1. Capital Asset Pricing and Arbitrage Pricing Theory
Chapter 8
Capital Asset Pricing and Arbitrage Pricing Theory

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. Assumptions Individual investors are price takers
Single-period investment horizon
Investments are limited to traded financial assets
No taxes, and transaction costs

4. Assumptions (cont.)
Information is costless and available to all investors
Investors are rational mean-variance optimizers
Homogeneous expectations

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. Resulting Equilibrium Conditions (cont.)
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

7. Capital Market Line
E(r)
CML M
E(rM) rf s sm

8. Slope and Market Risk Premium
M = Market portfolio rf = Risk free rate E(rM) - rf = Market risk premium E(rM) - rf = Market price of risk
= Slope of the CAPM s M

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. Security Market Line
E(r)
SML
E(rM) rf ß ß
= 1.0 M

11. SML Relationships b = [COV(ri,rm)] / sm2 Slope SML = E(rm) - rf
= market risk premium
SML = rf + b[E(rm) - rf]

12. Sample Calculations for SML
E(rm) - rf = .08 rf = .03
bx = 1.25
E(rx) = (.08) = .13 or 13%
by = .6
e(ry) = (.08) = .078 or 7.8%

13. Graph of Sample Calculations
E(r)
SML
Rx=13%
.08
Rm=11%
Ry=7.8% 3% ß .6
1.0
1.25 ß ß ß y m x

14. Disequilibrium Example
E(r)
SML
15%
Rm=11%
rf=3% ß
1.0
1.25

15. Disequilibrium Example
Suppose a security with a b 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. Security Characteristic Line
Excess Returns (i)
SCL . . . . . . . . . . . . . . . . . . . . . . . . . . .
Excess returns
on market index . . . . . . . . . . . . . . . . . . . . . . .
Ri = a i + ßiRm + ei

17. Using the Text Example p. 245, Table 8.5:
Excess
GM Ret.
Excess
Mkt. Ret.
Jan.
Feb. .
Dec
Mean
Std Dev
5.41
-3.44 .
2.43
-.60
4.97
7.24
.93 .
3.90
1.75
3.32

18. a a Regression Results: rGM - rf = + ß(rm - rf) ß
Estimated coefficient
Std error of estimate
Variance of residuals =
Std dev of residuals = 3.550
R-SQR = 0.575
-2.590
(1.547)
1.1357
(0.309)

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. Arbitrage Example from Text pp. 255-257
Current Expected Standard
Stock Price$ Return% Dev.% A B C D

21. Arbitrage Portfolio Mean Stan. Correlation Return Dev. Of Returns
A,B,C D

22. Arbitrage Action and Returns
E. Ret.
* P
* D
St.Dev.
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. 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