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Risk-adjusted probability measures in portfolio optimization with coherent measures of risk

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  • Miller, Naomi
  • Ruszczynski, Andrzej

Abstract

We consider the problem of optimizing a portfolio of n assets, whose returns are described by a joint discrete distribution. We formulate the mean-risk model, using as risk functionals the semideviation, deviation from quantile, and spectral risk measures. Using the modern theory of measures of risk, we derive an equivalent representation of the portfolio problem as a zero-sum matrix game, and we provide ways to solve it by convex optimization techniques. In this way, we reconstruct new probability measures which constitute part of the saddle point of the game. These risk-adjusted measures always exist, irrespective of the completeness of the market. We provide an illustrative example, in which we derive these measures in a universe of 200 assets and we use them to evaluate the market portfolio and optimal risk-averse portfolios.

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Bibliographic Info

Article provided by Elsevier in its journal European Journal of Operational Research.

Volume (Year): 191 (2008)
Issue (Month): 1 (November)
Pages: 193-206

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Handle: RePEc:eee:ejores:v:191:y:2008:i:1:p:193-206

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Web page: http://www.elsevier.com/locate/eor

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Cited by:
  1. Topaloglou, Nikolas & Vladimirou, Hercules & Zenios, Stavros A., 2011. "Optimizing international portfolios with options and forwards," Journal of Banking & Finance, Elsevier, vol. 35(12), pages 3188-3201.
  2. Xue, Jing-Hao & Titterington, D. Michael, 2011. "The p-folded cumulative distribution function and the mean absolute deviation from the p-quantile," Statistics & Probability Letters, Elsevier, vol. 81(8), pages 1179-1182, August.
  3. Borgonovo, Emanuele & Gatti, Stefano, 2013. "Risk analysis with contractual default. Does covenant breach matter?," European Journal of Operational Research, Elsevier, vol. 230(2), pages 431-443.
  4. Balbás, Alejandro & Balbás, Beatriz & Balbás, Raquel, 2010. "CAPM and APT-like models with risk measures," Journal of Banking & Finance, Elsevier, vol. 34(6), pages 1166-1174, June.
  5. Bigi, Giancarlo & Castellani, Marco & Pappalardo, Massimo & Passacantando, Mauro, 2013. "Existence and solution methods for equilibria," European Journal of Operational Research, Elsevier, vol. 227(1), pages 1-11.
  6. Lizyayev, Andrey & Ruszczyński, Andrzej, 2012. "Tractable Almost Stochastic Dominance," European Journal of Operational Research, Elsevier, vol. 218(2), pages 448-455.
  7. Włodzimierz Ogryczak & Tomasz Śliwiński, 2011. "On solving the dual for portfolio selection by optimizing Conditional Value at Risk," Computational Optimization and Applications, Springer, vol. 50(3), pages 591-595, December.
  8. Balbás, Alejandro & Balbás, Beatriz & Heras, Antonio, 2011. "Stable solutions for optimal reinsurance problems involving risk measures," European Journal of Operational Research, Elsevier, vol. 214(3), pages 796-804, November.
  9. Alejandro Balbás & Beatriz Balbás & Antonio Heras, 2010. "Stability of the optimal reinsurance with respect to the risk measure," Business Economics Working Papers wb100201, Universidad Carlos III, Departamento de Economía de la Empresa.

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