Fragmentation, Consolidation and

Competition for Listings

by

Marc L. Lipson

Department of Banking and FinanceTerry College of Business

University of GeorgiaAthens GA 30602-6253(706) 542-3644 (Phone)(706) 542-9434 (Fax)

mlipson@uga.edu

I am grateful to seminar participants at the Dealer Markets Conference at OhioState University, Georgia State University, and the University of Georgia foruseful suggestions and Maureen O’Hara for her suggestions while discussingthe paper at the 1998 American Finance Association Meetings. I wish to thankShane Corwin, Larry Glosten, Michael Goldstein, Jason Greene, Jeff Harris,Charles Jones, Gene Kandel, Jeff Netter, Annette Poulsen, Joe Sinkey, andWilliam Wilhelm for their invaluable comments. All remaining flaws are myresponsibility.

Fragmentation, Consolidationand Competition for Listings

Abstract

We contrast the liquidity of consolidated (auction) and fragmented (dealer)market structures in the presence of informed traders and price-sensitiveliquidity traders. In contrast to previous research, we identify conditions underwhich reduced consolidation leads to lower average trading costs for aparticular security. The essential intuition is that fragmentation enables large-volume liquidity traders to more easily work orders, and this may increasetrading activity enough to offset costs arising from increased informed trading.Our results suggest a link between listing decisions and characteristics oflisted assets that provides a potential explanation for typical listing patterns.Interestingly, the ability of fragmented markets to compete requires a certainminimum cost for small-volume traders to work an order. This suggests thattechnological advances that reduce trading costs may lead to the elimination ofdealer markets.

1

Fragmentation, Consolidationand Competition for Listings

Despite a growing consensus that consolidated market structures

enhance market liquidity, all securities do not trade on consolidated markets.1

For example, while the New York Stock Exchange (NYSE) provides a centralized

auction environment, the Nasdaq fragments order flow across multiple dealers.

Furthermore, consistent patterns in equity listing decisions suggest that listing

firms are neither indifferent between market structures nor universally

predisposed to select consolidated ones.2

We contrast consolidated (auction) markets and fragmented (dealer)

markets in a model with competitive market makers and price-sensitive

liquidity demand.3 We identify conditions under which a fragmented market

provides a lower average trading cost for a particular security than does a

consolidated market. For firms whose central concern is reducing capital costs

1 For recent discussions of consolidation, see Biais (1993), Lyons (1996), Board and Sutcliffe(1995), Madhavan (1995), Franks and Schaefer (1995), Pagano and Röell (1996), and the SECMarket 2000 Study, Chapter IV-1.2 See Baker and Meeks (1991), Cowan, Carter, Dark, and Singh (1992), Kadlec and McConnell(1994), McConnell, Dybevik, Haushalter, and Lie (1996), Corwin and Harris (1999), andAggarwal and Angel (1999) for discussions of domestic and international listing patterns.3 Early theoretical papers comparing market structures, such as Glosten (1989), Benveniste,Marcus and Wilhelm (1992), and Leach and Madhavan (1993), typically contrast monopolisticand competitive market-making in the context of single-dealer (consolidated) and multiple-dealer (fragmented) market structures. We follow recent work by Madhavan (1995) andPagano and Röell (1996), among others, and assume perfect competition and distinguishthese markets strictly on information structure.

2

by maximizing the liquidity of their shares, the optimal listing choice in this

case may be a dealer market.

The intuition that drives our analysis is the following. Since informed

traders prefer to trade large amounts, consolidation enables market makers to

better identify informed trading and reduce their losses to those traders. In a

competitive market, this translates into lower average trading costs.4 However,

since the trading patterns of large-volume liquidity traders, such as

institutional traders, are similar to those of informed traders, market makers

cannot distinguish perfectly between these liquidity trades and informed

trades. Thus, trading costs for large-volume liquidity traders are higher in a

consolidated market than in a fragmented market.5 Our model suggests that

when the trading activity of large-volume liquidity traders is decreasing in

trading costs, a fragmented market may increase trading activity by an amount

sufficient to reduce average trading costs even with increased informed trading.

Our model provides a number of important results. First, we provide an

explanation for the existence of fragmented markets despite the apparent

benefits of consolidation. Our explanation differs from those offered by

Aggarwal and Angel (1996), Angel (1997) and Schultz (1999), who emphasize

4 This effect has been highlighted by Pagano and Röell (1996) who compare a variety ofauction (consolidated) and dealer market (fragmented) structures and conclude thatconsolidated markets provide identical or lower average trading costs.5 This result is typical result in frameworks where market makers set prices contingent onobserved order flow. For example, similar distributions of trading costs are observed in Easleyand O’Hara (1987) and Madhavan (1995). In addition, Bloomfield and O’Hara (1999) presentexperimental market evidence that suggests that increased disclosure (consolidation) benefitsmarket makers at the expense of both liquidity traders and informed traders.

3

the role market makers play in promoting a security. Second, we establish a

link between firm characteristics and optimal listing choices that may help

explain commonly observed listing patterns. For example, our results are

consistent with Corwin and Harris (1999) who find that firm characteristics

affect the initial listing choice of firms that can list on either the NYSE or the

Nasdaq. Third, we show how alternative management objectives might affect

listing choices. For example, firms that wish to facilitate insider trading would

prefer a dealer market. Finally, we discuss the effects of changes in trading

technology on market competition. In particular, the success of fragmented

markets requires a minimum cost for small-volume liquidity traders to trade

strategically. This suggests that improvements in trading technology that

reduce trading costs for small-volume traders may eliminate dealer markets.

