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Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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TY - JOUR
T1 - Scenario generation for single-period portfolio selection problems with tail risk measures
T2 - coping with high dimensions and integer variables
AU - Fairbrother, Jamie
AU - Turner, Amanda
AU - Wallace, Stein
PY - 2018
Y1 - 2018
N2 - In this paper we propose a problem-driven scenario generation approach to the single-period portfolio selection problem which use 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 which 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, non-elliptical 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 which are gradually tightened, allowing one to telescope onto high quality solutions.
AB - In this paper we propose a problem-driven scenario generation approach to the single-period portfolio selection problem which use 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 which 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, non-elliptical 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 which are gradually tightened, allowing one to telescope onto high quality solutions.
KW - stochastic programming
KW - scenario generation
KW - portfolio selection
KW - risk measures
U2 - 10.1287/ijoc.2017.0790
DO - 10.1287/ijoc.2017.0790
M3 - Journal article
VL - 30
SP - 472
EP - 491
JO - INFORMS Journal on Computing
JF - INFORMS Journal on Computing
SN - 1091-9856
IS - 3
ER -