comparative analysis of return dynamics for a portfolio of stocks traded at nyse and at lse

Comparative analysis of return Comparative analysis of return dynamics for a portfolio of stocks dynamics for a portfolio of stocks

traded at NYSE and at LSEtraded at NYSE and at LSESalvatore MiccichèSalvatore Miccichè

http://lagash.dft.unipa.ithttp://lagash.dft.unipa.it

Observatory of Complex Observatory of Complex SystemsSystems

Dipartimento di Fisica e Tecnologie RelativeDipartimento di Fisica e Tecnologie Relative Università degli Studi di Palermo Università degli Studi di Palermo

Progetto Strategico - Incontro di progetto II anno - Palermo 23 Progetto Strategico - Incontro di progetto II anno - Palermo 23 Settembre 2005Settembre 2005

Comparative analysis of return dynamics for portfolios of stocks traded at Comparative analysis of return dynamics for portfolios of stocks traded at NYSE and LSENYSE and LSE

Observatory of Complex SystemsObservatory of Complex Systems

R. N. MantegnaR. N. Mantegna

F. LilloF. LilloS. MiccichèS. Miccichè

M. SpanòM. TumminelloM. TumminelloG. Vaglica

C. CoronnelloC. Coronnello

M. Glorioso

V. DesoutterA. Garas

R. Schäfer

EconophysicsEconophysics BioinformaticsBioinformatics Stochastic ProcessesStochastic Processes


Aim of the researchAim of the research•Compare the dynamics of price returns Compare the dynamics of price returns traded at different exchangestraded at different exchanges -- industry sector identification at different time industry sector identification at different time horizonhorizon - sector dynamics - sector dynamics - LSE and NYSE - LSE and NYSE - are there common (stylized) facts ? - are there common (stylized) facts ?

•Compare the information obtained by Compare the information obtained by using different techniques for extracting using different techniques for extracting information from a given correlation information from a given correlation matrixmatrix -- RMT, SLCA, ALCA, PMFG, …RMT, SLCA, ALCA, PMFG, … - what are the right variables to look at? - what are the right variables to look at?


Methods: RMTMethods: RMTStudy of the eigenvalueseigenvalues and

eigenvectorseigenvectors of the N×N correlation matrix.

Precise evaluation of the noise due to the finite length T of the

time-series

IDEAIDEA: significative eigenvalues can be associated to economic sectors.

Crucial parameter Q=N/T


Methods: SLCAMethods: SLCA

•Construct an ordered list of pair of stocks LConstruct an ordered list of pair of stocks Lordord ,by ranking all the ,by ranking all the possible pairs according to their distance dpossible pairs according to their distance d ijij.The first pair of L.The first pair of Lordord has the has the shortest distance.shortest distance.•The first pair of LThe first pair of Lordord gives the first two elements of the MST and the gives the first two elements of the MST and the link between them.link between them.•The construction of the MST continues by analyzing the list LThe construction of the MST continues by analyzing the list Lordord.At each .At each successive stage, a pair of elements is selected from Lsuccessive stage, a pair of elements is selected from Lordord and the and the corresponding link is added to the MST only if no loops are generated in corresponding link is added to the MST only if no loops are generated in the graph after the link insertion.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 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 .

Single Linkage Clustering Analysis

MST construction

N(N-1)/2 N(N-1)/2 N-1 N-1


Methods: ALCAMethods: 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 dtr between the new cluster t and any cluster r is recursively given by: ddtrtr =mean =mean {{d d prpr ,d ,d qrqr} } i.e. the distance between any element of cluster t and any element of cluster r 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 ris the mean distance between any two entities in clusters t and r . .

Average Linkage Clustering AnalysisAverage Linkage Clustering Analysis


Methods: PMFGMethods: PMFGThe 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 allowing a greater number of links and more complex topological structures than the MST (cliques and loops).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 a link can be included in the graph if and only if the graph with the new link included in the graph if and only if the graph with the new link included is still planarincluded is still planar.

A graph is planar f and only if it can be drawn on a planeit can be drawn on a plane (infinite in principle) without edge crossingswithout edge crossings.

Planar Maximally Filtered GraphPlanar Maximally Filtered Graph

It allows a measure on the intra-sector clustering through the computation of the Connection Strength

(3-cliques & 4-cliques).


