Estimating Covariance for Global Minimum Variance Portfolio: A Decision-Focused Learning Approach

Fuente: arXiv
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Main Authors: Kim, Juchan, Tae, Inwoo, Lee, Yongjae
Format: Preprint
Published: 2025
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author Kim, Juchan
Tae, Inwoo
Lee, Yongjae
author_facet Kim, Juchan
Tae, Inwoo
Lee, Yongjae
contents Portfolio optimization constitutes a cornerstone of risk management by quantifying the risk-return trade-off. Since it inherently depends on accurate parameter estimation under conditions of future uncertainty, the selection of appropriate input parameters is critical for effective portfolio construction. However, most conventional statistical estimators and machine learning algorithms determine these parameters by minimizing mean-squared error (MSE), a criterion that can yield suboptimal investment decisions. In this paper, we adopt decision-focused learning (DFL) - an approach that directly optimizes decision quality rather than prediction error such as MSE - to derive the global minimum-variance portfolio (GMVP). Specifically, we theoretically derive the gradient of decision loss using the analytic solution of GMVP and its properties regarding the principal components of itself. Through extensive empirical evaluation, we show that prediction-focused estimation methods may fail to produce optimal allocations in practice, whereas DFL-based methods consistently deliver superior decision performance. Furthermore, we provide a comprehensive analysis of DFL's mechanism in GMVP construction, focusing on its volatility reduction capability, decision-driving features, and estimation characteristics.
format Preprint
id arxiv_https___arxiv_org_abs_2508_10776
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Estimating Covariance for Global Minimum Variance Portfolio: A Decision-Focused Learning Approach
Kim, Juchan
Tae, Inwoo
Lee, Yongjae
Portfolio Management
Artificial Intelligence
Portfolio optimization constitutes a cornerstone of risk management by quantifying the risk-return trade-off. Since it inherently depends on accurate parameter estimation under conditions of future uncertainty, the selection of appropriate input parameters is critical for effective portfolio construction. However, most conventional statistical estimators and machine learning algorithms determine these parameters by minimizing mean-squared error (MSE), a criterion that can yield suboptimal investment decisions. In this paper, we adopt decision-focused learning (DFL) - an approach that directly optimizes decision quality rather than prediction error such as MSE - to derive the global minimum-variance portfolio (GMVP). Specifically, we theoretically derive the gradient of decision loss using the analytic solution of GMVP and its properties regarding the principal components of itself. Through extensive empirical evaluation, we show that prediction-focused estimation methods may fail to produce optimal allocations in practice, whereas DFL-based methods consistently deliver superior decision performance. Furthermore, we provide a comprehensive analysis of DFL's mechanism in GMVP construction, focusing on its volatility reduction capability, decision-driving features, and estimation characteristics.
title Estimating Covariance for Global Minimum Variance Portfolio: A Decision-Focused Learning Approach
topic Portfolio Management
Artificial Intelligence
url https://arxiv.org/abs/2508.10776