Sunshine Trading:

Liquidity Formation Using Preopening Periods

Magueye Dia

University of Toulouse

and

Sébastien Pouget

Georgia State University

November 2003

We would like to thank Bruno Biais for helpful suggestions. We have benefited from comments by Bruce Lehmman, Yee Cheng Loon, Venky Panchapagesan, Mame Marie Sow, Anand Venkateswaran, and the participants to the December 2002 conference of the NBER market microstructure group in Boston. We are grateful to Isidore Tanoe for providing us with the data. Magueye Dia is at University of Toulouse, and Sébastien Pouget is at the Robinson College of Business, Georgia State University. Part of this research was done while Dia was visiting Oxford University. Corresponding Author: Sébastien Pouget, Department of Finance, J. Mack Robinson College of Business, Georgia State University, 35 Broad Street, Atlanta, GA 30303. E-mail: [email protected]. Phone: (+1) 404 651 28 09. Fax: (+1) 404 651 26 30. Sunshine Trading: Liquidity Formation using Preopening Periods

Abstract

This paper studies liquidity formation in financial markets with costly participation and asymmetric information. We propose a theoretical model in which a preopening period is instrumental in the liquidity formation process. At equilibrium, expected utility maximizing traders use the preopening period to communicate their liquidity needs and (part of) their private information concerning stock valuation. This sunshine trading enhances liquidity and translates into higher gains from trade. To test our theory, we use data from the West-African Bourse. Three trading patterns are empirically documented: i) part of the large orders are placed early during the preopening period and are not cancelled, ii) for most of the stocks, tentative pr ices reveal information long before trading actually occurs, and iii) large volumes are transacted without significant price movements. Consistently with our model, we argue that market participants implement sunshine trading strategies bound to enhance market liquidity. We provide some implications of our findings for global portfolio management and for the design of financial markets.

2

1. Introduction

This paper studies the role of preopening periods in the liquidity formation process.

Many stock markets around the world (e.g. NASDAQ, Paris Bourse, Milan Borsa, Madrid

Borsa, Casablanca Stock Exchange, West -African Bourse among others) allow traders to place non-binding orders before trading actually occurs. These orders result in tentative prices that are being publicly disseminated. Because preopening periods do not give rise to transactions, their economic significance could be questioned. Despite the absence of transactions, the empirical and theoretical literature in market microstructure has underlined the role of preopening periods in the price discovery process. Biais, Hillion, and Spatt (1999) find that indicative prices in the Paris Bourse reflect learning of stocks’ equilibrium valuation.

Cao, Ghysels, and Hatheway (2000) highlight the same phe nomenon during the NASDAQ preopening period. Vives (1995) proposes a model where tentative prices reveal information.

Less attention however has been focused on the potential influence of preopening periods on liquidity formation and welfare.

We address these issues both theoretically and empirically. Our theoretical analysis is based on two premises. First, we consider that liquidity providers have to pay a cost to participate in the market. Second, we consider that there are information asymmetries between traders. In particular, we assume that traders with liquidity needs also possess superior information concerning asset’s valuation. This magnifies the difficulty of providing liquidity to the market. In this context, we show that a preopening period has a dual influence on the trading process. On the one hand, at equilibrium, traders use the preopening period to communicate the occurrence of liquidity shocks that need to be hedged. Liquidity providers only enter the market when such liquidity needs are preannounced. Liquidity (measured by the bid -ask spread) and welfare are enhanced thanks to the savings on the cost of market

3 participation. On the other hand, there exists an equilibrium where informed traders with liquidity needs rationally choose to reveal their information during the preopening period.

Such information improves liquidity and welfare through a reduction of the risk premium required by liquidity providers.

We also propose an empirical investigation of these results using data from the West-

African Bourse. Our focus on this stock exchange is driven by the crucial features underlying our model namely the existence of a preopening period, and the cost of market participation.

The first feature is an institutional characteristic that is implemented in the West-African

Bourse. The last feature is also likely to be prevalent for two reasons. On the one hand, if they were to participate in this market (and thus provide liquidity), the global portfolio managers would have to spend resources (time and research effort) to know about i) the macroeconomic conditions prevailing in West-Africa, and ii) the uncertainty surrounding a particular stock.

This information gathering process is likely to be more costly, in term of time and research effort, in the case of a developing market with relatively poor information availability than in the case of developed markets such as the U.S. or the European stock markets. On the other hand, this direct cost of information is reinforced by the fact that the West-African Bourse is not included in global indexes such as the MSCI World Index or the IFC Global Emerging

Markets Index. To the extent that portfolio managers are evaluated and compensated with respect to these benchmarks, this creates an additional cost of trading in West-Africa related to portfolio managers’ opportunity cost of time and effort. Overall, this discussion suggests that the West-African Bourse represents an ideal venue to try and empirically identify sunshine trading.

Our empirical results can be summarized as follows: i) part of the large orders are placed early during the preopening period and are not cancelled, ii) for most of the stocks, tentative prices reveal information long before trading actually occurs, and iii) large volumes

4 are transacted without significant price movements. Consistently with our model, we argue that market participants implement sunshine trading strategies bound to enhance market liquidity and welfare.

Our theoretical analysis is in the spirit of Laffont and Maskin (1990) since we model the trading process as a signaling game. Our approach differs from theirs in two dimensions.

First, in lieu of a risk-neutral insider, we consider a risk-averse insider who has two trading motivations: informed speculation and hedging. This is in line with Bhattacharya and Spiegel

(1991). Second, we study the role of alternative market mechanisms, namely the presence or not of a preopening period, and their welfare implications. Our study is also related to the work of Vives (1995), and Medrano and Vives (2001). These papers show that tentative prices can reveal information if the orders placed during the preopening period can be executed with a non-null probability. We complement these findings in three ways: i) we show that, even when agents can place non-binding orders, preopening periods can generate useful pricing information, ii) we address the issue of liquidity formation, and iii) we show that introducing a preopening period is Pareto optimal. Our result that insiders might have an incentive to reveal their private information during a round of preplay non-binding communication echoes the findings of Spatt and Srivastava (1991). They show that truthful preplay communication in initial public offerings can be part of an optimal auction mechanism. However, in their model, traders’ incentives to disclose private information are different: at equilibrium, announcing true valuations does not affect prices but it maximizes traders’ probability to receive the asset (in the spirit of a second pr ice auction).

This paper is related to the empirical literature on liquidity and price formation. Biais,

Hillion, and Spatt (1995) study the formation process of the order book in the Paris Bourse.

Lehmann and Modest (1994) investigate liquidity provision in the Tokyo Stock Exchange. De

Jong, Nijman, and Roell (1995), Chan and Lakonishok (1997), and Bessembinder (2002)

5 focus on the measurement of transaction costs in various market mechanisms. Biais, Hillion, and Spatt (1999), and Cao, Ghysels, and Hatheway (2000) study price formation during preopening periods in stock markets. The impact of communication through non-binding quotes on price discovery has also been investigated by Aggarwal and Conroy (2000) , for initial public offerings, and by Peiers (1997), for foreign exchange markets. Price discovery during trading periods has been the focus of numerous studies including Stoll and Whaley

(1990), Amihud and Mendelson (1991), and Madhavan and Panchapagesan (2000). Our work complements these papers by underlining the role of preopening periods in the liquidity formation process, and by showing how the close relationship between liquidity and price formation is magnified during preopening periods.

This paper is organized as follows. Section 2 presents our theoretical analysis. Section

3 describes the market organization and the data we use to evaluate our model. Liquidity and price formation are documented in Section 4 and 5, respectively. Section 6 concludes. The proof of the results is in the Appendix.

2. Theoretical analysis

2.1. Model

Consider a dynamic asset market with infinitely repeated interactions. Periods are indexed by t, where t Î [0,1,2,...,+¥[. There is one risky asset whose value V is equal to u with probability p and to d with probability 1-p. Without loss of generality, we shall assume that u=1, d=-1, and p =½. There are two investors: one insider (referred to as I), and one outsider

(referred to as O). Each investor accesses the marketplace through brokers. We do not model the relationship between investors and brokers in a principal-agent framework but rather

6 assume that their interests are perfectly aligned. Consequently, we do not explicitly model brokers’ behavior. 1

Investors are assumed to be risk averse. For period t, the insider’s utility function is

I I I I U (Wt ) = Wt if Wt , the wealth of the insider at the end of period t, is negative, and

I I I O O O O U (Wt ) = aWt otherwise. The outsider’s utility function is U (Wt ) = Wt if Wt , the wealth

O O O of the outsider at the end of period t, is negative, and U (Wt ) = bWt otherwise. We assume that a is smaller b, i.e. the insider is assumed to be more risk averse than the outsider. 2 We assume that wealth is fully consumed at the end of each period. 3 Traders have inter-temporal expected utilities given by:

t=+¥ Z Z t Z Z V (Wt ) = å{d E[U (Wt )]} t =0

The index Z stands for O (outsider) or I (insider). d is the rate at which future expected utility is discounted, with 0 < d £ 1.

The outsider participates in the market only if she pays a cost c. She has no private information and her reservation utility is zero. In line with Bhattacharya and Spiegel (1991), the insider has two trading motivations: informed speculation and hedging. He receives two independent private signals S1 and S2 that indicates the final value of the asset with probability p, with ½0.

With probability 1-l, he does not receive any asset, i.e. E=0. Since he is risk-averse, the

1 As it will become clear shortly, the only role of brokers in our model, besides transmitting investors’ orders to the market, is to communicate the occurrence of sunshine trading to outside investors. 2 These preferences have been chosen to simplify calculations. An important aspect of these utility functions is that, given that u>0>d, they create gains from trade when the insider sells his endowment of risky asset to the outsider.

7 insider will want to trade to hedge his position. For simplicity, we shall consider only the equilibria where the insider, when he receives a positive endowment shock, wants to fully hedge himself, i.e. to sell all his endowment. Insider’s participation in the market is costless.

The structure of the uncertainty is constant across periods and is represented as a tree diagram in Figure 1. After trading occurred, as in Benveniste, Marcus, and Wilhelm (1992), there is a probability g that the outsider learns the information held by the insider. 4 We consider that the outsider cannot observe the realization of each signal individually. She can only observe one of the following three joint realizations: HH, LL, and HL. At the end of period t, the realization of V becomes public knowledge.

Transactions occur as follows. First, the insider submits a limit order denoted (q,P) to trade a quantity q at a limit price P. Then, if she entered, the outsider submits a market order m to cle ar the market after observing (q,P).5 We will analyze two distinct market organizations: with or without a preopening period. During the preopening period, the insider submits a limit order (qA,PA) that is not binding. He can revise or cancel his order before trading actually occurs. The timeline of the trading game is depicted in Figure 2.

When there is no preopening period, an insider strategy is a couple of mappings (q,P):

{(S1, S 2, E)} ® {Â,Â} that prescribes a limit order (q,P)(S1,S2,E) on the basis of his private information. An outsider strategy is an action d Î(0,1) and a mapping m: {Â,Â} ® Â .

Action d gives outsider’s entry decision (d=1 if she enters, and d=0 if she does not enter).

