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CHAPTER 9 CapitalMarketTheory AnOverview 9 0 ChapterOutline 9 1Returns9 2Holding PeriodReturns9 3ReturnStatistics9 4AverageStockReturnsandRisk FreeReturns9 5RiskStatistics9 6SummaryandConclusions 9 1 9 1Returns DollarReturnsthesumofthecashreceivedandthechangeinvalueoftheasset indollars Time 0 1 PercentageReturnsthesumofthecashreceivedandthechangeinvalueoftheassetdividedbytheoriginalinvestment 9 2 9 1Returns DollarReturn Dividend ChangeinMarketValue 9 3 9 1Returns Example Supposeyoubought100sharesofWal Mart WMT oneyearagotodayat 25 Overthelastyear youreceived 20individends 20centspershare 100shares Attheendoftheyear thestocksellsfor 30 Howdidyoudo Quitewell Youinvested 25 100 2 500 Attheendoftheyear youhavestockworth 3 000andcashdividendsof 20 Yourdollargainwas 520 20 3 000 2 500 Yourpercentagegainfortheyearis 9 4 9 1Returns Example DollarReturn 520gain Time 0 1 3 000 20 PercentageReturn 9 5 9 2Holding PeriodReturns Theholdingperiodreturnisthereturnthataninvestorwouldgetwhenholdinganinvestmentoveraperiodofnyears whenthereturnduringyeariisgivenasri EndingMarketvalue BeginningMarketValue 1 Holding PeriodReturn 9 6 GeometricMeanReturnversusArithmeticMeanReturn 9 7 HoldingPeriodReturn Example Supposeyourinvestmentprovidesthefollowingreturnsoverafour yearperiod 9 8 HoldingPeriodReturn Example Aninvestorwhoheldthisinvestmentwouldhaveactuallyrealizedanannualreturnof9 58 So ourinvestormade9 58 onhismoneyforfouryears realizingaholdingperiodreturnof44 21 9 9 HoldingPeriodReturn Example Notethatthegeometricaverageisnotthesamethingasthearithmeticaverage 9 10 HoldingPeriodReturns Afamoussetofstudiesdealingwiththeratesofreturnsoncommonstocks bonds andTreasurybillswasconductedbyRogerIbbotsonandRexSinquefield Theypresentyear by yearhistoricalratesofreturnstartingin1926forthefollowingfiveimportanttypesoffinancialinstrumentsintheUnitedStates Large CompanyCommonStocksSmall companyCommonStocksLong TermCorporateBondsLong TermU S GovernmentBonds 20years U S TreasuryBills 3months 9 11 TheFutureValueofanInvestmentof 1in1925 59 70 17 48 Source Stocks Bonds Bills andInflation2003Yearbook IbbotsonAssociates Inc Chicago annuallyupdatesworkbyRogerG IbbotsonandRexA Sinquefield Allrightsreserved 1 775 34 9 12 ReturnVarianceandReturnStandardDeviation 9 13 9 3ReturnStatistics Thehistoryofcapitalmarketreturnscanbesummarizedbydescribingtheaveragereturnthestandarddeviationofthosereturnsthefrequencydistributionofthereturns 9 14 ReturnStatistics AnExample 9 15 9 16 9 17 HistoricalReturns 1926 2002 Source Stocks Bonds Bills andInflation2003Yearbook IbbotsonAssociates Inc Chicago annuallyupdatesworkbyRogerG IbbotsonandRexA Sinquefield Allrightsreserved 90 90 0 AverageStandardSeriesAnnualReturnDeviationDistributionLargeCompanyStocks12 2 20 5 SmallCompanyStocks16 933 2Long TermCorporateBonds6 28 7Long TermGovernmentBonds5 89 4U S TreasuryBills3 83 2Inflation3 14 4 9 18 Risk freeReturnsandRiskPremiums TheTreasurybillisusuallyusedastherisk freereturn TreasurybillsareU S federalgovernmentdebtthatwillmatureinoneyearorless 9 19 TheRiskPremiumistheadditionalreturn overandabovetherisk freerate resultingfrombearingrisk RiskPremiums ReturnsonRiskySecurities Risk freeReturn 9 20 WewillusetheStockMarketRiskPremiumalotinthenextfewchaptersandthroughoutthetext MarketRiskPremium ReturnontheStockMarket Risk freeReturn 9 21 AverageReturnontheStockMarket 12 2 TreasuryBills 3 8 therefore MarketRiskPremium 