投资学,9e,精要版,48772,48760,英文PPT Chap003.ppt 44页

CHAPTER3IntroductiontoRisk,Return,andtheHistoricalRecord 5-2InterestRateDeterminantsSupplyHouseholdsDemandBusinessesGovernment’sNetSupplyand/orDemandFederalReserveActions 5-3RealandNominalRatesofInterestNominalinterestrate:GrowthrateofyourmoneyRealinterestrate:GrowthrateofyourpurchasingpowerLetR=nominalrate,r=realrateandI=inflationrate.Then: 5-4EquilibriumRealRateofInterestDeterminedby:SupplyDemandGovernmentactionsExpectedrateofinflation 5-5Figure3.1DeterminationoftheEquilibriumRealRateofInterest 5-6EquilibriumNominalRateofInterestAstheinflationrateincreases,investorswilldemandhighernominalratesofreturnIfE(i)denotescurrentexpectationsofinflation,thenwegettheFisherEquation:Nominalrate=realrate+inflationforecast 5-7TaxesandtheRealRateofInterestTaxliabilitiesarebasedonnominalincomeGivenataxrate(t)andnominalinterestrate(R),theRealafter-taxrateis:Theafter-taxrealrateofreturnfallsastheinflationraterises. 5-8RatesofReturnforDifferentHoldingPeriodsZeroCouponBond,Par=$100,T=maturity,P=price,rf(T)=totalriskfreereturn 5-9Example3.2AnnualizedRatesofReturn 5-10Equation3.7EAREARdefinition:percentageincreaseinfundsinvestedovera1-yearhorizon 5-11Equation3.8APRAPR:annualizingusingsimpleinterest 5-12Table3.1APRvs.EAR 5-13Table3.2StatisticsforT-BillRates,InflationRatesandRealRates,1926-2009 5-14BillsandInflation,1926-2009Moderateinflationcanoffsetmostofthenominalgainsonlow-riskinvestments.AdollarinvestedinT-billsfrom1926–2009grewto$20.52,butwitharealvalueofonly$1.69.Negativecorrelationbetweenrealrateandinflationratemeansthenominalraterespondslessthan1:1tochangesinexpectedinflation. 5-15Figure3.3InterestRatesandInflation,1926-2009 5-16RiskandRiskPremiumsHPR=HoldingPeriodReturnP0=BeginningpriceP1=EndingpriceD1=DividendduringperiodoneRatesofReturn:SinglePeriod 5-17EndingPrice=110BeginningPrice=100Dividend=4HPR=(110-100+4)/(100)=14%RatesofReturn:SinglePeriodExample 5-18Expectedreturnsp(s)=probabilityofastater(s)=returnifastateoccurss=stateExpectedReturnandStandardDeviation 5-19StateProb.ofStaterinStateExcellent.250.3100Good.450.1400Poor.25-0.0675Crash.05-0.5200E(r)=(.25)(.31)+(.45)(.14)+(.25)(-.0675)+(0.05)(-0.52)E(r)=.0976or9.76%ScenarioReturns:Example 5-20Variance(VAR):VarianceandStandardDeviationStandardDeviation(STD): 5-21ScenarioVARandSTDExampleVARcalculation:σ2=.25(.31-0.0976)2+.45(.14-.0976)2+.25(-0.0675-0.0976)2+.05(-.52-.0976)2=.038ExampleSTDcalculation: 5-22TimeSeriesAnalysisofPastRatesofReturnTheArithmeticAverageofrateofreturn: 5-23GeometricAverageReturnTV=TerminalValueoftheInvestmentg=geometricaveragerateofreturn 5-24GeometricVarianceandStandardDeviationFormulasEstimatedVariance=expectedvalueofsquareddeviations 5-25GeometricVarianceandStandardDeviationFormulasWheneliminatingthebias,VarianceandStandardDeviationbecome: 5-26TheReward-to-Volatility(Sharpe)RatioSharpeRatioforPortfolios: 5-27TheNormalDistributionInvestmentmanagementiseasierwhenreturnsarenormal.Standarddeviationisagoodmeasureofriskwhenreturnsaresymmetric.Ifsecurityreturnsaresymmetric,portfolioreturnswillbe,too.Futurescenarioscanbeestimatedusingonlythemeanandthestandarddeviation. 5-28Figure3.4TheNormalDistribution 5-29NormalityandRiskMeasuresWhatifexcessreturnsarenotnormallydistributed?StandarddeviationisnolongeracompletemeasureofriskSharperatioisnotacompletemeasureofportfolioperformanceNeedtoconsiderskewandkurtosis 5-30SkewandKurtosisSkewEquation5.19KurtosisEquation5.20 5-31Figure3.5ANormalandSkewedDistributions 5-32Figure3.5BNormalandFat-TailedDistributions(mean=.1,SD=.2) 5-33ValueatRisk(VaR)AmeasureoflossmostfrequentlyassociatedwithextremenegativereturnsVaRisthequantileofadistributionbelowwhichliesq%ofthepossiblevaluesofthatdistributionThe5%VaR,commonlyestimatedinpractice,isthereturnatthe5thpercentilewhenreturnsaresortedfromhightolow. 5-34ExpectedShortfall(ES)Alsocalledconditionaltailexpectation(CTE)MoreconservativemeasureofdownsideriskthanVaRVaRtakesthehighestreturnfromtheworstcasesEStakesanaveragereturnoftheworstcases 5-35LowerPartialStandardDeviation(LPSD)andtheSortinoRatioIssues:NeedtoconsidernegativedeviationsseparatelyNeedtoconsiderdeviationsofreturnsfromtherisk-freerate.LPSD:similartousualstandarddeviation,butusesonlynegativedeviationsfromrfSortinoRatioreplacesSharpeRatio 5-36HistoricReturnsonRiskyPortfoliosReturnsappearnormallydistributedReturnsareloweroverthemostrecenthalfoftheperiod(1986-2009)SDforsmallstocksbecamesmaller;SDforlong-termbondsgotbigger 5-37HistoricReturnsonRiskyPortfoliosBetterdiversifiedportfolioshavehigherSharpeRatiosNegativeskew 5-38Figure5.7NominalandRealEquityReturnsAroundtheWorld,1900-2000 5-39Figure5.8StandardDeviationsofRealEquityandBondReturnsAroundtheWorld,1900-2000 5-40Figure5.9ProbabilityofInvestmentOutcomesAfter25YearswithaLognormalDistribution 5-41TerminalValuewithContinuousCompoundingWhenthecontinuouslycompoundedrateofreturnonanassetisnormallydistributed,theeffectiverateofreturnwillbelognormallydistributed.TheTerminalValuewillthenbe: 5-42Figure5.10AnnuallyCompounded,25-YearHPRs 5-43Figure5.11AnnuallyCompounded,25-YearHPRs 5-44Figure5.12WealthIndexesofSelectedOutcomesofLargeStockPortfoliosandtheAverageT-billPortfolio