Rosario Nunzio Mantegna

Transcription

1 Statistically validated networks of market members trading at the LSE electronic and dealers' market Rosario Nunzio Mantegna Central European University, Budapest, Hungary Palermo University, Palermo, Italy 28 May, 2013 Lorentz Center 1

2 Outline - I present results investigating the trading behavior of market members of a major stock exchange, the London Stock Exchange. - I discuss a methodology able to detect preferential relationships among market members in the (anonymous) electronic and (transparent) dealers' (off-book) venues of the market - I will discuss an important aspect of economic and social complex systems: the fundamental difference between anonymous and networked markets. - I will also discuss aspects of another networked market: the credit market for large firms in Japan. 28 May, 2013 Lorentz Center 2

3 LSE work is done in collaboration with Angelo Carollo Fabrizio Lillo 28 May, 2013 Gabriella Vaglica Michele Tumminello Lorentz Center 3

4 Our study is performed by investigating the trading action of market members of London Stock Market members (MMs) Exchange are not single investors. In fact, a market member may act on behalf of many different investors. A MM may act as an intermediary and/or can do client trading and/or proprietary trading. 28 May, 2013 Lorentz Center 4

5 At LSE there are two different market venues Market members (MMs) can execute their trades by submitting their orders in the electronic book in an anonymous form or can execute transaction in the dealers' off-book venue by directly interacting with other (known) MMs. Recorded transactions are anonymous in both cases. Also some non Members are allowed to trade in the off-book venue of the market. MM MM MM Electronic book MM MM MM MM Off-book venue MM MM n MM MM 28 May, 2013 Lorentz Center 5

6 Anonymous trading Bilateral trading 28 May, 2013 Lorentz Center 6

7 We have access to a version of the Rebuild Order Book of the London Stock Exchange with anonymized identity of the Market Members for the years The data include electronic transactions and off-book transactions. For the same period we also have access to the data of the Spanish Stock Market (BME) that are transparent to the identity of the Market member when the transaction is performed. However, in the case of the BME the off-book market present only a limited number of large (in volume) transactions. 28 May, 2013 Lorentz Center 7

8 Summary stastistics for 2004, in Angelo Carollo, Gabriella Vaglica, Fabrizio Lillo and Rosario N. Mantegna, Trading activity and price impact in parallel markets: SETS vs. off-book market at the London Stock Exchange, Quantitative Finance, Vol. 12, No. 4, April 2012, May, 2013 Lorentz Center 8

9 Are trades occurring among market members showing a deviation from a null hypothesis of random pairing? We investigate the preferential trading of MMs trading 5 highly liquid stocks (BP, HSBA, LLOY, RBS, and VOD) in both market venues during2005. The study is performed by using the transaction and order book records of the LSE having information about the (coded) identity of market members. A key problem of this analysis is to properly take into account the heterogeneity in the trading profile of different MMs. 28 May, 2013 Lorentz Center 9

10 The case of Market Members trading BP during 2005 Transactions Volume Transactions Volume Off1book Off1book On1book On1book Mean E E+07 min E E+00 max E E+09 std E E+08 Off-book Pdf 28 May, 2013 Lorentz Center 10 Nt

11 Over-expression of the number of tradings observed between two market members in a given venue Market member i is acting as a buyer in Nib transactions Market member j is acting as a seller in Njs transactions During the selected time period and in the considered venue the two market members did Nijbs transactions between them and all market members did Nt transactions 28 May, 2013 Lorentz Center 11

12 A statistical validation Suppose there are Nt transaction records in the investigated set. Suppose we are interested to compare the occurrence of two given states B and S of two market members MM i and MM j. Market member MM i is buying Nib times whereas market member MM j is selling Njs times. Let us call Nijbs the buy-sell transaction between them Total # of transactions Nt Nijbs Nib Njs # of buying transactions of MM i # of selling transactions of MM j # of B-S transactions between the two MMs What is the probability that the Nijbs B-S transactions occurs by chance? 28 May, 2013 Lorentz Center 12

