Sparsity and Stability for Minimum-Variance Portfolios

TL;DR

This paper investigates methods to improve the stability and sparsity of minimum-variance portfolios by combining covariance estimation, sparse modeling, and turnover constraints, demonstrating effective asset selection and low risk in empirical datasets.

Contribution

It introduces a novel approach that maintains low-risk profiles while automatically selecting assets and reducing turnover, addressing limitations of existing methods.

Findings

Efficient estimation methods can be combined with sparsity to maintain low risk.

LASSO-based sparsity alone is insufficient to reduce turnover over time.

The proposed approach achieves stable, sparse portfolios with low risk in real datasets.

Abstract

The popularity of modern portfolio theory has decreased among practitioners because of its unfavorable out-of-sample performance. Estimation errors tend to affect the optimal weight calculation noticeably, especially when a large number of assets is considered. To overcome these issues, many methods have been proposed in recent years, although most only address a small set of practically relevant questions related to portfolio allocation. This study therefore sheds light on different covariance estimation techniques, combines them with sparse model approaches, and includes a turnover constraint that induces stability. We use two datasets - comprising 319 and 100 companies of the S&P 500, respectively - to create a realistic and reproducible data foundation for our empirical study. To the best of our knowledge, this study is the first to show that it is possible to maintain the low-risk profile of efficient estimation methods while automatically selecting only a subset of assets and further inducing low portfolio turnover. Moreover, we provide evidence that using the LASSO as the sparsity-generating model is insufficient to lower turnover when the involved tuning parameter can change over time.