Optimal Dynamic Trading Strategies with Risk Limits
AbstractValue 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.
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Bibliographic InfoPaper provided by Yale School of Management in its series Yale School of Management Working Papers with number amz2567.
Date of creation: 01 Jul 2004
Date of revision:
Risk management; value at risk; tail conditional expectation;
Other versions of this item:
- Domenico Cuoco & Hua He & Sergei Issaenko, 2001. "Optimal Dynamic rading Strategies with Risk Limits," FAME Research Paper Series rp60, International Center for Financial Asset Management and Engineering.
- D91 - Microeconomics - - Intertemporal Choice - - - Intertemporal Household Choice; Life Cycle Models and Saving
- D92 - Microeconomics - - Intertemporal Choice - - - Intertemporal Firm Choice, Investment, Capacity, and Financing
- G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
- C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
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