第十章收益和风险CAPM(共47页)(英文).ppt

1、McGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved.10-0Chapter Outline10.1 Individual Securities10.2 Expected Return, Variance, and Covariance10.3 The Return and Risk for Portfolios10.4 The Efficient Set for Two Assets10.5 The Efficient Set for Many Securities10.6

2、 Diversification: An Example10.7 Riskless Borrowing and Lending10.8 Market Equilibrium10.9 Relationship between Risk and Expected Return (CAPM)10.10 Summary and ConclusionsMcGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved.10-110.1 Individual Securities The charac

3、teristics of individual securities that are of interest are the: Expected Return Variance and Standard Deviation Covariance and CorrelationMcGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved.10-210.2 Expected Return, Variance, and Covariance Consider the following

4、two risky asset world. There is a 1/3 chance of each state of the economy and the only assets are a stock fund and a bond fund. Rate of ReturnScenarioProbabilityStock fundBond fundRecession33.3%-7%17%Normal 33.3%12%7%Boom33.3%28%-3%McGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies, Inc. A

5、ll rights reserved.10-310.2 Expected Return, Variance, and CovarianceStock fundBond FundRate of Squared Rate of Squared Scenario Return Deviation Return Deviation Recession-7%3.24%17%1.00%Normal 12%0.01%7%0.00%Boom28%2.89%-3%1.00%Expected return11.00%7.00%Variance0.02050.0067Standard Deviation14.3%8

6、.2%McGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved.10-4Stock fundBond FundRate of Squared Rate of Squared Scenario Return Deviation Return Deviation Recession-7%3.24%17%1.00%Normal 12%0.01%7%0.00%Boom28%2.89%-3%1.00%Expected return11.00%7.00%Variance0.02050.006

7、7Standard Deviation14.3%8.2%10.2 Expected Return, Variance, and Covariance%11)(%)28(31%)12(31%)7(31)(SSrErEMcGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved.10-5Stock fundBond FundRate of Squared Rate of Squared Scenario Return Deviation Return Deviation Recessio

8、n-7%3.24%17%1.00%Normal 12%0.01%7%0.00%Boom28%2.89%-3%1.00%Expected return11.00%7.00%Variance0.02050.0067Standard Deviation14.3%8.2%10.2 Expected Return, Variance, and Covariance%7)(%)3(31%)7(31%)17(31)(BBrErEMcGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved.10-6

9、Stock fundBond FundRate of Squared Rate of Squared Scenario Return Deviation Return Deviation Recession-7%3.24%17%1.00%Normal 12%0.01%7%0.00%Boom28%2.89%-3%1.00%Expected return11.00%7.00%Variance0.02050.0067Standard Deviation14.3%8.2%10.2 Expected Return, Variance, and Covariance%24. 3%)7%11(2McGraw

10、-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved.10-7Stock fundBond FundRate of Squared Rate of Squared Scenario Return Deviation Return Deviation Recession-7%3.24%17%1.00%Normal 12%0.01%7%0.00%Boom28%2.89%-3%1.00%Expected return11.00%7.00%Variance0.02050.0067Standard

11、 Deviation14.3%8.2%10.2 Expected Return, Variance, and Covariance%01.%)12%11(2McGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved.10-8Stock fundBond FundRate of Squared Rate of Squared Scenario Return Deviation Return Deviation Recession-7%3.24%17%1.00%Normal 12%0.

12、01%7%0.00%Boom28%2.89%-3%1.00%Expected return11.00%7.00%Variance0.02050.0067Standard Deviation14.3%8.2%10.2 Expected Return, Variance, and Covariance%89. 2%)28%11(2McGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved.10-9Stock fundBond FundRate of Squared Rate of Sq

13、uared Scenario Return Deviation Return Deviation Recession-7%3.24%17%1.00%Normal 12%0.01%7%0.00%Boom28%2.89%-3%1.00%Expected return11.00%7.00%Variance0.02050.0067Standard Deviation14.3%8.2%10.2 Expected Return, Variance, and Covariance%)89. 2%01. 0%24. 3(31%05. 2McGraw-Hill/IrwinCopyright 2002 by Th