Since we do not model the source of trader demands or the effects of

trading in one security on the trading of other securities, we cannot identify an

optimal public policy toward market systems. For example, it is entirely

possible that an economy where all assets trade on consolidated markets

minimizes total trading costs. However, our results do provide one important

regulatory insight – even if an economy of consolidated markets is optimal, one

cannot rely on competition between exchanges to eliminate fragmentation.

Our analysis is closely related to that of Madhavan (1995). That paper

explores competition between dealers and their willingness to voluntarily report

4

executed order flow.6 The central result is that dealers may, in fact, report

trades in the absence of requirements to do so. In other words, even if there

were only fragmented markets, consolidated markets can naturally arise. Our

paper, on the other hand, explores competition between exchanges in the

presence of price sensitive liquidity demand. Our central result is that

fragmented markets can compete successfully. In other words, even if there

were only consolidated markets, fragmented markets can naturally arise.

This paper is organized as follows. Section 1 presents the basic model,

specifies an equilibrium for each market structure, and characterizes optimal

listing choices. Section 2 discusses the implications of the model and links the

model to commonly observed characteristics of markets. Section 3 summarizes

our analysis and results.

1. Basic Model

This paper examines a market where potential buyers and sellers trade

assets in either a consolidated (auction) market or in a fragmented (multiple

dealer) market. All dealers set competitive prices contingent on observed order

flows. Trading takes place during a single period and all agents are assumed to

6 Note that our paper and Madhavan (1995) consider consolidation as it applies to the tradesof all market participants equally. Madhavan (1996) and Lyons (1996) consider the effects ofrevealing the demand by liquidity traders prior to trading in an asset. Specifically, Madhavan(1996) examines the effects of revealing order imbalances prior to trading and demonstratesthat volatility and trading costs may actually increase. The intuition is similar to that ofHirshleifer (1971) who pointed out that revealing individual demands before trading mayimpede optimal risk sharing. Lyons (1996) makes the risk sharing/consolidation argumentand explicitly considers foreign exchange markets. Admati and Pfleiderer (1991) make asimilar observation in a model of sunshine trading - those who pre-announce trade sizes mayobtain lower trading costs at the expense of those who cannot pre-announce.

5

be risk neutral. Our model is identical to Easley and O’Hara (1987) except we

also examine trading in a multiple dealer market and we assume discretionary

(price-sensitive) liquidity trading.

The value of each traded asset i, denoted Vi, is revealed at the end of

trading and takes the value V ViH

i= +0 σ or V ViL

i= −0 σ with equal probability.

Thus, V0 is the unconditional value of every asset and σi is the standard

deviation of terminal value payoffs for asset i, which we refer to as the payoff’s

dispersion.7 Variation in dispersions captured by i may reflect different assets

at the same point in time (cross-sectional variation) or the same asset at

different points in time (time-series variation).

At the beginning of trading, one of three types of traders is chosen from a

pool of potential traders to trade in the market. This pool consists informed

traders, who know the payoff value of the asset, large-volume liquidity traders,

who desire to purchase or sell two shares of the asset, and small-volume

liquidity traders, who desire to buy or sell one share. 8 Let µI, µL, and µS denote

the proportion of informed, large-volume and small-volume liquidity traders,

respectively, in the pool of potential traders. Liquidity traders do not know the

payoff value of the asset and their decision to buy or sell is independent of the

7 The unconditional value of the asset does not enter into our results, so we assume the samevalue for all assets and at all time periods without any loss in generality.8 Single share or dual sized trading models of markets were introduced by Glosten andMilgrom (1985) and employed by Easley and O’Hara (1987), Benveniste, Marcus and Wilhelm(1992), Madhavan (1995), Madhavan (1996), and Easley, Kiefer and O’Hara (1997), amongothers. The two trade sizes reflect differences in demand across trader types. We do notexplicitly limit the shares traded by the informed trader since informed trading is implicitlydefined by the trade sizes of the other traders.

6

payoff value. The informed trader buys or sells, based on the asset’s payoff and

quoted prices, to maximize profits. Dealers do not observe the type of trader

placing orders.9 All trades are limited to integer shares.10

We assume the trading activity of large-volume liquidity traders is

decreasing in expected trading costs: they will not trade in an asset where the

expected average execution cost (per share) is greater than cL . We refer to cL as

the reservation price of the large-volume liquidity trader. Price sensitive

liquidity trading is a feature of a number of models (see, for example, Glosten

(1989) or Benveniste, Marcus and Wilhelm (1992)) and reflects the fact that

sophisticated traders, such as institutional traders, will concentrate trading

activities where their costs are lowest.11 While large-volume liquidity traders

are likely to be heterogeneous in their reservation trading cost, suggesting that

demand would be a declining function of price, our simple model is analytically

tractable and conveys the essential intuition.

9 Often the very same institutions who might trade on privately generated information at onetime will trade for liquidity reasons another. Long term relations between dealers and tradersmay mitigate, to some extent, the inability of dealers to distinguish between these motives(see Benveniste, Marcus and Wilhelm (1992)). However, the significant adverse selection costof trading found in Glosten and Harris (1988), Stoll (1989), George, Kaul and Nimalendran(1991), Afflect-Graves, Hedge, and Miller (1994), Huang and Stoll (1996), and Jones andLipson (1999a), among others, suggest that dealers are not completely successful atdistinguishing between these motives.10 In a later section we discuss in detail variations on the volume of demand by traders andlimits on the size of executed orders. We also examine the effects of fixed trading costsassociated with submitting orders. The initial formulation is the simplest model forillustrating our results.11 For example, Wall Street Journal articles on June 6, 1997 and June 30, 1997, discussed theshift in institutional trading to more liquid assets as execution costs increased during the lastthree years.

7

When large-volume liquidity traders do not trade the asset, a trader is

selected from the remaining population of traders: the small-volume liquidity

traders and informed traders. 12 We use µ S and µ I to denote the proportion of

small-volume and informed traders, respectively, which are in the pool of

traders when large-volume liquidity traders are not.

