Almost all of the research on equity factor investing deals with a priori predictability of the cross-section of stock market returns (i.e., models which use variables and data that would've have been available at the time of the prediction). I am curious if there's any research that deals with the a posteriori predictability. If you're unaware of research, then how would you approach this as a thought experiment.
For example, how much do firms' future profits determine future stocks prices? In other words, if I had a hypothetical crystal ball which showed me only future accounting statements, and nothing else, what would my edge be (i.e., what proportion of the variance of future returns would this data explain)?
Moreover, how could one begin to optimally use this information? Obviously, a private wire to the future should convey an insurmountable edge, but what should the edge player do with this information? E.g., should he simply discount future earnings or do something more sophisticated, as in translate his edge into Kelly optimal bets?
I am not concerned about the perils of look-ahead bias. Rather, I am interested in the types of data that might be worthwhile to predict and how this might relate back to insider information asymmetry, information leakage, surprises versus the consensus, and the value of investment research. Also, types of foresight need not be constrained to accounting items (except, obviously, future price/returns).