Pricing Behavior in an Off-Hours Computerized Market

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Pricing Behavior in an Off-Hours Computerized Market
Mark Coppejans

Department of Economics

Duke University
Ian Domowitz

Department of Finance

Smeal College of Business Administration

Pennsylvania State University

February 1999

This paper is a substantially different version of a working paper circulated under the title, The Performance of an Automated Trading System in an Illiquid Environment. We thank Gordon Kummel, of K2 Capital Management, Inc., for making the data available for this paper, and the Institute for Policy Research, Northwestern University, for financial support. We have benefited from the comments of seminar participants at Cornell University, Georgetown University, Indiana University, the Federal Reserve Bank of Kansas City, and the 1997 Olsen High Frequency Data Conference. Helpful suggestions also have been received from Dick Baillie, Charles Cao, Larry Glosten, and an anonymous referee. Correspondance may be sent to Ian Domowitz, Department of Finance, SCBA, Penn State University, University Park, PA 16802, phone 814-863-5620, email at

Automated markets are becoming increasingly widespread, and their efficiency properties are of corresponding concern to regulators and exchange policy makers. Many systems are implemented in settings characterized by a distinct lack of liquidity, however, often by design. We evaluate the performance of such a market, the GLOBEX overnight trading system, in absolute terms and relative to a liquid benchmark, the floor market of the Chicago Mercantile Exchange. Our results with respect to bid-ask spreads and adverse selection suggest that the nature of the environment is an important determinant of market performance, but that an automated market can operate well in a relatively illiquid setting. Price clustering, indicative of a lack of pricing efficiency, is prevalent on the automated system, but price resolution improves as trading frequency increases.
JEL classification: G14, G15, G29

Key words: automated trade execution, liquidity, bid-ask spreads, price clustering, market efficiency

1. Introduction

Economic interest in automated market structure is motivated by three interrelated factors. The form of the trading institution affects agent behavior, the properties of transactions prices, and welfare. This list is a primary contribution of the theoretical and experimental work on auction mechanisms, and is a finding emphasized in the literature on financial market microstructure.1 Second, the automated auction is transforming the landscape of financial markets. While debates exist with respect to the plausibility of the eventual dominance of such markets, their sheer number motivates research interest.2 Finally, the pricing and efficiency properties of automated markets have a strong influence on market regulation. Automated markets, their design, and consequent impact on the price discovery process are continuing concerns for a variety of regulatory bodies worldwide.3

Many systems are deliberately implemented in settings characterized by a distinct lack of liquidity. Such environments include “off hours” and overnight markets, markets characterized by listings of very new companies and derivative instruments, emerging market venues, and trading in illiquid classes of securities. Examples include LIFFE’s APT, the CBOT’s Project A, and the SATO system of the Mexican Stock Exchange.

The use of automated systems for such applications is generally driven by cost considerations, not by any logic implying that computerized market structure is somehow uniquely suited for the purpose intended. This raises an important question for regulators, exchange policy makers, and system designers: can a computerized auction perform well in an illiquid setting, thus satisfying the goals of the technology choice and the requirements of regulators?

We investigate this issue by studying some aspects of pricing on the GLOBEX automated trading system for futures contracts. GLOBEX is an “off hours” overnight trading system. Its functional design is a paradigm adhered to by over 70 percent of automated markets currently in operation.4 The market environment is generally thought to be illiquid, and we present evidence on this point. In order to do so, and to provide interpretation of the performance results, a benchmark, the floor market of the the Chicago Mercantile Exchange (CME) is used. The CME floor is thought to be one of the most liquid markets in the world, especially in the instruments considered in our analysis (see, for example, Laux and Senchack (1992)). We match trading data in the same instruments, during the same 24-hour day, across the two market structures.

The use of the floor market as a benchmark should not be confused with studies that attempt a comparison of floor versus automated trading during the same trading hours.5 We make no claims of superiority in terms of market structure, nor are we assessing relative market quality in an effort to inform policy makers with respect to the pros and cons of automated versus open outcry trading. Our focus is on pricing characteristics of the automated market in an illiquid setting. Previous empirical work on automated market structure has dealt exclusively with very liquid environments, often for reasons of data availability. Sometimes, as in our analysis of price clustering and market efficiency, absolute measures of performance are available. In other cases, the benchmark is required, because there exists no absolute measure for assessment purposes.

