How Lead-Lag Correlations Affect The Intraday Pattern Of Collective Stock Dynamics by OFR

Chester Curme

Boston University

Rosario N. Mantegna

University of Palermo, Palermo, Italy, and Central European University, Budapest, Hungary

Dror Y. Kenett

Office of Financial Research

Michele Tumminello

University of Palermo, Palermo, Italy

H. Eugene Stanley

Boston University


The degree of correlation among stock returns affects the possibility to diversify the risk of investment, and it plays a major role in financial spillover. During the last decade, the increasing level of correlation observed in financial markets has become a threat to market stability. Here, we analyze high frequency data of stock returns traded at the New York Stock Exchange in the periods 2001-03 and 2011-13. In each period we uncouple the factors contributing to the intraday pattern of synchronous correlations, including volatility, autocorrelations and lagged cross-correlations among assets. We find that intraday market dynamics have changed considerably in the last decade, and relate our findings to the dynamics of an underlying network of lead-lag relationships among equities. In particular, while in 2001-03 lagged cross-correlations contributed significantly to the intraday correlation profile, the increased degree of synchronous correlation observed in the period 2011-13 can be associated with the presence of many significant auto-correlations, especially at the end of a trading day, with a stronger coupling between auto-correlations and lagged cross-correlations of returns. The presented method of data analysis could be used to inform policy makers and financial institutions about market efficiency and risk of financial spillover, and could also be helpful for portfolio management.

How Lead-Lag Correlations Affect The Intraday Pattern Of Collective Stock Dynamics – Introduction

Filtering information out of vast multivariate datasets is a crucial step in managing and understanding the complex systems that underlie them. These systems are composed of many components, the interactions among which typically induce larger-scale organization or structure. A major scientific challenge is to extract insights into the large-scale organization of the system using data on its individual components.

Financial markets are a primary example of a setting in which this approach has value. When constructing an optimal portfolio of assets, for example, the goal is typically to allocate resources so as to balance the trade-off between return and risk. As has been understood at least since the work of Markowitz (1952), risk can be quantified by studying the co-movements of asset prices: placing a bet on a single group of correlated assets is risky, whereas this risk can at least in part be diversified away by betting on uncorrelated or anti-correlated assets. An understanding of the larger-scale structure of co-movements among assets can be helpful, not only in the pursuit of optimal portfolios, but also in for our ability to accurately measure marketwide systemic risks (Glasserman and Young, 2015; Kritzman and Li, 2010).

Time series obtained by monitoring the evolution of a multivariate complex system, such as time series of price returns in a financial market, can be used to extract information about the structural organization of such a system. This is generally accomplished by using the correlation between pairs of elements as a similarity measure, and analyzing the resulting correlation matrix. A spectral analysis of the sample correlation matrix can indicate deviations from a purely random matrix (Laloux et al., 1999; Plerou et al., 1999) or more structured models, such as the single index (Laloux et al., 1999). Clustering algorithms can also be applied to elicit information about emergent structures in the system from a sample correlation matrix (Mantegna, 1999). Such structures can also be investigated by associating a (correlation-based) network with the correlation matrix. One popular approach has been to extract the minimum spanning tree (MST), which is the tree connecting all the elements in a system in such a way to maximize the sum of node similarities (Mantegna, 1999; Bonanno et al., 2003; Onnela et al., 2003). Different correlation based networks can be associated with the same hierarchical tree, putting emphasis on different aspects of the sample correlation matrix. For instance, while the MST reflects the ranking of correlation coefficients, other methods, such as threshold methods, emphasize more the absolute value of each correlation coefficient. Researchers have also aimed to quantify the extent to which the behavior of one market, institution or asset can provide information about another through econometric studies (Hamao et al., 1990), partial-correlation networks (Kenett et al., 2010, 2012) and by investigating Granger-causality networks (Billio et al., 2012).

A network is defined as a set of nodes (such as people, companies, or airports), and links that connect the nodes on the basis of interaction or relationship. Such links can be structural, such as well-defined plane routes that connect airports. Alternatively, links can be functional, or derived using similarities between the activities of two nodes, such as similarities in the number of travelers in two airports. Such functional links can be derived using correlation measures, and correlation-based networks have been found to be a very important tool for investigating real world systems Tumminello et al. (2010); Kenett et al. (2010).

Intraday Pattern

Intraday Pattern

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