Mapping m prescribes the number of assets she wants to trade conditional on the insider’s limit order. We use the convention that positive numbers for q and m represent purchases. The conditional beliefs of the outsider are represented by a mapping that associates to each limit

3 This is equivalent to assuming that there is a unique consumption good that is used as numeraire and that is perishable. 4 Alternatively, this probability can be interpreted as the result of a statistical inference to detect whether traders are profiting from superior information. A explicit modeling of this detection effort is found in Desgranges and Foucault (2002).

8 order (q,P) a probability function g[. (q, P)] on {u, d}, where g[V = v (q, P)] is the probability that the outsider attaches to V=v given a limit orders (q,P).

When there is a preopening period, an insider strategy is a pair of mappings, (qA,PA):

{(S1,S2,E)} ® {Â,Â} and (q,P): {(S1,S2,E)} ® {Â,Â}. Mappings (qA,PA) prescribes a non- binding limit order (qA,PA)(S1,E) and mappings (q,P) a limit order (q,P)(S1,S2,E), on the basis of his private information. An outsider strategy is a pair of mappings, d: {Â, Â} ® (0,1) and m: {Â,Â} ® Â . Mapping d prescribes an entry decision (d=1 stands for entry) conditional on the insider’s non-binding limit order. Mapping m prescribes the number of assets she wants to trade conditional on the insider’s limit order. We use the convention that positive numbers for q and m represent purchases. The conditional beliefs of the outsider are represented by a mapping that associates to each collection of limit orders ((qA,PA),(q,P)) a

probability function g[. (qA, PA,q, P)] on {u, d}, where g[V = v (qA, PA,q, P)] is the probability that the outsider attaches to V=v given limit orders (qA,PA) and (q,P).

2.2. Equilibrium analysis

Consider that there is no preopening period before trading occurs. Proposition 1 establishes the existence of multiple equilibria. Multiplicity of equilibria is a common feature of signaling games. Following Laffont and Maskin (1990), we shall suppose that the insider can influence outsider’s beliefs. 6 It is then intuitive to focus on the equilibrium that is favored by the insider. In addition, since her participation constraint is always saturated, the outsider has no preferred equilibrium. Pareto optimality therefore also favors the best equilibrium of the insider. There is thus no conflict among traders regarding the equilibrium to be chosen.

5 Since the outsider observes (q,P) before submitting her order, we could also consider that she submits a limit order without affect the results. 6 This view is reinforced by the fact that insider’s preannouncement during the preopening period (when it exists) constitutes a plausible way to coordinate beliefs on the insider’s favorite equilibrium.

9 A perfect Bayesian equilibrium in our setting is a pair of strategy ((q*,P* ),( d*,m* )) and a family of conditional beliefs g[. .] such that: i) For all (q, P)Î{Â, Â}: g[. (q, P)] is the conditional probability of V obtained by updating the prior (p,1-p), using (q,P), in a Bayesian fashion.

O O ii) For all (q*, P *) and (d*, m*): E[U (Wt *)]³ 0 iii) For all (q*, P *), (q', P')Î{Â,Â} and (d*, m*):

I I I I E[U (Wt *) S1, S 2, E]³ E[U (Wt ') S1, S 2, E ]

Condition i) indicates that the outsider has rational expectations, and Condition ii) is her participation constraint. Condition iii) represents the incentive constraint of the insider.

PROPOSITION 1 (without preopening period)

There exist perfect Bayesian equilibria where q*= -E, d*=1 as long as the outsider has not detected an insider’s deviation and d*=0 otherwise, m*= Q and where i) P*= P0 irrespective of

S1 and S2 (pooling equilibrium), ii) P*=P+ if S1=S2=H, and P*=P- otherwise (semiseparating equilibrium), iii) P*= P’ if S1=S2=L, and P *= P” otherwise (semiseparating equilibrium), or iv) P *= P1 if S1=S2= H, P*=P2 if S1¹ S2, and P *= P3 if S1=S2=L. The explicit values of

+ - P0, P , P , P’, P”, P1, P2, and P3 are provided in the Appendix.

To show the existence of these equilibria, we check in the appendix that there exists a non- empty set of parameter for which the three conditions stated above holds. Notice that the equilibrium entry decision (d) is a trigger strategy. In our model, this trigger strategy allows the existence of other equilibria than the pooling equilibrium. If the insider deviates by setting a misleading price (for example, P+ instead of P-), he will be caught by the outsider with a non-null probability. This is because g is strictly greater than 0. In the event where the outsider observes that the insider mispriced the asset, she does not enter the market anymore.

The risk-averse insider thus faces a tradeoff between an immediate profit from his information

10 and a future disutility from receiving endowment shocks without being able to hedge them.

For some parameters’ values, the tradeoff is such that the insider is better off not deviating.

These equilibria have an interesting common property. The equilibrium pricing equals the expected value of the asset conditional on the information revealed at equilibrium minus a spread. Consider, for example, the pooling equilibrium price P0 (the same intuition carries forward to the other equilibrium prices). The Appendix shows that:

1 - b c é 2(1 - l )ù P0 = E[V]- Var[V] - ê1+ ú (1) 1 + b Q ë (1+ b)l û

At the pooling equilibrium, since the price does not depend on the signal of the insider, outsider’s beliefs are not affected by the trading process. The expected value of the asset for the outsider is thus equal to the unconditional expected value E[V], and the spread is thus

1 - b c é 2(1 - l )ù equal to s0 = Var[V] + ê1 + ú . In our model, the spread compensates the 1 + b Q (1 + b)l 14243 14ë 42443û a b outsider for her liquidity provision, and has a dual origin.7 First, because the outsider is risk- averse, she will be willing to provide liquidity only if she earns a risk premium. This effect is captured by a, and is in the spirit of Stoll (1978). Second, she will be willing to participate to the transactions only if she recovers the cost of market participation. This effect is captured by b. It is in line with Grossman and Miller (1988) and Admati and Pfleiderer (1991).

Two remarks will have implications for the role of the preopening period.

REMARK 1. In the semiseparating and separating equilibria, the outsider learns some information from the price and updates her beliefs accordingly. In this case, the pricing equations are similar to equation (1) except that they include conditional expectations. This implies that, across the various equilibria (pooling, semiseparating or separating), a varies

7 In our model, the outsider does not earn rents from imperfect competition because we consider that the insider is setting the price. If we were considering an adverse selection model where the outsider would quote bid and ask prices, the spread would reflect her monopoly power in addition to the two effects that we are describing.

11 and b remains constant. Thus, the spread varies only to the extent that the residual uncertainty faced by the outsider varies.

REMARK 2. When there is no preopening period, there is no semiseparating equilibrium where one of the two signals is revealed. The intuition is the following. Consider an equilibrium conjecture where the insider sets a semiseparating price that reveals S1 by choosing a higher price when S1=H then when S1=L. Let these prices be denoted by P and P, respectively, where P >P. This conjecture is not an equilibrium because, when S1=L and

S2=H, the insider has an incentive to deviate and to quote P instead of P. Since this deviation cannot be detected by the outsider, the trigger strategy that sustains the semiseparating and separating equilibria of Proposition 1 is useless. Thus, there is no equilibrium where one of the two signals is revealed.

Consider now that there is a preopening period before trading occurs. Proposition 2 establishes the existence of multiple equilibria. A perfect Bayesian equilibrium in this setting

is a pair of strate gy ((qA*,PA*,q*,P *), (d*,m*))and a family of conditional beliefs g[. .] such that:

i) For all (qA*,PA*,q*,P*)Î{Â,Â,Â,Â}: g[. (qA*,PA*,q*,P*)] is the conditional

probability of V obtained by updating the prior (p,1-p), using (qA*, PA*, q*, P *), in a

Bayesian fashion.

O O ii) For all (qA*, PA*, q*, P *) and (d*, m *) : E[U (Wt *)]³ 0

iii) For all (qA*,PA*,q*, P*), (qA', PA',q', P')Î{Â,Â,Â,Â} and (d*, m*) :

I I I I E[U (Wt *) S1, S2, E]³ E[U (Wt ') S1, S 2, E ]

The Conditions i), ii), and iii) have the same interpretation as earlier. In principle, one should check another condition stipulating that the strategy of the insider needs also to be optimal

12 conditional on signal S1 only. In our model, it is straightforward to show that this condition is always satisfied when Condition iii) holds.

PROPOSITION 2 (with preopening period)

There exist perfect Bayesian equilibria where qA*=q*= -E, d*=1 if qA ¹ 0 and d*=0 if qA = 0 as long as the outsider has not detected an insider’s deviation, and d*=0 otherwise, m*= Q, and

++ where i) P*=P00 irrespective of S1 and S2 (pooling equilibrium), ii) P*=P if S1=S2= H, and

P*=P-- otherwise (semiseparating equilibrium), iii) P*=P”’ if S1=S2= L, and P*=P”” otherwise (semiseparating equilibrium), iv) P*= P11 if S1=S2= H, P*=P22 if S1¹ S2, and

P*=P33 if S1=S2=L, or v) PA*= P*= P if S1=H , and PA*= P*=P otherwise if S1=L

++ -- (semiseparating equilibrium). The explicit values of P00 , P , P , P”’, P””, P11, P22, P33, P , and P are provided in the Appendix. 8

When there is a preopening period, the equilibrium prices have a form that is similar to the case where there is no preopening period. They equal the expected value of the asset conditional on the information revealed at equilibrium minus a spread. Consider again the pooling equilibrium price P00 (the same intuition carries forward to the other equilibrium prices). The Appendix shows that:

1 - b c P0 = E[V]- Var[V]- (2) 1+4b 243 {Q a ' b'

In this case, the spread equals a '+b '. It has again two components that compensate the outsider for bearing risk (a ') and for incurring the cost of market participation (b '). We remark that a'= a , i.e. the risk premium is the same as when there is no preopening period.

This property is true for the other equilibria as well. This is due to the fact that, whether or not there is a preopening period, the information revealed at equilibrium is the same for a given nature of equilibrium (pooling, semiseparating, or separating). Using the explicit pricing

13 formulas provided in the Appendix, it is straightforward to show that the compensation for the cost of market participation ( b ') is constant across equilibria.

Proposition 2 describes equilibria in which the outsider enters the market only if an

order is preannounced during the preopening period, i.e. only if qA ¹ 0 . Except from this, the equilibria are stated in Proposition 2 are essentially the same as those of Proposition 1. 9 There is however one important difference concerning the existence of a semiseparating equilibrium where signal S1 is revealed. Its existence is allowed by the fact that the insider quotes a price during the preopening period at a time when he does not know S2 yet. If he deviates and quotes P instead of P, the outsider will thus detect his deviation with a positive probability.

The trigger strategy described earlier then ensures that, for some parameters’ values, deviating is not profitable.

2.3. Role of the preopening period

In our model, the preopening period can enhance liquidity and welfare through two distinct channels that are related to the dual nature of the spread: A preopening period can generate savings on the cost of market participation, and can reduce the required risk premium.

Corollary 1 compares the component of the spread covering the cost of market participation with and without a preopening period.

