This paper revisits the relation between systematic skewness and returns, showing two main findings. First, the systematic skewness premium in individual stocks is time varying. When either skewness preference or systematic skewness is above rather than below the median, the premium is 4% higher. The combined effect of the two induces time variation in the premium of about 7%. Second, systematic skewness has significant additional explanatory power in explaining returns relative to most common characteristics, except size and momentum. These two results imply that skewness preference is an important determinant of expected returns providing a possible rationale for size and momentum.

Recent research has identified skewness and downside risk as one of the most important features of risk. We present a new distribution which makes modeling skewed risks no more difficult than normally distributed (symmetric) risks. Our distribution is a combination of the “downside” and “upside” half of two normal distributions, and its parameters can be calculated in closed form to match a given mean, variance, and skewness. Value at risk, expected shortfall, portfolio weights, and risk premia have simple expressions for our distribution and show economically meaningful deviations from the normal case already for very modest levels of skewness. An empirical application suggests that our distribution fits the data well.

Review of Finance, 2017, 21, 2169–2197. doi:10.1093/rof/rfw040 It has been brought to our attention that the distribution proposed in “A simple skewed distribution with asset pricing application” (Review of Finance, 2017) is not only a special case of Hansen’s (1994) skewed t distribution, as explained in our paper, but that it has also previously been introduced in other fields.1 The distribution has been known under different names in the literature such as “two-piece normal distribution” and “split normal distribution,” and it was first proposed by the psychologist Carl Gustav Fechner in Fechner (1897). As discussed in Wallis (2014), the distribution has since then been rediscovered in physics, statistics, and meteorology.2 While the contribution of our paper in terms of understanding skewness and its effects on value at risk, expected shortfall, portfolio weights, and asset pricing, and the closed-form parameterization of the distribution in our Appendix B is unaffected by this omission, our distribution is not new and should be correctly attributed to Fechner (1897).

Several theoretical studies suggest that coordination problems can cause arbitrageur crowding to push asset prices beyond fundamental value as investors feedback trade on each others’ demands. Using this logic, we develop a crowding model for momentum returns that predicts tail risk when arbitrageurs ignore feedback effects. However, crowding does not generate tail risk when arbitrageurs rationally condition on feedback. Consistent with rational demands, our empirical analysis generally finds a negative relation between crowding proxies constructed from institutional holdings and expected crash risk. Thus our analysis casts both theoretical and empirical doubt on crowding as a stand-alone source of tail risk.

We find that the relation between state variables, such as the t-bill rate and term spread, and consumption growth is time-varying. In the cross-section of U.S. stocks, risk premia for exposure to state variables vary over time accordingly. When a state variable predicts consumption strongly relative to its own history, its annualized risk premium increases by 6% (0.4 in Sharpe ratio). This effect implies that risk premia can switch signs and are increasing in the conditional variance of the state variable. These common drivers of time-varying risk premia are consistent with the Intertemporal CAPM. Benchmark factors contain the same conditional expected return effects as state variable risk premia.