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MaxVaR: Long Horizon Value at Risk in a Mark-to-Market Environment

9 Pages Posted: 26 Mar 2004  

Jacob Boudoukh

Interdisciplinary Center (IDC) Herzliyah - Adelson School of Entrepreneuship

Richard Stanton

University of California, Berkeley - Finance Group

Matthew P. Richardson

New York University (NYU) - Department of Finance; National Bureau of Economic Research (NBER); AQR Capital Management, LLC

Robert Whitelaw

New York University; National Bureau of Economic Research (NBER)

Multiple version iconThere are 2 versions of this paper

Date Written: March 2004

Abstract

The standard VaR approach considers only terminal risk, completely ignoring the sample path of portfolio values. In reality interim risk may be critical in a mark-to-market environment. Sharp declines in value may generate margin calls and affect trading strategies. In this paper we introduce the notion of MaxVaR, analogous to VaR in every way except it quantifies the probability of seeing a given loss on or before the terminal date rather than at the terminal date. Under standard set of assumptions we provide a simple formula for MaxVaR and examine the ratio of MaxVaR to VaR. For reasonable parameterizations MaxVaR may exceed VaR by over 40%. MaxVaR exceeds VaR by as much as 80% or more for high Sharpe Ratio hedge-fund-like return distributions.

Keywords: Value at risk, drawdown risk, long horizon risk

JEL Classification: G00

Suggested Citation

Boudoukh, Jacob and Stanton, Richard and Richardson, Matthew P. and Whitelaw, Robert, MaxVaR: Long Horizon Value at Risk in a Mark-to-Market Environment (March 2004). Available at SSRN: https://ssrn.com/abstract=520805 or http://dx.doi.org/10.2139/ssrn.520805

Jacob Boudoukh (Contact Author)

Interdisciplinary Center (IDC) Herzliyah - Adelson School of Entrepreneuship ( email )

P.O. Box 167
Herzliya, 46150
Israel

Richard H. Stanton

University of California, Berkeley - Finance Group ( email )

Haas School of Business
545 Student Services Building #1900
Berkeley, CA 94720-1900
United States
(510) 642-7382 (Phone)
(510) 643-1412 (Fax)

Matthew P. Richardson

New York University (NYU) - Department of Finance ( email )

44 West 4th Street
Suite 9-190
New York, NY 10012-1126
United States
212-998-0349 (Phone)
212-995-4233 (Fax)

National Bureau of Economic Research (NBER)

1050 Massachusetts Avenue
Cambridge, MA 02138
United States

AQR Capital Management, LLC ( email )

Greenwich, CT
United States

Robert F. Whitelaw

New York University ( email )

Stern School of Business
44 West 4th Street
New York, NY 10012-1126
United States
212-998-0338 (Phone)
212-995-4233 (Fax)

National Bureau of Economic Research (NBER)

1050 Massachusetts Avenue
Cambridge, MA 02138
United States

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