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Value-at-Risk Based Risk Management: Optimal Policies and Asset Prices

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  • Suleyman Basak
  • Alexander Shapiro

Abstract

This paper analyzes optimal, dynamic portfolio and wealth/consumption policies of utility maximizing investors who must also manage market-risk exposure using a given risk-management model. We focus on the industry standard, the Value-at-Risk (VaR) based risk management, and find that VaR risk managers often optimally choose a larger exposure to risky assets than non risk managers, and consequently incur larger losses, when losses occur. We suggest an alternative risk management model, based on the expectation of a loss, to remedy the shortcomings of VaR. A general-equilibrium analysis reveals that the presence of VaR risk managers in a pure-exchange economy amplifies the stock-market volatility at times of down markets (and low output) and attenuates the volatility at times of up markets.

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Bibliographic Info

Paper provided by New York University, Leonard N. Stern School of Business- in its series New York University, Leonard N. Stern School Finance Department Working Paper Seires with number 99-032.

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Date of creation: Oct 1999
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Handle: RePEc:fth:nystfi:99-032

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Postal: U.S.A.; New York University, Leonard N. Stern School of Business, Department of Economics . 44 West 4th Street. New York, New York 10012-1126
Phone: (212) 998-0100
Web page: http://w4.stern.nyu.edu/finance/
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  1. Cox, John C. & Huang, Chi-fu, 1989. "Optimal consumption and portfolio policies when asset prices follow a diffusion process," Journal of Economic Theory, Elsevier, vol. 49(1), pages 33-83, October.
  2. Basak, Suleyman, 1995. "A General Equilibrium Model of Portfolio Insurance," Review of Financial Studies, Society for Financial Studies, vol. 8(4), pages 1059-90.
  3. Grossman, S.J. & Vila, J-L., 1988. "Portfolio Insurance In Complete Markets: A Note," Papers 94, Princeton, Department of Economics - Financial Research Center.
  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. Linsmeier, Thomas J. & Pearson, Neil D., 1996. "Risk measurement: an introduction to value at risk," ACE Reports 14796, University of Illinois at Urbana-Champaign, Department of Agricultural and Consumer Economics.
  6. Brennan, Michael J & Schwartz, Eduardo S, 1989. "Portfolio Insurance and Financial Market Equilibrium," The Journal of Business, University of Chicago Press, vol. 62(4), pages 455-72, October.
  7. Grossman, Sanford J & Zhou, Zhongquan, 1996. " Equilibrium Analysis of Portfolio Insurance," Journal of Finance, American Finance Association, vol. 51(4), pages 1379-1403, September.
  8. Thomas J. Linsmeier & Neil D. Pearson, 1996. "Risk Measurement: An Introduction to Value at Risk," Finance 9609004, EconWPA.
  9. Stulz, ReneM., 1982. "Options on the minimum or the maximum of two risky assets : Analysis and applications," Journal of Financial Economics, Elsevier, vol. 10(2), pages 161-185, July.
  10. Lucas, Robert E, Jr, 1978. "Asset Prices in an Exchange Economy," Econometrica, Econometric Society, vol. 46(6), pages 1429-45, November.
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