Capital Asset Pricing and Arbitrage Pricing Theory

1. Capital Asset Pricing and Arbitrage Pricing Theory 7 Bodie, Kane and Marcus Essentials of Investments 9th Global Edition

2. 7.1 The Capital Asset Pricing Model

3. 7.1 The Capital Asset Pricing Model • Assumptions • Markets are competitive, equally profitable • No investor is wealthy enough to individually affect prices • All information publicly available; all securities public • No taxes on returns, no transaction costs • Unlimited borrowing/lending at risk-free rate • Investors are alike except for initial wealth, risk aversion • Investors plan for single-period horizon; they are rational, mean-variance optimizers • Use same inputs, consider identical portfolio opportunity sets

4. 7.1 The Capital Asset Pricing Model • Hypothetical Equilibrium • All investors choose to hold market portfolio • Market portfolio is on efficient frontier, optimal risky portfolio • Risk premium on market portfolio is proportional to variance of market portfolio and investor’s risk aversion • Risk premium on individual assets • Proportional to risk premium on market portfolio • Proportional to beta coefficient of security on market portfolio

5. Figure 7.1 Efficient Frontier and Capital Market Line

6. 7.1 The Capital Asset Pricing Model • Passive Strategy is Efficient • Mutual fund theorem: All investors desire same portfolio of risky assets, can be satisfied by single mutual fund composed of that portfolio • If passive strategy is costless and efficient, why follow active strategy? • If no one does security analysis, what brings about efficiency of market portfolio?

7. 7.1 The Capital Asset Pricing Model • Risk Premium of Market Portfolio • Demand drives prices, lowers expected rate of return/risk premiums • When premiums fall, investors move funds into risk-free asset • Equilibrium risk premium of market portfolio proportional to • Risk of market • Risk aversion of average investor

8. 7.1 The Capital Asset Pricing Model

9. 7.1 The Capital Asset Pricing Model • The Security Market Line (SML) • Represents expected return-beta relationship of CAPM • Graphs individual asset risk premiums as function of asset risk • Alpha • Abnormal rate of return on security in excess of that predicted by equilibrium model (CAPM)

10. Figure 7.2 The SML and a Positive-Alpha Stock

11. 7.1 The Capital Asset Pricing Model • Applications of CAPM • Use SML as benchmark for fair return on risky asset • SML provides “hurdle rate” for internal projects • In setting pricing for government offerings and tenders

12. 7.1 The Capital Asset Pricing Model What is the expected rate of return for a stock that has a beta of 1 if the expected return on the market is 15%? a.   15%. b.   More than 15%. c.   Cannot be determined without the risk-free rate.

13. 7.2 CAPM and Index Models

14. 7.2 CAPM and Index Models

15. Table 7.1 Monthly Return Statistics 01/06 - 12/10

16. Figure 7.3A: Monthly Returns

17. Figure 7.3B Monthly Cumulative Returns

18. Figure 7.4 Scatter Diagram/SCL: Google vs. S&P 500, 01/06-12/10

19. Table 7.2 SCL for Google (S&P 500), 01/06-12/10

20. 7.2 CAPM and Index Models • Estimation results • Security Characteristic Line (SCL) • Plot of security’s expected excess return over risk-free rate as function of excess return on market • Required rate = Risk-free rate + β x Expected excess return of index

21. 7.2 CAPM and Index Models • Predicting Betas • Mean reversion • Betas move towards mean over time • To predict future betas, adjust estimates from historical data to account for regression towards 1.0

22. True or False Stocks with a beta of zero offer an expected rate of return of zero. The CAPM implies that investors require a higher return to hold highly volatile securities. You can construct a portfolio with beta of .75 by investing .75 of the investment budget in T-bills and the remainder in the market portfolio.

23. 10) The market price of a security is $ 30. Its expected rate of return is 10%. The risk-free rate is 4%, and the market risk premium is 8%. What will the market price of the security be if its beta doubles (and all other variables remain unchanged)? Assume the stock is expected to pay a constant dividend in perpetuity.

24. 15) If the CAPM is valid, is the below situation possible?

25. 16) If the CAPM is valid, is the below situation possible?

