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Multi-Factor asset pricing

Multi-Factor asset pricing. And more on the homework. Review item. Define beta. Answer. Rate of return on asset j is Rate of return on the market portfolio is . My project: AOL. Regression: y = a + bx + e. where a and b are constants y is to be explained x is an explanatory variable

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Multi-Factor asset pricing

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  1. Multi-Factor asset pricing And more on the homework

  2. Review item • Define beta.

  3. Answer Rate of return on asset j is Rate of return on the market portfolio is

  4. My project: AOL

  5. Regression: y = a + bx + e • where a and b are constants • y is to be explained • x is an explanatory variable • e is a random error term

  6. For Beta • Rj = a + bRM + e • e = idiosyncratic risk (diversifiable risk) • b = beta • a = alpha = sample average advantage over the market • if statistically significant

  7. Components of risk • Diversifiable risk is unique, idiosyncratic, or unsystematic risk • Market risk is systematic or portfolio risk

  8. Diversifiable risk • It is eliminated by buying other assets, i.e., • can be "diversified away."

  9. Arbitrage pricing theory • Side-issue: Arbitrage is interesting in options, bonds, CAPM, and this course. • Notion: There are several factors (indexes). • They are found by regression analysis. • More notion: Each factor has its own beta. • Risk unrelated to the factors can be diversified away, leaving only systematic risk.

  10. The K-Factor Model The unexpected systematic return is explained by surprise in “factors.” Surprise in factors: F1, F2, … ,Fk Ri = E(Ri) + bi1F1 + bi2F2 + … + biKFk + ei

  11. Arbitrage pricing theory is like CAPM, … • Factor risk (previously market risk) remains even when the portfolio is fully diversified. • Factor risk is undiversifiable. • For any asset, the betas of factors measure factor risk. • Required return is linear in the factor betas.

  12. The market rewards the investor • not for bearing diversifiable risk but • only for bearing factor (or market) risk.

  13. The market rewards the investor • not for all the risk ( s ) of an asset • but only for its betas.

  14. Do low P/E firms contradict CAPM? • Price at t = Earnings at t+1/r-g • Price/Earnings = (1+g)/r-g • Low growth and or high risk imply low P/E • High risk implies high expected return. • Therefore low P/E means, on average, high return. Doesn’t contradict CAPM.

  15. How many assets in a diversified portfolio? • Not many. • About 30 well-chosen ones. • Statman JFQA Sept 87

  16. Diversification for an Equally Weighted Portfolio Total risk s2 P Unsystematicrisk Systematicrisk Number of Securities

  17. Investors need only two funds. • Figures 10.4, 10.5, and 10.6.

  18. MV MV MV Diversification, minimum variance B E(R) A s

  19. MV Diversification with a risk-free asset B E(R) A= risk-free asset s

  20. . Y . X Capital Market Line Expected returnof portfolio Indifference curve Capital market line . preferred . M . . Risk-freerate (Rf ) Standarddeviation ofportfolio’s return.

  21. Argument for the security market line • Only beta matters • A mix of T-Bills and the market can produce any beta. • An asset with that beta is no better or worse than the two-fund counterpart • Hence it has the same return.

  22. . T . S 0.8 Security Market Line Expected returnon security (%) T is undervalued. Its price rises Security market line (SML) . . M Rm Rf S is overvalued. Its price falls Beta ofsecurity 1

  23. Review item • Asset A has a beta of .8. • Asset B has a beta of 1.5. • Consider a portfolio with weights .4 on asset A and .6 on asset B. • What is the beta of the portfolio?

  24. Answer • Portfolio beta is .4*.8+.6*1.5 = 1.22. • Work it out this way: • DevP = .4 DevA + .6 Dev B • E[DevP*DevM] = .4 E[DevA*DevM] + .6*E[DevB*DevM]. • Divide by E[DevP squared].

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