Financial Risk Measurement and Joint Extreme Events: The Normal, Student-T, and Mixture of Normals

Abstract

We all know that the normal distribution does a poor job of representing the tails of the distribution for financial returns or P&L in the univariate case - observed distributions have fat tails. What receives less attention is that for a joint normal distribution events in the tails look as if they are independent: Extreme events will not occur together, whatever the correlation (except for the boundary cases of ±1). This has important implications because it is precisely the occurrence of joint losses in multiple assets that are most important for generating large overall losses. And it is generally accepted that, empirically, financial assets do exhibit joint extreme behavior.

Keywords: Risk management, extreme events, fat tails, fait-tailed distribution, extreme value theory

JEL Classification: g10, c10