Paper: arXiv 2611.13365

Authors: Peter B. Lerner

Abstract

The paper analyzes monthly reports of two companies: one market maker, Virtu, and one broker-dealer, SoHo, in the period between January 2021 and March 2024. The predictive power of standard methods for the probability laws of stock orders- linear regression and LSTM- is poor, despite their probability laws being relatively stable. However, the month-to-month correlations are highly stable and predictable. In this paper, we study the distributions of the sixteen datasets resulting from the 26 stock-trading parameters reported by brokerages under regulatory requirements.

Complexity vs Empirical Score

  • Math Complexity: 4.0/10
  • Empirical Rigor: 7.0/10
  • Quadrant: Street Traders — practical and empirical, lighter on theory

Why this score: The paper presents a solid empirical analysis of Rule 605 data, focusing on correlation stability rather than complex mathematical models. While the methodology is clear, the lack of publicly available code or data limits reproducibility. The novelty lies in the specific focus on correlation stability for regulatory data.

Research Flowchart

  flowchart TD
    A[Research Goal: Understand Predictability of Stock Orders & Rule 605 Parameters] --> B{Data Collection: Monthly Reports (Jan 2021 - Mar 2024)};
    B --> C[Data Sources: Virtu (Market Maker), SoHo (Broker-Dealer)];
    C --> D{Data Analysis: 16 datasets from 26 stock-trading parameters};
    D --> E{Computational Processes: Linear Regression, LSTM (for probability laws), Correlation Analysis (for month-to-month stability)};
    E --> F[Key Finding 1: Poor Predictive Power of Standard Methods (LR, LSTM) for Probability Laws];
    F --> G[Key Finding 2: High Stability & Predictability of Month-to-Month Correlations];