Prior empirical work and the characteristics of other markets also have implications with respect to the interpretation of our results. The design of a standard computerized continuous market does not, in and of itself, appear to generate a poor trading environment in terms of liquidity and performance characteristics. The Swiss SOFFEX market and the German DTB market, for example, are virtually identical in design to the GLOBEX system, but operate during regular trading hours. They both are generally thought to be quite liquid, and formal analysis supporting equal or greater liquidity in the DTB market relative to the LIFFE floor is provided by Pirrong (1996) and Frino, McInish, and Toner (1998).6 Taken together, these authors, and Kofman and Moser (1997), provide evidence of roughly equal bid-ask spreads, adverse selection components, and pricing efficiency across the automated and floor markets. Biais, Hillion, and Spatt (1995) document excellent liquidity provision in the CAC market of the Paris Bourse, a design based on CATS and also virtually identical to that of GLOBEX.

There also is a revealed preference over time for the computerized auction. The Toronto CATS system has replaced the traditional trading floor. The French MATIF recently converted to an automated setting, a particularly interesting experiment, since the floor was allowed to operate concurrently, while it lasted. Domowitz and Steil (1999) document fourteen full or partial conversions of floor markets to automated auctions over 1997-1998 alone. Such movement suggests that computerized markets are, at least, not believed to be inherently illiquid or to provide poor provision of trade execution services.

Our analysis of a computerized market in an illiquid environment is organized around four topics of interest in the literature on trading market structure. They are bid-ask spreads, adverse selection, price clustering, and price resolution. Each topic is separately motivated in sections 3 and 4. We examine trading in the S&P futures contract and futures contracts of the Deutschemark, Yen, and Swiss Franc. The GLOBEX data are new, and a description, within and across markets, is given in section 2, together with some institutional detail.

Our results with respect to bid-ask spreads and adverse selection suggest that the nature of the environment is an important determinant of market performance, but that an automated market can operate well in a relatively illiquid setting. Spreads, their adverse selection components, and the volatility of this cost of trading are roughly the same for the S&P contract, as for the floor benchmark. Although spreads are less sensitive to changes in trading activity on GLOBEX relative to the floor, the relationship between volatility and the spread appears to be the same across trading venues. In contrast, currency futures spreads are high in the overnight market, driven by a large adverse selection component. The environment within which the currency futures are traded is quite different from that of the S&P contract, however. We discuss the impact of the overnight interbank foreign exchange market in this context.

We then examine price clustering and resolution, motivated by their relationship to efficient pricing and to the degree with which the underlying value of the security is actually revealed. Pronounced clustering is found on GLOBEX, while the more liquid benchmark exhibits pricing behavior in line with theoretical values suggesting efficient pricing. An analysis based on time-varying Markov chains reveals, however, that price resolution improves on GLOBEX as the intensity of trading rises. This suggests better system performance as liquidity increases.

2. Institutions and Data

2.1. Automated Market Structure

Stoll (1992) characterizes a financial market as a communications system consisting of three components: an information system, an order-routing system, and a trade execution mechanism. An automated market might be described as a computerized blueprint for Stoll’s general description. The programming embodies specific rules concerning the form of allowable messages that traders can send and receive, as well as the nature of information displayed to system participants. With respect to execution, a separate rule set governs the process by which these messages are translated into transactions prices and quantity allocations. The heart of the transactions algorithm is a list of execution priorities assigned to each incoming order routed to the system.

Allowable messages in the GLOBEX system are bids and offers in terms of price-quantity pairs (limit orders), and instructions to hit an existing bid or lift an existing offer. The system displays a variety of information, most notably including separate displays of transactions, best bids and offers, and the five best bids and offers with aggregate quantity on both sides resting on an electronic limit order book. There are no personal identifiers attached to messages in the display.

GLOBEX is a strict price and time priority system, with some allowance for undisplayed order flow to be transacted at a lower secondary priority. New orders are filled at the best available price at the time or order entry. In case of ties at price, orders are filled on a first-in, first-out basis. A trader may elect to simply transact at the best bid or offer in the system, without submitting a contraside limit order. The maximum possible quantity will be traded by filling an order on the buy or sell side, subject to liquidity available in the system. Unfilled quantities remain on the order book until cancelled. Cancellation may occur at any time. The design is very similar to that of the CAC system operating on the Paris Bourse, for example.