14、e McGraw-Hill Companies, Inc. All rights reserved.10-10Stock fundBond FundRate of Squared Rate of Squared Scenario Return Deviation Return Deviation Recession-7%3.24%17%1.00%Normal 12%0.01%7%0.00%Boom28%2.89%-3%1.00%Expected return11.00%7.00%Variance0.02050.0067Standard Deviation14.3%8.2%10.2 Expect

15、ed Return, Variance, and Covariance0205. 0%3 .14McGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved.10-11Stock fundBond FundRate of Squared Rate of Squared Scenario Return Deviation Return Deviation Recession-7%3.24%17%1.00%Normal 12%0.01%7%0.00%Boom28%2.89%-3%1.00

16、%Expected return11.00%7.00%Variance0.02050.0067Standard Deviation14.3%8.2%10.3 The Return and Risk for PortfoliosNote that stocks have a higher expected return than bonds and higher risk. Let us turn now to the risk-return tradeoff of a portfolio that is 50% invested in bonds and 50% invested in sto

17、cks.McGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved.10-1210.3 The Return and Risk for PortfoliosRate of ReturnScenarioStock fundBond fundPortfoliosquared deviationRecession-7%17%5.0%0.160%Normal 12%7%9.5%0.003%Boom28%-3%12.5%0.123%Expected return11.00%7.00%9.0%

18、Variance0.02050.00670.0010Standard Deviation14.31%8.16%3.08%The rate of return on the portfolio is a weighted average of the returns on the stocks and bonds in the portfolio: SSBBPrwrwr%)17(%50%)7(%50%5McGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved.10-13Rate o

19、f ReturnScenarioStock fundBond fundPortfoliosquared deviationRecession-7%17%5.0%0.160%Normal 12%7%9.5%0.003%Boom28%-3%12.5%0.123%Expected return11.00%7.00%9.0%Variance0.02050.00670.0010Standard Deviation14.31%8.16%3.08%10.3 The Return and Risk for PortfoliosThe rate of return on the portfolio is a w

20、eighted average of the returns on the stocks and bonds in the portfolio: %)7(%50%)12(%50%5 . 9SSBBPrwrwrMcGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved.10-14Rate of ReturnScenarioStock fundBond fundPortfoliosquared deviationRecession-7%17%5.0%0.160%Normal 12%7%

21、9.5%0.003%Boom28%-3%12.5%0.123%Expected return11.00%7.00%9.0%Variance0.02050.00670.0010Standard Deviation14.31%8.16%3.08%10.3 The Return and Risk for PortfoliosThe rate of return on the portfolio is a weighted average of the returns on the stocks and bonds in the portfolio: %)3(%50%)28(%50%5 .12SSBB

22、PrwrwrMcGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved.10-15Rate of ReturnScenarioStock fundBond fundPortfoliosquared deviationRecession-7%17%5.0%0.160%Normal 12%7%9.5%0.003%Boom28%-3%12.5%0.123%Expected return11.00%7.00%9.0%Variance0.02050.00670.0010Standard De

23、viation14.31%8.16%3.08%10.3 The Return and Risk for PortfoliosThe expected rate of return on the portfolio is a weighted average of the expected returns on the securities in the portfolio. %)7(%50%)11(%50%9)()()(SSBBPrEwrEwrEMcGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies, Inc. All righ

24、ts reserved.10-16Rate of ReturnScenarioStock fundBond fundPortfoliosquared deviationRecession-7%17%5.0%0.160%Normal 12%7%9.5%0.003%Boom28%-3%12.5%0.123%Expected return11.00%7.00%9.0%Variance0.02050.00670.0010Standard Deviation14.31%8.16%3.08%10.3 The Return and Risk for PortfoliosThe variance of the

25、 rate of return on the two risky assets portfolio is BSSSBB2SS2BB2P)(w2(w)(w)(wwhere BS is the correlation coefficient between the returns on the stock and bond funds.McGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved.10-17Rate of ReturnScenarioStock fundBond fund

26、Portfoliosquared deviationRecession-7%17%5.0%0.160%Normal 12%7%9.5%0.003%Boom28%-3%12.5%0.123%Expected return11.00%7.00%9.0%Variance0.02050.00670.0010Standard Deviation14.31%8.16%3.08%10.3 The Return and Risk for PortfoliosObserve the decrease in risk that diversification offers.An equally weighted

