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**Tests of CAPM Security Market Line (ex ante)**

E(Ri) = Rf + Bi(E(RM) - Rf) SML in terms of historical returns (ex post) Ri = Rf + bi(RM - Rf) Assumes: b values are true estimates for B Index we use is the market portfolio CAPM is correct Regression tests: Ri = a0 + a1bi + ei a0 should not be different from Rf a1 should be Rm - Rf Ri and beta should be linearly related No variable other then bi should explain R

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**Tests of CAPM Early Studies: Black, Jensen and Scholes (1972)**

Fama and MacBeth (1973) Findings: - a0 is higher than Rf, a1 is smaller than RM - Rf - beta is the only measure of risk that explains average returns - The model is linear in beta Recent Studies: Fama and French (1992) Anomalies

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**Roll’s Critique of CAPM tests**

- Tests of CAPM are tests of the market portfolio’s mean-variance efficiency - Market portfolio can never be observed - As long as the proxy used for M is ex-post efficient, the betas calculated using this proxy will be linearly related to the returns. - CAPM cannot be used for performance evaluation

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**Arbitrage Pricing Theory**

Return generating process: Ri = ai + bi1F1 + bi2F2 + ….+ binFn + ei Taking expectations: E(Ri) = ai + bi1E(F1) + bi2E(F2)+ .+ binE(Fn)+ ei Ri - E(Ri) = bi1(F1 - E(F1)) + bi2(F2 - E(F2)) +... + bin(Fn - E(Fn)) +ei or Ri = E(Ri) + bi1f1 + bi2f2 + ….+ binfn + ei where fj = Fj - E(Fj): unanticipated change in Fj In Equilibrium: E(Ri) = 0 + bi11 + bi2 binn where 0 = Rf, 1, 2 … n are the risk premiums associated with each factor.

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**Roll & Ross and their four factors**

E(Ri) = Rf + Unexp Change in Inflation Unexp Change in Industrial Prod. Unexp Change in bond risk premium Unexp Change in yield curve

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