  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.
