Index Tracking with Cardinality Constraints: A Stochastic Neural Networks Approach

Abstract

Partial (replication) index tracking is a popular passive investment strategy. It aims to replicate the performance of a given index by constructing a tracking portfolio which contains some constituents of the index. The tracking error optimisation is quadratic and NP-hard when taking the ℓ₀ constraint into account so it is usually solved by heuristic methods such as evolutionary algorithms. This paper introduces a simple, efficient and scalable connectionist model as an alternative. We propose a novel reparametrisation method and then solve the optimisation problem with stochastic neural networks. The proposed approach is examined with S&P 500 index data for more than 10 years and compared with widely used index tracking approaches such as forward and backward selection and the largest market capitalisation methods. The empirical results show our model achieves excellent performance. Compared with the benchmarked models, our model has the lowest tracking error, across a range of portfolio sizes. Meanwhile it offers comparable performance to the others on secondary criteria such as volatility, Sharpe ratio and maximum drawdown.