Information-Theoretic Model for the Growth Optimal Portfolio of Stocks

Paper: arXiv 2611.07457

Authors: Eckhard Platen, Kevin Fergusson

Abstract

Drawing on information-theoretic principles and empirical evidence, a proxy for the growth-optimal portfolio of stocks (the benchmark) is constructed and modeled. The derivative of its activity time captures overreactions in trading behavior and follows a fast-moving, quasi-stationary scalar diffusion. The benchmark’s log-returns are predicted to follow a Student t distribution with degrees of freedom slightly less than four, and this prediction is tested empirically. With the benchmark as numeraire, the derived model enables benchmark-neutral pricing and hedging.

Complexity vs Empirical Score

• Math Complexity: 8.0/10
• Empirical Rigor: 7.0/10
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: This paper presents a highly mathematical framework rooted in information theory for modeling the growth-optimal portfolio. It combines rigorous theoretical derivations with empirical testing of its predictions, particularly regarding log-return distributions and stylized facts. The novelty lies in the information-theoretic approach to benchmark modeling and benchmark-neutral pricing.

Research Flowchart

  flowchart TD
    A[Research Goal: Model Growth-Optimal Portfolio & Its Dynamics] --> B{Key Methodology: Information-Theoretic Principles & Empirical Evidence};
    B --> C[Data/Inputs: Equities (Stocks) Market Data];
    C --> D{Computational Process: Construct Growth-Optimal Portfolio Proxy & Activity Time Derivative};
    D --> E{Computational Process: Analyze Activity Time Dynamics & Log-Returns Distribution};
    E --> F[Key Finding: Activity Time Derivative Captures Overreactions (Fast-Moving Scalar Diffusion)];
    F --> G[Key Finding: Benchmark Log-Returns Follow Student t (df < 4)];
    G --> H[Outcome: Enables Benchmark-Neutral Pricing & Hedging];