COROLLARY 1 (savings on the cost of market participation) b '< b .

The proof of corollary 1 is straightforward and is thus omitted.

8 When Proposition 2 does not specify a limit price PA*, the insider submits a market order during the preopening period. 9 In addition to the ones stated in proposition 2, the equilibria of the financial market without preopening period continue to be equilibria when there is a preopening period. Indeed, ignoring the “cheap talk” from the preopening period and playing strategies equivalent to those in the game without preopening period is an

14 Corollary 1 shows that the amount that the insider has to leave to the outsider to cover the cost of her market participation is lower when there is a preopening period. Remark 1 indicates that this result holds independently of the equilibrium considered. At equilibrium, the insider engages in sunshine trading: he participates in the preopening period and preannounces his willingness to trade only if he receives an endowment shock. As a response to this, the outsider enters the market only when there is a preannouncement. In line with

Admati and Pfleiderer (1991), sunshine trading coordinates the demand and the supply of liquidity: without a preopening period, the outsider enters the market at each period whereas, with a preopening period, she enters only if there is a liquidity shock (which occurs with probability l). If one focuses on a particular equilibrium (pooling, semiseparating, or separating), it is straightforward to show that this phenomena translates into a reduction of the spread. This reduction in the spread has two consequences. On the one hand, it translates into an increase in the welfare of the insider. S ince the outsider’s utility is constant across equilibria, the introduction of a preopening period generates a Pareto improvement. On the other, it relaxes the incentive constraints. The domain of existence of an equilibrium is thus larger when there is a preopening period.

Corollary 2 establishes that, for some parameter values, the semiseparating equilibrium where S1 is revealed during the preopening period is the unique equilibrium. All the other equilibria do not exist because all the cons traints cannot be simultaneously satisfied.

COROLLARY 2 (information revelation during the preopening period)

There is a non-empty set of parameters for which the semiseparating equilibrium where S1 is the unique equilibrium.

The intuition of Corollary 2 is related to the fact that the risk premium required by the outsider is reduced when the insider reveals only S1. As explained earlier, this relaxes the

equilibrium. This is a common feature of games with non-binding pre-play communication (see, for example, Spatt and Srivastava, 1991).

15 insider’s incentive constraint. At equilibrium, the insider submits a non-binding order during the preopening period with a limit price that reveals his information. This highlights an additional feature of sunshine trading, namely the revelation of private information. Corollary

2 implies that, in some circumstances, the only way to allow risk sharing among investors is to introduce a preopening period. Traders will implement sunshine trading to economize on the cost of market participation and to reduce the required risk premium.

Corollaries 1 and 2 are at the heart of our empirical investigations. Section 4 investigates the liquidity formation process that leads to Corollary 1 by studying the order placement strategies. Section 5 investigates the price formation process to evaluate if the information revelation process conjectured in Corollary 2 is present in the field.

3. Description of the Market and of the Data

3.1. Structure of the West-African Bourse

Based in Abidjan, the West-African Bourse was launched in September 1998. 10 It was created after the Ivory Coast Bourse. It can accommodate listing of companies originating from the various countries of the West-African Economic and Monetary Union (Union

Economique et Monétaire Ouest-Africaine). In 2000, 40 stocks were traded on the market. 39 were from Ivory Coast and 1 from Senegal. The West-African Bourse is an electronic order market. Orders can be placed by sixteen broker-dealers via computers located at the Bourse offices or at the brokerage houses themselves. Only these sixteen agents can place orders. 11

The West-African Bourse operates three times a week on Monday, Wednesday and Friday. 12

It is organized as a preopening period followed by a call market. During the preopening period, from 8:30 am to 10:30 am, broker-dealers can place limit orders that can be freely cancelled or revised. Each time an order is entered in the system, an indicative market

10 The West-African Bourse is also called the Bourse Régionale des Valeurs Mobilières or BRVM. 11 In 2002, a new broker-dealer has been authorized by the Bourse.

16 clearing price is computed and announced to the broker-dealers. Furthermore, these broker- dealers can observe the entire order book, i.e. the characteristics of the orders, the identity of the broker-dealer who placed the orders, and whether or not they trade for their own account.

At 10:30, the orders present in the book are used to build the aggregate supply and demand curves. The transaction price is the price that maximizes trading volume. 13 Buying (selling) orders with a limit price greater (smaller) than or equal to the market clearing price are executed. Rationing occurs when there is an order imbalance at the market clearing price.

Orders are executed proportionally to their proposed quantity. There is no time priority. If supply and demand do not cross, another trading session is organized on the same day which is similar to the previous one. A preopening period occurs from 11:00 to 11:30 (the orders present in the book at 10:30 are still valid for this new session). The orders are potentially filled at 11:30 using the same procedure as before.

3.2. The Data

Our data set includes all the orders submitted to the market from January 3rd, 2000 to

December 13th, 2000. This corresponds to 141 trading sessions. We have all the characteristics of the orders including their time of placement, their limit price, the quantity proposed, and the identity of the broker-dealers who placed the orders. However, we do not know whether broker -dealers act as principals or as agents. For each session, we computed the indicative prices, the market clearing price, and the quantities allocated to each broker- dealer.

Among the 40 stocks listed on the Bourse, we focus on the stocks that were included in the index of the Bourse. The index included 10 stocks at the end of 2000. Among these 10

12 Since the end of 2001, the Bourse is open daily. 13 If there are several volume maximizing prices, other criteria are applied until only one price remains. These criteria consist in choosing the price that i) minimizes excess demand, and ii) minimizes variation between

17 stocks, only three remained in the index throughout the year. We complemented our data set by choosing five additional stocks that remained in the index at least 2 quarters during the year 2000.

3.3. Summary Statistics

Market Activity - For each stock, Table 1 reports several descriptive statistics for the year

2000 including the average and standard deviation of the volume per trading session, the average number of orders per trading sessions, and the turnover defined as the total number of shares traded over the number of outstanding shares.

The volume per trading session, and the number of orders submitted to the market are on average quite low. These phenomena are reflected in a very low turnover. The market thus appears rather inactive. This is confirmed by the large number of trading sessions without trades. Interestingly, despite the apparent low liquidity, the transaction volume is quite volatile. This suggests that, from time to time, the market experiences shocks on the demand and/or on the supply of shares. This high trading volume volatility despite the low average volume suggests that the West-African Bourse is punctually able to accommodate large transactions. The extent of orders cancellations and modifications appears limited: overall, only 2% of the orders are cancelled, and only 7% are modified.

Broker-dealers’ Activity - Table 1 indicates that the number of broker -dealers active on the market is low. Between two and seven broker-dealers (out of sixteen) intervene on the market.

This means that all the broker -dealers are not providing liquidity at every trading session.

Following Ellis, Michaely, and O’Hara (2000), to assess the competitiveness of the Bourse, we computed for each stock the average Herfindahl index across the sessions with a non-null trading volume. For a given trading session, the index is equal to the sum of the squares of the

successive prices. If several prices still satisfy these constraints, the transaction price is the highest of these prices.

18 market share of each broker-dealer. The market share of a broker-dealer is computed as the ratio of the number of shares traded by the broker-dealer over the transaction volume. An index of one corresponds to a monopolistic situation while an index of 1/n, n being the number of active broker-dealers, corresponds to a situation where every broker-dealer handles the same volume. Table 1 shows that the Bourse is an oligopoly market. This result echoes the findings of Ellis, Michaely, and O’Hara (2000) who draw similar conclusions for the

NASDAQ market, and in particular for low volume stocks. Table 2 complements these results. It presents the broker -dealers’ activity in terms of order placement and shares traded averaged across stocks and trading sessions. Table 2 shows that 8 broker-dealers account for

99% of the transaction volume and that the 4 largest broker-dealers alone account for 89% of this volume. The Bourse thus appears as a concentrated trading venue where a few agents are making the market.

Transaction Costs - Table 3 presents a measure of transaction costs for the various stocks under study. This measure was constructed following Kehr, Krahnen, and Theissen (1998).

For each trading session, we added one buying market order in the order book, and computed the new transaction price (Pb). After canceling this buying order, we added one selling market order, and computed another transaction price (Ps). Transaction costs were measured by the

P - P following formula: b s where P* was the actual transaction price. We computed this P* measure by adding orders of various sizes: one, ten, a hundred, two hundred, five hundred, and one thousand. For each stock, we computed the average transaction cost across trading sessions where the additional buy or sell orders could find a counterpart. The number of trading sessions in which the or der book was not thick enough to allow execution of the additional orders is also provided. These trading sessions may be viewed as infinitely illiquid.

Table 3 suggests that average transaction costs are high on the West African Bourse. They represent from 2.6% to 16.4% of the transaction price for a one hundred-share order with an

19 average equal to 6.8% for the 8 stocks we consider. Compared to the findings of Kehr,

Krahnen, and Theissen (1998) concerning the opening call in Frankfurt, these transaction cost appear rather large. Moreover, there is a lot of trading sessions, from 26 up to 130 sessions depending on the stock considered, in which it was not even possible to add one-share orders and still find counterparts. This might again be a sign of extreme ly poor liquidity on the

Bourse. However, such a low liquidity is in some sense at odds with the fact that high volumes are observed on particular days. In fact, we shall argue that this measure consistently overestimates transaction cost since it only considers submitted orders and not latent orders.

In the context of an emerging market, the bias can be important because of the cost associated with market participation. This is consistent with the model presented in Section 2.

4. Liquidity formation

This section studies the liquidity formation process in the West-African Bourse. The summary statistics presented above suggest that the trading activity is on average quite low and volatile. The volatility of the returns is also low. To complement these points , Figure 3 shows the number of shares traded on the market along with the transaction price over the 141 trading days in our sample. Panels A trough H correspond to the 8 stocks under study sorted alphabetically. For all the stocks, the trading volume appe ars highly volatile while the prices are surprisingly stable. These features indicate that the market is punctually able to accommodate huge transactions without major price adjustments.

Building on these graphical impressions, we perform the following regressions. For each stock, we regress the absolute returns from the last trading sessions (a measure of the price volatility) onto the contemporaneous trading volume. The estimated equation is:

Pt - Pt -1 = a + b ´Qt + et Pt-1

20

t represents the time expressed in terms of trading sessions with a non-null trading volume. Pt

is the transaction price in CFA francs, and Qt is the trading volume in shares at time t. The results are in Table 4.

For the 8 stocks, the coefficient b appears not significantly different from zero.

Further, the regression R²s are extremely low. For the 8 stocks, we cannot accept the hypothesis that trading volume has an impact on prices, and in particular that high volumes translate into prices destabilization. This may appear counterintuitive as one would expect a thin market to generate high execution costs. This is however consistent with our theoretical model where liquidity flows to the market only when it is needed thanks to sunshine trading going on during the preopening period. Our subsequent empirical investigations aim at capturing the extent to which traders implement sunshine trading on the West-African Bourse.