27、portfolio (50% in stocks and 50% in bonds) has less risk than stocks or bonds held in isolation.McGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved.10-18Portfolo Risk and Return Combinations5.0%6.0%7.0%8.0%9.0%10.0%11.0%12.0%0.0%2.0%4.0%6.0%8.0%10.0% 12.0% 14.0% 16

28、.0%Portfolio Risk (standard deviation)Portfolio Return% in stocks Risk Return0%8.2%7.0%5%7.0%7.2%10%5.9%7.4%15%4.8%7.6%20%3.7%7.8%25%2.6%8.0%30%1.4%8.2%35%0.4%8.4%40%0.9%8.6%45%2.0%8.8%50.00%3.08%9.00%55%4.2%9.2%60%5.3%9.4%65%6.4%9.6%70%7.6%9.8%75%8.7%10.0%80%9.8%10.2%85%10.9%10.4%90%12.1%10.6%95%13

29、.2%10.8%100%14.3%11.0%10.4 The Efficient Set for Two AssetsWe can consider other portfolio weights besides 50% in stocks and 50% in bonds 100% bonds100% stocksMcGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved.10-19Portfolo Risk and Return Combinations5.0%6.0%7.0%

30、8.0%9.0%10.0%11.0%12.0%0.0%2.0%4.0%6.0%8.0%10.0% 12.0% 14.0% 16.0%Portfolio Risk (standard deviation)Portfolio Return10.4 The Efficient Set for Two AssetsWe can consider other portfolio weights besides 50% in stocks and 50% in bonds 100% bonds100% stocks% in stocks Risk Return0%8.2%7.0%5%7.0%7.2%10%

31、5.9%7.4%15%4.8%7.6%20%3.7%7.8%25%2.6%8.0%30%1.4%8.2%35%0.4%8.4%40%0.9%8.6%45%2.0%8.8%50%3.1%9.0%55%4.2%9.2%60%5.3%9.4%65%6.4%9.6%70%7.6%9.8%75%8.7%10.0%80%9.8%10.2%85%10.9%10.4%90%12.1%10.6%95%13.2%10.8%100%14.3%11.0% in stocks Risk Return0%8.2%7.0%5%7.0%7.2%10%5.9%7.4%15%4.8%7.6%20%3.7%7.8%25%2.6%8

32、.0%30%1.4%8.2%35%0.4%8.4%40%0.9%8.6%45%2.0%8.8%50%3.1%9.0%55%4.2%9.2%60%5.3%9.4%65%6.4%9.6%70%7.6%9.8%75%8.7%10.0%80%9.8%10.2%85%10.9%10.4%90%12.1%10.6%95%13.2%10.8%100%14.3%11.0% in stocks Risk Return0%8.2%7.0%5%7.0%7.2%10%5.9%7.4%15%4.8%7.6%20%3.7%7.8%25%2.6%8.0%30%1.4%8.2%35%0.4%8.4%40%0.9%8.6%45

33、%2.0%8.8%50%3.1%9.0%55%4.2%9.2%60%5.3%9.4%65%6.4%9.6%70%7.6%9.8%75%8.7%10.0%80%9.8%10.2%85%10.9%10.4%90%12.1%10.6%95%13.2%10.8%100%14.3%11.0% in stocks Risk Return0%8.2%7.0%5%7.0%7.2%10%5.9%7.4%15%4.8%7.6%20%3.7%7.8%25%2.6%8.0%30%1.4%8.2%35%0.4%8.4%40%0.9%8.6%45%2.0%8.8%50%3.1%9.0%55%4.2%9.2%60%5.3%

34、9.4%65%6.4%9.6%70%7.6%9.8%75%8.7%10.0%80%9.8%10.2%85%10.9%10.4%90%12.1%10.6%95%13.2%10.8%100%14.3%11.0% in stocks Risk Return0%8.2%7.0%5%7.0%7.2%10%5.9%7.4%15%4.8%7.6%20%3.7%7.8%25%2.6%8.0%30%1.4%8.2%35%0.4%8.4%40%0.9%8.6%45%2.0%8.8%50%3.1%9.0%55%4.2%9.2%60%5.3%9.4%65%6.4%9.6%70%7.6%9.8%75%8.7%10.0%

