Microstructure Theory and the Foreign Exchange Market

Home , Foreign exchange market, Market microstructure

Mark D. Flood

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

GROWING BODY OF theoretical literature, exchange market is also of special interest to known as the study of securities market micro- students of microstructure, because it combines structure, deals with the behavior of participants two very different arrangements for matching in securities markets and with the effects of in- buyers and sellers — bank dealers trade with formation and institutional rules on the economic one another both directly and through foreign performance of those markets. These institu- exchange brokers.1 tional factors may arise from technology, tradi- Standard models of exchange-rate determination or regulation. Microstructure and its impact tion concentrate on relatively long-run aspects, are important, because of the vast amounts of such as purchasing power parity. While micro- wealth which pass through securities markets — structure theory cannot address these issues including the foreign exchange market — directly, it can illuminate a more narrowly fo- every day. cused array of institutional concerns, such as Microstructure is of interest to students of the price information, the matching of buyers and foreign exchange market: microstructural analy- sellers, and optimal dealer pricing policies. De- ses of other markets have yielded insight into spite the substantial literature on microstructure, traders’ behavior and the effect of various insti- little attention has been paid to the particular tutional arrangements. Conversely, the foreign microstructure of the foreign exchange market.2

‘Similar arrangements exist for other securities—for exam- Cohen, Maier, Schwartz and Whitcomb (1979, 1986) and ple, the federal funds market and the secondary market Stoll (1985) have surveyed the microstructure literature. for Treasury securities—but these too have been relatively In addition to the early note by Allen (1977), very recently neglected in the literature. 2 there have appeared some microstructural studies of the The shaded insert on the opposite page provides a context foreign exchange market: Bossaerts and Hillion (1991), in which the microstructural approach can be compared Lyons (1991), Rai (1991) and Flood (1991). There is also with more traditional approaches to market efficiency. an empirical literature measuring the determinants of the Following some early articles by Demsetz (1968), Tinic bid-ask spread in the foreign exchange market. See Black (1972) and Tinic and West (1972), Garman (1976) per- (1989), Wei (1991) and Glassman (1987) as well as the formed the crucial task of defining market microstructure references therein. Because the focus of this article is on as an independent area of the literature, thus focusing the microstructure theory, such empirical studies receive little debate. Since then, market microstructure has burgeoned, attention here. led by Cohen, Maier, Schwartz and Whitcomb (1978a, Finally, although a consideration of the results of laborato- 1978b, 1981, 1983), Amihud and Mendelson (1980, 1986, ry experiments would expand the scope of this paper to 1988), Stoll (1978, 1985, 1989) and Ho and Stoll (1980, unwieldy dimensions, their role in establishing the sensitiv- 1981). See also Beja and Hakansson (1977), Cohen, ity of market behavior to institutional factors must at least Hawawini, Maier, Schwartz and Whitcomb (1980), Cohen, be acknowledged; see Plott (1982, 1991) for an in- Maier, Ness, Okuda, Schwartz and Whitcomb (1977), Ami- troduction. hud, Ho, and Schwartz (1985), Schreiber and Schwartz (1986), Schwartz (1988) and Cohen and Schwartz (1989).

FEDERAL RESERVE BANK OF St LOUIS I 53

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This paper examines the extant literature on market microstructure to determine how it might be applied to the foreign exchange Figure 1 market. Spot Market Volume by The paper begins with a brief description of Transactor (4/89) the foreign exchange market. Aspects of the customer literature concerned with institutional details (5.1%) are addressed second, noting how such details can affect the performance of the market. Next, the literature dealing with behavioral details, especially the communication and interpretation of price information, is considered. Finally, the interaction of institutional and behavioral factors, notably the bid-ask spread, is discussed.

INSTITUTIONAL BASICS OF THE FOREIGN EXCHANGE MARKET The foreign exchange market is the international market in which buyers and sellers of currencies “meet.”3 It is largely decentralized: the participants (classified as market-makers, (55.0%) brokers and customers) are physically separated ‘Interbank Brokered from one another; they communicate via tele- (39.9%) phone, telex and computer network. Trading volume is large, estimated at $128.9 billion for the U.S. market in April 1989. Most of this trad- change rates or simply to complete their own ing was between bank market-makers.~ international transactions. Market-makers may

trade for their own account — that is, they may The market is dominated by the market-makers maintain a long or short position in a foreign at commercial and investment banks, who trade currency — and require significant capitalization currencies with each other both directly and for that purpose. Brokers do not contact cus- through foreign exchange brokers (see figure IL” tomers and do not deal on their own account; Market-makers, as the name suggests, “make a instead, they profit by charging a fee for the market” in one or more currencies by providing service of bringing market-makers together. bid and ask prices upon demand. A broker ar- ranges trades by keeping a “book” of market- The mechanics of trading differ substantially between brokered transactions and direct deals. maker’s limit orders — that is, orders to buy (al- In the direct market, banks contact each other. ternatively, to sell) a specified quantity of for- The bank receiving a call acts as a market-maker eign currency at a specified price — from which he quotes the best bid and ask orders upon re- for the currency in question, providing a two- quest. The best bid and ask quotes on a broker’s way quote (bid and ask) for the bank placing book are together called the broker’s “inside the call. A direct deal might go as follows: spread.” The other participants in the market Mongobank: “Mongobank with a dollar-mark are the customers of the market-making banks, please?” who generally use the market to complete (Mongobank requests a spot market quote transactions in international trade, and central for U.S. dollars (USD) against German marks banks, who may enter the market to move ex- (DEM).) 3 For more thorough descriptions of the workings of the for- has roughly doubled every three years for the past eign exchange market, see Burnham (1991), Chrystal decade. 5 (1984), Kubarych (1983) and Riehl and Rodriguez (1983). Federal Reserve Bank of New York (l989a) lists 162 4 See Federal Reserve Bank of New York (1989a) and Bank market-making institutions (148 are commercial banks) and for International Settlements (815) (1990). Extending this 14 brokers; an earlier study, Federal Reserve Bank of New figure over 251 trading days per year, this implies a trad- York (1980), lists 90 market-making banks and 11 brokers. ing volume of roughly $32 trillion for all of 1989. Volume