The benchmark used in some of our analysis is the floor market of the CME. Rules and characteristics of open outcry trading are well known. Since we are not evaluating performance in terms of system design, we omit a detailed comparison of institutional details. Extensive comparisons exist in any case; see, for example, Harris (1990), Bollerslev and Domowitz (1991), and Pirrong (1996), a list which is hardly exhaustive.

2.2. Data

Our analysis is based on trading data for the September futures contracts on the S&P 500 index (SP), the Deutschemark (DM), the Yen, and the Swiss Franc (SF) over the period 7/1/94 through 9/1/94.7 Trading hours vary for the currencies relative to the stock index. On Central Standard Time, the trading week opens with GLOBEX trading on Sunday at 6:30 p.m., and closes on the floor on Friday. If Monday is a holiday and Tuesday is not, trading starts on Monday at 6:30 p.m. The floor stops trading in the S&P contract at 3:15 p.m., and GLOBEX opens at 3:45, with continuous trading up to a half hour before the floor again opens at 8:30 a.m. Currency floor trading ends at 2:00 p.m., with a GLOBEX opening at 2:30. It stays open until 6:45 a.m., and floor trading again resumes at 7:20.

GLOBEX trading data include all best bids and offers, as well as transactions prices, on a continuous basis. Continuous transactions data are available for trading on the CME floor.8 The number of observations varies, depending on trading system and contract type, ranging between roughly 3000 to 8000 transactions on GLOBEX and between about 72,000 to 95,000 transactions on the floor. Some of our analysis is restricted to more time-aggregated information, yielding roughly 1200 observations on floor trading as opposed to 2700 observations on GLOBEX activity, on a 15-minute basis.

2.3. Market Characteristics

A brief summary of the data is contained in Table I. Median prices and percentage returns are basically the same across trading venues, with the latter being zero to several decimal places. The volatility of logarithmic returns is lower on the floor by a factor of two to four, depending on the contract. The number of transactions per hour on the floor ranges from about 27 times that observed in the overnight market for the S&P contract to an average multiple of 67 for the currencies. There is anecdotal evidence that order size also is much lower overnight. Conversations with traders during the sample period generate complaints that it is difficult even to transact 100 contracts at a time in GLOBEX, while such an order is commonplace in the benchmark market.

Some theoretical models of trading behavior link volatility to volume.9 In these framworks, the combination of lower trading volume and higher returns volatility suggests a low level of liquidity in the electronic market. The impression of low liquidity relative to the benchmark is reinforced by examining the ratio of the standard deviation of price to the number of trades. This measure is suggested by a characterization of liquidity as the market’s ability to absorb quantity without an appreciable effect on price. For all contracts, this statistic is an order of magnitude smaller on the floor relative to GLOBEX. For the S&P 500 contract, for example, the ratio is 0.004 for the benchmark, and 0.045 for the automated system.

There are related, but competing, explanations of the volatility differences across trading venues. Higher volatility may be a function of system design. The German DTB market, however, is virtually identical to the GLOBEX system, and both Kaufman and Moser (1995) and Pirrong (1996) find volatility on DTB to be comparable to that on the floor-based LIFFE. Alternatively, higher volatility may be ascribed to information effects, both with respect to the composition of the trader population and other overnight trading activity. There is relatively little overnight trading in the equities underlying the index, compared to the currencies, for which the overnight interbank market operates. Interestingly, GLOBEX volatility is much higher, and differences with the benchmark greater, for the currencies than for the S&P contract. Finally, the characteristics of returns and associated volatility may be largely driven by bid-ask spreads. We return to this issue in the next section.

We report some additional information for the opening hour, closing hour, and the middle of the trading session in Table II. Statistics are given for the S&P contract and the DM contract. Differences across time of day for the other currencies are qualitatively the same as for the DM.

