Chap005风险与收益

INVESTMENTS|BODIE,KANE,MARCUSCopyright©2011byTheMcGraw-HillCompanies,Inc.Allrightsreserved.McGraw-Hill/IrwinCHAPTER5IntroductiontoRisk,Return,andtheHistoricalRecord风险与收益入门及历史回顾INVESTMENTS|BODIE,KANE,MARCUS5-2InterestRateDeterminants利率水平的决定因素•Supply供给–Households家庭•Demand需求–Businesses企业•Government’sNetSupplyand/orDemand政府净供给或需求–FederalReserveActions美联储行为INVESTMENTS|BODIE,KANE,MARCUS5-3RealandNominalRatesofInterest真实与名义利率•Nominalinterestrate:Growthrateofyourmoney•金钱增长•Realinterestrate:Growthrateofyourpurchasingpower•购买力增长•LetR=nominalrate,r=realrateandI=inflationrate.Then:iRriRr111INVESTMENTS|BODIE,KANE,MARCUS5-4EquilibriumRealRateofInterest真实利率的均衡如何达成•Determinedby:–Supply供给–Demand需求–Governmentactions政府行为–Expectedrateofinflation通胀预期INVESTMENTS|BODIE,KANE,MARCUS5-5Figure5.1DeterminationoftheEquilibriumRealRateofInterestINVESTMENTS|BODIE,KANE,MARCUS5-6EquilibriumNominalRateofInterest名义利率的均衡如何达成•Astheinflationrateincreases,investorswilldemandhighernominalratesofreturn通胀上升时投资者要求更高的名义利率•IfE(i)denotescurrentexpectationsofinflation,thenwegettheFisherEquation:费雪方程式•Nominalrate=realrate+inflationforecast()RrEiINVESTMENTS|BODIE,KANE,MARCUS5-7TaxesandtheRealRateofInterest税收与真实利率•Taxliabilitiesarebasedonnominalincome税赋是基于名义收入的–Givenataxrate(t)andnominalinterestrate(R),theRealafter-taxrateis:i是通胀率•Theafter-taxrealrateofreturnfallsastheinflationraterises税后真实收益被通胀侵蚀(1)()(1)(1)RtiritirtitINVESTMENTS|BODIE,KANE,MARCUS5-8RatesofReturnforDifferentHoldingPeriods比较不同持有期利率100()1()frTPTZeroCouponBond,Par=$100,T=maturity,P=price,rf(T)=totalriskfreereturnINVESTMENTS|BODIE,KANE,MARCUS5-9Example5.2AnnualizedRatesofReturn收益的年化率INVESTMENTS|BODIE,KANE,MARCUS5-10Equation5.7EAR•EARdefinition:percentageincreaseinfundsinvestedovera1-yearhorizon投资1年所获得的收益TfTrEAR111INVESTMENTS|BODIE,KANE,MARCUS5-11Equation5.8APR•APR:annualizingusingsimpleinterest•简单年化率TEARAPRT11INVESTMENTS|BODIE,KANE,MARCUS5-12Table5.1APRvs.EAR两者相隔不大前者计算简便，后者更为精确INVESTMENTS|BODIE,KANE,MARCUS5-13Table5.2StatisticsforT-BillRates,InflationRatesandRealRates,1926-2009短期国库券、通胀以及真实利率的统计数据INVESTMENTS|BODIE,KANE,MARCUS5-14BillsandInflation,1926-2009通货膨胀与短期国库券•Moderateinflationcanoffsetmostofthenominalgainsonlow-riskinvestments.低风险投资的大多数收益都会被通胀抵消•AdollarinvestedinT-billsfrom1926–2009grewto$20.52,butwitharealvalueofonly$1.69.投资短期国库券名义收益1:20.52，真实收益只有1:1.69•Negativecorrelationbetweenrealrateandinflationratemeansthenominalraterespondslessthan1:1tochangesinexpectedinflation.