Electronic limit order books during uncertain times: Evidence from Eurodollar futures in 2007 *

Transcription

1 Electronic limit order books during uncertain times: Evidence from Eurodollar futures in 2007 * Craig H. Furfine Kellogg School of Management Northwestern University 2001 Sheridan Road Evanston, IL c-furfine@kellogg.northwestern.edu January 2009 Abstract This paper examines how order submissions to the electronic limit order book for Eurodollar futures were affected when financial market turmoil generated a dramatic rise in interest rate uncertainty beginning August 9, We show that overall depth declined and that the shape of the order book moved away from best prices. We empirically model the decision to add or subtract depth to the order book and demonstrate that prior to August 9, both order placements and order cancellations tended to rapidly restore symmetry to the electronic limit order book. Following August 9, the relationship between the size and shape of the limit order book and incoming orders became muted whereas the responsiveness of order book updates to recent trading becomes enhanced. These results suggest that increased uncertainty changed the behavior of high-frequency (algorithmic) traders in this market in ways that reflected their reduced willingness to maintain standing orders in the order book. * The author wishes to thank seminar participants from the Kellogg School of Management at Northwestern University, The Federal Reserve Bank of Chicago, The University of Illinois at Chicago Business School, the Bank for International Settlements, the European Central Bank, and the Chicago Mercantile Exchange s University Roundtable for helpful comments and suggestions.

2 1. Introduction This paper analyzes order submission strategies in an electronic order book market and explores how such strategies change when uncertainty regarding the value of the underlying asset rises dramatically. Our study focuses on data from the Eurodollar futures market. This market trades claims whose payoffs are related to the level of future short-term interbank interest rates. We choose this market to explore because on August 9, 2007 interbank interest rates rose noticeably. For the remainder of 2007 and into 2008, there was increased uncertainty regarding the level of future interest rates, and therefore, the value of Eurodollar futures contracts. This allows us to focus on questions that have been relatively unexplored in the literature. In particular, we focus on the following questions: (1) Does a rise in uncertainty affect the appearance of a limit order book? (2) Does a rise in uncertainty affect the choice between submitting market versus limit orders? (3) Does a rise in uncertainty influence market participants decision to either submit new orders to or cancel existing orders from the electronic limit order book? By providing empirical evidence on these three questions, the findings in this paper extend the existing literature on limit order markets by examining how strategies change when information about the underlying asset becomes more uncertain. In this way, the study relates to the experimental work of (Bloomfield, O'Hara, & Saar, 2005) that shows that a trader s optimal trading strategy may evolve based upon the value of his private information. More generally, our analysis will allow us to comment on whether previously documented stylized facts about limit order markets are robust to a change in the nature of the information environment. By contrast, most previous empirical studies have studied a single market environment, implicitly assuming that all the data under examination can be modeled identically. Such studies, beginning with the Biais, et al. (1995) study of order flow on the Paris Bourse, have confirmed many predictions of microstructure theory. 1 Griffiths et al. (2000) study of data from the Toronto Stock Exchange explores the determinants of order aggressiveness, thereby analyzing not only the decision between submitting a market or limit 1 See, for example, Glosten s (1994) theoretical determination of the entire limit order book. Extensions of this framework are developed by Foucault et al. (2005) and Goettler et al. (2005).

3 order, but also the decision as to where in the order book to enter. Ranaldo (2004) explores data from the Swiss Stock Exchange and relates the aggressiveness of order placement to the current state of the limit order book whereas Hollifield et al. (2004) relate order aggressiveness to the trader s underlying asset valuation. Other empirical studies of limit order markets have explored related issues regarding execution quality (Lo et al. (2002)), the use and role of hidden orders (Bessembinder et al. (2008)), and the different strategies of various institutional investors (Aitken et al. (2007)). The findings in this paper also relate to recent interest in algorithmic trading strategies, which we casually define here to mean orders automatically submitted or cancelled based upon pre-defined rules without the need of further human intervention. 2 Electronic limit order markets facilitate greater reliance on algorithmic trading strategies and thus activity in such markets can be expected to increasingly reflect updates to the limit order book rather than trading. This relates to the findings in Hasbrouck and Saar (2005), who find that a large fraction of limit orders placed on the Island ECN are cancelled within two seconds. The order submission strategies we explore in this paper are analyzed at high frequency, and thus, can be expected to be influenced by any existing algorithmic trading strategies. Whereas much of the previous empirical work has explored markets in which the interesting question is often the determinants of order type (i.e. market or limit), our study examines a market where updates to the limit order book represent the overwhelming share (93-98%) of all message traffic on the electronic trading platform. We show that placing additional depth at the best bid or offer represents the most common order, but that elimination of depth at these same prices occurs with approximately the same frequency. Given the dramatic rise in orders placed and canceled by algorithmic players (Hendershott et al. (2007)), empirical work focusing on markets dominated by such activity may help us better understand the future of trading in more traditional markets. Further, our exploration of how order submission strategies are affected by increased uncertainty allow us to comment on whether such strategies are resilient to substantial changes in the market environment. 2 For instance, one such strategy might optimally break up a large order and submit many smaller orders at various prices within a limit order book in order to optimize execution quality for the total.