Opening and closing effects are evident in both markets, despite the nearly continuous segue of activity from one trading venue into another. This effect is much more pronounced for the S&P contract, however, than for the currencies. The number of S&P trades per hour at the open on GLOBEX is over three times that of the main trading session, while activity in the DM contract changes little. The use of GLOBEX S&P trading facilities just prior to the opening of the floor market is particularly notable, with a startling 103 trades in the hour just before the GLOBEX close, relative to about 12 at the GLOBEX open. There is no formal procedure on the floor to set an opening price, unlike many other markets. GLOBEX appears to be fulfilling the function of a pre-opening session during its last hour.

The variance of S&P price changes per trade drops sharply before the opening of the floor, from 0.14 at the GLOBEX open to only 0.02 at the close. The decline is purely a function of the larger number of trades. The standard deviation of price changes is almost constant across time of day. This stability of volatility across time of day also is observed for trading on the floor, and in both venues for the currency contracts.

We also report the first order serial correlation coefficient of price changes. It is negative but relatively large on GLOBEX, especially at the open and the close. Serial correlation in the benchmark market is generally smaller. Time of day differences are reasonably large in both venues. Filtering the data using a dynamic two-factor model (Engle and Watson (1981)) to account for unobservable changes in inventory and shocks to order flow reduces the magnitude of the correlations on GLOBEX, making them more comparable to the benchmark.

3. Bid-Ask Spreads and Adverse Selection

Transactions costs and information in computerized trading venues have been topics of debate beginning with the work of Melamed (1977). We investigate the former using the bid-ask spread. An examination of the adverse selection component of the spread may then shed some further light on the behavior of the spread and information processing in the automated overnight market. A standard model of price dynamics is used to tie the analyses together.

3.1. Model Specification

The approach to the examination of bid-ask spreads and adverse selection components is driven in part by data availability on both markets.10 We begin with the basic framework proposed by George, Kaul and Nimalendran (1991).

Let Rt denote the difference in transactions prices from time t to time t-1 and denote the unobservable expected return for the period between transactions at these points in time by Et. Define Qt to be an indicator taking on a value of +1 if the transaction is at the offer and -1 if the time t transaction is at the bid. The basic model can be expressed in terms of the following two equations:

, (1)


where s denotes the bid-ask spread and  is the adverse selection component of the spread. The disturbances, t and t, are assumed to be mean zero white-noise. The model's structure is based in part on the assumption, E(Qt|Qt-1)=0.

The emphasis of George, Kaul and Nimalendran (1991) is on the contribution of positive serial correlation of expected returns to spread component estimation. Huang and Stoll (1994) argue that on the level of transactions data, changes in expectations should be unimportant. We test this hypothesis using a moment condition derivable from the basic equations above, namely11

. (3)

The serial correlation coefficient is estimated by generalized method of moments (GMM), with the usual heteroskedasticity corrections to standard

errors. We fail to reject the null hypothesis of zero serial correlation in six of the eight cases at any reasonable level of statistical significance, and the point estimates in the remaining two are quite small.12 We therefore follow the suggestion of Huang and Stoll (1994), and consider estimation of the adverse selection component setting cov (Et Et-1) equal to zero.13 Our main results are obtained through an augmented version of equation (1),


in which Ft is a measure of market intensity, calculated as one plus the number of transactions per five minute period; and denote one plus the time (in minutes) to the open and close, respectively; and and are dummy variables, which take on the value of one during the hour just after the open and prior to the close, respectively. The time series on Qt is directly observable on GLOBEX; it is derived for the floor using the Lee and Ready (1991) algorithm.14 The spread, s, is now allowed to vary over time, in response to market conditions.15 This permits a calculation of the correlation of the average estimated spread with other variables of interest below.

The additional variables index potential differences with respect to liquidity considerations, as well as simply to account for opening and closing activity. The variable, Ft, provides a direct correction for differences in trading frequencies over the day. The term, max (Tt,o, Tt,c), serves much the same function, but indexes activity by time-of-day. Finally, the open and close dummies adjust for any differences in opening and closing activity across the two systems. In practice, the time-of-day effects appear to capture the bulk of any liquidity-related statistical variation in the data.

3.2 Bid-Ask Spreads

Bid-ask spread figures are contained in Table III. Point estimates and robust GMM standard errors are reported for overall activity, the open and the close, and for trading activity an hour after the open to an hour before the close. The tick size for the S&P contract is 0.05, while a tick for the currencies is 0.0001, scaled by 100 to be 0.01 in the table and discussion below. The magnitude of the benchmark floor spreads is about two ticks for all contracts, which represent slightly larger figures than reported by Laux and Senchack (1992).

