Dror Y. Kenett

Dominating Clasp of the Financial Sector Revealed by Partial Correlation Analysis of the Stock Market

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.

Quantifying the Behavior of Stock Correlations Under Market Stress

Understanding correlations in complex systems is crucial in the face of turbulence, such as the ongoing financial crisis. However, in complex systems, such as financial systems, correlations are not constant but instead vary in time. Here we address the question of quantifying state-dependent correlations in stock markets. Reliable estimates of correlations are absolutely necessary to protect a portfolio. We analyze 72 years of daily closing prices of the 30 stocks forming the Dow Jones Industrial Average (DJIA). We find the striking result that the average correlation among these stocks scales linearly with market stress reflected by normalized DJIA index returns on various time scales. Consequently, the diversification effect which should protect a portfolio melts away in times of market losses, just when it would most urgently be needed. Our empirical analysis is consistent with the interesting possibility that one could anticipate diversification breakdowns, guiding the design of protected portfolios.

Evolvement of uniformity and volatility in the stressed global financial village

Background In the current era of strong worldwide market couplings the global financial village became highly prone to systemic collapses, events that can rapidly sweep throughout the entire village. Methodology/Principal Findings We present a new methodology to assess and quantify inter-market relations. The approach is based on the correlations between the market index, the index volatility, the market Index Cohesive Force and the meta-correlations (correlations between the intra-correlations.) We investigated the relations between six important world markets—U.S., U.K., Germany, Japan, China and India—from January 2000 until December 2010. We found that while the developed “western” markets (U.S., U.K., Germany) are highly correlated, the interdependencies between these markets and the developing “eastern” markets (India and China) are volatile and with noticeable maxima at times of global world events. The Japanese market switches “identity”—it switches between periods of high meta-correlations with the “western” markets and periods when it behaves more similarly to the “eastern” markets. Conclusions/Significance The methodological framework presented here provides a way to quantify the evolvement of interdependencies in the global market, evaluate a world financial network and quantify changes in the world inter market relations. Such changes can be used as precursors to the agitation of the global financial village. Hence, the new approach can help to develop a sensitive “financial seismograph” to detect early signs of global financial crises so they can be treated before they develop into worldwide events.

Index Cohesive Force Analysis Reveals That the US Market Became Prone to Systemic Collapses Since 2002

Background The 2007–2009 financial crisis, and its fallout, has strongly emphasized the need to define new ways and measures to study and assess the stock market dynamics. Methodology/Principal Findings The S&P500 dynamics during 4/1999–4/2010 is investigated in terms of the index cohesive force (ICF - the balance between the stock correlations and the partial correlations after subtraction of the index contribution), and the Eigenvalue entropy of the stock correlation matrices. We found a rapid market transition at the end of 2001 from a flexible state of low ICF into a stiff (nonflexible) state of high ICF that is prone to market systemic collapses. The stiff state is also marked by strong effect of the market index on the stock-stock correlations as well as bursts of high stock correlations reminiscence of epileptic brain activity. Conclusions/Significance The market dynamical states, stability and transition between economic states was studies using new quantitative measures. Doing so shed new light on the origin and nature of the current crisis. The new approach is likely to be applicable to other classes of complex systems from gene networks to the human brain.

Global and local features of semantic networks: evidence from the Hebrew mental lexicon.

Background Semantic memory has generated much research. As such, the majority of investigations have focused on the English language, and much less on other languages, such as Hebrew. Furthermore, little research has been done on search processes within the semantic network, even though they are abundant within cognitive semantic phenomena. Methodology/Principal Findings We examine a unique dataset of free association norms to a set of target words and make use of correlation and network theory methodologies to investigate the global and local features of the Hebrew lexicon. The global features of the lexicon are investigated through the use of association correlations – correlations between target words, based on their association responses similarity; the local features of the lexicon are investigated through the use of association dependencies – the influence words have in the network on other words. Conclusions/Significance Our investigation uncovered Small-World Network features of the Hebrew lexicon, specifically a high clustering coefficient and a scale-free distribution, and provides means to examine how words group together into semantically related ‘free categories’. Our novel approach enables us to identify how words facilitate or inhibit the spread of activation within the network, and how these words influence each other. We discuss how these properties relate to classical research on spreading activation and suggest that these properties influence cognitive semantic search processes. A semantic search task, the Remote Association Test is discussed in light of our findings.

Partial correlation analysis: applications for financial markets

The presence of significant cross-correlations between the synchronous time evolution of a pair of equity returns is a well-known empirical fact. The Pearson correlation is commonly used to indicate the level of similarity in the price changes for a given pair of stocks, but it does not measure whether other stocks influence the relationship between them. To explore the influence of a third stock on the relationship between two stocks, we use a partial correlation measurement to determine the underlying relationships between financial assets. Building on previous work, we present a statistically robust approach to extract the underlying relationships between stocks from four different financial markets: the United States, the United Kingdom, Japan, and India. This methodology provides new insights into financial market dynamics and uncovers implicit influences in play between stocks. To demonstrate the capabilities of this methodology, we (i) quantify the influence of different companies and, by studying market similarity across time, present new insights into market structure and market stability, and (ii) we present a practical application, which provides information on the how a company is influenced by different economic sectors, and how the sectors interact with each other. These examples demonstrate the effectiveness of this methodology in uncovering information valuable for a range of individuals, including not only investors and traders but also regulators and policy makers.