The set of investigated stocksThe set of investigated stocksWe consider: NYSE - the 100 most capitalized stocks in 2002.

LSE - the 92 most traded stocks in 2002.

We consider high-frequency (intradayintraday) data. Transactions do not occur at the same time for all stocks.

We have to synchronizesynchronize/homogenizehomogenize the data:

NYSE: 5 min, 15 min, 30 min, 65 min, 195 min, 1 day NYSE: 5 min, 15 min, 30 min, 65 min, 195 min, 1 day trading time 6trading time 6hh30’ 30’ LSE: 5 min, 15 min, 51 min, 102 min, 255 min, 1 dayLSE: 5 min, 15 min, 51 min, 102 min, 255 min, 1 day trading time 8trading time 8hh30’30’

TTrades AAnd QQuotes (TAQTAQ) database maintained by NYSE (1995-20031995-2003)

RRebuild OOrder BBook (ROBROB) database maintained by LSE (20022002)


The set of investigated stocksThe set of investigated stocksNYSE 100 stocksNYSE 100 stocks

01 Technology 802 FinancialFinancial 2403 Energy 304 04 Consumer non-CyclicalConsumer non-Cyclical 11 1105 Consumer Cyclical 206 Healthcare 1207 Basic Materials 608 ServicesServices 2009 Utilities 210 Capital Goods 611 Transportation 212 Conglomerates 412 Conglomerates 4

LSE 92 stocksLSE 92 stocks

01 Technology 402 FinancialFinancial 2003 Energy 304 04 Consumer non-CyclicalConsumer non-Cyclical 12 1205 Consumer Cyclical 1006 Healthcare 607 Basic Materials 508 ServicesServices 1909 Utilities 610 Capital Goods 511 Transportation 212 Conglomerates 012 Conglomerates 0


The set of investigated stocksThe set of investigated stocks

LSE: 5 min, 1day NYSE: 5 min, LSE: 5 min, 1day NYSE: 5 min, 1day 1day


LSE day NYSE day

PREDICTION: 6 significative eigenvaluesPREDICTION: 6 significative eigenvaluesa Market Modeb Consumer Non-Cyclicalc Financiald Capital Goodse Technologyf Healthcareg ?h ?i ?

Is it by chance?

PREDICTION: 9 significative eigenvaluesPREDICTION: 9 significative eigenvaluesa Market Modeb Consumer Non-Cyclicalc ?d Healthcaree Utilities&Servicesf ?g ?h ?i Utilities

What is significant?What is not?

Daily data: RMTDaily data: RMT

Comparative analysis of return dynamics for portfolios of stocks traded at Comparative analysis of return dynamics for portfolios of stocks traded at NYSE and LSENYSE and LSEDaily data: SLCA - hierarchical organizationDaily data: SLCA - hierarchical organization

NYSE dayLSE day

FINANCIAL 10 out of 20FINANCIAL 10 out of 20SERVICES 02 out of 19SERVICES 02 out of 19


High level of correlationHigh level of correlation High level of correlationHigh level of correlation

Basic Materials is also observable


NYSE dayLSE dayDaily data: SLCA - topological organizationDaily data: SLCA - topological organization

Clusters are Clusters are essentially similaressentially similar to HTto HT

no star, small hubs no star, small hubs

Clusters are Clusters are differentdifferent from from HTHT

no star, small hubsno star, small hubs (NCC, STI, MEL, ...)(NCC, STI, MEL, ...)

TECHNOLOGY are clustered around ADITECHNOLOGY are clustered around ADICONSUMER NC are clustered around PGCONSUMER NC are clustered around PGHEALTHCARE are clustered around PFEHEALTHCARE are clustered around PFE

TECHNOLOGY too few to spot differenciesTECHNOLOGY too few to spot differenciesCONSUMER NC are clustered through BPCONSUMER NC are clustered through BPHEALTHCARE too few to spot differenciesHEALTHCARE too few to spot differencies


NYSE dayLSE dayDaily data: ALCADaily data: ALCA



Results similar to SLCAResults similar to SLCAUsually more structuredUsually more structured

Results similar to SLCAResults similar to SLCAUsually more structuredUsually more structured


