Sparsity and stability for minimum-variance portfolios

The popularity of modern portfolio theory has decreased among practitioners because of its unfavorable out-of-sample performance. Estimation risk tends to affect the optimal weight calculation noticeably, especially when a large number of assets are considered. To overcome these issues, many methods have been proposed in recent years, but only a few address practically relevant questions related to portfolio allocation. This study therefore uses different covariance estimation techniques, combines them with sparse model approaches, and includes a turnover constraint that induces stability. We use two datasets of the S&P 500 to create a realistic data foundation for our empirical study. We discover 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 find that simply using LASSO is insufficient to lower turnover when the model's tuning parameter can change over time.