For the S&P contract, the spread is nearly the same for the floor and GLOBEX, regardless of time period within the trading session. Overall, the floor spread is only 2 percent higher than that on GLOBEX. The largest difference is a spread of 0.110 on the floor at the open, compared to 0.103 during the GLOBEX closing hour, a natural comparison given the contiguity of trading sessions. On the other hand, GLOBEX spreads widen relative to the floor for the traded currencies, ranging from three to five ticks, with the lowest in the most heavily traded contract, the DM, and the highest for the least traded contract, the SF.

The relative intensities of trading activity do not appear to account for the difference in results across the two types of contracts. Correlations of the spread with the frequency of trading are reported in Table IV. Existing theoretical models deliver different predictions of the correlation between the spread and trading activity, depending on the specification of traders' preferences and information sets. The correlations here are large and uniformly positive, consistent with risk averse behavior. Correlations for the currencies are substantial, but somewhat smaller than those estimated for the S&P contract, a finding that is also observed in floor trading.

Overnight trading environments are not necessarily the same across instruments for a single automated trading mechanism, however. The institutional wedge between our two classes of contracts is the existence of the overnight interbank currency market. After-hours futures traders in currencies have the choice of trading the contracts directly on GLOBEX or dealing in the interbank market through the “exchange for physical” mechanism. There are several possible factors at work here. Overnight interbank trading activity can diminish liquidity in the automated market, especially for the Asian currency, relative to the floor. This would account, at least in part, for the wider spreads on GLOBEX. Another possibility is that he overnight spot market is so large relative to GLOBEX that independent price discovery does not occur on GLOBEX. Combined with the exchange for physical mechanism, this would suggest that spreads on GLOBEX might look more like those observed in the spot market. Interestingly, Lyons (1996) reports a spread of three ticks in the DM spot market, precisely the result obtained here for GLOBEX.16 Finally, there simply may be more risk and opportunities for adverse selection, given the relative market sizes. We investigate this issue further below.

In the last section, we raised the possibility that differences in the characteristics of price changes might be driven by bid-ask spreads. We investigate this issue further by computing the correlation of average spreads with price changes and volatility. Over the full trading session, the correlation with price changes is positive, excepting the Yen contract, consistent with the theoretical model of Amihud and Mendelson (1986) and the empirical results of Cao, Choe, and Hatheway (1997). Regardless of sign, however, the numbers are generally very small. This result holds both for GLOBEX and the benchmark, suggesting that returns themselves have little relationship with the size of the spread for the financial instruments considered here.

Volatility differences observed across trading venues do not appear to be directly attributable to the spread. There is generally a strong positive relationship between volatility and the spread, consistent with the results of Frino, McInish, and Toner (1998) for the DTB. Correlations computed over the full trading day are only slightly smaller on GLOBEX relative to the benchmark, however.

We also report the standard deviation of the spread, as a measure of variability in the cost of trading. Spread volatility is clearly a function of the size of spread, and otherwise appears to have little to do with the trading mechanism. For the S&P contract, spread volatility is roughly the same across markets, as is the size of the spread itself. On GLOBEX, variability increases as the spread increases across currencies, remaining roughly the same for currencies on the floor.

3.3. Adverse Selection

The adverse selection component of the spread may be higher for currencies, widening the spread during periods of increased market activity. Such a result would be consistent with the spreads reported in Table III and the correlations in Table IV. Trading in the interbank foreign exchange market takes place at high speeds, exacerbating the potential of adverse selection for GLOBEX currency traders operating in a thin market. The same possibility does not exist for trading in the S&P index contract after floor trading hours in Chicago and New York.

Estimates of the adverse selection proportion of the spread appear in Table V. The magnitudes of the estimates are in line with those in other studies. The S&P results are not grossly different than those obtained for a group of liquid Major Market Index stocks by Huang and Stoll (1994), for example. They report an average adverse selection component of 0.43 for large trades, which is an appropriate comparison given the large dollar value of futures trades considered here. The estimates of GLOBEX adverse selection components for currency contracts are similar to that reported for the Bund contract on the DTB by Frino, McInish, and Toner (1998).

