Reviving Beta? Bayesian Test of Efficiency and the CAPM

28 Pages Posted: 10 Jul 2001

Date Written: April 2001


In this paper, we employ a Bayesian framework to test the CAPM while explicitly accounting for the unobservability of the true market portfolio. We derive the posterior model odds ratio for comparing the view that the proxy is perfect (exact efficiency) to the view that its correlation with the market portfolio is less than one (approximate efficiency). We also compare the prior and the posterior expected correlation between the proxy and the market portfolio using a new methodology to choose priors that is both analytically tractable and intuitive. In marked contrast to the existing literature, the main result is that, in general, the data do not provide clear evidence against the CAPM. Posterior correlations are generally high enough to suggest that a belief in approximate efficiency is reasonable. These new results illustrate the importance of carefully choosing priors, and they show that even apparently innocuous assumptions can have unforeseen consequences.

JEL Classification: G12

Suggested Citation

Cremers, K. J. Martijn, Reviving Beta? Bayesian Test of Efficiency and the CAPM (April 2001). EFA 2001 Barcelona Meetings. Available at SSRN: or

K. J. Martijn Cremers (Contact Author)

University of Notre Dame ( email )

P.O. Box 399
Notre Dame, IN 46556-0399
United States

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