[Paper Review] Study of the Correlations Between Stocks of Different Markets

Ricardo Coelho, Peter Richmond+2 more|ArXiv.org|Oct 26, 2007

Complex Systems and Time Series Analysis3 citations

TL;DR

This study analyzes cross-market correlations between stocks on the London and New York stock exchanges using Random Matrix Theory and Minimal Spanning Trees. It finds that while markets remain largely separated geographically, New York's influence subtly emerges in the third-highest eigenvector, indicating cross-market sectoral influence, particularly in oil & gas and utilities, without significant market integration at the overall level.

ABSTRACT

We study correlations of a set of stocks selected from both the New York and London stock exchanges. Results are displayed using both Random Matrix Theory approach and the graphical visualisation of the Minimal Spanning Tree. For the set of stocks we study, cross correlations between markets do not mix the markets significantly. Geographical differences seem to dominate the output of a Random Matrix analysis. Only at the level of the third highest eigenvector do we see an effect of New York on the London data with the emergence of some common sectors with the larger eigenvectors in London and New York. The Minimal Spanning Trees show the broad separation of the markets as reflected in the second eigenvector of the Random Matrix analysis. However more detail is difficult to discern from the Minimal Spanning Trees analysis.

Motivation & Objective

• To investigate whether stocks from the London and New York stock exchanges exhibit significant cross-market correlations.
• To determine whether industrial sector clustering or geographical market location dominates in financial correlation structures.
• To assess the extent to which the New York market influences the London market through cross-correlations.
• To compare the effectiveness of Random Matrix Theory and Minimal Spanning Tree methods in revealing market structure.

Proposed method

• Computes log-returns for 939 large-cap stocks from NYSE and LON over 3,127 trading days (1994–2007), excluding dual-listed stocks.
• Constructs a correlation matrix using normalized returns, with elements defined by the standard correlation coefficient formula.
• Applies Random Matrix Theory to analyze the eigenvalue spectrum and identify non-random structure in the correlation matrix.
• Uses eigenvectors of the correlation matrix to identify sectoral and market-wide patterns, particularly focusing on the top three eigenvectors.
• Employs Minimal Spanning Tree (MST) visualization to represent correlation structures graphically, with color-coding for industrial sectors and market symbols.
• Performs comparative analysis with correlations computed at the same day and with LON one day ahead of NYSE to test lead-lag effects.

Experimental results

Research questions

• RQ1 Do stocks from the London and New York stock exchanges show significant cross-market correlations beyond those within each market?
• RQ2 Which factor—geographic market location or industrial sector—dominates the clustering structure in stock correlation networks?
• RQ3 To what extent does the New York market influence the correlation structure of the London market?
• RQ4 How do the results from Random Matrix Theory compare with those from Minimal Spanning Tree visualization in revealing market dynamics?

Key findings

• The highest eigenvector of the correlation matrix reflects a common market-wide trend, indicating a shared overall market movement across both exchanges.
• The second-highest eigenvector reveals a clear geographical separation between NYSE and LON stocks, consistent with market-based clustering.
• The third-highest eigenvector shows a measurable influence of NYSE on LON, particularly in the oil and gas and utilities sectors, indicating cross-market sectoral correlation.
• When LON data is one day ahead of NYSE, the influence of NYSE on LON becomes more apparent in the third eigenvector, suggesting a delayed but detectable impact.
• Minimal Spanning Trees confirm the geographical separation of markets but fail to capture the finer cross-market influences visible in the eigenvector analysis.
• The results suggest that geographical market identity is the dominant factor in stock correlation clustering, with industrial sector effects secondary.