>0,ABS((1-($G$271*-3.36762249469757+-0.430467009544373)/-16.4609232064666))<0.00005),0,1))","v":1},null,null,null,null,"Mean"]
[{"$f":"IF(OR(NOT(ISNUMBER($G$272)),ISERROR($G$272)),1,IF(AND(LEN($G$272)>0,ABS((1-($G$272*-2.56347358226776+-0.0202224254608154)/-0.789264500141144))<0.00005),0,1))","v":1},null,null,null,null,"sd"]
[]
[null,null,null,null,null,"In the table below the asset price column contains asset prices that are \"evenly\" spaced:  Each asset price is a fixed multiple of the asset price below it. [In this case the \"even\" spacing is in a geometrical rather than arithmetic sense.]"]
[]
[]
[]
[null,null,null,null,null,{"$f":"\"i)  In cells \" & ADDRESS(ROW(G289),COLUMN(G289),4)&\":\"&ADDRESS(ROW(G302),COLUMN(G302),4) & \" calculate the natural logs of the asset prices that are in the column to the left.\"","v":"i)  In cells G289:G302 calculate the natural logs of the asset prices that are in the column to the left."}]
[null,null,null,null,null,{"$f":"\"ii) Cells \" &ADDRESS(ROW(H289),COLUMN(H289),4)&\":\"&ADDRESS(ROW(H302),COLUMN(H302),4) & \" are the same as the cells to the left except they are 'shifted' by half a division.  So, for example, cell \"& ADDRESS(ROW(H289),COLUMN(H289),4)&\" contains a number that is midway between the numbers in cells \" & ADDRESS(ROW(G289),COLUMN(G289),4)&\" and \" &ADDRESS(ROW(G290),COLUMN(G290),4)&\".\"","v":"ii) Cells H289:H302 are the same as the cells to the left except they are 'shifted' by half a division.  So, for example, cell H289 contains a number that is midway between the numbers in cells G289 and G290."}]
[]
[null,null,null,null,null,{"$f":"\"iii) In cells \" &ADDRESS(ROW(I289),COLUMN(I289),4)&\":\"&ADDRESS(ROW(I302),COLUMN(I302),4) & \" calculate the probability that the log of the asset price in one year's time will be less than or equal to the log of the asset price in column \"& CHAR(CODE(\"A\")+COLUMN(H:H)-1)&\".  To do this you will need to use a function that calculates cumulative normal distributions.\"","v":"iii) In cells I289:I302 calculate the probability that the log of the asset price in one year's time will be less than or equal to the log of the asset price in column H.  To do this you will need to use a function that calculates cumulative normal distributions."}]
[]
[]
[null,null,null,null,null,{"$f":"\"iv) In cells \" &ADDRESS(ROW(J289),COLUMN(J289),4)&\":\"&ADDRESS(ROW(J302),COLUMN(J302),4) & \" calculate the difference between successive cumulative normal probabilities.  This will determine the probability that a future asset price will fall into the corresponding interval.\"","v":"iv) In cells J289:J302 calculate the difference between successive cumulative normal probabilities.  This will determine the probability that a future asset price will fall into the corresponding interval."}]
[]
[]
[null,null,null,null,null,"Asset price","ln(Asset price)","Shifted by 1/2 division","Cumulative normal probability","Difference between successive cumulative normal probabilities"]
[]
