公司理財教學課件：ch03 Risk and Return

CHAPTER3

RiskandReturnBasicreturnconceptsBasicriskconceptsStand-aloneriskPortfolio(market)riskRiskandreturn:CAPM/SMLWhatareinvestmentreturns?Investmentreturnsmeasurethefinancialresultsofaninvestment.Returnsmaybehistoricalorprospective(anticipated).Returnscanbeexpressedin:Dollarterms.Percentageterms.Whatisthereturnonaninvestmentthatcosts$1,000andissold

after1yearfor$1,100?Dollarreturn:Percentagereturn:$Received-$Invested$1,100-$1,000=$100.$Return/$Invested$100/$1,000=0.10=10%.Whatisinvestmentrisk?Typically,investmentreturnsarenotknownwithcertainty.Investmentriskpertainstotheprobabilityofearningareturnlessthanthatexpected.Thegreaterthechanceofareturnfarbelowtheexpectedreturn,thegreatertherisk.ProbabilitydistributionRateofreturn(%)50150-20StockXStockYWhichstockisriskier?Why?AssumetheFollowing

InvestmentAlternativesEconomyProb.T-BillHTCollUSRMPRecession0.108.0%-22.0%28.0%10.0%-13.0%Belowavg.0.208.0-2.014.7-10.01.0Average0.408.020.00.0

7.015.0Aboveavg.0.208.035.0-10.045.029.0Boom

0.108.050.0-20.030.043.01.00Whatisuniqueabout

theT-billreturn?TheT-billwillreturn8%regardlessofthestateoftheeconomy.IstheT-billriskless?Explain.DothereturnsofHTandCollectionsmovewithorcountertotheeconomy?HTmoveswiththeeconomy,soitispositivelycorrelatedwiththeeconomy.Thisisthetypicalsituation.Collectionsmovescountertotheeconomy.Suchnegativecorrelationisunusual.Calculatetheexpectedrateofreturnoneachalternative.r=expectedrateofreturn.rHT=0.10(-22%)+0.20(-2%) +0.40(20%)+0.20(35%) +0.10(50%)=17.4%.^^HThasthehighestrateofreturn.Doesthatmakeitbest?rHT17.4%Market15.0USR13.8T-bill8.0Collections1.7^Whatisthestandarddeviation

ofreturnsforeachalternative?T-bills=0.0%.HT=20.0%.Coll = 13.4%.USR = 18.8%.

M = 15.3%.HT:=((-22-17.4)20.10+(-2-17.4)20.20+(20-17.4)20.40+(35-17.4)20.20+(50-17.4)20.10)1/2=20.0%.Prob.RateofReturn(%)T-billUSRHT0813.817.4Standarddeviationmeasuresthestand-aloneriskofaninvestment.Thelargerthestandarddeviation,thehighertheprobabilitythatreturnswillbefarbelowtheexpectedreturn.Coefficientofvariationisanalternativemeasureofstand-alonerisk.ExpectedReturnversusRiskExpectedSecurityreturnRisk,HT17.4%20.0%Market15.015.3USR13.818.8T-bills8.00.0Collections1.713.4CoefficientofVariation:

CV=Expectedreturn/standarddeviation.CVT-BILLS =0.0%/8.0% =0.0.CVHIGHTECH =20.0%/17.4% =1.1.CVCOLLECTIONS =13.4%/1.7% =7.9.CVU.S.RUBBER =18.8%/13.8% =1.4.CVM =15.3%/15.0% =1.0.ExpectedReturnversusCoefficientofVariationExpectedRisk:Risk:SecurityreturnCVHT17.4%20.0%1.1Market15.015.31.0USR13.818.81.4T-bills8.00.00.0Collections1.713.47.9Returnvs.Risk(Std.Dev.):

Whichinvestmentisbest?PortfolioRiskandReturnAssumeatwo-stockportfoliowith$50,000inHTand$50,000inCollections.Calculaterpandp.^PortfolioReturn,rprpisaweightedaverage:rp=0.5(17.4%)+0.5(1.7%)=9.6%.rpisbetweenrHTandrColl.^^^^^^^^rp=wirini=1AlternativeMethodrp=(3.0%)0.10+(6.4%)0.20+(10.0%)0.40+(12.5%)0.20+(15.0%)0.10=9.6%.^EstimatedReturn(More...)EconomyProb.HTColl.Port.Recession0.10-22.0%

28.0%

3.0%Belowavg.0.20-2.014.76.4Average0.4020.0

0.010.0Aboveavg.0.2035.0-10.012.5Boom0.1050.0-20.015.0p=((3.0-9.6)20.10+(6.4-9.6)20.20+ (10.0-9.6)20.40+(12.5-9.6)20.20 +(15.0-9.6)20.10)1/2=3.3%.pismuchlowerthan:eitherstock(20%and13.4%).averageofHTandColl(16.7%).Theportfolioprovidesaveragereturnbutmuchlowerrisk.Thekeyhereisnegativecorrelation.Two-StockPortfoliosTwostockscanbecombinedtoformarisklessportfolioifr=-1.0.Riskisnotreducedatallifthetwostockshaver=+1.0.Ingeneral,stockshaver

