Optimal Dynamic Trading Strategies with Risk Limits

Operations Research, Vol. 56, pp. 358-368, 2008

26 Pages Posted: 14 Jul 2004 Last revised: 5 Dec 2011

See all articles by Domenico Cuoco

Domenico Cuoco

University of Pennsylvania - Finance Department

Hua He

Yale University - School of Management; Fudan University - International Finance

Sergey Isaenko

Concordia University, Quebec - Department of Finance

Date Written: April 1, 2001

Abstract

Value at Risk (VaR) has emerged in recent years as a standard tool to measure and control the risk of trading portfolios. Yet, existing theoretical analyses of the optimal behavior of a trader subject to VaR limits have produced a negative view of VaR as a risk-control tool. In particular, VaR limits have been found to induce increased risk exposure in some states and an increased probability of extreme losses. However, these conclusions are based on models that are either static or dynamically inconsistent. In this paper, we formulate a dynamically consistent model of optimal portfolio choice subject to VaR limits and show that the conclusions of earlier papers are incorrect if, consistently with common practice, the portfolio VaR is reevaluated dynamically making use of available conditioning information. In particular, we find that the risk exposure of a trader subject to a VaR limit is always lower than that of an unconstrained trader and that the probability of extreme losses is also lower. We also consider risk limits formulated in terms of Tail Conditional Expectation (TCE), a coherent risk measure often advocated as an alternative to VaR, and show that in our dynamic setting it is always possible to transform a TCE limit into an equivalent VaR limit, amid conversely.

Keywords: Risk management, value at risk, tail conditional expectation

JEL Classification: D91, D92, G11, C61

Suggested Citation

Cuoco, Domenico and He, Hua and Isaenko, Sergey, Optimal Dynamic Trading Strategies with Risk Limits (April 1, 2001). Operations Research, Vol. 56, pp. 358-368, 2008. Available at SSRN: https://ssrn.com/abstract=563901

Domenico Cuoco

University of Pennsylvania - Finance Department ( email )

The Wharton School
3620 Locust Walk
Philadelphia, PA 19104
United States

Hua He

Yale University - School of Management ( email )

135 Prospect Street
P.O. Box 208200
New Haven, CT 06520-8200
United States
203-432-6025 (Phone)
203-432-3003 (Fax)

HOME PAGE: http://som.yale.edu/~hh78/

Fudan University - International Finance

Shanghai
China

Sergey Isaenko (Contact Author)

Concordia University, Quebec - Department of Finance ( email )

John Molson School of Business
Concordia University. 1455 de Maisonneuve Blvd.W.
Montreal, Quebec, H3G 1M8
Canada
1-514-848-2424 ext.2797 (Phone)
1-514-848-4500 (Fax)

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