Tail risk management and the skewness premium

Abstract

In this paper, we analyze how tail risk impacts both asset prices and the optimal asset allocation. For this purpose, we consider an equilibrium model with investors exhibiting an empirically well-justifiable decreasing relative risk aversion (DRRA) and different investment horizons. In contrast to the seminal CAPM, two fund separation does no longer hold, and investors not only regard one risk measure such as the standard deviation but additionally care for the size of tail risk. The shorter the investment period, the more prone they are to negatively skewed returns. In particular, short-term investors not only hold a lower equity ratio than (else equal) long-term investors do, but they also reduce the fraction of assets with negative tail risk. Consistently, the more short-term investors are in a market, the higher the tail risk premium is, i.e., the additional expected return due to skewness beyond a given standard deviation. Consequently, these theoretical findings allow us to draw empirical predictions about (i) the drivers of the skewness premium, (ii) characteristics for markets in which the premium is especially severe, and (iii) the optimal investors’ asset allocation.