52

Mark D. Flood

Mark D. Flood is an economist at the Federal Reserve Bank ofSt. Louis. David H. Kelly provided research assistance.

Microstructure Theory andthe Foreign Exchange Market

GROWING BODY OF theoretical literature,known as the study of securities market micro-structure, deals with the behavior of participantsin securities markets and with the effects of in-formation and institutional rules on the economicperformance of those markets. These institu-tional factors may arise from technology, tradi-tion or regulation. Microstructure and its impactare important, because of the vast amounts ofwealth which pass through securities markets —

including the foreign exchange market —

every day.

Microstructure is of interest to students of theforeign exchange market: microstructural analy-ses of other markets have yielded insight intotraders’ behavior and the effect of various insti-tutional arrangements. Conversely, the foreign

exchange market is also of special interest tostudents of microstructure, because it combinestwo very different arrangements for matchingbuyers and sellers — bank dealers trade withone another both directly and through foreignexchange brokers.1

Standard models of exchange-rate determina-tion concentrate on relatively long-run aspects,such as purchasing power parity. While micro-structure theory cannot address these issuesdirectly, it can illuminate a more narrowly fo-cused array of institutional concerns, such asprice information, the matching of buyers andsellers, and optimal dealer pricing policies. De-spite the substantial literature on microstructure,little attention has been paid to the particularmicrostructure of the foreign exchange market.2

‘Similar arrangements exist for other securities—for exam-ple, the federal funds market and the secondary marketfor Treasury securities—but these too have been relativelyneglected in the literature.

2The shaded insert on the opposite page provides a contextin which the microstructural approach can be comparedwith more traditional approaches to market efficiency.Following some early articles by Demsetz (1968), Tinic(1972) and Tinic and West (1972), Garman (1976) per-formed the crucial task of defining market microstructureas an independent area of the literature, thus focusing thedebate. Since then, market microstructure has burgeoned,led by Cohen, Maier, Schwartz and Whitcomb (1978a,1978b, 1981, 1983), Amihud and Mendelson (1980, 1986,1988), Stoll (1978, 1985, 1989) and Ho and Stoll (1980,1981). See also Beja and Hakansson (1977), Cohen,Hawawini, Maier, Schwartz and Whitcomb (1980), Cohen,Maier, Ness, Okuda, Schwartz and Whitcomb (1977), Ami-hud, Ho, and Schwartz (1985), Schreiber and Schwartz(1986), Schwartz (1988) and Cohen and Schwartz (1989).

Cohen, Maier, Schwartz and Whitcomb (1979, 1986) andStoll (1985) have surveyed the microstructure literature.In addition to the early note by Allen (1977), very recentlythere have appeared some microstructural studies of theforeign exchange market: Bossaerts and Hillion (1991),Lyons (1991), Rai (1991) and Flood (1991). There is alsoan empirical literature measuring the determinants of thebid-ask spread in the foreign exchange market. See Black(1989), Wei (1991) and Glassman (1987) as well as thereferences therein. Because the focus of this article is onmicrostructure theory, such empirical studies receive littleattention here.Finally, although a consideration of the results of laborato-ry experiments would expand the scope of this paper tounwieldy dimensions, their role in establishing the sensitiv-ity of market behavior to institutional factors must at leastbe acknowledged; see Plott (1982, 1991) for an in-troduction.

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54

This paper examines the extant literature onmarket microstructure to determine how itmight be applied to the foreign exchangemarket.

The paper begins with a brief description ofthe foreign exchange market. Aspects of theliterature concerned with institutional detailsare addressed second, noting how such detailscan affect the performance of the market. Next,the literature dealing with behavioral details, es-pecially the communication and interpretationof price information, is considered. Finally, theinteraction of institutional and behavioral fac-tors, notably the bid-ask spread, is discussed.

INSTITUTIONAL BASICS OF THE

FOREIGN EXCHANGE MARKET

The foreign exchange market is the interna-tional market in which buyers and sellers ofcurrencies “meet.”3 It is largely decentralized:the participants (classified as market-makers,brokers and customers) are physically separatedfrom one another; they communicate via tele-phone, telex and computer network. Tradingvolume is large, estimated at $128.9 billion forthe U.S. market in April 1989. Most of this trad-ing was between bank market-makers.~

The market is dominated by the market-makersat commercial and investment banks, who tradecurrencies with each other both directly andthrough foreign exchange brokers (see figure IL”Market-makers, as the name suggests, “make amarket” in one or more currencies by providingbid and ask prices upon demand. A broker ar-ranges trades by keeping a “book” of market-maker’s limit orders — that is, orders to buy (al-ternatively, to sell) a specified quantity of for-eign currency at a specified price — from whichhe quotes the best bid and ask orders upon re-quest. The best bid and ask quotes on a broker’sbook are together called the broker’s “insidespread.” The other participants in the marketare the customers of the market-making banks,who generally use the market to completetransactions in international trade, and centralbanks, who may enter the market to move ex-

Figure 1Spot Market Volume byTransactor (4/89)

customer(5.1%)

change rates or simply to complete their owninternational transactions. Market-makers maytrade for their own account — that is, they maymaintain a long or short position in a foreigncurrency — and require significant capitalizationfor that purpose. Brokers do not contact cus-tomers and do not deal on their own account;instead, they profit by charging a fee for theservice of bringing market-makers together.

The mechanics of trading differ substantiallybetween brokered transactions and direct deals.In the direct market, banks contact each other.The bank receiving a call acts as a market-makerfor the currency in question, providing a two-way quote (bid and ask) for the bank placingthe call. A direct deal might go as follows:

Mongobank: “Mongobank with a dollar-markplease?”

(Mongobank requests a spot market quotefor U.S. dollars (USD) against German marks(DEM).)

3For more thorough descriptions of the workings of the for-eign exchange market, see Burnham (1991), Chrystal(1984), Kubarych (1983) and Riehl and Rodriguez (1983).