名义利率在实际上也没有随着预期通胀的上升完全上涨，这说明真实利率被侵蚀的更厉害INVESTMENTS|BODIE,KANE,MARCUS5-15Figure5.3InterestRatesandInflation,1926-2009利率与通胀INVESTMENTS|BODIE,KANE,MARCUS5-16RiskandRiskPremiums风险与溢价PDPPHPR0101HPR=HoldingPeriodReturn持有期P0=Beginningprice初始价格P1=Endingprice结束价格D1=Dividendduringperiodone期间红利RatesofReturn:SinglePeriod单期收益INVESTMENTS|BODIE,KANE,MARCUS5-17EndingPrice=110BeginningPrice=100Dividend=4HPR=(110-100+4)/(100)=14%RatesofReturn:SinglePeriodExample单期收益的例子INVESTMENTS|BODIE,KANE,MARCUS5-18Expectedreturnsp(s)=probabilityofastate状态概率r(s)=returnifastateoccurs状态下收益s=state状态ExpectedReturnandStandardDeviation期望收益()()()sErpsrsINVESTMENTS|BODIE,KANE,MARCUS5-19StateProb.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案例INVESTMENTS|BODIE,KANE,MARCUS5-20Variance(VAR):VarianceandStandardDeviation方差与标准差22()()()spsrsEr2STDStandardDeviation(STD):INVESTMENTS|BODIE,KANE,MARCUS5-21ScenarioVARandSTD如何计算•ExampleVARcalculation:σ2=.25(.31-0.0976)2+.45(.14-.0976)2+.25(-0.0675-0.0976)2+.05(-.52-.0976)2=.038•ExampleSTDcalculation:1949.038.INVESTMENTS|BODIE,KANE,MARCUS5-22TimeSeriesAnalysisofPastRatesofReturn历史收益的时间序列分析nsnssrnsrsprE11)(1)()()(TheArithmeticAverageofrateofreturn:收益率的算术平均值INVESTMENTS|BODIE,KANE,MARCUS5-23GeometricAverageReturn几何平均值1/1TVgnTV=TerminalValueoftheInvestment最终投资价值g=geometricaveragerateofreturn收益的几何平均值)1)...(1)(1(21nnrrrTVINVESTMENTS|BODIE,KANE,MARCUS5-24GeometricVarianceandStandardDeviationFormulas几何方差与标准差•EstimatedVariance=expectedvalueofsquareddeviations误差平方的期望21_2^1nsrsrnINVESTMENTS|BODIE,KANE,MARCUS5-25GeometricVarianceandStandardDeviationFormulas几何方差与标准差公式•Wheneliminatingthebias,VarianceandStandardDeviationbecome:标准差公式21_^11njrsrnINVESTMENTS|BODIE,KANE,MARCUS5-26TheReward-to-Volatility(Sharpe)Ratio风险收益比：夏普比•SharpeRatioforPortfolios:组合的夏普比ReturnsExcessofSDPremiumRiskINVESTMENTS|BODIE,KANE,MARCUS5-27TheNormalDistribution正态分布•Investmentmanagementiseasierwhenreturnsarenormal.如果收益正态分布投资管理就比较轻松–Standarddeviationisagoodmeasureofriskwhenreturnsaresymmetric.如果收益对称的话标准差是风险的一个好的度量–Ifsecurityreturnsaresymmetric,portfolioreturnswillbe,too.如果证券收益对称那么组合的收益也是对称的–Futurescenarioscanbeestimatedusingonlythemeanandthestandarddeviation.未来的收益就可以只用均值和方差估计出来INVESTMENTS|BODIE,KANE,MARCUS5-28Figure5.4TheNormalDistribution正态分布INVESTMENTS|BODIE,KANE,MARCUS5-29NormalityandRiskMeasures正态性与风险测度•Whatifexcessreturnsarenotnormallydistributed?如果超额收益不是正态分布–