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.
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v. Puelz, A. (2001). Value-at-Risk Based Portfolio Optimization. In: Uryasev, S., Pardalos, P.M. (eds) Stochastic Optimization: Algorithms and Applications. Applied Optimization, vol 54. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-6594-6_13
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DOI: https://doi.org/10.1007/978-1-4757-6594-6_13
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