4See Federal Reserve Bank of New York (1989a) and Bankfor International Settlements (815) (1990). Extending thisfigure over 251 trading days per year, this implies a trad-ing volume of roughly $32 trillion for all of 1989. Volume

has roughly doubled every three years for the pastdecade.

5Federal Reserve Bank of New York (l989a) lists 162market-making institutions (148 are commercial banks) and14 brokers; an earlier study, Federal Reserve Bank of NewYork (1980), lists 90 market-making banks and 11 brokers.

‘Interbank Brokered(39.9%)

(55.0%)

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Loans ‘n Things: “20-30”(Loans n’ Things will buy dollars at 2.1020DEM/USD and sell dollars at 2.1030 DEM/USD—the 2.10 part of the quote is understood.)

Mongohank: “Two mine.”(Mongobank buys $2,000,000 for DEM4,206,000 at 2.1030 DEMIUSD, for paymenttwo business days later. The quantity tradedis usually one of a handful of “customaryamounts.”)

Loans ‘n Things: “My marks to Loans ‘nThings Frankfurt.”

(Loans n’ Things requests that payment ofmarks be made to their account at theirFrankfurt branch. Payment will likely bemade via SWIFT.)e

Mongohank: ‘(My dollars to Mongobank NewYork.”

(Mongobank requests that payment of dol-lars be made to them in New York. Paymentwill most likely be made via CHIPS.)7

Spot transactions are made for “value date”(payment date) two business days later to allowsettlement arrangements to be made with cor-respondents or branches in other time zones.This period is extended when a holiday inter-venes in one of the countries involved. Paymentoccurs in a currency’s home country.

The other method of interbank trading isbrokered transactions. Brokers collect limitorders from bank market-makers. A limit orderis an offer to buy (alternatively to sell) a speci-fied quantity at a specified price. I,imit ordersremain with the broker until withdrawn by themarket- maker-

The advantages of brokered trading includethe rapid dissemination of orders to othermarket-makers, anonymity in quoting, and thefreedom not to quote to other market-makerson a reciprocal basis, which can be required inthe direct market. Anonymity allows the quotingbank to conceal its identity and thus its inten-tions; it also requires that the broker know whois an acceptable counterparty for whom. Limit

eThe Society for Worldwide Interbank Financial Telecommu-nication (SWIFT) is an electronic message network. In thiscase, it conveys a standardized payment order to a Ger-man branch or correspondent bank, which, in turn, effectsthe payment as a local interbank transfer in Frankfurt.

~TheClearing House for Interbank Payments System(CHIPS) is a private interbank payments system in NewYork City.

orders are also provided in part as a courtesyto the brokers as part of an ongoing businessrelationship that makes the market more liquid.Because his limit order is often a market-maker’sfirst indication of general price shift, Brookslikens the posting of an order with a broker “tosticking out the chin so as to be acquaintedwith the moment that the fight starts.”8 Schwartzpoints out that posting a limit order extends afree option to other traders.~

A market-maker who calls a broker for a quotegets the broker’s inside spread, along with thequantities of the limit orders. A typical call to abroker might proceed as follows:

Mongoank: “What is sterling, please?”(Mongobank requests the spot quote forU.S. dollars against British pounds (GBP).)

Fonnieister: “1 deal 40-42, one by two.”(Fonmeister Brokerage has quotes to buy£1,000,000 at 1.7440 USD/GBP, and to sell£2,000,000 at 1.7442 USD/GBP)

Mongobank; “I sell one at 40, to whom?”(Mongobank hits the bid for the quantitystated. Mongobank could have requested adifferent amount, which would have re-quired additional confirmation from the bid-ding bank.)

Fonmeisten [A pause while the deal is reportedto and confirmed by Loans ‘nThings] “Loans ‘n Things London.”

(Fonmeister confirms the deal and reports thecounterparty to Mongobank. Payment ar-rangements will be made and confirmedseparately by the respective back offices. Thebroker’s back office will also confirm thetrade with the banks.)

Value dates and payment arrangements are thesame as in the direct dealing case. In addition tothe payment to the counterparty bank, the banksinvolved share the broket-age fee. These fees arenegotiable in the United States. They are alsoquite low: roughly $20 per million dollars trans-acted.’°

tSee Brooks (1985), p. 25.9See Schwartz (1988), p. 239.

‘°SeeBurnham (1991), p. 141, note 16, and Kubarych(1983), p. 14.

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The final category of participants in the for-eign exchange market is the corporate cus-tomers of the market-making banks. Customersdeal only with the market-makers. They never gothrough brokers, who cannot adequately monitortheir creditworthiness. Typically, a customertransacts with a bank with which it already has awell-established relationship, so that corporatecreditwor-thiness is not a concern for the bank’sforeign exchange desk, and trustworthiness is notan issue for the customer. The mechanics of cus-tomer trading are similar to those of direct deal-ing between market-makers. A customer requestsa quote, and the bank makes a two-way market;the customer then decides to buy, sell or pass.The chief difference between this and an inter-bank relationship is that the customer is not ex-pected ever to reciprocate by making a market.

Participants in the foreign exchange market alsodeal for future value dates. Such dealing com-poses the forward markets. Active forward mar-kets exist for a few heavily traded currencies andfor several time intervals corresponding to active-ly dealt maturities in the money market. Marketscan also be requested and made for other ma-turities, however. Since the foreign exchangemarket is unregulated, standard contract speci-fications are matters of tradition and con-venience, and they can be modified by thetransacting agents.

Forward transactions generally occur in twodifferent ways: outright and swap. An outrightforward transaction is what the name implies, acontract for an exchange of currencies at somefuture value date. “Outrights” generally occuronly between market-making banks and theircommercial clients. The interbank market for out-rights is very small, because outright trading im-plies an exchange rate risk until maturity of thecontract. When outrights are concluded for acommercial client, they are usually hedged im-mediately by swapping the forward position tospot. This removes the exchange rate risk andleaves only interest rate risk.

