77Roll-notes-A Critique of the Asset Pricing Theory's Tests

77Roll-notes-A Critique of the Asset Pricing Theory's Tests...

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Roll R. Journal of Financial Economics , 4, 129-176 (1977). ciency and the CAPM cannot be tested separately, i.e., tests of CAPM is always a joint test of ME ± CAPM. Roll argues that if any ex-post mean variance e cient portfolio is selected as the market portfolio and betas are computed using this as the market proxy, then the following must hold. Where P is the proxy for the market portfolio, r p is the expected return on the proxy for the market portfolio, β ip is the beta for security i with the proxy market portfolio, and r zp is the minimum variance portfolio that has a zero beta with the market proxy portfolio. r i = r zp + β ip ( r p r zp ) (1) To calculate (optimal) fund F, we need max tg θ = P n i =1 w i ( r i r f ) / ( P n ij =1 σ ij w i w j ) 2 . Note that w i ( P n ij =1 σ ij w i w j )=2 P n j =1 σ ij w j . Let λ = P n i =1 w i ( r i r f ) / P n ij
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77Roll-notes-A Critique of the Asset Pricing Theory's Tests...

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