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1、6-1Copyright 2001 by Harcourt,Inc.All rights reserved.CHAPTER 6 Risk and Rates of ReturnnStand-alone risknPortfolio risknRisk&return:CAPM/SML6-2Copyright 2001 by Harcourt,Inc.All rights reserved.What is investment risk?Investment risk pertains to the probability of actually earning a low or negative
2、 return.The greater the chance of low or negative returns,the riskier the investment.6-3Copyright 2001 by Harcourt,Inc.All rights reserved.Probability distributionExpected Rate of ReturnRate ofreturn(%)100150-70Firm XFirm Y6-4Copyright 2001 by Harcourt,Inc.All rights reserved.Annual Total Returns,19
3、26-1998AverageStandardReturnDeviationDistributionSmall-companystocks 17.4%33.8%Large-companystocks 13.2 20.3Long-termcorporate bonds 6.1 8.6Long-termgovernment 5.7 9.2Intermediate-termgovernment 5.5 5.7U.S.Treasurybills 3.8 3.2Inflation 3.2 4.56-5Copyright 2001 by Harcourt,Inc.All rights reserved.In
4、vestment Alternatives(Given in the problem)Economy Prob.T-BillHTCollUSRMPRecession 0.1 8.0%-22.0%28.0%10.0%-13.0%Below avg.0.2 8.0-2.014.7-10.0 1.0Average0.4 8.020.00.07.0 15.0Above avg.0.2 8.035.0-10.045.0 29.0Boom0.1 8.050.0-20.030.0 43.01.06-6Copyright 2001 by Harcourt,Inc.All rights reserved.Why
5、 is the T-bill return independent of the economy?Will return the promised 8%regardless of the economy.6-7Copyright 2001 by Harcourt,Inc.All rights reserved.Do T-bills promise a completelyrisk-free return?No,T-bills are still exposed to the risk of inflation.However,not much unexpected inflation is l
6、ikely to occur over a relatively short period.6-8Copyright 2001 by Harcourt,Inc.All rights reserved.Do the returns of HT and Coll.move with or counter to the economy?nHT:Moves with the economy,and has a positive correlation.This is typical.nColl:Is countercyclical of the economy,and has a negative c
7、orrelation.This is unusual.6-9Copyright 2001 by Harcourt,Inc.All rights reserved.Calculate the expected rate of return on each alternative:k=expected rate of return.kHT=(-22%)0.1+(-2%)0.20+(20%)0.40+(35%)0.20+(50%)0.1=17.4%.6-10Copyright 2001 by Harcourt,Inc.All rights reserved.kHT17.4%Market15.0USR
8、13.8T-bill8.0Coll.1.7HT appears to be the best,but is it really?6-11Copyright 2001 by Harcourt,Inc.All rights reserved.Whats the standard deviationof returns for each alternative?=Standard deviation.=6-12Copyright 2001 by Harcourt,Inc.All rights reserved.T-bills=0.0%.HT=20.0%.Coll=13.4%.USR=18.8%.M=
9、15.3%.1/2 T-bills=(8.0 8.0)20.1+(8.0 8.0)20.2+(8.0 8.0)20.4+(8.0 8.0)20.2+(8.0 8.0)20.16-13Copyright 2001 by Harcourt,Inc.All rights reserved.Prob.Rate of Return(%)T-billUSRHT0813.817.46-14Copyright 2001 by Harcourt,Inc.All rights reserved.nStandard deviation(i)measures total,or stand-alone,risk.nTh
10、e larger the i,the lower the probability that actual returns will be close to the expected return.6-15Copyright 2001 by Harcourt,Inc.All rights reserved.Expected Returns vs.RiskSecurityExpectedreturnRisk,HT 17.4%20.0%Market 15.0 15.3USR 13.8*18.8*T-bills 8.0 0.0Coll.1.7*13.4*Seems misplaced.6-16Copy
