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. 2010 Dec 20;5(12):e15032.
doi: 10.1371/journal.pone.0015032.

Dominating clasp of the financial sector revealed by partial correlation analysis of the stock market

Dror Y Kenett  1 , Michele Tumminello, Asaf Madi, Gitit Gur-Gershgoren, Rosario N Mantegna, Eshel Ben-Jacob
Affiliations

Dominating clasp of the financial sector revealed by partial correlation analysis of the stock market

Dror Y Kenett et al. PLoS One. .

Abstract

What are the dominant stocks which drive the correlations present among stocks traded in a stock market? Can a correlation analysis provide an answer to this question? In the past, correlation based networks have been proposed as a tool to uncover the underlying backbone of the market. Correlation based networks represent the stocks and their relationships, which are then investigated using different network theory methodologies. Here we introduce a new concept to tackle the above question--the partial correlation network. Partial correlation is a measure of how the correlation between two variables, e.g., stock returns, is affected by a third variable. By using it we define a proxy of stock influence, which is then used to construct partial correlation networks. The empirical part of this study is performed on a specific financial system, namely the set of 300 highly capitalized stocks traded at the New York Stock Exchange, in the time period 2001-2003. By constructing the partial correlation network, unlike the case of standard correlation based networks, we find that stocks belonging to the financial sector and, in particular, to the investment services sub-sector, are the most influential stocks affecting the correlation profile of the system. Using a moving window analysis, we find that the strong influence of the financial stocks is conserved across time for the investigated trading period. Our findings shed a new light on the underlying mechanisms and driving forces controlling the correlation profile observed in a financial market.

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Conflict of interest statement

Competing Interests: The authors have declared that no competing interests exist.

Figures

Figure 1
Figure 1. Two measures of PCTN connectivity as function of the parameter .
The value formula image is the one used in the paper.
Figure 2
Figure 2. Top ten influential stocks according to the out-degree in both the partial correlation networks.
Figure 3
Figure 3. PCPG analysis of the 300 stocks, grouped by their corresponding sub-sector.
In this network we present how each sub-sector is affecting the other sub-sectors. The color of vertices is according to the economic sector each sub-sector belongs to. Specifically, basic materials (violet), capital goods (light green), conglomerates (orange), consumer cyclical (tan), consumer non cyclical (yellow), energy (blue), financial (green), healthcare (gray), services (cyan), technology (red), transportation (brown), and utilities (magenta). Sub-sectors with a positive relative influence formula image according to Eq.(5) are labeled in the figure. Sub-sectors labeled with numbers are listed in Table S2. We find two main hubs in the network - the investment services and the insurance life sub-sectors. The thickness and gray level of links is proportional to the logarithm of the weight of the link.
Figure 4
Figure 4. PCPG (partial correlations) of the 300 stocks.
Colors of vertices in the network are chosen according to the economic sector each stock belongs to. Specifically: basic materials (violet), capital goods (light green), conglomerates (orange), consumer cyclical (tan), consumer non cyclical (yellow), energy (blue), financial (green), healthcare (gray), services (cyan), technology (red), transportation (brown), and utilities (magenta).
Figure 5
Figure 5. PMFG (standard correlations) of the 300 stocks.
Colors of vertices in the network are chosen according to the economic sector each stock belongs to. Specifically: basic materials (violet), capital goods (light green), conglomerates (orange), consumer cyclical (tan), consumer non cyclical (yellow), energy (blue), financial (green), healthcare (gray), services (cyan), technology (red), transportation (brown), and utilities (magenta).
Figure 6
Figure 6. Sub-sector (undirected) network associated with the PMFG (standard correlations).
The thickness and gray level of links is proportional to the logarithm of the weight of the link. The color of vertices is according to the economic sector of activity.
Figure 7
Figure 7. Sector (directed) network associated with the PCPG (partial correlations).
The thickness and gray level of links is proportional to the logarithm of the weight of the link. Links are labeled according to the weight. The color of vertices is according to the economic sector of activity.
Figure 8
Figure 8. Sector (undirected) network associated with the PMFG (standard correlations).
The thickness and gray level of links is proportional to the logarithm of the weight of the link. Links are labeled according to the weight. The color of vertices is according to the economic sector of activity.
Figure 9
Figure 9. Scatter plot of the quantity (see Eq. 4) as estimated from real data, and as reconstructed by using factor models.
Figure 10
Figure 10. Running window application of the PCTN.
Using a 22-day time window, we perform the PCTN in each window, and rank the importance of each stock according to the number of stocks it influenced. The stocks are ordered according to their average influence over time. Most influential stocks are at the bottom of the figure 9 over the 10 most influential stocks are form the financial sector, 5 of them belonging to the sub-sector of investment services.
Figure 11
Figure 11. Running window application of the PCPG.
Here, each time window corresponds to four months of trading. For each time window we perform the PCPG analysis, and compute the relative influence formula image of each economic sub-sector. Here we present the results about formula image just for the 11 sub-sectors of activity that show a positive relative influence in at least one time window.
See this image and copyright information in PMC

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