# A Globally Optimal Portfolio for m-Sparse Sharpe Ratio Maximization

arXiv: https://arxiv.org/abs/2410.21100 · HTML: https://mlsanity.com/paper/2410.21100/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Oct 2024.

## Built on by (most cited first, 5 of 5)

- [Decision by Supervised Learning with Deep Ensembles: A Practical Framework for Robust Portfolio Optimization](https://mlsanity.com/paper/2503.13544/) (2025)
- [Decision-focused Sparse Tangent Portfolio Optimization](https://mlsanity.com/paper/2607.00581/) (2026)
- [Duality and Policy Evaluation in Distributionally Robust Bayesian Diffusion Control](https://mlsanity.com/paper/2506.19294/) (2025)
- [Linear Trading Position with Sparse Spectrum](https://mlsanity.com/paper/2508.18596/) (2025)
- [Learning to Optimize through Solver-Grounded Self-Play](https://mlsanity.com/paper/2609.34205/) (2026)

## Abstract (arXiv)

The Sharpe ratio is an important and widely-used risk-adjusted return in financial engineering. In modern portfolio management, one may require an m-sparse (no more than m active assets) portfolio to save managerial and financial costs. However, few existing methods can optimize the Sharpe ratio with the m-sparse constraint, due to the nonconvexity and the complexity of this constraint. We propose to convert the m-sparse fractional optimization problem into an equivalent m-sparse quadratic programming problem. The semi-algebraic property of the resulting objective function allows us to exploit the Kurdyka-Lojasiewicz property to develop an efficient Proximal Gradient Algorithm (PGA) that leads to a portfolio which achieves the globally optimal m-sparse Sharpe ratio under certain conditions. The convergence rates of PGA are also provided. To the best of our knowledge, this is the first proposal that achieves a globally optimal m-sparse Sharpe ratio with a theoretically-sound guarantee.