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Comparative analysis of return dynamics for a portfolio of stocks traded at NYSE and at LSE Salvatore Miccichè Observatory of Complex Systems Dipartimento di Fisica e Tecnologie Relative Università degli Studi di Palermo Progetto Strategico - Incontro di progetto II anno - Palermo 23 Settembre 2005

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Comparative analysis of return dynamics for portfolios of stocks traded at NYSE and LSE Observatory of Complex Systems R. N. Mantegna F. Lillo S. Miccichè M. Spanò M. Tumminello G. Vaglica C. Coronnello M. Glorioso V. Desoutter A. Garas R. Schäfer Econophysics Bioinformatics Stochastic Processes Econophysics Bioinformatics Stochastic Processes

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Comparative analysis of return dynamics for portfolios of stocks traded at NYSE and LSE Aim of the research Compare the dynamics of price returns traded at different exchanges - industry sector identification at different time horizon - sector dynamics - LSE and NYSE - are there common (stylized) facts ? Compare the dynamics of price returns traded at different exchanges - industry sector identification at different time horizon - sector dynamics - LSE and NYSE - are there common (stylized) facts ? Compare the information obtained by using different techniques for extracting information from a given correlation matrix - RMT, SLCA, ALCA, PMFG, … - what are the right variables to look at? Compare the information obtained by using different techniques for extracting information from a given correlation matrix - RMT, SLCA, ALCA, PMFG, … - what are the right variables to look at?

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Comparative analysis of return dynamics for portfolios of stocks traded at NYSE and LSE Methods: RMT eigenvalues eigenvectors Study of the eigenvalues and eigenvectors of the N×N correlation matrix. Precise evaluation of the noise due to the finite length T of the time-series IDEA IDEA: significative eigenvalues can be associated to economic sectors. Crucial parameter Q=N/T

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Comparative analysis of return dynamics for portfolios of stocks traded at NYSE and LSE Methods: SLCA Construct an ordered list of pair of stocks L ord,by ranking all the possible pairs according to their distance d ij.The first pair of L ord has the shortest distance.Construct an ordered list of pair of stocks L ord,by ranking all the possible pairs according to their distance d ij.The first pair of L ord has the shortest distance. The first pair of L ord gives the first two elements of the MST and the link between them.The first pair of L ord gives the first two elements of the MST and the link between them. The construction of the MST continues by analyzing the list L ord.At each successive stage, a pair of elements is selected from L ord and the corresponding link is added to the MST only if no loops are generated in the graph after the link insertion.The construction of the MST continues by analyzing the list L ord.At each successive stage, a pair of elements is selected from L ord and the corresponding link is added to the MST only if no loops are generated in the graph after the link insertion. At each step,when two elements or one element and a cluster or two clusters p and q merge in a wider single cluster t, the distance d tr between the new cluster t and any cluster r is recursively given by: d tr =min { d pr,d qr } i.e. the distance between any element of cluster t and any element of cluster r is the shortest distance between any two entities in clusters t and r. Single Linkage Clustering Analysis MST construction N(N-1)/2 N-1

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Comparative analysis of return dynamics for portfolios of stocks traded at NYSE and LSE Methods: ALCA At each step,when two elements or one element and a cluster or two clusters p and q merge in a wider single cluster t, the distance d tr between the new cluster t and any cluster r is recursively given by: d tr =mean { d pr,d qr } the distance between any element of cluster t and any element of cluster r is the mean distance between any two entities in clusters t and r. i.e. the distance between any element of cluster t and any element of cluster r is the mean distance between any two entities in clusters t and r. Average Linkage Clustering Analysis

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Comparative analysis of return dynamics for portfolios of stocks traded at NYSE and LSE Methods: PMFG The Planar Maximally Filtered Graph is a recently introduced graph. allowing a greater number of links and more complex topological structures than the MST (cliques and loops). The basic motivation is to obtain a graph retaining the same hierarchical properties of the MST, i.e. the same hierarchical tree of SLCA, but allowing a greater number of links and more complex topological structures than the MST (cliques and loops). a link can be included in the graph if and only if the graph with the new link included is still planar The construct on of the PMFG is done by relaxing the topological constraint of the MST construction protocol according to which no loops are allowed in a tree. Specifically, in the PMFG a link can be included in the graph if and only if the graph with the new link included is still planar. it can be drawn on a plane without edge crossings A graph is planar f and only if it can be drawn on a plane (infinite in principle) without edge crossings. Planar Maximally Filtered Graph It allows a measure on the intra-sector clustering through the computation of the Connection Strength (3-cliques & 4-cliques).

