In this paper we study some prominent downside risk measures for heavy tailed distribution. Using the notion of regular variation to define heavy tailed distributions we provide approximations of the risk measures in the tail region. We show that the downside risk measures produce similar and consistent ranking of risk. However, Expected Shortfall may not always distinguish between the differing risk levels of assets.

downside risk measures, heavy tailed distribution, regular variation
Criteria for Decision-Making under Risk and Uncertainty (jel D81), Portfolio Choice; Investment Decisions (jel G11),
Economics Letters
Erasmus School of Economics

Daníelsson, J, Jorgensen, B.N, Sarma, M, & de Vries, C.G. (2006). Comparing downside risk measures for heavy tailed. Economics Letters, 92(2), 202–208. doi:10.1016/j.econlet.2006.02.004