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Published byJacey Crossman Modified about 1 year ago

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1 Tests of CAPM Security Market Line (ex ante) E(R i ) = R f + B i (E(R M ) - R f ) SML in terms of historical returns (ex post) R i = R f + b i (R M - R f ) Assumes: b values are true estimates for B Index we use is the market portfolio CAPM is correct Regression tests: R i = a 0 + a 1 b i + e i a 0 should not be different from R f a 1 should be R m - R f R i and beta should be linearly related No variable other then b i should explain R

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2 Tests of CAPM Early Studies: Black, Jensen and Scholes (1972) Fama and MacBeth (1973) Findings: - a 0 is higher than R f, a1 is smaller than R M - R f - 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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3 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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4 Arbitrage Pricing Theory Return generating process: R i = a i + b i1 F 1 + b i2 F 2 + ….+ b in F n + e i Taking expectations: E(R i ) = a i + b i1 E(F 1 ) + b i2 E(F 2 )+.+ b in E(F n )+ e i R i - E(R i ) = b i1 (F 1 - E(F 1 )) + b i2 (F 2 - E(F 2 )) b in (F n - E(F n )) +e i or R i = E(R i ) + b i1 f 1 + b i2 f 2 + ….+ b in f n + e i where f j = F j - E(F j ): unanticipated change in F j In Equilibrium: E(R i ) = 0 + b i1 1 + b i b in n where 0 = R f, 1, 2 … n are the risk premiums associated with each factor.

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5 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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