Trading Strategies Generated Pathwise by Functions of Market Weights

TL;DR

This paper generalizes portfolio generating functions to path-dependent functionals involving current and past market weights, broadening the class of portfolios and improving conditions for outperforming the market without relying on probabilistic models.

Contribution

It introduces a pathwise, probability-free framework for functional portfolio generation, extending previous models to include path-dependent functionals and enhancing market outperforming conditions.

Findings

Wider class of portfolios generated by path-dependent functionals

Improved conditions for strong relative arbitrage

Enhanced market outperforming strategies over specific horizons

Abstract

Almost twenty years ago, E.R. Fernholz introduced portfolio generating functions which can be used to construct a variety of portfolios, solely in the terms of the individual companies' market weights. I. Karatzas and J. Ruf recently developed another methodology for the functional construction of portfolios, which leads to very simple conditions for strong relative arbitrage with respect to the market. In this paper, both of these notions of functional portfolio generation are generalized in a pathwise, probability-free setting; portfolio generating functions are substituted by path-dependent functionals, which involve the current market weights, as well as additional bounded-variation functions of past and present market weights. This generalization leads to a wider class of functionally-generated portfolios than was heretofore possible, and yields improved conditions for outperforming the market portfolio over suitable time-horizons.