Let's say I have three products that are correlated (e.g. AAPL, MSFT, and AMZN). I would like to construct a spread between these products and trade the mean-reverting spread. Specifically, sell the spread when it exceeds the fair value and buy the spread when it becomes cheap.
Now, depending on how I develop the hedge ratios between these products, the resulting spread would be different. For example if I use OLS with the returns of AAPL as the dependent variable (DV), the resulting spread would be different than MSFT as the DV.
My question is whether there exists an intuitive way to determine the DV or whether I should run three separate models and determine the DV based on the backtested results? What are some common practices in the industry?
Any resources to read more about this?