Why Cointegration Does Not Guarantee Profitable Pair Trading
Summary
The document explains why a statistically cointegrated pair can still perform poorly in a trading backtest. It identifies transaction costs as a major obstacle, especially when the spread between related securities is small, and warns that statistical mean reversion may occur too slowly to trade profitably. Cointegration or rejection of a unit-root null alone does not establish a practical entry and exit opportunity.
An illustrative pair of synthetic price series has a spread that appears mean reverting and passes an augmented Dickey–Fuller test, yet takes about a year to return from extremes to its mean. Because the spread is typically around one percent of the securities’ prices, costs of twenty basis points per leg plus commission could consume potential gains. The author also cautions that genuine cointegration relationships are uncommon among financial securities without an economic reason to remain linked. The example is constructed, so it illustrates the limitation of statistical evidence rather than proving a general outcome for all pairs.
Key ideas
- Cointegration tests do not show whether a spread reverts quickly enough to trade.
- Trading costs can overwhelm the gains available from a narrow spread.
- A spread may be statistically mean reverting while taking about a year to return from extremes.
- The example uses synthetic series, so it illustrates a risk rather than establishing a universal result.
- An economic link between securities may make a cointegration relationship more plausible.
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Full text
# What causes poor returns in pair trading of very cointegrated securities? # What causes poor returns in pair trading of very cointegrated securities? I've been running some backtests of a pair trading strategy on 1 year worth of 5 min bars of two securities and I've noticed pretty poor returns, especially once transaction costs are taken into account. As a sanity check I ran a few statistical tests on the residuals spread in MATLAB: - Augmented Dickey-Fuller Test rejected null with $p < 0.001$ - Lilliefors Test rejected null with $p < 0.001$ - (as an aside) Engle's ARCH Test rejected null with $p \sim 0$ This all begets the question, why are the returns so poor for a seemingly perfectly cointegrated pair? The potential factors I'm considering are poor choice of bar size, the data needs to be filtered, or I need to account for volatility somehow. Any help would be appreciated. ## Answer by Chris Taylor (score 6) https://quant.stackexchange.com/a/29918 A few possibilities - - Trading costs kill your returns (often a problem for very highly correlated securities) - Mean reversion of the cointegration spread is either very weak, or happens over periods which are too long to be practical, or there is no mean reversion whatsoever. For example, consider the following two securities, which are clearly very strongly related to one another. The ADF test on the difference in their prices rejects a unit root, with p < 0.01. However, plotting the difference in prices we see the following - The spread looks like it mean reverts (hence the ADF test rejected a unit root) but the speed is so slow that it is not practically useful, generally taking ~1 year to revert from the extremes to the mean. Also note that the spread is typically only about 1% of the securities price, so if you are paying 20 basis points trading costs on each leg, plus a commission, you are very unlikely to realize a profit on this trade. This is on two synthetic price series that I deliberately constructed to be cointegrated. Remember that cointegration is a concept that applies to two theoretical price series, and true cointegration relationships are almost never observed in finance (particularly among securities where there is no particular reason for a cointegration relationship to exist).
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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.