 | Optimal Dynamic Trading Strategies with Risk Limits
Winner
of the 2002 FAME Research Prize
Authors
Domenico
CUOCO - The Wharton School, University of Pennsylvania
Hua HE
- School of Management,
Yale University
Sergei ISSAENKO - The Wharton School, University
of Pennsylvania
Date
December
2001
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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, and conversely.
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