# 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.

• Try trading only when the error correction terms reaches a certain (sufficiently large) size and close the position only when the gap has decreased (economically) significantly. Then if cointegration persists in the future, you could expect larger profit for the given trades (unless the gap tends to close very slowly). – Richard Hardy Aug 31 '16 at 19:42

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).

• The size of the spread (compared to transactions cost) seems key to me. Two identical securities are perfectly cointegrated (I think) yet there is no money to be made there because there is no spread. And if many people are doing the pair trade the spread is going to reduce. – noob2 Aug 31 '16 at 12:50