Extreme Risk Management
Lisa R. Goldberg
University of California, Berkeley; Aperio Group
Michael Y. Hayes
University of Michigan, Stephen M. Ross School of Business
February 17, 2009
MSCI Barra Research Paper No. 2009-4
Quantitative risk management relies on a constellation of tools that are used to analyze portfolio risk. We develop the standard toolkit, which includes betas, risk budgets and correlations, in a general, coherent, mnemonic framework centered around marginal risk contributions. We apply these tools to generate side-by-side analyses of volatility and expected shortfall, which is a measure of average portfolio excess of value-at-risk. We focus on two examples whose importance is highlighted by the current economic crisis. By examining downside protection provided by an out-of-the-money put option we show that the diversification benefit of the option is greater for a risk measure that is more highly concentrated in the tail of the distribution. By comparing two-asset portfolios that are distinguished only by the likelihood of coincident extreme events, we show that expected shortfall measures market contagion in a way that volatility cannot.
Number of Pages in PDF File: 16
Keywords: risk management, quantitative extreme
Date posted: February 12, 2009 ; Last revised: February 19, 2009
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