Hidden Orders on Euronext: Nothing Is Quite As It Seems C

Hidden Orders on Euronext: Nothing is quite as it seems C. D’Hondta and R. De Winneb and A. Fran¸cois-Heudec

a FUCaM and University of Perpignan, b FUCaM, c University of Perpignan

First version: November 2002

This version: May 2004 Abstract

This paper is devoted to hidden order submission on Euronext for the stocks belonging to the CAC40 index during the last three months of 2002. The goal is twofold. On the one hand, we investigate the impact of hidden order use on market depth composition and pretrade transparency. On the other hand, we compare hidden order placement with usual order submission. Thanks to very complete order book data, we ﬁnd that more than half the volume available at the best limit during the continuous session is not visible on the market screens. Our results suggest that hidden order traders are mainly liquidity suppliers. They also appear to focus on a given market side at a point in time and are less concerned than usual order traders with what happens on the opposite market side. Finally, hidden orders seem to be more involved in splitting strategies than usual orders. JEL Classiﬁcations : G14, G10 Keywords : Hidden orders, Market depth, Order aggressiveness, Transparency, Euronext.

Acknowledgements The authors are grateful to Euronext for providing the data. They also wish to thank C. Bisi`ere, F. Declerck, C. Majois and I. Platten for suggestions and remarks. Comments are welcome. Mailing Address FUCaM-Catholic University of Mons, Department of Finance, chauss´ee de Binche 151, B- 7000 Mons, BELGIUM, tel. +32.65.323324, fax +32.65.323223, e-mail : [email protected]. 1 Introduction

Trades are easier to arrange when market participants actively announce their trading interests. In order-driven markets, liquidity suppliers expose limit orders to attract liquidity demanders. However, in a transparent market displaying the limit order book in real time, liquidity suppliers face the order exposure risk. Indeed, limit order book diffusion in real time affects the process of information inference and the revision of beliefs. Order exposure can be harmful if it reveals the traders’ motives, the price impact of future trades or valuable free trading options. Today, many stock exchanges or ATS1 rely on limit orders for liquidity supply and partially diffuse the order book in real time. To remain competitive, many transparent trading systems propose practices helping liquidity suppliers to control the order exposure risk. All of them allow limit order traders to cancel or modify their orders at any moment. Many markets such as Euronext, the Toronto Stock Exchange (TSX) or the Australian Stock Exchange (ASX) also give traders the opportunity to use hidden orders. In this context, these orders permit traders to disclose only a part of the total quantity they want to buy or sell. The total order size is registered in the order book but only the disclosed quantity is displayed on the market screens. Since the introduction of SuperSOES in 2000, Nasdaq market makers have also the ability to post additional depth in their quotes that is not visible to the market. This opportunity is also provided to MTS market makers. Although most trading systems moved towards greater transparency, the use of undisclosed quantities has thus become a widespread practice. Theoretically, it seems to be a trade-off between market liquidity and transparency. Hidden order use has been analyzed in few previous studies. Harris (1996) examined data for 300 stocks traded on the Paris Bourse and showed that 74% of orders was not fully disclosed when the remaining size is larger than FF500,000. His findings suggest that traders expose more when the tick size is large, when the order is not expected to stand long and when prices are not volatile. Aitken et al. (1996) reported that in 1993 about 6% of orders on the Australian Stock Exchange (ASX) was undisclosed, accounting for approximately 28% of volume. Later, Aitken et al. (2001) demonstrated that hidden quantities are used to reduce the option value of limit orders. More recently, Hasbrouck & Saar (2002) documented substantial use of undisclosed orders on the Island ECN.2 According to them, executed hidden orders constitute only about 3% of submitted limit orders but account for almost 12% of all order executions. Tuttle (2003) reported that hidden liquidity accounts for 25% of the inside depth in Nasdaq 100 stocks. She found that hidden size is additional depth provided to the market rather than a shift away from displayed depth to non-displayed depth.

1Alternative Trading Systems 2The broker dealer name The Island ECN is now Inet ATS.

1 In this paper, we provide an empirical analysis of hidden order use on Euronext.3 We especially focus on hidden orders submitted for the 40 stocks included in the CAC40 index for the period covering October through December 2002. Based on full order book data, our empirical study has two main strands. First, we investigate the impact of hidden order use on both market depth composition and pretrade transparency. Second, to compare hidden order placement with usual order submission, we analyze order aggressiveness and market conditions around order placement. In both cases, we try to highlight what characterizes traders using hidden quantities. Though this study is in line with previous research, it also contributes in several points to the existing literature. Indeed, full order book data make it possible to extend previous empirical works about market liquidity and hidden orders. Many papers dealing with market depth often focus on quantities available at the best quotes or on visible depth. In this paper, we assess market depth at several order book levels and we decompose it into its hidden and displayed components. This approach allows us to substantially document hidden depth magnitude and behavior, which was seldom reported in the past. Next, this study is also devoted to hidden order submission strategies. Previous papers often investigated the use of hidden orders with respect to some stock features (tick size, volatility, trading volume, idiosyncratic risk). By examining interactions between the order flow and the order book, the present paper completes empirical findings about order placement in a transparent order-driven market. Based on a comparison between hidden and usual order submission, we report some characteristics of hidden order traders. The main findings of our empirical work are the following ones. First of all, hidden orders have a large impact on market depth composition and pretrade transparency, especially at the top of the order book. We show that, all along the continuous session, more than half the volume available at the best limit is not visible on the market screens. Next, our results about order aggressiveness suggest that hidden order traders are mainly liquidity suppliers. They also appear to focus on a given market side at a point in time and look less concerned than usual order traders with what happens on the opposite side. Finally, we find evidence that hidden orders are more involved in splitting strategies than usual orders. The structure of the paper is organized as follows. Section 2 presents the theoretical context and an overview of the relevant literature. Section 3 describes our dataset and also reports a lot of statistics about hidden order use in our sample. In the next section, we analyze the impact of undisclosed quantities on market depth composition and pretrade transparency. Section 5 is devoted to order placement strategies. Section

3Euronext was created in September 2000 by the merger of the exchanges in Amsterdam, Brussels and Paris. It will be the ﬁrst fully integrated, cross-border, European market for equities, bonds, derivatives and commodities. At present, Euronext includes respectively the former exchanges of Amsterdam, Brussels, Lisbon, Porto, Paris and also the LIFFE.

2 6 concludes.

2 Theoretical Framework and Literature

2.1 Hidden Orders: A Trade-oﬀ between Liquidity and Trans- parency

Liquidity and transparency are essential qualities for financial markets. Roughly speaking, market liquidity reflects trading conditions. Precisely, a liquid market is one where any amount of a given security can be instantaneously converted to cash and back to securities at low costs [Harris (1990), Aitken & Comerton-Forde (2003)]. Today, the globalization of trading venues, the cross-listing of attractive assets and the develop- ment of alternative trading systems make market liquidity a key factor in competition between financial markets. Therefore, the concept of liquidity is of a great importance for both market authorities and participants [Auguy et al. (2000)]. On the one hand, traders wish that their trades are executed at the best conditions. On the other hand, the market authorities tend to offer the best execution. Another component of growing significance in market competitiveness is the level of transparency [Bloomfield & O’Hara (2000)]. O’Hara (1995) defines transparency as the ability for market participants to observe information about the trading process. In this context, quote transparency refers to limit order book diffusion while trade transparency refers to past trade reporting. A lot of both theoretical and empirical studies conclude that the transparency level may respectively affect execution costs, price formation process and globally market liquidity.4 On order-driven markets, orders are registered in an electronic limit order book with respect to their direction (buy or sell), their price (price priority) and their ar- rival time (time precedence). In such a market structure, traders are told liquidity suppliers or demanders according to the orders they use. Liquidity demanders submit ”marketable” orders that give them guarantees of an immediate execution in return for a less profitable trade price. Liquidity suppliers expose standing limit orders that translate their trading interests and allow them to control the trade price. Actually, trades are easier to arrange when market participants actively disclose their willingness to trade. However, traders who display standing limit orders face various risks. One of them is straight related to the market transparency level and is called the order exposure risk. Harris (1997) reports the costs of order exposure in detail. In transparent markets diffusing the limit order book in real time, liquidity suppliers run the risk that some

4See Madhavan (1995), Pagano & R¨oell (1996), Gemmill (1996), Flood et al. (1999), Madhavan et al. (2000), Scalia & Vacca (2001), Drudi & Massa (2002), Rindi (2002), Foucault et al. (2003), Boehmer et al. (2004) ...

