Estimating Covariance for Global Minimum Variance Portfolio: A Decision-Focused Learning Approach
This work addresses risk management in finance by improving portfolio optimization, though it is incremental as it adapts an existing decision-focused learning approach to a specific domain.
The paper tackled the problem of suboptimal investment decisions in portfolio optimization by applying decision-focused learning to estimate covariance for the global minimum-variance portfolio, showing that this approach consistently delivers superior decision performance compared to prediction-focused methods.
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.