  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.

Portfolio Management