[{"$f":"IF(OR(NOT(ISNUMBER($G$289)),ISERROR($G$289)),1,IF(AND(LEN($G$289)>0,ABS((1-($G$289*-3.16548883914948+ 0.273785471916199)/-18.5823302945828))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($I$289)),ISERROR($I$289)),1,IF(AND(LEN($I$289)>0,ABS((1-($I$289*-4.13782536983489+-0.163883686065674)/-4.30127015324631))<0.00005),0,1))","v":1},null,null,null,{"$f":"F290*F290/F291","v":386.36343609092495},null,{"$f":"G289-LN($F$289/$F$290)/2","v":-8.5377974552775612E-2}]
[{"$f":"IF(OR(NOT(ISNUMBER($G$290)),ISERROR($G$290)),1,IF(AND(LEN($G$290)>0,ABS((1-($G$290* 2.12335288524628+-0.356568217277527)/ 11.9291993981924))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($I$290)),ISERROR($I$290)),1,IF(AND(LEN($I$290)>0,ABS((1-($I$290*-1.41617953777313+ 0.126312017440796)/-1.28865028438884))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($J$290)),ISERROR($J$290)),1,IF(AND(LEN($J$290)>0,ABS((1-($J$290* 2.71679818630219+-0.0743967294692993)/-0.0723497576774838))<0.00005),0,1))","v":1},null,null,{"$f":"(EXP(20%/12)+0.3*SQRT(1/12))^F236*(EXP(20%/12)-0.3*SQRT(1/12))^(12-F236)*100","v":325.71492045658982},null,-8.5377974552775612E-2]
[{"$f":"IF(OR(NOT(ISNUMBER($G$291)),ISERROR($G$291)),1,IF(AND(LEN($G$291)>0,ABS((1-($G$291*-1.18747651576996+-0.300453186035156)/-6.96845037073342))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($I$291)),ISERROR($I$291)),1,IF(AND(LEN($I$291)>0,ABS((1-($I$291*-1.23561680316925+ 0.387939095497131)/-0.841316782112259))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($J$291)),ISERROR($J$291)),1,IF(AND(LEN($J$291)>0,ABS((1-($J$291*-0.855891108512878+-0.41042685508728)/-0.414097305595915))<0.00005),0,1))","v":1},null,null,274.58656668297118,null,-8.5377974552775612E-2]
[{"$f":"IF(OR(NOT(ISNUMBER($G$292)),ISERROR($G$292)),1,IF(AND(LEN($G$292)>0,ABS((1-($G$292* 4.87853467464447+-0.0407887697219849)/ 26.520445093251))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($I$292)),ISERROR($I$292)),1,IF(AND(LEN($I$292)>0,ABS((1-($I$292* 2.34041750431061+-0.219661235809326)/ 2.06707293197504))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($J$292)),ISERROR($J$292)),1,IF(AND(LEN($J$292)>0,ABS((1-($J$292*-2.83417999744415+ 0.119949460029602)/ 0.0695307346074916))<0.00005),0,1))","v":1},null,null,231.48396916250732,null,-8.5377974552775612E-2]
[{"$f":"IF(OR(NOT(ISNUMBER($G$293)),ISERROR($G$293)),1,IF(AND(LEN($G$293)>0,ABS((1-($G$293* 4.610555768013+ 0.221611738204956)/ 24.5365517710911))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($I$293)),ISERROR($I$293)),1,IF(AND(LEN($I$293)>0,ABS((1-($I$293* 2.75819718837738+ 0.0430663824081421)/ 2.58960285392898))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($J$293)),ISERROR($J$293)),1,IF(AND(LEN($J$293)>0,ABS((1-($J$293* 1.3921457529068+ 0.0946054458618164)/ 0.169504678304558))<0.00005),0,1))","v":1},null,null,195.14730318579629,null,-8.5377974552775612E-2]
[{"$f":"IF(OR(NOT(ISNUMBER($G$294)),ISERROR($G$294)),1,IF(AND(LEN($G$294)>0,ABS((1-($G$294* 1.84426486492157+-0.0155175924301147)/ 9.39576366226829))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($I$294)),ISERROR($I$294)),1,IF(AND(LEN($I$294)>0,ABS((1-($I$294*-4.3674248456955+ 0.327603578567505)/-3.18642776241374))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($J$294)),ISERROR($J$294)),1,IF(AND(LEN($J$294)>0,ABS((1-($J$294* 2.20051229000092+-0.0762492418289185)/ 0.184865547388755))<0.00005),0,1))","v":1},null,null,164.51450214228137,null,-8.5377974552775612E-2]