3 traders, called ”parasitic traders”, infer information from standing limit orders and try to get profit from them. Harris (1997) explains that order exposure may be harmful in three situations: (i) if it reveals the traders’ motives, (ii) if it reveals the potential price impact of future trades, (iii) if it reveals valuable free trading options. In all these cases, limit order traders can be victims of front-running strategies5 applied by parasitic traders. Since order exposure may lead to higher execution costs for liquidity suppliers, they tend to protect themselves by using hidden quantities. Recently, Tuttle (2003) and Pardo & Pascual (2003) propose that hidden orders are also used by traders to mitigate the adverse selection costs. According to them, liquidity providers prefer to submit undisclosed orders when the perceived risk of trading against informed traders is high. So, by using hidden quantities, liquidity suppliers reduce the option value of their orders, mitigate information asymmetry risk and prevent from unfavorable price reactions. Nowadays transparency is enhanced by the increasing automation and centraliza- tion of trading systems. More and more markets call upon limit orders for liquidity supply and diffuse the order book as well as the trades in real time. The order exposure risk becomes consequently higher for liquidity providers. To remain competitive, many trading systems have developed practices helping traders to reduce the order exposure risk. All of them permit traders to cancel or modify their orders at any time. Some, like Euronext, the ASX, the TSE or Inet ATS propose traders to use hidden orders. These orders allow traders to specify a partial display, or even a no display, of the total quantity they wish to trade. From both a theoretical and a practical point of view, hidden orders are really a trade-off between market liquidity and transparency. This kind of orders is a way for transparent trading systems to avoid that liquidity supply moves towards more opaque markets. Hence, hidden orders constitute an interesting area of research, especially for trading systems in which the level of transparency seems to be at the heart of controversial debates.6 On Euronext, hidden orders, also called iceberg orders or undisclosed orders, allow traders to show other market participants only a part of the total quantity they want to buy or sell. The total order size is registered in the order book but only the order disclosed quantity is displayed on the market screens.7 So hidden orders are placed in the order book according to their price and time precedences but only the disclosed size is visible to market participants. When a hidden order is filled for its exposed size, the disclosed quantity is automatically renewed and the order joins the end of the order queue at the same limit price. Hidden orders thus lose their time priority after execution

5Attempting to buy or sell securities ahead of an anticipated reaction to news, taking a position in order to beneﬁt from an upcoming market-moving transaction are examples of front-running strategies. 6Consider the switch to complete anonymity applied by Euronext in April 2001 or the recent decision of Euronext to diﬀuse the whole order book from December 2003. 7The order disclosed size must be at least 10 times the minimum trading lot.

4 of the displayed quantity. Concerning size modifications, only an increase of the visible quantity results in a loss of time precedence. These orders are accepted both in the pre- opening/closing phase and during the continuous trading session. At a call auction, hidden quantities contribute to the equilibrium price calculation. Once the auction price is given, buy (sell) hidden orders at a limit above (below) this price are fully filled. Hidden orders with a limit price equal to the equilibrium price receive priority for execution up to the displayed size. After execution of the exposed quantities, the disclosed quantity is automatically renewed and the order is positioned behind other orders at the same limit price and will be filled only after execution of fully disclosed orders.

2.2 Market Depth

Roughly speaking, market liquidity reflects trading conditions and is used to be associated with four properties : immediacy, tightness, depth and resiliency. Immediacy is the time component of liquidity. Tightness refers to the cost of turning around a position over a short time. Kyle (1985) defines depth as the size of an order flow inno- vation required to change prices a given amount. Resiliency measures the speed with which prices recover from a liquidity shock. Market depth refers to the quantities available at the quoted prices. Traders un- dergo an unfavorable price change when the size of their orders is larger than the quantity available at the best bid or ask price. So the market should be ”deep” in that trading costs for large orders should also be small. In market microstructure literature, a lot of studies have been devoted to market depth assessment. The oldest ones defined this liquidity measure as the total quantity available for trade at the best bid and ask quotes, ignoring orders outside the best prices [Lee et al. (1993), Ahn & Cheung (1999), Ahn et al. (2001)...]. Nowadays, access to more complete order data usually allows a more accurate estimation of market depth. For example, Danielsson & Payne (2001) look at determination of order book depth on an electronic FX broking system. They define depth as the quantities available in the order book at or within ’k’ ticks of the best limit price. They find that buy and sell side depths are uncorrelated while depth is strongly autocorrelated on the same market side. Although market depth assessment becomes more and more sophisticated, few studies consider the potential presence of hidden quantities. One of the few papers devoted to hidden liquidity on the Paris Bourse8 was written by Auguy & Le Saout (1999). They focus on market depth by taking into account undisclosed quantities in the order book. By rebuilding the book for five stocks over 15 trading days, they show that liquidity supply is much more plentiful than what market participants can see on the market screens. The authors find on average 35% of hidden quantities in the order

8The Paris Bourse is now called Euronext Paris.

5 book. Moreover, they demonstrate that undisclosed depth can enhance other liquidity proxies like the Kyle’s lambda or the weighted average spread. In a similar but more recent study, Tuttle (2003) describes the use of hidden depth in the Nasdaq market. She shows that hidden quantities represent 25% of the inside depth in Nasdaq 100 stocks. According to the author, hidden depth has no significant effect on effective half-spreads incurred by traders but is predictive of future market price movements. The present study builds partially upon and extends these empirical contributions on market depth assessment. To analyze the impact of hidden orders on market liquidity, we first rebuilt the order book for all the stocks included in the CAC40 index over the last three months of 2002. As in Danielsson & Payne (2001), we distinguished different levels of depth on both market sides: depth at the best limit, depth at the five best limits and depth in the whole order book.9 Then, we computed the volume (in value) available at each order book level. However, similarly to Auguy & Le Saout (1999) and Tuttle (2003), we decomposed market depth into its visible and hidden components. So we are able to empirically investigate the magnitude of hidden depth, the pattern of both disclosed and undisclosed quantities and also interactions between short-term volatility and market depth composition.

2.3 Order Submission Strategies

To improve understanding of traders’ behavior, many empirical papers focused on order placement strategies. One of the most major studies was reported by Biais et al. (1995) who analyzed the order flow dynamics on the Paris Bourse. They used very complete data including the prices and the disclosed quantities available at each of the five best limits of the order book.10 To assess both supply and demand of liquidity, they defined six categories of orders on each market side according to their aggressiveness. The three most aggressive order categories result in an immediate execution. Large orders are orders to buy or sell at a better price a larger quantity than that available at the best opposite limit. Market orders are orders to buy or sell a larger quantity than that proposed at the best opposite limit but, unlike the previous category, they are not allowed to walk up to the order book beyond the best limit. Small orders are orders to buy or sell a lower quantity than that available at the best opposite limit, so they result in a full and immediate execution. Orders within the best quotes are orders which generate price improvement. Orders at the best quote join the queue of orders at the best bid or ask limit. Finally, orders below the best quote are orders to buy or sell below the best bid or ask price.11 With this order classification, Biais et al. (1995) report a competitive behavior of

9We prefer an estimation by limits rather than by ticks to get a direct assessment of market transparency. 10The authors cannot observe directly hidden orders in their dataset. 11Orders to buy (sell) at a lower (higher) price than the best bid (ask).

6 liquidity suppliers. To gain price and time priority, traders quickly place orders within the best quotes when depth at the best limit or the spread is large. Their results evidence the presence of limit order traders monitoring the order book, competing to provide liquidity to the market when it is needed and rewarded, and quickly seizing favorable trading opportunities. Following the example of numerous authors [Bisière & Kamionka (2000), Griffiths et al. (2000), Ranaldo (2004), Degryse et al. (2002), Beber & Caglio (2003)...], we chose the Biais et al. (1995)’s order classification to investigate hidden order submission. In the present study, we first provide a comparative analysis of aggressiveness levels for hidden and usual orders. Next, we examine interactions between the order book and the order flow. Thanks to our very complete order book data, we can respectively assess the influence of the spread size, both displayed and hidden depths and the last order on the aggressiveness level of the incoming order.

