The authors test whether empirical factors used in the capital asset pricing model (CAPM), Fama–French model, and their variants have better explanatory power than co-moments, such as co-skewness, in explaining the cross-section of stock returns during crisis periods and noncrisis periods. The authors conduct tests for several crisis periods since 1929. They find that beta and size consistently show strong explanatory power during noncrisis periods, whereas co-skewness becomes significant during crisis periods.

The authors show that empirical factors, specifically beta and size, appear to work well only during normal (i.e., noncrisis) periods. This finding suggests that mechanically applying factor models, such as the CAPM and the Fama–French model, to estimate the cost of equity during crisis periods may yield misleading results.

In addition, some asset managers form their investment strategies using empirical factors. But as the authors’ results show, these factors have low explanatory power during crisis periods, which suggests that any outperformance or underperformance relative to such benchmarks may simply be the result of random chance and not managerial skill. Therefore, during crisis periods, other metrics need to be identified to distinguish managerial skill from luck.

Finally, many financial models use the mean and variance—first and second moments—of stock returns because many models typically assume that stock returns are normally distributed. But this assumption is inconsistent with empirical results that show that stock returns exhibit a higher likelihood of extreme events occurring (i.e., fatter tails). The authors’ results suggest that using the third moment (skewness) in models may help capture tail risk.

The authors seek to demonstrate which competing variables better explain the cross-section of stock returns. They compare empirical factors used in variants of the CAPM and the Fama–French model, such as market capitalization, book-to-market equity ratio, return momentum, and liquidity, with higher-order co-moments of returns. They evaluate how important these factors are during crisis and noncrisis periods.

The authors use monthly data of all stocks in the CRSP database from January 1926 to December 2012 as well as matching book value data from either Compustat (1926–2012) or Kenneth French’s data library (1926–1961). In addition to the stock data, they use the following variables: the CRSP value-weighted index as the market portfolio, the one-month T-bill as the risk-free rate, and various factor returns (the difference in the returns of portfolios capturing size, value/growth, momentum, and liquidity).

After sorting the stocks into various portfolios, the authors then perform their analysis around three sample periods: (1) the periods surrounding the 1929 crash and the 1987 crash, (2) the periods surrounding the dot-com bubble in the late 1990s and the recent credit crunch, and (3) the periods outside of two crisis periods between 1926 and 2012. They perform a time-series test of the variation in portfolio and market returns. Then the authors perform two-stage regressions to test the pricing power of variants of the CAPM and the Fama–French model with some specifications augmented to include return momentum, liquidity, and co-skewness.

The results of the authors’ study help highlight a very important point often forgotten in practice: We should not blindly apply models because even extremely useful models do not work all the time. For example, in comparing the cost of equity at the beginning and end of 2008, a mechanical application of the CAPM may lead to the counterintuitive result that a firm’s cost of equity had decreased by the end of the year, when the markets were severely dislocated.