Why is order flow so persistent?

📝 Abstract

Order flow in equity markets is remarkably persistent in the sense that order signs (to buy or sell) are positively autocorrelated out to time lags of tens of thousands of orders, corresponding to many days. Two possible explanations are herding, corresponding to positive correlation in the behavior of different investors, or order splitting, corresponding to positive autocorrelation in the behavior of single investors. We investigate this using order flow data from the London Stock Exchange for which we have membership identifiers. By formulating models for herding and order splitting, as well as models for brokerage choice, we are able to overcome the distortion introduced by brokerage. On timescales of less than a few hours the persistence of order flow is overwhelmingly due to splitting rather than herding. We also study the properties of brokerage order flow and show that it is remarkably consistent both cross-sectionally and longitudinally.

💡 Analysis

Order flow in equity markets is remarkably persistent in the sense that order signs (to buy or sell) are positively autocorrelated out to time lags of tens of thousands of orders, corresponding to many days. Two possible explanations are herding, corresponding to positive correlation in the behavior of different investors, or order splitting, corresponding to positive autocorrelation in the behavior of single investors. We investigate this using order flow data from the London Stock Exchange for which we have membership identifiers. By formulating models for herding and order splitting, as well as models for brokerage choice, we are able to overcome the distortion introduced by brokerage. On timescales of less than a few hours the persistence of order flow is overwhelmingly due to splitting rather than herding. We also study the properties of brokerage order flow and show that it is remarkably consistent both cross-sectionally and longitudinally.

📄 Content

Why is equity order flow so persistent? Bence T´oth1a,b, Imon Palit2c, Fabrizio Lillo3b,d,e, J. Doyne Farmer4f,b aCapital Fund Management, 23/25, rue de l’Universit´e 75007 Paris, France bSanta Fe Institute, 1399 Hyde Park Rd., Santa Fe NM 87501, USA cDepartment of Banking and Finance, Monash Univeristy, Melbourne, Australia dDipartimento di Fisica, Universit´a di Palermo, Palermo, Italy eScuola Normale Superiore di Pisa, Piazza dei Cavalieri 7, 56126 Pisa, Italy fInstitute for New Economic Thinking at the Oxford Martin School and Mathematical Institute, 24-29 St. Giles, Oxford OX1 3LB Abstract Order flow in equity markets is remarkably persistent in the sense that order signs (to buy or sell) are positively autocorrelated out to time lags of tens of thousands of orders, corresponding to many days. Two possible explanations are herding, corresponding to positive correlation in the behavior of different investors, or order splitting, correspond- ing to positive autocorrelation in the behavior of single investors. We investigate this using order flow data from the London Stock Exchange for which we have membership identifiers. By formulating models for herding and order splitting, as well as models for brokerage choice, we are able to overcome the distortion introduced by brokerage. On timescales of less than a few hours the persistence of order flow is overwhelmingly due to splitting rather than herding. We also study the properties of brokerage order flow and show that it is remarkably consistent both cross-sectionally and longitudinally. Keywords: Market microstructure; Order flow; Herding; Order splitting; Price impact; Behavioral finance JEL codes: G12, D44, D61, C62. 1Corresponding author. E-mail: ecneb.htot@gmail.com. Tel.: +33 1 49 49 59 49 2E-mail: imon.palit@monash.edu 3E-mail: fabrizio.lillo@sns.it 4E-mail: doynefarmer@gmail.com Preprint submitted to Elsevier December 2, 2014 arXiv:1108.1632v2 [q-fin.TR] 30 Nov 2014

1. Introduction Order flow in equity markets, defined as the process assuming value one for buyer initi- ated trades and minus one for seller initiated trades, is persistent in the sense that orders to buy tend to be followed by more orders to buy and orders to sell tend to be followed by more orders to sell. Positive serial autocorrelation for the first autocorrelation of or- der flow has been observed in many different markets5. In fact, order flow is remarkably persistent: As illustrated in Figure 1, all the coefficients of the autocorrelation function of signed order flow are positive out to large lags, corresponding in trade time to tens of thousands of transactions or in real time to many days6. This is highly consistent across different markets, stocks, and time periods. In this paper we perform an empirical study to elucidate the cause of this remarkable persistence. This study is based on a unique data set from the London Stock Exchange (LSE) with codes indicating the exchange member who executed each order. Members of the exchange may trade for their own accounts, but they may also act as brokers for investors who are not members of the exchange7. As we will argue here, this provides useful information about the patterns of behavior of investors8, even if it falls short of the fine grained data on the identity of investors that would make the results unequivocal. Our goal here is to distinguish between two fundamentally different types of behavior, order splitting and herding. Order splitting occurs when single investors split desired large trades into smaller pieces and execute them gradually. Our results here add to earlier evidence that order splitting is an important effect. The strategic motivations for order splitting were originally derived by Kyle (1985), who showed that an informed trader with a monopoly on private information would trade gradually in order to reduce impact. Early empirical studies by Chan and Lakonishok (1993, 1995) using brokerage data with information about investors showed that order splitting is widespread. Chor- dia, Roll, and Subrahmanyam (2002, 2005) found that daily order imbalances are serially 5 Positive autocorrelation for a single lag was observed in the Paris Bourse by Biais, Hillion and Spatt (1995), in foreign exchange markets by Danielsson and Payne (2012), and in the NYSE by Ellul et al. (2007) and Yeo (2008). See also Chordia, Roll, and Subrahmanyam (2002, 2005). 6 The extreme persistence of order flow was independently pointed out by Bouchaud et al. (2004) and Lillo and Farmer (2004). In fact order flow is so persistent that it is a long-memory process, i.e. its autocorrelation function is non-integrable (Beran, 1994). This has been shown for the London and New York stock exchanges by Lillo and Farmer (2004), for the Paris stock exchange by Bouchaud et al. (2004) and for the Spanish stock exchange by Vaglica et al. (2008) and Moro et al. (2009). Note that Axioglou and Skouras (2011) argue that order flow is much more persistent within a given day than ac

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