Paper: arXiv 2610.04348

Authors: Jongbong An, Donghan Kim

Abstract

We develop a price-based framework for stochastic portfolio theory in which trading strategies are generated from nominal price weights and evaluated relative to a price-weighted benchmark. Stock splits and reverse splits induce jumps in the generating weights without changing the value of existing investments. In a semimartingale market with predictable adjustment events, we incorporate the corresponding share adjustments into the self-financing condition and construct additively and multiplicatively generated strategies with explicit jump-corrected wealth decompositions. For additive generation, an entropy-based example exhibits relative wealth tending to $-\infty$ almost surely under repeated splits, demonstrating why the usual argument for long-horizon relative arbitrage does not extend directly. We also show that advance adjustment information alone provides no model-free guarantee of improved performance for functionally generated portfolios. For multiplicative generation, wealth-preserving restarts retain the classical portfolio allocation evaluated at the current price weights. We also establish a correspondence with the capitalization-based framework that preserves absolute wealth and yields a strategy-independent benchmark conversion. We illustrate the framework using daily NYSE data, comparing price- and capitalization-weighted benchmarks and the corresponding diversity-weighted portfolios across price- and capitalization-selected universes.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 7.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: This paper introduces a novel price-based framework for stochastic portfolio theory, addressing a significant gap in the literature by explicitly incorporating stock splits and reverse splits. It combines rigorous mathematical derivations with an empirical illustration using real-world NYSE data, demonstrating both theoretical depth and practical relevance. The work extends existing SPT concepts to a new domain, offering fresh insights into portfolio construction and performance evaluation.

Research Flowchart

  flowchart TD
    A[Research Goal: Price-Based SPT] --> B{Develop Price-Based Framework};
    B --> C{Incorporate Stock Splits/Reverse Splits};
    C --> D[Data: Daily NYSE Data];
    D --> E{Computational Process: Strategy Generation & Evaluation};
    E --> F[Key Finding 1: Jump-Corrected Wealth Decompositions];
    E --> G[Key Finding 2: Additive - No Long-Horizon Arbitrage under Splits];
    E --> H[Key Finding 3: Multiplicative - Wealth-Preserving Restarts];
    E --> I[Key Finding 4: Correspondence with Capitalization-Based SPT];