Return and Risk : CAPM and APT Reference: RWJ Chp. 11

1. Return and Risk : CAPM and APTReference: RWJ Chp. 11

2. 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.

3. Factor Models: Announcements, Surprises, and Expected Returns • The return on any security consists of two parts. • First the expected returns • Second is the unexpected or risky returns. • A way to write the return on a stock in the coming month is:

4. 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 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.

5. 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 company, such as a gold mining company striking gold, are examples of unsystematic risk.

6.  Risk: Systematic and Unsystematic We can break down the risk, U, of holding a stock into two components: systematic risk and unsystematic risk:  Total risk; U Nonsystematic Risk;  Systematic Risk; m n

7. Systematic Risk and Betas • The beta coefficient, b, tells us the response of the stock’s return to a systematic risk. • In the CAPM, b measured the responsiveness of a security’s return to a specific risk factor, the return on the market portfolio. • We shall now consider many types of systematic risk.

8. Systematic Risk and Betas • For example, suppose we have identified three systematic risks on which we want to focus: • Inflation • GDP growth • The dollar-euro spot exchange rate, S($,€) • Our model is:

9. Systematic Risk and Betas: Example • Suppose we have made the following estimates: • bI = -2.30 • bGDP = 1.50 • bS = 0.50. • Finally, the firm was able to attract a “superstar” CEO and this unanticipated development contributes 1% to the return.

10. Systematic Risk and Betas: Example We must decide what surprises took place in the systematic factors. If it was the case that the inflation rate was expected to be by 3%, but in fact was 8% during the time period, then FI = Surprise in the inflation rate = actual – expected = 8% - 3% = 5%

11. Systematic Risk and Betas: Example If it was the case that the rate of GDP growth was expected to be 4%, but in fact was 1%, then FGDP = Surprise in the rate of GDP growth = actual – expected = 1% - 4% = -3%

12. Systematic Risk and Betas: Example If it was the case that dollar-euro spot exchange rate, S($,€), was expected to increase by 10%, but in fact remained stable during the time period, then FS = Surprise in the exchange rate = actual – expected = 0% - 10% = -10%

13. Systematic Risk and Betas: Example Finally, if it was the case that the expected return on the stock was 8%, then

14. 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 ith stock in the list have returns:

15. Relationship Between the Return on the Common Factor & Excess Return Excess return If we assume that there is no unsystematic risk, then ei = 0 The return on the factor F

16. Relationship Between the Return on the Common Factor & Excess Return Excess return If we assume that there is no unsystematic risk, then ei = 0 The return on the factor F

17. Relationship Between the Return on the Common Factor & Excess Return Excess return Different securities will have different betas The return on the factor F

18. Portfolios and Diversification • We know that the portfolio return is the weighted average of the returns on the individual assets in the portfolio:

19. The weighed average of expected returns. • The weighted average of the betas times the factor. • The weighted average of the unsystematic risks. 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.

20. Portfolios and Diversification So the return on a diversified portfolio is determined by two sets of parameters: • The weighed average of expected returns. • 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.

21. 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.

22. Relationship Between b & Expected Return • If shareholders are ignoring unsystematic risk, only the systematic risk of a stock can be related to its expected return.

23. Relationship Between b & Expected Return SML Expected return D A B C b

24. 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.