Evidence on the Characteristics of Cross-sectional Variation in Stock Returns.

Daniel, Kent, and Sheridan Titman, 1997, Evidence on the characteristics of cross-sectional variation in stock returns, Journal of Finance 52, 1-33.

Research Question and General Results

This paper evaluates whether stock return patterns are consistent with a factor model. Authors propose three return-generating models and perform corresponding empirical tests. They find three factors identified by Fama and French (1993) cannot be regarded as compensations for factor risk. Instead, firm characteristics (e.g. book-to-market or market size) determine expected returns of a stock.

Theoretical Models

Model 1:

Returns depend on multiple factors and a separate time-varying distress factor. The book-to-market ratio might serve as a proxy for this distress factor. If the factor premium is positive, firms that load on that distress factor (high book-to-market ratio) should earn a positive risk premium.

Model 2:

The second model eliminates the time-varying distress factor and has a stable covariance matrix (time-invariant factor loadings). However, risk premia on factors vary through time and are negatively correlated with the past performance of firms. If a factor has a negative realization, firms that load on this factor will become distressed and earn a positive risk premium.

Model 3:

The model assumes the same covariance structure as the second. Yet, expected returns rest on observable and time-varying characteristics rather than factor loadings. Hence, there exist firms that both load on a distressed factor and have a relatively low return. The reason is that these firms’ characteristics indicate they are not distressed.

Empirical Results

Covariation Test:

In the model 1, covariances between stocks with high book-to-market ratio should be higher. To determine covariance changes, authors examine the pre-and post-formation return standard deviations of eight portfolios based on book-to market ratio and market capitalization. They find that standard deviations before and after portfolio formations are quite similar, which suggests that common variation is still present before and after firms are in the distress/growth portfolios. Therefore, the supposition that firms load on a separate distress factor is invalid.

Cross-sectional Test:

Models 1 and 2 illustrate returns are dependent on multiple factors and the intercepts in their factor models should be indistinguishable from zero. After controlling size and book-to-market, authors demonstrate the pre-formation factor loadings hardly determine stock returns. Also, the estimated intercepts in each portfolio are statistically different from zero. Besides, authors construct zero-cost characteristic-balanced portfolios that have equal book-to-market ratios and market capitalizations. The model 3 predicts average return from these portfolios should not be different from zero and the estimated intercepts based on Fama-French factor models need to be positive. The empirical results resonate with predictions of model 3.