26. 24) Two investment advisers are comparing performance. One averaged a 19% return and the other a 16% return. However, the beta of the first adviser was 1.5, while that of the second was 1. Can you tell which adviser was a better selector of individual stocks (aside from the issue of general movements in the market)? If the T-bill rate were 6% and the market return during the period were 14%, which adviser would be the superior stock selector? c.   What if the T-bill rate were 3% and the market return 15%?

27. 22) Assume the risk-free rate is 4% and the expected rate of return on the market is 15%. I am buying a firm with an expected perpetual cash flow of $ 600 but am unsure of its risk. If I think the beta of the firm is zero, when the beta is really 1, how much more will I offer for the firm than it is truly worth?

28. 7.3 CAPM and the Real World • CAPM is false based on validity of its assumptions • Useful predictor of expected returns • Untestable as a theory • Principles still valid • Investors should diversify • Systematic risk is the risk that matters • Well-diversified risky portfolio can be suitable for wide range of investors

29. 7.3 CAPM and the Real World Consider the statement: “If we can identify a portfolio that beats the S& P 500 Index portfolio, then we should reject the single-index CAPM.” Do you agree or disagree? Explain.

30. 7.4 Multifactor Models and CAPM

31. 7.4 Multifactor Models and CAPM

32. Table 7.3 Monthly Rates of Return, 01/06-12/10

33. Table 7.4 Regression Statistics: Alternative Specifications

34. 7.5 Arbitrage Pricing Theory • Arbitrage • Relative mispricing creates riskless profit • Arbitrage Pricing Theory (APT) • Risk-return relationships from no-arbitrage considerations in large capital markets • Well-diversified portfolio • Nonsystematic risk is negligible • Arbitrage portfolio • Positive return, zero-net-investment, risk-free portfolio

35. 7.5 Arbitrage Pricing Theory • Calculating APT • Returns on well-diversified portfolio

36. Table 7.5 Portfolio Conversion Steps to convert a well-diversified portfolio into an arbitrage portfolio *When alpha is negative, you would reverse the signs of each portfolio weight to achieve a portfolio A with positive alpha and no net investment.

37. Figure 7.5 Security Characteristic Lines

38. 7.5 Arbitrage Pricing Theory • Multifactor Generalization of APT and CAPM • Factor portfolio • Well-diversified portfolio constructed to have beta of 1.0 on one factor and beta of zero on any other factor • Two-Factor Model for APT

40. 7.5 Arbitrage Pricing Theory 29. Assume a market index represents the common factor and all stocks in the economy have a beta of 1. Firm-specific returns all have a standard deviation of 45%. Suppose an analyst studies 20 stocks and finds that one-half have an alpha of 3.5%, and one-half have an alpha of –3%. The analyst then buys $ 1 million of an equally weighted portfolio of the positive-alpha stocks and sells short $ 1.7 million of an equally weighted portfolio of the negative-alpha stocks. What is the expected profit (in dollars), and what is the standard deviation of the analyst’s profit How does your answer change if the analyst examines 50 stocks instead of 20? 100 stocks?

41. 7.5 Arbitrage Pricing Theory 31) The APT itself does not provide information on the factors that one might expect to determine risk premiums. How should researchers decide which factors to investigate? Is industrial production a reasonable factor to test for a risk premium? Why or why not?

42. 7.5 Arbitrage Pricing Theory 31) As a finance intern at Pork Products, Jennifer Wainwright’s assignment is to come up with fresh insights concerning the firm’s cost of capital. She decides that this would be a good opportunity to try out the new material on the APT that she learned last semester. As such, she decides that three promising factors would be (i) the return on a broad-based index such as the S& P 500; (ii) the level of interest rates, as represented by the yield to maturity on 10-year Treasury bonds; and (iii) the price of hogs, which are particularly important to her firm. Her plan is to find the beta of Pork Products against each of these factors and to estimate the risk premium associated with exposure to each factor. Comment on Jennifer’s choice of factors. Which are most promising with respect to the likely impact on her firm’s cost of capital? Can you suggest improvements to her specification?

43. 7.5 Arbitrage Pricing Theory