The consolidated and fragmented markets are structured as follows. In

each market, dealers post competitive quotes contingent on the size of the

order placed by a trader. In the consolidated market, traders execute their

order with a single dealer who, therefore, observes the total order flow. In the

fragmented market, there are two dealers. Traders can either trade at a single

dealer or split their order between dealers. The critical distinction between

these markets is the information set available to dealers for setting prices - in a

fragmented market only a portion of the order flow is observed by each dealer.

1.1. Notation and Equilibria

In this section, we characterize sub-game perfect Bayesian equilibria for

the trading environment and market structures described above. This requires

that all strategies are optimal in every trading round, given the strategies of

other players and the beliefs of the dealers, and that dealers’ beliefs are

12 There may be a link between the decision of large-volume liquidity traders to trade in themarket and the number of small-volume liquidity traders in the market besides that impliedby trading costs. For example, if large-volume (institutional) traders draw analysts to anasset, small-volume liquidity trading may be associated with large-volume trading. Most ofour results do not rely on the pool of traders remaining constant, they only require that thelikelihood of an informed trader being chosen increases when liquidity traders leave themarket. Thus, any positive correlation between large-volume and small-volume liquiditytrading would strengthen our results.

8

updated whenever possible using Bayes’ rule (conditioning on the specified

strategies). In essence, this equilibrium concept requires that dealers set

quotes that are ex-post rational.

Let pS and pL denote the prices quoted for orders of a single share (small)

and two shares (large), respectively. To characterize the equilibrium behavior

of the large-volume liquidity trader, let σ T and σ F denote the values of σ at

which the effective trading costs for large-volume liquidity traders (assuming

they remain in the market) would be equal to cL for the consolidated and

fragmented market structures, respectively. We must distinguish between the

two markets since trading costs for large-volume liquidity traders will vary

across market structures.

An interesting feature of this model, discussed in detail in Easley and

O’Hara (1987), concerns the optimal strategy of the informed trader. In

general, we would expect the informed trader, who profits on every trade, to

prefer large trades over small trades, all else equal. However, all else will not

generally be equal. Since the prices charged by dealers reflect the likelihood

they are trading with informed traders, the cost of establishing large positions

will be greater than cost of establishing smaller positions. The informed trader

must therefore consider the net profits of executing large or small orders. We

demonstrate in the Appendix that informed traders will strictly prefer to

execute large orders when µL > µI , and will randomly mix between large and

small orders otherwise. While the Appendix considers both cases, we restrict

9

our discussion to the case where informed traders submit both order sizes.

Both cases yield identical qualitative results.

Equilibrium prices are developed as follows. For each trading pattern,

and conditioning on the beliefs of the dealer, we calculate the probability of

executing a trade when the payoff of the asset is ViH and when it is Vi

L , and

then calculate the zero profit prices charged by the dealers. Since our market

structure is symmetric with respect to the payoffs of the asset, we limit our

analysis to market buys. The prices charged by dealers are expressed as the

unconditional value of the asset plus the product of the asset’s dispersion and

a term which is exactly equal to the conditional probability of trading with an

informed trader. Thus, prices explicitly describe the dealer’s updated beliefs

and we do not restate these beliefs in the equilibria. A detailed discussion of

these beliefs, particularly for out of equilibrium path events, is given in the

appendix along with all proofs of propositions.

Proposition 1 (Consolidated Market Equilibrium)There exists an equilibrium in the consolidated market with the followingstrategies:Dealer Strategy (Prices)

σ σiT≤ σ σi

T> Small orders V I L i

0 + −( )µ µ σ V I i0 + µ σ

Large order V I S i0 1

2+ +( )µ µ σ V i0 + σ

where σ µ µTL I Sc= +/ ( )1

2

Trader Strategies (Orders) Small-Volume Submit a small order

10

Large-Volume Submit a large order if σ σiT≤ , submit no order

otherwise Informed Submit a large order with probability

φ µ µ µ µ µ µ µ µ= + +( ) / ( )L S I L I S I L2 2 and submit asmall order otherwise.

A number of features of these results are worth noting. Since there is a

positive probability of trading with an informed trader, all prices exceed the

unconditional value of the asset. The underlying intuition, developed by

Glosten and Milgrom(1985) and Glosten (1987), is that dealers will condition

their prices on the order itself, charging more for a market buy and paying less

for a market sell. In general, this gives rise to bid-ask spreads even when there

are no inventory or order processing costs.

This equilibrium is essentially that described by Easley and O’Hara

(1987) and, therefore, we observe that prices charged for large orders always

exceeds the price charge for small orders.13 The underlying intuition is that

informed trader prefers to trade larger amounts. Notice that prices rise when

large-volume traders exit the market. This can be shown since the proportion

of informed traders, whose numbers remain constant, will rise when the

number of large-volume liquidity traders declines (i.e. µ µI I> ) and since

µ µI S+ 12 is strictly less than one. Notice also that the price charged for large

13 It might seem odd that the price for small orders depends on the proportion of large-volumeliquidity traders and the price for large orders depends on the proportion of small-volumeliquidity traders. However, this follows naturally from the fact that prices are determined bythe probability an informed trader submits each order size, and, as usual with mixedstrategies, the probabilities of a given action is determined by the payoffs of the alternative.Also, the possibility of negative prices for small orders is ruled out since we are presenting

11

orders when large-volume traders do not trade the asset is set to ViH , reflecting

the fact that only informed traders remain to submit large orders.