The adverse selection component is larger on the computerized system, relative to the benchmark, for all currencies and almost all time periods; the only exception is exhibited by the DM contract at the GLOBEX open, but the difference is small and statistically insignificant. Based on activity over the entire trading day, GLOBEX adverse selection components exceed their floor counterparts by 23 to 32 percent. These differences are largely driven by activity during the GLOBEX closing hour, compared with the opening of the floor. These are two nearly contiguous trading periods during which trading activity in both markets, as well as in the spot market, is particularly high.

In contrast, the adverse selection component for the S&P contract on GLOBEX is less than that observed for the benchmark. The floor component is about 17 percent higher, on average, a difference rising to 22 percent, if the open and close are excluded from the calculations.

The evidence suggests that while spreads and spread behavior in the automated mechanism may be similar to that observed on the floor, even in an illiquid environment, GLOBEX performance deteriorates in a setting characterized by high adverse selection. A similar result is produced by Frino, McInish, and Toner (1998), in their study of Bund trading on the DTB.

4. Price Clustering and Resolution

Price clustering represents the use of discrete price sets that are coarser than those determined by the market tick size. It is a market regularity studied empirically by Harris (1991) for stocks and by Goodhart and Curcio (1991) for trading in the interbank foreign exchange market. Interest in this phenomenon is motivated by its inconsistency with market efficiency (Osborne (1962), Niederhoffer (1966)) by its potential signaling of collusion (Christie and Schultz (1994)), and by its link to the degree with which the underlying value of the security is actually revealed (Ball, Torous, and Tschoegl (1985)).

To the extent that a trading mechanism should encourage value discovery through its design, the first and third interpretations above are relevant. We first investigate the clustering phenomenon, and then proceed to the issue of underlying value and price resolution.

4.1. A Markov Model of Price Clustering

Let jt be the frequency with which a price will be in discrete category j at time t. The vector of these frequencies is simply , where s indexes the total number of categories. Our definition of categories necessarily varies between the S&P contract and the currency futures. Prices in the S&P are written to two decimal places, e.g., 470.05. We create five natural price categories for the investigation of clustering, namely xxx.05  xxx.A5, xxx.10  xxx.B0, xxx.25  xxx.C5, xxx.50, and xxx.00, where A = { 0, 1, 3, 4, 5, 6, 8, 9 }, B = { 1,..., 4, 6,..., 9 }, and C = { 2, 7}. Round or even price points are xxx.50 and xxx.00. Currencies are traded to four decimal places, e.g., 0.7651. For these contracts, the categories are defined to be x.xxx1  x.xxxB, x.xxx5, and x.xxx0. Here, round price points are x.xxx5 and x.xxx0.

Simple averages of price category frequencies are reported in Table VI. In the interpretation of the results, it is important to note that for the S&P model, there are 8 possible values in the xxx.05 and xxx.10 categories, 2 possible values in the xxx.25 categories, and one each for the remainder. Similarly, there is one possible value in the currency x.xxx5 and x.xxx0 categories, and 8 values in the residual category. For example, the S&P stationary probability value reported in panel A for the xxx.05 category is 0.037. The probability of the price being in any one of the eight possible subcategories is 8(0.037) = 0.296.

Absence of price clustering implies that the stationary probability distribution should be uniform, appropriately modified by the scaling noted above. A standard chi-square goodness-of-fit test rejects this hypothesis for all contracts. The large number of observations involved will result in a formal statistical rejection for the most minor of deviations from the null.

Direct inspection of the table entries provides a more sensible perspective. For all contracts, the estimates of the stationary benchmark floor probabilities are virtually at their theoretical values under the null of no price clustering. Given our scaling, the S&P frequencies each should be compared with the value 0.05, with the comparable figure for currencies being 0.10. For the S&P, values such as 0.048 are common, for example. Similarly, in the currency analysis, values of 0.098-0.10, 0.103-0.104, and 0.107-0.108 dominate the results.

In contrast, GLOBEX trading exhibits clustering at the even price points. For the S&P contract, frequencies at xxx.00 and xxx.50 are 0.079 and 0.063, respectively. The frequency at truly odd price points is only 0.037.