4 Finally, our study is also related to work done of Goldstein and Kavajecz (2004), who document a large withdrawal of liquidity in the electronic limit order book following the large decline in the US stock market in October Beyond finding a similar shift in the limit order book following a rise in uncertainty, we will also explore the changes to the order placement strategies themselves that lead, in part, to the observed changes in the book. Our study provides the following evidence on our three questions of interest. First, we document substantial changes to the electronic limit order book following the rise in uncertainty. Most notably, we find that depth at best prices declined precipitously, despite the fact that the number of trades increased. We document that the decline in depth results from both a decline in the number of orders and also a decline in average order size. For near-term futures contracts, average depth at best prices falls by over 96%. We also show that remaining order book depth moves further from best prices. In the case of near-term contracts, average depth moves an additional tick further from the best price following the rise in uncertainty. The second question related to the factors determining a market participant s decision to either trade or make changes to the limit order book. We find that trading in Eurodollar futures shares most but not all the features of electronic stock markets examined in previous research. In particular, past trading tends to predict additional trading while wider bid-ask spreads tend to predict limit order book changes. When we explore how the market versus limit order decision is affected by a rise in uncertainty, we find traders seem to be more sensitive to recent trading, but less sensitive to spreads. This is consistent with market participants being less willing to post limit orders following August 9, 2007, and instead waiting until incoming market orders appear before submitting their own orders to trade. Finally, our third question of interest relates to traders desire to add to or subtract from orders already in the limit order book. We find that the order submission/cancellation decision can be explained, in part, not only by posted depth, but also the shape of the entire limit order book. When depth on the bid side is higher, traders are more likely to remove depth from the bid side of the book. When the depth on the bid side is farther from best prices, traders tend to add depth to the bid side of the book. Conversely, when depth on the ask side is higher, traders are more likely to add depth to the bid side of the book. When the depth on the ask side is

5 farther from best prices, traders tend to remove depth from the bid side of the book. Thus, message submission strategies tend to restore symmetry to the limit order book. We also document that recent buyer-initiated trading predicts placement of more limit-buy orders whereas selling predicts buy-order cancellations. Wider spreads predict additional depth being added to the book as well. Most importantly, we find that the rise in uncertainty dramatically changed market participants order submission strategies. In particular, we find that traders response to the size and shape of the limit order book as well as to the bid-ask spread becomes much less pronounced. At the same time, traders responsiveness to recent trading is enhanced. Supporting our earlier findings for the market/limit decision, our order submission model s results are consistent with high frequency algorithmic futures traders becoming less willing to post limit orders following the rise in uncertainty. The remainder of the paper is organized as follows. Section 2 explains the market for interbank lending that relates to the Eurodollar futures market and shows that a dramatic shift in this market occurred on August 9, Section 3 then explains the Eurodollar futures market and describes its electronic trading platform, GLOBEX. Section 4 presents summary evidence of electronic trading of Eurodollar contracts and documents how both trading and the limit order book changed following August 9, Section 5 presents an order prediction model to explore the decision to either trade or make changes to the limit order book while Section 6 does the same for the decision to add or cancel orders. Section 7 summarizes and concludes. 2. Interbank markets in 2007 The settlement value of a Eurodollar futures contract is determined by the value of the three-month dollar denominated London Interbank Offered Rate (3M Libor). The 3M Libor rate is determined each day by a survey of 16 banks, which are asked the rate at which they could borrow a reasonable amount in US dollars for a term of three months. The middle eight responses are averaged together and the result is published as the official 3M Libor rate. 3 3 Similar procedures are done for different maturities and also for different currencies. See