DEPENDENCY NETWORK AND NODE INFLUENCE: APPLICATION TO THE STUDY OF FINANCIAL MARKETS

Much effort has been devoted to assess the importance of nodes in complex networks. Examples of commonly used measures of node importance include node degree, node centrality and node vulnerability score (the effect of the node deletion on the network efficiency). Here we present a new approach to compute and investigate the mutual dependencies between network nodes from the matrices of node–node correlations. The dependency network approach provides a new system level analysis of the activity and topology of directed networks. The approach extracts topological relations between the networks nodes (when the network structure is analyzed), and provides an important step towards inference of causal activity relations between the network nodes (when analyzing the network activity). The resulting dependency networks are a new class of correlation-based networks, and are capable of uncovering hidden information on the structure of the network. Here, we present a review of the new approach, and an example of its application to financial markets. We apply the methodology to the daily closing prices of all Dow Jones Industrial Average (DJIA) index components for the period 1939–2010. Investigating the structure and dynamics of the dependency network across time, we find fingerprints of past financial crises, illustrating the importance of this methodology.

Quantifying meta-correlations in financial markets

Financial markets are modular multi-level systems, in which the relationships between the individual components are not constant in time. Sudden changes in these relationships significantly affect the stability of the entire system, and vice versa. Our analysis is based on historical daily closing prices of the 30 components of the Dow Jones Industrial Average (DJIA) from March 15th, 1939 until December 31st, 2010. We quantify the correlation among these components by determining Pearson correlation coefficients, to investigate whether mean correlation of the entire portfolio can be used as a precursor for changes in the index return. To this end, we quantify the meta-correlation – the correlation of mean correlation and index return. We find that changes in index returns are significantly correlated with changes in mean correlation. Furthermore, we study the relationship between the index return and correlation volatility – the standard deviation of correlations for a given time interval. This parameter provides further evidence of the effect of the index on market correlations and their fluctuations. Our empirical findings provide new information and quantification of the index leverage effect, and have implications to risk management, portfolio optimization, and to the increased stability of financial markets.

Analyses of antigen dependency networks unveil immune system reorganization between birth and adulthood

Much effort has been devoted to assess the importance of nodes in complex biological networks (such as gene transcriptional regulatory networks, protein interaction networks, and neural networks). Examples of commonly used measures of node importance include node degree, node centrality, and node vulnerability score (the effect of the node deletion on the network efficiency). Here, we present a new approach to compute and investigate the mutual dependencies between network nodes from the matrices of node-node correlations. To this end, we first define the dependency of node i on node j (or the influence of node j on node i), D(i, j) as the average over all nodes k of the difference between the i - k correlation and the partial correlations between these nodes with respect to node j. Note that the dependencies, D(i, j) define a directed weighted matrix, since, in general, D(i, j) differs from D( j, i). For this reason, many of the commonly used measures of node importance, such as node centrality, cannot be used. Hence, to assess the node importance of the dependency networks, we define the system level influence (SLI) of antigen j, SLI( j) as the sum of the influence of j on all other antigens i. Next, we define the system level influence or the influence score of antigen j, SLI( j) as the sum of D(i, j) over all nodes i. We introduce the new approach and demonstrate that it can unveil important biological information in the context of the immune system. More specifically, we investigated antigen dependency networks computed from antigen microarray data of autoantibody reactivity of IgM and IgG isotypes present in the sera of ten mothers and their newborns. We found that the analysis was able to unveil that there is only a subset of antigens that have high influence scores (SLI) common both to the mothers and newborns. Networks comparison in terms of modularity (using the Newmans algorithm) and of topology (measured by the divergence rate) revealed that, at birth, the IgG networks exhibit a more profound global reorganization while the IgM networks exhibit a more profound local reorganization. During immune system development, the modularity of the IgG network increases and becomes comparable to that of the IgM networks at adulthood. We also found the existence of several conserved IgG and IgM network motifs between the maternal and newborns networks, which might retain network information as our immune system develops. If correct, these findings provide a convincing demonstration of the effectiveness of the new approach to unveil most significant biological information. Whereas we have introduced the new approach within the context of the immune system, it is expected to be effective in the studies of other complex biological social, financial, and manmade networks.

Semantic organization in children with cochlear implants: computational analysis of verbal fluency

Purpose: Cochlear implants (CIs) enable children with severe and profound hearing impairments to perceive the sensation of sound sufficiently to permit oral language acquisition. So far, studies have focused mainly on technological improvements and general outcomes of implantation for speech perception and spoken language development. This study quantitatively explored the organization of the semantic networks of children with CIs in comparison to those of age-matched normal hearing (NH) peers. Method: Twenty seven children with CIs and twenty seven age- and IQ-matched NH children ages 7–10 were tested on a timed animal verbal fluency task (Name as many animals as you can). The responses were analyzed using correlation and network methodologies. The structure of the animal category semantic network for both groups were extracted and compared. Results: Children with CIs appeared to have a less-developed semantic network structure compared to age-matched NH peers. The average shortest path length (ASPL) and the network diameter measures were larger for the NH group compared to the CIs group. This difference was consistent for the analysis of networks derived from animal names generated by each group [sample-matched correlation networks (SMCN)] and for the networks derived from the common animal names generated by both groups [word-matched correlation networks (WMCN)]. Conclusions: The main difference between the semantic networks of children with CIs and NH lies in the network structure. The semantic network of children with CIs is under-developed compared to the semantic network of the age-matched NH children. We discuss the practical and clinical implications of our findings.