There is a great deal of serial correlation in the price frequencies, however. We therefore adopt the suggestion of Harris (1991), that an alternative approach should be based on a Markov chain formulation that characterizes time dependence in clustering frequencies.17

The probability of a transaction price changing from category i at time t-1 to category j at time t is given by Pij, with matrix representation P. Frequencies and population probabilities obey the summing up constraints,

and (5)

for all t. The first-order Markov chain model used here can then be written as


where the vector error is distributed with mean zero and a variance-covariance matrix of known form.18

Maximum likelihood estimates of the elements of P are obtained through sample averages of numbers of transitions between categories (e.g., Bartholomew(1975)). Space considerations preclude the reporting of all matrices. We checked the characteristics of the estimated matrices to verify the ergodic nature of the chain, and then computed the stationary probabilities for all categories, , j=1,...,s, via the relation19

, (7)

where es+1 denotes the (s+1)th column of the identity matrix of order s+1, Is+1. Denoting 1s as a (sx1) vector of ones,

. (8)

These stationary probabilities are reported in Table VII. Once again, a goodness-of-fit test rejects the null hypothesis of no clustering for all contracts. On the other hand, our remarks concerning the magnitude of frequencies relative to their theoretical values under the null could be repeated for the stationary probabilities of the Markov chain almost verbatim. In fact, the values of the stationary probabilities are identical to those of the average frequencies for the S&P contract. They also are extremely close for the currencies.20 In that case, the degree of clustering in the GLOBEX and benchmark markets appears to be reduced somewhat based on the dynamic model. The small changes cannot reverse our basic conclusions. Price clustering appears to be virtually absent in the benchmark market, while clustering at “round” fractions is clearly evident on GLOBEX. To the extent that clustering is an inverse measure of efficiency, the automated overnight system performance is relatively poor.

4.2. Price Resolution

We now consider the price resolution hypothesis of Ball, Torous, and Tschoegl (1985), in which greater trading activity implies a reduction in price clustering. Harris (1991) also motivates consideration of market intensity by noting that value discovery should be enhanced as the number of transactions per unit time increases. In particular, it is possible that clustering activity in GLOBEX ameliorates, and price discovery is enhanced, as the market environment becomes more liquid.

We begin with a static analysis. In the same spirit as the production of simple averages of frequencies in the last section, a set of linear probability models is estimated. Price category frequencies are computed based on 15-minute periods of trading. The frequencies are regressed on a constant, time-of-day indicators, and a measure of market intensity, F-1. F is computed as 1/1+T, where T is the frequency of transactions in a fifteen minute period. The coefficients on market intensity are different from zero at any reasonable level of statistical significance for all GLOBEX regressions.

Table VIII contains estimates of the derivatives of the price category probabilities with respect to T. The results are generally consistent with the price resolution hypothesis. The derivatives are negative for the round price points in the S&P contract models, and for the .xxx0 category in the currencies. Thus, increases in trading activity move prices away from .xxx0, but clustering on the other round point appears to be exacerbated for the Yen and Swiss Franc, in particular.

Diagnostic tests reveal that the regression residuals are highly serially correlated, suggesting the need for a dynamic framework. We generalize the Markov model of equation (6) to allow time variation in the transition probabilities, written as

. (9)

The idea behind this formulation is to examine how the transitions from price point to price point vary with market conditions. The price resolution hypothesis would suggest that as trading intensity increases, less clustering should be observed. This effect would be implied by a negative derivative of the diagonal elements of the transition matrix with respect to intensity that correspond to round price points.

In order to parameterize the model, we exploit a generalization of the interactive Markov chain concept of Conlisk (1976). Equation (9) is supplemented by

, (10)

where F is the measure of market intensity (one plus the number of transactions per fifteen minute period) and Di=j is a dummy variable equal to 1 if i=j and 0 otherwise. The function g is a linear parameterization of time-of-day effects, including dummy variables for the hour after the open and before the close, as well as the minimum of the time until the open and close, modeled in the same fashion as in the last section.