Applied to liquidity formation on the West-African Bourse, our model has seve ral empirical implications. First, to preannounce their liquidity needs, investors should place orders early during the preopening period. In particular, to the extent that large liquidity needs primarily require preannouncement, large orders should be obs erved early during the preopening. Then, in order to constitute credible announcements, these orders should not be cancelled before the call. Finally, if sunshine trading is successful on the Bourse, a significant part of the orders placed early should be eventually executed. Tables 5 and 6 address these issues. 14 To construct these tables, we classify the orders according to two dimensions: their size and their time of placement during the preopening period. Each dimension is divided in four quartiles. This creates a 16-cell table. The upper-left cell includes the orders pertaining to the fourth quartile in terms of size, and to the first quartile in terms of placement time. This

14 We have not analyzed order cancellations and modifications since only a fairly small fraction (overall 9%) of the orders is affected by such operations (see the summary statistics). We rather study the order book after cancellations and modifications occurred.

21 cell thus includes the (relatively) large orders that are placed (relatively) early during the preopening period. Table 5 presents the average proportion of orders of various sizes placed during the four intervals of the preopening period.15 The first quartile of placement time is on average 9:16 am. The second quartile of placement time is on average 9:39 am. The third quartile of placement time is on average 10:07 am. The first quartile of order size is on average 9 shares. The second quartile of order size is on average 32 shares. The third quartile of order size is on average 92 shares. Since sunshine trading is more likely to occur when large quantities have to be traded, our analysis will focus on large orders, i.e. orders pertaining to the 4th and 3rd size quartiles.

From Table 5, we can compute the proportion of large orders placed in the first part of the preopening period (before the median placement time). These proportions are 50% and

56% for the 4th and 3rd size quartiles respectively. This means that large orders are quite often placed early during the preopening period. T o verify that such large orders do not only reflect market manipulation, Table 6 reports the proportion of orders executed in each category. It indicates for each order size and each placement time the proportion of orders that have been

(partially) filled at the time of the call. From Table 6, we observe that 28% of the large orders placed early (4th and 3rd size quartiles, and 1st and 2nd time quartiles) are on average executed.

This indicates that a substantial part of these orders is “in the market”. Figure 4 illustrates these findings. It shows that large orders are uniformly distributed over time and that a substantial part of the orders placed in the first part of the preopening period end up executed.

These results may appear surprising if one believes that traders have an incentive to refrain from placing orders as long as these orders cannot be executed. Indeed, insiders may be willing to conceal their information as long as possible. Uninformed traders may be willing to wait to gather as much infor mation as possible. On the contrary, our theoretical analysis

15 Columns and rows do not always add up to 25% of the total number of orders. This happens when several observations fall on the limit between two quartiles. In this case, they were classified in the lower quartile.

22 states that traders may have an interest to preannounce their liquidity needs in order to attract potential liquidity providers. This is consistent with our empirical results. These results complement the empirical findings of Biais, Hillion and Spatt (1999) concerning the Paris

Bourse. Note that, in the West-African Bourse, an intense activity occurs well before the time of the call. On average, the median placement time is 9:39 am meaning that half of the orders are already placed more than 50 minutes before transactions occur. In contrast, the major part of the order placement in the Paris Bourse occurs during the last 30 minutes of the preopening period.

As a robustness check and to give an id ea of the number of shares attached to the large orders we focus on, Tables 7 and 8 reproduce the analysis displayed in Tables 5 and 7 respectively. 16 It appears that the large orders (4th and 3rd size quartiles) represent 97% of the quantities that are proposed on the market. These orders are thus of high economic importance in the context of the West -African Bourse. From Table 7, we obtain that 38% and 57% (for the 4th and 3rd size quartiles respectively) of the total quantity proposed via large orders are offered in the first part of the preopening period (before the median placement time).

Furthermore, Table 8 indicates that on average 28% of the quantity proposed via large orders placed early (4th and 3rd size quartiles, and 1st and 2nd time quartiles) is eventually exchanged at the time of the call. These results confirm the previous results obtained with orders. They indicate that when broker-dealers want to exchange large quantities of shares, they place large orders early during the preopening period, orders that are often executed during the call. At the beginning of this section, we showed that large traded quantities seem not to incur high execution costs. Our interpretation is that broker -dealers engage in sunshine trading to attract potential liquidity providers. The very low average trading volume in the West-African

Bourse suggests that, without sunshine trading, it would be very difficult to trade such large quantities of shares.

23 Along with Admati and Pfleiderer (1991), our model suggests that, for the sunshine trading to be effective, the preannouncement should be credible in the sense that agents engaging in sunshine trading should eventually trade the quantities they preannounced. The fairly low number of order cancellations or modifications indicates that offers made during the preopening period can indeed be considered as firm.

5. Price Formation

This section studies the price formation process in the West-African Bourse. When they place orders, broker -dealers have to post limit prices.17 Ove r the course of the preopening period, these orders are crossed and their limit prices translate into indicative prices. These indicative prices are publicly available. If traders engage in sunshine trading, we expect indicative prices during the preopenin g period to be related to call prices. It is clear that toward the end of the preopening period, tentative prices converge toward the call price: the call price per construction equals the last indicative price. However, our model suggests that, when trade rs implement sunshine trading, indicative prices computed early during the preopening period should also be related to the actual call price. Admati and Pfleiderer (1991) state that agents have to trade the quantities they preannounced. Extending this argument, our theoretical analysis shows that, when implementing sunshine trading with limit orders, agents should choose to preannounce prices at which they stand ready to trade.18 This implies a link between the early tentative prices and the transaction price.

To study this issue, we compute the average indicative price before and after the median placement time. We then regress the return from the previous trading session to the call onto the return from the previous trading session to the preopening period. For each stock, we use OLS regressions to estimate the following equation:

16 Table 8 does not take into account potential rationing. 17 Market orders are prohibited on the Bourse.

24 1 Pt - Pt -1 1 1 IPt - Pt-1 1 = A + B ´ + Et Pt-1 Pt -1

1 IPt represents the average indicative price during the first part of the preopening period. The results are in Table 9.

Indicative prices computed and announced during the first part of the preopening period are indeed related to the call price for 7 out of 8 stocks. This means that, by looking at early indicative prices, broker -dealers can have a pretty good idea of the price that will prevail on the market. This is consistent with our model where the limit price quoted by the insider during the preopening period equals the price he quotes at the trading stage.

Given that no transaction occurs during the preopening period, the informational content of indicative prices in terms of fundamental valuation could be questioned. In the context of sunshine trading, this issue becomes crucial since preannouncers are big participants and may try to manipulate market prices. On the other hand, our model shows that information revelation during the preopening period might be beneficial to the traders since it relaxes the participation constraint of the outsider. In fact, our model predicts that information revelation will take place during the preopening period at the semiseparating equilibrium where the insider reveals one of his signals. Theoretically, the informational content of the preopening period depends on the value of the parameters. It is thus an empirical question to know whether or not tentative prices reflect any information.

To address this issue, we follow Biais, Hillion, and Spatt (1999) and study whether the return between the previous trading session and the next trading session can be predicted by the return between the previous t rading session and the preopening period. For each stock, we use

OLS regressions to estimate the following equation:

1 Pt+1 - Pt-1 1 1 IPt - Pt-1 1 = a + b ´ + et Pt-1 Pt-1

18 This is reflected in Proposition 2 by the requirement that, at equilibrium, PA*=P*.

25 To have a measure of the total information that could have been revealed during the

preopening period, we also ran these regressions with the call price Pt instead of the mean

1 early indicative price IPt . The estimated equation was:

Pt +1 - Pt -1 Pt - Pt -1 = a + b ´ + et Pt -1 Pt -1

The results are in Tables 10 and 11. Table 10 indicates that, for some stocks, early indicative prices incorporate information. This is supported by the fact that b 1 is statistically significant

5 times out of 8 at the 10% error level (4 times out of 8 at the 5% error level). Pooling data from Tables 10 and 11, the amount of information revealed in the first part of the preopening period can be measure by the ratio between the R² of the regression using the average indicative price during the first part of the preopening period and the R² of the regression using the call price. Across the 8 stock, 44% of the information is on average revealed during the first part of the preopening period, i.e. long before trading takes place. In the context of our model, these results suggest that the market is in a semiseparating equilibrium where insiders reveal part of their information during the preopening period.

6. Conclusion

This paper studies liquidity formation in financial markets with costly participation and asymmetric information. We propose a theoretical model in which a preopening period is instrumental in the liquidity formation process. At equilibrium, expected utility maximizing traders use the preopening period to communicate their liquidity needs and (part of) their private information concerning st ock valuation. This sunshine trading enhances liquidity and translates into higher gains from trade. To evaluate our theory, we use data from the West-

African Bourse. Our empirical results can be summarized as follows: i) part of the large orders are place d early during the preopening period and are not cancelled, ii) for some

26 stocks, tentative prices reveal information long before trading actually occurs, and iii) large volumes are transacted without significant price movements. Consistently with our model, we argue that market participants implement sunshine trading strategies bound to enhance market liquidity.

This paper has implications for global portfolio management and for the design of financial markets. It suggests that the liquidity on the West Afr ican Bourse is higher than what is indicated by the regular state of the order book. Indeed the practice of sunshine trading appears to enable traders with high liquidity needs to attract liquidity providers. There is a latent liquidity that is not reflected in the order book because of the cost of market participation, and that is realized only when traders engage in sunshine trading. This paper also shows that the preopening period may play an important informational role and enhance welfare. Market organizers may thus have an interest in providing traders with pre-trade communication platforms such as preopening periods as a way mean to disseminate information regarding both liquidity needs and asset valuation.

Appendix

Proof of Proposition 1 Consider first the pooling equilibrium conjecture where, for any period t:

· The insider submits the limit order (q*,P* ) where q* =-E and P*=P0 irrespective of S1 and S2; · The outsider always enters the market (d*=1) and submits a market order m* =Q · For rational expectations, outsider’s beliefs are g[u (q*,P *)] =p , g[u (q, P)]= 0 , and g[d (q,P)] =1, for any (q, P) ¹ (q*,P *). The last two equalities specify out- equilibrium beliefs which mean that, if the outsider observes an out-of -equilibrium price, she suspects manipulation by the insider.

27 The price P0 is set by the insider to saturate the participation constraint of the outsider. For a given period t, this constraint is thus:

O O E[U (Wt )]= 0 (A1)

O O where Wt = Q(V - P0 ) - c if the insider receives an endowment shock, and Wt = -c otherwise. (A1) can be rewritten: l{g[u (q = Q, P = P )]U O (Q(u - P *) - c) + g[d (q = Q, P = P )]U O (Q(d - P *) - c)} 0 0 (A2) + (1 - l )U O (- c) = 0

Setting P0 = E[V] - s0 , (A2) yields the equation for the spread:

1 - b c æ 2(1 - l )ö s0 = Var[V] + ç1+ ÷ (A3) 1 + b Q è (1 + b)l ø Using our assumptions for u, d, and p , we get the pricing equation: 1- b c æ 2(1 - l )ö P* = P0 = - - ç1+ ÷ (A4) 1+ b Q è (1 + b)l ø

I I I At equilibrium, insider’s expected utility is E[U (W *) "(S1, S2), E = Q]= U (QP0 ) ,

I I I I I E[U (W *) "(S1, S2), E = 0]= 0 , and E[U (W *)]= lU (QP0 ) depending on the state of nature. For the incentive condition to be satisfied, this expected utility should be greater than the expected utility the insider would get if he deviates. The potential deviations are i) setting

(q, P *) = (0, P0 ) instead of (q*, P *) = (- Q, P0 ), i.e. not hedging an endowment shock, and ii) setting (q, P *) = (- Q, P0 ) instead of (q*, P *) = (0, P0 ) , i.e. purely speculating on information.