For the fragmented market we have an analogous proposition:14

Proposition 2 (Fragmented Market Equilibrium)There exists an equilibrium in the fragmented market with the followingstrategies:

Dealer Strategy (Prices)

σ σiF≤ σ σi

F> Small orders

V I

Si

0

121

+−

µµ

σ V I

Si

0

121

+−

µµ

σ

Large order V i0 + σ V i

0 + σwhere σ µ µF

S L Ic= −( ) /1 12

Trader Strategies (Orders) Small-Volume Submit a small order at one dealer Large-Volume Submit a small order at each dealer if σ σi

F≤ ,submit no order otherwise

Informed Submit a small order at each dealer

This equilibrium reflects the ability of large-volume liquidity traders to

work their orders so that they are less easily distinguished from the small-

volume traders. 15 The effect is to pool the trades of both liquidity trader types

and more evenly distribute the costs associated with informed trading.

Specifically, the large-volume liquidity trader executes a small order at each of

equilibrium for the case where informed traders submit both large and small orders - the casewhere µL ≤ µI .14 Note that we assume that the large-volume liquidity trader submits single share orders ateach of the dealers. One can easily construct and equilibrium where the large-volume tradersubmits large orders at only one of the dealers and the informed, once again, randomlychooses whether to submit small or large orders. The resulting costs for all traders areidentical to that in the equilibrium above.

12

the dealers. Note that the price on large orders is set to ViH since large-volume

traders do not trade those orders. The beliefs of dealers which give rise to that

pricing are discussed in the Appendix.

The fragmented market structure also allows informed traders to execute

greater volume. For example, when only informed and small-volume liquidity

traders are in the market, the informed traders trade two shares in a

fragmented market (one at each dealer), whereas they would be limited to one

share in a consolidated market.

1.2. Average Trading Costs and Optimal Listing Choices

We have shown that differences in market design can alter the trading

costs and the equilibrium behavior of traders. These differences will also affect

average trading costs and allow us to explore the optimal listing decisions of

listing firms. In fact, one of the contributions of this paper is to explicitly link

listing choices to characteristics of both listed assets and market designs.

Since asset values are related to asset liquidity (Amihud and Mendelson

(1986)), we assume the objective of the listing organization (the firm) is to

minimize average trading costs. Specifically, we assume the firm lists the asset

on the market structure where the expected trading costs of liquidity traders is

lowest. Of course, our model allows us to consider other objectives and these

are discussed later.

15 Economides and Schwartz (1995), Chan and Lakonishok (1993), Keim and Madhavan (1995)and Jones and Lipson (1999b) all present evidence that institutions regularly execute ordersin multiple trades, either through multiple brokers or over time.

13

We define trading costs as follows. Given that V0 is the ex-ante value of

the asset (as well as the long run average ex-post value of the asset), this

represents an appropriate benchmark for evaluating execution costs. We

therefore calculate the expected trading costs as the difference between

expected execution prices and V0. This cost is, essentially, the long run cost to

the trader of either buying or selling a share of the asset, given the market in

which the asset is traded and the equilibrium behavior of market participants.

Using this definition, and weighting costs by expected volume (details in

the appendix), we find that average trading costs in a consolidated market are

µ σI i when Tt σσ ≤ and µ σI i otherwise. On the fragmented market, average

trading costs are equal to µ

µσI

Si1 1

2− when σ σt

F≤ and µ

µσI

Si1 1

2− otherwise.

Consistent with the results of Pagano and Röell (1996), trading costs are lower

in the consolidated market when we hold constant the number of traders. This

illustrates the traditional view of consolidation - it facilitates the identification

of informed trading and reduces transaction costs. Clearly, if all traders bear

these costs equally, then a consolidated market is superior even if traders are

price sensitive. However, these costs will not be born equally by all traders if

the trading patterns of some traders are more similar to those of informed

traders than others. Price sensitive trading will therefore impact the

equilibrium number of traders in a market.

We have shown that trading costs rise when large-volume trading

decreases. What is essential to our analysis is the following. Since the large-

14

volume liquidity traders pay higher prices in a consolidated market, they will

reach their reservation price for lower levels of dispersion than on a fragmented

market. When they reach that point, average prices on the consolidated

market will rise. In some cases, the resulting average costs exceed those of a

fragmented market. In other cases, they do not. These two cases are

distinguished in the following proposition, which identifies the optimal listing

decision for an asset given its dispersion.

Proposition 3 (Optimal Listing Decision):The optimal listing decision for asset i as a function of the asset’sdispersion is the following:

(i) σ σiT< Consolidated Market

(iia) σ σ σ µ µTi

FS Land≤ < < 2 Fragmented Market

(iib) σ σ σ µ µTi

FI Land≤ < ≥ 2 Consolidated Market

(iii) σ σiF≥ Consolidated Market

The intuition underlying each of the cases in proposition 3 follow directly

from our earlier discussion. In case (i), all traders are present in the market.

In this case, consolidated market structures are optimal for the reasons

commonly given - consolidation reduces the profitability of informed trading.

In both case (iia) and (iib), we observe the decrease in liquidity brought about

by the decision of large-volume liquidity traders to reduce trading activity - in

case (iia) this reduction is sufficient that fragmented markets are preferred,

while in case (iib), the reduction is costly, but the advantage of consolidation

dominates the cost. Case (iii) is essentially like case (i), but large-volume

liquidity traders are not trading in either market.

15

Proposition 3 demonstrates that reduced consolidation provides the

lowest level of trading costs (highest liquidity) under some circumstances.

Most importantly, our listing decision depends not only on characteristics of

the markets, but depends as well on an observable characteristic of the asset -

its dispersion. Implications of our model are examined after we discuss a

number issues related to modeling decisions.

1.3. Robustness of results

There are two aspects of our model that drive our central results. First,

large-volume liquidity traders bear a greater proportion of trading loses to

informed traders than do small-volume traders in a consolidated market.

