【文章內(nèi)容簡(jiǎn)介】 FiguresfromTable1inMeirStatman,“HowManyStocksMakeaDiversifiedPortfolio?”Journal of Financial and Quantitative Analysis 22(September1987),pp.353–64,andderivedfromE.J.EltonandM.J.Gruber,“RiskReductionandPortfolioSize:AnAnalyticSolution,”Journal of Business50(October1977),pp.415–37.PortfolioDiversificationAverageannualstandarddeviation(%)NumberofstocksinportfolioDiversifiableriskNondiversifiablerisk1 10 20 30 40 1000Diversification:analyticalsolutionDiversification:analyticalsolution(2)Diversification:analyticalsolution(3)Ifweweretolookatthecasewherecovariancesarenotequaltozerowewouldfindthattheriskofalargeportfolioofstocksisapproximatelyequaltotheaveragecovariancebetweenallthestocks.?P2 ? CovAVPeterBernsteinonRiskandDiversification“Bigrisksarescarywhenyoucannotdiversifythem,especiallywhentheyareexpensivetounload。eventhewealthiestfamilieshesitatebeforedecidingwhichhousetobuy.Bigrisksarenotscarytoinvestorswhocandiversifythem。bigrisksareinteresting.Nosinglelosswillmakeanyonegobroke...bymakingdiversificationeasyandinexpensive,financialmarketsenhancethelevelofrisktakinginsociety.”P(pán)eterBernstein,inhisbook,CapitalIdeasHowcorrelationaffectsrisk:TheEfficientFrontierFTthisweekn Olympus–admitswrongdoing.n Eurozone–manyinterestingarticleshighlightingthe‘power’ofGreece,Germanroleandinterest,dangerstoItalyandothers.Focusononearticle:RobertJenkins,Insight()Greekrestructuring–exitfromtheeurozonen Greekgovtdecidesonexit.u Greekcitizensandpanieswithdraweurodepositswhilsttheyarestilleuros.Foreignlendersstoplendingandrecallloansasquicklyaspossible.u Govt.announcesanewdrachma.Capitalcontrolsareintroduced.Govtdebtisredenominatedindrachma.OlympussharepriceFTthisweek(cont)–Greekrestructuringn Valueofthedrachmaplunges,Greekinflationsoars.n Disputesoverprivatesectordebt.Aretheyindrachmaoreuros?Ifdrachmathenforeignbankshaveaproblem–assetvalueshavefallen.IfineurosthenGreekborrowershaveaproblemn Contagionmences.Portugesecitizensthinkitmighthappentothemandmoveouteurosfromthebanks.Similarmovesinseveralothercountries.n Europeanbanksindifficultiesbecauseofexposuretoeurodebtofvariouscountrieswithlikelydifficulties.Counterpartyriskmeansmarketinbankloansdriesup.Banklendinghalts!n BankscollapseunlessGovtrescuethem.TheStorytodaten TheriskofaportfoliodependsontheCovarianceorCorrelationbetweenassets.Varianceisimportantforanindividualassetbutbeeslessandlessimportantasaportfolioincludesmoreandmorestocks.n Theriskofaportfoliodependsontheaveragecovariancebetweenstocks.n Therelationshipbetweenriskandreturncanberepresentedgraphicallybyaquadraticfrontier.ThebestbinationsofriskandreturnareontheEfficientFrontier.Theshapeofthefrontierarisesfromthecovariancebetweenassets.HowCorrelationaffectsrisk:ariskfreeassetHowCorrelationaffectsrisk:ariskfreeasset(2)Tobin’sSeparationTheoremSimplifyingourRiskMeasuren Ourmessagesofarhasbeenthatwhenweaddsecuritiestogetherriskisaffectedbythecorrelation(covariance)betweenthem.Becausesecuritiesarelessthanperfectlycorrelated,riskisreduced.n Whilstthisisusefulasaconceptitisoperationallyverydifficulttouse.Thenumberofcorrelationsthatweneedtoconsidertoconstructoptimalportfoliosusingthissortofapproachisverylarge.Weneedtofindsomeothermeasureofriskthatwillenableustosimplifytheproblem.Onesuchmeasureisthebetaofasecurityorportfolio.Thebetaofasecuritycanbethoughtofas:the(standardised)sumofthesecurity’scovariancewithallsecuritiesn Sinceall securities isjustanotherwayofsayingthe market,thebetaofasecurityis:the(standardised)covarianceofthesecuritywiththe marketEstimatingBetan Betaisusuallyestimatedusinglinearregression.BetaisanoutputfromtheMarketModel.Thisassumesthatthereisalinearrelationshipbetweenthereturnonthemarketandthereturnonashare.Returnsonashareareregressedagainstreturnsonamarketindex.Rit=ai+biRmtcitaiisthealphaofshareIbiisthebetaofshareIBetaCoefficientsforSelectedCompanies(Table) BetaCompanyCoefficient( i)AlcatelLucent L’Oreal SAP Siemens Daimler PhilipsElectron Renault Volkswagen Source:Hillier,Ross,Westerfield,Jaffe,Jordan.CorporateFinance.PortfolioBetaCalculationsPortfolioBetahasaverydesirablecharacteristic.Itisthe(weighted)averageoftheindividualbetas.Amount PortfolioStock Invested Weights Beta(1) (2) (3) (4) (3)x(4)HaskellMfg. $6,000 50% Cleaver,Inc. 4,000 33% RutherfordCo. 2,000 17% Portfolio $12,000 100% Cash(risklessasset),PortfolioExpectedReturnsandBetasn AssumeyouwishtoholdaportfolioconsistingofariskyassetAandcash(arisklessasset).Giventhefollowinginformation,calculateportfolioexpectedreturnsandportfoliobetas,lettingtheproportionoffundsinvestedinassetArangefrom0to125%.AssetAhasabeta( )ofandanexpectedreturnof18%.ThereturnoncashattheCentralBank(riskfreerate)is7%.AssetAweights:0%,25%,50%,75%,100%,and125%.Cash(risklessasset),PortfolioExpectedReturnsandBetasProportion Proportion Portfolio Investedin Investedin Expected160