Why R^2 Is Low For A Good Trading Strategy

[Mistro]

Hello,



I am reading David Aronson TSSB Manual and in the book he states(after creating a simple strategy that is profitable) - "The R^2 is extremely low, as is the rule in financial applications. In most situations, the best predictors (the most likely to result in winning trades) are in the tails of the models distribution of predictions, the most extreme large and small values."



David suggests breaking our data into percentiles. That way we can model the extremes separately, for example, what is our profit factor when our indicator is in the bottom 10% and top 90%.



I am hoping someone can take his statement one step further. How might we asses predictor variables and why do we see most of the profits in the tails? An example would also be helpful.



Thank you.

[doomanx]

Firstly take the book with a hint of salt, as there are some fundamental flaws in his reasoning (although I think he's a good statistician and does a good job debunking a lot of the BS out there).



Can't remember this exact part of the book, but here's what I think he's getting at. Most financial signals have a very low R^2 (signal is tough to find/approx. EMH etc) but that isn't what makes it tradeable in the first place. What you're really looking for is statistical significance - is it really a non-random fluctuation? If it is, you can check if E[trade] - E[cost] > epsilon (where epsilon is the amount of money you get out of bed for) and you're good to go.



The point is that the above inequality is only satisfied when your model confidence is very high, which does not happen very often (due to the large noise bringing a lot of positive and negative contribution into the expectation), hence trades will only be executed when there is a large probability mass on some favourable outcome.



DISCLAIMER: This is not the entire trading problem (refer to Risk Management).

[NeroTulip]

It is a quasi-efficient markets argument: If there was a signal with very high R^2, every investor would rush to exploit it and arb it away, until R^2 is 0. In the real world, however, investors are limited by risk tolerance, and transaction costs, among other things. So R^2 does not go to 0, but settles at some low value where it is profitable for some investors to trade.