投资学历史数据中的收益与风险-课件

投资学第5章历史数据中的收益与风险IntroductiontoRisk,Return,andtheHistoricalRecord投资学第5章历史数据中的收益与风险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–ValueatRisk2本章主要内容2精品资料精品资料你怎么称呼老师？如果老师最后没有总结一节课的重点的难点，你是否会认为老师的教学方法需要改进？你所经历的课堂，是讲座式还是讨论式？教师的教鞭“不怕太阳晒，也不怕那风雨狂，只怕先生骂我笨，没有学问无颜见爹娘……”“太阳当空照，花儿对我笑，小鸟说早早早……”投资学历史数据中的收益与风险-ppt课件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)-Government’sNetSupplyand/orDemandFederalReserveActions55.1利率水平的确定利率水平的决定因素：55.1.1实际利率(realinterestrate)与名义利率(nominalinterestrate)消费者物价指数(CPI，consumerpriceindex)Nominalinterestrate(R):GrowthrateofyourmoneyRealinterestrate(r):Growthrateofyourpurchasingpower65.1.1实际利率(realinterestrat5.1.2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供给资金均衡资金借出均衡的真实利率利率75.1.2实际利率均衡-EquilibriumRe

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+inflationforecast85.1.3名义利率均衡-EquilibriumN5.1.4税收与实际利率

95.1.4税收与实际利率95.2持有期收益率ZeroCouponBond,Par=$100,T=maturity,P=price,rf(T)=totalriskfreereturn105.2持有期收益率ZeroCouponBond,PaExample5.2AnnualizedRatesofReturn11Example5.2AnnualizedRatesoEquation5.7实际年利率-EAREffectiveannualratedefinition:percentageincreaseinfundsinvestedovera1-yearhorizon12Equation5.7实际年利率-EAREffect5.2.1年百分比利率135.2.1年百分比利率13Equation5.8年百分比率-APR

14Equation5.8年百分比率-APR

14Table5.1APRvs.EAR15Table5.1APRvs.EAR155.2.2连续复利收益率当T趋于无限小时，可得连续复利(continuouscompounding)概念165.2.2连续复利收益率当T趋于无限小时，可得连续复利(cTable5.2StatisticsforT-BillRates,InflationRatesandRealRates,1926-200917Table5.2StatisticsforT-BilFigure5.3InterestRatesandInflation,1926-200918Figure5.3InterestRatesandFigure5.4NominalandRealWealthIndexesforInvestmentinTreasuryBills,1966-200519Figure5.4NominalandRealWe5.4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)205.4风险和风险溢价riskpremium5.4.1RiskandRiskPremiumsHPR=HoldingPeriodReturnP0=BeginningpriceP1=EndingpriceD1=DividendduringperiodoneRatesofReturn:SinglePeriod21RiskandRiskPremiumsHPR=HoEndingPrice= 110BeginningPrice= 100Dividend= 4HPR=(110-100+4)/(100)=14%RatesofReturn:SinglePeriodExample22EndingPrice= 110RatesofRe5.4.2期望收益expectedreturn与标准差standarddeviation：E-V方法WearenotsureabouttheeventualHPR,sowehavetoknowtheProbabilityDistributionofthefutureoutcome.WewillcharacterizePDintermsoftheirexpectedreturnE(r)andtheirstandarddeviationσ.235.4.2期望收益expectedreturn与标准差State

Prob.ofState rinState

Excellent .25 0.3100 Good .45 0.1400Poor .25 -0.0675Crash .05 -0.5200E(r)=(.25)(.31)+(.45)(.14)+(.25)(-.0675) +(0.05)(-0.52)E(r)=.0976or9.76%ScenarioReturns:Example24State Prob.ofState rinStatVariance(VAR):VarianceandStandardDeviationStandardDeviation(STD):25Variance(VAR):VarianceandStScenarioVARandSTDExampleVARcalculation:σ2=.25(.31-0.0976)2+.45(.14-.0976)2+.25(-0.0675-0.0976)2+.05(-.52-.0976)2=.038ExampleSTDcalculation:26ScenarioVARandSTDExampleVA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。27例：假定投资于某股票，初始价格100美元，持有期1年，现σ=450^0.5=21.213228σ=450^0.5=21.2132285.4.3超额收益与风险溢价–RiskandRiskpremiumsExample:rf=6%,rstockA=14%,sowhatis8%whichequalstorstockA-rf?rstockA-rf=excessreturn,orexcessreturn=actualreturn–riskfreerate.Theriskpremiumistheexpectedvalueoftheexcessreturn,thenE(r)-rf=riskpremium.WemeasurethereturnofaninvestmentwithitsE(r),wemeasuretheriskofaninvestmentwithitsriskpremium’sstandarddeviation.295.4.3超额收益与风险溢价–RiskandRis5.4.3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(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305.4.3超额收益与风险溢价–RiskandRis5.5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)andσ.Wemustinferfromitshistoryortimeseriesinordertoestimatethem.5.5.2期望收益与算术平均收益率的算术平均数arithmeticaverageofratesofreturn：315.5历史收益率时间序列分析5.5.1时间序列与情景分析5.5.2几何收益率

