1. 1 An Introduction to Asset Pricing Models – Chapter 8 Concerning: Reilly & Brown: Investment Analysis and Portfolio Management Dick Marcus 229-4103 marcus@uwm.edu

2. Slide 2 Generally, the higher the risk, the higher the return  But we want both high return and low risk To achieve this, we diversify over many assets and various asset classes  Stocks (both domestic and foreign)  Bonds (both domestic and foreign)

3. Slide 3 standard deviation as the measure of risk 100% Large Cap Value 100% Small Cap Growth Stocks Least Risk at 90% US Core Stocks & 10% Foreign Stocks*.13.10.08 RETURNS 100% Foreign Stocks *For illustration purposes. The risk-return trade-offs change over time. Risk - Return Tradeoffs: Stocks

4. Slide 4 standard deviation as the measure of risk 100% US Bonds 100% Foreign Bonds Least Risk at 70% US Bonds and 30% Foreign Bonds*.09.07.05 RETURNS *For illustration purposes. The risk-return trade-offs change over time. Risk - Return Tradeoffs: Bonds

5. Slide 5 standard deviation as the measure of risk.15.10.05 RETURNS US Stocks Only World Stocks Only EAFE (Europe, Australia, & the Far East) World Balanced EAFE Balanced US Balanced STOCKS ONLY STOCKS & BONDS Risk is reduced by using a combination of both stocks and bonds *For illustration purposes. The risk-return trade-offs change over time.

6. Slide 6 Markowitz portfolio model Requires extensive information:  We need variances, covariances, and weights for all the assets CAPM is more compact and efficient in data requirements: 1. We need betas 2. We need a risk free return 3. We need the market return Then we can estimate the rate of return and the standard deviation of the portfolio  P =   w i 2  I 2 +  w i w j Cov ij eqn 7.6 on page 219

7. Slide 7 E(R P ) = R F +  P (R M -R F ) Beta on a risk free asset is  F =0 Beta on the market is  M =1 Let w be the weight of money invested in the market and (1-w) in the risk free return The portfolio beta (  P ) will be a weighted average of 0 and 1, so the Beta of the Portfolio is also w.   P = (1-w)  F + w  M = (1-w)0 + w1 = w E(R P ) = (1-w)R F + w R M = R F +  P (R M -R F ) This is essentially Equation 8.6, page 248

8. Slide 8 Assumptions of Capital Market Theory 1. Investors seek to be on the efficient frontier 2. Borrow or lend at the risk-free rate 3. Homogeneous expectations 4. One-period horizon 5. Infinitely divisible investments 6. There are no taxes and no transaction costs 7. No inflation (or fully anticipated) 8. Capital markets are in equilibrium

9. Slide 9 Review of some statistic stuff pagers 241-242 There is zero covariance between a risk free asset and an asset Combining (1-w) of a risk free asset with w of a risky asset R i forms a portfolio  E(R P ) = (1-w)R F + w R i Standard deviation of this portfolio is: 1.  P = w  i 2. Because  P 2 = w 2  i 2 3. The square root of the equation in (2) is (1).

10. Slide 10 CML – The Capital Market Line Ex 8.2 on page 243 Can achieve M  When all money is invested in the market portfolio Can achieve R F  When all money is lent a the risk free rate Or anything along the CML  When levering the portfolio, we achieve more risk and more return on the CML PP E(R P ) RFRF CML M Efficient frontier borrowing lending

11. Slide 11 Diversification & Unsystematic Risk If total risk is 22%, and systematic risk is 18%, then 4% is unsystematic risk More securities, then total risk approaches market risk of about 17.8% Systematic Risk Number of Stocks in the Portfolio PP Unsystematic Risk.18.22

12. Slide 12 Optimal Portfolio Choice on the CML Indifference curves for a “good” and a “bad” Select the highest utility on the CML Can invest part in risk- free and part in the market at Point A PP E(R P ) RFRF CML M Efficient frontier A

13. Slide 13 The Separation Theorem The CML comes from the investment decisions of all investors The financing question is where to be on the CML Hence, the optimal investment decision is separate from the financing question.

14. Slide 14 Decompose Risk Components Each asset is a part of the market portfolio Market Model for finding beta is  R i = a i +  i R M +  i  Take the variance of both sides  Var(R i ) = Var(a i +  i R M +  i ) =  Var(R i ) = Var(  i R M ) + Var(  i ) =  Var(R i ) =  i 2  2 M +  2  i  Risk = systematic risk + unsystematic risk  Page 247

15. Slide 15 Security Market Line - SML The risk of an asset is its covariance with the market portfolio If little covariance, then less risk If a lot of covariance, then more risk Expected return Covariance RFRF SML 2M2M RMRM

16. Slide 16 SML – as Beta and Return Beta = Cov/Var So normalizing all by the variance of the market we have the usual SML Expected return Beta RFRF SML 1.0 RMRM Exhibit 8.6 page 249 E(R i ) = R F +  i (R M -R F ) or risk-free rate with a risk premium 0.0 C B A

17. Slide 17 Assets above the SML are expected to earn more than predicted by their risk  These are under-valued & are a buy such as point C Assets below the SML are expected to earn less than predicted by their risk  These are over-valued & are a sell such as point B Assets on the SML are expected to earn in line with their risk  Such as point A

18. Slide 18 The Characteristic Line Also called the “market model,” the regression of returns on market return is: R i =  i +  i R M +  i  Traditionally, this is 60 months of returns  Five years covers a business cycle, but not so long as to change the firm over-much. Suppose we use daily, weekly, or annual data?  Shorter time intervals tend to cause larger betas for big firms with weekly data and smaller betas for small firms with weekly data The market is usually the S&P 500 Composite Index, versus a global market return.