3 Euronext Data

At present, Euronext includes the former exchanges of Amsterdam, Brussels, Lisbon, Porto, Paris and also the LIFFE. This market offers a particularly appropriate testing ground for examining hidden orders. First, it relies on a transparent order-driven trading system allowing the use of hidden quantities. Second, Euronext is a totally computerized and centralized trading system which facilitates the fully capture of order flow and execution process. The availability of very complete data makes possible an empirical investigation of interactions between order submission strategies, order book dynamics and market liquidity. Our intraday data refer to all the stocks included in the CAC40 index over the period covering October through December 2002. Table 1 makes list of these stocks ranked by decreasing market value. During this period, the trading day takes place in several stages. The market opens with a call auction following a pre-opening phase. Then, the market switches over to continuous trading and closes with a call auction following a short pre-closing period. All along the trading session, the trading system automatically feeds information into the electronic data dissemination network. Market participants thus receive in real time the five latest trades along with the five best limits of the order book with the aggregate disclosed quantities.12 For the current study, we mainly used two data sets from the public Euronext database. The order data contain all information about orders: submission date and time, limit price, size, order type, order state... For hidden orders, a distinction between the total order size and the disclosed one is made. The trade data provide information

12Market members can observe at any time the entire content of the order book, except both the hidden quantities and the identiﬁcation codes.

7 about all the trades: execution date and time, trade size, price... Those public data include very rich information about the trading process. Besides, we received additional information from Euronext authorities such as the identification codes13 of market members and also a variable indicating whether they act for their own account or not. As dual trading is allowed on Euronext, market members are brokers-dealers.A distinction can thus be made between ”client orders” and ”dual trader orders”. This additional information makes possible a rebuilding of the order book14 over 63 trading days15 for the 40 stocks in our sample. Table 2 exhibits descriptive statistics about the cross-sectional distribution of daily market activity for the CAC40 stocks over the last three months of 2002. The results reflect the high level of trading activity in these stocks. The average daily number of trades per stock is 3 194, involving an average daily trading volume of 76 017 842 euros per stock. The average daily number of orders submitted per stock is 5 244. On average, 221 among these orders contain a hidden quantity. If we compare these daily statistics with those of Biais et al. (1995),16 we may conclude that trading activity for the CAC40 stocks has been dramatically intensified. To give general information about orders submitted for the 40 stocks in our sample, we report summary statistics in Table 3. First of all, when we look at the magnitude of hidden order use, we find that 4% of orders contains a hidden part. Previous studies provide results about hidden order submission on other markets. Aitken et al. (1996) reported that, in 1993, about 6% of orders on the ASX was undisclosed. D’Hondt et al. (2002) found that, in 1997, about 14% of limit orders on the French segment of Euro.NM was not fully displayed. Recently, Hasbrouck & Saar (2002) documented that executed hidden orders on Island represent only about 3% of submitted limit orders. However, a comparison with those findings would be delicate because both markets and stocks are not necessarily identical and hidden order submission is reported to be quite stock-dependent. Indeed, Aitken et al. (2001) demonstrated that hidden order use is negatively related to relative tick size and trading activity but positively related to volatility and order value. Next, when we focus on the trading phases, we find that the proportion of undisclosed orders is slightly larger over the continuous session than during the pre-auction periods. This result is consistent with the hypothesis that the order exposure risk is higher in a continuous trading session because information dissemination in real time is more valuable during this period than over a pre-opening or pre-closing phase.

13We got numerical codes which hide the real name of market members. These codes allow us to identify orders and trades involving the same market member. 14For more details about order book rebuilding see De Winne & D’Hondt (2004). 15We excluded December 24 from our sample period because the market closed at 2.00 p.m. this day. 16Biais et al. (1995) reported that in 1991 the average daily number of trades (orders) per CAC40 stock in their sample was 148.6 (160.6).

8 Table 3 also shows that 48% of orders is submitted by market members for their own account. However, market members seem to use a little more hidden quantities than their clients: 5% of dual trader orders are not fully disclosed. As expected, we can also note that traders use mainly limit orders. Finally, after ranking orders according to order size quartiles computed per stock, we can see that undisclosed orders are essentially large orders. This result is consistent with Harris (1996) and Raposo (2003) who reported that hidden orders are larger than usual orders.

4 Hidden Orders and Market Depth

To assess the impact of hidden order use on market depth composition, we first rebuilt the order book over the 63 trading days for each stock of our sample. Then, we defined three different levels of depth on each market side: depth at the best limit, depth at the 5 best limits and depth in the whole order book. Hence, for each stock, we computed, at any time of the period, the volume in value17 available at each order book level on both market sides. However, we decomposed market depth into its displayed and hidden components. In this way, we are able to examine the pattern of both displayed and hidden depths over the continuous trading session.18

4.1 Market depth decomposition

The ﬁrst issue we address is the proportion of visible depth at each level of the order book. During our sample period (October through December 2002), market participants can observe in real time the 5 best prices of the order book as well as the aggregate disclosed quantities available at each limit price. If only the 5 best limits are publicly displayed, traders are expected to use hidden quantities when their orders are likely to be registered in this part of the order book. Indeed, it is not worth using undisclosed quantities for orders which do not appear on the market screens. So, we propose the following assumption: Hypothesis 1 : The proportion of visible depth is smaller at the top of the order book (5 best limits) than in the whole order book. Next, if we consider that, on order-driven markets, most of trading activity is concentrated at the best prices, we tend to say that traders used to pay a special attention to the best limit. Hidden quantities are thus expected to be more easily discovered or inferred and consequently less frequent at this level of the order book. It is the reason why we also propose this second assumption: 17To allow comparisons across stocks, we multiplied the number of shares available by the opening stock price of the day. 18We focused exclusively on the continuous session (between 9.00 a.m and 5.30 p.m) because depth is mainly increasing during pre-auction phases.

9 Hypothesis 2: The proportion of visible depth is larger at the best limit than at the 5 best limits. To test both assumptions, we focused on the daily proportions of visible depth for each stock to perform statistical comparisons across order book levels. Hence, for each stock, we computed, for each continuous trading session, the time-weighted average displayed depth (disclosed quantities) as well as the time-weighted average total depth (disclosed + hidden quantities) at each order book level on each market side. Then, we calculated, for each stock and each day, the proportion of visible depth as the time- weighted average displayed depth divided by the time-weighted average total depth. This proportion was computed for each of the three order book levels we consider. For each stock, we used the 63 daily proportions of visible depth to perform paired t- tests of both assumptions. To facilitate interpretation, Table 4 reports the proportions of daily average displayed depth for each CAC40 stock as well as the daily means and medians across all stocks. Results for hypothesis 1 are presented in columns RB5 and RA5 while results for hypothesis 2 are reported in columns RB1 and RA1. Globally, we can see in Table 4 that, on average, around 80% of the volume available in the whole order book is visible on both market sides. However, this proportion falls to around 55% for the quantities available at the 5 best limits or even to around 45% at the best limit. If we look at the proportions reported stock by stock, we can conclude that differences across order book levels are statistically significant. Columns RB5 and RA5 present the results for hypothesis 1. Whatever the market side, the proportion of displayed depth at the 5 best limit is significantly smaller than in the whole order book. So hypothesis 1 is verified and traders seem to use hidden quantities for orders that are likely to be registered within the 5 best limits. Concerning hypothesis 2, results are reported in columns RB1 and RA1. The proportions of visible depth at the best bid (ask) prove to be significantly different from the proportions of visible depth at the 5 best bids (asks), but the difference direction is opposite as what we expected. Indeed, the proportions of displayed depth at the best limit is significantly smaller than at the 5 best limits. So hypothesis 2 is rejected and explanations can be proposed for this unexpected result. Even if undisclosed quantities are easier to be discovered or inferred at the best prices, traders submit hidden orders at this level of the order book. If it is true, we would find in our order aggressiveness analysis a large number of hidden orders placed at the best quote. An alternative is that traders mainly use undisclosed quantities for orders submitted within the 5 best limits, but the smaller proportion of visible depth at the best limit is due to hidden orders which arrive at the best prices as trading activity evolves. We will check both propositions in the next section devoted to order submission strategies. These first findings about market depth composition reveal that the impact of hidden order placement on pretrade transparency is quite large, especially at the top

10 of the order book. Indeed, less than half the quantities available at the best limit is not displayed on the market screens. Figure 1, which illustrates the average total and visible volumes for 5-minute intervals computed across all stocks and all trading days, conﬁrms the magnitude of hidden depth at the best prices. This ﬁgure also shows that disclosed volumes are quite constant over the continuous session while total depth moves much more. This result is consistent with Auguy & Le Saout (1999) who demonstrated that changes in total depth are mainly explained by variations in hidden quantities, especially at the best limit of the order book.

