A Simple Skewed Distribution with Asset Pricing Applications

Abstract

Abstract 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.