19. Slide 19 Do you borrow & lend at different rates? If you do, the rate of lending is often lower than borrowing. The slope of the CML varies from R F to M, than beyond M. PP E(R P ) RFRF CML F K Efficient frontier borrowing lending Exhibit 8.14 on page 257 RbRb

20. Slide 20 Zero-beta Model CAPM can be developed without a risk-free asset, with limited success. Instead, consider a zero-beta asset The return on the zero-beta asset substitutes for the risk-free one The market premium is the difference with the zero-beta asset E(R i ) = R z +  i (R M -R z )

21. Slide 21 CAPM with Transaction Costs Forming a market portfolio may be costly The likely result that the SML will be ‘thick’. Expected return Covariance RFRF SML 2M2M RMRM

22. Slide 22 Taxes! While many investments are tax-sheltered (IRS, Keogh, 401-k, 403-b, etc.) many assets suffer taxes This adjusts the rates of return to be after-tax rates of return The problem is that different people pay different taxes. In practice, finance theorists and practitioners tend to assume zero taxes for these reasons.

23. Slide 23 CAPM – Empirical Evidence OK in theory, but how does it work in practices. Questions: 1. Are betas stable, so that PAST betas describe risk for the future? 2. Do stocks with higher betas achieve higher returns? 1. Individual stock betas are volatile, but portfolio betas are more stable. Also, various published data vary on betas. Some use ‘adjustments’ to measured market betas for greater stability.

24. Slide 24 Is CAPM Useful? Given what we know of betas, the most positive results involve PORTFOLIO betas and return  Black, Jensen, & Scholes, 1972 show that higher beta portfolios hear higher returns in 1931 – 1957, but when looking at 1957 – 1965, they didn’t!  So, big beta stocks don’t always pay higher returns.

25. Slide 25 Other factors that seem to affect returns other than systematic risk 1. Skewness – return distributions aren’t normal, they are right-skewed. Low beta stocks do well 2. Size Effect – larger stocks seemed to have higher betas, but do less well The origin of the small firm effect, perhaps 3. P/E Effect – value stocks do well, if betas are smaller than they should be 4. Leverage – even after holding other factors constant, leverage is a significant variable in explaining cross-sectional returns

26. Slide 26 Fama & French JF 1992 Fama was famous in his support for CAPM But Fama & French showed how other factors other than beta mattered much more. Beta was insignificant in 1963-1990.  Size  Leverage  E/P ratio  Book-to-market equity (BE/ME) – Tobin’s Q

27. Slide 27 Fama-French techniques One variable at a time tests (Univariate tests):  Sort all stocks in sample by beta (or book-to-market ratio, or leverage, etc.)  Group stocks into deciles (10 groups)  See if the average ROR moves with beta (or book-to- market, etc.)  No clear pattern of beta & ROR Multivariate tests are shown on Exhibit 8.18.  ROR = a + bBeta +cln(ME) + dln(BE/ME) + etc.  “b” was insignificant, “c” was negative, “d” was positive

28. Slide 28 The Market Portfolio: R M Benchmark error – what if our tests of CAPM use the wrong market portfolio?  Then measures of performance will be incorrectly specified  A good example of this is Exhibit 8.21 on page 268  The actual portfolio is below the true SML, but will appear to have beaten the estimated one. Beta Expected Return TRUE SML True M Actual Portfolio Estimated SML Proxy M RF

29. Slide 29 Questions to consider… Page 272 (1) Why a straight line? Page 272 (4) What assets are in M? Page 273 (7) Std Dev of 4, 10, 20 stocks? Page 273 (13) Three criticisms of beta? Page 273 (14) Two portfolios of beta =1. Page 275 (24) What stocks should you pick according to Fama-French?

30. Slide 30 Problems to work… #2 p. 274. Find E(R U ) =.10+.85(.04)=.134  What is it if beta = 1? What if beta = 1.25? #3 p. 274, should you buy stock U?  ROR U = [24.75/22] – 1 =.125 which is less than that expected by the CAPM. #14b p. 276. Compute the alphas for X & Y   x =.12 - CAPM x =.12 – (.05 + 1.3(.10 -.05)) = +.005 CAPM x =.05 + 1.3(.10 -.05) =.115   Y =.09 - CAPM Y =.09 – (.05 +.7(.10 -.05)) = +.005 CAPM x =.05 +.7(.10 -.05) =.085 Both should be ABOVE the SML offering better return than expected.