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Optimal Dynamic Trading Strategies with Risk Limits

Author

Listed:
  • 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.

Suggested Citation

  • Domenico Cuoco & Hua He & Sergei Isaenko, 2004. "Optimal Dynamic Trading Strategies with Risk Limits," Yale School of Management Working Papers amz2567, Yale School of Management.
  • Handle: RePEc:ysm:somwrk:amz2567
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    File URL: http://icfpub.som.yale.edu/publications/2567
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Susanne Emmer & Claudia Klüppelberg & Ralf Korn, 2001. "Optimal Portfolios with Bounded Capital at Risk," Mathematical Finance, Wiley Blackwell, vol. 11(4), pages 365-384.
    4. Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
    5. 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, February.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Jeremy Berkowitz & Peter Christoffersen & Denis Pelletier, 2011. "Evaluating Value-at-Risk Models with Desk-Level Data," Management Science, INFORMS, pages 2213-2227.
    2. Hugonnier, Julien, 2012. "Rational asset pricing bubbles and portfolio constraints," Journal of Economic Theory, Elsevier, vol. 147(6), pages 2260-2302.
    3. 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.
    4. Leitner Johannes, 2007. "Pricing and hedging with globally and instantaneously vanishing risk," Statistics & Risk Modeling, De Gruyter, vol. 25(4/2007), pages 1-22, October.
    5. 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.
    6. Hugonnier, Julien & Prieto, Rodolfo, 2015. "Asset pricing with arbitrage activity," Journal of Financial Economics, Elsevier, vol. 115(2), pages 411-428.
    7. repec:bla:jrinsu:v:84:y:2017:i:2:p:539-565 is not listed on IDEAS
    8. 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.
    9. Xianzhe Chen & Weidong Tian, 2014. "Optimal portfolio choice and consistent performance," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 37(2), pages 453-474, October.
    10. Priscilla Serwaa Nkyira Gambrah & Traian Adrian Pirvu, 2014. "Risk Measures and Portfolio Optimization," Journal of Risk and Financial Management, MDPI, Open Access Journal, vol. 7(3), pages 1-17, September.
    11. 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.
    12. Lioui, Abraham & Poncet, Patrice, 2013. "Optimal benchmarking for active portfolio managers," European Journal of Operational Research, Elsevier, vol. 226(2), pages 268-276.
    13. José Vicente & Aloísio Araújo, 2010. "Social Welfare Analysis in a Financial Economy with Risk Regulation," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 12(3), pages 561-586, June.
    14. repec:bpj:strimo:v:35:y:2018:i:1-2:p:1-21:n:1 is not listed on IDEAS

    More about this item

    Keywords

    Risk management; value at risk; tail conditional expectation;

    JEL classification:

    • D91 - Microeconomics - - Micro-Based Behavioral Economics - - - Role and Effects of Psychological, Emotional, Social, and Cognitive Factors on Decision Making
    • D92 - Microeconomics - - Micro-Based Behavioral Economics - - - 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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