Second, the trading activity of some traders is decreasing in trading costs.

Taken together, these two characteristics suggest that allowing price sensitive

traders to more easily work their orders, their trading activity may rise enough

to offset any additional losses that arise from increased informed trading. This

section considers how changes in our model would impact our results,

discusses results for variations on the basic model, and highlights the critical

limitations of the model as presented.

Any model that exhibits the two characteristics just described may

provide cases where fragmented markets are superior. For example, Madhavan

(1995) presents a two period model where large-volume liquidity traders trade

both periods and small-volume liquidity traders enter the market for just one

period. Contrasting consolidated and fragmented markets, he shows that

trading costs of large-volume traders and informed traders are both reduced in

16

a fragmented market. If we add price sensitive liquidity trading, then results

similar to those presented here are likely to follow, suggesting that the intuition

derived in this paper is not an artifact of the particular model considered.

Our model relies on the assumption that large-volume liquidity traders

will take advantage of market fragmentation and work their orders into the

order flow of small-volume liquidity traders. This trading strategy is bound to

generate additional trading costs. However, since institutions regularly split

orders between brokers and also establish positions over time (see Economides

and Schwartz (1995), Chan and Lakonishok (1993), Keim and Madhavan

(1995) and Jones and Lipson (1999b)), the benefits appear to exceed the costs.

On the other hand, since all orders are not worked, these costs certainly exist.

In the context of our model, very large fixed costs would offset any advantages

to “working” orders and fragmented markets would not be beneficial.

A related, and more important, point is that we also implicitly rely on the

assumption that small-volume liquidity traders do not also work their orders

and behave strategically. In fact, it can be shown that if we allow small-volume

liquidity traders split their orders between dealers, they can avoid pooling with

large-volume traders. If trading takes place over time, as in Admati and

Pfleiderer (1988), Madhavan (1995), and Foster and Viswanathan (1990), one

can assume that small-volume traders have limited flexibility in timing their

trades. This assumption has been used to justify the decline in volume after

the open of trade. In the model we present, however, a necessary condition for

fragmented markets to be successful is some minimum marginal costs

17

associated with working an order. For example, this could be the fixed cost of

submitting an order since the marginal cost of working an order in our model

is submitting a second order. The Appendix presents an equilibrium for the

fragmented market where small-volume traders can work their orders. It

specifies a minimum marginal cost to small-volume traders for working an

order.

The fact that fixed trading costs play a role in supporting the competitive

capabilities of fragmented markets is and important point, and not a limitation

of the model. It illustrates how a market friction can affect competition in the

market for exchange services. Furthermore, it adds to the predictive ability of

the model. For example, as trading costs continue to decline with

improvements in connective technologies, we would expect fragmented (dealer)

markets to become less viable. In fact, it would appear that the very

technologies that facilitate multiple dealer markets might, in the end, lead to

their extinction.

Numerous changes can be accommodated within the basic structure of

our model. For example, the assumption that large-volume traders desire to

trade exactly twice the volume of the small-volume trader can be relaxed. In

this case, the large-volume liquidity trader trades one share at one dealer and

more or less than one share at the other, effectively creating “large” and “small”

orders on the fragmented market. This model, in which informed traders may

once again randomize between order sizes, retains the qualitative results

18

presented here. The critical effect is that some portion of the large-volume

trading activity is pooled with small-volume traders.

We have assumed that large-volume liquidity traders do not trade in a

stock if the execution costs exceed their limiting level. Our model can easily

accommodate the case where large-volume traders would trade only a single

share if the costs for trading two shares exceed their limit. The requirement for

our results is simply that there is some reduction in trading volume and this

raises the average cost.

One can adjust the number of dealers and obtain a richer set of results.

For example, additional dealers will provide additional venues for traders to

work orders. This will clearly benefit informed traders. It will also benefit

large-volume liquidity traders who desire to sell more than two shares.

We assumed that small-volume liquidity traders were not price sensitive.

In the next section we consider one possible result of relaxing this restriction.

In general, combining variations in price sensitivity with differences in trading

costs across market structures will provide a rich environment for considering

market design issues and may yield results which challenge standard

assumptions of market superiority. The exact results will depend on the

assumptions and provides useful directions for additional study. In general,

since our contribution is to identify ranges of parameters over which certain

behavior is observed, our results are likely to be robust to modest

perturbations of the assumptions.

19

2. Implications and Discussion

This section examines a few implications of our model and draws

attention to some empirical features of existing and historical markets that can

be readily explained in the context of the model.

2.1. Policy Implications

It is important to note that our analysis is a partial equilibrium analysis.

For example, we do not consider the important question of how large-volume

liquidity traders reallocate their trading activities across various securities. It

is entirely possible (if not likely given the work of Pagano and Röell (1996),

among others) that an economy where all securities trade on consolidated

markets would minimize informed trading and therefore minimize total trading

costs.

What we point out is that it may be profitable for an exchange to offer a

fragmented market to trade some securities. Specifically, a fragmented market

may very well be able to attract listings by providing lower average trading

costs for a given listing prospect than a consolidated market. In this sense, our

model captures an important potential method of competition between

exchanges and complements the recent work by Parlour and Seppi (1998) and

Foucault and Parlour (1998). Parlour and Seppi (1998) examine competition

between exchanges for order flow and explore the co-existence of various

market structures in equilibrium. Foucault and Parlour (1998) explore

competition between exchanges in their combinations of listing fees and

trading costs.

20

Another interesting question is whether fragmentation might be

beneficial under some circumstances. We provide one example by examining

the possibility that even small-volume liquidity traders may be sensitive to

execution prices. Specifically, let cS denote the average trading costs above

which even small-volume liquidity traders do not trade the asset - the

reservation price for small-volume traders. Following the same analysis as in

the previous section, we obtain the following proposition.

