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

22 Pages Posted: 17 May 2014

See all articles by Thomas Coleman

Thomas Coleman

University of Chicago - Irving B. Harris Graduate School of Public Policy Studies; Close Mountain Advisors LLC

Date Written: January 29, 2014

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

Suggested Citation

Coleman, Thomas, Financial Risk Measurement and Joint Extreme Events: The Normal, Student-T, and Mixture of Normals (January 29, 2014). Available at SSRN: https://ssrn.com/abstract=2437672 or http://dx.doi.org/10.2139/ssrn.2437672

Thomas Coleman (Contact Author)

University of Chicago - Irving B. Harris Graduate School of Public Policy Studies ( email )

1155 East 60th Street
Chicago, IL 60637
United States

Close Mountain Advisors LLC ( email )

19 Davenport Ave.
Unit B
Greenwich, CT 06830
United States

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