CHAPTER 9

1. CHAPTER 9 The Capital Asset Pricing Model

2. It is the 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) Bahattin Buyuksahin, JHU, Investment

3. Individual investors are price takers Single-period investment horizon Investments are limited to traded financial assets There are homogeneous expectations Assumptions: Investors Bahattin Buyuksahin, JHU, Investment

4. Information is costless and available to all investors No taxes and transaction costs Risk-free rate available to all Investors are rational mean-variance optimizers Assumptions: Assets Bahattin Buyuksahin, JHU, Investment

5. All investors will hold the same portfolio for risky assets – market portfolio, which contains all securities and the proportion of each security is its market value as a percentage of total market value held by all investors includes all traded assets suppose not: then price… -> included is on the efficient frontier asset weights: for each $ in risky assets, how much is in IBM? for stock i: market cap of stock i / market cap of all stocks Resulting Equilibrium Conditions Bahattin Buyuksahin, JHU, Investment

6. 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 Continued Bahattin Buyuksahin, JHU, Investment

7. Figure 9.1 The Efficient Frontier and the Capital Market Line Bahattin Buyuksahin, JHU, Investment

8. Market Risk Premium Bahattin Buyuksahin, JHU, Investment • The risk premium on the market portfolio will be proportional to its risk and the degree of risk aversion of the investor:

9. The risk premium on individual securities is a function of the individual security’s contribution to the risk of the market portfolio An individual security’s risk premium is a function of the covariance of returns with the assets that make up the market portfolio Return and Risk For Individual Securities Bahattin Buyuksahin, JHU, Investment

10. Using GE Text Example Bahattin Buyuksahin, JHU, Investment Covariance of GE return with the market portfolio: Therefore, the reward-to-risk ratio for investments in GE would be:

11. Using GE Text Example Continued Bahattin Buyuksahin, JHU, Investment Reward-to-risk ratio for investment in market portfolio: Reward-to-risk ratios of GE and the market portfolio: And the risk premium for GE:

12. Expected Return-Beta Relationship Bahattin Buyuksahin, JHU, Investment CAPM holds for the overall portfolio because: This also holds for the market portfolio:

13. Figure 9.2 The Security Market Line Bahattin Buyuksahin, JHU, Investment

14. Figure 9.3 The SML and a Positive-Alpha Stock Bahattin Buyuksahin, JHU, Investment

15. The Index Model and Realized Returns Bahattin Buyuksahin, JHU, Investment To move from expected to realized returns—use the index model in excess return form: The index model beta coefficient turns out to be the same beta as that of the CAPM expected return-beta relationship

16. Figure 9.4 Estimates of Individual Mutual Fund Alphas, 1972-1991 Bahattin Buyuksahin, JHU, Investment

17. The CAPM and Reality Is the condition of zero alphas for all stocks as implied by the CAPM met Not perfect but one of the best available Is the CAPM testable Proxies must be used for the market portfolio CAPM is still considered the best available description of security pricing and is widely accepted Bahattin Buyuksahin, JHU, Investment

18. Econometrics and the Expected Return-Beta Relationship Bahattin Buyuksahin, JHU, Investment • It is important to consider the econometric technique used for the model estimated • Statistical bias is easily introduced • Miller and Scholes paper demonstrated how econometric problems could lead one to reject the CAPM even if it were perfectly valid

19. Extensions of the CAPM Zero-Beta Model Helps to explain positive alphas on low beta stocks and negative alphas on high beta stocks Consideration of labor income and non-traded assets Merton’s Multiperiod Model and hedge portfolios Incorporation of the effects of changes in the real rate of interest and inflation Bahattin Buyuksahin, JHU, Investment

20. Extensions of the CAPM Continued Bahattin Buyuksahin, JHU, Investment • A consumption-based CAPM • Models by Rubinstein, Lucas, and Breeden • Investor must allocate current wealth between today’s consumption and investment for the future

21. Liquidity and the CAPM Liquidity Illiquidity Premium Research supports a premium for illiquidity. Amihud and Mendelson Acharya and Pedersen Bahattin Buyuksahin, JHU, Investment

22. Figure 9.5 The Relationship Between Illiquidity and Average Returns Bahattin Buyuksahin, JHU, Investment

23. Three Elements of Liquidity Bahattin Buyuksahin, JHU, Investment Sensitivity of security’s illiquidity to market illiquidity: Sensitivity of stock’s return to market illiquidity: Sensitivity of the security illiquidity to the market rate of return:

