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CHAPTER 9

CHAPTER 9. The Capital Asset Pricing Model. 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.

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CHAPTER 9

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  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)

  3. Individual investors are price takers Single-period investment horizon Can be extended to: All agents plan for the same time horizon (and information changes between “planning periods” are very predictable) Investments are limited to traded financial assets No taxes and transaction costs Like liquidity costs Assumptions

  4. Information is costless and available to all investors Investors are rational mean-variance optimizers There are homogeneous expectations Assumptions Continued

  5. All investors will hold the same portfolio for risky assets – market portfolio Market portfolio contains all securities and the proportion of each security is its market value as a percentage of total market value This is a solution to problem of maximizing Sharpe Ratio. Resulting Equilibrium Conditions

  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

  7. Figure 9.1 The Efficient Frontier and the Capital Market Line

  8. Market Risk Premium The risk premium on the market portfolio will be proportional to its risk and the degree of risk aversion of the average investor. (see CAPM-presentation2.pdf for more detail)

  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

  10. Using GE Text Example 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 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. Figure 9.2 The Security Market Line

  13. CAPM APPLICATIONS Buy or sell stocks (SML) This first one we talked about it last class, and we cover it in the next slides IRR (Internal rate of return) cut-offs, or hurdle-rate Note that any allocation of resources imply a opportunity cost problem Invest $100 on some project or in the market? The CAPM gives a required expected rate of return for such projects. Example: Company invests $100 million on project with beta of .5 and the market (expected) return is 14% and T-bill rate is 6%. The implied required return is 6%+.5(8%)=10%. Project should generate (at least) $10 million profits.

  14. Figure 9.3 The SML and a Positive-Alpha Stock • Alpha for a stock is the difference between expected return in excess of the fair expected return as predicted by the CAPM • Fair expected return always plot on the SML • In the picture to the left we have a positive alpha stock (17-15.6)>0

  15. In class exercise (SML use) Stock XYZ has expected return of 12% and beta is 1. Stock ABC has expected return of 13% and beta is 1.5. Market expected return is 11% and risk-free rate is 5%. Which stock is a better buy (based on CAPM)? Compute alpha for each stock. Plot the SML and indicate alpha for each stock

  16. In class exercise (CAPM as hurdle rate) You have a project opportunity for which you know it to have a beta of 1.3. You also know that the risk-free rate is 8% and expected return on the market portfolio is 16%. Would you invest in this project? In other words, what is the required internal rate of return (hurdle rate) implied by the CAPM for this project. If the expected return is 19% would you invest in this project?

  17. The Index Model and Realized Returns To move from expected to realized returns—use the index model in excess return form: Stock alpha is not the same alpha in the eq. above The index model beta coefficient turns out to be the same beta as that of the CAPM expected return-beta relationship

  18. Figure 9.4 Estimates of Individual Mutual Fund Alphas, 1972-1991 • There are “ex-post”, or after the fact, alphas • Ex-ante alpha, in equilibrium, is zero.

  19. 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

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