Pairs trading using dynamic hedge ratio - how to tell if stationarity of spread is due to genuine cointegration or shifting of hedge ratio?

Question

I'm very new to pairs trading, and am trying it out on a few dozen pairs.

It seems very natural to me to use a dynamic hedge ratio, as it seems likely that the ratio will move over time.

To accomplish this, I am using rolling linear regression (so I choose a lookback period of, say, 100 hours and I keep shifting this 100-hour window forward, run linear regression on that window to determine the "current" hedge ratio).

I have noticed, though, that by doing this, it seems like I can make a "stationary" spread out of just about any pair. I realize this is likely because part of the "stationarity" is due to the self-correcting nature of a rolling window regression, which over time will make the spread return to 0 by changing the hedge ratio, not because the spread actually reverted to the mean.

How can I address this? How can I tell if my spread is stationary due to real mean reversion, or just the shifting hedge ratio? Is there a better way of finding a hedge ratio?

I realize there's a lot loaded in this question, and I'll be happy to give a bounty to anyone who takes the time to respond deeply. Thank you!

Related question and discussion here: Pairs Trading - isn't any spread stationary if your rolling lin-reg window is small enough?

Answer 1

You are right. If the window is small enough every spread looks stationary. What you need is that the spread is steady enough.

The mathematical property which implies that pairs-trading works is called co-integration. You can test this statistically, for example, by the Engle–Granger two-step method.

For your context here the definition: Two instruments $x$ and $y$ are co-integrated if $\omega$ exists such that $x+\omega y$ is stationary. Where $\omega$ is the mentioned hedge ratio.