I've recently been looking into pairs trading through cointegration. So far I've used the log returns of stock A and stock B in a rolling OLS to find the hedge ratio. However, I've noticed that for a pair whereby stock A and B have massive differences in price that the hedge ratio still remains small. Say for example stock A was trading at 600 a share and stock B at 1. The log returns of these two stocks won't be too far off and so the resulting hedge ratio will end up around ~0-1. Therefore I would be shorting a really small position in stock B.
I'm almost certain that I've got something wrong in the above example so feel free to correct me.