We do not need to consider the deviations where P ¹ P0 because, in this case, the outsider’s beliefs are such that she would not trade. These deviations are thus equivalent to deviation i). This discussion implies that, for a pooling equilibrium to exist, the following inequalities must hold:

I I I U (QP0 ) ³ Pr(u S1 = S2 = H , E = Q)U (uQ) + Pr(d S1= S2 = H, E = Q)U (dQ) (A5)

I I 0 ³ Pr(u S1 = S2 = L, E = 0)U (- Q[u - P0 ]) + Pr(d S1= S2 = L, E = 0)U (- Q[d - P0 ]) (A6) In addition, in order for the insider to have an incentive to trade, it must be the case that:

P0 ³ d (A7)

28 We apply the same reasoning to characterize the semiseparating equilibrium where S1=S2= H is revealed. We conjecture that, for any period t, the following strategy profile is an equilibrium: · The insider submits the limit order (q*,P* ) where q* =-E, P* = P + if S1=S2= H, and

P* = P- if S1 ¹ S2 or S1=S2=L; · As long as she has not detected an insider’s deviation, the outsider always enters the market (d*=1) and submits a market order m*=Q. If she detects a deviation, she does not enter the market anymore (d*=0). p2 · For rational expectations, outsider’s beliefs are g[u (q*, P + )]= , 1+ 2 p2 - 2p

1- p2 g[u (q*, P - )]= , g[u (q, P)]= 0 , and g[d (q,P)] =1, for any 1 - 2p2 + 2 p (q, P) ¹ (q*,P *). In this case, the outsider’s participation constraint leads to the pricing equations: § If S1=S2= H,

2 p - 1 1 - b æ (2 p - 1)2 ö c æ 2(1 - l )ö P* = P + = - ç1 - ÷ - ç1 + ÷ (A8) 2 ç 2 2 ÷ ç ÷ 1 + 2 p - 2 p 1 + b è (1 + 2 p - 2 p)(1 - 2 p + 2 p)ø Q è (1 + b )l ø § If S1¹ S2 or S1=S2=L, 2 p - 1 1 - b æ (2 p - 1)2 ö c æ 2(1 - l )ö P* = P - = - - ç1- ÷ - ç1 + ÷ (A9) 2 ç 2 2 ÷ ç ÷ 1 - 2p + 2p 1 + b è (1 + 2 p - 2p)(1 - 2p + 2p)ø Q è (1+ b)l ø Insider’s potential deviation are i) setting (q, P*) = (0,P*) instead of (q*,P *) = (-Q,P *) , ii) setting (q, P *) = (-Q, P *) instead of (q*,P *) = (0, P *), and iii) setting (q*, P) = (- Q, P + ) instead of (q*, P *) = (- Q, P - ). The incentive constraint of the insider is satisfied if the following inequalities hold: U I (QP + )³ Pr(u S1 = S2 = H, E = Q)U I (uQ) + Pr(d S1 = S2 = H , E = Q)U I (dQ) (A10) U I (QP - )³ Pr(u S1¹ S 2, E = Q)U I (uQ) + Pr(d S1 ¹ S2, E = Q)U I (dQ) (A11) 0 ³ Pr(u S1 = S2 = H , E = 0)U I (- Q[u - P + ]) + Pr(d S1 = S2 = H , E = 0)U I (- Q[d - P + ]) (A12) 0 ³ Pr(u S1 = S2 = L, E = 0)U I (- Q[u - P- ]) + Pr(d S1 = S2 = L, E = 0)U I (- Q[d - P - ]) (A13)

29 If one considers only period t in isolation of the following trading periods, then deviation iii) will always be profitable because P + > P- , see equation (A15). In order to sustain equilibrium, we thus need a mechanism that makes semiseparating pricing optimal. This is the role of the trigger strategy of the outsider. If she observes a deviation which occurs with lg probability (1 - 2 p 2 + 2 p) , she does not enter the market anymore. This implies that, upon 2 deviating and being caught, then insider will not be able to hedge his endowment shocks anymore. The risk-averse insider thus faces a tradeoff between an immediate profit from his information and a future disutility from receiving endowment shocks without being able to hedge them. He will refrain from deviating if the following inequality holds:

1 I I l éæ 1 2 ö I + æ 1 2 ö I - ù E[U (W *)]= êç + p - p÷U (QP ) + ç - p + p÷U (QP )ú ³ 1- d 1 - d ëè 2 ø è 2 ø û 2 (A14) 1 æ I + l g 2 d ö çlU (QP ) - (1 - 2 p + 2 p)Q ÷ lgd 2 4 1 - d 1- d + (1- 2p + 2p)è ø 2 Finally, in order for the insider to have an incentive to trade and set semiseparating prices, it must be the case that: P + > P - ³ d (A15)

We apply the same reasoning to characterize the semiseparating equilibrium where S1=S2=L is revealed. We conjecture that, for any period t, the following strategy profile is an equilibrium: · The insider submits the limit order (q*,P* ) where q* =-E, P* = P' if S1=S2=L, and P* = P" if S1 ¹ S2 or S1=S2=H; · As long as she has not detected an insider’s deviation, the outsider always enters the market (d*=1) and submits a market order m*=Q. If she detects a deviation, she does not enter the market anymore (d*=0).

2 p - p 2 · For rational expectations, outsider’s beliefs are g[u (q*, P')]= , 1- 2p 2 + 2p

(1 - p)2 g[u (q*, P")] = , g[u (q, P)]= 0 , and g[d (q,P)] =1, for any 1 + 2 p 2 - 2 p (q, P) ¹ (q*,P *).

30 In this case, the outsider’s participation constraint leads to the pricing equations: § If S1=S2= L,

2 p - 1 1 - b æ (2 p - 1)2 ö c æ 2(1 - l )ö P* = P'= - - ç1- ÷ - ç1 + ÷ (A16) 2 ç 2 2 ÷ ç ÷ 1 + 2p - 2 p 1+ b è (1 + 2 p - 2p)(1 - 2p + 2p)ø Q è (1+ b)l ø § If S1¹ S2 or S1=S2=H, 2p - 1 1 - b æ (2 p - 1)2 ö c æ 2(1 - l )ö P* = P"= - ç1- ÷ - ç1+ ÷ (A17) 2 ç 2 2 ÷ ç ÷ 1- 2 p + 2p 1 + b è (1 + 2 p - 2p)(1 - 2p + 2 p)ø Q è (1 + b)l ø The incentive constraint of the insider is satisfied if the following inequalities hold: U I (QP') ³ Pr(u S1 = S2 = L, E = Q)U I (uQ) + Pr(d S1 = S2 = L, E = Q)U I (dQ) (A18)

U I (QP") ³ Pr(u S1 = S2 = H , E = Q)U I (uQ) + Pr(d S1 = S2 = H, E = Q)U I (dQ) (A19) 0 ³ Pr(u S1 = S2 = L, E = 0)U I (- Q[u - P']) + Pr(d S1 = S2 = L, E = 0)U I (- Q[d - P']) (A20) 0 ³ Pr(u S1 ¹ S2, E = 0)U I (- Q[u - P"]) + Pr(d S1 ¹ S2, E = 0)U I (- Q[d - P"]) (A21)

l éæ 1 2 ö I æ 1 2 ö I ù êç - p + p ÷U (QP") + ç + p - p ÷U (QP')ú ³ 1 - d ëè 2 ø è 2 ø û 2 (A22) 1 æ I l g 2 d ö çlU (QP") - (1 + 2 p - 2 p)Q ÷ lgd 2 4 1 - d 1 - d + (1 + 2 p - 2 p )è ø 2 Finally, in order for the insider to have an incentive to trade and set semiseparating prices, it must be the case that: P"> P'³ d (A23)

We apply the same reasoning to characterize the separating equilibrium. We conjecture that, for any period t, the following strategy profile is an equilibrium:

· The insider submits the limit order (q*,P* ) where q* =-E, P*=P1 if S1=S2= H, P*=P2

if S1¹ S2, and P *= P3 if S1=S2=L; · The outsider always enters the market (d*=1) as long as she has not detected an insider’s deviation, and submits a market order m*=Q. If she detects a deviation, she does not enter the market anymore (d*=0).

31 p2 · For rational expectations, outsider’s beliefs are g[u (q*, P )]= , 1 1 + 2 p2 - 2 p

1 (1 - p)2 g[u (q*, P )]= , g[u (q*, P )] = , g[u (q, P)]= 0 , and g[d (q,P)] =1, 2 2 3 1 + 2 p 2 - 2 p for any (q,P) ¹ (q*,P *) . In this case, the outsider’s participation constraint leads to the pricing equations: § If S1=S2= H, 1- b c æ 2(1- l)ö P* = P1 = E[V S1 = S2 = H ] - Var[V S1 = S2] - ç1 + ÷ 1 + b Q è (1+ b)l ø 2p - 1 1 - b 2p(1 - p) c æ 2(1 - l )ö = - - ç1+ ÷ 2 2 ç ÷ (A24) 1+ 2 p - 2p 1 + b (1+ 2 p - 2 p) Q è (1 + b)l ø § If S1¹ S2 , 1 - b c æ 2(1- l) ö P* = P2 = E[V S1 ¹ S2] - Var[V S1 = S2] - ç1 + ÷ 1 + b Q è (1+ b)l ø 1 - b 2p(1 - p) c æ 2(1 - l )ö = - - ç1+ ÷ 2 ç ÷ (A25) 1 + b (1 + 2p - 2 p) Q è (1 + b)l ø § If S1=S2= L, 1- b c æ 2(1 - l )ö P* = P3 = E[V S1 = S2 = L] - Var[V S1 = S2] - ç1 + ÷ 1 + b Q è (1+ b)l ø 2 p - 1 1- b 2 p(1- p) c æ 2(1 - l )ö = - - - ç1 + ÷ (A26) 2 2 ç ÷ 1 + 2p - 2 p 1+ b (1 + 2 p - 2p) Q è (1+ b)l ø The incentive constraint of the insider is satisfied if the following inequalities hold:

I I I U (QP1 ) ³ Pr(u S1 = S2 = H, E = Q)U (uQ) + Pr(d S1 = S2 = H, E = Q)U (dQ) (A27)

I I I U (QP2 )³ Pr(u S1 ¹ S2, E = Q)U (uQ) + Pr(d S1 ¹ S2, E = Q)U (dQ) (A28)

I I I U (QP3 ) ³ Pr(u S1= S2 = L, E = Q)U (uQ) + Pr(d S1 = S2 = L, E = Q)U (dQ) (A29)

I I 0 ³ Pr(u S1 = S2 = H , E = 0)U (- Q[u - P1 ]) + Pr(d S1 = S2 = H , E = 0)U (- Q[d - P1 ]) (A30)

I I 0 ³ Pr(u S1 ¹ S2, E = 0)U (- Q[u - P2 ]) + Pr(d S1 ¹ S2, E = 0)U (- Q[d - P2 ]) (A31)

I I 0 ³ Pr(u S1 = S2 = L, E = 0)U (- Q[u - P3 ]) + Pr(d S1 = S2 = L, E = 0)U (- Q[d - P3 ]) (A32)

32 l éæ 1 2 ö I I æ 1 2 ö I ù êç + p - p ÷U (QP1 ) + 2 p(1 - p )U (QP2 ) + ç + p - p ÷U (QP3 )ú ³ 1 - d ëè 2 ø è 2 ø û 1 æ l2g d ö (A33) ç U I QP 1 2 p 2 2 p Q ÷ çl ( 1 ) - ( - + ) ÷ lgd 2 4 1 - d 1 - d + (1 - 2 p + 2 p )è ø 2 Finally, in order for the insider to have an incentive to trade and set semiseparating prices, it must be the case that:

P1 > P2 > P3 ³ d (A34)

It is straightforward to verify that, when p=.55, l=d=g=.9, Q=10,000, c=300, a=1/4, and b=3/4, the equilibria characterized above exist. Q.E.D.

