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

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:

- 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.

# 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.*