[{"$f":"IF(OR(NOT(ISNUMBER($G$295)),ISERROR($G$295)),1,IF(AND(LEN($G$295)>0,ABS((1-($G$295*-1.42975270748138+ 0.361585140228271)/-6.69030232290446))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($I$295)),ISERROR($I$295)),1,IF(AND(LEN($I$295)>0,ABS((1-($I$295*-3.77743065357208+ 0.454682469367981)/-1.86353595414943))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($J$295)),ISERROR($J$295)),1,IF(AND(LEN($J$295)>0,ABS((1-($J$295* 3.01583111286163+ 0.165849447250366)/ 0.741565141184893))<0.00005),0,1))","v":1},null,null,138.69021489553751,null,-8.5377974552775612E-2]
[{"$f":"IF(OR(NOT(ISNUMBER($G$296)),ISERROR($G$296)),1,IF(AND(LEN($G$296)>0,ABS((1-($G$296* 0.456456542015076+-0.0740286111831665)/ 2.09938320073246))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($I$296)),ISERROR($I$296)),1,IF(AND(LEN($I$296)>0,ABS((1-($I$296*-0.866488814353943+-0.496358871459961)/-0.83399518731627))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($J$296)),ISERROR($J$296)),1,IF(AND(LEN($J$296)>0,ABS((1-($J$296*-2.3701649904251+-0.168180823326111)/-0.699197601985724))<0.00005),0,1))","v":1},null,null,116.91963600348669,null,-8.5377974552775612E-2]
[{"$f":"IF(OR(NOT(ISNUMBER($G$297)),ISERROR($G$297)),1,IF(AND(LEN($G$297)>0,ABS((1-($G$297* 2.72223770618439+ 0.44777512550354)/ 12.9448358203295))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($I$297)),ISERROR($I$297)),1,IF(AND(LEN($I$297)>0,ABS((1-($I$297* 1.18325650691986+ 0.452560305595398)/ 0.686646183632918))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($J$297)),ISERROR($J$297)),1,IF(AND(LEN($J$297)>0,ABS((1-($J$297*-4.00302350521088+ 0.146261692047119)/-0.621632031968461))<0.00005),0,1))","v":1},null,null,98.566443879867947,null,-8.5377974552775612E-2]
[{"$f":"IF(OR(NOT(ISNUMBER($G$298)),ISERROR($G$298)),1,IF(AND(LEN($G$298)>0,ABS((1-($G$298* 2.30141341686249+-0.25471293926239)/ 9.91747666411309))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($I$298)),ISERROR($I$298)),1,IF(AND(LEN($I$298)>0,ABS((1-($I$298* 0.869958996772766+-0.162068605422974)/-0.0942021266086182))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($J$298)),ISERROR($J$298)),1,IF(AND(LEN($J$298)>0,ABS((1-($J$298*-0.555611252784729+ 0.484474539756775)/ 0.417900770372591))<0.00005),0,1))","v":1},null,null,83.094202062290336,null,-8.5377974552775612E-2]
[{"$f":"IF(OR(NOT(ISNUMBER($G$299)),ISERROR($G$299)),1,IF(AND(LEN($G$299)>0,ABS((1-($G$299* 4.73193228244781+ 0.118060111999512)/ 20.2250765772865))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($I$299)),ISERROR($I$299)),1,IF(AND(LEN($I$299)>0,ABS((1-($I$299* 0.37890613079071+-0.347394347190857)/-0.338520781640594))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($J$299)),ISERROR($J$299)),1,IF(AND(LEN($J$299)>0,ABS((1-($J$299*-1.26659095287322+ 0.453994035720825)/ 0.384848021779618))<0.00005),0,1))","v":1},null,null,70.050679973643639,null,-8.5377974552775612E-2]