6 According to theory, the 3M Libor rate can be viewed as an average of the overnight interest rate expected to prevail over the next three months plus a small and (typically) stable term premium. That this was an accurate description of interbank markets during the first seven months of 2007 is shown in Figure 1. The dark solid line plots 3M Libor. The dotted line is the three-month Overnight Indexed Swap rate (OIS). The OIS is the fixed rate banks are willing to pay in exchange for receiving the average overnight rate over the maturity of the swap in this case, 3 months. Thus, the OIS represents the market s forecast of the average overnight rate over the coming three months and thus, this rate should approximate 3M Libor less a small term premium. As can be seen in Figure 1, the Libor-OIS spread was roughly constant at around 10 basis points for the first seven months of This means that banks required only a very small term premium to lend to each other for three months as opposed to overnight. Beginning on August 9, and related to the developing crisis in subprime mortgages and other financial markets more broadly, the spread between Libor and OIS widened dramatically. Further, for the remainder of the year, the Libor-OIS spread remained elevated and highly volatile. Thus, throughout the latter part of 2007, banks demanded a very high and variable term premium to extend credit over three months. While the reasons for this change have been the subject of much discussion (See, for example, (Taylor & Williams, 2008), (Caballero & Krishnamurthy, 2008)), for the purpose of our study, we assume that the underlying interest rate environment exogenously changed on August 9. Thus, our analysis will look for differences in Eurodollar futures markets before and after August 9, Eurodollar futures and the GLOBEX order data The Libor survey asks banks about the terms under which they could acquire funds in the spot interbank lending market. In practice, these interbank loans are uncollateralized and therefore subject the lender of funds to credit risk. Thus, in times of market stress such as those beginning on August 9, 2007, one might expect rationing of lending to have accompanied higher Libor-OIS spreads. Unlike actual interbank loans, a Eurodollar futures contract is exchange traded and to the extent that the exchange (in this case, the Chicago Mercantile

7 Exchange) can be viewed as virtually safe from failure, traders in Eurodollar futures do not incur substantial credit risk when they buy or sell Eurodollar contracts. The underlying asset of a Eurodollar futures contract is a $1 million three-month loan made at Libor. We write asset in quotes because these contracts are cash-settled. That is, a trader holding a long position in a settling Eurodollar contract does not actually enter into a three-month loan. Instead, positions in Eurodollar futures are marked to market reflecting daily changes in 3M Libor. For instance, suppose a trader buys a Eurodollar futures contract due to expire on December 15 at a price This is equivalent to the buyer locking into lending money for three months beginning December 15 at an annualized rate of 2.545%. If 3M Libor on December 15 is 2.45%, the trader will have accumulated marked-to-market gains on the trade of ($1 million x ¼ year x 9.5 basis points) = $ abstracting from time value considerations. 5 The constancy of the Libor-OIS spread prior to August 9, 2007 implies that it was reasonable to view these contracts solely as a means to hedge/speculate on unexpected changes to overnight interest rates. After August 9, 2007, pricing and trading of Eurodollar futures became influenced not only by expectations of overnight interest rates, but also by expectations regarding what had become volatile future term premiums. Eurodollar futures are traded both live in the pit and electronically. Pit trading occurs between 7:20 AM and 2:00 PM Chicago time. Electronic trading of Eurodollar futures occurs over the GLOBEX trading platform around the clock, except for a one hour period between 4:00 PM and 5:00 PM Chicago time. Electronic trading has increasingly been the dominant platform for trading futures, and the Eurodollar contract is no exception. For the entire year of 2007, 91.6 % of all Eurodollar contracts traded were done so over GLOBEX. Further, since August 9, electronic trading became even more dominant, with 93.3% of contracts traded electronically as compared to 90.5% traded electronically before August 9. Nevertheless, for the period of temporal overlap, the two markets are highly integrated, with floor traders being able to observe and enter trades in the GLOBEX system in real time. 4 Quotes on Eurodollar futures contracts are quoted as (10000 annualized 3 month rate). 5 Thus, every basis point movement in 3M Libor translates to a mark-to-market change worth $25 per contract.

8 At any point in time, Eurodollar futures contracts are traded across a spectrum of settlement dates extending ten years into the future. Because of the arbitrage relationship between Eurodollar futures prices and prices on interest rate swaps and the active use of interest rate swaps for the interest rate risk management of both financial and non-financial firms, there is a substantial amount of trading in Eurodollar futures contracts beyond the next contract to settle. 6 Because Eurodollar futures trading is likely a function of time horizon, we construct our data by connecting contracts together in a series such that the time to contract settlement is approximately constant throughout the sample period. In particular, we construct three sets of data using the following methodology. First, we eliminate the nearest contract because this contract trades with a tick size of 0.25 basis points, whereas all other contracts trade with a minimum tick of 0.5 basis points. Second, we consider only contracts that settle at the end of calendar quarters as these are the most heavily traded contracts. Finally, to consider that contracts at different horizons may have different trading characteristics, we construct our data from the nearest remaining quarterly contract, the third closest quarterly contract, and the fifth closest quarterly contract. For instance, our data for January 4, 2007 would contain the Mar 07 contract in the first quarterly data, the Sep 07 contract in the third quarter data, and the Mar 08 contract in the fifth quarter data. The data for March 4, 2007, however, would use the Jun 07 contract as the nearest quarter (since the Mar 07 contract would have moved to a narrower tick size), the Dec 07 contract as the third quarter contract, and the Jun 08 contract as the fifth quarter contract. Exploring contracts at different distances allows us to explore the possibility that market participants view uncertainty differently when looking forward over different horizons. The data we collect consists of every message submitted to the GLOBEX trading platform during These messages are of two broad types. The first type of message indicates that a trade has occurred. These messages report the time, price and size (number of 6 This is quite different from futures on the S&P 500, where well over 95% of the contracts traded are for the nearby settlement date. 7 We drop weekends, New York and London banking holidays, and all days after December 20 from the analysis since trading volume on these days are abnormally low.

