Index tracking via reparameterizable subset sampling in neural networks

Index tracking aims at replicating the benchmark index performance by constructing a tracking portfolio consisting of partial component stocks of the index. This is an NP-hard question because of the cardinality constraint which limits the number of component stocks in the tracking portfolios. This paper proposes a new method to solve this problem in an end-to-end way by using a continuous subset sampling relaxation which can provide differentiable gradients calculation in neural networks. The proposed approach is tested with the FTSE-100 index data and the S&P100 index data, and compared with widely used index tracking methods, such as the forward and backward selection and optimization solvers. According to the empirical results, our proposed approach achieves the best tracking performance for different evaluation criteria.