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Optimizing Measures of Risk: A Simplex-like Algorithm

Author

Listed:
  • Alejandro Balbás

    () (Universidad Carlos III)

  • Raquel Balbás Universidad

    (Autónoma de Madrid)

  • Silvia Mayoral

    () (Universidad de Navarra)

Abstract

The minimization of general risk or dispersion measures is becoming more and more important in Portfolio Choice Theory. There are two major reasons. Firstly, the lack of symmetry in the returns of many assets provokes that the classical optimization of the standard deviation may lead to dominated strategies, from the point of view of the second order stochastic dominance. Secondly, but not less important, many institutional investors must respect legal capital requirements, which may be more easily studied if one deals with a risk measure related to capital losses. This paper proposes a new method to simultaneously minimize several risk or dispersion measures. The representation theorems of risk measures are applied to transform the general risk minimization problem in a minimax problem, and later in a linear programming problem between infinite-dimensional Banach spaces. Then, new necessary and sufficient optimality conditions are stated and a simplex-like algorithm is developed. The algorithm solves the dual (and therefore the primal) problem and provides both optimal portfolios and their sensitivities. The approach is general enough and does not depend on any particular risk measure, but some of the most important cases are specially analyzed.

Suggested Citation

  • Alejandro Balbás & Raquel Balbás Universidad & Silvia Mayoral, 2006. "Optimizing Measures of Risk: A Simplex-like Algorithm," Faculty Working Papers 11/06, School of Economics and Business Administration, University of Navarra.
  • Handle: RePEc:una:unccee:wp1106
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    Keywords

    Risk Measure. Deviation Measure. Portfolio Selection. Infinite-Dimensional Linear Programming. Simpl;

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics

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