A swap is simply a combination of two simul-taneous trades: an outright forward contract andan opposing spot deal. For example, a bank might“swap in” six-month yen by simultaneously buyingspot yen and selling six-month forward

Figure 2Market-Maker Volume byType (4/89)

Futures and Options

(5.2%)

yen. Such a swap might be used to hedge an out-right purchase of six-month yen from a bank cus-tomer.’1 In effect, the swapping bank isborrowing yen for the six months of the outrightdeal. The foreign exchange market-maker swapsin yen — rather than simply borrow yen on atime deposit — because banks maintain separateforeign exchange and money market accounts foradministrative reasons. Swapping is generally thepreferred means of forward dealing (see figures 2and 3).

In practice, the vast majority of foreign ex-change transactions involve the U.S. dollar andsome other currency. The magnitude of U.S. for-eign trade and investment flows implies that, foralmost any other currency, the bilateral dollar ex-change markets will have the largest volume.Consequently, the dollar markets are the most li-quid. The possibility of triangular arbitrage en-forces the law of one price for the cross rates.The upshot is that liquidity considerations out-weigh transaction costs. A German wanting

“Hedging an outright purchase of currency with an oppos-ing swap deal still leaves an open spot purchase of thecurrency. This can be easily covered in the spot market.

c— swap(23.4%)

Outright Forward(4.6%)

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Figure 3Broker Volume byType (4/89)

swap(39.4%)

Options(3.5%)

pounds, for example, will typically convertmarks to dollars and then dollars to pounds,rather than trading marks for pounds directly.Though this is especially true in the Americanmarket, it holds for foreign markets as well.

The microstructure literature is by naturemarket-specific, and much of it concerns U. S.equity markets. This specificity has the advan-tage of realism, but it makes the immediate ap-plicability of some microstructural models to theforeign exchange market questionable. The firsttask is to define some basic microstructural con-cepts, identifying where the foreign exchangemarket fits into the context they provide. Sucha taxonomy is important, because one of thefundamental lessons of the microstructure lit-

12A similar situation obtains on the New York Stock Ex-change, where specialists act as either brokers or market-makers, depending on the level of activity in the market.

135ee Wolinsky (1990), p. 1. He goes onto analyze theoreti-cally the difference in the price discovery process betweencentralized and decentralized markets. Schwartz (1988),pp. 426-35, refers to centralization as “spatial consoli-dation.”

I CLASSIFYING MARKETS

erature is that institutional differences can af-fect the efficiency of pricing and allocation.

As described above, the foreign exchangemarket combines two disparate auction struc-tures for the same commodity: the interbankdirect market and the brokered market. Defyinga naive application of institutional Darwinism,whereby only the fitter of the two systemswould survive, these trading methods appear tocoexist comfortably.” The direct market can beclassified as a decentralized, continuous, open-bid, double-auction market. The brokered mar-ket is a quasi-centralized, continuous, limit-book,single-auction market. The meanings of theseclassifications are explained below.

Centralization

In a centralized market, “trades are carriedout at publicly announced prices and all tradershave access to the same trading opportunities.”In a decentralized market, in contrast, “pricesare quoted and transactions are concluded inprivate meetings among agents.”” A New YorkStock Exchange’s (NYSE) specialist system is acentralized market; the interbank direct marketfor foreign exchange is a decentralized one.

The distinction between centralized and de-centralized markets might seem to provide aneat dichotomy of possible market structures.The multiplicity of brokers in the foreign ex-change market violates this simple taxonomy,however. Each foreign exchange broker accum-ulates a subset of market-makers’ limit orders.This network of “brokerage nodes” is as dif-ferent from a fully centralized system as it isfrom a fully decentralized one. This arrange-ment is labeled here as “quasi-centralized.”

Most microstructural studies have confinedthemselves to centralized markets, especially theNYSE’s specialist system and the National Associ-ation of Securities Dealers Automated Quotation(NASDAQ) System on the over-the-counter (OTC)market.” Although there are a number of im-portant decentralized markets, including the in-terbank direct foreign exchange market, rela-

‘4For models of specialist systems, see Demsetz (1968), Tin-ic (1972), Garman (1976), Bradfield (1979), Amihud andMendelson (1980), Conroy and Winkler (1981), Glostenand Milgrom (1985) and Sirri (1989). For studies of theOTC market, see Tinic and West (1972), Benston andHagerman (1974), Ho and Macris (1985) and Stoll (1989).

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tively few studies have focused on the impactof decentralization.

There is some evidence that differences inthe degree of centralization between variousmarkets cause differences in market perfor-mance. Garbade, in studying the largely decen-tralized ‘!‘reasury securities market, concludesthat because brokerage tends to centralizetrading and price information, it “uses timemore efficiently,””eliminates the most importantarbitrages,” and benefits dealers by ensuring thatorders are executed according to price priority.”

The efficiency gains of centralized price infor-mation may imply economies of scale and, thus,a natural monopoly for brokers in securitiesmarkets. This is entirely consistent with the text-book presentation of the relativel greater opera-tional efficiency of centralized markets.” Thus,the fact that a number of brokers service theforeign exchange market seems to represent adiscrepancy between theory and reality. Brokersdo communicate among themselves, however, toeliminate the possibility of arbitrage betweenlimit order books. While this helps explain themultiplicity of brokers, it does not fully resolvethe issue of decentralization in the interbankdirect market.

Temporal Consolidation

The distinction between a continuous marketand a call market involves what Schwartz refersto as the degree of “temporal consolidation.””In a call market, trading occurs at pre-appointedtimes (the “calls”), with arriving transaction ord-ers detained until the next call for execution. Incontinuous markets, like the foreign exchangemarket, trading occurs at its own pace, andtransaction orders are processed as they arrive.A 1-ange of intermediate arrangements falls he-t~veenthese two extremes.

“See Garbade (1978). p. 497.

“The textbook argument counts trips to market. Briefly, ifthere are N traders, then a total of N trips to a centralmarketplace are required for each to haggle with everyoneelse; to pair them bilaterally requires a total of N(N-I)!2trips. If trips are costly, then centralization is more ef-ficient.

“See Schwartz (1988), pp. 435-47. Garman (1976), pp. 257’58, also describes continuous and call markets; he refersto these as asynchronous and synchronous markets,respectively.

