Decision-focused Sparse Tangent Portfolio Optimization

Sparse tangent portfolio optimization aims to learn an interpretable, low-cardinality portfolio in the tangency direction of the mean–variance frontier, yet 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 sum-to-k sparsity budget. This enables gradient flow through prediction, asset selection, and re-optimization, allowing the predictive model to directly optimize the portfolio performance. Across five major equity markets, our method consistently delivers higher out-of-sample Sharpe ratios than historical and prediction-focused baselines while producing meaningful sparse selections.