Paper: arXiv 2604.15519

Authors: Arshia Ghasemi, Siqi Shao, R. A. Serota

Abstract

We analyze historic S&P500 multi-day returns: from daily returns to those accumulated over up to ten days. Despite symmetry breaking between gains and losses in the distribution of returns, resulting in its positive mean and negative skew, realized variance (volatility squared) exhibits remarkably good linear dependence on the number of days of accumulation. Mean of the distribution also shows near perfect linear dependence as well. We analyze this phenomenon both analytically and numerically using a modified Jones-Faddy skew t-distribution.

Complexity vs Empirical Score

  • Math Complexity: 8.0/10
  • Empirical Rigor: 6.5/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper combines dense analytical derivations using confluent hypergeometric functions and skew t-distributions with rigorous Bayesian parameter estimation and empirical fitting to historical S&P500 multi-day return data.

Research Flowchart

  flowchart TD
    A[<b>Goal:</b> Analyze multi-day S&P500 return dynamics] --> B[<b>Data:</b> Historical daily to 10-day accumulated returns]
    B --> C[<b>Methodology:</b> Apply modified Jones-Faddy skew t-distribution]
    C --> D[<b>Processes:</b> Analytical modeling & Numerical simulations]
    D --> E[<b>Findings:</b> Linear scaling of volatility & mean returns]
    E --> F[<b>Conclusion:</b> Symmetry breaking in distribution despite stable linear scaling]

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1 of 23 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.