What pieces of limit order book information matter in explaining order choice by patient and impatient traders?

Abstract

In this paper, we extend the existing empirical evidence on the relationship between the state of the limit order book (LOB) and order choice. Our contribution is twofold: first, we propose a sequential ordered probit (SOP) model which allows studying patient and impatient traders’ choices separately; second, we consider two pieces of LOB information, the best quotes and the book beyond the best quotes. We find that both pieces of LOB information explain the degree of patience of an incoming trader and, afterwards, its order choice. Nonetheless, the best quotes concentrate most of the explanatory power of the LOB. The shape of the book beyond the best quotes is crucial in explaining the aggressiveness of patient (limit order) traders, while impatient (market order) traders base their decisions primarily on the best quotes. Patient traders’ choices depend more on the state of the LOB on the same side of the market, while impatient traders mostly look at the state of the LOB on the opposite side. The aggressiveness of both types of traders augments with the inside spread. However, patient (impatient) traders submit more (less) aggressive limit (market) orders when the depth of the own (opposite) best quote and the length of the own (opposite) side of the book increase. We also find that higher depth away from the best ask (bid) quote may signal that this quote is ‘too low (high)’, causing incoming impatient buyers (sellers) to be more aggressive and incoming patient sellers (buyers) to be more conservative.

Keywords:

• Limit orders
• Market orders
• Limit order book
• Order aggressiveness
• Order-driven markets

Acknowledgements

We wish to thank David Abad, Sonia Falconieri, Pierre Giot, Angelo Ranaldo, Andreu Sansó, José Vidal, and Klaus F. Zimmermann, and two anonymous referees for their suggestions on previous versions of this paper. We acknowledge the insightful comments of the participants at seminars at Universidad Carlos III de Madrid (Spain), Université Catholique de Louvain (Belgium), and Bolsa de Madrid (Spain), and participants at the Namur's Workshop on Automated Auction Markets (Belgium). This work was partially supported by the European Commission Project HPRN-CT-2002-00232 ‘MICFINMA: Microstructure of Financial Markets in Europe’. Roberto Pascual also acknowledges the financial sponsorship of the Fulbright Grant and the Spanish Ministry of Education, Culture and Sports, and of the Spanish DGICYT projects BEC2001-2552-C03-03, SEJ2004-07530-C04-04, and SEJ2007-67895-C04-03. The first version of this paper was completed while Roberto Pascual was a Visiting Scholar at the New York University Salomon Center. David Veredas is also a member of ECORE, the recently created association between CORE and ECARES.

The scientific responsibility is assumed by the authors.

Notes

†All this theoretical and empirical literature is revised in detail in the next section.

‡Recent empirical and theoretical research (see Harris 1998, Anand et al. 2005, Bloomfield et al. 2005, Kaniel and Liu 2006) has shown that, under certain circumstances, traders that are presumed to be more inclined to be impatient, such as informed traders, may choose to submit orders that a priori are more appropriate for patient traders.

§Rosu (2005) also considers the whole LOB in his theoretical model. In this case, however, there are no clear cut predictions regarding best quotes versus the book beyond the best quotes.

†This arises because limit order submitters are not allowed to submit orders at or away from the best quotes.

†If we assume a logistic distribution, equations (1) and (2) will define an ordered logit model. Preliminary estimations provide identical results under either assumption. Since related studies such as Griffiths et al. (2000) and Ranaldo (2004) assume normality, we also base our analysis on the ordered probit model.

‡The following discussion is equivalent for an impatient trader that has to choose between three types of market orders, from lower to higher aggressiveness: a non-aggressive market order, a market-to-limit order, and an aggressive market order. In terms of notation, we would replace L by M.

§See Borooah (2001, pp. 23–24) and Greene (2003, pp. 738–739) for further details on this issue.

†We also considered the quoted depth as an alternative to the number of orders. The correlation between both proxies was very high, so that our main findings barely differed. In this final version, we only report the analysis based on the number of orders.

†Beber and Caglio (2005) and Chan (2005) report a positive connection between momentum and order aggressiveness.

