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

TL;DR

This paper introduces a decision-focused learning approach for estimating covariance in global minimum variance portfolios, improving decision quality over traditional methods by directly optimizing portfolio performance.

Contribution

It develops a novel decision-focused learning method for GMVP that leverages the analytic gradient of decision loss, outperforming conventional estimation techniques.

Findings

DFL-based methods outperform traditional estimators in portfolio decisions.

The approach reduces portfolio volatility effectively.

Theoretical derivation of gradient enhances understanding of decision-driven estimation.

Abstract

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.