Nonlinear shifts and dislocations in financial market structure and composition

ArXiv ID: 2403.15163 “View on arXiv”

Authors: Unknown

Abstract

This paper develops new mathematical techniques to identify temporal shifts among a collection of US equities partitioned into a new and more detailed set of market sectors. Although conceptually related, our three analyses reveal distinct insights about financial markets, with meaningful implications for investment managers. First, we explore a variety of methods to identify nonlinear shifts in market sector structure and describe the mathematical connection between the measure used and the captured phenomena. Second, we study network structure with respect to our new market sectors and identify meaningfully connected sector-to-sector mappings. Finally, we conduct a series of sampling experiments over different sample spaces and contrast the distribution of Sharpe ratios produced by long-only, long-short and short-only investment portfolios. In addition, we examine the sector composition of the top-performing portfolios for each of these portfolio styles. In practice, the methods proposed in this paper could be used to identify regime shifts, optimally structured portfolios, and better communities of equities.

Keywords: portfolio optimization, market sectors, regime shifts, Sharpe ratio, equities

Complexity vs Empirical Score

• Math Complexity: 7.0/10
• Empirical Rigor: 6.5/10
• Quadrant: Holy Grail
• Why: The paper employs advanced mathematical techniques like network analysis, time series segmentation, and statistical physics concepts, placing it in the high math category. It also demonstrates strong empirical rigor through backtesting portfolio strategies (long-only, long-short, short-only) with Sharpe ratios and sector composition analysis on real-world equity data.

  flowchart TD
    A["Research Goal<br>Identify structural shifts & sector relationships in US equities"] --> B["Data Input<br>US equities partitioned into market sectors"]
    B --> C["Analysis 1: Nonlinear Shifts<br>Develop new mathematical techniques to detect regime changes"]
    B --> D["Analysis 2: Network Structure<br>Map connected sector-to-sector relationships"]
    B --> E["Analysis 3: Portfolio Sampling<br>Simulate Long-only, Long-short, Short-only portfolios"]
    C --> F{"Key Findings"}
    D --> F
    E --> F
    F --> G["Outcomes<br>Identified regime shifts<br>Optimal portfolio structures<br>Better equity communities"]