Blending factors…. the problem with intersections

I have recently been working on an academic paper on using multiple factors to invest. This is a marked departure from most of my other academic work (which generally involves hedge fund data). This research is also directly relevant to my investing work. While the research itself is still ongoing and I am not ready to share the conclusions, I had a couple of insights on how difficult it is to combine factors that I’d share.

The technique I’ve been using to combine factors is looking for intersections – I believe value stocks outperform growth stocks and past winners outperform losers. I want to buy stocks that are both value stocks AND past winners. (Incidentally, there is a rigorous academic paper arguing for this exact factor combination by the managers of one of the most successful quantitative investing shops).

This works well… to an extent. The more factors you add, the fewer stocks will get through. As an example, if you wanted the top 10% of stocks by value (say P/E ratios) and the top 10% of stocks by past returns, and the two were uncorrelated, your filter would return about 1% of stocks in the universe. Adding a 3rd uncorrelated factor, say size (small cap firms generally outperform larger ones), would reduce the filtered stocks even further to about 0.1% of stocks in the universe.

Beyond 3 factors, it is impossible to use intersections to combine factors. The resulting sample size is simply too small. One could (and I have) relaxed the constraints on each individual constraint, and in that manner blend more factors, but this feels artificial and might even be to the detriment of the screen.

To use a sports analogy (and since the NBA championships are on), I could ask for the top 10% of 3 point shooters and top 10% of overall point scorers and I’d probably get Stephen Curry and a few others. If I then add top 10% of assists to my criteria, I probably won’t have a single player in the league fitting the bill. IF I then relax my criteria to be the top 30% of 3 point shooters, overall point scorers and assists, I’d probably get players in there again, but it’s unclear I’d like them over my original 2 factor criteria that returned Curry and co.

So intersections are tough to work with.