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. 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 code is publicly available.

Many investors prefer to hold a small, carefully chosen group of stocks rather than hundreds, since smaller portfolios are easier to manage and cheaper to trade. However, choosing which stocks to hold and how much to invest in each is difficult because it depends on predicting how each stock will perform in the future. The standard approach trains a prediction model to forecast stock returns, and then separately uses those forecasts to pick stocks and decide allocations. The trouble is that accurate prediction does not always lead to good investment decisions. We develop a method that trains the prediction model and the stock-picking step together as an integrated system. This way, the model learns to make forecasts that directly lead to better portfolios, rather than just accurate return predictions. Tested on stocks from Europe, the UK, Korea, and Japan, our method consistently produces better risk-adjusted returns than standard approaches, with the largest gains in markets containing many stocks to choose from. More broadly, our work shows that predictive models can be trained by directly accounting for how their forecasts will be used in downstream financial optimization tasks.