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Loans ‘n Things: “20-30” orders are also provided in part as a courtesy I (Loans n’ Things will buy dollars at 2.1020 to the brokers as part of an ongoing business DEM/USD and sell dollars at 2.1030 DEM/USD relationship that makes the market more liquid. —the 2.10 part of the quote is understood.) Because his limit order is often a market-maker’s first indication of general price shift, Brooks Mongohank: “Two mine.” likens the posting of an order with a broker “to I (Mongobank buys $2,000,000 for DEM sticking out the chin so as to be acquainted 4,206,000 at 2.1030 DEMIUSD, for payment with the moment that the fight starts.”8 Schwartz two business days later. The quantity traded points out that posting a limit order extends a I is usually one of a handful of “customary free option to other traders.~ amounts.”) Loans ‘n Things: “My marks to Loans ‘n A market-maker who calls a broker for a quote I Things Frankfurt.” gets the broker’s inside spread, along with the (Loans n’ Things requests that payment of quantities of the limit orders. A typical call to a marks be made to their account at their broker might proceed as follows: I Frankfurt branch. Payment will likely be Mongoank: “What is sterling, please?” made via SWIFT.)e (Mongobank requests the spot quote for Mongohank: ‘(My dollars to Mongobank New U.S. dollars against British pounds (GBP).) I York.” Fonnieister: “1 deal 40-42, one by two.” (Mongobank requests that payment of dol- (Fonmeister Brokerage has quotes to buy lars be made to them in New York. Payment £1,000,000 at 1.7440 USD/GBP, and to sell will most likely be made via CHIPS.)7 I £2,000,000 at 1.7442 USD/GBP) Spot transactions are made for “value date” (payment date) two business days later to allow Mongobank; “I sell one at 40, to whom?” I settlement arrangements to be made with cor- (Mongobank hits the bid for the quantity respondents or branches in other time zones. stated. Mongobank could have requested a This period is extended when a holiday inter- different amount, which would have re- venes in one of the countries involved. Payment quired additional confirmation from the bid- I occurs in a currency’s home country. ding bank.) The other method of interbank trading is Fonmeisten [A pause while the deal is reported I brokered transactions. Brokers collect limit to and confirmed by Loans ‘n orders from bank market-makers. A limit order Things] “Loans ‘n Things London.” is an offer to buy (alternatively to sell) a speci- (Fonmeister confirms the deal and reports the fied quantity at a specified price. I,imit orders counterparty to Mongobank. Payment ar- I remain with the broker until withdrawn by the rangements will be made and confirmed separately by the respective back offices. The market- maker- broker’s back office will also confirm the The advantages of brokered trading include trade with the banks.) I the rapid dissemination of orders to other market-makers, anonymity in quoting, and the Value dates and payment arrangements are the freedom not to quote to other market-makers same as in the direct dealing case. In addition to I on a reciprocal basis, which can be required in the payment to the counterparty bank, the banks the direct market. Anonymity allows the quoting involved share the broket-age fee. These fees are bank to conceal its identity and thus its inten- negotiable in the United States. They are also tions; it also requires that the broker know who quite low: roughly $20 per million dollars trans- I is an acceptable counterparty for whom. Limit acted.’°

t eThe Society for Worldwide Interbank Financial Telecommu- See Brooks (1985), p. 25. I 9 nication (SWIFT) is an electronic message network. In this See Schwartz (1988), p. 239. case, it conveys a standardized payment order to a Ger- man branch or correspondent bank, which, in turn, effects ‘°SeeBurnham (1991), p. 141, note 16, and Kubarych the payment as a local interbank transfer in Frankfurt. (1983), p. 14. I ~TheClearing House for Interbank Payments System (CHIPS) is a private interbank payments system in New I York City.

S NOVFMRFR/OFCFMRPR 1001 56

The final category of participants in the foreign exchange market is the corporate customers of the market-making banks. Customers Figure 2 deal only with the market-makers. They never go Market-Maker Volume by through brokers, who cannot adequately monitor Type (4/89) their creditworthiness. Typically, a customer transacts with a bank with which it already has a c— swap well-established relationship, so that corporate (23.4%) Futures and Options creditwor-thiness is not a concern for the bank’s (5.2%) foreign exchange desk, and trustworthiness is not an issue for the customer. The mechanics of customer trading are similar to those of direct dealing between market-makers. A customer requests a 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 interbank relationship is that the customer is not expected ever to reciprocate by making a market.

