Cross-Correlation Networks: visualizing influence in the S&P 100

Traders and investors treat correlation in different ways. Investors generally aim to balance the correlation in their portfolio to avoid concentrating risk, while short term terms flock to highly correlated pairs and sectors.

Most of the time people refer to correlation they mean contemporaneous correlation, i.e. the correlation of returns in the same time period. This type of correlation doesn’t involve prediction, rather it shows the relationship between simultaneous changes in random variables as they evolve over time. This measure can be highly valuable: we have shown in the past how we can use Correlation Filtering to cluster components of the S&P 500.

Today we will be taking a look at a different method: cross-correlation. This provides a measure of how two random variables are related between time periods, rather than in the current time period alone. Think of cross-correlation as a function which returns the correlation of one time series against the time lags of another, thus providing us with a method to determine causality. We can use this method to map the lead/lag relationships between stocks.

For example, the following network graph shows the influence network amongst stocks in the S&P 100. This is a directional graph, an arrow drawn from stock A to stock B implies that A pulls B through time periods. In other words, the graph shows which stocks are leaders within the S&P 100 (click to englarge):

xcorThe graph was created by filtering the cross-correlation matrix for S&P 100 index components above a threshold value. Then we weighted each node’s size by the OutDegree: i.e. the number of out-bound links from the node.

With this type of filtering, we can immediately see the leaders within the index. Stocks like UPS and Fedex (FDX) are majorly connected within the index, exerting influence on large swathe of components. At the top of the graph we can see the influence of Excelon (EXC), with links between other connected stocks like Occidental (OXY), Apache (APA), and Exxon Mobile (XOM). This graph also shows the importance of Southern Co (SO), a $41 billion utility company with strong links to the rest of the index.


To check out the fun for yourself, visit our SliceMatrix signup page. Explore Minimum Spanning Trees and Filtered Correlation Networks for the S&P 400, S&P 500, S&P 600 and NASDAQ 100 indexes.

Network Graph from SliceMatrix

Network Graph from SliceMatrix


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4 replies »

    • we looked at +/- 3 time periods, should have mentioned this is daily returns data. first edges were drawn if abs(cross-corr) was >= threshold value. edge width is scaled by total strength of magnitude. date range: 3/19/2009 to 3/23/2015

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  1. Hi, this does not necessarily show causality. All it shows is a picture of what happened between 3/19/2009 and 3/23/2015 (making use of the given parameters set). To show causality, and to assess the predictive value of the analysis, a different type of study is required.

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