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Comparative analysis of return dynamics for a portfolio of stocks traded at NYSE and at LSE

Observatory of Complex Systems. http://lagash.dft.unipa.it. Comparative analysis of return dynamics for a portfolio of stocks traded at NYSE and at LSE. Salvatore Miccichè. Dipartimento di Fisica e Tecnologie Relative Università degli Studi di Palermo.

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Comparative analysis of return dynamics for a portfolio of stocks traded at NYSE and at LSE

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

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

  3. 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 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?

  4. Comparative analysis of return dynamics for portfolios of stocks traded at NYSE and LSE Methods: RMT 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: significative eigenvalues can be associated to economic sectors. Crucial parameter Q=N/T

  5. Comparative analysis of return dynamics for portfolios of stocks traded at NYSE and LSE Methods: SLCA Single Linkage Clustering Analysis 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 dtr between the new cluster t and any cluster r is recursively given by: dtr =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 . MST construction • Construct an ordered list of pair of stocks Lord ,by ranking all the possible pairs according to their distance dij.The first pair of Lord has the shortest distance. • The first pair of Lord gives the first two elements of the MST and the link between them. • The construction of the MST continues by analyzing the list Lord.At each successive stage, a pair of elements is selected from Lord and the corresponding link is added to the MST only if no loops are generated in the graph after the link insertion. N(N-1)/2  N-1

  6. Comparative analysis of return dynamics for portfolios of stocks traded at NYSE and LSE Methods: ALCA Average Linkage Clustering Analysis 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 dtr between the new cluster t and any cluster r is recursively given by: dtr =mean {d pr ,d qr} 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 .

  7. Comparative analysis of return dynamics for portfolios of stocks traded at NYSE and LSE Methods: PMFG Planar Maximally Filtered Graph The Planar Maximally Filtered Graph is a recently introduced graph. 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). 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. A graph is planar f and only if it can be drawn on a plane (infinite in principle) without edge crossings. It allows a measure on the intra-sector clustering through the computation of the Connection Strength (3-cliques & 4-cliques).

  8. 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 2002.LSE - the 92 most traded stocks in 2002. Trades And Quotes (TAQ) database maintained by NYSE (1995-2003) RebuildOrderBook (ROB) database maintained by LSE (2002) 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 6h30’ LSE: 5 min, 15 min, 51 min, 102 min, 255 min, 1 daytrading time 8h30’

  9. Comparative analysis of return dynamics for portfolios of stocks traded at NYSE and LSE The set of investigated stocks LSE 92 stocks01 Technology 402 Financial 2003 Energy 304 Consumer non-Cyclical 1205 Consumer Cyclical 1006 Healthcare 607 Basic Materials 508Services 1909 Utilities 610 Capital Goods 511 Transportation 212 Conglomerates 0 NYSE 100 stocks01 Technology 802 Financial 2403 Energy 304 Consumer non-Cyclical 1105 Consumer Cyclical 206 Healthcare 1207 Basic Materials 608 Services 2009 Utilities 210 Capital Goods 611 Transportation 212 Conglomerates 4

  10. 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

  11. Comparative analysis of return dynamics for portfolios of stocks traded at NYSE and LSE Daily data: RMT LSE day NYSE day PREDICTION: 6 significative eigenvalues a Market Mode b Consumer Non-Cyclical c Financial d Capital Goods e Technology f Healthcare g ? h ? i ? PREDICTION: 9 significative eigenvalues a Market Mode b Consumer Non-Cyclical c ? d Healthcare e Utilities&Services f ? g ? h ? i Utilities What is significant? What is not? Is it by chance?

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

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

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

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

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

  17. Comparative analysis of return dynamics for portfolios of stocks traded at NYSE and LSE LSE day NYSE day BP RBS NCC STI SHEL AVZ MEL ENstrength q3=1 strong intra-sector degree high strong extra-sector ENstrength q3=1 strong intra-sector degree high strong extra-sector FINstrength q3=.91  strong intra-sector degree high  strong extra-sector (RBS acts as hub) FINstrength q3=.92  strong intra-sector degree high  strong extra-sector (RBS acts as hub) SERstrength q3=.092  poor intra-sector degree low  poor extra-sector (RBS acts as hub) SERstrength q3=.092  poor intra-sector degree low  poor extra-sector (RBS acts as hub) HEALTHCAREshows a behavior different from HT and similar to MST

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

  19. Comparative analysis of return dynamics for portfolios of stocks traded at NYSE and LSE 5-min data: SLCA - hierarchical organization LSE 5-min NYSE 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 correlation low level of clustering low level of clustering SECTORS are not present SECTORS are not present

  20. Comparative analysis of return dynamics for portfolios of stocks traded at NYSE and LSE 5-min data: SLCA - topological organization LSE 5-min NYSE 5-min 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” “SECTORS are not present”

  21. 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 Similar to SLCA results

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

  23. Comparative analysis of return dynamics for portfolios of stocks traded at NYSE and LSE 5-minute data: PMFG LSE 5-min NYSE 5-min GE RBS WMT SHEL STI ENstrength q3=1 strong intra-sector degree high strong extra-sector ENstrength q3=1 strong intra-sector degree high strong extra-sector FINstrength q3=.69  strong intra-sector degree high  strong extra-sector (STI acts as hub) FINstrength q3=.75  strong intra-sector degree high  strong extra-sector (RBS acts as hub)

  24. 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 0.47  0 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: STI 21  24 NCC 26  11 WMT 9  67 Energy and Financial are exceptions. However, even if the sector is maintained, there are changes in the internal topology: RBS 42  62 SHEL 24  37

  25. Comparative analysis of return dynamics for portfolios of stocks traded at NYSE and LSE Conclusions • 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). • 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 • part overlapping but in part specific to the selected investigating method. • All the approaches detect information but not exactly the same one.

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