In-Sample and Out-of-Sample Sharpe Ratios of Multi-Factor Asset Pricing Models

Abstract

For many multi-factor asset pricing models proposed in the recent literature, their implied tang-ency portfolios have substantially higher sample Sharpe ratios than that of the value-weighted market portfolio. In contrast, such high sample Sharpe ratio is rarely delivered by professional fund managers. This makes it difficult for us to justify using these asset pricing models for performance evaluation. In this paper, we explore if estimation risk can explain why the high sample Sharpe ratios of asset pricing models are difficult to realize in reality. In particular, we provide finite sample and asymptotic analyses of the joint distribution of in-sample and out-of-sample Sharpe ratios of a multi-factor asset pricing model. For an investor who does not know the mean and co-variance matrix of the factors in a model, the out-of-sample Sharpe ratio of an asset pricing model is substantially worse than its in-sample Sharpe ratio. After taking into account of estimation risk, our analysis suggests that many of the newly proposed asset pricing models do not provide superior out-of-sample performance than the value-weighted market portfolio.