Statistical arbitrage on the JSE based on partial co-integration

Abstract

Early forms of statistical arbitrage exploited the mean reversion of a model error extracted from pairs of instruments with a tendency to move together. Pairs trading was extended by Engle and Granger and by Johansen to include several co-integrated instruments. Partial co-integration was proposed by Clegg and Krauss to allow for model errors that contain both random walk and mean-reverting components. In this paper we implement a modified version of partial co-integration using a Kalman filter approach that allows the behaviour of the mean-reverting error component to be optimised. Co-integrated sets of shares are compiled over the period from January 1990 to November 2020 based on membership of sectors on the Johannesburg Stock Exchange. We demonstrate that optimal selection of the Kalman filter gain enables the improvement of risk-adjusted returns generated by the partial co-integration strategy. We optimise the parameters that define the partial co-integration trading strategy and find that it significantly outperforms market returns and a strategy based on normal co-integration. We observe higher returns during bear cycles compared with bull cycles, making statistical arbitrage based on partial co-integration an attractive option to combine with trading strategies that perform well during bull markets.