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- 1. Capital Asset Pricing andArbitrage Pricing Theory Prof. Karim Mimouni 1
- 2. Capital Asset Pricing Model (CAPM) 2
- 3. Assumptions• Individual investors are price takers• Single-period investment horizon• Investments are limited to traded financial assets• No taxes, and transaction costs 3
- 4. Assumptions (cont.)• Information is costless and available to all investors• Homogeneous expectations 4
- 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 5
- 6. The Efficient Frontier and the Capital Market Line 6
- 7. 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 σM = Slope of the CML 7
- 8. Expected Return and Risk on Individual Securities E (ri ) − rf = β i ( E (rM ) − rf )M = Market portfoliorf = Risk free rateE(ri) - rf = Risk premium on security iE(rM) - rf = Market risk premium 8
- 9. The Security Market Line and Positive Alpha Stock 9
- 10. • Determine the equation of the SML and plot it when: ( E (r M ) − rf ) = 0.08and rf = 0.03 10
- 11. Application• You are in an economy where Rf=9%, E(Rm)=20%.• Determine the equation of the SML line in this economy.• A stock has a beta=1.5. Determine the required rate of return. Give your recommendation when you think its expected return will be 22%.• Do the same analysis when beta=-0.5 and investor expect the return to be 7% 11
- 12. Estimating the Index Model• Using historical data on T-bills, S&P 500 and individual securities• Regress risk premiums for individual stocks against the risk premiums for the S&P 500• Slope is the beta for the individual stock 12
- 13. Characteristic Line for GM 13
- 14. Security CharacteristicLine for GM: Summary Output 14
- 15. Multifactor Models 15
- 16. • Limitations for CAPM• Market Portfolio is not directly observable• Research shows that other factors affect returns 16
- 17. Fama French Research • Returns are related to factors other than market returns • Size • Book value relative to market value • Three factor model better describes returns • Example : GME (rGM ) − r f = β GM , M ( E (rM ) − rf ) + β GM ,SMB ( E (rSMB ) − rf ) + β GM , HML ( E (rHML ) − rf ) 17
- 18. Regression Statistics for the Single- index and FF Three-factor Model 18
- 19. Arbitrage Pricing Theory 19
- 20. • Arbitrage - arises if an investor can construct a zero beta investment portfolio with a return greater than the risk-free rate• If two portfolios are mispriced, the investor could buy the low-priced portfolio and sell the high-priced portfolio• In efficient markets, profitable arbitrage opportunities will quickly disappear 20
- 21. Security Line CharacteristicsE (rP ) − rf = β P ( E (rM ) − rf ) 21
- 22. 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 22

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