9 contracts) transacted. The second type of message reports the time as well as the aggregate number of orders and aggregate number of contracts at any of the five best bid or offer prices and is generated any time there is a change to the number, price, or total number of contracts in the book at any of the ten given prices. 8 The timestamp in the data is accurate to the hundredth of a second. Despite the messages having times given with such precision, it is still possible for a given message to aggregate orders. For instance, a given message might simultaneously update depth at the second best bid and the third best offer. This feature of the data will influence how messages are categorized, which we describe in more detail later in the paper. Finally, it is worth highlighting a difference between the methodologies used to fill orders for Eurodollar futures on GLOBEX relative to procedures commonly used by other electronic limit order book markets. Previous empirical studies have examined financial markets where the orders in the limit order book are queued according to absolute price and time priority. That is, orders at a given price are filled in the order in which they were first entered, with visible orders taking priority over hidden orders. For Eurodollar contracts, orders are filled using a combination of time and pro-rata allocation mechanisms. For instance, suppose there are 5 standing sell orders for 20 contracts each at a given price and an incoming buy order for 60 contracts arrive. The first standing order gets absolute priority and therefore gets filled in its entirety. The remaining orders, however, are filled according to a pro-rata algorithm, so in this case, each of the remaining 4 orders would receive a partial fill of 10 contracts. 9 Due to this matching algorithm, traders may have incentives to submit limit orders in amounts greater than their actual desire to trade and then to cancel those orders if they are not partially filled quickly. This possibility will be discussed further below. 8 In this way, the data is quite similar to that explored by Biais et al. (1995). 9 The matching algorithm is somewhat more complicated than this in that a minimum of two contracts must be allocated during the pro-rata phase and that fractional fills are rounded down to the nearest contract. Then, residual contracts not filled in the pro-rata phase are allocated according to absolute time priority. See (CME Group, 2008).

10 4. Uncertainty, trading, and the limit order book for Eurodollar futures Table 1 presents summary statistics for Eurodollar futures contracts at the three different horizons, separating the period before August 9 from the period after. Statistics in this table were based on messages arriving between 1:00 AM and 3:00 PM Chicago time in order to eliminate the influence of the thin trading that occurs during the evening hours. The first point to note is that these contracts are heavily traded. In the period before August 9, the first, third, and fifth quarterly futures contract traded 1934, 3630, and 3391 times per day, respectively. The sum total number of contracts traded range from over 217,000 per day for the first quarter contract to over 416,000 per day for the third quarter contract. Thus, the average trade size was approximately 100 contracts. Comparing these numbers to the daily averages following August 9, we see that the number of trades increased for contracts at all three time horizons. However, average trade size fell to between contracts, consistent with a decline in the number of total contracts traded. For all of these contracts, the minimum tick size is 0.5 basis points. Thus, the minimum possible bid-ask spread is 0.5. Column three of Table 1 reports the time-weighted average spread in each of these contracts. The reported values near 0.5 imply that both before and after August 9, these contracts were almost always trading at the narrowest possible spread although there is statistical evidence that spreads widened by a few hundredths of a basis point during the period of uncertainty. Columns four through seven indicate that following August 9, depth at best prices in the limit order book fell dramatically. For instance, prior to August 9, the time-weighted average depth at the best bid or offer for the first quarter contract was over 29,000, or approximately 290 times the average trade size. Following August 9, depth at best prices for this same contract fell to 989 contracts, a decline of over 96%. For the other contracts, depth at best prices fell by nearly three-fourths for the third quarter contract and by approximately twothirds for the fifth quarter contract. Looking beyond the best prices, we see that depth declined dramatically throughout the limit order book. For the first quarter contract, depth outside of best prices fell from 14,999 to 2,884 contracts a decline of 80%. Depth outside of the best prices for the third- and fifth quarterly contract declined by 60% and 50%, respectively.

