A Scalable Algorithm For Sparse Portfolio Selection

The sparse portfolio selection problem is one of the most famous and frequently-studied problems in the optimization and financial economics literatures. In a universe of risky assets, the goal is to construct a portfolio with maximal expected return and minimum variance, subject to an upper bound o...

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Bibliographic Details
Published in:arXiv.org
Main Authors: Bertsimas, Dimitris, Cory-Wright, Ryan
Format: Paper
Language:English
Published: Ithaca Cornell University Library, arXiv.org 28.03.2021
Subjects:
Algorithms
Approximation
Cutting
Economic conditions
Economic models
Heuristic methods
Linear functions
Lower bounds
Optimization
Performance enhancement
Portfolio management
Representations
Upper bounds
ISSN:2331-8422
Online Access:Get full text
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Summary:The sparse portfolio selection problem is one of the most famous and frequently-studied problems in the optimization and financial economics literatures. In a universe of risky assets, the goal is to construct a portfolio with maximal expected return and minimum variance, subject to an upper bound on the number of positions, linear inequalities and minimum investment constraints. Existing certifiably optimal approaches to this problem do not converge within a practical amount of time at real world problem sizes with more than 400 securities. In this paper, we propose a more scalable approach. By imposing a ridge regularization term, we reformulate the problem as a convex binary optimization problem, which is solvable via an efficient outer-approximation procedure. We propose various techniques for improving the performance of the procedure, including a heuristic which supplies high-quality warm-starts, a preprocessing technique for decreasing the gap at the root node, and an analytic technique for strengthening our cuts. We also study the problem's Boolean relaxation, establish that it is second-order-cone representable, and supply a sufficient condition for its tightness. In numerical experiments, we establish that the outer-approximation procedure gives rise to dramatic speedups for sparse portfolio selection problems.
Bibliography:SourceType-Working Papers-1
ObjectType-Working Paper/Pre-Print-1
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ISSN:2331-8422
DOI:10.48550/arxiv.1811.00138