Lecture 2 - Asset Pricing Models

1AssetPricingModels2Learningobjectives•Aftercompletionofthischapteryoushouldbeableto:–intuitivelyunderstandthe:•Portfoliotheory•Relationshipbetweenriskandreturn•Systematicandunsystematic(unique)risk•capitalmarketline(CML)•capitalassetpricingmodel(CAPM)andthesecuritymarketline(SML)•linkbetweentheCMLandSML–applytheCAPMinpricingriskyassetsincludingshare3Learningobjectives•Aftercompletionofthischapteryoushouldbeableto:–understandtheimportanceofportfoliodiversificationininvestmentdecisionmaking–understandthemeanvarianceopportunityset–describeportfolioconstructionmethods–usetheCAPMtojustifyvaluesforrelevantinputparameters–understandtheimportanceofassumptionsunderlyingtheCAPM–explainthedifficultiesassociatedwithtestingtheCAPM–debatewhethertheCAPMisanappropriatemodeltopriceriskyassets.4Chapteroutline1Introduction2PortfolioTheory3TheCAPM4UsingtheCAPM5TestingtheCAPM6ExtensionstotheCAPM7SummaryCONTEXTOFDISCUSSION1.ALLDECISIONMAKERSARERISKAVERSE2.ALLDECISIONMAKERSPREFERTHEHIGHESTPOSSIBLERETURNFORTHELOWESTPOSSIBLERISK3.INVESTORSAREINTERESTEDONLYINTHEMEANANDVARIANCEOFRETURNSPOSSIBLEATTITUDETOWARDSRISK1DESIREFORRISK2RISKAVERSE3RISKNEUTRALOtherassumptions•Investorisrational•Willrankvariousalternativeinvestments•Investorisriskaverse•Dislikeincreasevarianceininvestmentreturns•Oneperiodinvestmenthorizon•Nofrictionstoinvesting•Notransactioncosts•Notaxes•CanborrowandlendatriskfreerateBehaviourofAustraliaAssetClasses•Equity–S&P/ASX200AccumulationIndex•Property–S&P/ASXREITsIndex•Cash–Cumulativeyieldonthe90daybankacceptedbill•FixedInterest–UBSCommonwealthBondAccumulationIndexBehaviourofAustraliaAssetClassesEquity$307Property$278FixedInterest$241Cash$212CPIRosefrom100to$142insameperiodComputationofreturnsrevisited•SupposethesharepriceofABCis$100.Attheendoftheyearthereisanequalchancethatthestockwillbeworth$90,$110or$130.•Thereforereturncouldbe-10%,10%or30%Whataboutexpectedreturn?Expectedreturn=1/3(-10+10+30)=+10or10%Theexpectedendofyearprice=FV(1+r)=$100(1.1)=$110ThePresentValue,PV=$110/(1.1)=$100•TheexpectedreturnisthereforethecorrectrateatwhichtodiscountexpectedcashflowforABC’sstock•IftheoddareunchangedandweobservethestockofABCoveralargenumberofyears,returnwillbe-10%athirdoftime,10%afurtherthirdand30%fortherest.Determiningthediscountrateofaninvestment•HowcanwedeterminethediscountratetoapplytothecashflowsofariskyinvestmentwithsameriskassayASXAllOrdinaryIndex?