11 The data also allow us to comment on whether the observed changes in depth were driven by changes to the number of traders in the book or by changes to the typical order size or some combination of these two effects. As shown in Table 1, orders at best prices and orders at other prices declined at all three time horizons following August 9, However, the magnitude of the decline in orders is less than the decline in depth, suggesting that the average size of a limit order fell throughout the limit order book as well. The previous discussion suggests that the shape of the order book was affected by the onset of the crisis period. To comment on this directly, we construct a measure of the average location of depth relative to best prices. That is, we assign depth a weight of 1 if it is at the best bid or offer price, a weight of 2 if it is at the next best price, and so on through the fifth level of the book, where depth is assigned a weight of 5. We then take a weighted average of the depth to construct a number between 1 and 5 measuring where in the book depth is located, on average. Column 8 in Table 1 reports this average value for our three contracts. For instance, we observe that for the first quarter contract prior to August 9, 2007, depth in the limit order book had an average location of 1.888, which means that the average placement of depth was between the first and second best price. For the two more distant contracts, average depth location is slightly above 2, reflecting that average depth is somewhere between the second and third best price. Looking at the changes to average depth location following August 9, 2007, we see that across all three contracts, location increased. For the nearest contract, average depth location rose by 1 tick, implying a movement away from best prices of 0.5 basis points. For the more distant contracts, depth location rose as well, but by a noticeably smaller amount of approximately 0.15 tick or less than 0.1 basis point. 10 The final column of Table 1 reports the average number of messages both trades and order book updates for each contract. For the first quarter contract, an average of 27,203 messages regarding this contract was submitted to the GLOBEX system each day prior to August 9. Given that these data are aggregated over a 14 hour period, this means that messages regarding this contract were received every 1.8 seconds. Message traffic is higher for 10 Depth location is equivalent to ticks because typically, there are no holes in the limit order book over the best five prices.

12 the third- and fifth quarter contracts. During the same time period, two messages arrive per second for the third quarter contract and message arrival is 2.3 messages per second for the fifth quarter contract. Following August 9, message traffic roughly doubled at all three contract horizons. The evidence presented in this section has identified the major changes that occurred in the limit order book for Eurodollar futures following the dramatic increase in interest rate uncertainty that began on August 9, In particular, we provided evidence on our first question of interest, namely does a rise in uncertainty affect the appearance of a limit order book? We document that although trading of Eurodollar futures rose, depth at best prices declined precipitously after August 9. While this was partly explained by a decline in orders, order size reduction played an important role. The overall shape of the order book changed, too, following August 9, 2007, with the average order moving farther away from best prices. Message traffic doubled. 5. Order prediction models: Trades or order book updates In this section, we estimate the first of two prediction models. These two models focus on our two remaining questions of interest, respectively. In this section, we will explore whether a rise in uncertainty affects the choice between submitting market orders or updates to the limit order book. In section 6, we examine whether a rise in uncertainty influences market participants decision to either submit or cancel orders that remain in the limit order book. Our first order prediction model will attempt to distinguish the factors that influence traders decision to either immediately transact at the best available prices or to otherwise undertake some action that would be reflected in an update to the limit order book. This initial analysis has been described by (Bloomfield, O'Hara, & Saar, 2005) as the make or take decision in financial markets, whereby traders decide whether to place a limit order and make liquidity or execute a market order and take liquidity. This motivates our first empirical model. Define the variable TRADE to be equal to 1 if a given message is a trade and 0

13 otherwise. We are interested in knowing which observable variables influence the determination of TRADE by making TRADE the dependent variable in a logit estimation. The first independent variable included in this analysis is LOGDEPTH, which is defined as the natural log of the total number of contracts (in thousands) in the limit order book one second prior to the given GLOBEX message. 11 Recall that the GLOBEX data allow us to measure the limit order book at the five best bid and five best ask prices, and therefore LOGDEPTH reflects standing orders across ten prices. Microstructure theory generally views orders in the book as potential competitors to an incoming order and this view has been supported by (Ranaldo, 2004) and (Griffiths, Smith, Turnbull, & White, 2000), who find that high levels of depth tend to predict a market order rather than an additional limit order. Thus, one might expect that the sign of LOGDEPTH to be positive. The second explanatory variable included in this analysis is DEPTHLOCATION, which we define as the weighted average placement of depth in the order book. As described earlier, we weight each contract on both sides of the order book according to its level relative to best price, with a weight of 1 attached to depth at either the best bid or ask price and a weight of 5 attached to depth placed four ticks away from best prices. DEPTHLOCATION proxies for the shape of the limit order book, which our specification will allow to affect incoming orders. High values of DEPTHLOCATION indicate a valley-shaped order book, which might be expected to attract more limit orders. Low values of DEPTHLOCATION suggest a lot of standing orders at best prices, which might increase the likelihood of an incoming market order. Thus, our prior is for the sign of DEPTHLOCATION to be negative. Our third explanatory variable is RECENTTRADING, which we define to be the number of contracts bought or sold in the five seconds ending at least one second prior to the incoming message. There are theoretical reasons why trades might arrive in bunches ((Admati & Pfleiderer, 1988), (Easley & O'hara, 1992)) and the information content of the time between trades has been examined empirically (Dufour & Engle, 2000). To the extent that trades cluster 11 Although our analysis is undertaken at the message level, we use calendar time to lag our explanatory variables. As highlighted earlier, multiple messages arrive each second and we wanted the explanatory variables to reasonably reflect what might be observed by a high-frequency trader. Results reported are robust to varying the lag up to 5 seconds.

