Sparse Index Tracking: Simultaneous Asset Selection and Capital Allocation via $\ell_0$-Constrained Portfolio

TL;DR

This paper introduces a new sparse index tracking method using an $ 0$-norm constraint for easier asset control, along with an efficient algorithm, demonstrated on major index datasets.

Contribution

It proposes a novel $ 0$-norm constrained formulation for sparse index tracking and develops an efficient primal-dual splitting algorithm for practical implementation.

Findings

Effective asset selection and allocation control demonstrated on S&P500 and Russell3000 datasets.

Reduced transaction costs through turnover sparsity constraints.

Algorithm shows computational efficiency and practical applicability.

Abstract

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 $\ell_p$-norm regularizations as a continuous surrogate of the $\ell_0$-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 $\ell_0$-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.