Paper: arXiv 2409.10859

Abstract

Macroscopic properties of equity markets affect the performance of active equity strategies but many are not adequately captured by conventional models of financial mathematics and econometrics. Using the CRSP Database of the US equity market, we study empirically several macroscopic properties defined in terms of market capitalizations and returns, and highlight a list of stylized facts and open questions motivated in part by stochastic portfolio theory. Additionally, we present a systematic backtest of the diversity-weighted portfolio under various configurations and study its performance in relation to macroscopic quantities. All of our results can be replicated using codes made available on our online repository.

Complexity vs Empirical Score

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

Why this score: The paper is mathematically dense, drawing heavily on stochastic portfolio theory (SPT) with functionally generated portfolios and interacting particle systems, yet it is highly empirically rigorous, featuring a systematic backtest using CRSP data, providing reproducible code, and reporting stylized facts based on decades of market data.

Research Flowchart

  flowchart TD
  A["Research Goal:<br>Investigate macroscopic properties<br>of equity markets and impact<br>on active strategies"] --> B["Data Source:<br>CRSP US Equity Database<br>Market Capitalizations & Returns"]
  B --> C["Methodology 1:<br>Empirical study of<br>macroscopic properties<br>(Stylized Facts)"]
  B --> D["Methodology 2:<br>Systematic backtest of<br>Diversity-Weighted Portfolio"]
  C --> E["Computational Analysis:<br>Stochastic Portfolio Theory<br>metrics & market dynamics"]
  D --> E
  E --> F["Key Outcomes:<br>1. Identified macroscopic stylized facts<br>2. Open research questions<br>3. Portfolio performance<br>vs. market quantities<br>4. Replicable code repository"]

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5 of 151 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.