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

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  • Suleyman Basak
  • Alex Shapiro

Abstract

This article analyzes optimal, dynamic portfolio and wealth/consumption policies of utility maximizing investors who must also manage market-risk exposure using Value-at-Risk (VaR). We 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 amplifies the stock-market volatility at times of down markets and attenuates the volatility at times of up markets. Article published by Oxford University Press on behalf of the Society for Financial Studies in its journal, The Review of Financial Studies.

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Paper provided by Wharton School Rodney L. White Center for Financial Research in its series Rodney L. White Center for Financial Research Working Papers with number 06-99.

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Handle: RePEc:fth:pennfi:06-99

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  1. 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.
  2. Grossman, S.J. & Vila, J-L., 1988. "Portfolio Insurance In Complete Markets: A Note," Papers 94, Princeton, Department of Economics - Financial Research Center.
  3. Basak, Suleyman, 1995. "A General Equilibrium Model of Portfolio Insurance," Review of Financial Studies, Society for Financial Studies, vol. 8(4), pages 1059-90.
  4. 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.
  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. Thomas J. Linsmeier & Neil D. Pearson, 1996. "Risk Measurement: An Introduction to Value at Risk," Finance 9609004, EconWPA.
  7. Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
  8. Grossman, Sanford J & Zhou, Zhongquan, 1996. " Equilibrium Analysis of Portfolio Insurance," Journal of Finance, American Finance Association, vol. 51(4), pages 1379-1403, September.
  9. 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.
  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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