A Gentle Introduction to Stochastic Portfolio Theory (and its Inverse)

10 min readJul 22, 2023

I made a brief comment about Stochastic Portfolio Theory that sparked some interest and a post or two by Alberto Bueno-Guerrero recently. Few, it would seem, are aware of this body of work so this article comprises:

  1. A short teaser for stochastic portfolio theory

And for fun:

2. An illustration of what we might call inverse stochastic portfolio theory, which is where we take a heuristic portfolio construction technique and show that it would arise as the result of an optimization.

Stochastic Portfolio Theory (e.g. AbeBooks). Markowitz is the first name to appear in the acknowledgements.

A Characterisation of Stochastic Portfolio Theory

Stochastic Portfolio Theory comprises a collection of observations (theorems) about growth rates of portfolios that can be rebalanced in continuous time. Creator Robert Fernholz describes it thus:

A novel mathematical framework for analyzing portfolio behaviour and equity market structure … providing insight into questions of market equilibrium and arbitrage [that] can be used to construct portfolios with controlled behaviour … and has been the basis for successful investment strategies employed for over a decade by the institutional equity manager INTECH, where I have served as chief investment officer.