Scenario Generation for Single-Period Portfolio Selection Problems with Tail Risk Measures: Coping with High Dimensions and Integer Variables

Jamie Fairbrother (), Amanda Turner () and Stein Wallace
Additional contact information
Jamie Fairbrother: STOR-i Centre for Doctoral Training, Lancaster University, Lancaster LA1 4YR, United Kingdom
Amanda Turner: STOR-i Centre for Doctoral Training, Lancaster University, Lancaster LA1 4YR, United Kingdom

INFORMS Journal on Computing, 2018, vol. 30, issue 3, 472-491

Abstract: In this paper, we propose a problem-driven scenario-generation approach to the single-period portfolio selection problem that uses tail risk measures such as conditional value-at-risk. Tail risk measures are useful for quantifying potential losses in worst cases. However, for scenario-based problems, these are problematic: because the value of a tail risk measure only depends on a small subset of the support of the distribution of asset returns, traditional scenario-based methods, which spread scenarios evenly across the whole support of the distribution, yield very unstable solutions unless we use a very large number of scenarios. The proposed approach works by prioritizing the construction of scenarios in the areas of a probability distribution that correspond to the tail losses of feasible portfolios. The proposed approach can be applied to difficult instances of the portfolio selection problem characterized by high dimensions, nonelliptical distributions of asset returns, and the presence of integer variables. It is also observed that the methodology works better as the feasible set of portfolios becomes more constrained. Based on this fact, a heuristic algorithm based on the sample average approximation method is proposed. This algorithm works by adding artificial constraints to the problem that are gradually tightened, allowing one to telescope onto high-quality solutions.

Keywords: stochastic programming; scenario generation; portfolio selection; risk measures (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (2)

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https://doi.org/10.1287/ijoc.2017.0790 (application/pdf)

Related works:
Working Paper: Scenario generation for single-period portfolio selection problems with tail risk measures: coping with high dimensions and integer variables (2017)
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Persistent link: https://EconPapers.repec.org/RePEc:inm:orijoc:v:30:y:2018:i:3:p:472-491

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