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.

摘要

早期形式的统计套利利用从具有一起移动趋势的工具对中提取的模型误差的均值回归。Engle 和 Granger 以及 Johansen 将配对交易扩展到包括几个联合工具。Clegg 和 Krauss 提出了部分协整，以允许包含随机游走和均值回复组件的模型误差。在本文中，我们使用卡尔曼滤波器方法实现了部分协整的修改版本，该方法允许优化均值回复误差分量的行为。1990 年 1 月至 2020 年 11 月期间，根据约翰内斯堡证券交易所的行业成员资格编制了协整股。我们证明了卡尔曼滤波器增益的最佳选择能够提高部分协整策略产生的风险调整回报。我们优化了定义部分协整交易策略的参数，发现它明显优于市场回报和基于正常协整的策略。与牛市周期相比，我们观察到熊市周期的回报更高，这使得基于部分协整的统计套利与牛市期间表现良好的交易策略相结合成为一个有吸引力的选择。