The lexical ratio: A new perspective on portfolio diversification

TL;DR

The paper introduces the lexical ratio (LR), a new textual data-based metric for portfolio diversification that captures non-numerical asset relationships, improving risk management and return optimization.

Contribution

It presents the lexical ratio (LR), a novel diversification metric leveraging textual data and information theory, with demonstrated theoretical robustness and empirical advantages over traditional measures.

Findings

LR outperforms traditional metrics in optimizing portfolio returns

LR captures unique diversification aspects beyond correlation-based measures

LR is robust across different market conditions

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.