4.2 Market depth composition and short-term volatility

Ahn et al. (2001) reported that short-term volatility affects order flow composition and thus market depth. To examine explicitly how order flow composition is related to the liquidity-driven price volatility, they decomposed short-term volatility into upside and downside measures. According to them, when there is a paucity of limit orders on the ask (bid) side, the temporary order imbalance results in upside (downside) volatility. This will encourage traders to place more limit sell (buy) orders. Hence, the authors demonstrated that short-term volatility arising from the ask (bid) side at time t − 1 induces traders to submit limit sell (buy) orders rather than market sell (buy) orders at time t, so that market depth on the ask (bid) side increases. Similarly, we investigate in this paper the influence of short-term volatility on market depth composition. Theoretically, price volatility encourages limit order submission [Handa et al. (1997), Foucault (1999)]. However, price volatility also affects the order exposure risk. Copeland & Galai (1983) explain that the option value of limit orders is affected by volatility. Furthermore, Harris (1996) found that traders expose more limit orders when prices are not volatile. Therefore, price volatility should induce traders to use more hidden orders. Then, we propose the following assumption: Hypothesis : Price volatility arising from the ask (bid) side should have an impact on sell (buy) market depth composition, so that hidden depth proportion on the ask (bid) side is expected to be positively related to upside (downside) price volatility.

To address the above hypothesis, we conducted an empirical analysis on a 5-minute intervals basis and we estimated the following regressions:

5bids + + − − 5bids 5bids HDPt = α1 + β1 RISKt−1 + β1 RISKt−1 + ρ1 HDPt−1 + ²t (1)

5asks + + − − 5asks 5asks HDPt = α2 + β2 RISKt−1 + β2 RISKt−1 + ρ2 HDPt−1 + ²t (2)

5bids where HDPt is the time-weighted average proportion of hidden depth at the 5 5asks best bids during time interval t, HDPt is the time-weighted average proportion of + − hidden depth at the 5 best asks during time interval t, RISKt−1 and RISKt−1 are

11 the upside and downside measures of volatility during time interval t − 1. The upside (downside) volatility is computed as the sum of absolute returns based on positive 19 5bids 5asks (negative) return observations within the interval t − 1. ²t and ²t are usual 5bids 5asks random error terms. The inclusion of HDPt−1 and HDPt−1 allows to control for autocorrelation in hidden depth magnitude. Like Ahn et al. (2001), we estimated Equations 1 and 2 using Generalized Method of Moments. Estimates were calculated cross-sectionally and are presented in Table 5. 5bids 5asks First, HDPt (HDPt ) is positively and significantly related to the downside (upside) volatility. This confirms our expectations. When liquidity-driven price volatility arises from the bid (ask) side, this induces potential buyers (sellers) to submit hidden buy (sell) orders because the exposure risk is higher. So traders seem to be aware of the order exposure risk and they perceive it higher when prices are volatile. 5bids 5asks Second, it is interesting to notice that HDPt (HDPt ) is negatively related to upside (downside) volatility. Ahn et al. (2001) indicated that when the price moves up (down), traders submit market buy (sell) orders instead of limit buy (sell) orders because of the probability of execution. Besides, Table 3 shows us that hidden orders are only limit orders. This might explain why hidden depth proportion decreases on the bid (ask) side when the upside (downside) volatility increases. Finally, whatever the market side, the proportion of hidden depth is positively autocorrelated. The coefficients ρ are positive and significant for both equations.

5 Hidden Order Submission Strategies

Over the period covering October through December 2002, 12 059 812 orders were submitted during the continuous trading session for the 40 stocks in our sample. Order book data made it possible to associate each order with the state of the order book prevailing just before its introduction. To account for the time a trader needs to react to what he can observe on the market screens [Kaniel & Liu (2001)], we implemented a minimum delay of 5 seconds between the placement time of any order and the state of the prevailing order book.

5.1 Order Aggressiveness Analysis

To delimit the order submission activity in the order book, we ﬁrst computed the proportion of orders placed within the 5 best limits. We consider as orders within the 5 best limits both orders resulting in an immediate execution when submitted and buy (sell) orders with a limit price equal or higher (lower) than the ﬁfth best price prevailing

19Like Ahn et al. (2001), we implicitly assume that the mean return is zero and we measure the cumulative price ﬂuctuation within the interval rather than the average price ﬂuctuation for each trade.

12 on the bid (ask) side of the order book when submitted. In our sample, we found that, on average, 90% of all orders (with a hidden part or not) joins the 5 best limits of the book when submitted. Most of the order placement activity is thus concentrated at the top of the order book, which is diffused in real time on the market screens. Next, we used the methodology of Biais et al. (1995) described in Subsection 2.3 to categorize orders. Identically, we defined the level of order aggressiveness according to the time for execution. We inferred it from order price and size in comparison with both the price and the displayed quantities available at the best limit on the opposite side of the order book.20 To identify potential disparities in aggressiveness, we conducted this classification for several order groups. First, we considered all orders. Next, we distinguished hidden from usual orders. Finally, we took the order direction (buy or sell) into account. To make possible statistical comparisons across order groups, we conducted this order aggressiveness analysis stock by stock.21 Table 6 reports the average unconditional probabilities of orders according to their aggressiveness level as well as the results of statistical comparisons between usual and hidden orders. When we consider all orders, we observe that the most frequent order category is orders placed below the best quote. This finding is still true whatever both the order group (usual or hidden) and the order direction (buy or sell). However, when we consider the other aggressiveness categories, a quite striking difference appears between usual and hidden orders: on average 35% of usual orders takes liquidity by resulting in an immediate execution when they arrive on the market while only 17% of hidden orders does likewise. So few hidden orders are aggressive in comparison with usual ones. On the one hand, the first two categories constitute only 13% of hidden orders. This phenomenon may be explained by Euronext requirements for acceptance of undisclosed quantities. Indeed, hidden quantities are prohibited with must be filled orders22 which are very aggressive orders. On the other hand, less than 4% of hidden orders are classified as ”small orders”, which represents a significant difference with usual orders. This finding can be related to one of our previous results which states that hidden orders are mainly large-sized orders. If we had took into account only the disclosed quantity of hidden orders to define their aggressiveness level, we would observe a significant switch from category 2 to category 3. In this case, the frequency of ”small orders” would increase although the most frequent events would remain hidden orders submitted below the best quote. All differences between usual and hidden orders are statistically significant and hold whatever the order direction. To summarize, in comparison with usual orders, hidden orders are mainly liquidity providing. Less than 20% of hidden orders takes

20For an order aggressiveness analysis dealing with both disclosed and hidden quantities, see De Winne & D’Hondt (2004). 21Both t-test and Wilcoxon test were performed. 22This order type is now called ”market orders” for all stocks traded on Euronext.

13 liquidity when submitted. Therefore, hidden order traders appear to be mainly liquidity suppliers rather than liquidity demanders. Table 6 brings also an answer to the question raised in the previous section about hidden order placement at the best quote. We can observe that around 33% of hidden orders are placed below the best quote while around 48% of them are submitted either within the best quotes23 or at the best price. So hidden orders are proportionally more present at the best limit than at the next prices. This ﬁnding is the reason why the proportion of visible (hidden) depth is smaller (higher) at the best limit than at the 5 best limits.

5.2 Market Conditions around Order Placement

In this subsection, we focus on how the state of the order book can affect order placement. The high quality of our data makes possible a detailed investigation of market conditions around order submission. We analyzed interactions between the order book and the order flow as in Biais et al. (1995). First, we examined the order flow given the state of the order book. Second, we looked at the probabilities of orders conditional on the previous order. In both cases, we compared hidden order submission with usual order placement. Our goal was to highlight potential features in hidden order traders’ behavior. The empirical frequencies of the different order categories conditional on the prevailing order book state for respectively usual and hidden orders are reported in Tables 7 and 8. Identically to Biais et al. (1995), we aggregated for simplicity orders resulting in an immediate execution when submitted. The state of the order book is characterized by the spread size and the depth available at the best limit on both market sides. It’s important to notice that we distinguished displayed and hidden quantities available at the best quotes. Hence, observations were classified in several steps. First of all, orders were divided into two groups according to whether the prevailing spread was larger or smaller than the daily median for the given stock. Next, we classified orders of both groups according to respectively the displayed depth at the best bid, the displayed depth at the best ask, the hidden depth at the best bid and the hidden depth at the best ask. For each stock, each kind of depth was defined to be small if it is smaller than its daily median. To assess the impact of both displayed and hidden depths, we performed statistical comparisons. So empirical frequencies were computed stock by stock and t-tests were performed between frequencies conditional on the spread and frequencies conditional on both the spread and the depth. We made this comparison for each kind of depth. Tables 7 and 8 report the average empirical frequencies as well as the results of t-tests.

