C10.risk and return lessons from market history

RiskandReturnLessonsfromMarketHistory Chapter10 ChapterOutline 10 1Returns10 2Holding PeriodReturns持有期间收益率10 3ReturnStatistics10 4AverageStockReturnsandRisk FreeReturns10 5RiskStatistics10 6Moreonaveragereturns 10 1Return 1 Dollarreturns thesumofthecashreceivedandthechangeinvalueoftheasset indollars 2 PercentageReturnsthesumofthecashreceivedandthechangeinvalueoftheassetdividedbytheinitialinvestment DollarReturn Dividend ChangeinMarketValue DollarReturn 1 100gain 6000 100 5000 Returns Example PercentageReturn Theholdingperiodreturnisthereturnthataninvestorwouldgetwhenholdinganinvestmentoveraperiodofnyears whenthereturnduringyeariisgivenasri 10 2HoldingPeriodReturns 10 2Holding PeriodReturns Afamoussetofstudiesdealingwithratesofreturnsoncommonstocks bonds andTreasurybillswasconductedbyRogerIbbotsonandRexSinquefield Theypresentyear by yearhistoricalratesofreturnstartingin1926forthefollowingfiveimportanttypesoffinancialinstrumentsintheUnitedStates Large companyCommonStocksSmall companyCommonStocksLong termCorporateBondsLong termU S GovernmentBondsU S TreasuryBills 10 3ReturnStatistics收益统计 描述资本市场的简单浓缩方法 频数分布thefrequencydistributionofthereturns Thehistoryofcapitalmarketreturnscanbesummarizedbydescribingthe averagereturnthestandarddeviationofthosereturns HistoricalReturns 1926 2004 Source Stocks Bonds Bills andInflation2005Yearbook IbbotsonAssociates Inc Chicago annuallyupdatesworkbyRogerG IbbotsonandRexA Sinquefield Allrightsreserved 90 90 0 AverageStandardSeriesAnnualReturnDeviationDistributionLargeCompanyStocks12 4 20 3 SmallCompanyStocks17 533 1Long TermCorporateBonds6 28 6Long TermGovernmentBonds5 89 3U S TreasuryBills3 83 1Inflation3 14 3 10 4AverageStockReturnsandRisk FreeReturns TheRiskPremiumistheaddedreturn overandabovetherisk freerate resultingfrombearingrisk Oneofthemostsignificantobservationsofstockmarketdataisthelong runexcessofstockreturnovertherisk freereturn Theaverageexcessreturnfortheperiod1926through2004was fromlargecompanycommonstocks 8 6 12 4 3 8 fromsmallcompanycommonstocks 13 7 17 5 3 8 fromlong termcorporatebonds 2 4 6 2 3 8 10 5RiskStatistics Thereisnouniversallyagreed upondefinitionofrisk Themeasuresofriskthatwediscussarevariance V方差 standarddeviation SD标准差 Thestandarddeviationisthestandardstatisticalmeasureofthespreadofasample anditwillbethemeasureweusemostofthistime Itsinterpretationisfacilitatedbyadiscussionofthenormaldistribution NormalDistribution 以大公司为例 Alargeenoughsampledrawnfromanormaldistributionlookslikeabell shapedcurve Probability Returnonlargecompanycommonstocks 99 74 3s 48 5 2s 28 2 1s 7 9 012 4 1s32 7 2s53 0 3s73 3 Theprobabilitythatayearlyreturnwillfallwithin20 3percentofthemeanof12 4percentwillbeapproximately2 3 68 26 95 44 Example ReturnandVariance Variance 0045 4 1 0015StandardDeviation 03873 10 6MoreonaveragereturnsArithmeticvs GeometricMean算数收益率与几何收益率 Arithmeticaverage returnearnedinanaverageperiodovermultipleperiodsGeometricaverage AveragecompoundreturnperperiodovermultipleperiodsThegeometricaveragewillbelessthanthearithmeticaverageunlessallthereturnsareequalWhichisbetter Thearithmeticaverageisoverlyoptimisticforlonghorizons Thegeometricaverageisoverlypessimisticforshorthorizons GeometricReturn Example Recallourearlierexample So ourinvestormadeanaverageof9 58 peryear realizingaholdingperiodreturnof44 21 GeometricReturn Example Notethatthegeometricaverageisnotthesameasthearithmeticaverage ForecastingReturn Toaddressthetimerelationinforecastingreturns useBlume sformula where TistheforecasthorizonandNisthenumberofyearsofhistoricaldataweareworkingwith TmustbelessthanN QuickQuiz Whichoftheinvestmentsdiscussedhashadthehig