Sparsity and Stability for Minimum-Variance Portfolios

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.