In the context of a backtesting engine, is it better to have strategy generate trade signals in the range from -1 to 1 or as exact predicted returns (e.g. -12% or 26%).
The difference lies in how to regress the underlying model: whether to put (the response variable) returns as 1 (for positive) or -1 (for negative) (and use a logit model) or put exact historical return values (and use a linear model).
The reason for asking this is that I found a model that gives me an R^2 of almost 0 (which would seem rubbish in terms of predicting returns), but when backtesting it performs well and is actually a good proxy for relative signal strength (although the returns it gives are 0.17% or -0.09% etc).
It seems that by assigning 1 for positive returns I am losing some of the information; on the other hand trying to predict exact returns seems like a tall order -- I do not like that R^2 might not correspond to backtest results at all.
Which approach is better? Is there some standard literature on this (be it backtesting component design or alpha strategy design)?