Quantized Portfolio Theory

Abstract

J.L. Kelly's maximization of single-period growth revealed an optimal allocation strategy, and exposed a hidden information rate1. Ed Thorp then demonstrated2 how this allocation strategy could be applied to investment portfolios and coincidentally led straight to mean-variance optimization (MVO) which was introduced by Harry M. Markowitz3. This work investigates the implications of the growth/information-rate equivalence and reveals an unintuitive result –all trading signals must be binary. Trading on binary signals may seem too jarring to be practical, but arbitrary smoothness can be realized the same way arbitrary colour gradients are possible in digital imaging. Binary signalling also creates portfolio allocation weights that are extremely robust to highly variable expected return estimates produced by factor data outliers.
Pushing further into information theory and entropy, it's shown how the diffusion assumption that has traditionally been applied to equity, should actually be applied to debt instead. This change creates a fundamental framework of “demand diffusion” that drives wealth concentration in a way that remains entirely consistent with the most basic understanding of economic activity. “Demand diffusion” also lays the groundwork to allow competitive market economies to be modelled –at a fundamental level– as a system of competing strains of viral infections. Modelling economic systems as competing viral infections is surprisingly consistent with many micro and macro economic ideas and processes: Price elasticity of demand, survival of the fittest, product feature copying, supply and demand, advertising conversion rates, customer attrition rates, product/business life-cycle, direct and viral advertising, are all incorporated in this “economic infection” framework without contradicting economic reality.
With demand diffusion, the distribution of asset returns could likely be modelled as a series of viral reasons to buy, and viral reasons to sell.

Keywords: Quantized Markowitz Modern Portfolio Theory Portfolio Construction Tactical Asset Allocation Kelly Criterion Financial Signals Information Quant Quantitative Trading Investing Hamming Codes Data Decompression Heat Equation