Nonnegative Sparse Group Lasso with an Application in Financial Index Tracking

Index tracking mainly focuses on replicating or tracking the performance of a financial index which is also a popular passive portfolio management strategy. The classical methods often considerthe full replication consisted of all asserts of an index. However, the full replication often suffers from small and illiquid positions and high cost as the number of asserts increasing. Thus, the investors intend to purchase sparse portfolios. In stock markets, besides, there are still apparently existing group effects among stocks. This paper proposes the nonnegative sparse group lasso method for model selection and estimation to grouped variables without overlapping. We provide almost necessary and sufficient conditions for the variable selection and estimation consistency of the method in finite dimensional group cases. To get the solutions of the model, we derive a computational method based on coordinate decent algorithm. To track the index, the nonnegative sparse group lasso outperforms other current methods with group effects such as nonnegativeelastic net, according to tracking error.