How To Approach Multi-Period Optimisation

Introduction

This is where I hit you with some clickbait about Ken Griffin saying multi-period optimisation being the last frontier Citadel is solving. But I’m not going to do that… Or have I just done so? Hmm…

Anyway, you should care about multi-period optimisation because the portfolio problem is actually a sequential decision. Think about it, your signals are not single period predictors with a one-period cliff in alpha decay. That is to say, your signals produce a prediction, and this prediction plays out over many periods, and the strength (and relevance) of this prediction slowly decreases over the course of its lifetime.

With single period optimisers, there is literally no way that you can capture this dynamic. Instead, all you get to do is to plug in single period returns, have it spit out optimal holdings, then you subtract your current holdings from them and trade that.

There’s a pretty big problem here if you haven’t realized it yet. Not accounting for how your alphas decay means that your optimisers cannot account for a world where the decay might be so rapid that it is not worth trading at all, or that the alpha decay is so slow that you can take your time trading in with no rush whatsoever.