NYSE day - ALCALSE day - ALCA Daily data: ALCADaily data: ALCA

LSE day - SLCA NYSE day - SLCA

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

NYSE dayLSE day


NYSE dayLSE day

ENEN strength q3=1 strong intra-sector degree high strong extra-sector

FINFIN strength q3=.92 strong intra-sector degree high strong extra-sector (RBS acts as hub)

SERSER strength q3=.092 poor intra-sector degree low poor extra-sector (RBS acts as hub)



SERSER strength q3=.092 poor intra-sector degree low poor extra-sector (RBS acts as hub)HEALTHCAREHEALTHCARE shows a behavior different from HT and similar to MST

NCC

MEL

STIRBS

SHELAVZ

BP


5-minute data: RMT5-minute data: RMTLSE 5-min NYSE 5-min

12 significative eigenvalues12 significative eigenvalues

The correspondence between The correspondence between eigenvalues and economic sectors is less eigenvalues and economic sectors is less clear.clear.

What is significant?What is significant?What is not?What is not?

26 significative eigenvalues26 significative eigenvalues

The correspondence between The correspondence between eigenvalues and economic sectors is less eigenvalues and economic sectors is less clear.clear.

What is significant?What is significant?What is not?What is not?

Comparative analysis of return dynamics for portfolios of stocks traded at Comparative analysis of return dynamics for portfolios of stocks traded at NYSE and LSENYSE and LSE5-min data: SLCA - hierarchical 5-min data: SLCA - hierarchical

organizationorganizationLSE 5-min NYSE 5-min



low level of correlationlow level of correlation low level of correlationlow level of correlationlow level of clusteringlow level of clustering low level of clusteringlow level of clustering

SECTORS are not presentSECTORS are not present SECTORS are not presentSECTORS are not present


NYSE 5-minLSE 5-min

5-min data: SLCA - topological organization5-min data: SLCA - topological organization

2 LARGE hubs:2 LARGE hubs:

RBS degree 29RBS degree 29SHEL degree 17SHEL degree 17

3 LARGE hubs: 3 LARGE hubs:

WMT degree 24WMT degree 24GE degree 21GE degree 21STI degree 15STI degree 15

““SECTORS are not present”SECTORS are not present” ““SECTORS are not present”SECTORS are not present”


5-minute data: ALCA5-minute data: ALCANYSE 5-minLSE 5-min

Similar to SLCA resultsSimilar to SLCA results Similar to SLCA resultsSimilar to SLCA results


5-minute data: PMFG5-minute data: PMFGLSE 5-min NYSE 5-min


5-minute data: PMFG5-minute data: PMFGLSE 5-min NYSE 5-min




FINFIN strength q3=.69 strong intra-sector degree high strong extra-sector (STI acts as hub)

RBSSHEL

WMTGE

STI


5-minute data: PMFG5-minute data: PMFGConnection strenght is Connection strenght is usually lower than at 1-dayusually lower than at 1-day

Basic Materials 0.47 0

Connection strenght is Connection strenght is usually lower than at 1-dayusually 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 42 62SHELSHEL 24 37

Energy and Financial are exceptions. However, even if the sector is maintained, there are changes in the internal topology:

STI STI 21 24NCCNCC 26 11WMTWMT 9 67


ConclusionsConclusions

•RMT and hierarchical clustering methods are able to RMT and hierarchical clustering methods are able to point out information present in the correlation matrix of point out information present in the correlation matrix of the investigated system.the investigated system.•The information that is detected with these methods is The information that is detected with these methods is ininpart overlapping but in part specific to the selected part overlapping but in part specific to the selected investigating method.investigating method.•All the approaches detect information but not exactly All the approaches detect information but not exactly the same one.the same one.

•The system is more hierarchically structured at daily The system is more hierarchically structured at daily time horizons conferming that the market needs a time horizons conferming that the market needs a finite amount of time to assess the correct degree of finite amount of time to assess the correct degree of cross correlation between pairs of stocks.cross correlation between pairs of stocks.•Financial and Energy seem to be structured even at Financial and Energy seem to be structured even at a low time horizon (LSE more than NYSE).a low time horizon (LSE more than NYSE).

comparative analysis of return dynamics for a portfolio of stocks traded at nyse and at lse

Documents

element of cluster t

element of cluster r

new cluster t

portfolios of stocks

wider single cluster

clusters t

stocks lord

distance dtr