A Basket Half Full: Sparse Portfolios

TL;DR

This paper develops a high-dimensional approach for constructing sparse portfolios, providing theoretical bounds and empirical evidence of robustness during market downturns, addressing limitations of existing methods.

Contribution

It introduces a theoretically grounded method for sparse portfolio estimation in high dimensions, with proven oracle bounds and practical robustness analysis.

Findings

Sparse portfolios are robust during recessions.

The proposed method outperforms non-sparse strategies in adverse markets.

Theoretical analysis provides oracle bounds and distribution guidance.

Abstract

The existing approaches to sparse wealth allocations (1) are limited to low-dimensional setup when the number of assets is less than the sample size; (2) lack theoretical analysis of sparse wealth allocations and their impact on portfolio exposure; (3) are suboptimal due to the bias induced by an $\ell_1$-penalty. We address these shortcomings and develop an approach to construct sparse portfolios in high dimensions. Our contribution is twofold: from the theoretical perspective, we establish the oracle bounds of sparse weight estimators and provide guidance regarding their distribution. From the empirical perspective, we examine the merit of sparse portfolios during different market scenarios. We find that in contrast to non-sparse counterparts, our strategy is robust to recessions and can be used as a hedging vehicle during such times.