Proof of Proposition 2 Consider first the pooling equilibrium conjecture where, for any period t:

· The insider submits the non-binding market order (qA*,.) and the limit order (q*,P*)

where qA*=q*=-E and P*=P00 irrespective of S1 and S2; · As long as she has not detected a deviation:

- If qA ¹ 0 , the outsider enters the market (d*=1) and she submits m*=0.

- If qA =0 , the outsider does not enter the market (d*=0).

· For rational expectations, outsider’s beliefs are g[u (qA*,PA*,q*,P *)]=p ,

g[u (q A,PA,q,P)] = 0, and g[d qA ,PA,q,P] =1, for any

(qA,PA,q,P) ¹ (qA*,PA*,q*,P *). The last two equalities specify out-equilibrium beliefs which mean that, if the outsider observes an out-of-equilibrium price, she suspects manipulation by the insider.

The price P00 is set by the insider to saturate the participation constraint of the outsider. For a given period t, this constraint is thus:

O O E[U (Wt )]= 0 (B1)

O O where Wt = Q(V - P00) - c if the insider receives an endowment shock, and Wt = 0 otherwise. (B1) can be rewritten:

O ïìg[u (qA = q = Q, PA = P = P00)]U (Q(u - P *) - c) ïü l + 1 - l U O 0 = 0 (B2) í O ý ( ) ( ) îï + g[d (qA = q = Q, PA = P = P00 )]U (Q(d - P *) - c)þï

Setting P00 = E[V]- s00, (B2) yields the equation for the spread:

33 1 - b c s = Var[V] + (B3) 00 1 + b Q

Using our assumptions for u, d, and p , we get the pricing equation: 1 - b c P* = P = - - (B4) 00 1 + b Q

I I I At equilibrium, insider’s expected utility is E[U (W *) "(S1, S2), E = Q] = U (QP00 ),

I I I I I E[U (W *) "(S1, S2), E = 0]= 0 , and E[U (W *)]= lU (QP00 ) depending on the state of nature. For the incentive condition to be satisfied, this expected utility should be greater than the expected utility the insider would get if he deviates. The potential deviations are i) setting

(q, P *) = (0, P00 ) instead of (q*, P *) = (- Q, P00), i.e. not hedging an endowment shock, ii) setting (q, P *) = (- Q, P00 ) instead of (q*, P *) = (0, P00 ), i.e. pure ly speculating on information, iii) setting (q A , q, P *) = (0,0, P00) instead of (q A *, q*, P *) = (- Q,-Q, P00), and iv) setting (q A , q, P *) = (- Q,-Q, P00) instead of (q A *, q*, P *) = (0,0, P00) . We do not need to consider the deviations where P ¹ P0 because, in this case, the outsider’s beliefs are such that she would not trade. These deviations are thus equivalent to deviations i) and iii). This discussion implies that, for a pooling equilibrium to exist, the following inequalities must hold:

I I I U (QP00 ) ³ Pr(u S1 = S2 = H , E = Q )U (uQ) + Pr(d S1 = S2 = H , E = Q)U (dQ) (B5)

I I 0 ³ Pr(u S1 = S2 = L, E = 0)U (- Q[u - P00]) + Pr(d S1 = S2 = L, E = 0)U (- Q[d - P00]) (B6) In addition, in order for the insider to have an incentive to trade, it must be the case that:

P00 ³ d (B7)

We apply the same reasoning to characterize the semiseparating equilibrium where S1=S2= H is revealed. We conjecture that, for any period t, the following strategy profile is an equilibrium:

· The insider submits the non-binding market order (qA*,.) and the limit order (q*,P*)

++ -- where qA*=q*=-E and P* = P if S1=S2=H, and P* = P if S1 ¹ S2 or S1=S2= L; · As long as she has not detected a deviation:

- If qA ¹ 0 , the outsider enters the market (d*=1) and she submits m*=0.

- If qA =0 , the outsider does not enter the market (d*=0).

34 p2 · For rational expectations, outsider’s beliefs are g[u (q *,., q*, P ++ )]= , A 1 + 2p 2 - 2 p

1- p2 g[u (q *,., q*, P -- )]= , g[u (q ,P ,q,P)] = 0, and g[d q ,P ,q,P] =1, A 1 - 2p2 + 2 p A A A A

for any (qA, PA,q, P) ¹ (qA*,PA*,q*,P *). In this case, the outsider’s participation cons traint leads to the pricing equations: § If S1=S2= H,

2p - 1 1 - b æ (2 p - 1)2 ö c P* = P ++ = - ç1- ÷ - (B8) 2 ç 2 2 ÷ 1 + 2 p - 2p 1 + b è (1 + 2 p - 2p)(1 - 2p + 2p)ø Q § If S1¹ S2 or S1=S2=L,

2 p - 1 1- b æ (2 p - 1)2 ö c P* = P -- = - - ç1- ÷ - (B9) 2 ç 2 2 ÷ 1 - 2 p + 2 p 1+ b è (1 + 2 p - 2p)(1 - 2p + 2p)ø Q

Insider’s potential deviation are i) setting (qA*,PA*,q,P *) = (qA*,PA*,0, P *) instead of

(qA*,PA*,q*,P *) = (qA*,PA*,-Q,P *) , ii) setting (qA*,PA*,q,P *) = (qA*,PA*,-Q, P *) instead of (qA*,PA*,q*,P *) = (qA*,PA*,0,P *), iii) setting

+ - (qA *, PA *, q*, P) = (qA *, PA *,-Q, P ) instead of (qA *, PA*, q*, P *) = (qA *, PA *,-Q, P ). The incentive constraint of the insider is satisfied if the following inequalities hold: U I (QP ++ ) ³ Pr(u S1 = S2 = H, E = Q)U I (uQ) + Pr(d S1 = S2 = H , E = Q)U I (dQ) (B10) U I (QP -- ) ³ Pr(u S1 ¹ S 2, E = Q)U I (uQ) + Pr(d S1 ¹ S 2, E = Q)U I (dQ) (B11) 0 ³ Pr(u S1 = S2 = H , E = 0)U I (- Q[u - P ++ ])+ Pr(d S1 = S2 = H, E = 0)U I (- Q[d - P ++ ]) (B12) 0 ³ Pr(u S1 = S2 = L, E = 0)U I (- Q[u - P -- ]) + Pr(d S1 = S2 = L, E = 0)U I (- Q[d - P-- ]) (B13) If one considers only period t in isolation of the following trading periods, then deviation iii) will always be profitable because P ++ > P -- , see equation (B15). In order to sustain equilibrium, we thus need a mechanism that makes semiseparating pricing optimal. This is the role of the trigger strategy of the outsider. If she observes a deviation which occurs with lg probability (1 - 2 p 2 + 2 p) , she does not enter the market anymore. This implies that, upon 2 deviating and being caught, then insider will not be able to hedge his endowment shocks anymore. The risk-averse insider thus faces a tradeoff between an immediate profit from his

35 information and a future disutility from receiving endowment shocks without being able to hedge them. He will refrain from deviating if the following inequality holds:

1 I I l éæ 1 2 ö I ++ æ 1 2 ö I -- ù E[U (W *)]= êç + p - p÷U (QP )+ ç - p + p÷U (QP )ú ³ 1- d 1- d ëè 2 ø è 2 ø û 2 (B14) 1 æ I ++ l g 2 d ö çlU (QP )- (1- 2 p + 2 p)Q ÷ lgd 2 4 1 - d 1 - d + (1- 2 p + 2 p) è ø 2 Finally, in order for the insider to have an incentive to trade and set semiseparating prices, it must be the case that: P ++ > P -- ³ d (B15)

We apply the same reasoning to characterize the semiseparating equilibrium where S1=S2=L is revealed. We conjecture that, for any period t, the following strategy profile is an equilibrium:

· The insider submits the non-binding market order (qA*,.) and the limit order (q*,P*)

where qA*=q*=-E and P* = P'' ' if S1=S2=L, and P* = P'''' if S1 ¹ S2 or S1=S2= H; · As long as she has not detected a deviation:

- If q A ¹ 0 , the outsider enters the market (d*=1) and she submits m*=0.

- If q A = 0 , the outsider does not enter the market (d*=0).

2 p - p2 · For rational expectations, outsider’s beliefs are g[u (q *,., q*, P' '')] = , A 1- 2 p2 + 2p

(1 - p)2 g[u (q *,., q*, P' ''')] = , g[u (q ,P ,q,P)] = 0, and A 1 + 2 p 2 - 2 p A A

g[d qA, PA,q,P] =1, for any (qA,PA,q,P) ¹ (qA*,PA*,q*,P *). In this case, the outsider’s participation constraint leads to the pricing equations: § If S1=S2= L,

2 p - 1 1- b æ (2 p - 1)2 ö c P* = P''' = - - ç1 - ÷ - (B16) 2 ç 2 2 ÷ 1+ 2 p - 2 p 1+ b è (1 + 2p - 2 p)(1 - 2 p + 2 p)ø Q § If S1¹ S2 or S1=S2=H, 2 p - 1 1 - b æ (2 p - 1)2 ö c P* = P''' '= - ç1- ÷ - (B17) 2 ç 2 2 ÷ 1 - 2p + 2p 1 + b è (1 + 2 p - 2p)(1 - 2p + 2 p)ø Q The incentive constraint of the insider is satisfied if the following inequalities hold:

36 U I (QP' '') ³ Pr(u S1 = S2 = L, E = Q)U I (uQ) + Pr(d S1 = S2 = L, E = Q)U I (dQ) (B18) U I (QP' ''') ³ Pr(u S1 = S2 = H, E = Q)U I (uQ) + Pr(d S1 = S2 = H , E = Q)U I (dQ) (B19) 0 ³ Pr(u S1 = S2 = L, E = 0)U I (- Q[u - P'' ']) + Pr(d S1 = S2 = L, E = 0)U I (- Q[d - P' '']) (B20) 0 ³ Pr(u S1 ¹ S2, E = 0)U I (- Q[u - P' ''']) + Pr(d S1 ¹ S2, E = 0)U I (- Q[d - P''' ']) (B21)

l éæ 1 2 ö I æ 1 2 ö I ù êç - p + p ÷U (QP'' '') + ç + p - p ÷U (QP''')ú ³ 1 - d ëè 2 ø è 2 ø û 2 (B22) 1 æ I l g 2 d ö çlU (QP''' ') - (1 + 2 p - 2 p )Q ÷ lgd 2 4 1 - d 1 - d + (1 + 2 p - 2 p )è ø 2 Finally, in order for the insider to have an incentive to trade and set semiseparating prices, it must be the case that: P''''> P'''³ d (B23)

We apply the same reasoning to characterize the separating equilibrium. We conjecture that, for any period t, the following strategy profile is an equilibrium:

· The insider submits the non-binding market order (qA*,.) and the limit order (q*,P*)

where qA*=q*=-E, and P *= P11 if S1=S2=H, P*=P22 if S1¹ S2, and P*=P33 if S1=S2=L; · As long as she has not detected a deviation:

- If qA ¹ 0 , the outsider enters the market (d*=1) and she submits m*=0.