Participants in the foreign exchange market also deal for future value dates. Such dealing com- poses the forward markets. Active forward markets exist for a few heavily traded currencies and for several time intervals corresponding to active- ly dealt maturities in the money market. Markets can also be requested and made for other ma- Outright Forward turities, however. Since the foreign exchange (4.6%) market is unregulated, standard contract speci- fications are matters of tradition and con- venience, and they can be modified by the yen. Such a swap might be used to hedge an out- transacting agents. right purchase of six-month yen from a bank customer.’1 In effect, the swapping bank is Forward transactions generally occur in two borrowing yen for the six months of the outright different ways: outright and swap. An outright deal. The foreign exchange market-maker swaps forward transaction is what the name implies, a in yen — rather than simply borrow yen on a contract for an exchange of currencies at some time deposit — because banks maintain separate future value date. “Outrights” generally occur foreign exchange and money market accounts for only between market-making banks and their administrative reasons. Swapping is generally the commercial clients. The interbank market for out- preferred means of forward dealing (see figures 2 rights is very small, because outright trading im- and 3). plies an exchange rate risk until maturity of the contract. When outrights are concluded for a In practice, the vast majority of foreign ex- commercial client, they are usually hedged im- change transactions involve the U.S. dollar and mediately by swapping the forward position to some other currency. The magnitude of U.S. for- spot. This removes the exchange rate risk and eign trade and investment flows implies that, for leaves only interest rate risk. almost any other currency, the bilateral dollar exchange markets will have the largest volume. A swap is simply a combination of two simul- Consequently, the dollar markets are the most li- taneous trades: an outright forward contract and quid. The possibility of triangular arbitrage en- an opposing spot deal. For example, a bank might forces the law of one price for the cross rates. “swap in” six-month yen by simultaneously buying The upshot is that liquidity considerations out- spot yen and selling six-month forward weigh transaction costs. A German wanting

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

FEDERAL RESERVE BANK OF St LOUIS I 57 erature is that institutional differences can af- I Figure 3 fect the efficiency of pricing and allocation. Broker Volume by As described above, the foreign exchange Type (4/89) market combines two disparate auction struc- I tures for the same commodity: the interbank swap direct market and the brokered market. Defying (39.4%) Options a naive application of institutional Darwinism, (3.5%) whereby only the fitter of the two systems I would survive, these trading methods appear to coexist comfortably.” The direct market can be classified as a decentralized, continuous, open- I bid, double-auction market. The brokered market is a quasi-centralized, continuous, limit-book, single-auction market. The meanings of these I classifications are explained below. Centralization I In a centralized market, “trades are carried out at publicly announced prices and all traders have access to the same trading opportunities.” In a decentralized market, in contrast, “prices I are quoted and transactions are concluded in private meetings among agents.”” A New York Stock Exchange’s (NYSE) specialist system is a I centralized market; the interbank direct market for foreign exchange is a decentralized one. pounds, for example, will typically convert I marks to dollars and then dollars to pounds, The distinction between centralized and de- rather than trading marks for pounds directly. centralized markets might seem to provide a Though this is especially true in the American neat dichotomy of possible market structures. market, it holds for foreign markets as well. The multiplicity of brokers in the foreign ex- 1 change market violates this simple taxonomy, however. Each foreign exchange broker accum- ulates a subset of market-makers’ limit orders. CLASSIFYING MARKETS This network of “brokerage nodes” is as dif- I ferent from a fully centralized system as it is The microstructure literature is by nature from a fully decentralized one. This arrange- market-specific, and much of it concerns U. S. ment is labeled here as “quasi-centralized.” I equity markets. This specificity has the advan- tage of realism, but it makes the immediate ap- Most microstructural studies have confined plicability of some microstructural models to the themselves to centralized markets, especially the foreign exchange market questionable. The first NYSE’s specialist system and the National Associ- I task is to define some basic microstructural con- ation of Securities Dealers Automated Quotation cepts, identifying where the foreign exchange (NASDAQ) System on the over-the-counter (OTC) market fits into the context they provide. Such market.” Although there are a number of im- I a taxonomy is important, because one of the portant decentralized markets, including the in- fundamental lessons of the microstructure lit- terbank direct foreign exchange market, rela-

4 I 12A similar situation obtains on the New York Stock Ex- ‘ For models of specialist systems, see Demsetz (1968), Tin- change, where specialists act as either brokers or market- ic (1972), Garman (1976), Bradfield (1979), Amihud and makers, depending on the level of activity in the market. Mendelson (1980), Conroy and Winkler (1981), Glosten 13 5ee Wolinsky (1990), p. 1. He goes onto analyze theoreti- and Milgrom (1985) and Sirri (1989). For studies of the cally the difference in the price discovery process between OTC market, see Tinic and West (1972), Benston and I centralized and decentralized markets. Schwartz (1988), Hagerman (1974), Ho and Macris (1985) and Stoll (1989). pp. 426-35, refers to centralization as “spatial consoli- I dation.” ~ nn-, 58

tively few studies have focused on the impact Most rnicroeconorriic models assume call mar- of decentralization. kets. In a Walrasian thtonnemerir model, for cx- ample, an auctioneer calls out a series of prices There is some evidence that differences in the degree of centralization between various and receives buy and sell orders at each price. markets cause differences in market perfor- When a price is found for which the quantities mance. Garbade, in studying the largely decen- supplied and demanded are equal, all transactions are consummated at that price. Interestingly tralized ‘!‘reasury securities market, concludes enough, Walras based this price discovery that because brokerage tends to centralize model on the mechanics of the Paris Bourse. trading and price information, it “uses time more efficiently,””eliminates the most important Temporal consolidation can affect the perfor- arbitrages,” and benefits dealers by ensuring that mance of a market. Theoretical work indicates orders are executed according to price priority.” how continuous trading can alter- allocations, The efficiency gains of centralized price infor- the process of price discovery and even the ulti- mation may imply economies of scale and, thus, mate equilibrium price.” The basic thrust of a natural monopoly for brokers in securities these arguments is that, with continuous ttading, markets. This is entirely consistent with the text- earlier transactions satisfy some consumer’s and book presentation of the relativel greater opera- producers, causing shifts in supply and detnand tional efficiency of centralized markets.” Thus, that affect prices for later transactions. As a the fact that a number of brokers service the result, the Pareto-efficiency characteristic of foreign exchange market seems to represent a Walrasian equilibria does not necessarily obtain discrepancy between theory and reality. Brokers in continuous markets.” do communicate among themselves, however, to On the other hand, the periodic batching of eliminate the possibility of arbitrage between limit order books. While this helps explain the orders that occurs in a call market also has dis- advantages. The difference in time between ord- multiplicity of brokers, it does not fully resolve er placement and execution can impose real the issue of decentralization in the interbank direct market. costs on investors. A recurring argument in the literature is the willingness of investor-s to pat’ Temporal Consolidation more — a liquidity premium — for the ability to trade immediately. Similarly, periodic calls delay The distinction between a continuous market any information conveyed by prices until the and a call market involves what Schwartz refers time of the call, introducing price uncet-taintv in to as the degree of “temporal consolidation.”” the period between the calls. In a call market, trading occurs at pre-appointed times (the “calls”), with arriving transaction ord- In sum, a trade-off exists between the alloca- ers detained until the next call for execution. In tional efficiency of the nearly ‘Nalrasian call continuous markets, like the foreign exchange market system and the informational efficiency market, trading occurs at its own pace, and and immediacy of the continuous market sys- 20 transaction orders are processed as they arrive. tem. it is not clear whether the microstruc- A 1-ange of intermediate arrangements falls he- ture of the foreign exchange market represents t~veenthese two extremes. a globally optimal balance of these relative ad-

