Quantifying dimensional change in stochastic portfolio theory

Paper: arXiv 2303.00858

Authors: Erhan Bayraktar, Donghan Kim, Abhishek Tilva

Abstract

In this paper, we develop the theory of functional generation of portfolios in an equity market with changing dimension. By introducing dimensional jumps in the market, as well as jumps in stock capitalization between the dimensional jumps, we construct different types of self-financing stock portfolios (additive, multiplicative, and rank-based) in a very general setting. Our study explains how a dimensional change caused by a listing or delisting event of a stock, and unexpected shocks in the market, affect portfolio return. We also provide empirical analyses of some classical portfolios, quantifying the impact of dimensional change in portfolio performance relative to the market.

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 6.0/10 (capped from 6.5: transaction costs not modelled; no out-of-sample test; see penalty flags)
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper provides an advanced mathematical framework extending Stochastic Portfolio Theory to markets with changing dimensions due to listings and delistings. It combines rigorous stochastic calculus with empirical analyses of classical portfolios to evaluate the impact of dimensional shocks.

Research Flowchart

  flowchart TD
    A["Research Goal: Quantify impact of market dimensional changes (listings/delistings) on portfolio returns"] --> B["Inputs: Equity market capitalizations & dimensional/capitalization jumps"]
    B --> C["Methodology: Extend Functional Portfolio Theory to changing dimensions"]
    C --> D["Construct Self-Financing Portfolios<br>(Additive, Multiplicative, Rank-based)"]
    D --> E["Empirical Analysis of Classical Portfolios"]
    E --> F["Outcomes: Quantified impact of listing/delisting events & market shocks on relative portfolio performance"]