财务管理第五章风险和收益

5-1Chapter5RiskandReturn5-2GlossaryStandardDeviation标准差或者标准离差Expectedreturn期望回报率Normaldistribution正态分布Coefficientofvariation离差系数variance方差ContinuousDistributions连续分布discretedistribution离散分布CertaintyEquivalent(CE)资本回收保证量RiskPreference风险偏好RiskIndifference风险中立RiskAversion风险规避TheCapitalAssetPricingModel(CAPM)资本资产定价模型SystematicRisk系统风险UnsystematicRisk非系统风险5-3DefiningReturnIncomereceivedonaninvestmentplusanychangeinmarketprice,usuallyexpressedasapercentofthebeginningmarketpriceoftheinvestment.Dt+(Pt-Pt-1)Pt-1R=5-4ReturnExampleThestockpriceforStockAwas$10pershare1yearago.Thestockiscurrentlytradingat$9.50pershare,andshareholdersjustreceiveda$1dividend.Whatreturnwasearnedoverthepastyear?5-5ReturnExampleThestockpriceforStockAwas$10pershare1yearago.Thestockiscurrentlytradingat$9.50pershare,andshareholdersjustreceiveda$1dividend.Whatreturnwasearnedoverthepastyear?$1.00+($9.50-$10.00)$10.00R==5%5-6DefiningRiskGreaterthevariability,theriskierthesecurityissaidtobeThevariabilityofreturnsfromthosethatareexpected.5-7DeterminingExpectedReturn(DiscreteDist.)R=S(Ri)(Pi)Ristheexpectedreturnfortheasset,Riisthereturnfortheithpossibility,Piistheprobabilityofthatreturnoccurring,nisthetotalnumberofpossibilities.ni=15-8HowtoDeterminetheExpectedReturnandStandardDeviationStockBWRiPi(Ri)(Pi)-.15.10-.015-.03.20-.006.09.40.036.21.20.042.33.10.033Sum1.00.090Theexpectedreturn,R,forStockBWis.09or9%5-9DeterminingStandardDeviation标准差或者标准离差(RiskMeasure)ni=1s=S(Ri-R)2(Pi)StandardDeviation,s,isastatisticalmeasureofthevariabilityofadistributionarounditsmean.Itisthesquarerootofvariance(方差）.Note,thisisforadiscretedistribution（离散分布）.5-10HowtoDeterminetheExpectedReturnandStandardDeviationStockBWRiPi(Ri)(Pi)(Ri-R)2(Pi)-.15.10-.015.00576-.03.20-.006.00288.09.40.036.00000.21.20.042.00288.33.10.033.00576Sum1.00.090.017285-11DeterminingStandardDeviation(RiskMeasure)s=S(Ri-R)2(Pi)s=.01728s=.1315or13.15%ni=15-12CoefficientofVariationTheratioofthestandarddeviationofadistributiontothemeanofthatdistribution.ItisameasureofRELATIVErisk.CV=s/RCVofBW=.1315/.09=1.465-13Discretevs.ContinuousDistributions连续分布00.050.10.150.20.250.30.350.4-15%-3%9%21%33%DiscreteContinuous00.0050.010.0150.020.0250.030.035-50%-41%-32%-23%-14%-5%4%13%22%31%40%49%58%67%5-14DeterminingExpectedReturn(ContinuousDist.)R=S(Ri)/(n)Ristheexpectedreturnfortheasset,Riisthereturnfortheithobservation,nisthetotalnumberofobservations.ni=15-15DeterminingStandardDeviation(RiskMeasure)ni=1s=S(Ri-R)2(n)Note,thisisforacontinuousdistributionwherethedistributionisforapopulation.Rrepresentsthepopulationmeaninthisexample.5-16ContinuousDistributionProblemAssumethatthefollowinglistrepresentsthecontinuousdistributionofpopulationreturnsforaparticularinvestment(eventhoughthereareonly10returns).9.6%,-15.4%,26.7%,-0.2%,20.9%,28.3%,-5.9%,3.3%,12.2%,10.5%CalculatetheExpectedReturnandStandardDeviationforthepopulationassumingacontinuousdistribution.5-17Let’sUsetheCalculator!Enter“Data”first.Press:2ndData2ndCLRWork9.6ENTER-15.4ENTER26.7ENTERNote,weareinputtingdataonlyforthe“X”variableandignoringentriesforthe“Y”variableinthiscase.5-18Let’sUsetheCalculator!Enter“Data”first.Press:-0.2ENTER20.9ENTER28.3ENTER-5.9ENTER3.3ENTER12.2ENTER10.5ENTER5-19Let’sUsetheCalculator!ExamineResults!Press:2ndStatthroughtheresults.Expectedreturnis9%forthe10observations.Populationstandarddeviationis13.32%.Thiscanbemuchquickerthancalculatingbyhand,butslowerthanusingaspreadsheet.5-20CertaintyEquivalent(CE)资本回收保证量istheamountofcashsomeonewouldrequirewithcertaintyatapointintimetomaketheindividualindifferentbetweenthatcertainamountandanamountexpectedtobereceivedwithriskatthesamepointintime.RiskAttitudes5-21CertaintyequivalentExpectedvalueRiskPreference风险偏好Certaintyequivalent=ExpectedvalueRiskIndifference风险中立CertaintyequivalentExpectedvalueRiskAversion风险规避MostindividualsareRiskAverse.RiskAttitudes5-22RiskAttitudeExampleYouhavethechoicebetween(1)aguaranteeddollarrewardor(2)acoin-flipgambleof$100,000(50%chance)or$0(50%chance).Theexpectedvalueofthegambleis$50,000.Maryrequiresaguaranteed$25,000,ormore,tocalloffthegamble.Raleighisjustashappytotake$50,000ortaketheriskygamble.Shannonrequiresatleast$52,000tocalloffthegamble.5-23WhataretheRiskAttitudetendenciesofeach?RiskAttitudeExampleMaryshows“riskaversion”becauseher“certaintyequivalent”theexpectedvalueofthegamble.Raleighexhibits“riskindifference”becauseher“certaintyequivalent”equalstheexpectedvalueofthegamble.Shannonrevealsa“riskpreference”becauseher“certaintyequivalent”theexpectedvalueofthegamble.5-24RP=S(Wj)(Rj)RPistheexpectedreturnfortheportfolio,Wjistheweight(investmentproportion)forthejthassetintheportfolio,Rjistheexpectedreturnofthejthasset,misthetotalnumberofassetsintheportfolio.DeterminingPortfolioExpectedReturnmj=15-25DeterminingPortfolioStandardDeviationmj=1mk=1sP=SSWjWksjkWjistheweight(investmentproportion)forthejthassetintheportfolio,Wkistheweight(investmentproportion)forthekthassetintheportfolio,sjkisthecovariancebetweenreturnsforthejthandkthassets