“See Garbade (1978). p. 497. mand in each such call market would require an infinite “The textbook argument counts trips to market. Briefly, if trading volume over the course of a day. Cohen and there are N traders, then a total of N trips to a central Schwartz (1989) recommend an electronic order-routing marketplace are required for each to haggle with everyone system for the stock exchanges. to facilitate the placement else; to pair them bilaterally requires a total of N(N-I)!2 and revision of orders, This would encourage additional trips. If trips are costly, then centralization is more ef- trading volume, making more frequent calls feasible. ficient. “See Stoll (1985), p. 72, and especially Schwartz (1988), “See Schwartz (1988), pp. 435-47. Garman (1976), pp. 257’ pp. 442-53, for a more thorough exposition of the pros and 58, also describes continuous and call markets; he refers cons of temporal consolidation. Intermediate arrangements to these as asynchronous and synchronous markets, are also possible. For example, Schwartz argues that many of the problems caused by infrequent batching in a respectively. call market might be overcome by expanding access to “See Hahn (1984), Negishi (1962), Beja and Hakansson the market with computer technology, whereby the in- (1977), as well as the references therein. creased number of traders would allow for more frequent “A continuous market cannot be viewed as a continuum of calls. infinitesimally lived call markets. Clearing supply and de-

FEDERAL RESERVE BANK OF St LOUIS 59

vantages. A persistent deviation from optimality providers of “predictable immediacy.” Market I might be explained, for example, by arguing participants are willing to pay a liquidity pre- that the allocational benefits of a call market mium, usually embedded in a market-maker’s system are a public good. spread, for the reduction in search costs im- plied by constant access to a counterparty. The I Communication of Prices costs of “finding” the other side of a transaction The terms “open-bid” and “limit-book” refer to can be further broken down into the liquidity ways in which price information is communi- concession, the cost of communicating the information and the cost of waiting for potential I cated. In an open-bid market — the open outcry system on the futures exchanges, for example counterparties to respond.22 Other things equal, an efficient system of price communication is — offers to buy or sell at a specified price are I announced to all agents in the market. At the one that minimizes such transaction costs. While opposite extreme, in a sealed-bid market, orders the communication of price information is a are known only to the entity placing the order central function of securities markets, the fact and perhaps to a disinterested auctioneer. that the systems of price communication in the I foreign exchange market are not fully central- Direct trading in foreign exchange approxi- ized suggests that these systems do not represent mates the standard open-bid structure. The a cost-minimizing arrangement. salient difference between the foreign exchange I market and the standard arrangement is the bilateral pairing of participants in the foreign Structure of Prices exchange market. In principle, any participant I can contact a market-maker at any time for a The terms “double-auction” and “single-auction” price quote. The bilateral nature of such con- refer to the nature of the prices quoted. In a tacts and the time consumed by each contact double-auction market, certain participants pro- I together imply, however, that all participants vide prices on both sides of the market, that is, cannot be simultaneously informed of the cur- both bid and ask prices. Participants providing rent quotes of a market-maker. This practical double-auction quotes upon demand are known constraint on the dissemination of price infor- as market-makers, and they must have sufficient I mation is significant: it introduces the possibility capitalization to back up their quotes. In a single- of genuine arbitrage, that is, of finding two auction market, prices are specified either’ to market-makers whose current bid-ask spreads buy or to sell, but not both. In the foreign ex- I do not overlap. change market, market-makers provide double- auction prices, while brokers try to aggregate The limit order book, which is used by both single-auction quotes into two-way (inside) foreign exchange brokers and stock exchange specialists, is another intermediate form of price spreads. A broker’s book may occasionally be I empty on one or both sides. Rather than make communication. Although it would be possible a market in such cases, the broker provides, in principle for foreign exchange brokerage I books to be fully open for public inspection, in respectively, a single-auction quote or none at all. practice only certain orders — namely, the best Thus, whether double or single-auction prices bid and ask on each book — are revealed to market-makers, while the others remain con- are quoted depends largely on whether the agent quoting prices is providing market-making I cealed. As in the direct market, market-makers must contact brokers bilaterally to get these “in- services or simply attempting to acquire (or sell) the commodity. This issue is related to the side spreads.” Knowledge of the concealed limit orders would be of speculative value to market- degree of centralization in the market. The I absence of market-makers in a single-auction makers, because an imbalanced book suggests that large future price movements are more market, together with the presence of search likely in one direction than the other. costs, results in a tendency toward centraliza- I tion of price information, thus facilitating the More generally, price communication is inti- search for a counterparty. Inversely, decentrali- I mately related to the role of market-makers as zation of price information leads to a tendency 2lThi5 term is due to Demsetz (1968), p. 35. Tinic (1972), “See Logue (1975), p. 118. I p. 79, calls in “liquidity services.” a 60 toward double-auction prices, again to facilitate to the lnarket. For example, there may he a the search for a counterparty.” stochastic process that generates the “true” equilibrium price. Second, probability models of palticipants’ subjective beliefs about prices can MODELING TRADERS’ BEHAVIOR be used. Cont-oy and Winkler, for example, at- The microstructure liter’ature extends well be- tribute subjective normal price distributions to yond a simple description of market institutions. market-makers, who use Bayesian updating to Modeling the behavior of market participants is learn about the prices of incoming limit orders.” central to almost all discussions of micro- Objective processes can coexist with subjective structure. Although numerous approaches to beliefs about those processes. Harsanyi suggests such modeling have been taken, two common a consistency requirement for the subjective concerns are of special interest. These are the price distributions of multiple agents; these dis- treatment of price information by market par- tributions are each equated with a conditional ticipants, and determination of the bid-ask spread. distribution of a single distribution known to all.” The latter raises the interrelated issues of inven- Models can be further classified according to tory and quantity transacted. how they telate supply and demand. In particu- Price Expectations lar, there are both models with single price processes and with dual price processes. In dual Modeling the interpretation of price informa- price models, purchase orders (whether market tion is a crucial step in constrtcting microstruc- or limit orders) are generated by one process, tural models of price discovery.” Many diverse while sale order-s are generated by another.” approaches have been taken in such modeling. ‘I’he salient point here is that purchase and sale An almost universal simplification is to model orders come from independent distributions. securities markets in partial equilibrium, so that ‘rhis independence is especially clear in Conroy prices are not determined endogeneously in the and Winkler, where the distributional assump- traditional general equilibrium sense. This allows tions are explicit; there, independence implies the modeler to focus on the microstructure’s that any sequence of buy orders, regardless of finer details. Another common simplification is their prices arid quantities, has no effect on the to assume that agents ignore the impact of their subjective probability of a sell order at any price. own behavior on the market.” Statistical independence implicitly restricts the Rather than explicitly model such forces as ways in which orders can be generated. Put-- general equilibrium or recursive beliefs, models chase and sale orders are somehow motivated posit probability distributions that produce the independently, although the cause of this prices of orders in the market. Modelers have separation is not always specified. Statistical in- included randomness at one or both of two lev- dependence is not a necessary component of a els, depending on their focus. First, order dual price process, however. Cohen, Maier, prices can be generated by objective distribu- Schwartz and Whitcomb (1981), for example, as- tions, that is, by stochastic processes exogenous sume that actual market hid and ask prices are