GeometricAverageReturnTV=投资终值(TerminalValueoftheInvestment)g=几何平均收益率(geometricaveragerateofreturn)325.5.2几何收益率

GeometricAverage5.5.4方差与标准差

335.5.4方差与标准差

335.5.5报酬-风险比率(夏普比率)

TheReward-to-Volatility(Sharpe)RatioSharpeRatioforPortfolios=RiskPremiumSDofExcessReturnWewouldliketoknowthetrade-offbetweenreward(theriskpremium)andrisk(asmeasuredbystandarddeviationorSD)345.5.5报酬-风险比率(夏普比率)

TheReward

5.6正态分布-TheNormalDistributionInvestmentmanagementiseasierwhenreturnsarenormal./data/quincunx.htmlStandarddeviationisagoodmeasureofriskwhenreturnsaresymmetric.Ifsecurityreturnsaresymmetric,portfolioreturnswillbe,too.Futurescenarioscanbeestimatedusingonlythemeanandthestandarddeviation.355.6正态分布-TheNormalDistrib

5.6正态分布-TheNormalDistribution365.6正态分布-TheNormalDistribNormalityandRiskMeasuresWhatifexcessreturnsarenotnormallydistributed?StandarddeviationisnolongeracompletemeasureofriskSharperatioisnotacompletemeasureofportfolioperformanceNeedtoconsiderskewandkurtosis37NormalityandRiskMeasuresWha5.7偏离正态偏度，亦称三阶矩(third-ordermoments)峰度：385.7偏离正态偏度，亦称三阶矩(third-orderm图5.5A正态与偏度分布

(mean=6%SD=17%)39图5.5A正态与偏度分布

(mean=6%SD图5.5B正态与厚尾分布(mean=.1,SD=.2)40图5.5B正态与厚尾分布(mean=.1,SD=ValueatRisk(VaR)AmeasureoflossmostfrequentlyassociatedwithextremenegativereturnsVaRisthequantileofadistributionbelowwhichliesq%ofthepossiblevaluesofthatdistributionThe5%VaR,commonlyestimatedinpractice,isthereturnatthe5thpercentilewhenreturnsaresortedfromhightolow.41ValueatRisk(VaR)AmeasureoExpectedShortfall(ES)Alsocalledconditionaltailexpectation(CTE)MoreconservativemeasureofdownsideriskthanVaRVaRtakesthehighestreturnfromtheworstcasesEStakesanaveragereturnoftheworstcases42ExpectedShortfall(ES)AlsocaCovarianceandCorrelationPortfolioriskdependsonthecorrelationbetweenthereturnsoftheassetsintheportfolioCovarianceandthecorrelationcoefficientprovideameasureofthewayreturnsoftwoassetsvary43CovarianceandCorrelationPortTwo-SecurityPortfolio:Return

44Two-SecurityPortfolio:Return

=VarianceofSecurityi

=VarianceofSecurityj

=CovarianceofreturnsforSecurityiandSecurityjTwo-SecurityPortfolio:Risk45=VarianceofSecurityi

=CovarianceofreturnsforSecurityiandSecurityjTwo-SecurityPortfolio:Risk

46=CovarianceTwo-SecurityPortfolio:Risk

47Two-SecurityPortfolio:Risk

45.8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485.8股权收益与长期债券收益的历史记录5.8.1平均收益表5.3各个时期的资产历史收益率1926-200549表5.3各个时期的资产历史收益率1926-200549图5.61926-2005年历史收益率50图5.61926-2005年历史收益率505.8.2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515.8.2风险资产组合的其他统计量51表5.4资产的历史超额收益率1926-200552表5.4资产的历史超额收益率1926-200552图5.7世界名义和实际股权收益率

1900-200053图5.7世界名义和实际股权收益率

1900-200053图5.8世界股权和债券实际收益率的年标准差1900-200054图5.8世界股权和债券实际收益率的年标准差1900-25.9长期投资555.9长期投资555.9.1长期投资的风险与对数正态分布连