Optimal Dynamic rading Strategies with Risk Limits
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 ?nd 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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- Suleyman Basak & Alex Shapiro, .
"Value-at-Risk Based Risk Management: Optimal Policies and Asset Prices,"
Rodney L. White Center for Financial Research Working Papers
06-99, Wharton School Rodney L. White Center for Financial Research.
- 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.
- Suleyman Basak & Alexander Shapiro, 1999. "Value-at-Risk Based Risk Management: Optimal Policies and Asset Prices," New York University, Leonard N. Stern School Finance Department Working Paper Seires 99-032, New York University, Leonard N. Stern School of Business-.
- Suleyman Basak & Alex Shapiro, . "Value-at-Risk Based Risk Management: Optimal Policies and Asset Prices," Rodney L. White Center for Financial Research Working Papers 6-99, Wharton School Rodney L. White Center for Financial Research.
- 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.
- 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.
- Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
- Susanne Emmer & Claudia Klüppelberg & Ralf Korn, 2001. "Optimal Portfolios with Bounded Capital at Risk," Mathematical Finance, Wiley Blackwell, vol. 11(4), pages 365-384.
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