12 2 3 8 8 4 9 22 9 4AverageStockReturnsandRisk FreeReturns Oneofthemostsignificantobservationsofstockmarketdataisthislong runexcessofstockreturnovertherisk freereturn Theaverageexcessreturnfromlargecompanycommonstocksfortheperiod1926through1999was8 4 12 2 3 8 Theaverageexcessreturnfromsmallcompanycommonstocksfortheperiod1926through1999was13 2 16 9 3 8 Theaverageexcessreturnfromlong termcorporatebondsfortheperiod1926through1999was2 4 6 2 3 8 9 23 RiskPremia SupposethatTheWallStreetJournalannouncedthatthecurrentrateforon yearTreasurybillsis5 Whatistheexpectedreturnonthemarketofsmall companystocks Recallthattheaverageexcessreturnfromsmallcompanycommonstocksfortheperiod1926through1999was13 2 Givenarisk freerateof5 wehaveanexpectedreturnonthemarketofsmall companystocksof18 2 13 2 5 9 24 TheRisk ReturnTradeoff 9 25 RatesofReturn1926 2002 Source Stocks Bonds Bills andInflation2000Yearbook IbbotsonAssociates Inc Chicago annuallyupdatesworkbyRogerG IbbotsonandRexA Sinquefield Allrightsreserved 9 26 RiskPremiums RateofreturnonT billsisessentiallyrisk free Investinginstocksisrisky buttherearecompensations ThedifferencebetweenthereturnonT billsandstocksistheriskpremiumforinvestinginstocks AnoldsayingonWallStreetis Youcaneithersleepwelloreatwell 9 27 StockMarketVolatility Source Stocks Bonds Bills andInflation2000Yearbook IbbotsonAssociates Inc Chicago annuallyupdatesworkbyRogerG IbbotsonandRexA Sinquefield Allrightsreserved Thevolatilityofstocksisnotconstantfromyeartoyear 9 28 9 5RiskStatistics Thereisnouniversallyagreed upondefinitionofrisk Themeasuresofriskthatwediscussarevarianceandstandarddeviation Thestandarddeviationisthestandardstatisticalmeasureofthespreadofasample anditwillbethemeasureweusemostofthistime Itsinterpretationisfacilitatedbyadiscussionofthenormaldistribution Readexampleonp247 9 29 NormalDistribution Alargeenoughsampledrawnfromanormaldistributionlookslikeabell shapedcurve Probability Returnonlargecompanycommonstocks 99 74 3s 49 3 2s 28 8 1s 8 3 012 2 1s32 7 2s53 2 3s73 7 About2 3oftheyearlyreturnswillbebetween 8 3 and 32 7 theprobabilitythatayearlyreturnwillfallwithin20 5percentofthemeanof12 2percentwillbeapproximately2 3 68 26 95 44 20 5 9 30 NormalDistribution Source Stocks Bonds Bills andInflation2002Yearbook IbbotsonAssociates Inc Chicago annuallyupdatesworkbyRogerG IbbotsonandRexA Sinquefield Allrightsreserved 9 31 9 6SummaryandConclusions Thischapterpresentsreturnsforfourassetclasses LargeCompanyStocksSmallCompanyStocksLong TermGovernmentBondsTreasuryBillsStockshaveoutperformedbondsovermostofthetwentiethcentury althoughstockshavealsoexhibitedmorerisk 9 32 9 6SummaryandConclusions Thestatisticalmeasuresinthischapterarenecessarybuildingblocksforthematerialofthenextthreechapters 9 33 Multiplechoices 1 AcapitalgainoccurswhenA thesellingpriceislessthanthepurchaseprice B thepurchasepriceislessthanthesellingprice C thereisnodividendpaid D thereisnoincomecomponentofreturn E never astheycannotexist 9 34 Answer B 9 35 2 Youbought100sharesofstockat 20each Attheendoftheyear youreceivedatotalof 400individends andyourstockwasworth 2 500total Whatwasyourtotalreturn A 20 B 45 C 50 D 90 E Noneoftheabove 9 36 Answer BRationale Invest 20 100 2 000 Return 2 500 400 2 000 2 000 45 9 37 ThepricesforIMBoverthelast3yearsaregivenbelow Assumingnodividendswerepaid whatwasthe3 yearholdingperiodreturn Giventhefollowinginformation Year1return 10 Year2re
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