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Optimal Dynamic Trading Strategies with Risk Limits

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  • Domenico Cuoco
  • Hua He
  • Sergei Isaenko

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.

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Bibliographic Info

Paper provided by Yale School of Management in its series Yale School of Management Working Papers with number amz2567.

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Date of creation: 01 Jul 2004
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Handle: RePEc:ysm:somwrk:amz2567

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

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References

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  1. Basak, Suleyman & Shapiro, Alexander, 2001. "Value-at-Risk-Based Risk Management: Optimal Policies and Asset Prices," Review of Financial Studies, Society for Financial Studies, vol. 14(2), pages 371-405.
  2. Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
  3. Alexander, Gordon J. & Baptista, Alexandre M., 2002. "Economic implications of using a mean-VaR model for portfolio selection: A comparison with mean-variance analysis," Journal of Economic Dynamics and Control, Elsevier, vol. 26(7-8), pages 1159-1193, July.
  4. Dong-Hyun Ahn & Jacob Boudoukh & Matthew Richardson & Robert F. Whitelaw, 1999. "Optimal Risk Management Using Options," Journal of Finance, American Finance Association, vol. 54(1), pages 359-375, 02.
  5. Susanne Emmer & Claudia Kl├╝ppelberg & Ralf Korn, 2001. "Optimal Portfolios with Bounded Capital at Risk," Mathematical Finance, Wiley Blackwell, vol. 11(4), pages 365-384.
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Cited by:
  1. Lioui, Abraham & Poncet, Patrice, 2013. "Optimal benchmarking for active portfolio managers," European Journal of Operational Research, Elsevier, vol. 226(2), pages 268-276.
  2. Das, Sanjiv R. & Statman, Meir, 2013. "Options and structured products in behavioral portfolios," Journal of Economic Dynamics and Control, Elsevier, vol. 37(1), pages 137-153.
  3. Hugonnier, Julien, 2012. "Rational asset pricing bubbles and portfolio constraints," Journal of Economic Theory, Elsevier, vol. 147(6), pages 2260-2302.
  4. Alexander, Gordon J. & Baptista, Alexandre M. & Yan, Shu, 2012. "When more is less: Using multiple constraints to reduce tail risk," Journal of Banking & Finance, Elsevier, vol. 36(10), pages 2693-2716.
  5. Diana Barro & Elio Canestrelli, 2012. "Dynamic tracking error with shortfall control using stochastic programming," Working Papers 2012_18, Department of Economics, University of Venice "Ca' Foscari", revised 2012.
  6. Fulbert, Tchana Tchana & Georges, Tsafack, 2013. "The Implications of VaR and Short-Selling Restrictions on the Portfolio Manager Performance," MPRA Paper 43797, University Library of Munich, Germany.

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