Chapter4RiskandReturn風險與報酬DollarReturnsTotaldollarreturn=incomefrominvestment+capitalgain(loss)duetochangeinpriceExample:Youboughtabondfor$9501yearago.Youhavereceivedtwocouponsof$30each.Youcansellthebondfor$975today.Whatisyourtotaldollarreturn?Income=Capitalgain=Totaldollarreturn=PercentageReturnsItisgenerallymoreintuitivetothinkintermsofpercentagesthandollarreturnsDividendyield=income/beginningpriceCapitalgainsyield=(endingprice–beginningprice)/beginningpriceTotalpercentagereturn=dividendyield+capitalgainsyieldDefiningReturnIncomereceivedonaninvestmentplusanychangeinmarketprice,usuallyexpressedasapercentofthebeginningmarketpriceoftheinvestment.Dt

+(Pt-Pt-1

)Pt-1R=ReturnExampleThestockpriceforStockAwas$10pershare1yearago.Thestockiscurrentlytradingat$9.50pershareandshareholdersjustreceiveda$1dividend.Whatreturnwasearnedoverthepastyear?ExerciseSupposeafirm’sstockissellingfor$10.50.Theyjustpaida$1dividendanddividendsareexpectedtogrowat5%peryear.Whatistherequiredreturn?R=Whatisthedividendyield?Whatisthecapitalgainsyield?RiskPremiums（風險溢價）The“extra”returnearnedfortakingonriskTreasurybillsareconsideredtoberisk-freeTheriskpremiumisthereturnoverandabovetherisk-freerateHistoricalRiskPremiumsLargestocks:12.7–3.9=8.8%Smallstocks:17.3–3.9=13.4%Long-termcorporatebonds:6.1–3.9=2.2%Long-termgovernmentbonds:5.7–3.9=1.8%ExpectedReturnsExpectedreturnsarebasedontheprobabilitiesofpossibleoutcomesInthiscontext,“expected”meansaverageiftheprocessisrepeatedmanytimesThe“expected”returndoesnotevenhavetobeapossiblereturnDeterminingExpectedReturn(DiscreteDist.離散型分布)

R=S(Ri)(Pi)Ristheexpectedreturn

（期望報酬）fortheasset,Ri

isthereturnfortheithpossibility,Piistheprobabilityofthatreturnoccurring,nisthetotalnumberofpossibilities.ni=1Example:ExpectedReturnsSupposeyouhavepredictedthefollowingreturnsforstocksCandTinthreepossiblestatesofnature.Whataretheexpectedreturns?State Probability C TBoom 0.3 0.15 0.25Normal 0.5 0.10 0.20Recession ??? 0.02 0.01RC=RT=HowtoDeterminetheExpectedReturnandStandardDeviation

StockBW

Ri

Pi (Ri)(Pi)

-.15 .10 -.015 -.03 .20 -.006 .09 .40 .036 .21 .20 .042 .33 .10 .033

Sum

1.00

.090 Theexpectedreturn,R,forStockBWis.09or9%HowtoDeterminetheExpectedReturnandStandardDeviation

StockBW

Ri

Pi (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 .00576

Sum

1.00

.090 .01728DeterminingStandardDeviation(RiskMeasure)s=S(Ri-R)2(Pi)s=.01728s=.1315or13.15%ni=1Example:VarianceandStandardDeviationConsiderthepreviousexample.Whatarethevarianceandstandarddeviationforeachstock?StockC2==StockT2==DeterminingExpectedReturn(ContinuousDist.連續(xù)型分布)

R=S(Ri)/(n)Ristheexpectedreturnfortheasset,Riisthereturnfortheithobservation,nisthetotalnumberofobservations.ni=1DeterminingStandardDeviation(RiskMeasure)ni=1s=S(Ri-R)2(n)Note,thisisforacontinuousdistributionwherethedistributionisforapopulation.Rrepresentsthepopulationmeaninthisexample.RiskAttitudeExampleYouhavethechoicebetween(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.SystematicRiskisthevariabilityofreturnonstocksorportfoliosassociatedwithchangesinreturnonthemarketasawhole.UnsystematicRiskisthevariabilityofreturnonstocksorportfoliosnotexplainedbygeneralmarketmovements.Itisavoidablethroughdiversification.TotalRisk=SystematicRisk+UnsystematicRiskTotalRisk=Systematic