35、80%9.8%10.2%85%10.9%10.4%90%12.1%10.6%95%13.2%10.8%100%14.3%11.0% in stocks Risk Return0%8.2%7.0%5%7.0%7.2%10%5.9%7.4%15%4.8%7.6%20%3.7%7.8%25%2.6%8.0%30%1.4%8.2%35%0.4%8.4%40%0.9%8.6%45%2.0%8.8%50%3.1%9.0%55%4.2%9.2%60%5.3%9.4%65%6.4%9.6%70%7.6%9.8%75%8.7%10.0%80%9.8%10.2%85%10.9%10.4%90%12.1%10.6%

36、95%13.2%10.8%100%14.3%11.0% in stocks Risk Return0%8.2%7.0%5%7.0%7.2%10%5.9%7.4%15%4.8%7.6%20%3.7%7.8%25%2.6%8.0%30%1.4%8.2%35%0.4%8.4%40%0.9%8.6%45%2.0%8.8%50%3.1%9.0%55%4.2%9.2%60%5.3%9.4%65%6.4%9.6%70%7.6%9.8%75%8.7%10.0%80%9.8%10.2%85%10.9%10.4%90%12.1%10.6%95%13.2%10.8%100%14.3%11.0% in stocks

37、Risk Return0%8.2%7.0%5%7.0%7.2%10%5.9%7.4%15%4.8%7.6%20%3.7%7.8%25%2.6%8.0%30%1.4%8.2%35%0.4%8.4%40%0.9%8.6%45%2.0%8.8%50%3.1%9.0%55%4.2%9.2%60%5.3%9.4%65%6.4%9.6%70%7.6%9.8%75%8.7%10.0%80%9.8%10.2%85%10.9%10.4%90%12.1%10.6%95%13.2%10.8%100%14.3%11.0% in stocks Risk Return0%8.2%7.0%5%7.0%7.2%10%5.9%

38、7.4%15%4.8%7.6%20%3.7%7.8%25%2.6%8.0%30%1.4%8.2%35%0.4%8.4%40%0.9%8.6%45%2.0%8.8%50%3.1%9.0%55%4.2%9.2%60%5.3%9.4%65%6.4%9.6%70%7.6%9.8%75%8.7%10.0%80%9.8%10.2%85%10.9%10.4%90%12.1%10.6%95%13.2%10.8%100%14.3%11.0% in stocks Risk Return0%8.2%7.0%5%7.0%7.2%10%5.9%7.4%15%4.8%7.6%20%3.7%7.8%25%2.6%8.0%3

39、0%1.4%8.2%35%0.4%8.4%40%0.9%8.6%45%2.0%8.8%50%3.1%9.0%55%4.2%9.2%60%5.3%9.4%65%6.4%9.6%70%7.6%9.8%75%8.7%10.0%80%9.8%10.2%85%10.9%10.4%90%12.1%10.6%95%13.2%10.8%100%14.3%11.0% in stocks Risk Return0%8.2%7.0%5%7.0%7.2%10%5.9%7.4%15%4.8%7.6%20%3.7%7.8%25%2.6%8.0%30%1.4%8.2%35%0.4%8.4%40%0.9%8.6%45%2.0

40、%8.8%50%3.1%9.0%55%4.2%9.2%60%5.3%9.4%65%6.4%9.6%70%7.6%9.8%75%8.7%10.0%80%9.8%10.2%85%10.9%10.4%90%12.1%10.6%95%13.2%10.8%100%14.3%11.0% in stocks Risk Return0%8.2%7.0%5%7.0%7.2%10%5.9%7.4%15%4.8%7.6%20%3.7%7.8%25%2.6%8.0%30%1.4%8.2%35%0.4%8.4%40%0.9%8.6%45%2.0%8.8%50%3.1%9.0%55%4.2%9.2%60%5.3%9.4%