“See Hahn (1984), Negishi (1962), Beja and Hakansson(1977), as well as the references therein.

“A continuous market cannot be viewed as a continuum ofinfinitesimally lived call markets. Clearing supply and de-

Most rnicroeconorriic models assume call mar-kets. In a Walrasian thtonnemerir model, for cx-ample, an auctioneer calls out a series of pricesand receives buy and sell orders at each price.When a price is found for which the quantitiessupplied and demanded are equal, all transactionsare consummated at that price. Interestinglyenough, Walras based this price discoverymodel on the mechanics of the Paris Bourse.

Temporal consolidation can affect the perfor-mance of a market. Theoretical work indicateshow continuous trading can alter- allocations,the process of price discovery and even the ulti-mate equilibrium price.” The basic thrust ofthese arguments is that, with continuous ttading,earlier transactions satisfy some consumer’s and

producers, causing shifts in supply and detnandthat affect prices for later transactions. As aresult, the Pareto-efficiency characteristic ofWalrasian equilibria does not necessarily obtainin continuous markets.”

On the other hand, the periodic batching oforders that occurs in a call market also has dis-advantages. The difference in time between ord-er placement and execution can impose realcosts on investors. A recurring argument in theliterature is the willingness of investor-s to pat’more — a liquidity premium — for the ability totrade immediately. Similarly, periodic calls delayany information conveyed by prices until thetime of the call, introducing price uncet-taintv inthe period between the calls.

In sum, a trade-off exists between the alloca-tional efficiency of the nearly ‘Nalrasian callmarket system and the informational efficiencyand immediacy of the continuous market sys-tem.20 it is not clear whether the microstruc-ture of the foreign exchange market representsa globally optimal balance of these relative ad-

mand in each such call market would require an infinitetrading volume over the course of a day. Cohen andSchwartz (1989) recommend an electronic order-routingsystem for the stock exchanges. to facilitate the placementand revision of orders, This would encourage additionaltrading volume, making more frequent calls feasible.

“See Stoll (1985), p. 72, and especially Schwartz (1988),pp. 442-53, for a more thorough exposition of the pros andcons of temporal consolidation. Intermediate arrangementsare also possible. For example, Schwartz argues thatmany of the problems caused by infrequent batching in acall market might be overcome by expanding access tothe market with computer technology, whereby the in-

creased number of traders would allow for more frequentcalls.

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vantages. A persistent deviation from optimalitymight be explained, for example, by arguingthat the allocational benefits of a call marketsystem are a public good.

Communication of Prices

The terms “open-bid” and “limit-book” refer toways in which price information is communi-cated. In an open-bid market — the open outcrysystem on the futures exchanges, for example— offers to buy or sell at a specified price areannounced to all agents in the market. At theopposite extreme, in a sealed-bid market, ordersare known only to the entity placing the orderand perhaps to a disinterested auctioneer.

Direct trading in foreign exchange approxi-mates the standard open-bid structure. Thesalient difference between the foreign exchangemarket and the standard arrangement is thebilateral pairing of participants in the foreignexchange market. In principle, any participantcan contact a market-maker at any time for aprice quote. The bilateral nature of such con-tacts and the time consumed by each contacttogether imply, however, that all participantscannot be simultaneously informed of the cur-rent quotes of a market-maker. This practicalconstraint on the dissemination of price infor-mation is significant: it introduces the possibilityof genuine arbitrage, that is, of finding twomarket-makers whose current bid-ask spreadsdo not overlap.

The limit order book, which is used by bothforeign exchange brokers and stock exchangespecialists, is another intermediate form of pricecommunication. Although it would be possiblein principle for foreign exchange brokeragebooks to be fully open for public inspection, inpractice only certain orders — namely, the bestbid and ask on each book — are revealed tomarket-makers, while the others remain con-cealed. As in the direct market, market-makersmust contact brokers bilaterally to get these “in-side spreads.” Knowledge of the concealed limitorders would be of speculative value to market-makers, because an imbalanced book suggeststhat large future price movements are morelikely in one direction than the other.

More generally, price communication is inti-mately related to the role of market-makers as

2lThi5 term is due to Demsetz (1968), p. 35. Tinic (1972),p. 79, calls in “liquidity services.”

providers of “predictable immediacy.” Marketparticipants are willing to pay a liquidity pre-mium, usually embedded in a market-maker’sspread, for the reduction in search costs im-plied by constant access to a counterparty. Thecosts of “finding” the other side of a transactioncan be further broken down into the liquidityconcession, the cost of communicating the in-formation and the cost of waiting for potentialcounterparties to respond.22 Other things equal,an efficient system of price communication isone that minimizes such transaction costs. Whilethe communication of price information is acentral function of securities markets, the factthat the systems of price communication in theforeign exchange market are not fully central-ized suggests that these systems do not representa cost-minimizing arrangement.

Structure of Prices

The terms “double-auction” and “single-auction”refer to the nature of the prices quoted. In adouble-auction market, certain participants pro-vide prices on both sides of the market, that is,both bid and ask prices. Participants providingdouble-auction quotes upon demand are knownas market-makers, and they must have sufficientcapitalization to back up their quotes. In a single-auction market, prices are specified either’ tobuy or to sell, but not both. In the foreign ex-change market, market-makers provide double-auction prices, while brokers try to aggregatesingle-auction quotes into two-way (inside)spreads. A broker’s book may occasionally beempty on one or both sides. Rather than makea market in such cases, the broker provides,respectively, a single-auction quote or none at all.

Thus, whether double or single-auction pricesare quoted depends largely on whether theagent quoting prices is providing market-makingservices or simply attempting to acquire (or sell)the commodity. This issue is related to thedegree of centralization in the market. Theabsence of market-makers in a single-auctionmarket, together with the presence of searchcosts, results in a tendency toward centraliza-tion of price information, thus facilitating thesearch for a counterparty. Inversely, decentrali-zation of price information leads to a tendency

“See Logue (1975), p. 118.