0.65,soriskisloweredbutnoteliminated.Investorstypicallyholdmanystocks.Whathappenswhenr=0?Whatwouldhappentothe

riskofanaverage1-stock

portfolioasmorerandomly

selectedstockswereadded?pwoulddecreasebecausetheaddedstockswouldnotbeperfectlycorrelated,butrpwouldremainrelativelyconstant.^Large015Prob.211

35%;Large

20%.Return#StocksinPortfolio10 20 30 40 2,000+CompanySpecific(Diversifiable)RiskMarketRisk200Stand-AloneRisk,pp(%)35Stand-aloneMarketDiversifiableMarketriskisthatpartofasecurity’sstand-aloneriskthatcannotbeeliminatedbydiversification.Firm-specific,ordiversifiable,riskisthatpartofasecurity’sstand-aloneriskthatcanbeeliminatedbydiversification.riskriskrisk=+.ConclusionsAsmorestocksareadded,eachnewstockhasasmallerrisk-reducingimpactontheportfolio.pfallsveryslowlyafterabout40stocksareincluded.Thelowerlimitforpisabout20%=M.Byformingwell-diversifiedportfolios,investorscaneliminateabouthalftheriskinessofowningasinglestock.No.Rationalinvestorswillminimizeriskbyholdingportfolios.Theybearonlymarketrisk,sopricesandreturnsreflectthislowerrisk.Theone-stockinvestorbearshigher(stand-alone)risk,sothereturnislessthanthatrequiredbytherisk.Cananinvestorholdingonestockearnareturncommensuratewithitsrisk?Marketrisk,whichisrelevantforstocksheldinwell-diversifiedportfolios,isdefinedasthecontributionofasecuritytotheoverallriskinessoftheportfolio.Itismeasuredbyastock’sbetacoefficient.Forstocki,itsbetais:bi=(riM

si)/sMHowismarketriskmeasuredforindividualsecurities?Howarebetascalculated?Inadditiontomeasuringastock’scontributionofrisktoaportfolio,betaalsowhichmeasuresthestock’svolatilityrelativetothemarket.UsingaRegressiontoEstimateBetaRunaregressionwithreturnsonthestockinquestionplottedontheYaxisandreturnsonthemarketportfolioplottedontheXaxis.Theslopeoftheregressionline,whichmeasuresrelativevolatility,isdefinedasthestock’sbetacoefficient,orb.UsethehistoricalstockreturnstocalculatethebetaforKWE.YearMarketKWE125.7%40.0%28.0%-15.0%3-11.0%-15.0%415.0%35.0%532.5%10.0%613.7%30.0%740.0%42.0%810.0%-10.0%9-10.8%-25.0%10-13.1%25.0%CalculatingBetaforKWErKWE=0.83rM+0.03R2=0.36-40%-20%0%20%40%-40%-20%0%20%40%rMrKWEWhatisbetaforKWE?Theregressionline,andhencebeta,canbefoundusingacalculatorwitharegressionfunctionoraspreadsheetprogram.Inthisexample,b=0.83.CalculatingBetainPracticeManyanalystsusetheS&P500tofindthemarketreturn.Analyststypicallyusefourorfiveyears’ofmonthlyreturnstoestablishtheregressionline.Someanalystsuse52weeksofweeklyreturns.Ifb=1.0,stockhasaveragerisk.Ifb>1.0,stockisriskierthanaverage.Ifb<1.0,stockislessriskythanaverage.Moststockshavebetasintherangeof0.5to1.5.Canastockhaveanegativebeta?Howisbetainterpreted?FindingBetaEstimatesontheWebG.Enterthetickersymbolfora“StockQuote”,suchasIBMorDell.Whenthequotecomesup,lookinthesectiononFundamentals.ExpectedReturnversusMarketRiskWhichofthealternativesisbest?ExpectedSecurityreturnRisk,bHT17.4%1.29Market15.01.00USR13.80.68T-bills8.00.00Collections1.7-0.86UsetheSMLtocalculateeach

alternative’srequiredreturn.TheSecurityMarketLine(SML)ispartoftheCapitalAssetPricingModel(CAPM).SML:ri=rRF+(RPM)bi.AssumerRF=8%;rM=rM

=15%.RPM=(rM

-rRF)=15%-8%=7%.^RequiredRatesofReturnrHT

=8.0%+(7%)(1.29) =8.0%+9.0% =17.0%.rM =8.0%+(7%)(1.00) =15.0%.rUSR =8.0%+(7%)(0.68) =12.8%.rT-bill =8.0%+(7%)(0.00) =8.0%.rColl =8.0%+(7%)(-0.86) =2.0%.ExpectedversusRequiredReturns^rrHT17.4%17.0%UndervaluedMarket15.015.0FairlyvaluedUSR13.812.8UndervaluedT-bills8.08.0FairlyvaluedColl1.72.0Overvalued..Coll..HTT-bills.USRrM

=15

rRF=8-1 0 1 2 .SML:ri=rRF

+(RPM)biri=8%

+(7%)biri(%)Risk,biSMLandInvestmentAlternativesMarketCalcula