14 in time in the Eurodollar futures market, we would expect the sign on RECENTTRADING to be positive. In addition, much of the focus of algorithmic trading strategies has been about how to optimally break up large orders into smaller pieces that can be executed sequentially. To the extent that this activity is widespread, this, too, would suggest a positive coefficient. Our fourth explanatory variable is SPREAD, which is an indicator variable that equals 1 whenever the distance between the low ask and the high bid exceeds its minimum value of 0.5 one second prior to the incoming message. We choose the indicator specification rather than the observed level of the spread because, as was documented in Table 1, spreads in this market are almost always at the minimum tick size of 0.5 basis points. Numerous authors have shown that the width of the spread has been shown to influence the nature of incoming orders, with wider spreads typically predicting the arrival of new limit orders that narrow the spread. Therefore, we predict that the sign of SPREAD will be negative. Finally, we include a variable UNCERTAINTY, which is equal to 1 if the given message arrives on August 9, 2007 or thereafter and 0, otherwise. We additionally interact UNCERTAINTY with the previously mentioned explanatory variables to allow for statistical tests of differences between the period before and after August 9, As mentioned, we have collected every GLOBEX message for the calendar year However, to minimize the influence of intraday variation in trading behavior while still focusing on the time when trading is most active, we further restrict our sample of messages to include only those that arrive been 8:00 AM and 11:00 AM Central Time. Despite these restrictions, our samples for the three futures contracts remain rather large, with over 3 million observations for the first quarter contract, over 11 million observations for third quarter contract, and nearly 14 million observations for the fifth quarter contract. Table 2A report means and standard deviations of our four explanatory variables based on this message level data. The first column reports statistics on LOGDEPTH and confirms what we reported in the daily average data in Table 1. Overall depth in the limit order book fell following August 9, 2007 for contracts at all three horizons. The second column confirms our earlier finding that depth tended to move further away from best prices after August 9, The third column indicates that during the busy morning trading periods, the average trading in

15 any given five second period is on the order of contracts. The fourth column reports the statistics for SPREAD, which is an indicator for a spread that is wider than the minimum tick size of 0.5. The mean value of for the first quarter contract prior to August 9, 2007 indicates that over 97% of messages arrive when the spread (one second earlier) was at its minimum possible size. Table 3 reports the coefficients and robust standard errors from the logit regression of the trade indicator TRADE on the above-mentioned independent variables. As indicated in the first column of Table 3, prior to August 9, 2007, LOGDEPTH does not always enter significantly. For the first quarter contract, the coefficient on LOGDEPTH enters with a positive sign. This suggests that when depth in the order book is high, the next message is more likely to be a trade. This is consistent with previous microstructure findings that view the order book as competition for execution. Therefore, when depth is high, market participants become more likely to submit a market order. For the more distant contracts, depth in the book appears to have no significant predictive power prior to August 9, The second column reports results for DEPTHLOCATION. Only for the first quarter contract does this variable seem to relate to the decision to trade or make an order book update. According to the positive coefficient, when depth is further from best prices, on average, the next message is more likely to be a trade. Not only is this contrary to our prior, it is also not robust in that the estimated coefficients on DEPTHLOCATION are not statistically different from zero for either the third or fifth quarter contract. The signs of the coefficients on the remaining two variables are both highly significant and are consistent with our theoretical priors. In particular, RECENTTRADING enters with a positive sign, consistent with the clustering of incoming trades. The variable SPREAD enters with a negative sign, as expected. When the bid-ask spread exceeds its minimum level, incoming messages tend to update the limit order book. Table 3 also indicates whether the magnitudes of the estimated coefficients differ according to whether the data are before or after the period of greater uncertainty beginning on August 9, The first column reports that the estimated coefficients on LOGDEPTH fell across all three horizons. In the case of the first quarter contract, the coefficient became less

