I was looking for the methods of calculating spread in pairs trading and I come across this answer from Jacques Joubert in which he said that $\text{Stock Price}_A- \text{Stock Price}_B*\text{Hedge ratio}$ is a "Beta neutral hedge ratio". I don't understand this point, why the hedge ratio in this regression is beta neutral. If we purchase $x$ shares of stockA an short $x*hedge ratio$ of stock B, would it be the same to dollar neutral rather than beta neutral because it ends up using the same amount of money but different amount of stocks for A and B due to differences in prices?
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