[Paper Review] On financial market correlation structures and diversification benefits across and within equity sectors

Nick James, Max Menzies+1 more|arXiv (Cornell University)|Feb 21, 2022

Complex Systems and Time Series Analysis59 references33 citations

TL;DR

This study analyzes 20 years of US equity data to quantify diversification benefits across and within sectors using cross-correlation matrices and network diagnostics. It finds that collective market behavior—measured by the leading eigenvalue and modularity—increases during crises, reducing diversification efficacy, and identifies a 36-stock portfolio uniformly sampled across 9 sectors as optimal for risk reduction.

ABSTRACT

We study how to assess the potential benefit of diversifying an equity portfolio by investing within and across equity sectors. We analyse 20 years of US stock price data, which includes the global financial crisis (GFC) and the COVID-19 market crash, as well as periods of financial stability, to determine the `all weather' nature of equity portfolios. We establish that one may use the leading eigenvalue of the cross-correlation matrix of log returns as well as graph-theoretic diagnostics such as modularity to quantify the collective behaviour of the market or a subset of it. We confirm that financial crises are characterised by a high degree of collective behaviour of equities, whereas periods of financial stability exhibit less collective behaviour. We argue that during times of increased collective behaviour, risk reduction via sector-based portfolio diversification is ineffective. Using the degree of collectivity as a proxy for the benefit of diversification, we perform an extensive sampling of equity portfolios to confirm the old financial adage that 30-40 stocks provide sufficient diversification. Using hierarchical clustering, we discover a `best value' equity portfolio for diversification consisting of 36 equities sampled uniformly from 9 sectors. We further show that it is typically more beneficial to diversify across sectors rather than within. Our findings have implications for cost-conscious retail investors seeking broad diversification across equity markets.

Motivation & Objective

• To assess the effectiveness of sector-based portfolio diversification across different market regimes.
• To quantify how collective market behavior during crises undermines traditional diversification benefits.
• To determine the minimal number of equities needed for effective risk reduction, particularly across sectors.
• To identify an optimal, cost-effective equity portfolio that maximizes diversification benefits.

Proposed method

• Analyzes 20 years of daily log returns from 339 US equities using cross-correlation matrices.
• Uses the leading eigenvalue of the correlation matrix as a proxy for collective market behavior.
• Applies modularity from network theory to detect sector-level independence and community structure.
• Employs hierarchical clustering to identify optimal equity groupings for diversification.
• Performs exhaustive portfolio sampling across varying sizes and sector compositions to evaluate risk reduction.
• Uses random matrix theory to distinguish non-random market structure from noise in correlations.

Experimental results

Research questions

• RQ1 How does collective market behavior, as measured by the leading eigenvalue, vary across financial crises and stable periods?
• RQ2 To what extent does sector-based diversification reduce portfolio risk during periods of high market correlation?
• RQ3 What is the minimal number of equities required to achieve sufficient diversification, and does this number vary by sector composition?
• RQ4 Is it more effective to diversify across sectors or within sectors in terms of risk reduction?
• RQ5 Can a uniformly sampled 36-stock portfolio across 9 sectors be identified as optimal for diversification?

Key findings

• During financial crises such as the GFC (2008/2009) and the 2020 COVID-19 crash, the leading eigenvalue of the correlation matrix increases significantly, indicating heightened collective market behavior.
• Periods of financial stability exhibit lower collective behavior, allowing for more effective diversification through unsystematic risk reduction.
• The study confirms the 30–40 stock rule for diversification, with a 36-stock portfolio uniformly sampled from 9 sectors identified as optimal for minimizing risk.
• Diversification across sectors is consistently more effective than within-sector diversification, especially during market stress.
• Modularity and the leading eigenvalue show consistent trends: high collectivity during crises reduces diversification benefits.
• The optimal 36-stock portfolio achieves strong risk reduction, suggesting that broad sector coverage is more effective than concentration within a single sector.