Financial Risk Measurement and Joint Extreme Events: The Normal, Student-t, and Mixture of Normals | Hanlon Financial Systems Center

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

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

seminar date: 
Thursday, November 21, 2013 - 5:00pm
seminar location: 
Thomas Coleman, PhD, Adjunct Professor of Finance - University of Chicago

We all know that there are more extreme events in the return or P&L distribution than the normal would predict (tails are fat). What receives less attention is that jointly normal random variables become independent far out in the tails, so that joint normality imposes independence on extreme events (except the boundary cases of 1). This independence in the tails potentially 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.

This paper has two objectives. First, to discuss and compare the behavior of four bivariate distributions: the normal, Student-t, two-point mixture of normals, and meta normal / Student-t (normal copula with Student-t marginals). The conclusion is that the Student-t and the two-point mixture of normals both exhibit or approximate tail dependence in a way that the joint normal and meta normal / Student-t do not. Second, to examine, in a limited manner, the empirical behavior of some representative financial assets and compare these with the four distributions discussed.



Thomas Coleman is the author of Quantitative Risk Management, published by Wiley and A Practical Guide to Risk Management published by the Research Foundation of the CFA Institute (the most widely distributed Research Foundation monograph, available for free download

Mr. Coleman is Senior Advisor at the Becker Friedman Institute for Research in Economics at the University of Chicago, a center for the support of inquiry on central questions of economic and social significance. He is also Adjunct Professor of Finance at the University of Chicago Booth School of Business. Prior to returning to academia in 2012, Mr. Coleman worked in the finance industry for over twenty years, with considerable experience in trading, risk management, and quantitative modeling. Positions in the finance arena included head of Quantitative Analysis and Risk Control at Moore Capital Management, Llc (a large multi-asset hedge fund manager) responsible for firm-wide risk management and supporting quantitative infrastructure; a director and founding member of Aequilibrium Investments Ltd., a London-based hedge fund manager, with responsibility for risk management, portfolio management, and research; and a variety of positions on the sell side, with roles in fixed income derivatives research and trading at TMG Financial Products, Lehman Brothers, and S.G. Warburg in London. 

Before entering the financial industry Mr. Coleman was an academic, teaching graduate and undergraduate economics and finance at the State University of New York at Stony Brook. Mr. Coleman earned his PhD in economics from the University of Chicago, and his BA in physics from Harvard. He is the author, together with Roger Ibbotson and Larry Fisher, of Historical U.S. Treasury Yield Curves, and continues to publish in various journals.