1. Bodie Kane Marcus Perrakis RyanINVESTMENTS, Fourth Canadian Edition Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 7-1 Chapter 7

2. Bodie Kane Marcus Perrakis RyanINVESTMENTS, Fourth Canadian Edition Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 7-2 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. Bodie Kane Marcus Perrakis RyanINVESTMENTS, Fourth Canadian Edition Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 7-3 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. Bodie Kane Marcus Perrakis RyanINVESTMENTS, Fourth Canadian Edition Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 7-4 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. Bodie Kane Marcus Perrakis RyanINVESTMENTS, Fourth Canadian Edition Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 7-5 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. Bodie Kane Marcus Perrakis RyanINVESTMENTS, Fourth Canadian Edition Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 7-6  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 Capital Asset Pricing Model (CAPM)

7. Bodie Kane Marcus Perrakis RyanINVESTMENTS, Fourth Canadian Edition Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 7-7  Individual investors are price takers  Single-period investment horizon  Investments are limited to traded financial assets  No taxes, and transaction costs Assumptions

8. Bodie Kane Marcus Perrakis RyanINVESTMENTS, Fourth Canadian Edition Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 7-8  Information is costless and available to all investors  Investors are rational mean-variance optimizers  There are homogeneous expectations Assumptions (cont’d)

9. Bodie Kane Marcus Perrakis RyanINVESTMENTS, Fourth Canadian Edition Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 7-9 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. Bodie Kane Marcus Perrakis RyanINVESTMENTS, Fourth Canadian Edition Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 7-10  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 Resulting Equilibrium Conditions

11. Bodie Kane Marcus Perrakis RyanINVESTMENTS, Fourth Canadian Edition Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 7-11  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’d)

12. Bodie Kane Marcus Perrakis RyanINVESTMENTS, Fourth Canadian Edition Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 7-12 Capital Market Line E(r) E(r M ) rfrf M CML mm 

13. Bodie Kane Marcus Perrakis RyanINVESTMENTS, Fourth Canadian Edition Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 7-13 M=The market portfolio r f =Risk free rate E(r M ) - r f =Market risk premium = Slope of the CML Slope and Market Risk Premium

14. Bodie Kane Marcus Perrakis RyanINVESTMENTS, Fourth Canadian Edition Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 7-14 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. Bodie Kane Marcus Perrakis RyanINVESTMENTS, Fourth Canadian Edition Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 7-15  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 Expected Return and Risk on Individual Securities

16. Bodie Kane Marcus Perrakis RyanINVESTMENTS, Fourth Canadian Edition Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 7-16 Security Market Line E(r) E(r M ) rfrf SML M ß ß= 1.0

17. Bodie Kane Marcus Perrakis RyanINVESTMENTS, Fourth Canadian Edition Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 7-17   = Cov(r i,r m ) /  m 2 Slope SML =E(r m ) - r f =market risk premium E(r) SML = r f + [E(r m ) - r f ] Beta M = Cov (r M,r M ) /   2 =  M 2 /  M 2 = 1 SML Relationships

18. Bodie Kane Marcus Perrakis RyanINVESTMENTS, Fourth Canadian Edition Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 7-18 E(r m ) - r f =.08r f =.03 a)  x = 1.25 E(r x ) =.03 + 1.25(.08) =.13 or 13% b  y =.6 E(r y ) =.03 +.6(.08) =.078 or 7.8% Sample Calculations for SML

19. Bodie Kane Marcus Perrakis RyanINVESTMENTS, Fourth Canadian Edition Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 7-19 Graph of Sample Calculations E(r) R x =13% SML m ß ß 1.0 R m =11% R y =7.8% 3% x ß 1.25 y ß.6.08

20. Bodie Kane Marcus Perrakis RyanINVESTMENTS, Fourth Canadian Edition Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 7-20 Disequilibrium Example E(r) 15% SML ß 1.0 R m =11% r f =3% 1.25

21. Bodie Kane Marcus Perrakis RyanINVESTMENTS, Fourth Canadian Edition Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 7-21  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 Disequilibrium Example

22. Bodie Kane Marcus Perrakis RyanINVESTMENTS, Fourth Canadian Edition Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 7-22 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. Bodie Kane Marcus Perrakis RyanINVESTMENTS, Fourth Canadian Edition Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 7-23 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. Bodie Kane Marcus Perrakis RyanINVESTMENTS, Fourth Canadian Edition Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 7-24 Black’s Zero Beta Model Formulation

25. Bodie Kane Marcus Perrakis RyanINVESTMENTS, Fourth Canadian Edition Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 7-25 Efficient Portfolios and Zero Companions Q P Z(Q) Z(P) E[r z (Q) ] E[r z (P) ] E(r) 

26. Bodie Kane Marcus Perrakis RyanINVESTMENTS, Fourth Canadian Edition Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 7-26 Zero Beta Market Model CAPM with E(r z (M) ) replacing r f

27. Bodie Kane Marcus Perrakis RyanINVESTMENTS, Fourth Canadian Edition Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 7-27 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. Bodie Kane Marcus Perrakis RyanINVESTMENTS, Fourth Canadian Edition Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 7-28 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. Bodie Kane Marcus Perrakis RyanINVESTMENTS, Fourth Canadian Edition Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 7-29 CAPM with a Liquidity Premium f (c i ) = liquidity premium for security i f (c i ) increases at a decreasing rate

30. Bodie Kane Marcus Perrakis RyanINVESTMENTS, Fourth Canadian Edition Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 7-30 Illiquidity and Average Returns Average monthly return (%) Bid-ask spread (%)