11、right 2001 by Harcourt,Inc.All rights reserved.Coefficient of Variation(CV)Standardized measure of dispersionabout the expected value:Shows risk per unit of return.CV=.Std dev kMean6-17Copyright 2001 by Harcourt,Inc.All rights reserved.0AB A=B,but A is riskier because largerprobability of losses.=CV
12、A CVB.k6-18Copyright 2001 by Harcourt,Inc.All rights reserved.Portfolio Risk and ReturnAssume a two-stock portfolio with$50,000 in HT and$50,000 in Collections.Calculate kp and p.6-19Copyright 2001 by Harcourt,Inc.All rights reserved.Portfolio Return,kpkp is a weighted average:kp=0.5(17.4%)+0.5(1.7%
13、)=9.6%.kp is between kHT and kCOLL.kp=S S wiki.ni=16-20Copyright 2001 by Harcourt,Inc.All rights reserved.Alternative Methodkp=(3.0%)0.10+(6.4%)0.20+(10.0%)0.40 +(12.5%)0.20+(15.0%)0.10=9.6%.Estimated ReturnEconomyProb.HTColl.Port.Recession 0.10-22.0%28.0%3.0%Below avg.0.20-2.0 14.7 6.4Average 0.40
14、20.0 0.0 10.0Above avg.0.20 35.0-10.0 12.5Boom 0.10 50.0-20.0 15.06-21Copyright 2001 by Harcourt,Inc.All rights reserved.CVp=0.34.3.3%9.6%p=3.3%.1 2/(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)20.106-22Copyright 2001 by Harcourt,Inc.All rights reserved.n p=3.3%is much low
15、er than that of either stock(20%and 13.4%).n p=3.3%is lower than average of HT and Coll=16.7%.n Portfolio provides average k but lower risk.nReason:negative correlation.6-23Copyright 2001 by Harcourt,Inc.All rights reserved.General statements about risknMost stocks are positively correlated.rk,m 0.6
16、5.n 35%for an average stock.nCombining stocks generally lowers risk.6-24Copyright 2001 by Harcourt,Inc.All rights reserved.Returns Distribution for Two Perfectly Negatively Correlated Stocks(r=-1.0)and for Portfolio WM25150-10-10-100015152525Stock WStock MPortfolio WM.6-25Copyright 2001 by Harcourt,
17、Inc.All rights reserved.Returns Distributions for Two Perfectly Positively Correlated Stocks(r=+1.0)and for Portfolio MMStock M01525-10Stock M01525-10Portfolio MM01525-106-26Copyright 2001 by Harcourt,Inc.All rights reserved.What would happen to theriskiness of an average 1-stockportfolio as more ra
18、ndomlyselected stocks were added?n p would decrease because the added stocks would not be perfectly correlated but kp would remain relatively constant.6-27Copyright 2001 by Harcourt,Inc.All rights reserved.Large015Prob.21Even with large N,p 20%6-28Copyright 2001 by Harcourt,Inc.All rights reserved.#
19、Stocks in Portfolio102030 40 2,000+Company Specific RiskMarket Risk20 0Stand-Alone Risk,p p(%)356-29Copyright 2001 by Harcourt,Inc.All rights reserved.nAs more stocks are added,each new stock has a smaller risk-reducing impact.n p falls very slowly after about 10 stocks are included,and after 40 sto
20、cks,there is little,if any,effect.The lower limit for p is about 20%=M.6-30Copyright 2001 by Harcourt,Inc.All rights reserved.Stand-alone Market Firm-specificMarket risk is that part of a securitys stand-alone risk that cannot be eliminated by diversification,and is measured by beta.Firm-specific ri
21、sk is that part of a securitys stand-alone risk that can be eliminated by proper diversification.risk risk risk=+6-31Copyright 2001 by Harcourt,Inc.All rights reserved.nBy forming portfolios,we can eliminate about half the riskiness of individual stocks(35%vs.20%).6-32Copyright 2001 by Harcourt,Inc.