[{"$f":"IF(OR(NOT(ISNUMBER($G$300)),ISERROR($G$300)),1,IF(AND(LEN($G$300)>0,ABS((1-($G$300*-3.29042017459869+ 0.0807961225509644)/-13.3390609147099))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($I$300)),ISERROR($I$300)),1,IF(AND(LEN($I$300)>0,ABS((1-($I$300*-1.43408238887787+-0.0492253303527832)/-0.0567968739759277))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($J$300)),ISERROR($J$300)),1,IF(AND(LEN($J$300)>0,ABS((1-($J$300* 0.910164713859558+ 0.339419484138489)/ 0.355929133797365))<0.00005),0,1))","v":1},null,null,59.054634896082206,null,-8.5377974552775612E-2]
[{"$f":"IF(OR(NOT(ISNUMBER($G$301)),ISERROR($G$301)),1,IF(AND(LEN($G$301)>0,ABS((1-($G$301*-2.2567480802536+ 0.366763830184937)/-8.45194662418459))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($I$301)),ISERROR($I$301)),1,IF(AND(LEN($I$301)>0,ABS((1-($I$301*-4.14519369602203+-0.121267914772034)/-0.1249388788287))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($J$301)),ISERROR($J$301)),1,IF(AND(LEN($J$301)>0,ABS((1-($J$301* 3.38272154331207+ 0.379268646240234)/ 0.394132723298086))<0.00005),0,1))","v":1},null,null,49.784668814374299,null,-8.5377974552775612E-2]
[{"$f":"IF(OR(NOT(ISNUMBER($G$302)),ISERROR($G$302)),1,IF(AND(LEN($G$302)>0,ABS((1-($G$302*-3.15070927143097+ 0.419498085975647)/-11.3545484937454))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($I$302)),ISERROR($I$302)),1,IF(AND(LEN($I$302)>0,ABS((1-($I$302* 4.48640167713165+ 0.10016655921936)/ 0.100659181952609))<0.00005),0,1))","v":1},{"$f":"IF(OR(NOT(ISNUMBER($J$302)),ISERROR($J$302)),1,IF(AND(LEN($J$302)>0,ABS((1-($J$302*-3.83770525455475+-0.406385540962219)/-0.409362801122885))<0.00005),0,1))","v":1},null,null,41.969834430749522,null,-8.5377974552775612E-2]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Index"]
[{"$f":"SUM($A$306:$C$334)","v":7},null,null,null,9,"Calculating confidence intervals on an asset's future price."]
[]
[null,null,null,null,null,{"$f":"\"An asset has a spot price of $\" & I310& \", an expected yearly return of \" & TEXT(I311,\"0%\")& \", and a volatility of \" & TEXT(I312,\"0%\")&\".  Within a confidence level of \"&TEXT(I315,\"0.0%\")&\" - what is the lowest value the asset's price be in \" & I314 & \" years.?\"","v":"An asset has a spot price of $80, an expected yearly return of 8%, and a volatility of 25%.  Within a confidence level of 99.0% - what is the lowest value the asset's price be in 0.5 years.?"}]
[]
[]
[null,null,null,null,null,"Spot price [S]",null,"[$]",80]
[null,null,null,null,null,"Expected return [m]",null,"[%]",0.08]
[null,null,null,null,null,"Volatility [s]",null,"[%]",0.25]
[]
[null,null,null,null,null,"Future time [T]",null,"[yrs]",0.5]
[null,null,null,null,null,"Confidence level [p]",null,"[%]",0.99]
[]
[{"$f":"IF(OR(NOT(ISNUMBER($J$317)),ISERROR($J$317)),1,IF(AND(LEN($J$317)>0,ABS((1-($J$317* 2.72238314151764+-0.158469676971436)/ 11.8374438480205))<0.00005),0,1))","v":1},null,null,null,null,"Mean of ln(ST) = ln(S) + (m - s2/2)*T"]