Risk+ Unsystematic

RiskSystematicRiskRiskfactorsthataffectalargenumberofassetsAlsoknownasnon-diversifiableriskormarketriskIncludessuchthingsaschangesinGDP,inflation,interestrates,etc.TotalRisk=SystematicRisk+UnsystematicRiskTotalRiskUnsystematicriskSystematicriskSTDDEVOFPORTFOLIORETURNNUMBEROFSECURITIESINTHEPORTFOLIOFactorsuniquetoaparticularcompanyorindustry.Forexample,thedeathofakeyexecutiveorlossofagovernmentaldefensecontract.TotalRiskTotalrisk=systematicrisk+unsystematicriskThestandarddeviationofreturnsisameasureoftotalriskForwelldiversifiedportfolios,unsystematicriskisverysmallConsequently,thetotalriskforadiversifiedportfolioisessentiallyequivalenttothesystematicriskPortfolios(組合）AportfolioisacollectionofassetsAnasset’sriskandreturnisimportantinhowitaffectstheriskandreturnoftheportfolioTherisk-returntrade-offforaportfolioismeasuredbytheportfolioexpectedreturnandstandarddeviation,justaswithindividualassetsCorrelationCoefficient（相關系數）Astandardizedstatisticalmeasureofthelinearrelationshipbetweentwovariables.Itsrangeisfrom-1.0(perfectnegativecorrelation),through0(nocorrelation),to+1.0(perfectpositivecorrelation).Combiningsecuritiesthatarenotperfectly,positivelycorrelatedreducesrisk.DiversificationandtheCorrelationCoefficientINVESTMENTRETURNTIMETIMETIMESECURITYESECURITYFCombinationEandFExample:PortfolioWeights（權重）Supposeyouhave$15,000toinvestandyouhavepurchasedsecuritiesinthefollowingamounts.Whatareyourportfolioweightsineachsecurity?$2000ofDCLK$3000ofKO$4000ofINTC$6000ofKEIDCLK:2/15=.133KO:3/15=.2INTC:4/15=.267KEI:6/15=.4

RP=S(Wj)(Rj)RP

istheexpectedreturnfortheportfolio,Wjistheweight(investmentproportion)forthejthassetintheportfolio,Rjistheexpectedreturnofthejthasset,misthetotalnumberofassetsintheportfolio.DeterminingPortfolio ExpectedReturnmj=1Example:ExpectedPortfolioReturnsConsidertheportfolioweightscomputedpreviously.Iftheindividualstockshavethefollowingexpectedreturns,whatistheexpectedreturnfortheportfolio?DCLK:19.65%KO:8.96%INTC:9.67%KEI:8.13%E(RP)=證券投資組合的具體做法

1、選擇足夠數量的證券組合2、把投資報酬呈負相關的證券放在一起3、把風險大、中等、小的證券放在一起CAPMisamodelthatdescribestherelationshipbetweenriskandexpected(required)return;inthismodel,asecurity’sexpected(required)returnistherisk-freerateplusapremiumbasedonthesystematicriskofthesecurity.CapitalAsset

PricingModel(CAPM)1. Capitalmarketsareefficient.2. Homogeneousinvestorexpectations overagivenperiod.3. Risk-freeassetreturniscertain (use short-tointermediate-term Treasuriesasaproxy).4. Marketportfoliocontainsonly

systematicrisk(useS&P500Index orsimilarasaproxy).CAPMAssumptionsCalculating“Beta”

onYourCalculatorTimePd.MarketMyStock19.6%12%2-15.4%-5%326.7%19%4-.2%3%520.9%13%628.3%14%7-5.9%-9%83.3%-1%912.2%12%1010.5%10%TheMarketandMyStockreturnsare“excessreturns”andhavetherisklessratealreadysubtracted.Anindexofsystematicrisk.Itmeasuresthesensitivityofastock’sreturnstochangesinreturnsonthemarketportfolio.Thebetaforaportfolioissimplyaweightedaverageoftheindividualstockbetasintheportfolio.WhatisBeta?Example:PortfolioBetasConsiderthepreviousexamplewiththefollowingfoursecuritiesSecurity Weight BetaDCLK .133 4.03KO .2 0.84INTC .167 1.05KEI .4 0.59Whatistheportfoliobeta?MeasuringSystematicRiskHowdowemeasuresystematicrisk?WeusethebetacoefficienttomeasuresystematicriskWhatdoesbetatellus?Abetaof1impliestheassethasthesamesystematicriskastheoverallmarketAbeta<1impliestheassethaslesssystematicriskthantheoverallmarketAbeta>1impliestheasset

hasmoresystematicriskthantheoverallmarketCharacteristicLines andDifferentBetasEXCESSRETURNONSTOCKEXCESSRETURNONMARKETPORTFOLIOBeta<1(defensive)Beta=1Beta>1(aggressive)Eachcharacteristiclinehasadifferentslope.TotalversusSystematicRiskConsiderthefollowinginformation:

StandardDeviation

BetaSecurityC 20% 1.25SecurityK 30% 0.95Whichsecurityhasmoretotalrisk?Whichsecurityhasmoresystematicrisk?Whichsecurityshouldhavethehigherexpectedreturn?Rjistherequiredrateofreturnforstockj,Rfistherisk-freerateofreturn,bj

isthebetaofstockj(measuressystematicriskofstockj),RMistheexpectedreturnforthemarketportfolio.SecurityMarketLineRj=Rf+bj(RM-Rf)SecurityMarketLineRj=Rf+bj(RM-Rf)bM=1.0SystematicRisk(Beta)RfRMRequiredReturnRiskPremiumRisk-freeReturnLisaMilleratBasketWondersisattemptingtodeterminetherateofreturnrequiredbytheirstockinvestors.Lisaisusinga6%Rf

andalong-termmarketexpectedrateofreturnof10%.Astockanalystfollowingthefirmhascalculatedthatthefirmbetais1.2.Whatistherequiredrateofreturn

onthestockofBasketWonders?DeterminationoftheRequiredRateofReturnRBW=Rf

+bj(RM-Rf)RBW=6%+1.2(10%-6%)RBW=10.8%TherequiredrateofreturnexceedsthemarketrateofreturnasBW’sbetaexceeds