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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
2、 negative 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
3、 Total Returns,1926-1998AverageStandardReturnDeviationDistributionSmall-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 4.50 17.4%0 13.2%0 6.1%0 5.7%0 5.5%0 3.8
4、%0 3.2%6 - 5Copyright 2001 by Harcourt, Inc.All rights reserved.Investment 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
5、-20.030.0 43.01.06 - 6Copyright 2001 by Harcourt, Inc.All rights reserved.Why 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
6、 still exposed to the risk of inflation.However, not much unexpected inflation is likely 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
7、 correlation. This is typical.nColl: Is countercyclical of the economy, and has a negative correlation. This is unusual.6 - 9Copyright 2001 by Harcourt, Inc.All rights reserved.Calculate the expected rate of return on each alternative:.Pk = kn1=iiik = expected rate of return.kHT = (-22%)0.1 + (-2%)0
8、.20 + (20%)0.40 + (35%)0.20 + (50%)0.1 = 17.4%.6 - 10Copyright 2001 by Harcourt, Inc.All rights reserved.kHT17.4%Market15.0USR13.8T-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 alt
9、ernative? = Standard deviation. = = =Variance2 .P)kk(n1ii2i 6 - 12Copyright 2001 by Harcourt, Inc.All rights reserved. T-bills = 0.0%. HT = 20.0%. Coll= 13.4%. USR= 18.8%. M= 15.3%.1/2 T-bills= .P)kk(n1ii2i (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 20
10、01 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.nThe larger the i , the lower the probability that actual returns will be close to the expected
11、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 - 16Copyright 2001 by Harcourt, Inc.All rights reserved.Coefficient of Variation (CV)Sta
12、ndardized 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.= CVA CVB. k6 - 18Copyright 2001 by Harcourt, Inc.All rights reserved
13、.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%) = 9.6%.kp is between kHT and kCOLL.kp = S S wiki.
14、 .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 20.0 0.0 10.0Above avg. 0
15、.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
16、 lower 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 corr
17、elated. rk,m 0.65.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
18、 - 25Copyright 2001 by Harcourt, 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 o
19、f an average 1-stockportfolio as more randomlyselected 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 - 28Copyri
20、ght 2001 by Harcourt, Inc.All rights reserved.# 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 slow
21、ly after about 10 stocks are included, and after 40 stocks, 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 elimi
22、nated by diversification, and is measured by beta.Firm-specific risk 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 risk
23、iness of individual stocks (35% vs. 20%).6 - 32Copyright 2001 by Harcourt, Inc.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 rig
24、hts reserved.nNO!nStand-alone risk as measured by a stocks or CV is not important to 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
25、return, for a given security. Therefore, no compensation can be earned for the additional risk 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
26、if the stock is held in a well-diversified portfolio.6 - 36Copyright 2001 by Harcourt, Inc.All rights 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
27、- 37Copyright 2001 by Harcourt, Inc.All rights reserved.YearkM ki 115% 18% 2 -5-10 312 16.ki _kM_-505101520201510 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 ris
28、kier 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. 1.7 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% + (1
29、5% 8%) bi .ki (%)Risk, bi6 - 47Copyright 2001 by Harcourt, Inc.All rights reserved.Calculate beta for a portfolio with 50% HT and 50% Collectionsbp= 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
30、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 2001 by Harcourt, Inc.All rights reserved.If investors raise inflation expectations by 3%, what would happen to the S
31、ML?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, Inc.All rights reserved.If inflation did not changebut risk aversion increasedenough to cause the marketr
32、isk 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 (%)SML2After increasein risk aversionRisk, bi181581.0D D RPM = 3%6 - 53Copyright 2001 by Harcourt, Inc.Al
33、l 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 rights reserved.nInvestors seem to be concerned with both market risk and total risk. Therefo
34、re, 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.