23Buy (sell) orders placed within the spread generate price improvement and become the best bid (ask).

14 Griffiths et al. (2000) found that aggressive orders are more likely when the prevailing order book has a narrow spread, large depth on the same market side as the order or small depth on the opposite side. Our results are consistent with theirs. First, the spread influence on order placement is similar for both usual and hidden orders. Purchases and sales are more frequent when the spread is narrow while buy and sell orders within the quotes are more likely when the spread is large. Biais et al. (1995) reported these liquidity effects. Traders supply liquidity when it is scarce and take it when it is plentiful. Second, usual orders tend to be more aggressive when the displayed depth is large on the same market side or small on the opposite market side. This reflects undercutting behavior and competition among traders on the same market side. Moreover, usual orders are more likely to be aggressive when the hidden depth is large on the opposite market side. When the spread is narrow, 28% (31%) of buy (sell) usual orders generates an immediate trade when the hidden depth on the ask (bid) side is large at the best limit. This phenomenon could be explained by traders who discover hidden quantities available at the best opposite limit and try to trade against them again. This result is consistent with Pardo & Pascual (2003) who found that hidden orders temporally increase the aggressiveness of traders when revealed to the market place.24 This implicitly supposes two phenomenons. First of all, some traders try to detect hidden quantities and could adopt a specific behavior. Next, traders who look for hidden quantities must feel satisfaction in trading against hidden orders. It suggests that they profit from the available liquidity and do not consider hidden orders as orders placed by informed traders. As for hidden orders, results in Table 8 are quite similar but less pronounced. Indeed, the magnitude of the displayed depth available at the best bid (ask) seems to have less impact on sell (buy) hidden order aggressiveness. This could suggest that hidden order traders focus on a given market side at a point in time and are less concerned with what happens on the opposite market side than usual order traders are. Furthermore, whatever the side of the order book, the hidden depth appears to affect hidden order aggressiveness less systematically. To finish this subsection, we analyzed the impact of the last order on next order aggressiveness. In order to focus on aggressiveness influence rather than on order type (hidden or usual), we computed and presented the transition probability matrix for usual and hidden orders separately. So Table 9 (10), which only refers to usual (hidden) orders following an another usual (hidden) order, exhibits the empirical frequencies of each order category conditional upon the category of the previous order. To examine how the probability of observing a given order varies as a function of the previous one, we have to compare frequencies within each column. To make interpretation easier, we also reported the unconditional frequencies in Tables 9 and 10.

24The authors analyzed the market response when the presence of hidden orders is publicly revealed with execution.

15 For both hidden and usual orders, we find the diagonal effect as reported in Biais et al. (1995) and more recently in Degryse et al. (2002). The probability that a given order category occurs is larger just after the same category of order than unconditionally. In other words, an order of a given category is likely to be followed by an order of the same category. In Table 9, this diagonal effect is the highest for the first two categories. A large usual order is around 6 times more likely after a large usual order than unconditionally. A market usual order is around 4 times more frequent after a market usual order than unconditionally. For the other categories, the conditional probabilities are on average twice as high as the unconditional frequencies. Results are similar when we analyze Table 10. However, even if the diagonal effect is important for categories 1 and 2, it is the highest for the third category. Indeed, a small hidden order on the bid (ask) side is 10 (20) times more likely after a small hidden buy (sell) than unconditionally. In addition to the diagonal effect, Tables 9 and 10 also provide evidence of traders’ strategic behavior. Buy (sell) orders within the quotes are also frequent after sell (buy) orders within the spread. This interaction between both market sides leads to a spread decrease and is more pronounced for hidden orders. This result confirms that traders compete to supply liquidity. In the microstructure literature, three explanations are generally proposed for the diagonal effect. It could result from strategic order splitting, from imitating behavior or from similar reactions successively to the same event. To test the order splitting hypothesis, we examined the identification code associated with each order. Indeed, our order data identify the market member submitting the orders as well as the account (client or own) for which the orders are placed. Hence, we assumed that two similar consecutive orders submitted by the same market member for the same account are split orders.25 Then, we computed the average proportion of split orders for each couple of identical successive orders. This proportion was calculated stock by stock to allow statistical comparisons between usual and hidden orders.26 To facilitate interpretation, we present the global average proportions in Table 11. For usual orders, the global average proportion of split orders fluctuate from 30 to 46% without any difference between market sides. As for hidden orders, these proportions are often significantly larger. Actually, more than 90% of successive hidden orders of categories 1, 3, 7 and 9 can be defined as split orders. This also holds for around 70% of hidden orders consecutively placed below the best price. Consequently, similar successive hidden orders appear to be significantly more involved in splitting strategies than similar successive usual orders. Therefore, hidden order submission should not be considered as a simple alternative to splitting strategies for large orders.

25A similar assumption is also used by Ellul et al. (2003). 26Both t-test and Wilcoxon test were performed.

16 6 Conclusion

This paper analyzes hidden order placement for all the stocks belonging to the CAC40 index over the period covering October through December 2002. Based on very complete order book data, this empirical study has two main strands. On the one hand, we assess the impact of hidden order use on market depth composition and pretrade transparency. On the other hand, we compare hidden order submission with usual order placement to identify what characterizes hidden order traders. All along this paper, we highlighted a lot of empirical findings which are interesting from both a theoretical and a practical point of view. The main results can be summarized as follows. First, given the magnitude of hidden depth, the impact of hidden orders on pretrade transparency is quite large, especially at the top of the order book. Indeed, more than half the volume available at the best limit at any time during the continuous session is not visible on the market screens. Consequently, hidden order use tends to substantially reduce pretrade transparency. Second, short-term volatility influences market depth composition significantly. The liquidity-driven price volatility arising from the bid (ask) side encourages hidden buy (sell) order placement. This finding tends to prove that traders are aware of the order exposure risk and use hidden quantities when this risk increases. Third, our order aggressiveness analysis reveals that hidden order traders are mainly liquidity suppliers. On average 35% of usual orders takes liquidity by resulting in an immediate execution when they arrive on the market while only 17% of hidden orders does likewise. Next, the spread influence on order placement is similar for both usual and hidden orders. Purchases and sales are more frequent when the prevailing spread is narrow whereas orders within the quotes are more frequent when the spread is large. As expected, traders supply liquidity when it is scarce and take it when it is plentiful. As for depth impact, usual orders are more likely to be aggressive when the displayed depth is large (small) on the same (opposite) market side but also when the hidden depth is large on the opposite market side. It suggests that some traders attempt to execute their own orders against hidden quantities. This behavior supposes that they do not consider hidden orders as orders placed by informed traders. Then, the magnitude of both displayed and hidden quantities available on the opposite market side does not systematically affect hidden order submission. Hidden order traders appear to focus on a given market side and seem less concerned than usual order traders with what happens on the opposite market side. Finally, an examination of the identification codes reports evidence that hidden orders are more involved in splitting strategies than usual orders. Therefore, hidden order submission should not be viewed as a simple alternative to splitting strategies

17 for large orders.

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21 Tables and ﬁgures

List of stocks belonging to the CAC40 index

Code Name Market value 4161 TOTAL FINA ELF 94 968 905 182 4166 OREAL 49 622 962 544 25743 AVENTIS 42 491 517 822 4157 SANOFI SYNTHELABO 41 807 670 827 26990 BNP PARIBAS 29 719 771 455 4154 CARREFOUR 29 157 761 966 55149 ORANGE 22 628 445 583 4462 SOCIETE GENERALE 18 678 726 421 4213 LVMH MOET VUITTON 18 078 690 429 4188 GROUPE DANONE 17 350 188 574 4180 SUEZ 16 764 208 315 4187 AXA 16 747 788 709 72275 CREDIT AGRICOLE 15 156 752 325 4150 AIRLIQUIDE 12 652 195 278 4245 VIVENDI UNIVERSAL 12 519 113 337 29512 RENAULT 12 295 036 642 29636 ST MICROELECTRONICS 12 154 957 808 42349 CREDIT LYONNAIS 11 528 687 052 4181 LAF ARGE 10 845 082 838 4292 SCHNEIDER ELECTRIC 10 621 969 271 45057 DEXIA 10 528 766 064 4252 PEUGEOT 9 773 596 987 4178 BOUY GUES 8 937 838 936 49388 EADS 8 747 187 814 36064 FRANCE TELECOM 8 583 835 968 49471 VIVENDI ENVIRON. 8 243 339 548 4250 PINAULT PRINTEMPS 7 772 049 480 4322 SAINT GOBAIN 7 748 000 691 4353 CASINO GUICHARD 6 190 074 050 4170 ACCOR 5 976 229 500 4448 LAGARDERE 5 419 796 693 4351 VINCI 5 212 842 310 223 AGF 4 829 133 422 1526 TF 1 4 584 769 199 4237 T HALES 4 535 460 112 44450 THOMSON MULTIMEDIA 4 428 081 156 4234 MICHELIN 3 851 747 013 4230 SODEXHO ALLIANCE 3 106 085 317 4438 ALCAT EL 2 924 479 010 4340 CAP GEMINI 2 026 487 546

Table 1: For each stock belonging to the CAC40 index, the numerical code, the name and also the market value estimated on October 1, 2002 are reported.