“Note that the converse does not appear to hold. That is, extreme informational and comoutational resources on the centralization does not tend to eliminate double-auction part of agents, and models based on it are usually intrac- quoting. For example, the NASDAO system on the OTC table. Intermediate approaches allowing a finite degree of stock market centralizes price information while still sup- recursion must somehow justify the truncation of recursive porting numerous market-makers for every stock. beliefs, just as the standard model of atomistic agents allows no beliefs about beliefs and is justified by an as- “Notably, the term “price” is generally too inexact in a sumption on the relative size of individual agents. microstructurat context. One must often distinguish at a minimum between quoted prices, transaction prices and “See shaded insert on opposite page. equilibrium prices. There are also reservation prices, “See Harsanyi (1982), especially chapter 9, and the refer- market-clearing prices and closing prices (see Schwartz ences therein. His consistency requirement identifies a (1988), chapter 9, for the distinction between equilibrium unique equilibrium for the game. and clearing prices). If unspecified here, the intended defi- nition should be clear from the context. ~ market order is an order to trade at the best price available; a limit order specifies a price. These models “The alternative, which dates at least to Keynes’ “beauty represent a strain of the literature that was pioneered by contest,” is recursive beliefs, in which an agent considers Demsetz using straightforward supply and demand sched- the feedback of her own actions on the beliefs of others, ules (see shaded insert on page 63). Similar approaches and thence how the behavior on the other agents might af- were later taken by Garman (1976), Amihud and Mendet- fect her own beliefs, etc. See Keynes (1936), p. 156. The son (1980) and Conroy and Winkler (1981), among others. limiting case—an infinite recursion of beliefs—presumes

