Mao’s formulation seemed more broadly applicable…
This week I attended another of the excellent quant seminars I’ve written about before. This time the talk was about stochastic modeling of equity markets and was presented by Robert Fernholz of Intech. Intech is evidently a subsidiary of Janus which manages some large amount of money presumably based on some of the portfolio management theory on which Dr. Fernholz is an expert. If you visit their site, you’ll be greeted by a bigger version of their credo which I’ve, um, honored as this post’s banner: “Math is power.”
Right then. While Mao would likely have been capable of convincing me otherwise, it’s probably best for everyone involved that portfolio managers are running around with esoteric mathematical models rather than the sorts of munitions favored by 20th century Chinese revolutionaries…
My interest in the talk was largely spurred by my interest in a variant of a problem I’ve discussed here namely, how-to generate useful synthetic markets. As I’d written before, the problem isn’t impossibly difficult for a constrained set of instruments. So, generating useful models for analyzing a pair trading strategy across pairs of correlated instruments is possible and it allows you to apply option-pricing techniques to the analysis of trading strategies. Swell. But if I want to do the same thing for a portfolio management strategy that’s looking at, say, the entire US market things become more complex.
As an example, consider applying this technique to a sector rotation model. In order for the synthetic markets you generate to produce meaningful or interesting results would seem to require that you capture the behavior of how equities within a sector interrelate and also how sectors relate to one another. It gets complicated pretty quickly.
Robert Fernholz has spent many years working on this kind of problem applying tools of a mathematical sophistication I will never wield, so hearing what he had to say had to be interesting. And it was. I think. His talk was very mathematically rigorous and unless you had read and digested his earlier papers beforehand, I don’t think you’d have a great shot at following him in great detail. The high point of his talk, for me, was his sequitur following a particularly dense bunch of proofs that “…now we will leave the world of math for that of statistics”.
After he had spoken for an hour packed with dense slides showing increasingly realistic (and complex) models he stopped to field questions. A couple of the professors who had hosted the event gamely tried with a few inquiries, but the rest of the crowd blinked and emitted a stony silence and a few sideways glances meant to ascertain if they were the only ones lost in space…
While I don’t think I was deep-space-nine lost, I certainly didn’t master every point made during the talk and I don’t think I came away from it any closer to achieving my own, limited, goals wrt developing concrete techniques for applying MC simulation across so diffuse a set of instruments as a nation’s equity markets. But it did give me an appreciation for the different approaches taken to related problems.
While the extremely precise theoretical approach taken by academics is ultimately necessary, the fact that Dr Fernholz spent an awful lot of work just coming up with a model in which markets didn’t necessarily devolve to one uber instrument reminded me of one of the more distasteful characteristics of philosophy. While it may not be possible to formally prove that the chair I’m sitting on exists to the satisfaction of some kind of philosopher, it certainly isn’t profitable to argue about it.
