Chapter 7

1. Chapter 7 The Capital Asset Pricing Model

2. Chapter Summary • Objective: To present the basic version of the model and its applicability. • Assumptions • Resulting Equilibrium Conditions • The Security Market Line (SML) • Black’s Zero Beta Model • CAPM and Liquidity

3. Demand for Stocks and Equilibrium Prices • Imagine a world where all investors face the same opportunity set • Each investor computes his/her optimal (tangency) portfolio – as in Chapter 6 • The demand of this investor for a particular firm’s shares comes from this tangency portfolio

4. Demand for Stocks and Equilibrium Prices (cont’d) • As the price of the shares falls, the demand for the shares increases • The supply of shares is vertical, fixed and independent of the share price • The CAPM shows the conditions that prevail when supply and demand are equal for all firms in investor’s opportunity set

5. Summary Reminder • Objective: To present the basic version of the model and its applicability. • Assumptions • Resulting Equilibrium Conditions • The Security Market Line (SML) • Black’s Zero Beta Model • CAPM and Liquidity

6. 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

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

8. Assumptions (cont’d) • Information is costless and available to all investors • Investors are rational mean-variance optimizers • There are homogeneous expectations

9. Summary Reminder • Objective: To present the basic version of the model and its applicability. • Assumptions • Resulting Equilibrium Conditions • The Security Market Line (SML) • Black’s Zero Beta Model • CAPM and Liquidity

10. Resulting Equilibrium Conditions • All investors will hold the same portfolio of 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 • The market portfolio is on the efficient frontier and, moreover, it is the tangency portfolio

11. 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

12. E(r) CML M E(rM) rf  m Capital Market Line

13. Slope and Market Risk Premium M = The market portfolio rf = Risk free rate E(rM) - rf = Market risk premium = Slope of the CML

14. Summary Reminder • Objective: To present the basic version of the model and its applicability. • Assumptions • Resulting Equilibrium Conditions • The Security Market Line (SML) • Black’s Zero Beta Model • CAPM and Liquidity

15. 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

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

17. SML Relationships  = Cov(ri,rm) / m2 Slope SML = E(rm) - rf = market risk premium E(r)SML = rf + [E(rm) - rf] BetaM = Cov (rM,rM) / sM2 = sM2 / sM2 = 1

18. Sample Calculations for SML E(rm) - rf = .08 rf = .03 a) x = 1.25 E(rx) = .03 + 1.25(.08) = .13 or 13% b) y = .6 E(ry) = .03 + .6(.08) = .078 or 7.8%

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

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

21. Disequilibrium Example • Suppose a security with a  of 1.25 is offering expected return of 15% • According to SML, it should be 13% • Under-priced: offering too high of a rate of return for its level of risk

22. Summary Reminder • Objective: To present the basic version of the model and its applicability. • Assumptions • Resulting Equilibrium Conditions • The Security Market Line (SML) • Black’s Zero Beta Model • CAPM and Liquidity

23. Black’s Zero Beta Model • 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

24. Black’s Zero Beta Model Formulation

25. E(r) Q P E[rz (Q)] Z(Q) Z(P) E[rz (P)] s Efficient Portfolios and Zero Companions

26. Zero Beta Market Model CAPM with E(rz (M)) replacing rf

27. Summary Reminder • Objective: To present the basic version of the model and its applicability. • Assumptions • Resulting Equilibrium Conditions • The Security Market Line (SML) • Black’s Zero Beta Model • CAPM and Liquidity

28. CAPM & Liquidity • Liquidity – cost or ease with which an asset can be sold • Illiquidity Premium • Research supports a premium for illiquidity • Amihud and Mendelson

29. CAPM with a Liquidity Premium f (ci) = liquidity premium for security i f (ci) increases at a decreasing rate

30. Average monthly return (%) Bid-ask spread (%) Illiquidity and Average Returns