投资学第5章利率史与风险溢价1 studentppt课件

1、精选,投资学第5章,历史数据中的收益与风险IntroductiontoRisk,Return,andtheHistoricalRecord,精选,2,本章主要内容利率水平的确定-InterestRateDeterminants期望收益与波动性ExpectedReturnanditsVariance风险价值ValueatRisk,精选,3,5.1利率水平的确定,利率水平的决定因素：资金供给(居民)-Households资金需求(企业)-Businesses资金供求的外生影响(政府)-GovernmentsNetSupplyand/orDemandFederalReserveActions,精选,

2、4,5.1.1实际利率(realinterestrate)与名义利率(nominalinterestrate),消费者物价指数(CPI，consumerpriceindex)Nominalinterestrate(R):GrowthrateofyourmoneyRealinterestrate(r):Growthrateofyourpurchasingpower,精选,5,5.1.2实际利率均衡-EquilibriumRealRateofInterest,四因素：供给、需求、政府行为和通胀率,资金,均衡资金借出,均衡的真实利率,利率,E,E,需求,供给,利率,均衡的真实利率,利率,均衡资金借出

3、,均衡的真实利率,利率,资金,均衡资金借出,均衡的真实利率,利率,精选,6,5.1.3名义利率均衡-EquilibriumNominalRateofInterest,费雪方程(Fisherequation)含义：名义利率应该随预期通胀率的增加而增加Astheinflationrateincreases,investorswilldemandhighernominalratesofreturnIfE(i)denotescurrentexpectationsofinflation,thenwegettheFisherEquation:Nominalrate=realrate+inflationfo

4、recast,精选,7,5.1.4税收与实际利率,精选,8,5.2持有期收益率,ZeroCouponBond,Par=$100,T=maturity,P=price,rf(T)=totalriskfreereturn,精选,9,Example5.2AnnualizedRatesofReturn,精选,10,Equation5.7实际年利率-EAR,Effectiveannualratedefinition:percentageincreaseinfundsinvestedovera1-yearhorizon,精选,11,5.2.1年百分比利率,精选,12,Equation5.8年百分比率-AP

5、R,精选,13,Table5.1APRvs.EAR,精选,14,5.2.2连续复利收益率,当T趋于无限小时，可得连续复利(continuouscompounding)概念,精选,15,Table5.2StatisticsforT-BillRates,InflationRatesandRealRates,1926-2009,精选,16,Figure5.3InterestRatesandInflation,1926-2009,精选,17,Figure5.4NominalandRealWealthIndexesforInvestmentinTreasuryBills,1966-2005,精选,18,

6、5.4风险和风险溢价riskpremium,5.4.1持有期收益holdingperiodreturn股票收益包括两部分：红利收益(dividends)与资本利得(capitalgains)持有期收益率(holding-periodreturn),精选,19,RiskandRiskPremiums,HPR=HoldingPeriodReturnP0=BeginningpriceP1=EndingpriceD1=Dividendduringperiodone,RatesofReturn:SinglePeriod,精选,20,EndingPrice=110BeginningPrice=100Div

7、idend=4HPR=(110-100+4)/(100)=14%,RatesofReturn:SinglePeriodExample,精选,21,5.4.2期望收益expectedreturn与标准差standarddeviation：E-V方法,WearenotsureabouttheeventualHPR,sowehavetoknowtheProbabilityDistributionofthefutureoutcome.WewillcharacterizePDintermsoftheirexpectedreturnE(r)andtheirstandarddeviation.,精选,22,

8、StateProb.ofStaterinStateExcellent.250.3100Good.450.1400Poor.25-0.0675Crash.05-0.5200,E(r)=(.25)(.31)+(.45)(.14)+(.25)(-.0675)+(0.05)(-0.52)E(r)=.0976or9.76%,ScenarioReturns:Example,精选,23,Variance(VAR):,VarianceandStandardDeviation,StandardDeviation(STD):,精选,24,ScenarioVARandSTD,ExampleVARcalculatio

9、n:2=.25(.31-0.0976)2+.45(.14-.0976)2+.25(-0.0675-0.0976)2+.05(-.52-.0976)2=.038ExampleSTDcalculation:,精选,25,例：假定投资于某股票，初始价格100美元，持有期1年，现金红利为4美元，预期股票价格由如下三种可能，求其期望收益和方差。,精选,26,=4500.5=21.2132,精选,27,5.4.3超额收益与风险溢价RiskandRiskpremiums,Example:rf=6%,rstockA=14%,sowhatis8%whichequalstorstockA-rf?rstockA-r