13 A statistical validation is possible The probability of having exactly Nijbs B-S transactions between MM i and MM j is given by the Hypergeometric distribution Hypergeometric distribution: Expected number of buy-sell transactions under a random null hypotesis: p-value associated to a detection of a number of transactions Nijbs X: P(N ijbs N t, N ib, N js ) = p =1 Nijbs 1 N 28 May, 2013 Lorentz Center $ js ' 13 i=0! # # " # % $ N ib N ijbs N ib i $! &# &# %"! # # " &# % ( ' % $ # % % N t N ib N js N ijbs N t N js N t $ & & % X = x P(x N t, N ib, N js ) N t N ib N js i & ( ( & ( ( ' $ & & %

14 Statistically validated networks Tumminello M, Miccichè S, Lillo F, Piilo J, Mantegna RN (2011) Statistically Validated Networks in Bipartite Complex April 19, PLoS 2011 Swissquote & EPFL day Lorentz on quantitative Center finance May, 2013 ONE 6(3): e doi: /journal.pone Systems.

15 Our statistical validation is done by performing a multiple testing hypothesis and therefore we need a multiple hypothesis test correction. The most restrictive multiple hypothesis test correction is the so-called: Bonferroni correction. It is defined as follow: by requiring a θ statistical threshold for the single test, the threshold B for the multiple test procedure is set to B=θ/T where T is the total number of tested hypotheses. We address the statistically validated network obtained with the Bonferroni correction as the Bonferroni network Another less restrictive multiple hypothesis test correction is the False Discovery Rate (FDR) correction. 28 May, 2013 Lorentz Center 15

16 Daily analysis: 252 trading days of 2005 market members Fraction of links validated in two consecutive days Statistical threshold θ= May, 2013 Lorentz Center 16

17 Original Daily scale Bonferroni Electronic book Dealers' market seller buyer Black arrows are validated links (at the Bonferroni level) 28 May, 2013 Lorentz Center 17

18 Original Weekly scale Bonferroni Dealers' market Electronic book 28 May, 2013 Lorentz Center 18

19 Original Monthly scale Bonferroni Dealers' market Electronic book 28 May, 2013 Lorentz Center 19

20 Original Whole period Bonferroni Dealers' market Electronic book 28 May, 2013 Lorentz Center 20

21 Daily scale 28 May, 2013 Lorentz Center 21

22 Weekly scale 28 May, 2013 Lorentz Center 22

23 28 May, 2013 Lorentz Center 23

24 The dealers' market is a networked market whereas the anonymous electronic market presents only a limited amont of statistical validations of preferential trading relationships. This conclusion is supported by the fact that persistence of the statistically validated trading relationship is observed only in the dealers' market whereas in the electronic market the identity of validated links is strongly fluctuating over time. We measure the persistence of specific links present in trading network by computing the mutual information of links as defined in D-M Song, M. Tumminello, W.-X. Zhou, and R. N. Mantegna, Evolution of worldwide stock markets, correlation structure, and correlation-based graphs, Phys. Rev. E 84, (2011) 28 May, 2013 Lorentz Center 24

25 Bonferroni network original network 28 May, 2013 Lorentz Center 25

26 We can compare the Off-book book price with the On-book price present at the moment of the transaction 28 May, 2013 Lorentz Center 26

27 Approximately 95% of the Off-book transactions occurs within the spread or at the best bid or best ask Occurrence of the Z=(P-bid)/(ask-bid) for the BP stock traded Off-book by LSE market members during May May, 2013 Lorentz Center 27

28 By using this information we can infer from the combined On-book Off-book data who is the initiator of the Off-book transaction best bid Seller initiated Buyer initiated best ask In analogy with the Lee and Ready algorithm 28 May, 2013 Lorentz Center 28

29 Another networked market: the credit market for large Japanese firms. Banks Large firms Work done in collaboration with: L. Marotta, S. Miccichè, Y. Fujiwara, H. Iyetomi, H. Aoyama, and M. Gallegati 28 May, 2013 Lorentz Center 29

