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Extreme Risk Management

16 Pages Posted: 12 Feb 2009 Last revised: 19 Feb 2009

Lisa R. Goldberg

University of California, Berkeley; Aperio Group

Michael Y. Hayes


Jose Menchero

MSCI Barra

Indrajit Mitra

University of Michigan, Stephen M. Ross School of Business

Date Written: February 17, 2009


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.

Keywords: risk management, quantitative extreme

Suggested Citation

Goldberg, Lisa R. and Hayes, Michael Y. and Menchero, Jose and Mitra, Indrajit, Extreme Risk Management (February 17, 2009). MSCI Barra Research Paper No. 2009-4. Available at SSRN: or

Lisa R. Goldberg (Contact Author)

University of California, Berkeley ( email )

Department of Statistics
367 Evans Hall
Berkeley, CA 94720-3860
United States

Aperio Group ( email )

3 Harbor Drive
Suite 315
Sausalito, CA 94965
United States

Michael Y. Hayes

MSCI Inc. ( email )

2100 Milvia St.
Berkeley, CA 94704
United States

Jose Menchero

MSCI Barra ( email )

555 California Street, Suite 1400
San Francisco, CA 94104
United States

Indrajit Mitra

University of Michigan, Stephen M. Ross School of Business ( email )

701 Tappan Street
Ann Arbor, MI MI 48109
United States

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