Assessing the Size of Asset Pricing Tests under Perfect Ex Ante Efficiency

Abstract

The capital asset-pricing model (CAPM) asserts that in equilibrium the market portfolio is the tangency portfolio of the efficient frontier spanned by all risky assets. Conceptually, the tangency portfolio represents an ex ante efficient portfolio, while the market portfolio represents an ex post one. In practice, these two portfolios differ in that the value-weighted market portfolio corresponds to a buy-and-hold investment strategy, whereas the tangency portfolio relates to a constant-weight rebalanced strategy. Traditional tests of (ex ante) portfolio efficiency (e.g., the famous test of Gibbons, Ross, and Shanken (GRS, 1989)), however, have mostly focused on the efficiency of the market portfolio. Hence, the size of such tests are distorted because the tests are not correctly specified for the underlying null hypothesis of ex ante efficiency. Using simulations, we find that traditional tests, including the GRS and the GMM tests, seriously overreject the efficiency of the market portfolio under various ditributional specifications. The over-rejection problem is especially severe when the efficiency of the value-weighted market portfolio is tested with respect to equal-weighted portfolios.