Market proxies, correlation, and relative mean-variance efficiency: still living with the roll critique

A pricing restriction is developed to test the validity of the CAPM conditional on a prior belief about the correlation between the true market return and the proxy return used in the test. Distinguishing this pricing restriction from competing tests also based upon the relative efficiency of the proxy return is a consideration for the proxy's mismeasurement of the market return. Failure to account for this mismeasurement biases tests of the CAPM towards rejection by overstating the inefficiency of the proxy. A time-varying version of this pricing restriction links mismeasurement of the market return to time-variation in beta. This paper is a revision to Working Paper QAU07-2, "The Relative Efficiency of Endogenous Proxies: Still Living with the Roll Critique."