投資學(xué)第5章利率史與風(fēng)險(xiǎn)溢價(jià)

投資學(xué)第5章歷史數(shù)據(jù)中的收益與風(fēng)險(xiǎn)IntroductiontoRisk,Return,andtheHistoricalRecord12本章主要內(nèi)容利率程度確實(shí)定-InterestRateDeterminants期望收益與動(dòng)搖性–ExpectedReturnanditsVariance風(fēng)險(xiǎn)價(jià)值–ValueatRisk35.1利率程度確實(shí)定利率程度的決議要素：資金供應(yīng)(居民)-Households資金需求(企業(yè))-Businesses資金供求的外生影響(政府)-Government’sNetSupplyand/orDemandFederalReserveActions45.1.1實(shí)踐利率(realinterestrate)與名義利率(nominalinterestrate)消費(fèi)者物價(jià)指數(shù)(CPI，consumerpriceindex)Nominalinterestrate(R):GrowthrateofyourmoneyRealinterestrate(r):Growthrateofyourpurchasingpower55.1.2實(shí)踐利率平衡-EquilibriumRealRateofInterest四要素：供應(yīng)、需求、政府行為和通脹率●●資金平衡資金借出平衡的真實(shí)利率利率E’E需求供應(yīng)利率平衡的真實(shí)利率利率平衡資金借出平衡的真實(shí)利率利率資金平衡資金借出平衡的真實(shí)利率利率供應(yīng)資金平衡資金借出平衡的真實(shí)利率利率65.1.3名義利率平衡-EquilibriumNominalRateofInterest費(fèi)雪方程(Fisherequation)含義：名義利率應(yīng)該隨預(yù)期通脹率的添加而添加Astheinflationrateincreases,investorswilldemandhighernominalratesofreturnIfE(i)denotescurrentexpectationsofinflation,thenwegettheFisherEquation:Nominalrate=realrate+inflationforecast75.1.4稅收與實(shí)踐利率

85.2持有期收益率ZeroCouponBond,Par=$100,T=maturity,P=price,rf(T)=totalriskfreereturn5-9Example5.2AnnualizedRatesofReturn5-10Equation5.7實(shí)踐年利率-EAREffectiveannualratedefinition:percentageincreaseinfundsinvestedovera1-yearhorizon115.2.1年百分比利率5-12Equation5.8年百分比率-APR

5-13Table5.1APRvs.EAR145.2.2延續(xù)復(fù)利收益率當(dāng)T趨于無限小時(shí)，可得延續(xù)復(fù)利(continuouscompounding)概念5-15Table5.2StatisticsforT-BillRates,InflationRatesandRealRates,1926-20215-16Figure5.3InterestRatesandInflation,1926-202117Figure5.4NominalandRealWealthIndexesforInvestmentinTreasuryBills,1966-2005185.4風(fēng)險(xiǎn)和風(fēng)險(xiǎn)溢價(jià)riskpremium5.4.1持有期收益holdingperiodreturn股票收益包括兩部分：紅利收益(dividends)與資本利得(capitalgains)持有期收益率(holding-periodreturn)5-19RiskandRiskPremiumsHPR=HoldingPeriodReturnP0=BeginningpriceP1=EndingpriceD1=DividendduringperiodoneRatesofReturn:SinglePeriod5-20EndingPrice= 110BeginningPrice= 100Dividend= 4HPR=(110-100+4)/(100)=14%RatesofReturn:SinglePeriodExample215.4.2期望收益expectedreturn與規(guī)范差standarddeviation：E-V方法WearenotsureabouttheeventualHPR,sowehavetoknowtheProbabilityDistributionofthefutureoutcome.WewillcharacterizePDintermsoftheirexpectedreturnE(r)andtheirstandarddeviationσ.5-22State 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:Example5-23Variance(VAR):VarianceandStandardDeviationStandardDeviation(STD):5-24ScenarioVARandSTDExampleVARcalculation:σ2=.25(.31-0.0976)2+.45(.14-.0976)2+.25(-0.0675-0.0976)2+.05(-.52-.0976)2=.038ExampleSTDcalculation:25例：假定投資于某股票，初始價(jià)錢100美圓，持有期1年，現(xiàn)金紅利為4美圓，預(yù)期股票價(jià)錢由如下三種能夠，求其期望收益和方差。26σ=450^0.5=21.2132275.4.3超額收益與風(fēng)險(xiǎn)溢價(jià)–RiskandRiskpremiumsExample:rf=6%,rstockA=14%,sowhatis8%whichequalstorstockA-rf?rstockA-rf=excessreturn,orexcessreturn=actualreturn–riskfreerate.Theriskpremiumistheexpectedvalueoftheexcessreturn,thenE(r)-rf=riskpremium.WemeasurethereturnofaninvestmentwithitsE(r),wemeasuretheriskofaninvestmentwithitsriskpremium’sstandarddeviation.285.4.3超額收益與風(fēng)險(xiǎn)溢價(jià)–RiskandRiskpremiums例：上例中我們得到股票的預(yù)期報(bào)答率E(r)為14％，假設(shè)無風(fēng)險(xiǎn)收益率為rf8％。初始投資100元于股票，其風(fēng)險(xiǎn)溢價(jià)(E(r)-rf)為6元，作為其承當(dāng)風(fēng)險(xiǎn)〔規(guī)范差為21.2元〕的補(bǔ)償。投資者對(duì)風(fēng)險(xiǎn)資產(chǎn)投資的稱心度取決于其風(fēng)險(xiǎn)厭惡(riskaversion)程度295.5歷史收益率時(shí)間序列分析5.5.1時(shí)間序列與情景分析WedonotknowthePDoffutureoutcomes,aswellastheirE(r)andσ.Wemustinferfromitshistoryortimeseriesinordertoestimatethem.5.5.2期望收益與算術(shù)平均收益率的算術(shù)平均數(shù)arithmeticaverageofratesofreturn：305.5.2幾何收益率

