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Bayesian inference in asset pricing tests

Journal of Financial Economics, 26 (1990): 221-254

Campbell R. Harvey

Duke University, Durham, NC 27708, USA

Guofu Zhou

Washington University, St. Louis, MO 63130, USA


We test the mean-variance efficiency of a given portfolio using a Bayesian framework. Our test is more direct than Shanken's (1987b), because we impose a prior on all the parameters of the multivariate regression model. The approach is also easily adapted to other problems. We use Monte Carlo numerical integration to accurately evaluate 90-dimensional integrals. Posterior-odds ratios are calculated for 12 industry portfolios from 1926-1987. The sensitivity of the inferences to the prior is investigated by using three different distributions. The Probability that the given portfolio is mean-variance efficient is small for a range of plausible priors.