1. Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 1 Chapter 8 Capital Asset Pricing and Arbitrage Pricing Theory

2. Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 2 Capital Asset Pricing Model (CAPM) Equilibrium model that underlies all modern financial theory Derived using principles of diversification with simplified assumptions Markowitz, Sharpe, Lintner and Mossin are researchers credited with its development

3. Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 3 Assumptions Individual investors are price takers Single-period investment horizon Investments are limited to traded financial assets No taxes, and transaction costs

4. Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 4 Assumptions (cont.) Information is costless and available to all investors Investors are rational mean-variance optimizers Homogeneous expectations

5. Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 5 Resulting Equilibrium Conditions All investors will hold the same portfolio for risky assets – market portfolio Market portfolio contains all securities and the proportion of each security is its market value as a percentage of total market value

6. Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 6 Risk premium on the market depends on the average risk aversion of all market participants Risk premium on an individual security is a function of its covariance with the market Resulting Equilibrium Conditions (cont.)

7. Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 7 E(r) E(r M ) rfrfrfrf M CML mmmm Capital Market Line 

8. Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 8 M=Market portfolio r f =Risk free rate E(r M ) - r f =Market risk premium E(r M ) - r f =Market price of risk =Slope of the CAPM Slope and Market Risk Premium M 

9. Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 9 Expected Return and Risk on Individual Securities The risk premium on individual securities is a function of the individual security’s contribution to the risk of the market portfolio Individual security’s risk premium is a function of the covariance of returns with the assets that make up the market portfolio

10. Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 10 E(r) E(r M ) rfrfrfrf SML M ß ß = 1.0 Security Market Line

11. Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 11 SML Relationships  = [COV(r i,r m )] /  m 2 Slope SML =E(r m ) - r f =market risk premium SML = r f +  [E(r m ) - r f ]

12. Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 12 Sample Calculations for SML E(r m ) - r f =.08r f =.03  x = 1.25 E(r x ) =.03 + 1.25(.08) =.13 or 13%  y =.6 e(r y ) =.03 +.6(.08) =.078 or 7.8%

13. Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 13 E(r) R x =13% SML m m ß ß 1.0 R m =11% R y =7.8% 3% x x ß 1.25 y y ß.6.08 Graph of Sample Calculations

14. Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 14 E(r) 15% SML ß 1.0 R m =11% r f =3% 1.25 Disequilibrium Example

15. Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 15 Disequilibrium Example Suppose a security with a  of 1.25 is offering expected return of 15% According to SML, it should be 13% Underpriced: offering too high of a rate of return for its level of risk

16. Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 16 Security Characteristic Line Excess Returns (i) SCL.................................................................................................... Excess returns on market index R i =  i + ß i R m + e i

17. Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 17 Using the Text Example p. 245, Table 8.5: Jan.Feb...DecMean Std Dev 5.41-3.44..2.43-.604.977.24.93..3.901.753.32 Excess Mkt. Ret. Excess GM Ret.

18. Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 18 Estimated coefficient Std error of estimate Variance of residuals = 12.601 Std dev of residuals = 3.550 R-SQR = 0.575 ß ß -2.590(1.547)1.1357(0.309) r GM - r f = + ß(r m - r f ) Regression Results:  

19. Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 19 Arbitrage Pricing Theory Arbitrage - arises if an investor can construct a zero investment portfolio with a sure profit Since no investment is required, an investor can create large positions to secure large levels of profit In efficient markets, profitable arbitrage opportunities will quickly disappear

20. Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 20 Arbitrage Example from Text pp. 255- 257 Current ExpectedStandard Stock Price$ Return% Dev.% A 10 25.0 29.58 B 10 20.0 33.91 C 10 32.5 48.15 D 10 22.5 8.58

21. Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 21 Arbitrage Portfolio Mean Stan. Correlation ReturnDev. Of Returns Portfolio A,B,C25.836.400.94 D22.258.58

22. Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 22 Arbitrage Action and Returns E. Ret. St.Dev. * P * D Short 3 shares of D and buy 1 of A, B & C to form P You earn a higher rate on the investment than you pay on the short sale

23. Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 23 APT and CAPM Compared APT applies to well diversified portfolios and not necessarily to individual stocks With APT it is possible for some individual stocks to be mispriced - not lie on the SML APT is more general in that it gets to an expected return and beta relationship without the assumption of the market portfolio APT can be extended to multifactor models