[{"$f":"IF(OR(NOT(ISNUMBER($J$318)),ISERROR($J$318)),1,IF(AND(LEN($J$318)>0,ABS((1-($J$318* 0.0566357374191284+-0.165264010429382)/-0.155252131932741))<0.00005),0,1))","v":1},null,null,null,null,"Standard deviation of ln(ST) = s*T1/2"]
[]
[{"$f":"IF(OR(NOT(ISNUMBER($K$320)),ISERROR($K$320)),1,IF(AND(LEN($K$320)>0,ABS((1-($K$320*-4.29397761821747+ 0.131253004074097)/-17.0238640770857))<0.00005),0,1))","v":1},null,null,null,null,{"$f":"TEXT(I315,\"0.0%\")& \"   confidence   limit   on   lowest  value  of \"","v":"99.0%   confidence   limit   on   lowest  value  of "},null,null,null,"ln(ST)"]
[{"$f":"IF(OR(NOT(ISNUMBER($K$321)),ISERROR($K$321)),1,IF(AND(LEN($K$321)>0,ABS((1-($K$321*-1.67947828769684+-0.481099724769592)/-91.73454494059))<0.00005),0,1))","v":1},null,null,null,null,{"$f":"TEXT(I315,\"0.0%\")& \"   confidence   limit   on   lowest  value  of \"","v":"99.0%   confidence   limit   on   lowest  value  of "},null,null,null,"ST"]
[]
[null,null,null,null,null,{"$f":"\"Continuing with the example above:  Within a confidence level of \" & TEXT(I315,\"0%\") & \" - below what value will the asset be in \" & I314 & \" years?\"","v":"Continuing with the example above:  Within a confidence level of 99% - below what value will the asset be in 0.5 years?"}]
[]
[]
[{"$f":"IF(OR(NOT(ISNUMBER($J$326)),ISERROR($J$326)),1,IF(AND(LEN($J$326)>0,ABS((1-($J$326* 2.78119146823883+-0.021327018737793)/ 343.938595245566))<0.00005),0,1))","v":1},null,null,null,null,{"$f":"\"With \" & TEXT(I315,\"0.0%\") & \" confidence asset will be below:\"","v":"With 99.0% confidence asset will be below:"}]
[]
[null,null,null,null,null,{"$f":"\"Continuing with the example above:  Within a confidence level of \" & TEXT(I315,\"0%\") & \" - between which values will the asset be in \" & I314 & \" years? [Assume that the \" & TEXT(1-I315,\"0.0%\") & \" of values ourside the \" & TEXT(I315,\"0.0%\") & \" limit are equally distributed above the upper confidence value and below the lower confidence value.]\"","v":"Continuing with the example above:  Within a confidence level of 99% - between which values will the asset be in 0.5 years? [Assume that the 1.0% of values ourside the 99.0% limit are equally distributed above the upper confidence value and below the lower confidence value.]"}]
[]
[]
[]
[{"$f":"IF(OR(NOT(ISNUMBER($J$332)),ISERROR($J$332)),1,IF(AND(LEN($J$332)>0,ABS((1-($J$332*-3.70119869709015+ 0.355152726173401)/-478.024641680538))<0.00005),0,1))","v":1},null,null,null,null,"Between this upper value:"]
[{"$f":"IF(OR(NOT(ISNUMBER($J$333)),ISERROR($J$333)),1,IF(AND(LEN($J$333)>0,ABS((1-($J$333* 3.30152809619904+ 0.390198945999146)/ 172.037271237901))<0.00005),0,1))","v":1},null,null,null,null,"And this lower value:"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Index"]
[{"$f":"SUM($A$336:$C$360)","v":2},null,null,null,{"$f":"E305+1","v":10},"Calculating confidence intervals on an asset's future price (alternate formula)"]
[]
[null,null,null,null,null,"Spot price [S]",null,"[$]",80]
[null,null,null,null,null,"Expected return [m]",null,"[%]",0.08]
