1. PRICING MODELS: CAPM FNCE 455 Lloyd Kurtz Santa Clara University 1

2. From Markowitz to Sharpe 2 “Markowitz came along, and there was light. Markowitz said a portfolio has expected return and risk. Expected return is related to the expected return of the securities, but risk is more complicated. Risk is related to the risks of the individual components as well as the correlations. “That makes risk a complicated feature, and one that human beings have trouble processing. You can put estimates of risk/return correlation into a computer and find efficient portfolios. In this way, you can get more return for a given risk and less risk for a given return, and that's efficiency a la Markowitz.” William Sharpe, interview with Dow Jones Asset Manager magazine, May/June 1998

3. CAPM sees two kinds of risk 3 Since this risk can be diversified away, you cannot expect compensation for bearing it. Since this risk is unavoidable, investors will seek compensation (in the form of higher returns) for bearing it.

4. The CAPM 4 “I did my dissertation under a strongly simplified assumption that only one factor caused correlation. [I found that] prices would adjust until expected returns were higher for securities that had higher betas, where beta was the coefficient with "the factor.“ [Markowitz’s] Portfolio Theory focused on the actions of a single investor with an optimal portfolio. You wondered what would happen to risk and return if everyone followed Markowitz and built efficient portfolios. I said what if everyone was optimizing? They've all got their copies of Markowitz and they're doing what he says.... At that point, what can you say about the relationship between risk and return? The answer is that expected return is proportionate to beta relative to the market portfolio. William Sharpe, interview with Dow Jones Asset Manager magazine, May/June 1998

5. CAPM Assumptions Highly liquid market (perfect competition) All investors have the same time horizon Investors can borrow or lend unlimited amounts No taxes or transaction costs Therefore: no distinction between capital gains and dividends All investors analyze securities in the same way – homogenous expectations All investors attempt to construct efficient frontier portfolios, as recommended by Markowitz 5 See BK&M, p. 193

6. Beta is… “The sensitivity of a security’s returns to the systematic or market factor.” 6

7. Beta and expected return 7 “It was, Sharpe wrote, the simplest model of the market he could build ‘without assuming away the existence of interrelationships among securities.’ ” - Fox

8. The power of CAPM You can price any risky investment if you have three inputs: The risk-free rate Market return forecast A forecast of Beta for your investment 8

9. CAPM in one formula E (r i ) = r f + β i [ E(r m ) – r f ] 9

10. CAPM in One Formula E (r i ) = r f + β i [ E(r m ) – r f ] 10 Expected return of the investment Risk-free rate Expected risky return of the market Expected Beta of the investment

11. Uses of CAPM Asset pricing Solve for expected return Solve for beta Managing portfolio risk in market timing strategies Raise beta in anticipation of rising market Reduce beta in anticipation of falling market Risk/diversification management tool Search for zero or negative beta assets 11

12. Asset Pricing: LSI Logic E (r LSI ) = r f + β LSI [ E(r m ) – r f ] E (r LSI ) = 1% + 1.8 [ 8% - 1% ] E (r LSI ) = 12.6% 12 * Assumptions and inputs: 1 – one year time horizon 2 – r f = one year bond yield 3 – LSI historical beta is 1.6. Some practitioners would adjust this beta downward because betas tend to regress to the mean (1.0) over time. 4 – Expected market return is S&P 500 dividend yield plus my forecast of EPS growth.

13. A good investment in CAPM 13

14. High beta stocks need to do well! 14 LSI’s return needs to be above this point to contribute to superior risk-adjusted returns.

15. LSI Logic – CAPM Targets Price: $8 Price to be on SML: $9.00 $8 * 1.126 = $9.00 Buying with any target price above $9.00 would be good for risk-adjusted returns. Buying at any target price below $9.00 would be a drag on risk-adjusted returns. 15

16. Market timing If you have the ability to anticipate market direction… Raise the beta of the portfolio in anticipation of a rising market Reduce the beta of the portfolio in anticipation of a falling market Studies show most managers do the opposite… 16

17. Risk mgt: negative beta…find it if you can! 17

18. Advantages of CAPM Clear Theoretically impeccable Easily calculated Intuitive 18

19. And we all lived happily ever after... 19

20. Problems with CAPM Unrealistic Assumptions Simple or Simplistic? Poor Explainer of Past Results 20

21. Three years ended 12/06 21

22. Three years (cont’d) 22

23. Rhyme? Reason? 23 Over the this three year period there was no discernible relationship between observed betas and returns. Knowing sector betas beforehand would have given us no insight into future returns.

24. But remember CAPM is an Expectations Framework The betas and returns that matter are the ones projected at the time of the investment Still, would we take CAPM seriously if it failed to explain returns over long time periods? 24

25. Is it worth paying attention to? “We know that the CAPM is not a perfect model and that ultimately it will be far from the last word on security pricing. Still, the logic of the model is compelling, and more sophisticated models of security pricing all rely on the key distinction between systematic and diversifiable risk. The CAPM therefore provides a useful framework for thinking rigorously about the relationship between security risk and return.” - BK&M, p. 206-207 25

26. Reminder No class Wednesday 4/18 26