Proposition 4 (Existence of only Fragmented Market Structures)Consider a σi , cL , and cS such that

(a)µ

µσ µ µ σI

Si L I S ic

1 12

12−

< < +( )

(b)µ

µσ µ

µ µσI

Si S

I

I Sic

1 12−

< <+

then there exists no equilibrium in the consolidated market where liquiditytraders trade, while there exists an equilibrium in the fragmented marketwhere both large-volume and small-volume liquidity traders trade.

As shown before, the reservation price for large-volume liquidity traders

will be exceeded earlier on a consolidated market than a fragmented market.

When this happens, the trading costs for small-volume liquidity traders rises

on the consolidated market and may even exceed the cost for small-volume

traders in a fragmented market. If this is the case, there exist reservation

prices for the small-volume traders such that they would not trade on the

consolidated market but would trade on a fragmented market.

21

Under the conditions in proposition 4, the consolidated market is

essentially a market where only the informed traders would ever trade (and

even they are indifferent since their profits are zero). 16 On the other hand, the

fragmented market sets prices as originally shown in proposition 2. These

results suggest that there are conditions under which, for certain assets, only a

fragmented market can sustain meaningful trading in the asset.17 The

essential lesson is that perhaps the cross subsidy of trading costs implemented

by fragmentation (the transfer in costs from larger to smaller traders) is

something that can be beneficial to certain listing firms at certain points in

their development.

2.2. Alternative Listing Objectives

We initially assumed a firm’s objective is to minimize average trading

costs. However, alternative objectives can also be considered. For example, a

fragmented market generally benefits informed traders. Given that there must

be returns to information gathering to have informationally efficient prices

(Grossman and Stiglitz (1980)) and under some conditions allowing insider

trading increases either total welfare or firm value (Leland (1992) and Khanna,

16 A consolidated market still exists, of course, but only in the technical sense that thereexists a price at which a dealer would be willing to trade. This price exists only because wehave a finite (two point) distribution for asset payoffs. Benveniste, Marcus and Wilhelm(1992) present a model with price sensitive trading and similarly discount the existence ofcorner solution equilibria. In Glosten (1989) asset distributions are continuous and no pricefunction exists.17 This result contrasts that of Glosten (1989), who argues that a monopolist specialist marketcan remain open where a competitive fragmented market may not. His argues that specialistscan smooth out earnings over time by taking losses at one point (when adverse selection is

22

Slezak and Bradley (1994)), a fragmented market may be optimal even in those

situations where it has greater average trading costs.18

Of course, a manager who profits from insider trading and makes listing

choices, may also choose a fragmented market simply to increase his or her

own profits. Also, if the firm wishes to provide low trading costs for individuals

who establish their own positions (as opposed to individuals who have invested

in pension funds, mutual funds and other institutions), a consolidated market

is preferred. Similarly, a firm that wishes to attract institutional traders would

prefer a fragmented market. The point is that our model identifies significant

links between governance structures, welfare, and listing decisions.

2.3. Empirical Observations

One of the difficulties with abstract theories is that the distribution of

parameters is generally unknown. In our model, for example, the distribution

of asset dispersions will determine how many firms would prefer to list on one

market structure rather than another, or how changes in parameters will affect

the distribution of firms across market structures. For this reason we cannot

make predictive statements as to what should be observed in practice.

However, we can describe how observed behaviors can be explained in the

great and markets would therefore collapse) and obtaining offsetting profits from liquiditytraders at another point (when adverse selection is low).18 The need to consider informed trading in the context of market structure has recently beenpointed out by Schnitzlein (1996), who explores informed trading and market structures inexperimental markets.

23

context of the model and provide either new explanations for common empirical

observations or, in some cases, explanations where none are available.

Listing Decisions

Consider the fact that firms regularly switch from the Nasdaq (a

fragmented market structure) to the NYSE or AMEX (consolidated specialist

markets). This “one way street” has often been attributed to the NYSE’s rule

500, which limited the ability of firms to change listings. It may also simply be

due to the choice of listing requirements (see Foucault and Parlour (1998) and

Corwin and Harris (1999)) or the need for newly public firms to be promoted

(Aggarwal and Angel (1996) and Angel (1997)).

Our model suggests an additional factor. If dispersion in payoffs is

generally decreasing over time, then a firm which finds itself originally in

condition (iia) of proposition 3 (and therefore listed on the Nasdaq), will

eventually satisfy condition (i) and change listings (to the AMEX or NYSE) and

is unlikely to return to the Nasdaq since dramatic reductions in size (increases

in dispersion) are uncommon. In our model, therefore, the change in listings is

a natural result of changes in the nature of the listing asset and not a result of

institutional constraints. In this respect, our results are consistent with Chan

and Lakonishok (1997) who find that trading costs are lower on the Nasdaq

than on the NYSE for small firms while the reverse is true for large firms. They

are also consistent with Corwin and Harris (1999) who find that riskier firms

list on Nasdaq.

24

An interesting implication of our model is that the exchanges may, in

fact, set their listing requirements so that they attract only the firms that

would be best traded on the exchange. Furthermore, as rule 500 is relaxed

and it is easier for firms to leave the NYSE for the Nasdaq, we would expect

little movement away from the NYSE. Those firms that do move, we would

expect to be the more volatile firms.

Finally, attention has often focused on changes in spreads when firms

change listings. Specifically, Christie and Huang (1994) document reductions

in effective spreads when firms changed to the national exchanges from the

Nasdaq, and Christie and Schultz (1994), Christie, Harris and Schultz (1994),

and Dutta and Madhavan (1997) suggest that the drop in spreads is due to less

that perfectly competitive behavior on the Nasdaq. Our model provides an

alternative explanation.