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Comparative analysis of return dynamics for portfolios of stocks traded at NYSE and LSE The set of investigated stocks We consider: NYSE - the 100 most capitalized stocks in LSE - the 92 most traded stocks in intraday synchronizehomogenize We consider high-frequency (intraday) data. Transactions do not occur at the same time for all stocks. We have to synchronize/homogenize the data: NYSE: 5 min, 15 min, 30 min, 65 min, 195 min, 1 day trading time 6 h 30 LSE: 5 min, 15 min, 51 min, 102 min, 255 min, 1 daytrading time 8 h 30 NYSE: 5 min, 15 min, 30 min, 65 min, 195 min, 1 day trading time 6 h 30 LSE: 5 min, 15 min, 51 min, 102 min, 255 min, 1 day trading time 8 h 30 TAQTAQ Trades And Quotes (TAQ) database maintained by NYSE ( ) R O BROB2002 Rebuild Order Book (ROB) database maintained by LSE (2002)

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Comparative analysis of return dynamics for portfolios of stocks traded at NYSE and LSE The set of investigated stocks NYSE 100 stocks Financial 04 Consumer non-Cyclical 11 Services 12 Conglomerates 4 NYSE 100 stocks 01 Technology 8 02 Financial Energy 3 04 Consumer non-Cyclical Consumer Cyclical 2 06 Healthcare Basic Materials 6 08 Services Utilities 2 10 Capital Goods 6 11 Transportation 2 12 Conglomerates 4 LSE 92 stocks Financial 04 Consumer non-Cyclical 12 Services 12 Conglomerates 0 LSE 92 stocks 01 Technology 4 02 Financial Energy 3 04 Consumer non-Cyclical Consumer Cyclical Healthcare 6 07 Basic Materials 5 08 Services Utilities 6 10 Capital Goods 5 11 Transportation 2 12 Conglomerates 0

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Comparative analysis of return dynamics for portfolios of stocks traded at NYSE and LSE The set of investigated stocks LSE: 5 min, 1day NYSE: 5 min, 1day

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Comparative analysis of return dynamics for portfolios of stocks traded at NYSE and LSE LSE day NYSE day PREDICTION: 6 significative eigenvalues aMarket Mode bConsumer Non-Cyclical cFinancial dCapital Goods eTechnology fHealthcare g? h? i? Is it by chance? PREDICTION: 9 significative eigenvalues aMarket Mode bConsumer Non-Cyclical c? dHealthcare eUtilities&Services f? g? h? iUtilities What is significant? What is not? Daily data: RMT

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Comparative analysis of return dynamics for portfolios of stocks traded at NYSE and LSE Daily data: SLCA - hierarchical organization NYSE dayLSE day FINANCIAL 10 out of 20 SERVICES 02 out of 19 FINANCIAL 18 out of 24 SERVICES 04 out of 20 High level of correlation Basic Materials is also observable

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Comparative analysis of return dynamics for portfolios of stocks traded at NYSE and LSE NYSE day LSE day Daily data: SLCA - topological organization Clusters are essentially similar to HT no star, small hubs Clusters are different from HT no star, small hubs (NCC, STI, MEL,...) TECHNOLOGY are clustered around ADI CONSUMER NC are clustered around PG HEALTHCARE are clustered around PFE TECHNOLOGY too few to spot differencies CONSUMER NC are clustered through BP HEALTHCARE too few to spot differencies

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Comparative analysis of return dynamics for portfolios of stocks traded at NYSE and LSE NYSE day LSE day Daily data: ALCA FINANCIAL 16 out of 20 SERVICES 03 out of 19 FINANCIAL 16 out of 24 SERVICES 05 out of 20 Results similar to SLCA Usually more structured Results similar to SLCA Usually more structured

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Comparative analysis of return dynamics for portfolios of stocks traded at NYSE and LSE NYSE day - ALCALSE day - ALCA Daily data: ALCA LSE day - SLCANYSE day - SLCA

