An L_1 then L_0 approach to the cardinality constrained mean-variance and mean-CVaR portfolio optimization problems

Cardinality constrained portfolio optimization problems are widely used portfolio optimization models which incorporate restriction on the number of assets in the portfolio. Being mixed-integer programming problems make them NP-hard thus computationally challenging, specially for large number of ass...

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Bibliographic Details
Published in:Mathematics and Modeling in Finance 2024-07, Vol.4 (1), p.97-113
Main Authors: Maziar Salahi, Tahereh Khodamoradi
Format: Article
Language:English
Subjects:
cardinality constraint
mean-cvar
portfolio optimization
Online Access:Get full text
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Summary:Cardinality constrained portfolio optimization problems are widely used portfolio optimization models which incorporate restriction on the number of assets in the portfolio. Being mixed-integer programming problems make them NP-hard thus computationally challenging, specially for large number of assets. In this paper, we consider cardinality constrained mean-variance (CCMV) and cardinality constrained mean-CVaR (CCMCVaR) models and propose a hybrid algorithm to solve them. At first, it solves the relaxed model by replacing L_0-norm, which bounds the number of assets, by L_1-norm. Then it removes those assets that do not significantly contribute on the portfolio and apply the original CCMV or CCMCVaR model to the remaining subset of assets. To deal with the large number of scenarios in the CCMCVaR model, conditional scenario reduction technique is applied. Computational experiments on 3 large data sets show that the proposed approach is competitive with the original models from risk, return and Sharpe ratio perspective while being significantly faster.
ISSN:2783-0578
2783-056X
DOI:10.22054/jmmf.2024.78407.1125