Quote from Rationalize:
Keen to discuss .. & maybe also divergence from mean vs divergence of mean.
Sure...
So the basic principle is rather simple. It ain't rocket engineering, that's for sure. Suppose we start with a time series that we believe exhibits some mean-reversion properties. Also, let's say that, in your latest observation, you establish that the model residual is, say, n (where, for simplicity, let's assume your model is some flavor of multiple regression). Next you fit some sort of a AR model to your time series (I actually do it to the residuals) and you establish the speed of mean-reversion, e.g. smth like a half-life. The last step is to obtain the volatility of the residual time series in the most bog-standard manner (stdev). Now you have pretty much everything you need to calculate what I call the ex-ante Sharpe over the period equal to the half-life. Your denominator, i.e. the return, is n/2 plus carry. Your numerator is the volatility from above (normalized to the half-life as well). Once you have the half-life Sharpe, you can "annualize" it to bring everything to a consistent basis. None of this is particularly scientific and it doesn't even have to be that rigorous, i.e. you can estimate your inputs whichever way you like, including waving fingers in the air.
Again, we can discuss the technical details of the specific steps separately, but my point here is more about a consistent framework for entries and exits. You can make the approach above systematic (not that I recommend it). Specifically, suppose you have a limited risk budget and you scan your opportunity set for trades, say, every day. As soon as you establish that either a) an existing trade's ex-ante Sharpe has fallen below a set threshold; or, b) a new trade exists that has a higher ex-ante Sharpe than an existing trade; you exit the existing trade and, in case b), strap on the new one. You can also make the size of the trade dependent on the Sharpe.
Now, obviously, this is all VERY simplistic and there's lots of devils in the details. However, I really like to use the above as a self-consistent starting point that you can refine to your heart's content (sky's the limit). As I mentioned, we can talk further about the gory details, including the "divergence" issues (if I understand what you mean correctly, there may be a way to deal with some of them).
