chapter 11 Risk and Return in Capital Markets USTB

Dr.XiaoMingUSTB1Chapter11RiskandReturninCapitalMarketsUniversityofScienceandTechnologyBeijingDonglingSchoolofEconomicsandmanagementChapterOutline11.1AFirstLookatRiskandReturn11.2HistoricalRisksandReturnsofStocks11.3TheHistoricalTradeoffBetweenRiskandReturn11.4CommonVersusIndependentRisk11.5DiversificationinStockPortfolios11.1AFirstLookatRiskandReturn•Considerhowaninvestmentwouldhavegrownifitwereinvestedineachofthefollowingfromtheendof1929untilthebeginningof2012:–Standard&Poor’s500(S&P500)–SmallStocks–WorldPortfolio–CorporateBonds–TreasuryBillsFigure11.1Valueof$100InvestedattheEndof1925infivesecuritiesinUSTable11.1RealizedReturns,inPercent(%)forFourSecurities,Year-End1925–193511.2HistoricalRisksandReturnsofStocks•ComputingHistoricalReturns–RealizedReturns–IndividualInvestmentRealizedReturns•Therealizedreturnfromyourinvestmentinthestockfromttot+1is:11111ttttttttttDivPPDivPPRPPPDividendYieldCapitalGainYield(Eq.11.1)Example11.1RealizedReturnProblem:•Microsoftpaidaone-timespecialdividendof$3.08onNovember15,2004.SupposeyouboughtMicrosoftstockfor$28.08onNovember1,2004andsolditimmediatelyafterthedividendwaspaidfor$27.39.Whatwasyourrealizedreturnfromholdingthestock?Solution:Plan:•WecanuseEq11.1tocalculatetherealizedreturn.Weneedthepurchaseprice($28.08),thesellingprice($27.39),andthedividend($3.08)andwearereadytoproceed.Example11.1RealizedReturnExecute:•UsingEq.11.1,thereturnfromNov1,2004untilNov15,2004isequalto•This8.51%canbebrokendownintothedividendyieldandthecapitalgainyield:1113.08(27.3928.08)0.0851,or8.51%28.08tttttDivPPRP113.08DividendYield=.1097,or10.97%28.0827.3928.08CapitalGainYield=0.0246,or2.46%28.08tttttDivPPPPExample11.1RealizedReturnEvaluate:•Thesereturnsincludeboththecapitalgain(orinthiscaseacapitalloss)andthereturngeneratedfromreceivingdividends.Bothdividendsandcapitalgainscontributetothetotalrealizedreturn—ignoringeitheronewouldgiveaverymisleadingimpressionofMicrosoft’sperformance.Example11.1RealizedReturn•ComputingHistoricalReturns–IndividualInvestmentRealizedReturns•Forquarterlyreturns(oranyfourcompoundingperiodsthatmakeupanentireyear)theannualrealizedreturn,Rannual,isfoundbycompounding:12341(1)(1)(1)(1)annualRRRRR(Eq.11.2)11.2HistoricalRisksandReturnsofStocksExample11.2CompoundingRealizedReturnsProblem:•SupposeyoupurchasedMicrosoftstock(MSFT)onNov1,2004andhelditforoneyear,sellingonOct31,2005.Whatwasyourannualrealizedreturn?Solution:Plan:•WeneedtoanalyzethecashflowsfromholdingMSFTstockforeachquarter.Inordertogetthecashflows,wemustlookupMSFTstockpricedataatthepurchasedateandsellingdate,aswellasatanydividenddates.Fromthedatawecanconstructthefollowingtabletofilloutourcashflowtimeline:Example11.2CompoundingRealizedReturnsPlan(cont’d):•Next,computetherealizedreturnbetweeneachsetofdatesusingEq.11.1.ThendeterminetheannualrealizedreturnsimilarlytoEq.11.2bycompoundingthereturnsforalloftheperiodsintheyear.Example11.2CompoundingRealizedReturnsExecute:•InExample11.1,wealreadycomputedtherealizedreturnforNov1,2004toNov15,2004as8.51%.Wecontinueasinthatexample,usingEq.11.1foreachperioduntilwehaveaseriesofrealizedreturns.Forexample,fromNov15,2004toFeb15,2005,therealizedreturnis1110.08(25.9327.39)0.0504,or5.04%27.39tttttDivPPRPExample11.2CompoundingRealizedReturnsExecute(cont’d):•Thetablebelowincludestherealizedreturnateachperiod.Example11.2CompoundingRealizedReturnsExecute(cont’d):•Wethendeterminetheone-yearreturnbycompounding.123451(1)(1)(1)(1)11(1.0851)(0.9496)(0.9861)(1.0675)(0.9473)1.02751.02751.0275or2.75%annualannualannualRRRRRRRRExample11.2CompoundingRealizedReturnsEvaluate:•Byrepeatingthesesteps,wehavesuccessfullycomputedtherealizedannualreturnsforaninvestorholdingMSFTstockoverthisone-yearperiod.Fromthisexercisewecanseethatreturnsarerisky.MSFTfluctuatedupanddownovertheyearandended-uponlyslightly(2.75%)attheend.Example11.2CompoundingRealizedReturns•AverageAnnualReturns–AverageAnnualReturnofaSecurity121(...)TTRRRR(Eq.11.3)11.2HistoricalRisksandReturnsofStocksFigure11.2TheDistributionofAnnualReturnsforFourUSSecurities,1926–2012Figure11.3AverageAnnualReturnsintheU.S.forFourUSSecurities,1926–2012•TheVarianceandVolatilityofReturns:–Variance–StandardDeviation(Eq.11.4)222121()()...()1TVarRRRRRRRT()SDRVarR(Eq.11.5)11.2HistoricalRisksandReturnsofStocksExample11.3ComputingHistoricalVolatilityProblem:•Usingthedatabelow,whatisthestandarddeviationoftheS&P500’sreturnsfortheyears2005-2009?Solution:Plan:•Withthefivereturns,computetheaveragereturnusingEq.11.3becauseitisaninputtothevarianceequation.Next,computethevarianceusingEq.11.4andthentakeitssquareroottodeterminethestandarddeviation,asshowninEq.11.5.Example11.3ComputingHistoricalVolatilityExecute:•IntheprevioussectionwealreadycomputedtheaverageannualreturnoftheS&P500duringthisperiodas3.1%,sowehaveallofthenecessaryinputsforthevariancecalculation:•ApplyingEq.11.4,wehave:22212222221511()()()...()1(.049.031)(.158.031)(.055.031)0.370.031.265.031.058TVarRRRRRRRT