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Comparative analysis of return dynamics for portfolios of stocks traded at NYSE and LSE Daily data: PMFG NYSE day LSE day

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Comparative analysis of return dynamics for portfolios of stocks traded at NYSE and LSE NYSE dayLSE day EN EN strength q 3 =1 strong intra-sector degree high strong extra-sector FIN FIN strength q 3 =.92 strong intra-sector degree high strong extra-sector (RBS acts as hub) SER SER strength q 3 =.092 poor intra-sector degree low poor extra-sector (RBS acts as hub) EN EN strength q 3 =1 strong intra-sector degree high strong extra-sector FIN FIN strength q 3 =.91 strong intra-sector degree high strong extra-sector (RBS acts as hub) SER SER strength q 3 =.092 poor intra-sector degree low poor extra-sector (RBS acts as hub) HEALTHCARE HEALTHCARE shows a behavior different from HT and similar to MST NCC MEL STIRBS SHEL AVZ BP

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Comparative analysis of return dynamics for portfolios of stocks traded at NYSE and LSE 5-minute data: RMT LSE 5-min NYSE 5-min 12 significative eigenvalues 12 significative eigenvalues The correspondence between eigenvalues and economic sectors is less clear. What is significant? What is not? 26 significative eigenvalues 26 significative eigenvalues The correspondence between eigenvalues and economic sectors is less clear. What is significant? What is not?

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Comparative analysis of return dynamics for portfolios of stocks traded at NYSE and LSE 5-min data: SLCA - hierarchical organization LSE 5-minNYSE 5-min FINANCIAL 04 out of 20 SERVICES 02 out of 19 FINANCIAL 05 out of 24 SERVICES 03 out of 20 low level of correlation low level of clustering SECTORS are not present

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Comparative analysis of return dynamics for portfolios of stocks traded at NYSE and LSE NYSE 5-min LSE 5-min 5-min data: SLCA - topological organization 2 LARGE hubs: RBS degree 29 SHEL degree 17 3 LARGE hubs: WMT degree 24 GE degree 21 STI degree 15 SECTORS are not present

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Comparative analysis of return dynamics for portfolios of stocks traded at NYSE and LSE 5-minute data: ALCA NYSE 5-min LSE 5-min Similar to SLCA results

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Comparative analysis of return dynamics for portfolios of stocks traded at NYSE and LSE 5-minute data: PMFG LSE 5-min NYSE 5-min

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Comparative analysis of return dynamics for portfolios of stocks traded at NYSE and LSE 5-minute data: PMFG LSE 5-minNYSE 5-min EN EN strength q 3 =1 strong intra-sector degree high strong extra-sector FIN FIN strength q 3 =.75 strong intra-sector degree high strong extra-sector (RBS acts as hub) EN EN strength q 3 =1 strong intra-sector degree high strong extra-sector FIN FIN strength q 3 =.69 strong intra-sector degree high strong extra-sector (STI acts as hub) RBS SHEL WMT GE STI

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Comparative analysis of return dynamics for portfolios of stocks traded at NYSE and LSE 5-minute data: PMFG Connection strenght is usually lower than at 1-day Basic Materials Connection strenght is usually lower than at 1-day Energy and Financial are exceptions. However, even if the sector is maintained, there are changes in the internal topology: RBS RBS SHEL SHEL Energy and Financial are exceptions. However, even if the sector is maintained, there are changes in the internal topology: STI STI NCC NCC WMT WMT 9 67

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Comparative analysis of return dynamics for portfolios of stocks traded at NYSE and LSE Conclusions RMT and hierarchical clustering methods are able to point out information present in the correlation matrix of the investigated system. RMT and hierarchical clustering methods are able to point out information present in the correlation matrix of the investigated system. The information that is detected with these methods is in The information that is detected with these methods is in part overlapping but in part specific to the selected investigating method. All the approaches detect information but not exactly the same one. All the approaches detect information but not exactly the same one. The system is more hierarchically structured at daily time horizons conferming that the market needs a finite amount of time to assess the correct degree of cross correlation between pairs of stocks. The system is more hierarchically structured at daily time horizons conferming that the market needs a finite amount of time to assess the correct degree of cross correlation between pairs of stocks. Financial and Energy seem to be structured even at a low time horizon (LSE more than NYSE). Financial and Energy seem to be structured even at a low time horizon (LSE more than NYSE).

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