Pair trading: Hege ratio by price ratio or by regression on the stocks

So I feel things like this question do exist on the site however I failed to form a conclusion based on what was written, so I decided to formulate my query as exactly as possible and hopefully anyone else as confused as I am will find an answer here and be able to go from this page enlightened - with this is mind:

I understand that pair trading relies on the cointegration of 2(or more) stocks. They tend to maintain a certain position relative to each other probabilistically maintaining a certain 'spread'.

By regressing one stock relative to the other you can attain a beta value often used in pair trading algorithms, which is used to define said spread. This regressed beta seems to be often used to indicate how much one should buy of one stock relative to the other.

I am also aware that if one were to hedge in a dollar neutral fashion by going long on one stock as much as one has gone short on the other (in dollar terms) then one is resilient to overall market movement.

My question is that the former seems to be far more common than the latter in pair trading and I wanted to know why?

At a glance it would seem that the regressed beta gives you the amount one stock moves relative to the other in general but - provided that this beta didn't happen to equal the ratio of one price to the other - one would still remain exposed to large market movements being either more long or short in dollar terms.

The dollar neutral hedge ratio would not represent the ratio of how much the stocks move relative to each other but one can still use the spread(with this regressed beta which here doesn't get used to choose how much we buy of one stock or the other), establish one should go long or short on each stock in the pair respectively, and then one could bet in a dollar neutral fashion giving market movement protection. The second question is why is this not done more?

• hedge means to hedge risk factor movement while dollar neutral cannot guarantee such property – XYQ May 27 at 1:51
• Presumably under that conditions Beta was positive if one knows (believes) that the spread is to shrink one can place whatever bets they like on the short and long(guaranteed by the positive beta) ? – East May 27 at 22:08