41、65%6.4%9.6%70%7.6%9.8%75%8.7%10.0%80%9.8%10.2%85%10.9%10.4%90%12.1%10.6%95%13.2%10.8%100%14.3%11.0% in stocks Risk Return0%8.2%7.0%5%7.0%7.2%10%5.9%7.4%15%4.8%7.6%20%3.7%7.8%25%2.6%8.0%30%1.4%8.2%35%0.4%8.4%40%0.9%8.6%45%2.0%8.8%50%3.1%9.0%55%4.2%9.2%60%5.3%9.4%65%6.4%9.6%70%7.6%9.8%75%8.7%10.0%80%9

42、.8%10.2%85%10.9%10.4%90%12.1%10.6%95%13.2%10.8%100%14.3%11.0% in stocks Risk Return0%8.2%7.0%5%7.0%7.2%10%5.9%7.4%15%4.8%7.6%20%3.7%7.8%25%2.6%8.0%30%1.4%8.2%35%0.4%8.4%40%0.9%8.6%45%2.0%8.8%50%3.1%9.0%55%4.2%9.2%60%5.3%9.4%65%6.4%9.6%70%7.6%9.8%75%8.7%10.0%80%9.8%10.2%85%10.9%10.4%90%12.1%10.6%95%1

43、3.2%10.8%100%14.3%11.0% in stocks Risk Return0%8.2%7.0%5%7.0%7.2%10%5.9%7.4%15%4.8%7.6%20%3.7%7.8%25%2.6%8.0%30%1.4%8.2%35%0.4%8.4%40%0.9%8.6%45%2.0%8.8%50%3.1%9.0%55%4.2%9.2%60%5.3%9.4%65%6.4%9.6%70%7.6%9.8%75%8.7%10.0%80%9.8%10.2%85%10.9%10.4%90%12.1%10.6%95%13.2%10.8%100%14.3%11.0% in stocks Risk

44、 Return0%8.2%7.0%5%7.0%7.2%10%5.9%7.4%15%4.8%7.6%20%3.7%7.8%25%2.6%8.0%30%1.4%8.2%35%0.4%8.4%40%0.9%8.6%45%2.0%8.8%50%3.1%9.0%55%4.2%9.2%60%5.3%9.4%65%6.4%9.6%70%7.6%9.8%75%8.7%10.0%80%9.8%10.2%85%10.9%10.4%90%12.1%10.6%95%13.2%10.8%100%14.3%11.0% in stocks Risk Return0%8.2%7.0%5%7.0%7.2%10%5.9%7.4%

45、15%4.8%7.6%20%3.7%7.8%25%2.6%8.0%30%1.4%8.2%35%0.4%8.4%40%0.9%8.6%45%2.0%8.8%50%3.1%9.0%55%4.2%9.2%60%5.3%9.4%65%6.4%9.6%70%7.6%9.8%75%8.7%10.0%80%9.8%10.2%85%10.9%10.4%90%12.1%10.6%95%13.2%10.8%100%14.3%11.0% in stocks Risk Return0%8.2%7.0%5%7.0%7.2%10%5.9%7.4%15%4.8%7.6%20%3.7%7.8%25%2.6%8.0%30%1.

46、4%8.2%35%0.4%8.4%40%0.9%8.6%45%2.0%8.8%50%3.1%9.0%55%4.2%9.2%60%5.3%9.4%65%6.4%9.6%70%7.6%9.8%75%8.7%10.0%80%9.8%10.2%85%10.9%10.4%90%12.1%10.6%95%13.2%10.8%100%14.3%11.0% in stocks Risk Return0%8.2%7.0%5%7.0%7.2%10%5.9%7.4%15%4.8%7.6%20%3.7%7.8%25%2.6%8.0%30%1.4%8.2%35%0.4%8.4%40%0.9%8.6%45%2.0%8.8

47、%50%3.1%9.0%55%4.2%9.2%60%5.3%9.4%65%6.4%9.6%70%7.6%9.8%75%8.7%10.0%80%9.8%10.2%85%10.9%10.4%90%12.1%10.6%95%13.2%10.8%100%14.3%11.0% in stocks Risk Return0%8.2%7.0%5%7.0%7.2%10%5.9%7.4%15%4.8%7.6%20%3.7%7.8%25%2.6%8.0%30%1.4%8.2%35%0.4%8.4%40%0.9%8.6%45%2.0%8.8%50%3.1%9.0%55%4.2%9.2%60%5.3%9.4%65%6