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toward double-auction prices, again to facilitatethe search for a counterparty.”

MODELING TRADERS’ BEHAVIOR

The microstructure liter’ature extends well be-yond a simple description of market institutions.Modeling the behavior of market participants iscentral to almost all discussions of micro-structure. Although numerous approaches tosuch modeling have been taken, two commonconcerns are of special interest. These are thetreatment of price information by market par-ticipants, and determination of the bid-ask spread.The latter raises the interrelated issues of inven-tory and quantity transacted.

Price Expectations

Modeling the interpretation of price informa-tion is a crucial step in constrtcting microstruc-tural models of price discovery.” Many diverseapproaches have been taken in such modeling.An almost universal simplification is to modelsecurities markets in partial equilibrium, so thatprices are not determined endogeneously in thetraditional general equilibrium sense. This allowsthe modeler to focus on the microstructure’sfiner details. Another common simplification isto assume that agents ignore the impact of theirown behavior on the market.”

Rather than explicitly model such forces asgeneral equilibrium or recursive beliefs, modelsposit probability distributions that produce the

prices of orders in the market. Modelers haveincluded randomness at one or both of two lev-els, depending on their focus. First, orderprices can be generated by objective distribu-tions, that is, by stochastic processes exogenous

to the lnarket. For example, there may he astochastic process that generates the “true”equilibrium price. Second, probability models ofpalticipants’ subjective beliefs about prices canbe used. Cont-oy and Winkler, for example, at-tribute subjective normal price distributions tomarket-makers, who use Bayesian updating tolearn about the prices of incoming limit orders.”Objective processes can coexist with subjectivebeliefs about those processes. Harsanyi suggestsa consistency requirement for the subjectiveprice distributions of multiple agents; these dis-tributions are each equated with a conditionaldistribution of a single distribution known to all.”

Models can be further classified according tohow they telate supply and demand. In particu-lar, there are both models with single priceprocesses and with dual price processes. In dualprice models, purchase orders (whether marketor limit orders) are generated by one process,while sale order-s are generated by another.”‘I’he salient point here is that purchase and saleorders come from independent distributions.‘rhis independence is especially clear in Conroyand Winkler, where the distributional assump-tions are explicit; there, independence impliesthat any sequence of buy orders, regardless oftheir prices arid quantities, has no effect on thesubjective probability of a sell order at any price.

Statistical independence implicitly restricts theways in which orders can be generated. Put--chase and sale orders are somehow motivatedindependently, although the cause of thisseparation is not always specified. Statistical in-dependence is not a necessary component of adual price process, however. Cohen, Maier,Schwartz and Whitcomb (1981), for example, as-sume that actual market hid and ask prices are

“Note that the converse does not appear to hold. That is,centralization does not tend to eliminate double-auctionquoting. For example, the NASDAO system on the OTCstock market centralizes price information while still sup-porting numerous market-makers for every stock.

“Notably, the term “price” is generally too inexact in amicrostructurat context. One must often distinguish at aminimum between quoted prices, transaction prices andequilibrium prices. There are also reservation prices,market-clearing prices and closing prices (see Schwartz(1988), chapter 9, for the distinction between equilibriumand clearing prices). If unspecified here, the intended defi-nition should be clear from the context.

“The alternative, which dates at least to Keynes’ “beautycontest,” is recursive beliefs, in which an agent considersthe feedback of her own actions on the beliefs of others,and thence how the behavior on the other agents might af-fect her own beliefs, etc. See Keynes (1936), p. 156. Thelimiting case—an infinite recursion of beliefs—presumes

extreme informational and comoutational resources on thepart of agents, and models based on it are usually intrac-table. Intermediate approaches allowing a finite degree ofrecursion must somehow justify the truncation of recursivebeliefs, just as the standard model of atomistic agents al-lows no beliefs about beliefs and is justified by an as-sumption on the relative size of individual agents.

“See shaded insert on opposite page.“See Harsanyi (1982), especially chapter 9, and the refer-

ences therein. His consistency requirement identifies aunique equilibrium for the game.

~ market order is an order to trade at the best price avail-able; a limit order specifies a price. These modelsrepresent a strain of the literature that was pioneered byDemsetz using straightforward supply and demand sched-ules (see shaded insert on page 63). Similar approacheswere later taken by Garman (1976), Amihud and Mendet-son (1980) and Conroy and Winkler (1981), among others.

FEDERAL RESERVE SANK OF St LOUIS

I 61

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62

independent Poisson processes and give inves-tors joint subjective distributions over thoseprices. For the latter distributions, probabilisticindependence of bid and ask prices is not ex-plicitly required. Black (1989) models quantities(independent of prices) of market orders. Quan-tities supplied and demanded are drawn fromdifferent distributions, but the distributions areconstrained to have the same mean. Garbade(1978), on the other hand, assumes a single,unknown and fixed equilibrium price, aroundwhich market-makers set their spreads. Incom-ing buy and sell orders arrive via randomprocesses whose mean arrival rates depend onthe difference between the quoted bid (or ask)price and the exogenous equilibrium price and,thus, are not independent.

The most common alternative to separate pur-chase and sale processes is to model prices assome function of a single scalar process. Thisapproach is in the spirit of the efficient marketsliterature, which posits a unique value for asecurity conditional on the available informa-tion, Ross (1987) points out that this approachcan be regarded conceptually as a special caseof the dual price process, with supply and de-mand infinitely elastic at a common price. Manyauthors reveal their theoretical roots by usingterminology drawn from the literature on effi-cient markets. Thus, for example, Barnea des-cribes a stock’s “intrinsic value,” which follows arandom walk.” Similarly, Copeland and Galaiposit a “‘true’ underlying asset value - -- known(cx ante) to all market participants.”° In con-trast1 Garbade’s (1978) exogenous equilibriumprice is unknown.

