I am currently working on a stat arb that is giving me a little bit of trouble. I'm under the impression that most stat arbs are going to use prices such that we can choose a ratio N such that: Price of Stock A = Price of Stock B * N. Then you can choose whatever test you want for cointegration and create your model.
However, what I am currently working on uses notional values of different contracts. Then I fit the notional value using a regression model. When I do this I end up with a bias term that has a very large variance (due to large changes in notional value of multiple contracts). However, the rest of the parameters have very low variance. Therefore I cannot realistically model the asset using prices due to the large variance with my bias term (even though R-squared is 0.98). Think N above is now a stochastic variable and is present in my regression which leads to the large variance in my bias term. This leads me to use log returns in which the bias term is 0.
When using log returns you end up not choosing optimal entry/exit times for your model. Therefore I am left with the awful choice of either: a) Choosing a bad hedging ratio, or b) choosing less than optimal entry/exit times.
Any insight or possible errors I have made would be greatly appreciated.