FEDERAL RESERVE SANK OF St LOUIS I 61

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independent Poisson processes and give inves- We take the dealer’s opinion of the “true” price of tors joint subjective distributions over those the stock to be exogenously determined by his in- prices. For the latter distributions, probabilistic formation set and ask how the dealer prices rela- independence of bid and ask prices is not ex- tive to his “true” price... plicitly required. Black (1989) models quantities This subjectivization of the pricing process is (independent of prices) of market orders. Quan- significant, because it allows for heterogeneous tities supplied and demanded are drawn from expectations and thus for more realistic model- different distributions, but the distributions are ing of price discovery. constrained to have the same mean. Garbade (1978), on the other hand, assumes a single, Research into the microstructure of the for- unknown and fixed equilibrium price, around eign exchange market should presume such het- which market-makers set their spreads. Incom- erogeneity among market-makers. There are ing buy and sell orders arrive via random numerous market-makers for foreign exchange: processes whose mean arrival rates depend on The Federal Reserve Bank of New York (FRB-NY) the difference between the quoted bid (or ask) (1989a) lists 162 dealing institutions in the U.S. price and the exogenous equilibrium price and, interbank market. There would be little point in thus, are not independent. such superfluity if all market-makers were iden- tical. Furthermore, it is well known that “taking The most common alternative to separate pur- a view,” that is, speculating on future prices, is 32 chase and sale processes is to model prices as routine for many participants. To omit this some function of a single scalar process. This heterogeneity from a model is to ignore an im- approach is in the spirit of the efficient markets portant characteristic of the market. literature, which posits a unique value for a security conditional on the available informa- The large proportion of market-makers in the tion, Ross (1987) points out that this approach foreign exchange market has another important can be regarded conceptually as a special case modeling implication. It implies that a single- of the dual price process, with supply and de- price process is more appropriate as a theoreti- mand infinitely elastic at a common price. Many cal representation of agents’ expectations. Mar- authors reveal their theoretical roots by using ket-makers consistently face other market-makers, terminology drawn from the literature on effi- who can hold positive or negative inventories of cient markets. Thus, for example, Barnea des- foreign currency with equal ease. A quote that cribes a stock’s “intrinsic value,” which follows a is “off the market” on the high side will be hit random walk.” Similarly, Copeland and Galai (i.e., traded upon) just as surely as a quote that posit a “‘true’ underlying asset value - -- known is off on the low side. This is also true of cus- (cx ante) to all market participants.”° In con- tomers, who normally enter the market with a Garbade’s (1978) exogenous equilibrium predilection to either buy or sell. As Burnham trast1 3 price is unknown. notes:’ It is possible to extend the single price ap- The customer knows that if the first marketmaker proach beyond the efficient markets tradition is too far off the market price, he can unexpected- by modeling the value of a security subjectively ly take the other side of the quote and resell the rather than as an objective fact. Glosten and position to a second marketmaker. Milgrom (1985), for example, begin with an ex- The point is that the market-maker must expect ogenous random value representing the consen- to be penalized for underestimating as well as sus value of a stock given all public information. overestimating his counterparty’s valuation of Investors do not act on this exogenous value the currency. From the perspective of the mar- directly; instead, they act on their expectation ket-maker, who quotes a spread and observes a of it, conditional on their information set. Ho response, the forces determining short-run ef- and Stoll personalize price expectations in a fective demand and supply are not merely re- similar fashion:” lated, but indistinguishable.

“See Barnea (1974), pp. 512-14. “See, for example, Kubarych (1983), p. 29, or Burnham (1991), p. 139. ‘°SeeCopeland and Galai (1983), p. 1458. “See Burnham (1991), p. 136. “See Ho and Stoll (1981), p. 48. For a similar example, see Stoll (1978), especially p. 1136.

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£9 I 64 perative of arbitrage avoidance must he re- specialists allow them to exact monopoly rents garded as the first priority in individual market- from other investors. In his view, the natural niaker pricing, to which all other factors (e.g., monopoly argument, while used as an apology purchasing power parity) must be subordinated. for barriers to entry, remains unsupported em- pirically: “There is no empirical evidence to sup- port the proposition that lmarket-making] is, in fact, a natut-al monopoly.”~Indeed, if market- Market-makers’ Bid-Ask Spreads making is a natural monopoly, barriers to entry should he unnecessary. ‘l’he bid-ask spread has attracted consider-able interest in the literature on market microstruc- The foreign exchange market has no apparent ture. The complexity of modeling the spread is barriers to entry other than the need for suffi- largely because it requires incorporating a sub- cient capitalization. It also has no apparent bar- stantial amount of institutional detail. At a facile riers to exit. The market supports a large and theoretical level,, a market-maker’s spread appears mci-easing number of competing market-makers. to be a direct violation of the latv of one price, Unless it can be sho~-vnthat there is some sub- since it assigns two prices to the same com- tle restriction in the foreign exchange market modity. Several explanations have been offered that prevents consolidation of the market-making to resolve this seeming inconsistency. They can function, one must conclude that market-making be roughly categorized as involving the cost of per se is not a natural monopoly.” The multi- dealer services, the cost of adverse selection and tude of market-makers also implies that they the cost of holding inventory.” cannot earn monopoly rents by embedding a premium for predictable immediacy in the The dealer services argument can be traced spread, although the spread may still cover the back at least as far as Stigler (1964), who argues costs of processing orders. that stock exchange specialists charge a “job- ber’s turn” as compensation for the costs of act- Other research suggests that a market-maker’s ing as a specialist. The analysis of dealer services job is more complex than the mere sale of was formalized by Demsetz (1968), who identi- counterparty services. A second explanation for fied “predictable immediacy” as the particular the bid-ask spread — adverse selection — can service for which investors are willing to pay. he traced to Bagehot (1971). He starts with This identification hints at the complex question “liquidity-motivated transactors” who pay the of what liquidity is and where it comes fi-orn. In market-maker the price of the spread in ex- a busy market, liquidity is a public good: a con- change for the service of predictable immedi- tinuous stream of buyers and sellers generates acy. The market-maker also confronts traders predictable immediacy as a by-product of their who have inside information, however, and who trading. can therefore speculate profitably at the expense of the market-maket-.” The market-maker must ‘l’he determinants of the level of compensation charge everyone a widet- spread to compensate are themselves a topic of debate. Stigler argues for losses to the information-motivated traders. that, because centralization of exchange limits I fixed costs and aggregates separate transaction Because of the relatively abstract nature of orders into less risky actuarial order flows, it currencies as commodities, it is difficult to con- implies economies of scale and thus a natural struct examples of ‘‘inside” information on monopoly for market-making.’” Smidt (1971) foreign exchange rates. One exception is money I counters that barriers to entry among NYSE supply announcements, which, if known before

