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15.8 Summary

Pairs trading or, more generally, statistical arbitrage refer to market-neutral strategies that arbitrage on the relative value of assets. Some key concepts include:

  • Mean reversion of a time series means that there is a long-term average value around which the series may fluctuate over time but eventually will revert back to. This allows the contrarian strategy of buying low and selling high (as opposed to a momentum-based strategy, which would buy as the price increases and sell while the price decreases).

  • Cointegration refers to assets that are not mean reverting themselves, but combined together in the right way become mean reverting.

  • Pairs trading is a strategy invented in the 1980s that combines two cointegrated assets to generate a synthetic mean-reverting asset. This mean reversion implies that the strategy is not affected by the market trend, that is, it is market neutral. This is in contrast to momentum-based strategies that precisely follow the market trend and exhibit a high market exposure.

  • Implementation of pairs trading requires:

    • discovering cointegrated assets, for example, via cointegration statistical tests;
    • tracking the cointegration relationship over time, either via rolling least squares or the Kalman filtering; and
    • executing the actual trading, typically with a simple thresholded strategy.

  • Kalman filtering, originally developed in the 1960s for vehicle guidance and navigation, is key to tracking cointegration over time. A variety of different state-space models can be formulated to track cointegration and then solved via the Kalman algorithm.

  • Statistical arbitrage is the generalization of pairs trading to more than two assets. This requires more sophisticated multivariate modeling of the assets (VECM modeling) to discover the cointegration relationships.