Value-at-Risk Based Portfolio Optimization
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.
KeywordsFinance Investment analysis Stochastic Optimization Value at Risk
Unable to display preview. Download preview PDF.
- Basak S., Shapiro A. (1999), “Value-at-Risk Based Risk Management: Optimal Policies and Asset Prices”, Working paper, The Wharton School.Google Scholar
- Beder T. S. (1995), “VAR: Seductive but dangerous”, Financial Analysts Journal, Sep/Oct, 12–24.Google Scholar
- 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
- Markowitz H. M. (1959), Portfolio Selection: Efficient Diversification of Investments, John Wiley, New York.Google Scholar
- McKay R., Keefer T.E. (1996), “VaR is a dangerous technique”, Corporate Finance - Searching for systems integration supplement, 30.Google Scholar
- Mulvey J. M., Vanderbei R. J., Zenios S. A. (1995), “Robust optimization of large-scale systems”, Operations Research, 43, 264281.Google Scholar
- Puelz A. v. (1999), “Stochastic convergence model for portfolio selection”, working paper.Google Scholar
- Simons K. (1996), “Value at risk - new approaches to risk management”, New England Economic Review Sep/Oct, 3–13.Google Scholar
- 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