Specifically, if there are costs to switching listings, a firm on the Nasdaq

may wait until it is quite sure that circumstances have changed sufficiently

(expected future dispersion is sufficiently low) that a switch to the NYSE is

justified. Furthermore, firms will wait until they are confident that they will be

able to meet the NYSE continued listing requirements. The listing change may

therefore occur after the firm has experienced lowered dispersions. In this

case, the drop in spreads is explained by a combination of a delay in changing

listings and the natural decrease in listing costs as firms eventually move to

the appropriate listing market.

Collapse of Small Firm Auction Markets

25

Aggarwal and Angel (1999) discuss the introduction and eventual

collapse of the AMEX Emerging Companies Marketplace and Rasch (1994)

notes the similar collapse of specialized small firm auction markets

internationally. While the authors identify a number of historical and market

structure explanations for this collapse, in the context of our model the

collapse might be explained as follows: the firms targeted by the AMEX and the

specialized markets may have been those firms that required a less

consolidated market structure to attract sufficient liquidity. In effect, the

failure of these markets may have resulted from a mismatch in market design

as well as the scandals that accompanied the AMEX Emerging Companies

Marketplace and the resulting loss in trader confidence.

3. Conclusion

We consider listing decisions in a model with competing market

structures and price-sensitive liquidity trading. We show that, depending on

the relative importance of reducing informed trading profits (by centralizing

information on order flow) or encouraging trading by large liquidity providers

(by reducing their costs of executing large trades), either a fragmented or

consolidated market structure may provide the lowest average trading costs.

This model provides a framework for examining competition between

exchanges as well as providing a theoretical basis for some common listing

patterns. Our model suggests, for example, that competition for listings will

not lead to an economy where all securities trade on consolidated markets.

26

However, sufficient reductions in trading costs for small-volume traders may

eliminate the competitive advantage of fragmented markets.

While there is no doubt that sponsorship of stocks is an important

characteristic of dealer markets and may affect listing patterns (Aggarwal and

Angel (1996), Angel (1997), Schultz (1999)), our model suggests that an

additional factor is uncertainty about firm value. Consistent with our results,

Corwin and Harris (1999) present evidence that firm characteristics (industry

and volatility) affect the initial listing choice of firms that can list both on the

NYSE and Nasdaq. Clearly, additional studies are needed to distinguish the

relative influence of these factors.

27

Appendix

Proposition 1 and 2We present the proof for market buys, market sells are symmetric. In

every case we calculate prices, given equilibrium strategies and beliefs, asfollows. First, we calculate the probability a dealer trades the asset given thefinal payoff is Vi

H (the informed trader buys) and ViL (the informed trader does

not buy). We then solve for the equilibrium price from the zero profit conditionfor dealers.

For example, consider a consolidated market in which the informedtrader submits exclusively large orders. The probability of observing a largemarket buy when the asset value is Vi

H is 1/2 µL + µI : the probability a large-volume trader is chosen times the probability the large-volume trader buys (onehalf) plus the probability an informed trader is chosen (who will certainly buy).The probability of observing a large market buy when the asset value is Vi

L is1/2 µL. Now, given a price for a large order, pL, the dealer’s expected profits,which must equal zero in equilibrium, are

12

12

12

12 0( )( ) ( )( )µ µ µL I L i

HL L i

Lp V p V+ − + − = .

The first term is the probability the payoff value is ViH (one half), times theprobability of trading, times the payoff. The second term is similarly described.Substituting V Vi

Hi= +0 σ and V Vi

Li= −0 σ and solving for pL, we get

VLI

I Li= +

+0 µ

µ µσ

An interesting case is the calculation of prices when the informed tradermixes between large and small orders. When the informed trader submits onlylarge orders, the prices on large orders will exceed those for small orders. Insome cases, total profits (payoff value less price paid times the size of the order)will still be larger with large orders and the informed optimally submits onlylarge orders. Now assume that this is not the case. The informed trader willcertainly not submit only small orders since, if that were the equilibriumstrategy, the price on large orders would be lower than the price on smallorders and the informed would be better off trading a larger amount at evenbetter prices. Hence, the informed must submit both order sizes. For this tobe true, the expected profits from submitting each order size must be equal.From this condition we find the proportion of large orders submitted inequilibrium.

Specifically, let φ denote the probability with which the informed tradersubmits a large order. In a consolidated market where the informed tradermixes order sizes, the probability of observing a large order when the payoffvalue is ViH is 1/2 µL + φµI . The equilibrium prices for large and small ordersare then calculated as described above, with φ undefined. Letting pL and pS

denote the prices for large and small order thus calculated, we set the expected

28

profits from large and small orders equal to each other, 2( ) ( )V p V piH

L iH

S− = − ,and solve for

φ µ µ µ µµ µ µ µ

=++

2

2I L S L

I L S I

This will be less than one so long as µL is less than µI. When φ is greater thanone, the informed trader submits only large orders.

The equilibrium prices for a consolidated market calculated in thismanner, for both cases, are given below. Note that when the large-volumeliquidity trader is not present in the market, only small orders are submitted sono mixing strategy need be calculated

Order µ µL I> µ µL I≤Small V 0 V I L i

0 + −( )µ µ σLarge V I I L i

0 + +[ / ( )]µ µ µ σ V I S i0 1

2+ +( )µ µ σAs would be expected, small orders are executed at better prices than largeorders in both cases. The prices for a fragmented market are given in the text.

The remainder of the proof is to verify that strategies of all players arebest responses to each other and to verify that beliefs are consistent with thegiven strategies. The prices were derived from the trading behaviors using theprocedure just outlined. The trading strategies are optimal given the pricessince (1) large-volume liquidity traders do not trade when the equilibrium priceexceeds cL , (2) small-volume liquidity traders always trade, regardless of thepricing schedule, (3) the informed trader maximizes profits either by submittingexclusively large orders or mixing between orders as described above. Thus, allthe strategies are best responses. The beliefs (prices) of the dealer reflect thetrading strategies of the players and are, therefore, consistent with thosestrategies.

