Portfolio Selection with Multiple Spectral Risk Constraints

20 Pages Posted: 15 Nov 2012 Last revised: 25 Mar 2015

See all articles by Carlos Abad

Carlos Abad

Columbia University - Department of Industrial Engineering and Operations Research (IEOR)

Garud Iyengar

Columbia University - Department of Industrial Engineering and Operations Research (IEOR)

Date Written: March 13, 2015

Abstract

We propose an iterative gradient-based algorithm to efficiently solve the portfolio selection problem with multiple spectral risk constraints. Since the conditional value at risk (CVaR) is a special case of the spectral risk measure, our algorithm solves portfolio selection problems with multiple CVaR constraints. In each step, the algorithm solves very simple separable convex quadratic programs; hence, we show that the spectral risk constrained portfolio selection problem can be solved using the technology developed for solving mean-variance problems. The algorithm extends to the case where the objective is a weighted sum of the mean return and either a weighted combination or the maximum of a set of spectral risk measures. We report numerical results that show that our proposed algorithm is very efficient; it is at least one order of magnitude faster than the state-of-the-art general purpose solver for all practical instances. One can leverage this efficiency to be robust against model risk by including constraints with respect to several different risk models.

Keywords: large scale portfolio optimization, coherent risk measures, first-order algorithms

JEL Classification: C61, C63, G11

Suggested Citation

Abad, Carlos and Iyengar, Garud, Portfolio Selection with Multiple Spectral Risk Constraints (March 13, 2015). Advanced Risk & Portfolio Management Paper. Available at SSRN: https://ssrn.com/abstract=2175038 or http://dx.doi.org/10.2139/ssrn.2175038

Carlos Abad (Contact Author)

Columbia University - Department of Industrial Engineering and Operations Research (IEOR) ( email )

321 S.W. Mudd Building
500 West 120th Street
New York, NY 10027
United States

Garud Iyengar

Columbia University - Department of Industrial Engineering and Operations Research (IEOR) ( email )

331 S.W. Mudd Building
500 West 120th Street
New York, NY 10027
United States
+1 212-854-4594 (Phone)
+1 212-854-8103 (Fax)

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