1. The Capital Asset Pricing Model
Chapter 9
Bodi Kane Marcus Ch 5

2. Capital Asset Pricing Model (CAPM)
Irwin/McGraw-Hill
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
Irwin/McGraw-Hill
Assumptions
Individual investors are price takers
Single-period investment horizon
Investments are limited to traded financial assets
No taxes, and transaction costs

4. Irwin/McGraw-Hill
Assumptions (cont’d)
Information is costless and available to all investors
Investors are rational mean-variance optimizers
Homogeneous expectations

5. Resulting Equilibrium Conditions
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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’d)
Irwin/McGraw-Hill
Resulting Equilibrium Conditions (cont’d)
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  m Problem 9-7,8,9,12; p313
Irwin/McGraw-Hill
E(r)
E(rM) rf M
CML m 
Problem 9-7,8,9,12; p313

8. Slope and Market Risk Premium
Irwin/McGraw-Hill
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  M

9. Expected Return and Risk on Individual Securities
Irwin/McGraw-Hill
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 = 1.0 M Problem 9-6,10,11
Irwin/McGraw-Hill
E(r)
E(rM) rf
SML M ß
= 1.0
Problem 9-6,10,11

11. Bodi Kane Marcus Ch 5 6
E( rA )
<
E( rB ) A
> B
impossible

12. Bodi Kane Marcus Ch 5 10
E( rA )
<
E( rM ) A
> M
impossible

13. Bodi Kane Marcus Ch 5 11
E( rA )
<
E( rM ) A M
possible

14. SML Relationships = [COV(ri,rm)] / m2
Irwin/McGraw-Hill
SML Relationships
= [COV(ri,rm)] / m2
Slope SML = E(rm) - rf
= market risk premium
SML = rf + [E(rm) - rf]
Betam = [Cov (ri,rm)] / sm2
= sm2 / sm2 = 1

15. Sample Calculations for SML
Irwin/McGraw-Hill
Sample Calculations for SML
RPM=E(rm) - rf = .08 rf = .03
x = 1.25
E(rx) = (.08) = .13 or 13%
y = .6
e(ry) = (.08) = .078 or 7.8%

16. Graph of Sample Calculations
Irwin/McGraw-Hill
E(r)
Rx=13%
SML m ß
1.0
Rm=11%
Ry=7.8% 3% x
1.25 y .6
.08
Exercise

17. Disequilibrium Example
Irwin/McGraw-Hill
E(r)
15%
SML ß
1.0
Rm=11%
rf=3%
1.25

18. Disequilibrium Example
Irwin/McGraw-Hill
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

19. Black’s Zero Beta Model p.301
Irwin/McGraw-Hill
Black’s Zero Beta Model p.301
Absence of a risk-free asset
Combinations of portfolios on the efficient frontier are efficient
All frontier portfolios have companion portfolios that are uncorrelated
Returns on individual assets can be expressed as linear combinations of efficient portfolios

20. Black’s Zero Beta Model Formulation
Irwin/McGraw-Hill
Black’s Zero Beta Model Formulation

21. Efficient Portfolios and Zero Companions
Irwin/McGraw-Hill
Efficient Portfolios and Zero Companions Q P
Z(Q)
Z(P)
E[rz (Q)]
E[rz (P)]
E(r) s

22. Zero Beta Market Model CAPM with E(rz (m)) replacing rf
Irwin/McGraw-Hill
Zero Beta Market Model
CAPM with E(rz (m)) replacing rf

23. CAPM & Liquidity Liquidity Illiquidity Premium
Irwin/McGraw-Hill
CAPM & Liquidity
Liquidity
Illiquidity Premium
Research supports a premium for illiquidity
Amihud and Mendelson

24. CAPM with a Liquidity Premium
Irwin/McGraw-Hill
CAPM with a Liquidity Premium
f (ci) = liquidity premium for security i
f (ci) increases at a decreasing rate

25. Illiquidity and Average Returns
Irwin/McGraw-Hill
Illiquidity and Average Returns
Average monthly return(%)
Bid-ask spread (%)

26. Bodi Kane Marcus Ch 5
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