It is possible to extend the single price ap-proach beyond the efficient markets traditionby modeling the value of a security subjectivelyrather than as an objective fact. Glosten andMilgrom (1985), for example, begin with an ex-ogenous random value representing the consen-sus value of a stock given all public information.Investors do not act on this exogenous valuedirectly; instead, they act on their expectationof it, conditional on their information set. Hoand Stoll personalize price expectations in asimilar fashion:”

We take the dealer’s opinion of the “true” price ofthe stock to be exogenously determined by his in-formation set and ask how the dealer prices rela-tive to his “true” price...

This subjectivization of the pricing process issignificant, because it allows for heterogeneousexpectations and thus for more realistic model-ing of price discovery.

Research into the microstructure of the for-eign exchange market should presume such het-erogeneity among market-makers. There arenumerous market-makers for foreign exchange:The Federal Reserve Bank of New York (FRB-NY)(1989a) lists 162 dealing institutions in the U.S.interbank market. There would be little point insuch superfluity if all market-makers were iden-tical. Furthermore, it is well known that “takinga view,” that is, speculating on future prices, isroutine for many participants.32 To omit thisheterogeneity from a model is to ignore an im-portant characteristic of the market.

The large proportion of market-makers in theforeign exchange market has another importantmodeling implication. It implies that a single-price process is more appropriate as a theoreti-cal representation of agents’ expectations. Mar-ket-makers consistently face other market-makers,who can hold positive or negative inventories offoreign currency with equal ease. A quote thatis “off the market” on the high side will be hit(i.e., traded upon) just as surely as a quote thatis off on the low side. This is also true of cus-tomers, who normally enter the market with apredilection to either buy or sell. As Burnhamnotes:’3

The customer knows that if the first marketmakeris too far off the market price, he can unexpected-ly take the other side of the quote and resell theposition to a second marketmaker.

The point is that the market-maker must expectto be penalized for underestimating as well asoverestimating his counterparty’s valuation ofthe currency. From the perspective of the mar-ket-maker, who quotes a spread and observes aresponse, the forces determining short-run ef-fective demand and supply are not merely re-lated, but indistinguishable.

“See Barnea (1974), pp. 512-14.

‘°SeeCopeland and Galai (1983), p. 1458.“See Ho and Stoll (1981), p. 48. For a similar example, see

Stoll (1978), especially p. 1136.

“See, for example, Kubarych (1983), p. 29, or Burnham(1991), p. 139.

“See Burnham (1991), p. 136.

FEDERAL RESERVE BANK OF ST. LOUIS

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perative of arbitrage avoidance must he re-garded as the first priority in individual market-niaker pricing, to which all other factors (e.g.,purchasing power parity) must be subordinated.

Market-makers’ Bid-Ask Spreads

‘l’he bid-ask spread has attracted consider-ableinterest in the literature on market microstruc-ture. The complexity of modeling the spread islargely because it requires incorporating a sub-stantial amount of institutional detail. At a faciletheoretical level,, a market-maker’s spread appearsto be a direct violation of the latv of one price,

since it assigns two prices to the same com-modity. Several explanations have been offeredto resolve this seeming inconsistency. They canbe roughly categorized as involving the cost ofdealer services, the cost of adverse selection andthe cost of holding inventory.”

The dealer services argument can be tracedback at least as far as Stigler (1964), who arguesthat stock exchange specialists charge a “job-ber’s turn” as compensation for the costs of act-ing as a specialist. The analysis of dealer serviceswas formalized by Demsetz (1968), who identi-fied “predictable immediacy” as the particularservice for which investors are willing to pay.This identification hints at the complex questionof what liquidity is and where it comes fi-orn. Ina busy market, liquidity is a public good: a con-

tinuous stream of buyers and sellers generatespredictable immediacy as a by-product of theirtrading.

‘l’he determinants of the level of compensationare themselves a topic of debate. Stigler arguesthat, because centralization of exchange limitsfixed costs and aggregates separate transactionorders into less risky actuarial order flows, itimplies economies of scale and thus a naturalmonopoly for market-making.’” Smidt (1971)counters that barriers to entry among NYSE

specialists allow them to exact monopoly rentsfrom other investors. In his view, the naturalmonopoly argument, while used as an apologyfor barriers to entry, remains unsupported em-pirically: “There is no empirical evidence to sup-port the proposition that lmarket-making] is, infact, a natut-al monopoly.”~Indeed, if market-making is a natural monopoly, barriers to entryshould he unnecessary.

The foreign exchange market has no apparentbarriers to entry other than the need for suffi-cient capitalization. It also has no apparent bar-riers to exit. The market supports a large andmci-easing number of competing market-makers.Unless it can be sho~-vnthat there is some sub-tle restriction in the foreign exchange marketthat prevents consolidation of the market-makingfunction, one must conclude that market-makingper se is not a natural monopoly.” The multi-tude of market-makers also implies that theycannot earn monopoly rents by embedding apremium for predictable immediacy in thespread, although the spread may still cover thecosts of processing orders.

Other research suggests that a market-maker’sjob is more complex than the mere sale ofcounterparty services. A second explanation forthe bid-ask spread — adverse selection — canhe traced to Bagehot (1971). He starts with“liquidity-motivated transactors” who pay themarket-maker the price of the spread in ex-change for the service of predictable immedi-acy. The market-maker also confronts traderswho have inside information, however, and whocan therefore speculate profitably at the expenseof the market-maket-.” The market-maker mustcharge everyone a widet- spread to compensatefor losses to the information-motivated traders.

Because of the relatively abstract nature ofcurrencies as commodities, it is difficult to con-struct examples of ‘‘inside” information onforeign exchange rates. One exception is moneysupply announcements, which, if known before

“This is essentially the same taxonomy as provided by Bar-nea and Logue (1975), although they use the terms‘liquidity theory,” “adversary theory,” and “dynamic

price/inventory adlustment theory,” respectively.

‘“See Stigler (1964), p. 129.

‘7See Smidt (1971), p. 64.“For example, in the context of the OTC stock market, Ben-

ston and Hagerman (1974), p. 362, conlecture that. “deal-ers may face positively sloped marginal cost curves whichshift down as industry output increases.” The idea is thatmarket-making per se is not a natural monopoly, even

though the industry as a whole experiences economies otscale. Hamilton (1976) also addresses the natural monopo-ly question; Reinganum (1990) provides evidence on li-quidity premia for NYSE vs. NASDAQ stocks.

