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

Abstract

Using available return data, many multi-factor asset pricing models present impressive in-sample Sharpe ratios, significantly surpassing that of the market portfolio. Such a performance, however, contradicts the conventional wisdom in finance. Investors cannot realistically attain the in-sample Sharpe ratios. They obtain the out-of-sample Sharpe ratios, which are significantly lower. Estimation risk is one reason for this performance deterioration. We theoretically study the effect of estimation risk by obtaining the exact distributions of in-sample and out-of-sample Sharpe ratios, and argue that such effect needs to be considered in model comparisons.

Keywords: asset pricing model; Sharpe ratio; estimation risk; model comparison; exact and asymptotic distributions; stochastic representation

JEL Classification: C10; C11; G11; G12