Even though all strategies are consistent with beliefs (prices), in somecases the beliefs are conditioned on actions that are not executed inequilibrium. These “off equilibrium path” beliefs are a source of concern sincethey are generally unconstrained and may determine equilibrium actions. Inthis model, the off equilibrium path beliefs are those associated with thesubmission of large orders in a fragmented market and the submission of largeorders when only small-volume liquidity traders are assumed to be in themarket. We discuss each of these below.

The large-volume trader submits small orders to each of the dealers in afragmented market because the dealer assumes an informed trader submits alarge order and, therefore, the dealer charges a maximum price. While thelarge-volume liquidity trader would never submit only large orders (the spreadon small orders would be zero and the trader would be better off splitting upthe order), one can reformulate the model with large-volume liquidity tradersmixing between large and small orders. One obtains numerical results that areidentical to those derived here. This may seem counter-intuitive, but what

29

happens is the informed trader’s strategy is altered as well, and the resultingequilibrium trading costs are the same.

Now consider beliefs when large-volume traders are not in the market.We determined the cut-off ranges for large-volume traders based on the coststhey would incur if they traded the asset. Above the cut-off, we assume thedealer believes any trades must originate with an informed trader. This beliefcan be relaxed substantially. What is relevant for our analysis is that thereexist no equilibria above the cutoffs in which large-volume traders would trade.The reason is simply that no pricing schedule can be derived which bothassumes large-volume traders trade and also generates trading costs below thecut-off.

Proposition 3This proposition is driven by the average trading costs of liquidity traders.These costs are calculated as follows. First, we calculate the expected tradingvolume of each liquidity trader under the given market conditions. We thencalculate a weighted average price using these expected volumes and subtractthe unconditional value of the asset. For example, let pL and pS denote theprices (per share) for large and small orders in a given market. The expectedtrading volume of each liquidity trader is the probability that the trader ischosen to trade multiplied by the size of the order. The expected trading costwould be equal to

2

2 20µ

µ µµ

µ µL

L SL

S

L SSp p V

( ) ( )++

+−

Proceeding in this manner, the expected trading costs under each marketcondition are shown below. These are used to determine optimal listingchoices.

All LiquidityTraders

Only Small-VolumeLiquidity Traders

Consolidated Market, µ µL I> 2

2

µ µ σµ µ µ µ

I L i

I L L S( )( )+ + µ σI i

Consolidated Market, µ µL I≤µ σI i µ σI i

Fragmented Market 2

2 2

µ σµ µ µ

I i

I L S+ +2

2

µµ µ

I

I S+

Proposition 4This proposition is stated and proved for the case where informed traders mixbetween order sizes. An analogous proposition and proof can be generated for

30

the alternate case. We begin by showing that in the consolidated market thereare no equilibria in which either liquidity trader trades in the market. First,consider whether both large-volume and small-volume liquidity traders wouldtrade in the consolidated market. The equilibrium price schedule given thesebeliefs charge a large-volume liquidity trader

( )µ µ σI S i+ 12 .

However, this exceeds the reservation price for large-volume liquidity traders incondition (a) of the proposition. Now consider whether only small-volumeliquidity traders would trade in this market. Given the equilibrium priceschedule, the small-volume liquidity trader would pay

µ σ µµ µ

σI iI

I Si=

+.

However, this exceeds the reservation price for small-volume liquidity tradersin condition (b) of the proposition. Finally, we consider whether only large-volume liquidity traders would trade in this market. If this were the case, thenthe spread on small orders would be equal to zero and it would be optimal forsmall-volume traders to trade. Thus, there are no equilibria in which liquiditytraders would trade the asset.

For a fragmented market, the parameters are such that an equilibriumidentical to that in Proposition 2 is feasible. In Proposition 2, both liquiditytraders trade in the asset. Finally, it can be shown that each of the twoconditions does not specify null sets and are not mutually exclusive.

Equilibrium with Strategic Small-Volume TradersLet F denote the marginal costs of submitting a second order. This isessentially the fixed cost of submitting any order, though the cost forsubmitting a first order is irrelevant to our analysis. We present below anequilibrium for a Fragmented Market assuming that even small-volumeliquidity traders strategically work orders. Specifically, we assume that small-volume traders can submit very small orders – one half the size of a smallorder.

Fragmented Market Equilibrium

Assume that iS

IF σµ

µ

211 −

> . There exists an equilibrium in the fragmented

market with the following strategies:

31

Dealer Strategy (Prices)

σ σiF≤ σ σi

F> Very small orders 0V 0V Small orders

V I

Si

0

121

+−

µµ

σ V I

Si

0

121

+−

µµ

σ

Large orderiV σ+0 V i

0 + σwhere σ µ µF

S L Ic= −( ) /1 12

Trader Strategies (Orders) Small-Volume Submit a small order at one dealer Large-Volume Submit a small order at each dealer if σ σi

F≤ ,submit no order otherwise

Informed Submit a small order at each dealer

The dealer strategy assumes that an uninformed trader places a very smallorder. However, this is an out of equilibrium path belief since the extra cost ofsubmitting and order exceeds the benefit – i.e. the fixed costs in this caseexceed the spread. Given the choice by the small-volume traders, all the otherbeliefs are rational. Of course, one could specify a number of off-equilibriumpath beliefs and these would determine the perceived benefit for the small-volume liquidity trader for working an order. The belief we have chosen is theone that provides small-volume liquidity traders with the greatest benefit fromworking an order.

32

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