22 Cross-sectional distribution of daily market activity

Statistic Mean Max Median Min Daily return -0.0010 0.2499 -0.0020 -0.1743 Hi − Lo 0.0532 0.3351 0.0468 0.0084 Number of trades 3 194 27 438 2 373 329 T rading volume (shares) 2 957 175 87 625 404 1 357 942 76 603 T rading volume (euros) 76 017 842 1 017 806 085 44 971 865 3 475 230 Number of orders 5 244 33 579 4 185 840 Number of hidden orders 221 1 025 194 10 Number of dual trader orders 2 508 25 501 2 016 321

Table 2: For the 63 trading days and for each stock of our sample, we computed the daily return, diﬀerence between highest and lowest price divided by the lowest price, number of trades, trading volume in shares and in euros, number of orders, number of hidden orders and number of dual trader orders. This table presents summary statistics about the cross-sectional distribution of these daily averages across all the stocks included in the CAC40 index.

Summary statistics about orders

Usual Orders Hidden Orders All Orders All the sample 12 658 489 556 098 13 214 587 100% 96% 4% 100% Continuous session 11 543 902 515 910 12 059 812 91% 96% 4% 100% P re − opening/closing periods 1 114 587 40 188 1 154 775 9% 97% 3% 100% Client orders 6 589 280 263 733 6 853 013 52% 96% 4% 100% Dual trader orders 6 069 209 292 365 6 361 574 48% 95% 5% 100% Limit orders 11 459 505 556 098 12 015 603 91% 95% 5% 100% Market orders 1 198 984 0 1 198 984 9% 100% 0% 100% Small orders 3 531 605 19 823 3 551 428 25% 28% 4% Inferior median orders 3 253 102 28 353 3 281 455 25% 26% 5% Superior median orders 3 167 399 57 983 3 225 382 25% 25% 10% Large orders 2 706 383 449 939 3 156 322 25% 21% 81%

Table 3: Both usual and hidden orders are classiﬁed according to their submission time, their initiator (market member or client), their type (market or limit order) and their total size. For each stock, order size quartiles per day were computed and 4 order size categories were deﬁned: small orders (Q3).

23 Proportions of daily average displayed depth Stock RB1 RA1 RB5 RA5 RB RA 223 0.4870 0.5510 0.5236∗∗∗ 0.5501∗∗∗ 0.8018 0.8216 1526 0.3847 0.3272 0.3877∗∗∗ 0.3654∗∗∗ 0.6508 0.6050 4150 0.4669∗ 0.5104∗∗ 0.5190 0.5458∗∗∗ 0.6065 0.8190 4154 0.4251∗∗∗ 0.4792∗∗∗ 0.5163 0.5436∗∗∗ 0.5381 0.7613 4157 0.5354∗∗∗ 0.5608∗∗∗ 0.5826∗∗∗ 0.6188 0.7624 0.6473 4161 0.6900∗∗∗ 0.6485∗∗∗ 0.7437∗∗∗ 0.7045∗∗∗ 0.8232 0.8932 4166 0.5015∗∗∗ 0.5174∗∗∗ 0.5731∗∗∗ 0.5975∗∗∗ 0.8632 0.7723 4170 0.3918 0.3986∗∗∗ 0.4286∗∗∗ 0.4602∗∗∗ 0.6132 0.7121 4178 0.4494∗∗∗ 0.3201∗∗∗ 0.4789∗∗∗ 0.4260∗∗∗ 0.7663 0.8044 4180 0.4701∗∗∗ 0.4850∗∗∗ 0.5372∗∗∗ 0.5407∗∗∗ 0.8513 0.8387 4181 0.5252∗∗ 0.3986∗∗∗ 0.5623∗∗∗ 0.4727∗∗∗ 0.7655 0.8091 4187 0.4504∗∗∗ 0.4455∗∗∗ 0.5437∗∗∗ 0.5478∗∗∗ 0.7665 0.7808 4188 0.5365 0.5138∗ 0.5492∗∗∗ 0.5584∗∗∗ 0.6756 0.7137 4213 0.3936∗∗∗ 0.3772∗∗∗ 0.4264∗∗∗ 0.4150∗∗∗ 0.4878 0.5845 4230 0.3870 0.4107∗∗ 0.3957∗∗∗ 0.3843∗∗∗ 0.6143 0.5696 4234 0.4387 0.4507 0.4553∗∗∗ 0.4835∗∗ 0.7687 0.5916 4237 0.3384∗∗∗ 0.3170∗ 0.4345∗∗∗ 0.3955∗∗∗ 0.7401 0.7392 4245 0.3854∗∗∗ 0.3780∗∗∗ 0.5033∗∗∗ 0.4860∗∗∗ 0.7907 0.8435 4250 0.3972∗∗∗ 0.4187∗∗∗ 0.4595∗∗∗ 0.4869∗∗∗ 0.6864 0.7040 4252 0.4486∗∗∗ 0.4306 0.4897∗∗∗ 0.4583∗∗∗ 0.6838 0.6688 4292 0.3717∗∗∗ 0.4142 0.4316∗∗∗ 0.4415∗∗∗ 0.7027 0.7279 4322 0.4078∗∗∗ 0.3428∗∗∗ 0.4739∗∗∗ 0.4015∗∗∗ 0.7164 0.6601 4340 0.3092∗∗∗ 0.2946∗∗∗ 0.3751∗∗∗ 0.3744∗∗∗ 0.6244 0.6888 4351 0.4090 0.4063∗∗∗ 0.4301∗∗∗ 0.4629∗∗∗ 0.6627 0.7418 4353 0.4184 0.5003∗ 0.4506∗∗∗ 0.5316∗ 0.7291 0.5630 4438 0.6143∗∗∗ 0.6131∗∗∗ 0.7416∗∗∗ 0.7390∗∗∗ 0.9163 0.9274 4448 0.4712 0.4508 0.5054∗∗∗ 0.4759∗∗∗ 0.7190 0.6686 4462 0.4855∗∗∗ 0.4756∗∗∗ 0.5563∗∗∗ 0.5683∗∗∗ 0.7260 0.8074 25743 0.5977∗∗∗ 0.5806∗∗∗ 0.6558∗∗∗ 0.6191∗∗∗ 0.6955 0.6818 26990 0.4448∗∗∗ 0.3993∗∗∗ 0.5330∗∗∗ 0.4990∗∗∗ 0.7010 0.7714 29512 0.3650∗∗∗ 0.3620∗∗∗ 0.4236∗∗∗ 0.4228∗∗∗ 0.6480 0.7192 29636 0.6060∗∗∗ 0.6306∗∗∗ 0.7741 0.7880∗ 0.7588 0.8168 36064 0.4028∗∗∗ 0.4215∗∗∗ 0.5609∗∗∗ 0.5657∗∗∗ 0.8730 0.8939 42349 0.1365∗∗∗ 0.4655∗∗∗ 0.2568∗∗∗ 0.5678∗∗∗ 0.4892 0.7672 44540 0.3198∗∗∗ 0.3456∗∗∗ 0.3712∗∗∗ 0.4305∗∗∗ 0.6580 0.6670 45057 0.3941∗∗∗ 0.4461∗∗∗ 0.5285∗∗∗ 0.5443∗ 0.6637 0.5363 49388 0.3562∗∗∗ 0.3539∗ 0.3989∗∗∗ 0.4089∗∗∗ 0.7599 0.5287 49471 0.4141∗∗∗ 0.3666∗∗∗ 0.4726∗∗∗ 0.4138∗∗∗ 0.8147 0.7819 55149 0.4605∗∗∗ 0.4326∗∗∗ 0.5349∗∗∗ 0.5484∗∗∗ 0.8552 0.8754 72275 0.4052∗∗∗ 0.3731∗∗∗ 0.4725∗∗∗ 0.4367∗∗∗ 0.8321 0.9169 Mean 0.4444 0.4676 0.5494 0.5656 0.7956 0.8047 Median 0.4149 0.3586 0.4538 0.4110 0.6185 0.6780

