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Preprint (Author's original)arXiv.org - Non-exclusive license to distribute, Open
Preprint
Efficient Solution of Portfolio Optimization Problems via Dimension Reduction and Sparsification
21 Jun 2023
Abstract
The Markowitz mean-variance portfolio optimization model aims to balance
expected return and risk when investing. However, there is a significant
limitation when solving large portfolio optimization problems efficiently: the
large and dense covariance matrix. Since portfolio performance can be
potentially improved by considering a wider range of investments, it is
imperative to be able to solve large portfolio optimization problems
efficiently, typically in microseconds. We propose dimension reduction and
increased sparsity as remedies for the covariance matrix. The size reduction is
based on predictions from machine learning techniques and the solution to a
linear programming problem. We find that using the efficient frontier from the
linear formulation is much better at predicting the assets on the Markowitz
efficient frontier, compared to the predictions from neural networks. Reducing
the covariance matrix based on these predictions decreases both runtime and
total iterations. We also present a technique to sparsify the covariance matrix
such that it preserves positive semi-definiteness, which improves runtime per
iteration. The methods we discuss all achieved similar portfolio expected risk
and return as we would obtain from a full dense covariance matrix but with
improved optimizer performance.
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Details
- Title
- Efficient Solution of Portfolio Optimization Problems via Dimension Reduction and Sparsification
- Creators
- Cassidy K BuhlerHande Y Benson
- Resource Type
- Preprint
- Language
- English
- Academic Unit
- Decision Sciences (and Management Information Systems)
- Other Identifier
- 991020635791504721