24. CAPM: Examples of Practical Problems 1 Bahattin Buyuksahin, JHU Investments

25. CAPM: Examples of Practical Problems 2 Bahattin Buyuksahin, JHU Investments

26. CAPM: Examples of Practical Problems 3 Bahattin Buyuksahin, JHU Investments

27. CAPM: Examples of Practical Problems 4 Bahattin Buyuksahin, JHU Investments

28. CAPM: Examples of Practical Problems 5 Bahattin Buyuksahin, JHU Investments

29. CAPM: Examples of Practical Problems 6 Bahattin Buyuksahin, JHU Investments

30. CAPM: Examples of Practical Problems 7 Bahattin Buyuksahin, JHU Investments

31. CAPM: Examples of Practical Problems 8 Bahattin Buyuksahin, JHU Investments

32. Index model vs. CAPM Bahattin Buyuksahin, JHU Investments • Risk • CAPM (theoretical, unobservable portfolio) • Index model (observable, “proxy” portfolio)

33. Index model vs. CAPM 2 Bahattin Buyuksahin, JHU Investments • Beta Relationship • CAPM (no expected excess return for any security) • Index model (average realized alpha is 0) • Fig 10.3

34. Market Model Bahattin Buyuksahin, JHU Investments • Idea • use realized excess returns • Equivalence • CAPM + Market model = Index model

35. Summary Bahattin Buyuksahin, JHU Investments CAPM Factor model Index model Market model

36. CHAPTER 10 Arbitrage Pricing Theory and Multifactor Models of Risk and Return

37. Single Factor Model Returns on a security come from two sources Common macro-economic factor Firm specific events Possible common macro-economic factors Gross Domestic Product Growth Interest Rates Bahattin Buyuksahin, JHU, Investment

38. Single Factor Model Equation ri= Return for security I = Factor sensitivity or factor loading or factor beta F = Surprise in macro-economic factor (F could be positive, negative or zero) ei = Firm specific events Bahattin Buyuksahin, JHU, Investment

39. Multifactor Models 1 Bahattin Buyuksahin, JHU Investments • Necessity • CAPM • not practical • Index model • practical • unique factor is unsatisfactory • example: Table 10.2 (very small R2) • Solution • multiple factors

40. Multi-factor Models 2 Bahattin Buyuksahin, JHU Investments • Factors in practice • business cycles factors • examples (Chen Roll Ross) • industrial production % change • expected inflation % change • unanticipated inflation % change • LT corporate over LT gvt. bonds • LT gvt. bonds over T-bills • interpretation • residual variance = firm specific risk

41. Multi-factor Models 3 Bahattin Buyuksahin, JHU Investments • Factors in practice • firm characteristics (Fama and French) • firm size • difference in return • between firms with low vs. high equity market value • proxy for business cycle sensitivity? • market to book • difference in return • between firms with low vs. high BTM ratio • proxy for bankruptcy risk?

42. Multifactor Models 4 Use more than one factor in addition to market return Examples include gross domestic product, expected inflation, interest rates etc. Estimate a beta or factor loading for each factor using multiple regression. Bahattin Buyuksahin, JHU, Investment

43. Multifactor Model Equation ri= E(ri) + GDPGDP + IRIR + ei ri= Return for security I GDP= Factor sensitivity for GDP IR= Factor sensitivity for Interest Rate ei= Firm specific events Bahattin Buyuksahin, JHU, Investment

44. Multifactor SML Models E(r) = rf + GDPRPGDP + IRRPIR GDP = Factor sensitivity for GDP RPGDP = Risk premium for GDP IR = Factor sensitivity for Interest Rate RPIR= Risk premium for Interest Rate Bahattin Buyuksahin, JHU, Investment

45. Arbitrage Pricing Theory (APT) Bahattin Buyuksahin, JHU Investments • Nature of arbitrage • APT • well-diversified portfolios • individual assets • APT vs. CAPM • APT vs. Index models • single factor • multi-factor

46. 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 Bahattin Buyuksahin, JHU, Investment

47. APT & Well-Diversified Portfolios rP = E (rP) + bPF + eP F = some factor For a well-diversified portfolio: eP approaches zero Similar to CAPM, Bahattin Buyuksahin, JHU, Investment

48. Figure 10.1 Returns as a Function of the Systematic Factor Bahattin Buyuksahin, JHU, Investment

49. Figure 10.2 Returns as a Function of the Systematic Factor: An Arbitrage Opportunity Bahattin Buyuksahin, JHU, Investment

50. Figure 10.3 An Arbitrage Opportunity Bahattin Buyuksahin, JHU, Investment