“This is essentially the same taxonomy as provided by Bar- though the industry as a whole experiences economies ot I nea and Logue (1975), although they use the terms scale. Hamilton (1976) also addresses the natural monopo- ‘liquidity theory,” “adversary theory,” and “dynamic ly question; Reinganum (1990) provides evidence on li- price/inventory adlustment theory,” respectively. quidity premia for NYSE vs. NASDAQ stocks. ‘“See Stigler (1964), p. 129. “This situation is called adverse selection, because, in a I 7 market with competing market-makers, the one who gets ‘ See Smidt (1971), p. 64. the insider’s business is a loser rather than a winner. “For example, in the context of the OTC stock market, Ben- Bagehot also posits a third class of investors, who only ston and Hagerman (1974), p. 362, conlecture that. “deal- think they have inside information; they speculate, but lose ers may face positively sloped marginal cost curves which on average, and are indistinguishable to the market-maker shift down as industry output increases.” The idea is that from the liquidity-motivated traders. market-making per se is not a natural monopoly, even

FEDERAL RESERVE BANK OF St LOUIS S 1 65

publicly distributed, might provide a basis for over time in the face of a stochastic order flow, I profitable speculation. Another form of informa- will shift both bid and ask rates downward (up- tion that can be construed as inside information ward) and increase the width of the spread when is knowledge of an arbitrage opportunity. Con- a positive (negative) inventory has accumulated.2 sider a hypothetical market in which there are We should expect two of these three ration- I numerous decentralized market-makers who do ales for the spread to apply to market-makers’ not quote spreads, but single prices at which bid-ask spreads in the foreign exchange market. they are willing both to buy and sell. Unless Because there are numerous market-makers, there were a perfect consensus among the mar- I competition should eliminate their ability to earn ket-makers on the value of the foreign currency, monopoly rents by charging a premium for pre- all of them would be vulnerable to arbitrage. A dictable immediacy per se. The adverse selec- decentralized market makes a perfect consensus tion argument does apply in the foreign ex- I difficult to achieve. Without centralizing price change market, however, since the spread allows information, it is impossible to know if no arbi- market-makers some protection against arbit- trage opportunities exist. A bid-ask spread, in rage opportunities. Arbitrage opportunities can contrast, allows a market-maker to include an I be construed as a form of inside information in error tolerance in her prices, thus facilitating a a market where price information is not cen- price consensus: it is easier to get bid-ask tralized. In accordance with the dynamic optimi- spreads to overlap than to get scalar prices to I- zation models, a market-maker’s inventory level coincide. The spread also provides the mar- should affect the spread, widening and shifting ket-maker with some degree of protection I from adverse selection in the form of arbitrage. it as inventories accumulate. The bid-ask spread is also affected by invento- Brokers’ Spreads ry considerations. This idea dates back at least as far as Barnea and Logue (1975)A°The notion So far, the discussion of the bid-ask spread I of a desired inventory level for the market- has focused on models in which bid and ask maker underlies all of these models. In the prices are set by individual market-makers. The simplest case, the desired level is set at zero, dual role of the stock exchange specialist sug- I and a constant spread is shifted up and down gests that this is only part of the story. Spreads on a price scale to equalize the probability of are produced in two fundamentally different receiving a purchase order with that of receiv- ways. It is only when limit orders are sparse I ing a sale order. The result is that the expected that a NYSE specialist must step in as a market- change in Inventory is always equal to zero, and maker to provide an “orderly market.”~’When (with all trades for one round lot) the inventory limit order volume is sufficient, the specialist I level follows a simple random walk. acts as a broker, accounting for incoming limit An undesirable implication of random-walk orders on the lhnit order book, and pairing market orders against them. Cohen, Maier, models of inventory is the inevitable bankruptcy Schwartz and Whitcomb (1979) note that inade- of the market-maker. Finite capitalization levels quate attention has been given to the fact that I for market-makers impose upper and lower not all prices are market-maker spreads. The bounds on allowable inventories. Because inven- market often makes itself without specialist as- tory follows a random walk, with probability sistance, through the aggregation of limit ord- one It will reach either its upper or lower bound I ers on the book. in a finite number of trades.” The dynamic op- timization models of Bradfield (1979), Amihud The foreign exchange market differs from the and Mendelson (1980) and Ho and Stoll (1981) NYSE in that the market-making and brokerage I resolve this problem. They conclude that a roles are separated: market-makers do not act market-maker, optimizing his bid and ask prices as brokers, and brokers do not make markets,

I °Bameaand Logue attribute It to Smldt (1971), although ~Seeshaded insert on page 66. 43 Smith’s paper does not explicitly develop the connection The NYSE defines this role in rule 104: “the specialist between the market-makei’s inventory and his spread- For- should maintain a continuous market with price continuity mal models of the relationship between inventories and and close bid and asked prices, and minimize the effect of spreads can be found in Stoll (1978), Amihud and Mendel- I temporary disparity between public supply and demand.” son (1980), Ho and Stoll (1981) and Sirri (1989), among others. See Leffler and Faiwefl (1963), pp. 211-12. I 4l5~, for example, Ross (1983), pp. 106-07. NOVEMBERFDE~EM8ER1991 66

