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Chapter 7

Chapter 7. Capital Asset Pricing and Arbitrage Pricing Theory. Capital Asset Pricing Model (CAPM). Equilibrium model that underlies all modern financial theory Derived using principles of diversification with simplified assumptions

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Chapter 7

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  1. Chapter7 Capital Asset Pricing and Arbitrage Pricing Theory

  2. Capital Asset Pricing Model (CAPM) • 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

  3. Assumptions • Individual investors are price takers • Single-period investment horizon • Investments are limited to traded financial assets • No taxes, and transaction costs

  4. Assumptions (cont.) • Information is costless and available to all investors • Investors are rational mean-variance optimizers • Homogeneous expectations

  5. Resulting Equilibrium Conditions • 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

  6. Resulting Equilibrium Conditions (cont.) • 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

  7. Capital Market Line E(r) CML M E(rM) rf s sm

  8. Slope and Market Risk Premium M = Market portfolio rf = Risk free rate E(rM) - rf = Market risk premium E(rM) - rf = Market price of risk = Slope of the CAPM s M

  9. Expected Return and Risk on Individual Securities • The risk premium on individual securities is a function of the individual security’s contribution to the risk of the market portfolio • Individual security’s risk premium is a function of the covariance of returns with the assets that make up the market portfolio

  10. Security Market Line E(r) SML E(rM) rf ß ß = 1.0 M

  11. SML Relationships b = [COV(ri,rm)] / sm2 Slope SML = E(rm) - rf = market risk premium SML = rf + b[E(rm) - rf]

  12. Sample Calculations for SML E(rm) - rf = .08 rf = .03 bx = 1.25 E(rx) = .03 + 1.25(.08) = .13 or 13% by = .6 e(ry) = .03 + .6(.08) = .078 or 7.8%

  13. Graph of Sample Calculations E(r) SML Rx=13% .08 Rm=11% Ry=7.8% 3% ß .6 1.0 1.25 ß ß ß y m x

  14. Disequilibrium Example E(r) SML 15% Rm=11% rf=3% ß 1.0 1.25

  15. Disequilibrium Example • Suppose a security with a b of 1.25 is offering expected return of 15% • According to SML, it should be 13% • Underpriced: offering too high of a rate of return for its level of risk

  16. Security Characteristic Line Excess Returns (i) SCL . . . . . . . . . . . . . . . . . . . . . . . . . . Excess returns on market index . . . . . . . . . . . . . . . . . . . . . . . . Ri = ai + ßiRm + ei

  17. Using the Text Example p. 231, Table 7.5 Excess GM Ret. Excess Mkt. Ret. Jan. Feb. . . Dec Mean Std Dev 5.41 -3.44 . . 2.43 -.60 4.97 7.24 .93 . . 3.90 1.75 3.32

  18. Regression Results: a rGM - rf = + ß(rm - rf) a ß Estimated coefficient Std error of estimate Variance of residuals = 12.601 Std dev of residuals = 3.550 R-SQR = 0.575 -2.590 (1.547) 1.1357 (0.309)

  19. 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

  20. Arbitrage Example from Text pp. 241-243 Current Expected Standard Stock Price$ Return% Dev.% A 10 25.0 29.58 B 10 20.0 33.91 C 10 32.5 48.15 D 10 22.5 8.58

  21. Arbitrage Portfolio Mean Stan. Correlation Return Dev. Of Returns Portfolio A,B,C 25.83 6.40 0.94 D 22.25 8.58

  22. Arbitrage Action and Returns E. Ret. * P * D St.Dev. Short 3 shares of D and buy 1 of A, B & C to form P You earn a higher rate on the investment than you pay on the short sale

  23. APT and CAPM Compared • 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

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