16 positive, while for the other two contracts, the coefficient went from being zero to becoming negative. One interpretation of this finding is that following the rise in uncertainty, market participants began to view orders in the book less like competition for trades and more like signals for how the book was expected to evolve. Consistent with this interpretation, we found earlier that message traffic rose considerably following August 9, 2007, suggesting that incoming messages were less likely to convey instructions to trade and more likely to reflect order book updates. The negative coefficients on LOGDEPTH during the later period suggest that following a rise in uncertainty, high depth in the book predicted more order book updates. We examine this possibility further in the next section when we study more closely the different types of order book updates. Table 3 reports that the magnitude of the coefficients on RECENTTRADING became larger following August 9, The higher coefficient on RECENTTRADING implies that incoming trade orders were more likely to follow recent trading after August 9, This may indicate that more traders were waiting on the sidelines without placing limit orders until the perceived probability of order execution was increased by the observation of recent trading. An examination of the marginal effects from the logit regression suggests that a one unit increase in RECENTTRADING implied a 0.2% increased likelihood of the next message being a trade in the first quarterly contract before August 9, Following August 9, the same increase in RECENTTRADING implied a 0.8% increase. Thus, the coefficients imply roughly a four-times larger impact of recent trading on the decision to trade. Although the magnitude of these marginal effects may seem economically small, the size of the impacts are significant given that the unconditional probability of an incoming message being an order book update is well over 90%. Table 3 also reports that the coefficients on SPREAD became smaller in magnitude. A lower magnitude of the negative coefficient on SPREAD indicates that after August 9, 2007, wide spreads in the book did not predict additional limit order placement to the same extent that they did prior to the rise in uncertainty. This, too, is suggestive of more reluctance to place orders in the limit order book. An analysis of the marginal effects of SPREAD on the next incoming order suggests that when the spread is wider than the minimum tick size, the next

17 incoming order for the first quarterly contract is 4% less likely to be a trade before August 9, 2007, but only 2.5% less likely to be a trade after August 9. Given the high unconditional expectation of an order book update, the change in the marginal impact of a wide spread is economically large. Taken together, these findings suggest that after the rise in uncertainty, market participants were less willing to maintain limit orders, conditional on the state of the book and recent trading activity, following August 9, To explore this issue more directly, it is necessary to look specifically at the content of the message traffic. We study this message traffic in greater detail in the next section as a prelude to examining our last question of interest, namely whether the rise in uncertainty generated a change in traders willingness to add or subtract depth from the limit order book. 6. Order prediction models: To add or subtract from the limit order book Before beginning a more detailed examination of Eurodollar message traffic, it is helpful to emphasize a key difference between the electronic order books examined by previous research and those being examined here. Looking back at the first and last columns of Table 1, we can see that only a very small fraction of messages are actually trades. Using data from before August 9, we find that only 1934/27203 = 7.0% of all messages related to the first quarter contract are trades and this percentage is 3.7% and 2.9% for the other two contracts. Thus, the traditional microstructure analysis of what determines a trade versus a limit order placement can only be expected to explain a small fraction of messaging behavior in Eurodollar futures markets. Therefore, to more fully understand the behavior of market participants in Eurodollar futures markets, we need to examine more than the traditional make or take analysis that was described in Section 5 and additionally focus on the nature of the order book update process. In this section, we examine the approximately 93%-97% of all messages that reflect updates to the limit order book yet do not reflect a trade. To do so, we need a way to classify each incoming message. Following in the spirit of (Biais, Hillion, & Spatt, 1995), we first

18 categorize messages into eight groups. 12 We describe our order classification procedure for buyer-initiated (that is, bid-side) messages, but note that we classify ask-side messages analogously. We begin by defining a Type 1 message as one that adds depth at a price higher than the previous highest bid. Type 2 messages add depth at the high bid. Type 3 messages move depth to the highest bid, by which we mean that the message contains instructions to increases depth at the best bid while simultaneously reducing depth elsewhere in the book by the same amount. Type 4 messages add depth somewhere away from the best bid price. Type 5 messages move depth within the book, but at prices below the best bid price. The final message types reflect that many incoming messages indicate a withdrawal of depth from the limit order book and are defined as counterparts to messages of types 2 through 4. Type 6 messages reduce depth somewhere in the book but not at the best bid (opposite of Type 4). Type 7 moves depth away from the best bid (opposite of Type 3), and Type 8 messages decrease depth at the best bid (opposite of Type 2). Table 4 reports summary statistics on the six most common types of orders. Table 4A reports statistics on buy messages and Table 4B reports statistics on messages related to sell orders. Perhaps the most notable finding in these statistics is the prevalence of order book updates at best prices. Messages reflecting changes to the order book at the best price are by far the most common message type. For example, Type 2 messages (those that add new depth to the order book at the best bid price) represented 17.0% (4622.4/ ) of all messages for the first quarter contract during the early part of These messages were 16.2% and 13.9% of all messages for the third and fifth quarter contracts, respectively. Perhaps surprisingly, removals of depth at the best bid price were just as common, with the number of Type 8 messages (decrease of depth at best price) being approximately equal to the number of Type 2 messages. The widespread cancellations of previously placed orders documented by the high number of Type 8 messages suggest an explanation for some of our earlier findings. Recall we 12 Recall that a single GLOBEX message can include both buy and sell components and therefore, adding the number of buy messages to the number of sell messages will give a number greater than the total number of messages reported in Table 1.