- If qA =0 , the outsider does not enter the market (d*=0). p2 · For rational expectations, outsider’s beliefs are g[u (q *,., q*, P )] = , A 11 1 + 2p 2 - 2 p

1 (1 - p )2 g[u (q *,., q*, P )] = , g[u (q *,., q*, P )] = , g[u (q , P , q, P)] = 0 , A 22 2 A 33 1 + 2 p 2 - 2 p A A

and g[d qA ,PA,q,P] =1, for any (qA,PA,q,P) ¹ (qA*,PA*,q*,P *). In this case, the outsider’s participation cons traint leads to the pricing equations: § If S1=S2= H, 1 - b c P* = P = E[V S1 = S2 = H ] - Var[V S1 = S2] - 11 1 + b Q 2 p - 1 1 - b 2 p(1 - p ) c = - - (B24) 1 + 2 p 2 - 2 p 1 + b (1 + 2 p 2 - 2 p) Q

37 § If S1 ¹ S2 , 1 - b c P* = P = E[V S1 ¹ S2]- Var[V S1 = S2] - 22 1 + b Q 1 - b 2p(1 - p) c = - - (B25) 1 + b (1 + 2p2 - 2p) Q § If S1=S2= L, 1 - b c P* = P = E[V S1 = S2 = L] - Var[V S1 = S2] - 33 1 + b Q

2 p - 1 1 - b 2 p(1 - p) c = - - - (B26) 1 + 2 p 2 - 2 p 1 + b (1 + 2 p 2 - 2 p) Q The incentive constraint of the insider is satisfied if the following inequalities hold:

I I I U (QP11) ³ Pr(u S1 = S2 = H, E = Q)U (uQ) + Pr(d S1 = S2 = H , E = Q)U (dQ) (B27)

I I I U (QP22 ) ³ Pr(u S1 ¹ S 2, E = Q)U (uQ) + Pr(d S1 ¹ S 2, E = Q)U (dQ) (B28)

I I I U (QP33 ) ³ Pr(u S1 = S 2 = L, E = Q )U (uQ) + Pr(d S1 = S 2 = L, E = Q)U (dQ) (B29)

I I 0 ³ Pr(u S1 = S2 = H , E = 0)U (- Q[u - P11]) + Pr(d S1 = S2 = H , E = 0)U (- Q[d - P11]) (B30)

I I 0 ³ Pr(u S1 ¹ S2, E = 0)U (- Q[u - P22]) + Pr(d S1 ¹ S2, E = 0)U (- Q[d - P22 ]) (B31)

I I 0 ³ Pr(u S1 = S2 = L, E = 0)U (- Q[u - P33 ]) + Pr(d S1 = S2 = L, E = 0)U (- Q[d - P33 ]) (B32)

l éæ 1 2 ö I I æ 1 2 ö I ù êç + p - p ÷U (QP11) + 2 p(1 - p )U (QP22 ) + ç + p - p ÷U (QP33)ú ³ 1 - d ëè 2 ø è 2 ø û 1 æ l2g d ö (B33) ç U I QP 1 2 p 2 2 p Q ÷ çl ( 11) - ( - + ) ÷ lgd 2 4 1 - d 1 - d + (1 - 2 p + 2 p) è ø 2 Finally, in order for the insider to have an incentive to trade and set semiseparating prices, it must be the case that:

P11 > P22 > P33 ³ d (B34)

We apply the same reasoning to characterize the semiseparating equilibrium where S1 is revealed. We conjecture that, for any period t, the following strategy profile is an equilibrium:

· The insider submits the non-binding limit order (qA*,PA*) and the limit order (q*,P* )

where qA*=q*=-E and PA * = P* = P if S1=H, and PA*= P*= P if S1=L;

38 · As long as she has not detected a deviation:

- If q A ¹ 0 , the outsider enters the market (d*=1) and she submits m*=0.

- If q A = 0 , the outsider does not enter the market (d*=0).

· For rational expectations, outsider’s beliefs are g [u (q A *, PA * = P, q*, P* = P)]= p ,

g[u (q A *, PA * = P, q*, P* = P)] = 1 - p , g[u (q A , PA , q, P)] = 0 , and

g[d q A , PA , q, P] = 1 , for any (q A , PA , q, P) ¹ (q A *, PA *, q*, P *). In this case, the outsider’s par ticipation constraint leads to the pricing equations: § If S1=H, 1- b c P* = P = E[V S1 = H ]- Var[V S1]- 1+ b Q

1 - b c = 2 p - 1 - 4 p(1 - p) - (B35) 1 + b Q § If S1=L , 1 - b c P* = P = E[V S1 = L] - Var[V S1]- 1 + b Q

1 - b c = -(2 p - 1) - 4 p(1 - p) - (B36) 1 + b Q The incentive constraint of the insider is satisfied if the following inequalities hold: U I (QP) ³ Pr(u S1 = S2 = H , E = Q)U I (uQ) + Pr(d S1 = S2 = H , E = Q)U I (dQ) (B37) U I (QP) ³ Pr(u S1 = S2 = L, E = Q)U I (uQ) + Pr(d S1 = S2 = L, E = Q)U I (dQ) (B38) 0 ³ Pr(u S1 = S2 = H , E = 0)U I (- Q [u - P])+ Pr(d S1 = S2 = H , E = 0)U I (- Q[d - P]) (B39) 0 ³ Pr(u S1 = S2 = L, E = 0)U I (- Q[u - P])+ Pr(d S1 = S2 = L, E = 0)U I (- Q[d - P]) (B40)

l é1 I 1 I ù U (QP)+ U (QP) ³ 1-d ëê2 2 ûú 2 (B41) 1 æ I l g 2 d ö çlU (QP)- (1+ 2p - 2 p)Q ÷ lgd 2 4 1- d 1- d + (1 + 2 p - 2 p)è ø 2 Finally, in order for the insider to have an incentive to trade and set semiseparating prices, it must be the case that:

P > P ³ d (B42)

39 It is straightforward to verify that, when p=.55, l=d=g=.9, Q=10,000, c=300, a=1/4, and b=3/4, the equilibria characterized above exist. Q.E.D.

Proof of Corollary 2 When p=.7, l=d=g=.9, Q=10,000, c= 500, a=1/4, and b=3/4, it is straightforward to verify that the unique equilibrium is the semiseparating equilibrium where S1 is revealed during the preopening period. Q.E.D.

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41 Table 1 – Trading activity This table presents various measures of trading activity for the 8 stocks under study. The average and the standard deviation of the trading volume, and the average number of orders are computed over the 141 trading sessions in 2000. The turnover is defined as the total number of shares traded over the number of outstanding shares for the year 2000. The average and the standard deviation of the number of active broker-dealers are computed across the trading sessions with a non-null order placement. The average Herfindahl index and the average 1/number of broker-dealers are computed across the trading sessions with a non-null trading volume. BICC stands for Banque Internationale pour le Commerce et l’Industrie de Côte d’Ivoire. BLHC stands for Blohorn – Côte d’Ivoire. CIEC stands for Compagnie Ivoirienne d’Electricité. PALC stands for Palm – Côte d’Ivoire. SGBC stands for Société Générale de Banques en Côte d’Ivoire. SHEC stands for Shell – Côte d’Ivoire. SNTS stands for Société Nationale de Télécommunication. NA stands for “Not Available”.

BICC BLHC CIEC PALC SGBC SHEC SNTS STBC Average Volume 246 88 100 141 116 71 1719 73

Standard Deviation of the Volume 772 253 168 378 494 170 7211 295

Turnover 0.0231 NA 0.0050 0.0050 0.0053 0.0139 0.0242 NA

Number of Trading Sessions without Trades 54 38 24 73 105 33 3 57

Average Number of Orders 10 9 16 13 8 8 31 11

Proportion of Cancelled Orders (in %) 1.41 2.86 3.27 1.00 1.25 3.19 2.95 1.08

Proportion of Modified Orders (in %) 4.44 11.45 9.95 5.79 4.83 8.38 5.55 9.32

Average Number of Active Broker-Dealers 2.21 3.49 4.52 4.67 2.76 3.72 7.35 3.48 Standard Deviation of the Number of Active Broker-Dealers 0.98 1.44 1.44 1.54 1.05 1.47 0.26 1.77

Average Herfindahl Index 0.81 0.54 0.49 0.57 0.81 0.49 0.52 0.58 Average 1/number of broker-dealers 0.56 0.35 0.25 0.25 0.44 0.32 0.20 0.41

42 Table 2 – Broker-dealers’ activity

This table presents the number of orders placed and the number of shares traded by each broker-dealer, averaged across stocks and trading sessions.

Average Number Average Number of Orders of Shares Traded BD1 3.1 33 BD2 6.8 70 BD3 2.6 151 BD4 3.1 101 BD5 35.9 3117 BD6 5.7 334 BD7 0.4 8 BD8 2.4 20 BD9 0.0 0 BD10 1.1 126 BD11 0.2 3877 BD12 1.3 27 BD13 0.3 2 BD14 0.2 1 BD15 10.1 494 BD16 32.3 4779

43 Table 3 – Transaction costs

The measure of transaction costs we used is inspired by Kehr, Krahnen, and Theissen (1998). For each trading session, we added one buying market order in the orderbook, and computed the new transaction price (Pb). After canceling this buying order, we added one selling market order, and computed another transaction price (Ps). P - P Transaction costs were measured by the following formula: b s where P* was the actual transaction price. P* We computed this measure with orders of various sizes: one, ten, hundred, two hundred, five hundred, one thousand. For each stock, we computed the average transaction cost across trading sessions where the additional buy and sell orders could find a counterpart. The number of trading sessions (out of 141) in which the orderbook was not thick enough to allow execution of the additional orders is also provided.

