Improved parameter estimation and simple trading algorithm for sparse, mean-reverting portfolios

Abstract. We examine the problem of finding sparse, mean reverting portfolios based on multivariate historical time series. After mapping optimal portfolio selection into a generalized eigenvalue problem, two different heuristic algorithms are referenced for finding the solution in a subspace which satisfies the cardinality constraint. Having identified the optimal portfolio, we outline the known methods for finding the long-term mean and introduce a novel approach based on pattern matching. Furthermore, we present a simple convergence trading algorithm with a decision theoretic approach, which can be used to compare the economic viability of the different methods and test the effectiveness of our end-to-end process by extensive simulations on generated and historical real market data.