Index Tracking via Sparse Bayesian Regression and Collaborative Neurodynamic Optimization

Index tracking is a primary passive investment strategy. Many existing methods, such as cardinality-constrained and regularized regressions, need to prespecify parameters to generate sparse portfolios to track indices, which complicates the tracking procedure and may compromise tracking performance. This article addresses index tracking and enhanced index tracking via Bayesian learning and collaborative neurodynamic optimization. Specifically, we formulate a sparse Bayesian regression problem for index tracking. Furthermore, we reformulate the problem for enhanced index tracking by adding constraints based on a second-order stochastic domination rule. To overcome the nonconvexity of the objective function in the formulated problems, we propose a sparse Bayesian regression algorithm based on multiple recurrent neural networks in the collaborative neurodynamic optimization framework. We demonstrate the superiority of the proposed methods to mainstream baselines in terms of predictability, consistency, sparsity, and profitability via experimentation on the data from seven major stock markets.