Roll's critique

Roll's critique is a famous analysis of the validity of empirical tests of the capital asset pricing model (CAPM) by Richard Roll. It concerns methods to formally test the statement of the CAPM, the equation

This equation relates the asset expected return ${\displaystyle E(R_{i})}$ to the asset covariance ${\displaystyle \beta _{im}}$ with the market portfolio return ${\displaystyle R_{m}}$. The market return is defined as the wealth-weighted sum of all investment returns in the economy.

Roll's critique makes two statements regarding the market portfolio:

1. Mean-Variance Tautology: Any mean-variance efficient portfolio ${\displaystyle R_{p}}$ satisfies the CAPM equation exactly:

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