When does a cointegration test, which looks for a connection between two apparently wandering price paths, work for pairs trading? In their May 2016 paper entitled “Cointegration and Relative Value Arbitrage”, Binh Do and Robert Faff investigate the conditions under which cointegration successfully identifies stocks for pairs trading. Their basic pairs trading strategy is to each month:

- Identify cointegrated pairs based on daily total returns over the last 12 months.
- Over the next six months, buy (sell) the relatively undervalued (overvalued) stock when cointegrated pair spread exceeds its selection interval mean by two standard deviations.
- Close positions when the spread reverts to its historical mean or the trading period ends, whichever occurs first.
- Closed trades may be reopened as signaled, if there is more than a month left in the trading interval.

They then refine the strategy by constraining selected pairs to those that are close economic substitutes, corresponding to a low cointegration coefficient. Pairs passing (failing) this constraint move together in the long run without any price scaling (only with scaling of prices for one member of the pair). While they focus on pairs of individual stocks, they also consider trading of pairs of small groups (baskets) of stocks. Their benchmark is a conventional pairs trading strategy that identifies pairs with the smallest sums of squared differences in normalized daily prices over the past 12 months, and then trades as specified above over the next six months. Using daily data for a broad sample of U.S. common stocks during July 1962 through December 2013, *they find that:*

- Pairs selected based on the cointegration strategy:
- Comprise less than 1% of all possible pairs.
- Tend to involve stocks with smaller market capitalization, higher total volatility, higher idiosyncratic volatility and lower liquidity than those selected based on the conventional minimum distance strategy.

- Regarding basic strategy portfolio performance:
- During the first half of the sample period (1963-1988), the cointegration strategy and the benchmark strategy generate similar average gross monthly returns (1.1%), with similar probabilities of opened pair convergence (70%).
- During the second half of the sample period (1989-2013), the cointegration strategy generates zero average gross monthly return, compared to positive but declining return for the benchmark strategy, with similar but much lower probabilities of opened pair convergence (59%). Cointegration strategy losses on opened pairs that fail to converge are much more severe during this subperiod than during the first half.

- Constraining pairs selected via cointegration to close economic substitutes as defined above improves portfolio performance.
- Over the entire sample period, a constrained cointegration portfolio generates average gross monthly return of about 1% with 71% probability of opened pair convergence, outperforming both the unconstrained and the benchmark strategies.
- The constrained strategy exhibits significantly positive average portfolio return in the second

subperiod. However, close economic substitutes are much rarer during this subperiod. - For opened pairs that fail to converge, losses for close economic substitutes are much lower than for other cointegrated pairs. This difference explains the loss of profitability of the basic cointegration strategy during the second half of the sample period when close economic substitutes become rare.
- Reasonable estimates of institutional trading frictions and shorting costs cut average return in half over the full sample period. However, the constrained strategy exhibits significant net profitability in both subperiods.

- Findings are generally robust to:
- Different portfolio weighting and stock price normalization approaches.
- Using a two-year pair selection interval (although the one-year interval works better).
- Using baskets of three stocks rather than individual stocks (in fact increasing the number of qualifying pairs and therefore trading opportunities).

In summary, *evidence indicates that pairs trading strategies based on cointegration should focus on close economic substitutes, excluding other purely statistical substitutes.*

Cautions regarding findings include:

- Trading frictions would be substantially higher for most individual investors than those used in the study.
- Empirical preemption of an alternative cointegration test (“yields poorer trading results”) and selection of the level of cointegration constraint defining close economic substitutes introduces snooping bias. Results therefore overstate expectations.
- The data collection/processing burden implied by the methodology may be costly and beyond reach of most investors, who would bear costs/fees for delegation to an investment/fund manager.

See other pairs trading research summaries. In particular, see “Pairs Trading Net Profitability” for more information on trading friction assumptions applied above.

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