1. McGraw-Hill/Irwin Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved CHAPTER 11 An Alternative View of Risk and Return The Arbitrage Pricing Theory

2. Slide 2 Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill/Irwin Key Concepts and Skills Understand the decomposition of a security’s return into expected and unexpected components Discuss the relative importance of systematic and unsystematic risk in determining a portfolio’s return Compare and contrast the CAPM and Arbitrage Pricing Theory

3. Slide 3 Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill/Irwin Chapter Outline 11.1 Factor Models: Announcements, Surprises, and Expected Returns 11.2 Risk: Systematic and Unsystematic 11.3 Systematic Risk and Betas 11.4 Portfolios and Factor Models 11.5 Betas and Expected Returns 11.6 The Capital Asset Pricing Model and the Arbitrage Pricing Theory 11.7 Empirical Approaches to Asset Pricing

4. Slide 4 Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill/Irwin 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.

5. Slide 5 Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill/Irwin 11.1 Factor Models: Announcements, Surprises, and Expected Returns The return on any security consists of two parts. –First, the expected returns –Second, the unexpected or risky returns A way to write the return on a stock in the coming month is:

6. Slide 6 Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill/Irwin Factor Models: Announcements, Surprises, and Expected Returns Any announcement can be broken down into two parts, the anticipated (or expected) part and the surprise (or innovation): –Announcement = Expected part + Surprise. The expected part of any announcement is the part of the information the market uses to form the expectation, R, of the return on the stock. The surprise is the news that influences the unanticipated return on the stock, U.

7. Slide 7 Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill/Irwin 11.2 Risk: Systematic and Unsystematic A systematic risk is any risk that affects a large number of assets, each to a greater or lesser degree. An unsystematic risk is a risk that specifically affects a single asset or small group of assets. Unsystematic risk can be diversified away. Examples of systematic risk include uncertainty about general economic conditions, such as GNP, interest rates or inflation. On the other hand, announcements specific to a single company are examples of unsystematic risk.

8. Slide 8 Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill/Irwin Risk: Systematic and Unsystematic Systematic Risk: m Nonsystematic Risk:  n 22 Total risk We can break down the total risk of holding a stock into two components: systematic risk and unsystematic risk: 

9. Slide 9 Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill/Irwin 11.3 Systematic Risk and Betas The beta coefficient, , tells us the response of the stock’s return to a systematic risk. In the CAPM,  measures the responsiveness of a security’s return to a specific risk factor, the return on the market portfolio. We shall now consider other types of systematic risk.

10. Slide 10 Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill/Irwin Systematic Risk and Betas For example, suppose we have identified three systematic risks: inflation, GNP growth, and the dollar-euro spot exchange rate, S($,€). Our model is:

11. Slide 11 Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill/Irwin Systematic Risk and Betas: Example Suppose we have made the following estimates:  I = -2.30  GNP = 1.50  S = 0.50 Finally, the firm was able to attract a “superstar” CEO, and this unanticipated development contributes 1% to the return.

12. Slide 12 Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill/Irwin Systematic Risk and Betas: Example We must decide what surprises took place in the systematic factors. If it were the case that the inflation rate was expected to be 3%, but in fact was 8% during the time period, then: F I = Surprise in the inflation rate = actual – expected = 8% – 3% = 5%

13. Slide 13 Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill/Irwin Systematic Risk and Betas: Example If it were the case that the rate of GNP growth was expected to be 4%, but in fact was 1%, then: F GNP = Surprise in the rate of GNP growth = actual – expected = 1% – 4% = – 3%

14. Slide 14 Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill/Irwin Systematic Risk and Betas: Example If it were the case that the dollar-euro spot exchange rate, S($,€), was expected to increase by 10%, but in fact remained stable during the time period, then: F S = Surprise in the exchange rate = actual – expected = 0% – 10% = – 10%

15. Slide 15 Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill/Irwin Systematic Risk and Betas: Example Finally, if it were the case that the expected return on the stock was 8%, then:

16. Slide 16 Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill/Irwin 11.4 Portfolios and Factor Models Now let us consider what happens to portfolios of stocks when each of the stocks follows a one-factor model. We will create portfolios from a list of N stocks and will capture the systematic risk with a 1-factor model. The i th stock in the list has return:

17. Slide 17 Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill/Irwin Relationship Between the Return on the Common Factor & Excess Return Excess return The return on the factor F If we assume that there is no unsystematic risk, then  i = 0.

18. Slide 18 Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill/Irwin Relationship Between the Return on the Common Factor & Excess Return Excess return The return on the factor F If we assume that there is no unsystematic risk, then  i = 0.

19. Slide 19 Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill/Irwin Relationship Between the Return on the Common Factor & Excess Return Excess return The return on the factor F Different securities will have different betas.

20. Slide 20 Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill/Irwin Portfolios and Diversification We know that the portfolio return is the weighted average of the returns on the individual assets in the portfolio:

21. Slide 21 Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill/Irwin Portfolios and Diversification The return on any portfolio is determined by three sets of parameters: In a large portfolio, the third row of this equation disappears as the unsystematic risk is diversified away. 1.The weighted average of expected returns. 2.The weighted average of the betas times the factor. 3.The weighted average of the unsystematic risks.

22. Slide 22 Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill/Irwin Portfolios and Diversification So the return on a diversified portfolio is determined by two sets of parameters: 1.The weighted average of expected returns. 2.The weighted average of the betas times the factor F. In a large portfolio, the only source of uncertainty is the portfolio’s sensitivity to the factor.

23. Slide 23 Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill/Irwin 11.5 Betas and Expected Returns The return on a diversified portfolio is the sum of the expected return plus the sensitivity of the portfolio to the factor.

24. Slide 24 Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill/Irwin Relationship Between  & Expected Return If shareholders are ignoring unsystematic risk, only the systematic risk of a stock can be related to its expected return.

25. Slide 25 Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill/Irwin Relationship Between  & Expected Return Expected return  A B C D SML

26. Slide 26 Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill/Irwin 11.6 The Capital Asset Pricing Model and the Arbitrage Pricing Theory APT applies to well diversified portfolios and not necessarily to individual stocks. With APT it is possible for some individual stocks to be mispriced - not lie on the SML. APT is more general in that it gets to an expected return and beta relationship without the assumption of the market portfolio. APT can be extended to multifactor models.

27. Slide 27 Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill/Irwin 11.7 Empirical Approaches to Asset Pricing Both the CAPM and APT are risk-based models. Empirical methods are based less on theory and more on looking for some regularities in the historical record. Be aware that correlation does not imply causality. Related to empirical methods is the practice of classifying portfolios by style, e.g., –Value portfolio –Growth portfolio

28. Slide 28 Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill/Irwin Quick Quiz Differentiate systematic risk from unsystematic risk. Which type is essentially eliminated with well diversified portfolios? Define arbitrage. Explain how the CAPM be considered a special case of Arbitrage Pricing Theory?