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Essential Assumption of Pairs Trading Wrong?

Posted in Technical Trading

Do stock pairs that track in the past reliably track in the future? In his January 2014 paper entitled “On the Persistence of Cointegration in Pairs Trading”, Matthew Clegg assesses the persistence of cointegration among pairs of liquid U.S. stocks. Specifically, he investigates whether pairs of equities that are cointegrated in an initial interval are likely to be cointegrated in a subsequent interval. He uses calendar years as initial intervals and focuses on next years as subsequent intervals. He also considers shorter subsequent intervals. He employs a variety of methods to measure pair cointegration to ensure robustness of findings. Using daily returns for constituents of the S&P 500 (as of August 13, 2013) during January 2002 through December 2012, allowing ten years of persistence tests, he finds that:

  • Using the Augmented Dickey-Fuller test, an average of 5.0% of stock pairs are cointegrated during any given year, which is about the percentage expected by chance. Of the pairs that are cointegrated during one year, an average of 4.9% are cointegrated during the next year. Based on both overall and year-by-year results, evidence offers very little support for a belief that pair cointegration persists from one year to the next.
  • Using the Phillips–Perron test, an average of 5.3% of stock pairs are cointegrated during any given year. Of the pairs that are cointegrated during one year, an average of 4.5% are cointegrated during the next year. Based on both overall and year-by-year results, evidence again offers very little support for a belief that pair cointegration persists from one year to the next.
  • Alternative tests produce similar results. For the most favorable test, an average of 6.0% of stock pairs are cointegrated during any given year. Of the pairs that are cointegrated during one year, an average of 7.2% are cointegrated during the next year. In other words, it appears that the best case for identifying cointegrated pairs for a one-year trading period is about a 7% success rate.
  • Nor does testing of shorter intervals of cointegration persistence with monthly granularity support the hypothesis that cointegration is a short­‐term phenomenon that dissipates over time.
  • Across different methods, the incidence of pair cointegration is markedly higher during the 2008-2009 financial crisis.

In summary, evidence does not support a belief that cointegration of pairs of liquid U.S. stocks persists to an extent that encourages a pairs trading strategy.

Cautions regarding findings include:

  • Running many tests on same data introduces snooping bias, such that results from the most favorable test likely overstates expectations.
  • As noted in the paper, pairs trading in other equity markets or with exchange-traded funds (ETF) rather than individual stocks may work better.
  • As noted in the paper, the test methodology incorporates survivorship bias, and there are many instances of missing daily data resulting in exclusion of stocks from consideration.
  • Also as noted in the paper, non-normality of daily stock returns and volatility clustering may affect cointegration tests.
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