“This situation is called adverse selection, because, in amarket with competing market-makers, the one who getsthe insider’s business is a loser rather than a winner.Bagehot also posits a third class of investors, who onlythink they have inside information; they speculate, but loseon average, and are indistinguishable to the market-makerfrom the liquidity-motivated traders.

IIII

SFEDERAL RESERVE BANK OF St LOUIS

1 65

publicly distributed, might provide a basis forprofitable speculation. Another form of informa-tion that can be construed as inside informationis knowledge of an arbitrage opportunity. Con-sider a hypothetical market in which there arenumerous decentralized market-makers who donot quote spreads, but single prices at whichthey are willing both to buy and sell. Unlessthere were a perfect consensus among the mar-ket-makers on the value of the foreign currency,all of them would be vulnerable to arbitrage. Adecentralized market makes a perfect consensusdifficult to achieve. Without centralizing priceinformation, it is impossible to know if no arbi-trage opportunities exist. A bid-ask spread, incontrast, allows a market-maker to include anerror tolerance in her prices, thus facilitating aprice consensus: it is easier to get bid-askspreads to overlap than to get scalar prices tocoincide. The spread also provides the mar-ket-maker with some degree of protectionfrom adverse selection in the form of arbitrage.

The bid-ask spread is also affected by invento-ry considerations. This idea dates back at leastas far as Barnea and Logue (1975)A°The notionof a desired inventory level for the market-maker underlies all of these models. In thesimplest case, the desired level is set at zero,and a constant spread is shifted up and downon a price scale to equalize the probability ofreceiving a purchase order with that of receiv-ing a sale order. The result is that the expectedchange in Inventory is always equal to zero, and(with all trades for one round lot) the inventorylevel follows a simple random walk.

An undesirable implication of random-walkmodels of inventory is the inevitable bankruptcyof the market-maker. Finite capitalization levelsfor market-makers impose upper and lowerbounds on allowable inventories. Because inven-tory follows a random walk, with probabilityone It will reach either its upper or lower boundin a finite number of trades.” The dynamic op-timization models of Bradfield (1979), Amihudand Mendelson (1980) and Ho and Stoll (1981)resolve this problem. They conclude that amarket-maker, optimizing his bid and ask prices

°Bameaand Logue attribute It to Smldt (1971), althoughSmith’s paper does not explicitly develop the connectionbetween the market-makei’s inventory and his spread- For-mal models of the relationship between inventories andspreads can be found in Stoll (1978), Amihud and Mendel-son (1980), Ho and Stoll (1981) and Sirri (1989), amongothers.

4l5~, for example, Ross (1983), pp. 106-07.

over time in the face of a stochastic order flow,will shift both bid and ask rates downward (up-ward) and increase the width of the spread whena positive (negative) inventory has accumulated.2

We should expect two of these three ration-ales for the spread to apply to market-makers’bid-ask spreads in the foreign exchange market.Because there are numerous market-makers,competition should eliminate their ability to earnmonopoly rents by charging a premium for pre-dictable immediacy per se. The adverse selec-tion argument does apply in the foreign ex-change market, however, since the spread allowsmarket-makers some protection against arbit-rage opportunities. Arbitrage opportunities canbe construed as a form of inside information ina market where price information is not cen-tralized. In accordance with the dynamic optimi-zation models, a market-maker’s inventory levelshould affect the spread, widening and shiftingit as inventories accumulate.

Brokers’ Spreads

So far, the discussion of the bid-ask spreadhas focused on models in which bid and askprices are set by individual market-makers. Thedual role of the stock exchange specialist sug-gests that this is only part of the story. Spreadsare produced in two fundamentally differentways. It is only when limit orders are sparsethat a NYSE specialist must step in as a market-maker to provide an “orderly market.”~’Whenlimit order volume is sufficient, the specialistacts as a broker, accounting for incoming limitorders on the lhnit order book, and pairingmarket orders against them. Cohen, Maier,Schwartz and Whitcomb (1979) note that inade-quate attention has been given to the fact thatnot all prices are market-maker spreads. Themarket often makes itself without specialist as-sistance, through the aggregation of limit ord-ers on the book.

The foreign exchange market differs from theNYSE in that the market-making and brokerageroles are separated: market-makers do not actas brokers, and brokers do not make markets,

~Seeshaded insert on page 66.43The NYSE defines this role in rule 104: “the specialist

should maintain a continuous market with price continuityand close bid and asked prices, and minimize the effect oftemporary disparity between public supply and demand.”See Leffler and Faiwefl (1963), pp. 211-12.

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Tberef ore, it is even more appropriate to model separate limit ot dci s. <I his arrangcnwnt mightbrokered spreads as determined in a fundamen< be modeled as a pali of exti eme oi dci statisti(tall different wa~<from market-maker spreads. from independent disti ibutions of pm cha e andThe separation of roles also has other implica- sale limit orders. The disti ibution of these statis-tions for modeling foreign exchange brokerage. tics would have to be conditional on limit 01 der

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ers transact immediately and are removed fromthe book.~~Perhaps because of its complexity,such a derivation has not been attempted.

Cohen, Maier, Schwartz and Whitcomb (1979)model limit orders as generated by “yawl” distri-butions These distributions satisfy three heu-ristics for the incentives of investors placinglimit orders~~The heuristics are motivated by anotion of the centralized exchange as a marketfor immediacy; placers of limit orders produceimmediacy, and placers of market orders con-sume it. This relationship between limit andmarket orders is formalized in Cohen, Maier,Schwartz and Whitcomb (1981), where each halfof the brokered spread is assumed to be gener-ated by a compound Poisson process A mini-mum brokered spread results: if the limit order’sbid (ask) price is sufficiently close to the special-ist’s ask (bid), the benefit to the investor of beingable to specify the price of a limit otder is over-whelmed by the cost of foregone immediacy.