•UsetheexpectedrateofreturnontheMarketPortfolioi.ereturninvestorsexpectforforgoinginvestinginriskfreeasset–Thisisthesumoftheriskfreerateandapremiumforrisk–MarketPortfoliocomprisesofeveryriskyassetineconomy–UseofAllOrdinaryjustaproxy•PortfolioRisk•Howdowedeterminethediscountrateforaninvestmentthathasn’tgotaveragemarketrisk?•Toanswerthisquestion,let’sfirsttryandmeasuretheriskofaportfolio….ASSUMEARANDOMVARIABLE,X,HASTHEFOLLOWINGDISTRIBUTIONXT={xi}GIVENTHEVALUESFORTHEVECTORXT,THEMEANANDVARIANCEOFTHEDISTRIBUTIONCANBECOMPUTEDAS:X2015251001Niix3010205/100/1NxNiixORMEAN=20COMPUTATIONOFMEANxipixipi200.24150.23250.25300.26100.22201pxiNiixCOMPUTATIONOFTHEVARIANCExixxi2xxipipi2xxi20000.2015-5250.25255250.2530101000.22010-101000.220total50VARIANCEOFTHEVALUESIS50COMPUTATIONOFVARIANCEOR50250511212NiixNx07.750ComputationofvarianceTHEREFORE,THEVARIANCEOFADISTRIBUTION,R,GIVENBY:21)()(RRPERVARiNii(1)PortfolioreturnsTHERETURNANDEXPECTEDRETURNOFTWOASSETPORTFOLIO(X,Y,)GIVENBYRxy=wRx+(1-w)Ry(2)E(Rxy)=wE(Rx)+(1-w)E(Ry)(3)PortfolioreturnSTATEOFECONOMYPROBABILITYXYBAD0.325%-6%AVERAGE0.415%18%GOOD0.3-5%30%ExpectedReturnsE(R)=RPiNii1THEEXPECTEDRETURNOFxGIVENBY:=0.3(0.25)+0.4(0.15)+0.3(-0.05)=0.075+0.06+-0.015=0.12OR12%THEEXPECTEDRETURNONyGIVENBY:=0.3(-0.06)+0.4(0.18)+0.3(0.3)=-0.018+0.072+0.09=0.144OR14.4%THEVARIANCEISTHEEXPECTATIONOFTHESQUAREDERRORFROMTHEMEANVARR=E(Ri–E(R))2=2)(1RERPiNiiVARx=0.3(0.25-0.12)2+0.4(0.15-0.12)2+0.3(-0.05-0.12)2=0.3(0.0169)+0.4(0.0009)+0.3(0.0289)=0.0141=119.00141.0OR11.9%VARy=0.3(-0.06-0.144)2+0.4(0.18-0.144)2+0.3(0.3-0.144)2=0.3(0.041616)+0.4(0.001296)+0.3(0.024336)=0.020304=142.0020304.0OR14.2%PORTFOLIOANDRISKREDUCTION•Portfolioisacollectionof(stockandbonds)investments•Assetsarepositivelybutnotperfectlycorrelated•Uniqueriskcanbediversifiedawaybutsystematic/marketriskcannot•UniqueriskalsocalledUnsystematicriskDIVERSIFICATIONANDITSIMPACTONRISK051015NumberofSecuritiesPortfoliostandarddeviationMarketriskUniqueriskRISK,RETURNANDPORTFOLIOSELECTIONReturn%ABKCLEfficientPortfoliosCOMBININGASSETSINAPORTFOLIOREDUCESRISKASSUME60%OFYOURWEALTHISINVESTEDINSECURITYxAND40%INy.ASSUMEAGAINTHATTHERETURNONxIS20%ANDyIS28%.THERETURNONPORTFOLIOCOMPRISING0.6OFxAND0.4OFyISGIVENBY:COMBININGASSETSINAPORTFOLIOREDUCESRISKRETURNxy=wRx+(1-w)Ry=0.6(0.20)+0.4(0.28)=0.232OR23%THEEXPECTEDRETURNONxIS18%ANDTHEEXPECTEDRETURNONyIS12%.45%ISINVESTEDINxAND55%INy.E(Rxy)=wE(Rx)+(1-w)E(Ry)=0.45(0.18)+0.55(0.12)=0.081+0.066=0.147or14.7%RESTATINGEQUATIONS(1),(2)AND(3)2)(1)(RRPERVARiNii(1)Rxy=wRx+(1-w)Ry(2)E(Rxy)=wE(Rx)+(1-w)E(Ry)(