Return Calculations

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1、Chapter1ReturnCalculationsUpdated:June24,2014InthisChapterwecoverassetreturncalculationswithanemphasisonequityreturns.Section1.1coversbasictimevalueofmoneycalculations.Section1.2coversassetreturncalculations,includingbothsimpleandcontin-uouslycompoundedreturns.Section1.

2、3illustratesassetreturncalculationsusingR.1.1TheTimeValueofMoneyThissectionreviewsbasictimevalueofmoneycalculations.Theconceptsoffuturevalue,presentvalueandthecompoundingofinterestaredefinedanddiscussed.1.1.1Futurevalue,presentvalueandsimpleinterest.Consideranamount$inv

3、estedforyearsatasimpleinterestrateofperannum(whereisexpressedasadecimal).Ifcompoundingtakesplaceonlyattheendoftheyearthefuturevalueafteryearsis:=$(1+)×···×(1+)=$·(1+)(1.1)Overthefirstyear,$growsto$(1+)=$+$×whichrepresentstheinitialprinciple$plusthepa

4、ymentofsimpleinterest$×fortheyear.Overthesecondyear,thenewprinciple$(1+)growsto$(1+)(1+)=$(1+)2andsoon.12CHAPTER1RETURNCALCULATIONSExample1Futurevaluewithsimpleinterest.Considerputting$1000inaninterestcheckingaccountthatpaysasimpleannualpercentagerateof3%Thef

5、uturevalueafter=15and10yearsis,respectively,11=$1000·(103)=$103055=$1000·(103)=$1159271010=$1000·(103)=$134392Overthefirstyear,$30ininterestispaid;overthreeyears,$15927ininterestisaccrued;overfiveyears,$34392ininterestisaccrued¥Thefuturevalueformula(1.1)

6、definesarelationshipbetweenfourvari-ables:andGiventhreevariables,thefourthvariablecanbedetermined.Givenandandsolvingforgivesthepresentvalueformula:=(1.2)(1+)Givenandtheannualinterestrateontheinvestmentisdefinedas:µ¶1=−1(1.3)Finally,gi

7、venandwecansolvefor:ln()=(1.4)ln(1+)Theexpression(1.4)canbeusedtodeterminethenumberyearsittakesforaninvestmentof$todouble.Setting=2in(1.4)gives:ln(2)07=≈ln(1+)whichusestheapproximationsln(2)=06931≈07andln(1+)≈forclosetozero(seetheAppendix).

8、Theapproximation≈07iscalledtheruleof70.Example2Usingtheruleof70.1.1THETIMEVALUEOFMONEY3Thetablebelowsummar