Market Proxies as Factors in Linear Asset Pricing Models: Still Living with the Roll Critique

A new model misspecification measure for linear asset pricing models is proposed for the case where misspecification maps to latency of one of the pricing factors; in this case, the market return. This measure is suited both for testing models that include the market return as a pricing factor in a traditional sense (i.e., whether the chosen model does or does not price a collection of risky assets) and ranking those models (i.e., determining which model performs best). The proposed measure is used in pricing portfolios reflecting the size, value, and momentum premia. The conditional CAPM of Jagannathan and Wang (1996) is found to best the performance of both the simple CAPM and the ICAPM of Petkova (2006). Moreover, it is discovered that winner stocks in a momentum portfolio may have higher market betas than loser stocks.