Machine learning and portfolio optimization

Ban, G-Y and El Karoui, N E and Lim, A E B (2016) Machine learning and portfolio optimization. Management Science. ISSN 0025-1909 (In Press)

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Abstract

The portfolio optimization model has limited impact in practice due to estimation issues when applied with real data. To address this, we adapt two machine learning methods, regularization and cross-validation, for portfolio optimization. First, we introduce performance-based regularization (PBR), where the idea is to constrain the sample variances of the estimated portfolio risk and return, which steers the solution towards one associated with less estimation error in the performance. We consider PBR for both mean-variance and mean-CVaR problems. For the mean-variance problem, PBR introduces a quartic polynomial constraint, for which we make two convex approximations: one based on rank-1 approximation and another based on a convex quadratic approximation. The rank-1 approximation PBR adds a bias to the optimal allocation, and the convex quadratic approximation PBR shrinks the sample covariance matrix. For the mean-CVaR problem, the PBR model is a combinatorial optimization problem, but we prove its convex relaxation, a QCQP, is essentially tight. We show that the PBR models can be cast as robust optimization problems with novel uncertainty sets and establish asymptotic optimality of both Sample Average Approximation (SAA) and PBR solutions and the corresponding efficient frontiers. To calibrate the right hand sides of the PBR constraints, we develop new, performance-based k-fold cross-validation algorithms. Using these algorithms, we carry out an extensive empirical investigation of PBR against SAA, as well as L1 and L2 regularizations and the equally-weighted portfolio. We find that PBR dominates all other benchmarks for two out of three of Fama-French data sets.

Item Type: Article
Additional Information: © 2016 INFORMS
Subjects: P > Portfolio investment
R > Risk
Subject Areas: Management Science and Operations
DOI: 10.1287/mnsc.2016.2644
Date Deposited: 26 Aug 2016 10:43
Last Modified: 08 Sep 2017 16:24
URI: http://lbsresearch.london.edu/id/eprint/545

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