†According to the Focus Monthly Bulletin of June 2006 of the World Federation of Exchanges (www.world-exchanges.org), the Spanish market is the fourth European market in terms of market capitalization ($US 1116 146 millions), right after the LSE ($US 3370 070 millions), Euronext ($US 3192 428 millions) and the Deustche Bourse ($US 1412 118 millions). The SSE is also the fourth European market in terms of total value of share trading.

‡Because of the allowance of hidden limit orders, however, depth improvements are possible.

§Limit orders at a price equal to the best quote on the opposite side of the book and of smaller (larger) size than the quantity available at that opposite quote cannot be distinguished in practice from market (market to limit) orders. Therefore, we pool them as C5-market (C6-market to limit) orders. Similarly, we put together limit orders that walk up or down the book and become totally fulfilled with C7-market orders, and market-to-limit orders with size smaller that the available depth as C5-market orders. Limit orders that walk up or down the book but are only partially executed represent less than 0.3% of all orders submitted. These orders are also considered C7. By a limit order that walks up or down the book we mean a limit order to buy (sell) which price is above (below) the prevailing best ask (bid) quote and which size is larger than the depth available at the best opposite quote. This order will consume the best ask (bid) quote on the book, and the excess will be executed at less favourable ask (bid) prices until it either fully executes or reaches a quote above (below) the limit price.

¶for all types of orders, brokers may specify special conditions. (a) ‘Execute or eliminate’ means the order must be executed immediately. In case of partial execution, the unexecuted part must be eliminated right away. (b) ‘Fill or kill’ also requires instantaneous execution. In this case, partial execution is not possible. The order must be fully executed or fully eliminated. (c) ‘Minimum execution’ implies that at least a given part of the order must be immediately executed. If the minimum execution is not possible, the whole order must be eliminated. If the minimum execution is possible, the rest of the order must be treated as a regular order. (d) Finally, partially undisclosed limit orders, known as ‘iceberg’ orders, are allowed. Our database does not identify orders submitted with special conditions. Hidden orders, for example, are only detectable upon execution. In practical terms, orders with these conditions are therefore undistinguishable from some of the seven categories of aggressiveness defined above. In this paper, we consider the undisclosed depth when classifying orders. We classify all orders relative to the total depth (disclosed plus undisclosed) available at the best quotes. Market orders with size larger than the disclosed depth at the best-opposite quote on the book are classified as C7 if and only if they exhaust all the available depth at that quote.

†The IBEX-35 is composed of the 35 most liquid and active SIBE-listed stocks during the most recent six-month control period. The composition is ordinarily revised twice a year. Extraordinary revisions are possible due to major events like mergers or new stock issues. During 2000, a total of 37 stocks were index constituents.

‡Similar patterns are reported by Ranaldo (2004), for the Swiss Stock Exchange, Griffiths et al (2000) for the Toronto Stock Exchange, Biais et al. (1995) for the Paris Bourse, now Euronext, Al-Suhaibani and Kryzanowski (2000) for the Saudi Stock Market, and Beber and Caglio (2005) for the NYSE.

§Biais et al. (1995) argue that this diagonal effect may reflect imitative behaviour by uninformed traders, order splitting, traders reacting to the same public information, or competition between liquidity providers.

†No one of these measures is universally accepted or employed. The values between zero and one have no natural interpretation, though it has been suggested that the pseudo-R ² value increases as the fit of the model improves. In a comparative analysis performed by Veall and Zimmermann (1996), these authors conclude that, for the particular case of the ordered probit model, the pseudo-R ² due to McKelvey–Zavoina outperforms the other measures and has a strong numerical relationship to the OLS-R ² in the latent variable. The Veall–Zimmermann and the Cragg–Uhler's measures also perform reasonably well. We include the McFadden's pseudo-R ² because it is the most common in statistical packages. For a review of all these goodness-of-fit measures see Veall and Zimmermann (1996). As in standard regression analysis, we use adjusted versions of these measures to take into account the inclusion of additional explanatory variables.

†We have also performed likelihood-ratio tests to compare the three model specifications. For all the stocks and for all the stages of the SOP model, the BQM model is found to beat the BM model, and the CBM to beat the BQM at the 1% level. Therefore, we corroborate that the book beyond the best quotes matters. Moreover, the chi-square values suggest that secondary levels of the book are more useful to explain patient traders' decisions than to impatient traders' decisions. These findings are available upon request from the authors.