Because models of the informational contentof brokered spreads are few, the literatureoffers little guidance in modeling brokeredquotes in the foreign exchange market. ‘I’heyawl distribution is the only explicit distribu-tional form for brokered spreads in the litera-ture. Unfoi-tunately, its heuristic basis cannot betransferred directly to the foreign exchangemarket, because market-makers there differfrom stock market investors. Indeed, this maybe an instance in which the foreign exchangemarket informs microstructure theory ratherthan the other way around. The extant ap-proaches to brokerage treat it as a servicefacilitating predictable immediacy. This aspect ofbrokerage is redundant in the foreign exchange

market, because of the multitude of market-makei-s, each providing immediacy. This redun-dancv suggests instead that foreign exchangehi-okerage serves some other function.

One motive for trading through a foreign ex-change broker is to maintain anonymity — thename of the hank placing a limit order is notrevealed unless a deal is consummated and thenonly to the counterpart~’.1°Anonymity is valu-able, because revealing a need to buy or sell a

cui-rency puts a market-maker at a bargainingdisadvantage. In addition, anonymity can helppair market-makers who ordinarily would notcontact each other directly. ‘l’hese issues havenot been explored at a theoretical level. Until anadequate microstructural model of the strategicbenefits of anonymity is developed, the theoreti-cal understanding of foreign exchange broker-age will be limited

CONCLUSION’S

Students of the foreign exchange market candraw several lessons from the literature onmarket microstructure. The most fundamentalof these is that the institutional details of ex-change in a market can affect all aspects —

price, allocational, informational and operational— of the market’s efficiency. A multitude ofmarket-makers who can provide liquidity, orpredictable immediacy, arises in response to thedecentralization of the market. As a result,search costs are reduced relative to a worldwithout market-makers, because finding one ofmany market-makers amounts to finding acounterpartv. Brokerage also reduces searchcosts by achieving a degree of centralization inprice information.

An unanswered question is why the specificcombination of trading structures characteristicof the foreign exchange market — a decentral-ized, open-book, direct arrangement and aquasi-centralized, limit-hook, brokered arrange-ment — should coexist. Apparently, each struc-ture has relative advantages, but a full analysisof these advantages is lacking. Is there a singlemicrosti-ucture that would combine the relativeadvantages of the chrect and brokered arrange-ments? Put another way, why does the micro-structure of the foreign exchange market differfrom that of the stock exchanges, the futurespits and the OTC stock market? Answering thesequestions will require a fuller specification ofthe objectives of a trading system and a betterunderstanding of the impact of rnicrostructuralarrangements on those goals.

These issues pro\’ide a motive for deeper in-vestigation of the behavior of the foreign cx-

45The yawl distribution, named for its resemblance to a sail-boat, is a probability distribution contrived for modeling thegeneration of buy (or sell) limit orders. See Cohen, Maier,Schwartz and Whitcomb (1979, 1983, 1986) for details.

465ee Kubarych (1983), p. 16, Burnham (1991), p. 141, andFederal Reserve Bank of New York (l989b), p. 41-3.

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~4Anorder statistic is defined as follows: the sample realiza-tions of a finite number of independent random variablesare ranked in increasing order, and the kth order statisticis the kth number in that list. For the foreign exchangemarket, the modeling is still more complex, since brokerscompare books amongst themselves in the sense that in-coming orders can cross against any book.

NOVEMBER/DECEMBER 1991

68

change m~u’ketand its participants. Market-makers are the crucial element: they pi-ovide alltr~msactionprices in the market and are in-volved in at least one sidle of every deal. Themicrostructure literature has developed numer-ous models of the interpretation and setting of

prices by traders. 1’he diversity of expectationsmodels used in the literature illustrates the im-

portance of tailoring such models to the specificenvironment confronted by market participants.Given that a foreign exchange market-maker’sdouble-auction quote can be hit on either side(bid or ask) with equal ease, he must try tomaneuver his spread to bracket the market’sconsensus valuation of the foreign currency. Inother words, suppliers and demanders of cur-rency are indistinguishable to the market-makercx ante. The inability to separate the forces die-termining effective demand from those tIe-termining effective supply in the very short runimply that a single-price expectations process(rather than a dual-price process) is appropriatein modeling market-makers in the foreign ex-

change market.

A market-maker’s bid-ask spread serves severalpurposes. Competition among market-makers inthe foreign exchange market implies that theyshould be unable to charge a monopoly premi-um for the set-vice of predictable immediacy. In-stead, the spread obviates the need for perfectprice consensus by giving the market-makersome protection from arbitrageurs with superiorprice information. While arbitrage avoidancemust he considered a primary goal in setting amarket-maker’s bid and ask quotes, the spread

provides flexibility elsewhere. Just as arbitrageayoidance is concerned with accurately estimat-ing current prices, speculation is concernedwith estimating future prices. B~’changing insize and shifting up or down, the spread cancontrol stochastically the market-maker’s foreigncurrency inventory in the face of random orderflows. Systematic empirical studs’ of the effectof inventories on market-makers’ spreads is stillneeded, however.

The brokered spread is less well understoodthan the market-maker’s spread, and certainareas are ripe for further research. Theoreticalmodels of hrokered spreads are few. The exist-ing rationales for brokerage maintain that it

provides liquidity services. In the foreign ex-change market, however, numerous market-makers make the liquidity services providedl bybrokerage superfluous. Descriptions of the for-eign exchange market suggest instead that

anonymity is an important motive for trading inthe broket-ed market. Yet the stt-ategic value ofanonymity in foreign exchange quoting is notwell understood at a theoretical level. In addi-tion. there is not a clear understanding of thedifferences in price information between amat-ket-maker’s spread and a ht’oker’s spread;this too remains a topic for future i-esearch.

From a broader perspective, a better under-standing of institutional choice and change asregards securities market mnicrostructure isnecessary. Most microstructural research hasbeen devoted to analyzing the impact of micro-structural factors on important economic vari-ables, such as price and allocation. Relativellittle attention has been paid to the effect ofeconomic factot-s on the choice of an institution-al microstructure.

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