Table 4: For each stock, the proportion of daily average visible depth at each order book level for both market sides is reported. RB1 (RA1) refers to the daily time-weighted average displayed depth divided by the daily time-weighted average total depth at the best bid (ask). RB5 (RA5) refers to the daily time-weighted average displayed depth divided by the daily time-weighted average total depth at the 5 best bids (asks). RB (RA) refers to the daily time-weighted average displayed depth divided by the daily time-weighted average total depth in the whole order book on the bid (ask) side. Both mean and median proportions of daily average visible depth across stocks are also provided. Statistical comparisons between RB5 (RA5) and RB (RA) were conducted (hypothesis 1) and the results are reported in columns RB5 (RA5). Statistical comparisons between RB1 (RA1) and RB5 (RA5) were conducted (hypothesis 2) and the results are reported in columns RB1 (RA1). *Significant at the 10% level, **Significant at the 5% level, ***Significant at the 1% level.24 GMM estimates for regression of hidden depth proportion on lagged upside and downside volatility

BID SIDE ASK SIDE + − + − β1 β1 ρ1 β2 β2 ρ2 −0.6135∗∗∗ 0.4972∗∗∗ 0.7795∗∗∗ 0.1619∗∗∗ −0.2587∗∗∗ 0.7805∗∗∗

Table 5: Results refer to Equations 1 and 2. β+ (β−) refers to upside (downside) volatility at time t − 1. ρ refers to hidden depth proportion at time t − 1. Coefficients are calculated cross-sectionally. *Significant at the 10% level, **Significant at the 5% level, ***Significant at the 1% level.

Unconditional frequencies of orders according to their aggressiveness level Sample Large orders Market orders Small orders Orders within Orders at Orders below ALL 0.0463 0.0569 0.2593 0.1527 0.1687 0.3160 UO 0.0463 0.0534 0.2544 0.1684 0.1674 0.3101 HO 0.0311∗∗∗ 0.1048∗∗∗ 0.0373∗∗∗ 0.2663∗∗∗ 0.2237∗∗∗ 0.3368∗∗ BUO 0.0450 0.0544 0.2391 0.1704 0.1775 0.3135 BHO 0.0290∗∗∗ 0.1018∗∗∗ 0.0354∗∗∗ 0.2691∗∗∗ 0.2328∗∗∗ 0.3319 SUO 0.0480 0.0528 0.2665 0.1678 0.1588 0.3061 SHO 0.0334∗∗∗ 0.1082∗∗∗ 0.0395∗∗∗ 0.2634∗∗∗ 0.2140∗∗∗ 0.3417∗∗∗

Table 6: Unconditional probabilities of order categories according to the aggressiveness level are presented. The order classification used is described in subsection 2.3. ALL refers to all orders, UO to usual orders, HO to hidden orders, BU(H)O to usual (hidden) buy orders and SU(H)O to usual (hidden) sell orders. Statistical comparisons between usual and hidden orders were performed. *Significant at the 10% level, **Significant at the 5% level, ***Significant at the 1% level.

25 Empirical frequencies of usual orders given the state of the order book Buy Buy within Buy at Buy below Sell Sell within Sell at Sell below Unconditional 0.17 0.07 0.09 0.15 0.20 0.08 0.08 0.16 LARGE Spread

Large spread 0.12 0.12 0.09 0.16 0.14 0.13 0.08 0.16

Large DD Bid 0.13∗∗∗ 0.14∗∗∗ 0.08∗∗∗ 0.14∗∗∗ 0.13∗∗∗ 0.13∗∗∗ 0.09∗∗ 0.16∗∗∗ Small DD Bid 0.11∗∗∗ 0.10∗∗∗ 0.10∗∗∗ 0.17∗∗∗ 0.15∗∗∗ 0.13∗∗ 0.08∗∗∗ 0.16∗∗∗ Large DD Ask 0.11∗∗ 0.12∗∗∗ 0.09∗∗∗ 0.16∗∗∗ 0.15∗∗∗ 0.15∗∗∗ 0.08∗∗∗ 0.14∗∗∗ Small DD Ask 0.12∗∗∗ 0.12∗∗∗ 0.09∗∗∗ 0.16∗∗∗ 0.13∗∗∗ 0.11∗∗∗ 0.09∗∗∗ 0.18∗∗∗

Large HD Bid 0.11∗∗∗ 0.11∗∗∗ 0.08∗∗∗ 0.13∗∗∗ 0.17∗∗∗ 0.14∗∗∗ 0.09∗∗∗ 0.17∗ Small HD Bid 0.12∗∗∗ 0.13∗∗∗ 0.09∗∗∗ 0.16∗∗∗ 0.13∗∗∗ 0.13∗∗∗ 0.08∗∗∗ 0.16∗∗∗ Large HD Ask 0.14∗∗∗ 0.13∗∗∗ 0.10∗∗∗ 0.16∗∗ 0.14∗∗∗ 0.12∗∗∗ 0.07∗∗∗ 0.14∗∗∗ Small HD Ask 0.11∗∗∗ 0.12∗∗∗ 0.09∗∗∗ 0.15∗∗∗ 0.14∗∗∗ 0.13∗∗∗ 0.09∗∗∗ 0.17∗∗∗ NARROW Spread 26 Narrow spread 0.22 0.03 0.09 0.15 0.24 0.03 0.08 0.16

Large DD Bid 0.25∗∗∗ 0.04∗∗∗ 0.08 0.14∗∗∗ 0.22∗∗∗ 0.03∗∗∗ 0.08∗∗∗ 0.16∗∗∗ Small DD Bid 0.19∗∗∗ 0.03∗∗∗ 0.08∗∗∗ 0.17∗∗∗ 0.26∗∗∗ 0.03∗∗∗ 0.08∗∗∗ 0.16∗∗∗ Large DD Ask 0.20∗∗∗ 0.03∗∗ 0.09∗∗∗ 0.15∗∗∗ 0.27∗∗∗ 0.04∗∗∗ 0.08∗∗ 0.14∗∗∗ Small DD Ask 0.23∗∗∗ 0.04∗∗∗ 0.08∗∗∗ 0.15∗∗∗ 0.21∗∗∗ 0.03∗∗∗ 0.08 0.18∗∗∗

Large HD Bid 0.19∗∗∗ 0.03∗∗∗ 0.07∗∗∗ 0.12∗∗∗ 0.31∗∗∗ 0.04∗∗∗ 0.08∗∗∗ 0.16∗∗∗ Small HD Bid 0.22∗∗∗ 0.03∗∗∗ 0.09∗∗∗ 0.17∗∗∗ 0.22∗∗∗ 0.03∗∗∗ 0.08∗∗∗ 0.16∗∗∗ Large HD Ask 0.28∗∗∗ 0.04∗∗∗ 0.09∗∗∗ 0.15∗∗∗ 0.21∗∗∗ 0.03∗∗∗ 0.07∗∗∗ 0.13∗∗∗ Small HD Ask 0.19∗∗∗ 0.04∗∗∗ 0.08∗∗∗ 0.15∗∗∗ 0.25∗∗∗ 0.04∗∗∗ 0.08∗∗∗ 0.17∗∗∗

Table 7: Empirical frequencies of usual order categories conditional on the state of the prevailing order book are reported. Each row is a probability vector adding up to 100% conditional on the order book state. The latter is characterized by the spread size and both displayed and hidden depths available at the best limit on each market side. For each stock, the spread (depth) is defined to be narrow (small) if it is smaller than its daily median. DD (HD) refers to the disclosed (hidden) depth. The unconditional probabilities of each order category are also provided. Statistical comparisons were performed to assess the impact of both displayed and hidden depths. *Significant at the 10% level, **Significant at the 5% level, ***Significant at the 1% level. Empirical frequencies of hidden orders given the state of the order book Buy Buy within Buy at Buy below Sell Sell within Sell at Sell below Unconditional 0.09 0.13 0.12 0.18 0.09 0.12 0.10 0.17 LARGE Spread

