Decision-focused Sparse Tangent Portfolio Optimization
2026-07-01 • Machine Learning
Machine Learning
AI summaryⓘ
The authors address the problem of creating simple and effective investment portfolios that maximize returns relative to risk, while limiting the number of assets included. Since directly solving this problem is very hard, they develop a new learning approach that smoothly selects a fixed number of assets and integrates prediction with portfolio optimization. Their method allows the model to better focus on actual investment performance rather than just prediction accuracy. Tests across multiple stock markets show that their approach often leads to portfolios with better risk-adjusted returns, especially when many assets are considered.
Sparse portfolio optimizationTangency portfolioMean-variance frontierSharpe ratioCardinality constraintConvex programmingDecision-focused learningGradient flowTop-k operatorOut-of-sample performance
Authors
Haeun Jeon, Seunghoon Choi, Hyunglip Bae, Yongjae Lee, Woo Chang Kim
Abstract
Sparse tangent portfolio optimization aims to learn an interpretable, low-cardinality portfolio in the tangency direction of the mean-variance frontier. However, the associated cardinality-constrained formulation is NP-hard, and standard predict-then-optimize pipelines often misalign forecasting accuracy with downstream portfolio quality. We propose an end-to-end decision-focused learning framework that reformulates Sharpe ratio maximization as a Disciplined Parametrized Programming (DPP)-compliant convex programming layer and replaces discrete selection with a smooth top-$k$ operator enforcing an exact cardinality $k$. This enables gradient flow through prediction, asset selection, and re-optimization, allowing the predictive model to directly optimize portfolio performance. Across four major equity markets, our method achieves competitive and often superior out-of-sample Sharpe ratios compared with historical and prediction-focused baselines, with particularly strong gains in larger asset universes. Our \href{https://github.com/feuerwerksh/Diffble-card-SR}{code} is publicly available.