10、f=excessreturn,orexcessreturn=actualreturnriskfreerate.Theriskpremiumistheexpectedvalueoftheexcessreturn,thenE(r)-rf=riskpremium.WemeasurethereturnofaninvestmentwithitsE(r),wemeasuretheriskofaninvestmentwithitsriskpremiumsstandarddeviation.,精选,28,5.4.3超额收益与风险溢价RiskandRiskpremiums,例：上例中我们得到股票的预期回报率E(

11、r)为14，若无风险收益率为rf8。初始投资100元于股票，其风险溢价(E(r)-rf)为6元，作为其承担风险（标准差为21.2元）的补偿。投资者对风险资产投资的满意度取决于其风险厌恶(riskaversion)程度,精选,29,5.5历史收益率时间序列分析,5.5.1时间序列与情景分析WedonotknowthePDoffutureoutcomes,aswellastheirE(r)and.Wemustinferfromitshistoryortimeseriesinordertoestimatethem.5.5.2期望收益与算术平均收益率的算术平均数arithmeticaverageofr

12、atesofreturn：,精选,30,5.5.2几何收益率GeometricAverageReturn,TV=投资终值(TerminalValueoftheInvestment),g=几何平均收益率(geometricaveragerateofreturn),精选,31,5.5.4方差与标准差,精选,32,5.5.5报酬-风险比率(夏普比率)TheReward-to-Volatility(Sharpe)Ratio,Wewouldliketoknowthetrade-offbetweenreward(theriskpremium)andrisk(asmeasuredbystandarddevi

13、ationorSD),精选,33,5.6正态分布-TheNormalDistribution,Investmentmanagementiseasierwhenreturnsarenormal.,精选,34,5.6正态分布-TheNormalDistribution,精选,35,NormalityandRiskMeasures,Whatifexcessreturnsarenotnormallydistributed?StandarddeviationisnolongeracompletemeasureofriskSharperatioisnotacompletemeasureofportfoli

14、operformanceNeedtoconsiderskewandkurtosis,精选,36,5.7偏离正态,偏度，亦称三阶矩(third-ordermoments)峰度：,精选,37,图5.5A正态与偏度分布(mean=6%SD=17%),精选,38,图5.5B正态与厚尾分布(mean=.1,SD=.2),精选,39,ValueatRisk(VaR),AmeasureoflossmostfrequentlyassociatedwithextremenegativereturnsVaRisthequantileofadistributionbelowwhichliesq%ofthepossi

15、blevaluesofthatdistributionThe5%VaR,commonlyestimatedinpractice,isthereturnatthe5thpercentilewhenreturnsaresortedfromhightolow.,精选,40,ExpectedShortfall(ES),Alsocalledconditionaltailexpectation(CTE)MoreconservativemeasureofdownsideriskthanVaRVaRtakesthehighestreturnfromtheworstcasesEStakesanaveragere

16、turnoftheworstcases,精选,41,CovarianceandCorrelation,PortfolioriskdependsonthecorrelationbetweenthereturnsoftheassetsintheportfolioCovarianceandthecorrelationcoefficientprovideameasureofthewayreturnsoftwoassetsvary,精选,42,Two-SecurityPortfolio:Return,精选,43,Two-SecurityPortfolio:Risk,精选,44,Two-SecurityP

17、ortfolio:Risk,精选,45,Two-SecurityPortfolio:Risk,精选,46,5.8股权收益与长期债券收益的历史记录,5.8.1平均收益与标准差基本结论：高风险、高收益,精选,47,表5.3各个时期的资产历史收益率1926-2005,精选,48,图5.61926-2005年历史收益率,精选,49,5.8.2风险资产组合的其他统计量5.8.3夏普比率5.8.4时间序列相关性5.8.5偏度与峰度5.8.6历史风险溢价的估计5.8.7全球历史数据,精选,50,表5.4资产的历史超额收益率1926-2005,精选,51,图5.7世界名义和实际股权收益率1900-2000,精

18、选,52,图5.8世界股权和债券实际收益率的年标准差1900-2000,精选,53,5.9长期投资,精选,54,5.9.1长期投资的风险与对数正态分布,连续复利的收益率若呈正态分布，则实际的持有期收益率为对数正态分布终值为：,精选,55,5.9.2夏普比率回顾,夏普比率的时间维度5.9.3长期未来收益率模拟5.9.4长期预测,精选,56,图5.10AnnuallyCompounded,25-YearHPRsfromBootstrappedHistoryandANormalDistribution(50,000样本),精选,57,图5.11AnnuallyCompounded,25-YearHPRsfromBootstrappedHistory(50,000Observation),精选,58,图5.12WealthIndexesofSelectedOutcomesofLargeStockPor