Large spread 0.04 0.19 0.11 0.17 0.05 0.18 0.10 0.16

Large DD Bid 0.04∗∗∗ 0.23∗∗∗ 0.09∗∗∗ 0.16∗∗∗ 0.04∗∗ 0.18∗∗∗ 0.10∗∗∗ 0.16∗∗ Small DD Bid 0.04 0.16∗∗∗ 0.14∗∗∗ 0.18∗∗∗ 0.05∗∗∗ 0.18∗∗∗ 0.10∗∗∗ 0.15 Large DD Ask 0.04∗ 0.19∗ 0.12∗∗∗ 0.17∗∗∗ 0.05∗∗∗ 0.21∗∗∗ 0.08∗∗∗ 0.14∗∗∗ Small DD Ask 0.05∗∗∗ 0.19∗∗ 0.11 0.17 0.04∗ 0.15∗∗∗ 0.12∗∗∗ 0.17∗∗∗

Large HD Bid 0.04∗∗∗ 0.19∗∗ 0.12∗∗∗ 0.20∗∗∗ 0.05∗∗∗ 0.17∗∗∗ 0.09∗∗∗ 0.14∗∗∗ Small HD Bid 0.04 0.19 0.11∗∗∗ 0.16∗∗∗ 0.05∗∗ 0.19 0.10∗∗∗ 0.16∗∗∗ Large HD Ask 0.04∗∗∗ 0.19∗∗∗ 0.11 0.15∗∗∗ 0.05∗∗∗ 0.17∗∗∗ 0.11∗∗∗ 0.18∗∗∗ Small HD Ask 0.04∗∗ 0.19 0.11∗∗∗ 0.18∗∗∗ 0.05 0.18∗∗ 0.10∗∗∗ 0.15∗∗∗ NARROW Spread 27 Narrow spread 0.14 0.07 0.13 0.19 0.13 0.05 0.11 0.18

Large DD Bid 0.15∗∗∗ 0.08∗∗∗ 0.11∗∗∗ 0.18∗∗∗ 0.12∗∗∗ 0.06∗∗ 0.11∗∗∗ 0.19∗∗∗ Small DD Bid 0.12∗∗∗ 0.06∗∗∗ 0.14∗∗∗ 0.21∗∗∗ 0.14∗∗∗ 0.05∗∗∗ 0.10∗∗∗ 0.18∗∗∗ Large DD Ask 0.13∗∗∗ 0.07∗∗∗ 0.13∗∗∗ 0.20 0.14∗∗∗ 0.06∗∗∗ 0.10∗∗∗ 0.17∗∗∗ Small DD Ask 0.15∗∗∗ 0.06∗∗∗ 0.12∗∗∗ 0.19∗∗∗ 0.12∗∗∗ 0.05∗∗∗ 0.12∗∗∗ 0.19∗∗∗

Large HD Bid 0.14 0.06 0.14∗∗∗ 0.21∗∗∗ 0.14∗∗∗ 0.06 0.10 0.15∗∗∗ Small HD Bid 0.14∗∗∗ 0.07∗∗∗ 0.12∗∗∗ 0.18∗∗∗ 0.13∗∗∗ 0.05 0.11∗∗∗ 0.20∗∗∗ Large HD Ask 0.15∗∗∗ 0.07∗ 0.13 0.16∗∗∗ 0.13 0.05∗∗∗ 0.11∗∗∗ 0.20∗∗∗ Small HD Ask 0.13∗∗∗ 0.07 0.13∗∗ 0.20∗∗∗ 0.14∗∗∗ 0.06∗∗∗ 0.10∗∗∗ 0.17∗∗∗

Table 8: Empirical frequencies of hidden order categories conditional on the state of the prevailing order book are reported. Each row is a probability vector adding up to 100% conditional on the order book state. The latter is characterized by the spread size and both displayed and hidden depths available at the best limit on each market side. For each stock, the spread (depth) is defined to be narrow (small) if it is smaller than its daily median. DD (HD) refers to the disclosed (hidden) depth. The unconditional probabilities of each order category are also provided. Statistical comparisons were performed to assess the impact of both displayed and hidden depths. *Significant at the 10% level, **Significant at the 5% level, ***Significant at the 1% level. Empirical frequencies of usual orders given the last usual order Order t Order t-1 1 2 3 4 5 6 7 8 9 10 11 12 1 12 5 17 9 6 11 1 1 7 4 7 20 2 5 12 17 5 7 12 1 2 8 3 11 17 3 4 4 29 7 8 12 1 2 9 3 7 14 4 2 2 12 19 9 15 1 1 7 12 7 13 5 2 3 13 8 15 17 2 2 11 6 8 13 6 2 2 10 7 9 26 2 2 11 7 7 15

7 1 1 6 3 7 20 14 5 19 8 5 11 8 1 2 7 3 12 16 6 11 18 5 7 12 9 1 2 8 3 7 13 4 4 32 7 7 12 10 1 1 6 11 7 13 2 2 14 20 8 15 11 1 3 10 5 9 13 2 3 15 8 14 17 12 2 2 10 6 8 14 2 2 13 7 8 26

Unconditional 2 3 12 7 9 16 2 3 15 7 8 16

Table 9: The empirical frequency of each of the twelve order categories conditional on the previous usual order is given. Each row (column) refers to a given order at time t-1 (t). Each row represents a probability vector adding up to 100%. We got these empirical probabilities after pooling all stocks. Category 1 (7) refers to large buy (sell) orders. Category 2 (8) refers to market buy (sell) orders. Category 3 (9) refers to small buy (sell) orders. Category 4 (10) refers to buy (sell) orders within the spread. Category 5 (11) refers to buy (sell) orders at the best bid (ask). Category 6 (12) refers to buy (sell) orders below the best bid (ask). Unconditional frequencies are also provided.

28 Empirical frequencies of hidden orders given the last hidden order Order t Order t-1 1 2 3 4 5 6 7 8 9 10 11 12 1 9 6 3 8 9 16 1 5 1 4 4 34 2 3 15 3 8 12 19 1 6 1 4 10 18 3 4 7 21 3 15 10 1 4 1 1 7 26 4 2 4 1 23 11 20 1 3 1 14 7 13 5 2 5 2 13 17 23 1 5 1 10 8 13 6 1 4 2 10 9 42 2 3 2 8 6 11

7 1 5 1 6 7 13 7 8 7 9 12 24 8 1 6 1 5 11 17 3 16 4 6 9 21 9 1 3 1 2 5 7 2 7 41 5 12 14 10 2 3 1 15 10 15 1 3 1 17 10 22 11 1 4 1 11 9 13 1 5 3 13 15 24 12 1 3 1 9 7 12 1 3 1 8 8 46

Unconditional 1 4 2 12 10 22 2 4 2 10 8 23

Table 10: The empirical frequency of each of the twelve order categories conditional on the previous hidden order is given. Each row (column) refers to a given order at time t-1 (t). Each row represents a probability vector adding up to 100%. We got these empirical probabilities after pooling all stocks. Category 1 (7) refers to large buy (sell) orders. Category 2 (8) refers to market buy (sell) orders. Category 3 (9) refers to small buy (sell) orders. Category 4 (10) refers to buy (sell) orders within the spread. Category 5 (11) refers to buy (sell) orders at the best bid (ask). Category 6 (12) refers to buy (sell) orders below the best bid (ask). Unconditional frequencies are also provided.

Average proportions of split orders

Category Usual orders Hidden orders Bid side 1 − 1 44 96∗∗∗ 2 − 2 39 56∗∗∗ 3 − 3 39 98∗∗∗ 4 − 4 30 31 5 − 5 34 48∗∗∗ 6 − 6 42 71∗∗∗ Ask side 7 − 7 46 90∗∗∗ 8 − 8 41 66∗∗∗ 9 − 9 41 94∗∗∗ 10 − 10 30 25∗∗ 11 − 11 37 41 12 − 12 42 75∗∗∗

Table 11: For both usual and hidden orders, the global average proportions (expressed in %) of split orders are reported. Categories 1 and 7 refer to ’large orders’, categories 2 and 5 refer to ’market orders’, categories 3 and 9 refer to ’small orders’, categories 4 and 10 refer to ’orders within the spread’, categories 5 and 11 refer to ’orders at the best quote’ and categories 6 and 12 refer to ’orders below the best quote’.

29 Depth patterns at the best limit of the order book 30

Figure 1: Each continuous trading hour was partitioned into 5-minute intervals. Then, for each interval, we computed time-weighted average volumes in value available at the best limit of the order book across all CAC40 stocks and all days. Visible depth refers to disclosed quantities while total depth is measured by both hidden and displayed quantities.