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Value-at-Risk Based Portfolio Optimization

  • Amy v. Puelz
Part of the Applied Optimization book series (APOP, volume 54)

Abstract

The Value at Risk (VaR) metric, a widely reported and accepted measure of financial risk across industry segments and market participants, is discrete by nature measuring the probability of worst case portfolio performance. In this paper I present four model frameworks that apply VaR to ex ante portfolio decisions. The mean-variance model, Young’s (1998) minimax model and Hiller and Eckstein’s (1993) stochastic programming model are extended to incorporate VaR. A fourth model, that is new, implements stochastic programming with a return aggregation technique. Performance tests are conducted on the four models using empirical and simulated data. The new model most closely matches the discrete nature of VaR exhibiting statistically superior performance across the series of tests. Robustness tests of the four model forms provides support for the argument that VaR-based investment strategies lead to higher risk decision than those where the severity of worst case performance is also considered.

Keywords

Finance Investment analysis Stochastic Optimization Value at Risk 

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References

  1. [1]
    Bai D., Carpenter T., Mulvey J. (1997), “Making a case for robust optimization”, Management Science, 43, 895–907.zbMATHCrossRefGoogle Scholar
  2. [2]
    Basak S., Shapiro A. (1999), “Value-at-Risk Based Risk Management: Optimal Policies and Asset Prices”, Working paper, The Wharton School.Google Scholar
  3. [3]
    Beder T. S. (1995), “VAR: Seductive but dangerous”, Financial Analysts Journal, Sep/Oct, 12–24.Google Scholar
  4. [4]
    Birge J. R., Rosa C. H. (1995), “Modeling investment uncertainty in the costs of global CO2 emission policy”, European Journal of Operational Research, 83, 466–488.zbMATHCrossRefGoogle Scholar
  5. [5]
    Carido D. R., Kent T., Myers D. H., Stacy C., Sylvanus M., Turner A. L., Watanabe K., Ziemba W. T. (1994), “The Russell-Yasuda Kasai model: An asset/liability model for Japanese insurance company using multistage stochastic programming”, Interfaces, 24, 29–49.CrossRefGoogle Scholar
  6. [6]
    Cariâo D. R., Ziemba W. T. (1998), “Formulation of the RussellYasuda Kasai financial planning model”, Operations Research, 46, 433–449.MathSciNetCrossRefGoogle Scholar
  7. [7]
    Dahl H., Meeraus A., Zenio, S. A. (1993), “Some financial optimization models: I risk management”, in: Financial Optimization, Zenios, ed., Cambridge University Press, Cambridge, 3–36.Google Scholar
  8. [8]
    Duffle D., Pan J. (1997), “An overview of value at risk”, Journal of Derivatives, 4, 7–49.CrossRefGoogle Scholar
  9. [9]
    Golub B., Holmer M., McKendall R., Pohlman L., Zenios S. A. (1995), “A stochastic programming model for money management”, European Journal of Operational Research, 85, 282–296.zbMATHCrossRefGoogle Scholar
  10. [10]
    Hiller R. S., Eckstein J. (1993), “Stochastic dedication: Designing fixed income portfolios using massively parallel benders decomposition”, Management Science, 39, 1422–1438.zbMATHCrossRefGoogle Scholar
  11. [11]
    Holmer M. R., Zenios S. A. (1995), “The productivity of financial intermediation and the technology of financial product management”, Operations Research, 43, 970–982.CrossRefGoogle Scholar
  12. [12]
    Kalin D., Zagst R. (1999), “Portfolio optimization: volatility constraints versus shortfall constraints”, OR Spektrum, 21, 97–122.MathSciNetzbMATHCrossRefGoogle Scholar
  13. [13]
    Koskosidis Y. A., Duarte A. M. (1997), “A scenario-based approach to active asset allocation”, Journal of Portfolio Management, 23, 74–85.CrossRefGoogle Scholar
  14. [14]
    Lucas A., Klaassen P. (1998), “Extreme returns, downside risk, and optimal asset allocation”, Journal of Portfolio Management, 25, 71–79.CrossRefGoogle Scholar
  15. [15]
    Markowitz H. M. (1959), Portfolio Selection: Efficient Diversification of Investments, John Wiley, New York.Google Scholar
  16. [16]
    McKay R., Keefer T.E. (1996), “VaR is a dangerous technique”, Corporate Finance - Searching for systems integration supplement, 30.Google Scholar
  17. [17]
    Mulvey J. M., Vanderbei R. J., Zenios S. A. (1995), “Robust optimization of large-scale systems”, Operations Research, 43, 264281.Google Scholar
  18. [18]
    Pritsker M. (1997), “Evaluating value at risk methodoligies: Accuracy versus computational time”, Journal of Financial Services Research, 12, 201–242.CrossRefGoogle Scholar
  19. [19]
    Puelz A. v. (1999), “Stochastic convergence model for portfolio selection”, working paper.Google Scholar
  20. [20]
    Simons K. (1996), “Value at risk - new approaches to risk management”, New England Economic Review Sep/Oct, 3–13.Google Scholar
  21. [21]
    Stambaugh F. (1996), “Risk and value at risk”, European Management Journal, 14, 612–621.CrossRefGoogle Scholar
  22. [22]
    Uryasev S., Rockafellar R. T. (1999), “Optimization of Conditional Value-at-Risk”, Research Report #99–4, Center for Applied Optimization at the University of Florida.Google Scholar
  23. [23]
    Vladimirou H., Zenios S. A. (1997), “Stochastic linear programs with restricted recourse”, European Journal of Operational Research, 101, 177–192.zbMATHCrossRefGoogle Scholar
  24. [24]
    Young M. R. (1998), “A minimax portfolio selection rule with linear programming solution”, Management Science, 44, 673–683.zbMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2001

Authors and Affiliations

  • Amy v. Puelz
    • 1
  1. 1.Edwin L. Cox School of BusinessSouthern Methodist UniversityDallasUSA

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