Risk Measures for Investment Values and Returns Based on Skewed-Heavy Tailed Distributions: Analytical Derivations and Comparison

Abstract

The skewed generalized t (SGT) displays an exceptional ability in modelling the tails of the empirical distributions of returns of financial and other assets. This feature makes it an appealing candidate for the computation of value at risk and expected shortfall measures, used by regulators, investors, portfolio managers and actuaries to measure and manage the risk exposure of their assets. This paper makes a specific contribution by deriving the analytical equations for the computation of value at risk, expected shortfall and downside risk measures for asset values and returns based on the SGT distribution. An assessment using simulations and estimation show that risk measures based on returns overestimate risk exposure.