# Sparse Index Tracking: Simultaneous Asset Selection and Capital Allocation via ℓ0-Constrained Portfolio

arXiv: https://arxiv.org/abs/2309.10152 · HTML: https://mlsanity.com/paper/2309.10152/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 42 references that are in the map.
- First posted on arXiv 22 Jul 2023.

## Builds on (most cited first, 7 of 7)

- [Convergence Analysis of Alternating Direction Method of Multipliers for a Family of Nonconvex Problems](https://mlsanity.com/paper/1410.1390/) (2014)
- [Playing with Duality: An Overview of Recent Primal-Dual Approaches for Solving Large-Scale Optimization Problems](https://mlsanity.com/paper/1406.5429/) (2014)
- [Global convergence of splitting methods for nonconvex composite optimization](https://mlsanity.com/paper/1407.0753/) (2014)
- [Proximal Splitting Algorithms for Convex Optimization: A Tour of Recent Advances, with New Twists](https://mlsanity.com/paper/1912.00137/) (2019)
- [Robust Time-Varying Graph Signal Recovery for Dynamic Physical Sensor Network Data](https://mlsanity.com/paper/2202.06432/) (2022)
- [A General Destriping Framework for Remote Sensing Images Using Flatness Constraint](https://mlsanity.com/paper/2104.02845/) (2021)
- [Epigraphical Relaxation for Minimizing Layered Mixed Norms](https://mlsanity.com/paper/2008.04565/) (2020)

## Abstract (arXiv)

Sparse index tracking is a prominent passive portfolio management strategy that constructs a sparse portfolio to track a financial index. A sparse portfolio is preferable to a full portfolio in terms of reducing transaction costs and avoiding illiquid assets. To achieve portfolio sparsity, conventional studies have utilized ℓp-norm regularizations as a continuous surrogate of the ℓ0-norm regularization. Although these formulations can construct sparse portfolios, their practical application is challenging due to the intricate and time-consuming process of tuning parameters to define the precise upper limit of assets in the portfolio. In this paper, we propose a new problem formulation of sparse index tracking using an ℓ0-norm constraint that enables easy control of the upper bound on the number of assets in the portfolio. Moreover, our approach offers a choice between constraints on portfolio and turnover sparsity, further reducing transaction costs by limiting asset updates at each rebalancing interval. Furthermore, we develop an efficient algorithm for solving this problem based on a primal-dual splitting method. Finally, we illustrate the effectiveness of the proposed method through experiments on the S&P500 and Russell3000 index datasets.