[null,null,null,null,null,"Volatility [s]",null,"[%]",0.25]
[]
[null,null,null,null,null,"Future time [T]",null,"[yrs]",0.5]
[null,null,null,null,null,"Number sd's",null,"[#]",{"$f":"NORMSINV((1+I315)/2)","v":2.5758293035488999}]
[null,null,null,null,null,"Confidence level [p]",null,"[%]",{"$f":"1-(1-NORMSDIST(I342))*2","v":0.99}]
[]
[{"$f":"IF(OR(NOT(ISNUMBER($H$345)),ISERROR($H$345)),1,IF(AND(LEN($H$345)>0,ABS((1-($H$345*-0.575786232948303+ 0.0261715650558472)/-74.3941777008661))<0.00005),0,1))","v":1},null,null,null,null,"Upper limit"]
[{"$f":"IF(OR(NOT(ISNUMBER($H$346)),ISERROR($H$346)),1,IF(AND(LEN($H$346)>0,ABS((1-($H$346*-2.58831441402435+ 0.134934902191162)/-134.43202269835))<0.00005),0,1))","v":1},null,null,null,null,"Lower limit"]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[null,null,null,null,null,null,null,"Copyright (c) 2020 Tykoh Group Pty Ltd.  All rights reserved.",null,null,null,null,null,null,null,"Index"]
[null,null,null,null,null,null,null,"www.tykoh.com"]

{"sheet":"Multi_asset","index":26,"n_rows":29,"n_cols":13,"rows_kept":29,"cut":false,"hidden":false,"merged":[[28,4,28,10],[0,3,0,9],[3,3,4,11],[18,5,18,7],[15,3,16,11],[27,4,27,10]]}
[null,null,null,"Click here to see what your answer should look like."]
[{"$f":"SUM($A$3:$A$13)","v":1},null,1,"Calculating return of a portfolio of assets",null,null,null,null,null,null,"Asset_Evolution","Multi_asset"]
[]
[null,null,null,"A set of assets comprises a portfolio.  The returns of each asset together with their portfolio weights are shown below.  Find the portfolio return."]
[]
[]
[null,null,null,"Asset","Return","Portfolio weight"]
[null,null,null,"# 1",0.06,0.2]
[null,null,null,"# 2",0.1,0.25]
[null,null,null,"# 3",0.11,0.55000000000000004]
[]
[{"$f":"IF(OR(NOT(ISNUMBER($F$12)),ISERROR($F$12)),1,IF(AND(LEN($F$12)>0,ABS((1-($F$12* 0.248638987541199+ 0.0788928270339966)/ 0.103135128319263))<0.00005),0,1))","v":1},null,null,"Portfolio return"]
[null,null,null,null,null,null,null,null,null,null,null,null,"Index"]
[{"$f":"SUM($A$15:$A$28)","v":1},null,{"$f":"C2+1","v":2},"Calculating volatility of a portfolio of assets"]
[]
[null,null,null,"A set of assets comprises a portfolio.  The asset covariance matrix is shown below together with each asset's portfolio weights.  Find the portfolio volatility."]
[]
[]
[null,null,null,null,null,"Variance / covariance matrix"]
[null,null,null,"Asset",null,"#1","#2","#3",null,"Portfolio weight"]
[null,null,null,"# 1",null,0.01,6.000000000000001E-3,6.0000000000000001E-3,null,0.2]
[null,null,null,"# 2",null,6.000000000000001E-3,0.09,2.4E-2,null,0.25]
[null,null,null,"# 3",null,6.0000000000000001E-3,2.4E-2,0.04,null,0.55000000000000004]
[]
[{"$f":"IF(OR(NOT(ISNUMBER($F$25)),ISERROR($F$25)),1,IF(AND(LEN($F$25)>0,ABS((1-($F$25*-0.671417117118835+-0.239694833755493)/-0.349292238760323))<0.00005),0,1))","v":1},null,null,"Portfolio volatility"]
[]
[]
[null,null,null,null,"Copyright (c) 2020 Tykoh Group Pty Ltd.  All rights reserved.",null,null,null,null,null,null,null,"Index"]
[null,null,null,null,"www.tykoh.com"]

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