30 We have partitioned the bipartite credit network in communities (clusters) by using a clustering algorithm working directly on the bipartite graph and using a modularity measure adapted to bipartite graphs Our dataset is based on a survey of firms quoted in the Japanese stock exchange markets (Tokyo, Osaka, Nagoya). The data were compiled from the firms' financial statements and survey by Nikkei Media Marketing, Inc. in Tokyo. They include the information about each firm's borrowing obtained from financial institutions; the amounts of borrowing and their classification into short-term and long-term borrowings based on 1-year contracts. We examined the period from the years 1980 to 2012 (more than three decades). M.J. Barber, Modularity and community detection in bipartite networks, Phys. Rev. E76, (2007). 28 May, 2013 Lorentz Center 30

31 The number of clusters is increasing over the years 28 May, 2013 Lorentz Center 31

32 bank or firm label bank or firm label bank or firm label bank or firm label 28 May, 2013 Lorentz Center 32

33 Each bank is characterized by a specific attribute: - City banks - Regional banks - Life insurance banks - insurance banks etc Each firm is characterized by economic sectors and subsectors: - Electric and electronic equipment - Services - Wholesale trade - Real estate etc 28 May, 2013 Lorentz Center 33

34 Statistical validation of over-expression of attributes For a given set of elements we count how many of some selected attributes are present in our complete set. We count the same information also inside each subset of interest. For the sake of simplicity, let us focus on a specific attribute (say bank classification) but a similar conclusion applies for different attributes. For each subset a and for each bank classification k we have the number N a,k of banks of type k present in the subset a, the number N a is the number of elements of subset a, N k is the number of banks of type k in the subset and the number N n is the number of banks in the complete set. The probability that X elements of subset a belongs to bank type k under a random null hypothesis is again given by the hypergeometric distribution H(X N n,n a,n k ) and a p-value can therefore be associated to the observation of N a,k occurrence. Again this is a multiple hypothesis test procedure and a Bonferroni threshold is set as 0.01/N ch for each test of each cluster, where N ch is the number of characterizing aspects that are tested. In the example the number of different bank types. July 24, 2010 Unwinding Complexity - Port Douglas - Australia 34

35 We investigate the evolution over the years of the over-expression of attributes characterizing the clusters of banks and firms We investigate as attributes: -) the classification of banks; -) the geographical location of firms; -) the economic sectors of firms. 28 May, 2013 Lorentz Center 35

36 The evolution over time of the largest cluster

37 Another large cluster 28 May, 2013 Lorentz Center 37

38 A smaller and more limited example 28 May, 2013 Lorentz Center 38

39 Communities flow years p =1 X 1 i= 0 $ M' $ & ) N M ' & ) % i (% K i ( $ N' & ) % K( Similarly to what done by Musmeci et al we validate the presence of a directed link between a cluster at year t and a cluster at year t+1 by using again the hypergeometric distribution Each node is a cluster obtained in a given year. Arrow indicates validation of the assumption that elements in common at years t and t+1 are over-expressed with respect to a random null hypothesis Total # of elements in the two years N M X K # of elements of cluster A # of elements of cluster B # of co-occurrence of elements A and B 28 May, 2013 Lorentz Center 39

40 We believe the above results provide evidence that the credit market is a networked market where attributes like the nature of the bank, its localization, and the nature of the firm, its localization and its economic sectors play an important role in determining the probability that a credit relationships will be agreed between a firm and a bank. 28 May, 2013 Lorentz Center 40

41 The raise of the shadow banking system in Japan? Credit from Other non financial Institutions Credit ratio credit ratio Commercial/Non commercial credit ratios Year Year Commercial credit ratio Non commercial credit ratio Total Total credit 0e+00 1e+07 2e+07 3e+07 4e long short Year Code "Unknown" in the database 28 May, 2013 Lorentz Center 41 Year

42 Connections of the code "Unknown" in the database May, 2013 Lorentz Center 42

43 Conclusions Network preferential trading relationships are present in the off-book venue of the LSE. Network preferential relationships can be detected with a method based on the statistical validation against a null hypothesis taking into account heterogeneity of market members. Network preferential relationships are also observed in the credit market. 28 May, 2013 Lorentz Center 43