Tail Risk Attribution

Abstract

Tail risk refers to the shape of the left tail of the distribution of investment returns. Return distributions are traditionally described in terms of their first for moments: mean return, volatility, skewness and kurtosis. Attribution is a descriptive approach used in portfolio analysis to explain a certain magnitude as the sum of contributions from portfolio constituents as well as contributions from constituent attributes. In this research note, we propose a tail risk attribution methodology which allows to explain portfolio modified value-at-risk in terms of contributions from assets as well as mean, volatility, skewness and kurtosis. The approach is free of any residuals.

Keywords: tail risk, attribution, modified VaR, value-at-risk, normal VaR, risk contribution, Euler theorem, linear homogeneous