The inclusion of lagged state probabilities in the transition structure is the defining feature of the interactive Markov chain model. This specification allows interaction between traders, as evidenced through their transactions, whereas the standard chain model assumes such interactions away (see Conlisk (1976)). In our case, the lagged state probabilities also constitute a statistic for market behavior up to and including that at time t-1. The dependence of Pij on state i is motivated largely by the fact that Pij can be considered to be a measure of the attractive power of the ith state. The crucial element of  to Pij() might intuitively be i. A more pragmatic reason concerns the degree of parameterization of the model, which can grow to over a hundred parameters without such restrictions. Given our constraints across rows of P, the dummy variables allow for different effects on transactions that remain at the same set of price points, as opposed to shifts to other price points available in the market.

Even with such restrictions, the parameterization is still extremely rich, and we adopt an additional modeling strategy to make estimation and inference tractable. The constant terms, , are fixed at values such that conditional on all other parameters being zero, a uniform distribution is obtained over rows of the transition matrix. This permits an intuitively reasonable interpretation of the estimates of the time-varying components. Parameter estimates now measure movements away from uniformity; uniformity should obtain were clustering not an influence on price transitions.

Estimation of the model is based on the natural orthogonality conditions implied by equations (9) and (10). We implement the adding-up constraint through an additional set of moment restrictions,

, (11)

for j=1,...,s, which work extremely well in practice.21 As with the linear probability models, we estimate the model on data at 15 minute intervals.

The parameters generally are estimated precisely, in the sense of small standard errors. Space considerations preclude the reporting of all parameter estimates, which by themselves have little intuitive content in any case. We report the more interpretable derivatives of P, with respect to  and F. We further limit this reporting to the diagonal elements of the transition matrix in Table IX, which contains estimates of and , for i=j, evaluated at the means of the data for all contracts and both market venues. There is little variation over time of day, and we do not report separate sets of estimates for the open and close.

We have included past state probabilities largely to control for the effects of previous trading activity. On the other hand, examination of the derivatives of the diagonal elements with respect to mildly reinforces the evidence of clustering on GLOBEX. Some negative derivatives for odd price points are observed, suggesting avoidance of odd prices.

For the round fractions, derivatives of price transitions with respect to intensity now are uniformly negative for GLOBEX. Increases in activity tend to move trading away from round numbers to other price points, consistent with the price resolution hypothesis. This finding supports the notion of improved system performance as the environment becomes more liquid. The qualitative conclusions are the same across time of day. The price resolution hypothesis also is generally supported in the benchmark market, but a comparison here is less relevant than others in the paper, and we do not elaborate further. Price clustering is virtually absent on the floor in any case, accounting in part for the small magnitudes of the reported derivatives.

5. Concluding Remarks

As the presence of automated trading systems becomes more wide-spread, their efficiency properties are of increasing concern to regulators, exchange policy makers, and system builders. The use of such market structure, at least at the present time, remains prevalent in settings characterized by a distinct lack of liquidity, including overnight trading, the introduction of new instruments, emerging markets, and trading in illiquid classes of securities more generally. We provide some evidence on pricing behavior in one such market. A balanced view of the results suggests that the automated system performs reasonably well in a variety of dimensions.

Not all illiquid environments are created alike, however. The magnitude, components, and behavior of the bid-ask spread for the S&P futures contract on GLOBEX look very much like that observed on the benchmark floor market. In contrast, GLOBEX currency futures exhibit high spreads, driven by large adverse selection components. The main difference between environments in the trading of the instruments is the operation of the overnight spot foreign exchange market. The potential for adverse selection is arguably much higher in the overnight currency futures market, relative to the trading of the index future. Harris (1990) and Stoll (1992) note that traders on an automated system may be reluctant to submit limit orders and supply liquidity in the face of increased adverse selection. Liquidity suffers, and pricing deteriorates as a consequence. Our results in this respect are consistent with those of Frino, McInish, and Toner (1998). They find that the performance of the automated DTB system deteriorates during periods of high adverse selection, relative to the benchmark of floor trading on LIFFE.

The empirical results in this paper alone do not imply that market liquidity is exogenously determined relative to the automated trading mechanism. We do not, therefore, claim a clear "natural experiment" within which to study system performance. It is arguably the case that the demand for trade execution services and what resources to expend on the development of information may depend on the mechanism. On the other hand, liquidity provision is excellent in many markets of same or similar design to that studied here, operating during regular trading hours. Our findings suggest that the nature of the environment is an important determinant of market performance, but that an automated market can operate well in a relatively illiquid setting.

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Table I

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