BICC BLHC CIEC PALC SGBC SHEC SNTS STBC Transaction cost for the trading of 1 additional share 5.0 3.8 2.5 9.2 3.3 1.9 1.7 3.3 Number of trading sessions without liquidity 99 84 66 84 130 65 26 92

Transaction cost for the trading of 10 additional shares 5.3 12.5 5.3 9.7 4.3 2.4 1.9 3.9 Number of trading sessions without liquidity 104 114 106 90 132 80 29 100

Transaction cost for the trading of 100 additional shares 6.2 16.4 5.2 10.9 3.9 3.6 2.6 5.6 Number of trading sessions without liquidity 122 121 134 96 135 108 64 129

Transaction cost for the trading of 200 additional shares 6.7 26.0 3.73 14.6 3.3 2.6 3.0 3.1 Number of trading sessions without liquidity 127 133 140 102 138 120 77 133

Transaction cost for the trading of 500 additional shares 10.0 59.5 * 16.7 3.3 4.5 4.0 3.9 Number of trading sessions without liquidity 134 139 141 113 138 130 95 138

Transaction cost for the trading of 1000 additional shares 16.4 * * 22.7 5 4.8 5.6 * Number of trading sessions without liquidity 138 141 141 126 139 135 105 141

44 Table 4 – Regression of the instantaneous price volatility onto the trading volume

This table presents the result of OLS regression of the absolute returns onto the trading volume. The return at date t is computed as the difference between the price at date t and the price at date t-1, divided by the price at date t-1. Only the days with a non-null trading volume are considered. The number of observations is consequently not the same for all the stocks. P -values are reported in parenthesis.

Number of Intercept a Coefficient b R² Observations BICC 0.0041 -0.0000 0.00 87 (0.15) (0.78) BLHC 0.0027 0.0000 0.02 103 (0.00) (0.21) CIEC 0.0143 0.0000 0.00 117 (0.00) (0.74) PALC 0.0131 -0.0000 0.00 68 (0.00) (0.79) SGBC 0.0346 -0.0000 0.06 36 (0.00) (0.16) SHEC 0.0052 -0.0000 0.00 108 (0.00) (0.64) SNTS 0.0064 -0.0000 0.00 138 (0.00) (0.87) STBC 0.0076 0.0000 0.02 84 (0.00) (0.23)

45 Table 5 – Distribution of orders according to their size and their time of placement during the preopening period For each of the 8 stocks, orders are classified in sixteen categories according to the placement time quartile and the size quartile they belong to. Table 5 averages these data. The upper-left cell of the table represents the large orders placed early. The first quartile of placement time is on average 9:16 am. The second quartile of placement time is on average 9:39 am. The third quartile of placement time is on average 10:07 am. The first quartile of order size is on average 9 shares. The second quartile of order size is on average 32 shares. The third quartile of order size is on average 92 shares.

Time of Placement 1st Quartile 2nd Quartile 3rd Quartile 4th Quartile sum Order Size 4th Quartile 6% 7% 6% 6% 25% 3rd Quartile 7% 7% 5% 5% 24% 2nd Quartile 7% 7% 6% 5% 25% 1st Quartile 6% 5% 7% 8% 26% sum 25% 25% 25% 25% 100%

Table 6 – Proportion of orders executed at the call as a function of their size and placement time during the preopening period For each size and time category, this table reports the proportion of orders (partially) filled at the time of the call, averaged across the 8 stocks.

Time of Placement 1st Quartile 2nd Quartile 3rd Quartile 4th Quartile average Order Size 4th Quartile 25% 24% 35% 58% 36% 3rd Quartile 32% 32% 36% 58% 39% 2nd Quartile 37% 37% 41% 58% 43% 1st Quartile 34% 34% 43% 53% 41% average 32% 32% 39% 57% 40%

46 Table 7 – Distribution of proposed quantities over the sixteen categories of orders

This table reports the proportion of the total quantity that has been proposed by each type of orders, averaged over the 8 stocks.

Time of Placement 1st Quartile 2nd Quartile 3rd Quartile 4th Quartile sum Order Size 4th Quartile 17% 18% 23% 33% 91% 3rd Quartile 2% 2% 1% 2% 6% 2nd Quartile 1% 1% 1% 0% 2% 1st Quartile 0% 0% 0% 0% 1% sum 19% 21% 25% 35% 100%

Table 8 – Proportion of the executed quantities proposed by each type of orders that are eventually executed For each category, this table reports the proportion of quantities that have been exchanged at the time of the call, averaged across the 8 stocks. Potential rationing is not taken into account.

Time of Placement 1st Quartile 2nd Quartile 3rd Quartile 4th Quartile average Order Size 4th Quartile 25% 24% 35% 58% 36% 3rd Quartile 32% 32% 36% 58% 39% 2nd Quartile 37% 37% 41% 58% 43% 1st Quartile 34% 34% 43% 53% 41% average 32% 32% 39% 57% 40%

47 Table 9 – Price discovery regressions

This table presents the result of OLS regression of the returns from the previous trading session to the call onto the returns from the previous trading session to the first part of the preopening period. The return at date t is computed as the difference between the price at date t and the price at date t-1, divided by the price at date t-1. Only the days with a non-null trading volume are considered. The number of observations is consequently not the same for all the stocks. The data is conditional on the existence of indicative prices in the first part of the preopening period. This further reduces the number of observations. P-values are reported in parenthesis.

Number of Intercept A 1 Coefficient B 1 R² Observations BICC 0 1 1.00 20

BLHC -0,0011 0.0148 0.00 45 (0.18) (0.74) CIEC -0.0019 0.2395 0.12 62 (0.55) (0.00) PALC -0.0049 0.7353 0.71 10 (0.62) (0.00) SGBC -0.0608 0.3233 0.41 8 (0.04) (0.08) SHEC -0.0013 0.5451 0.25 54 (0.23) (0.00) SNTS 0.0001 0.4446 0.44 69 (0.91) (0.00) STBC -0.0012 0.8993 0.41 26 (0.47) (0.00)

48 Table 10 – Information revealed by indicative prices

This table presents the result of OLS regression of the returns from the previous trading session to the next trading session onto the returns from the previous trading session to the first part of the preopening period. The return at date t is computed as the difference between the price at date t and the price at date t -1, divided by the price at date t-1. Only the days with a non-null trading volume are considered. The number of observations is consequently not the same for all the stocks. The data is conditional on the existence of indicative prices in the first part of the preopening period. This further reduces the number of observations. P-values are reported in parenthesis.

Number of Intercept alpha 1 Coefficient beta 1 R² Observations BICC 0.0052 0.9736 0.79 20 (0.33) (0.00) BLHC -0.0021 0.0234 0.00 45 (0.09) (0.73) CIEC -0.0036 0.1362 0.01 62 (0.53) (0.36) PALC -0.0175 0.4496 0.45 10 (0.13) (0.03) SGBC -0.0680 0.5485 0.44 8 (0.10) (0.07) SHEC -0.0026 -0.0154 0.00 54 (0.07) (0.93) SNTS 0.0001 0.4871 0.33 69 (0.97) (0.00) STBC -0.0012 0.8795 0.27 26 (0.59) (0.01)

49 Table 11 – Information incorporated in transaction prices

This table presents the result of OLS regression of the returns from the previous trading session to the next trading session onto the returns from the previous trading session to the current trading session. The return at date t is computed as the difference between the price at date t and the price at date t-1, divided by the price at date t-1. Only the days with a non-null trading volume are considered. The number of observations is consequently not the same for all the stocks. The data is conditional on the existence of indicative prices in the first part of the preopening period. This further reduces the number of observations. P-values are reported in parenthesis.

Number of Intercept alpha Coefficient beta R² Observations BICC -0.0052 0.9736 0.79 20 (0.33) (0.00) BLHC -0.0011 0.8329 0.31 45 (0.28) (0.00) CIEC -0.0029 1.2653 0.56 62 (0.44) (0.00) PALC -0.0141 0.5556 0.52 10 (0.17) (0.01) SGBC 0.0297 1.4906 0.83 8 (0.10) (0.00) SHEC -0.0026 0.3374 0.09 54 (0.05) (0.03) SNTS -0.0008 0.8296 0.42 69 (0.60) (0.00) STBC -0.0001 1.1069 0.85 26 (0.95) (0.00)

50 Figure 1 – Structure of the uncertainty of a trading period t

This figure represents the structure of the uncertainty underlying each period t of the trading game, with tÎ(0,1,2,…). The random variables are independent and identically distributed across periods. V is the final value of the asset V. E is the endowment of the insider. S1 and S2 are his two private signals.

p S2=H E=Q l 1-p S2=L S1=H p S2=H p 1-l E=0 1-p S2=L V=u p S2=H 1-p E=Q l 1-p S2=L S1=L p p S2=H 1-l E=0 1-p S2=L

1-p S2=H E=Q l p 1- p S2=L S1=H 1-p S2=H 1-p 1-l E=0 p S2=L V=d 1-p S2=H p E=Q l p S2=L S1=L 1-p S2=H 1-l E=0 p S2=L

51 Figure 2 – Timing of trading period t

This figure represents the timing of one trading period t with tÎ(0,1,2,…). The final value of the asset V is a random variable that takes the value u with probability p, and the value d with probability 1-p. The endowment E is a random variable that takes the value Q with probability l, and the value 0 with probability 1 -l. When V=u, signal Si, where iÎ{1,2}, takes the value H with probability p and the value L with probability 1-p. S1 and S2 are independent. If there is no preopening period, the outsider cannot observe the non-binding limit order (qA,PA). To enter the market, the outsider has to pay a cost c. At the trading stage, the insider submits an order (q,P) to exchange q shares at a limit price P. We consider that the outsider cannot observe the realization of each signal individually. She can only observe on of the following three joint realizations: HH, LL , and HL.

•Insider receives Preopening •Outsider decides Trading: •V is publicly endowment E period(if any): whether or not to revealed and •Insider submits a enter the market consumption •Insider observes Insider submits a limit order (q,P) and pay the cost c occurs signal S1 non-binding limit •After observing order (q ,P ) •Insider receives •Outsider observes A A (q,P), Outsider if signal S2 the joint she entered realization of the submits a market signals S1 and S2 order to trade m with probability g units of the asset

52 Figure 3 – Volume and Price over the 141 trading sessions in our sample

Panel A – BICC Panel B – BLHC

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trading volume transaction price trading volume transaction price

Panel C – CIEC Panel D – PALM

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trading volume transaction price trading volume transaction price

53 Figure 3 (continued) – Volume and Price over the 141 trading sessions in our sample

Panel E – SGBC Panel F – SHEC

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trading volume transaction price trading volume transaction price

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trading volume transaction price trading volume transaction price

54 Figure 4 – Large orders during the preopening period

This figure represents the distribution of large orders (i.e. orders pertaining to the 4th and 3rd size quartiles) over the four time qua rtiles of the preopening period. It also indicates the amount of orders executed in each time quartile. The numbers are averages across stocks, and across the 2 size quartiles.

30%

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0% 1st Time Quartile 2nd Time Quartile 3rd Time Quartile 4th Time Quartile

proportion of orders executed proportion of the large orders placed in the various time quartiles

55