22、All rights reserved.If you chose to hold a one-stock portfolio and thus are exposed to more risk than diversified investors,would you be compensated for all the risk you bear?6-33Copyright 2001 by Harcourt,Inc.All rights reserved.nNO!nStand-alone risk as measured by a stocks or CV is not important t
23、o a well-diversified investor.nRational,risk averse investors are concerned with p,which is based on market risk.6-34Copyright 2001 by Harcourt,Inc.All rights reserved.nThere can only be one price,hence market return,for a given security.Therefore,no compensation can be earned for the additional ris
24、k of a one-stock portfolio.6-35Copyright 2001 by Harcourt,Inc.All rights reserved.nBeta measures a stocks market risk.It shows a stocks volatility relative to the market.nBeta shows how risky a stock is if the stock is held in a well-diversified portfolio.6-36Copyright 2001 by Harcourt,Inc.All right
25、s reserved.How are betas calculated?nRun a regression of past returns on Stock i versus returns on the market.Returns=D/P+g.nThe slope of the regression line is defined as the beta coefficient.6-37Copyright 2001 by Harcourt,Inc.All rights reserved.YearkM ki 115%18%2-5-10 312 16.ki _kM_-5051015202015
26、10 5-5-10Illustration of beta calculation:Regression line:ki=-2.59+1.44 kM6-38Copyright 2001 by Harcourt,Inc.All rights reserved.nIf beta=1.0,average stock.nIf beta 1.0,stock riskier than average.nIf beta kMarket 15.0 15.0 Fairly valuedUSR 13.8 12.8 Undervalued:k kT-bills 8.0 8.0 Fairly valuedColl.1
27、.7 2.0 Overvalued:k kExpected vs.Required Returns k k 6-46Copyright 2001 by Harcourt,Inc.All rights reserved.Coll.HTT-bills.USRSMLkM =15 kRF=8-1 0 1 2.SML:ki=8%+(15%8%)bi.ki(%)Risk,bi6-47Copyright 2001 by Harcourt,Inc.All rights reserved.Calculate beta for a portfolio with 50%HT and 50%Collectionsbp
28、=Weighted average =0.5(bHT)+0.5(bColl)=0.5(1.29)+0.5(-0.86)=0.22.6-48Copyright 2001 by Harcourt,Inc.All rights reserved.The required return on the HT/Coll.portfolio is:kp =Weighted average k =0.5(17%)+0.5(2%)=9.5%.Or use SML:kp=kRF+(kM kRF)bp =8.0%+(15.0%8.0%)(0.22)=8.0%+7%(0.22)=9.5%.6-49Copyright
29、2001 by Harcourt,Inc.All rights reserved.If investors raise inflation expectations by 3%,what would happen to the SML?6-50Copyright 2001 by Harcourt,Inc.All rights reserved.SML1Original situationRequired Rate of Return k(%)SML200.5 1.01.5 Risk,bi181511 8New SMLD D I=3%6-51Copyright 2001 by Harcourt,
30、Inc.All rights reserved.If inflation did not changebut risk aversion increasedenough to cause the marketrisk premium to increase by3 percentage points,whatwould happen to the SML?6-52Copyright 2001 by Harcourt,Inc.All rights reserved.kM =18%kM =15%SML1Original situationRequired Rate of Return(%)SML2
31、After increasein risk aversionRisk,bi181581.0D D RPM=3%6-53Copyright 2001 by Harcourt,Inc.All rights reserved.Has the CAPM been verified through empirical tests?nNot completely.Those statistical tests have problems that make verification almost impossible.6-54Copyright 2001 by Harcourt,Inc.All right
32、s reserved.nInvestors seem to be concerned with both market risk and total risk.Therefore,the SML may not produce a correct estimate of ki:ki=kRF+(kM kRF)b+?6-55Copyright 2001 by Harcourt,Inc.All rights reserved.nAlso,CAPM/SML concepts are based on expectations,yet betas are calculated using historical data.A companys historical data may not reflect investors expectations about future riskiness.