A model that includes a factor that captures news related to future Gross Domestic Product (GDP) growth along with the market factor can explain the cross-section of equity returns about as well as the Fama-French model can. Furthermore, the Fama-French factors HML and SMB appear to contain mainly news related to future GDP growth. When news related to future GDP growth is present in the asset-pricing model, HML and SMB lose much of their ability to explain the cross-section.

We test whether the profitability of HML, SMB, and WML can be linked to future Gross Domestic Product (GDP) growth. Using data from ten countries, we find that HML and SMB contain significant information about future GDP growth. This information is to a large degree independent of that in the market factor. Even in the presence of popular business cycle variables, HML and SMB retain their ability to predict future economic growth in some countries. Our results support a risk-based explanation for the performance of HML and SMB. Little evidence is found to support such an explanation in the case of WML.

This paper proposes modified versions of the Sharpe ratio and Jensen's alpha, which are appropriate in a simple continuous-time model. Both are derived from optimal portfolio selection. The modified Sharpe ratio equals the ordinary Sharpe ratio plus half of the volatility of the fund. The modified alpha also differs from the ordinary alpha by a second-moment adjustment. The modified and the ordinary Sharpe ratios may rank funds differently. In particular, if two funds have the same ordinary Sharpe ratio, then the one with the higher volatility will rank higher according to the modified Sharpe ratio. This is justified by the underlying dynamic portfolio theory. Unlike their discrete-time versions, the continuous-time performance measures take into account that it is optimal for investors to change the fractions of their wealth held in the fund vs. the riskless asset over time.

This is the first study that uses Merton's (1974) option pricing model to compute default measures for individual firms and assess the effect of default risk on equity returns. The size effect is a default effect, and this is also largely true for the book‐to‐market (BM) effect. Both exist only in segments of the market with high default risk. Default risk is systematic risk. The Fama–French (FF) factors SMB and HML contain some default‐related information, but this is not the main reason that the FF model can explain the cross section of equity returns.