Introduction to Stochastic Portfolio Theory
Abstract
I present the ideas of Stochastic Portfolio Theory in a simple one dimensional trading context. Additive functional portfolio generation and multiplicative functional generation using a potential are contrasted. The Master Equation introduced by Fernholz is described both in discrete time and in continuous time. The drift of the Master equation (driving the noise harvesting property of functionally generated portfolios) is linked to the concavity of the potential function. The link with the dual view of Optimal Transport is made. Conditions for the success of functionally generated trading strategies are described. A concrete example based on the trading of equity futures is then introduced. Historical simulations and their statistical interpretation are given. The relationship between functional trading and market making is outlined.
