Paper: arXiv 2411.06080

Abstract

Portfolio diversification, traditionally measured through asset correlations and volatilitybased metrics, is fundamental to managing financial risk. However, existing diversification metrics often overlook non-numerical relationships between assets that can impact portfolio stability, particularly during market stresses. This paper introduces the lexical ratio (LR), a novel metric that leverages textual data to capture diversification dimensions absent in standard approaches. By treating each asset as a unique document composed of sectorspecific and financial keywords, the LR evaluates portfolio diversification by distributing these terms across assets, incorporating entropy-based insights from information theory. We thoroughly analyze LR’s properties, including scale invariance, concavity, and maximality, demonstrating its theoretical robustness and ability to enhance risk-adjusted portfolio returns. Using empirical tests on S&P 500 portfolios, we compare LR’s performance to established metrics such as Markowitz’s volatility-based measures and diversification ratios. Our tests reveal LR’s superiority in optimizing portfolio returns, especially under varied market conditions. Our findings show that LR aligns with conventional metrics and captures unique diversification aspects, suggesting it is a viable tool for portfolio managers.

Complexity vs Empirical Score

  • Math Complexity: 7.5/10
  • Empirical Rigor: 6.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper uses advanced information theory (Shannon entropy) and derived formulas for its new metric, indicating high mathematical density. It also conducts empirical tests on S&P 500 portfolios with backtest-ready comparisons to established metrics, though it lacks code or datasets in the excerpt.

Research Flowchart

  flowchart TD
  A["Research Goal: Introduce Lexical Ratio (LR) for portfolio diversification"] --> B["Methodology: Process textual & financial data from S&P 500"]
  B --> C["Data: Asset descriptions & sector-specific keywords"]
  C --> D["Computation: Compute LR using entropy-based analysis<br>(treating assets as documents)"]
  D --> E["Comparison: Benchmark LR against Markowitz volatility<br>& diversification ratios"]
  E --> F["Findings: LR enhances risk-adjusted returns & captures<br>unique non-numerical diversification aspects"]