Sparse portfolio optimization with robust risk under uncertain returns
Sparsity Regularized and Robust Mean Variance Portfolio Selection Under Ellipsoidal Uncertainty
Machine Learning
Summary
Picking the best mix of investments is tricky when expected returns are not exactly known and when you want to keep the number of investments small. The authors study a method that both handles uncertainty in predictions and encourages picking fewer assets, which can help reduce complexity and costs. They analyze the math behind these choices and create a smart search algorithm that can quickly ignore many bad combinations. Tests on real market data show their approach works well compared to existing tools.
What this means in practice
- •For quantitative portfolio managers: Improve investment portfolios by reliably selecting fewer assets under uncertain returns with guaranteed risk limits.
- •For financial software developers: Integrate efficient algorithms for robust sparse portfolio optimization into asset management platforms to enhance performance and scalability.
Authors
Deniz Akkaya, Emre Can Yayla, Buse Şen, Mustafa Ç. Pınar
Abstract
We investigate mean-variance portfolio selection with an $\ell_0$-penalty to promote sparsity in asset allocations. Uncertainty in the mean return vector is incorporated through an ellipsoidal uncertainty set, yielding a robust sparse optimization framework. We characterize the structure of both local and global minimizers and exploit these properties in the risk minimization and return maximization formulations. Building on this structural insight, we develop a branch-and-bound algorithm tailored to the resulting robust sparse portfolio problems, together with a new pruning rule that can discard exponentially many candidate portfolios in a single step. Extensive computational experiments on real market data, together with comparisons against a mixed-integer second-order cone programming solver, demonstrate the effectiveness and competitiveness of the proposed approach.