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FVflFPM RFSFPVF RaNK OF St WuiS a 67

ers transact immediately and are removed from cui-rency puts a market-maker at a bargaining I the book.~~Perhaps because of its complexity, disadvantage. In addition, anonymity can help such a derivation has not been attempted. pair market-makers who ordinarily would not contact each other directly. ‘l’hese issues have Cohen, Maier, Schwartz and Whitcomb (1979) not been explored at a theoretical level. Until an I model limit orders as generated by “yawl” distri- adequate microstructural model of the strategic butions These distributions satisfy three heu- benefits of anonymity is developed, the theoreti- ristics for the incentives of investors placing cal understanding of foreign exchange broker- limit orders~~The heuristics are motivated by a age will be limited I notion of the centralized exchange as a market for immediacy; placers of limit orders produce immediacy, and placers of market orders con- CONCLUSION’S I sume it. This relationship between limit and market orders is formalized in Cohen, Maier, Students of the foreign exchange market can Schwartz and Whitcomb (1981), where each half draw several lessons from the literature on of the brokered spread is assumed to be gener- market microstructure. The most fundamental I ated by a compound Poisson process A mini- of these is that the institutional details of ex- mum brokered spread results: if the limit order’s change in a market can affect all aspects — bid (ask) price is sufficiently close to the special- price, allocational, informational and operational — of the market’s efficiency. A multitude of I ist’s ask (bid), the benefit to the investor of being able to specify the price of a limit otder is over- market-makers who can provide liquidity, or predictable immediacy, arises in response to the whelmed by the cost of foregone immediacy. decentralization of the market. As a result, I Because models of the informational content search costs are reduced relative to a world of brokered spreads are few, the literature without market-makers, because finding one of offers little guidance in modeling brokered many market-makers amounts to finding a quotes in the foreign exchange market. ‘I’he counterpartv. Brokerage also reduces search I yawl distribution is the only explicit distribu- costs by achieving a degree of centralization in tional form for brokered spreads in the litera- price information. ture. Unfoi-tunately, its heuristic basis cannot be An unanswered question is why the specific I transferred directly to the foreign exchange combination of trading structures characteristic market, because market-makers there differ of the foreign exchange market — a decentral- from stock market investors. Indeed, this may ized, open-book, direct arrangement and a I be an instance in which the foreign exchange quasi-centralized, limit-hook, brokered arrange- market informs microstructure theory rather ment — should coexist. Apparently, each struc- than the other way around. The extant ap- ture has relative advantages, but a full analysis proaches to brokerage treat it as a service of these advantages is lacking. Is there a single I facilitating predictable immediacy. This aspect of microsti-ucture that would combine the relative brokerage is redundant in the foreign exchange advantages of the chrect and brokered arrange- market, because of the multitude of market- ments? Put another way, why does the micro- I makei-s, each providing immediacy. This redun- structure of the foreign exchange market differ dancv suggests instead that foreign exchange from that of the stock exchanges, the futures hi-okerage serves some other function. pits and the OTC stock market? Answering these questions will require a fuller specification of One motive for trading through a foreign ex- I the objectives of a trading system and a better change broker is to maintain anonymity — the understanding of the impact of rnicrostructural name of the hank placing a limit order is not arrangements on those goals. revealed unless a deal is consummated and then 1 1 only to the counterpart~’. °Anonymity is valu- These issues pro\’ide a motive for deeper in- able, because revealing a need to buy or sell a vestigation of the behavior of the foreign cx- I 4 45 ~ Anorder statistic is defined as follows: the sample realiza- The yawl distribution, named for its resemblance to a sail- tions of a finite number of independent random variables boat, is a probability distribution contrived for modeling the are ranked in increasing order, and the kth order statistic generation of buy (or sell) limit orders. See Cohen, Maier, I is the kth number in that list. For the foreign exchange Schwartz and Whitcomb (1979, 1983, 1986) for details. market, the modeling is still more complex, since brokers 46 5ee Kubarych (1983), p. 16, Burnham (1991), p. 141, and compare books amongst themselves in the sense that in- Federal Reserve Bank of New York (l989b), p. 41-3. I coming orders can cross against any book.

NOVEMBER/DECEMBER 1991 68

change m~u’ketand its participants. Market- anonymity is an important motive for trading in makers are the crucial element: they pi-ovide all the broket-ed market. Yet the stt-ategic value of tr~msactionprices in the market and are in- anonymity in foreign exchange quoting is not volved in at least one sidle of every deal. The well understood at a theoretical level. In addi- microstructure literature has developed numer- tion. there is not a clear understanding of the ous models of the interpretation and setting of differences in price information between a prices by traders. 1’he diversity of expectations mat-ket-maker’s spread and a ht’oker’s spread; models used in the literature illustrates the im- this too remains a topic for future i-esearch. portance of tailoring such models to the specific environment confronted by market participants. From a broader perspective, a better under- Given that a foreign exchange market-maker’s standing of institutional choice and change as double-auction quote can be hit on either side regards securities market mnicrostructure is (bid or ask) with equal ease, he must try to necessary. Most microstructural research has maneuver his spread to bracket the market’s been devoted to analyzing the impact of micro- consensus valuation of the foreign currency. In structural factors on important economic vari- other words, suppliers and demanders of cur- ables, such as price and allocation. Relativel rency are indistinguishable to the market-maker little attention has been paid to the effect of cx ante. The inability to separate the forces die- economic factot-s on the choice of an institution- termining effective demand from those tIe- al microstructure. termining effective supply in the very short run imply that a single-price expectations process (rather than a dual-price process) is appropriate REFERENCES in modeling market-makers in the foreign ex- Allen, Wiliam A. ‘A note on uncertainty, transaction costs change market. and interest parity,” Journal of Monetary Economics (July 1977), pp. 367-73. A market-maker’s bid-ask spread serves several purposes. Competition among market-makers in Amihud, Yakov, Thomas S. Y. Ho, and Robert A. Schwartz, the foreign exchange market implies that they eds. Market Making and the Changing Structure of the Securities Industry, (Lexington Books, 1985). should be unable to charge a monopoly premium for the set-vice of predictable immediacy. 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