GeometricAverageReturnTV=投資終值(TerminalValueoftheInvestment)g=幾何平均收益率(geometricaveragerateofreturn)315.5.4方差與規(guī)范差方差=期望值偏離的平方(expectedvalueofsquareddeviations)歷史數(shù)據(jù)的方差估計(jì)：無偏化處置：325.5.5報(bào)酬-風(fēng)險(xiǎn)比率(夏普比率)

TheReward-to-Volatility(Sharpe)RatioSharpeRatioforPortfolios=RiskPremiumSDofExcessReturnWewouldliketoknowthetrade-offbetweenreward(theriskpremium)andrisk(asmeasuredbystandarddeviationorSD)5-335.6正態(tài)分布-TheNormalDistributionInvestmentmanagementiseasierwhenreturnsarenormal.mathsisfun/data/quincunx.htmlStandarddeviationisagoodmeasureofriskwhenreturnsaresymmetric.Ifsecurityreturnsaresymmetric,portfolioreturnswillbe,too.Futurescenarioscanbeestimatedusingonlythemeanandthestandarddeviation.345.6正態(tài)分布-TheNormalDistribution5-35NormalityandRiskMeasuresWhatifexcessreturnsarenotnormallydistributed?StandarddeviationisnolongeracompletemeasureofriskSharperatioisnotacompletemeasureofportfolioperformanceNeedtoconsiderskewandkurtosis365.7偏離正態(tài)偏度，亦稱三階矩(third-ordermoments)峰度：37圖5.5A正態(tài)與偏度分布

(mean=6%SD=17%)38圖5.5B正態(tài)與厚尾分布(mean=.1,SD=.2)5-39ValueatRisk(VaR)AmeasureoflossmostfrequentlyassociatedwithextremenegativereturnsVaRisthequantileofadistributionbelowwhichliesq%ofthepossiblevaluesofthatdistributionThe5%VaR,commonlyestimatedinpractice,isthereturnatthe5thpercentilewhenreturnsaresortedfromhightolow.5-40ExpectedShortfall(ES)Alsocalledconditionaltailexpectation(CTE)MoreconservativemeasureofdownsideriskthanVaRVaRtakesthehighestreturnfromtheworstcasesEStakesanaveragereturnoftheworstcases7-41CovarianceandCorrelationPortfolioriskdependsonthecorrelationbetweenthereturnsoftheassetsintheportfolioCovarianceandthecorrelationcoefficientprovideameasureofthewayreturnsoftwoassetsvary7-42Two-SecurityPortfolio:Return+portfolioexpectedreturnsecurityireturnsecurityjreturnsecurityiexpectedreturnsecurityjexpectedreturn7-43=VarianceofSecurityi=VarianceofSecurityj=CovarianceofreturnsforSecurityiandSecurityjTwo-SecurityPortfolio:Risk7-44=CovarianceofreturnsforSecurityiandSecurityjTwo-SecurityPortfolio:Risk通用公式：

7-45Two-SecurityPortfolio:Risk通用公式：

465.8股權(quán)收益與長期債券收益的歷史記錄5.8.1平均收益與規(guī)范差根本結(jié)論：高風(fēng)險(xiǎn)、高收益47表5.3各個(gè)時(shí)期的資產(chǎn)歷史收益率1926-200548圖5.61926-2005年歷史收益率495.8.2風(fēng)險(xiǎn)資產(chǎn)組合的其他統(tǒng)計(jì)量5.8.3夏普比率5.8.4時(shí)間序列相關(guān)性5.8.5偏度與峰度5.8.6歷史風(fēng)險(xiǎn)溢價(jià)的估計(jì)5.8.7全球歷史數(shù)據(jù)50表5.4資產(chǎn)的歷史超額收益率1926-200551圖5.7世界名義和實(shí)踐股權(quán)收益率

1900-200052圖5.