48、.4%9.6%70%7.6%9.8%75%8.7%10.0%80%9.8%10.2%85%10.9%10.4%90%12.1%10.6%95%13.2%10.8%100%14.3%11.0% in stocks Risk Return0%8.2%7.0%5%7.0%7.2%10%5.9%7.4%15%4.8%7.6%20%3.7%7.8%25%2.6%8.0%30%1.4%8.2%35%0.4%8.4%40%0.9%8.6%45%2.0%8.8%50%3.1%9.0%55%4.2%9.2%60%5.3%9.4%65%6.4%9.6%70%7.6%9.8%75%8.7%10.0%80%9.8%1

49、0.2%85%10.9%10.4%90%12.1%10.6%95%13.2%10.8%100%14.3%11.0%McGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved.10-20Portfolo Risk and Return Combinations5.0%6.0%7.0%8.0%9.0%10.0%11.0%12.0%0.0%2.0%4.0%6.0%8.0%10.0% 12.0% 14.0% 16.0%Portfolio Risk (standard deviation)P

50、ortfolio Return% in stocks Risk Return0%8.2%7.0%5%7.0%7.2%10%5.9%7.4%15%4.8%7.6%20%3.7%7.8%25%2.6%8.0%30%1.4%8.2%35%0.4%8.4%40%0.9%8.6%45%2.0%8.8%50%3.1%9.0%55%4.2%9.2%60%5.3%9.4%65%6.4%9.6%70%7.6%9.8%75%8.7%10.0%80%9.8%10.2%85%10.9%10.4%90%12.1%10.6%95%13.2%10.8%100%14.3%11.0%10.4 The Efficient Set

51、 for Two Assets100% stocks100% bondsNote that some portfolios are “better” than others. They have higher returns for the same level of risk or less. These compromise the efficient frontier.McGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved.10-21Two-Security Portfo

52、lios with Various Correlations 100% bondsreturn 100% stocks = 0.2 = 1.0 = -1.0McGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved.10-22Portfolio Risk/Return Two Securities: Correlation Effects Relationship depends on correlation coefficient -1.0 +1.0 The smaller th

53、e correlation, the greater the risk reduction potential If = +1.0, no risk reduction is possibleMcGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved.10-23Portfolio Risk as a Function of the Number of Stocks in the PortfolioNondiversifiable risk; Systematic Risk; Mar

54、ket RiskDiversifiable Risk; Nonsystematic Risk; Firm Specific Risk; Unique Riskn In a large portfolio the variance terms are effectively diversified away, but the covariance terms are not. Thus diversification can eliminate some, but not all of the risk of individual securities.Portfolio riskMcGraw-

55、Hill/IrwinCopyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved.10-2410.5 The Efficient Set for Many SecuritiesConsider a world with many risky assets; we can still identify the opportunity set of risk-return combinations of various portfolios.return PIndividual AssetsMcGraw-Hill/Irw

56、inCopyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved.10-2510.5 The Efficient Set for Many SecuritiesGiven the opportunity set we can identify the minimum variance portfolio.return Pminimum variance portfolioIndividual AssetsMcGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Compan

57、ies, Inc. All rights reserved.10-2610.5 The Efficient Set for Many SecuritiesThe section of the opportunity set above the minimum variance portfolio is the efficient frontier.return Pminimum variance portfolioefficient frontierIndividual AssetsMcGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Compa

58、nies, Inc. All rights reserved.10-27Optimal Risky Portfolio with a Risk-Free Asset In addition to stocks and bonds, consider a world that also has risk-free securities like T-bills100% bonds100% stocksrfreturn McGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved.10-

59、2810.7 Riskless Borrowing and LendingNow investors can allocate their money across the T-bills and a balanced mutual fund100% bonds100% stocksrfreturn Balanced fundCMLMcGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved.10-2910.7 Riskless Borrowing and LendingWith a

60、 risk-free asset available and the efficient frontier identified, we choose the capital allocation line with the steepest slope return Pefficient frontierrfCMLMcGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved.10-3010.8 Market EquilibriumWith the capital allocatio