19 found that when message traffic increased following August 9, 2007, the coefficient on LOGDEPTH in our logit model declined and even turned negative for the two more distant contracts. In some microstructure models, limit order traders are viewed as the more patient traders (Foucault, Kadan, & Kandel, 2005). According to this view, the typical limit order would wait in the limit order book until executed. In this view of the trading environment, we might expect higher depth to push traders towards market orders since depth in the order book is competition for execution. In Eurodollar futures markets, the rapid message traffic contains a high degree of cancellations of previous orders. It could be, therefore, that some of the depth in the limit order book can be viewed as temporary much like was documented by (Hasbrouck & Saar, 2005). In this view of message submissions, higher depth might signal that depth is temporarily above the level it would be with only traditional, patient limit order traders and therefore should be predictive of future messages that will reduce depth. This interpretation would be consistent with our earlier findings. An alternative interpretation to the high level of order cancellations relates to the order matching procedures described earlier. Since orders are filled, in part, by a pro-rata method, traders might knowingly place larger than desired limit orders expecting a partial fill and then immediately cancel the remaining unwanted order shortly thereafter. Although it is difficult to test this hypothesis directly, we are skeptical that this is what is driving our observing such a high level of order cancellations. In analysis (not reported) of similar data from S&P 500 futures, a market with strict price and time priority rules, we find that the distribution of message types to be indistinguishable from what is reported in Table 4. We now turn to a more careful examination of the decision to place or cancel limit orders, which will allow us to provide evidence on our third and final question of interest, namely did the rise in uncertainty change traders willingness to add or cancel orders in the limit order book. To conduct the analysis, we distinguish messages that increase depth in the order book from those that decrease depth. We further consider that a message that moves depth to best prices is more closely associated with additional interest to buy, and therefore group these messages with those that provide new depth. Similarly, messages that move depth away from best prices are grouped with messages that remove depth. In this manner, we can

20 convert our eight message categories into a set of three categories, which are ordered by the relative interest in trading. The highest category, therefore, identifies messages of Types 1-4, containing messages that add depth at best prices or at prices better than best price, move depth to best prices, or add depth to any other prices. The middle category identifies Type 5 messages that neither add nor subtract overall depth and also do not affect best prices. The final category identifies messages of Types 6-8, which remove depth at prices away from best prices, move depth from best prices, or remove depth from best prices. Formally, we define our two three-valued message indicators as BIDTYPE and ASKTYPE, respectively, for bid-side and ask-side messages. These variables are assigned a value of 3 when a given message adds depth to the limit order book or moves depth to best prices, a value of 2 when depth is neither added nor subtracted and depth at best prices is unchanged, and a value of 1 when depth is subtracted from the book or moved away from best prices. Note as these variables values are ordered according to increasing interest in trading, the ordered logit methodology is appropriate and is what we will employ. Columns 1 and 5 of Table 2B indicate that the average values of BIDTYPE and ASKTYPE are not statistically different from 2, which implies that for all three horizons, both before and after August 9, additions to depth are approximately as common as subtractions. The set of explanatory variables that we include in the analysis are the same as those used earlier, with some modifications. We continue to include the variable SPREAD, which indicates a bid-ask spread larger than the minimum tick size. Because wide spreads are expected to encourage new limit orders, we expect this variable to enter with a positive sign. The other variables from the previous analysis are amended to distinguish activity on the bidside from that from the ask-side. This is because a trader s buy-side order will depend on depth on the bid-side differently from that on the ask-side. Thus, we define LOGDEPTHBID and LOGDEPTHASK as the natural log of the total depth reported one second prior to the given message summed over the five best prices on the bid-side and ask-side, respectively. According to our prior suggestions that high levels of depth might tend to lead to greater order cancellations, we predict that the coefficient on LOGDEPTHBID (LOGDEPTHASK) should be negative in our model when the dependent variable is BIDTYPE (ASKTYPE). That is, high depth

21 on the same side of the book as an incoming order should predict a cancellation. By contrast, depth on the opposite of the book might be expected to predict additional limit orders. This might be expected since, on average, we expect the book to be roughly symmetric. Therefore, we predict that the coefficient on LOGDEPTHASK (LOGDEPTHBID) should be positive in our model when the dependent variable is BIDTYPE (ASKTYPE). We also distinguish the location of depth on both the bid and ask sides of the book with our variables DEPTHLOCATIONBID and DEPTHLOCATIONASK. These variables are the same weighted-average location of depth defined earlier, only calculated separately for the bid and ask sides of the book. We would expect, on average, our depth location variables to predict incoming orders in a way that would restore the limit order book to a symmetrical appearance. Thus, when DEPTHLOCATIONBID is large when most of the bid-side depth is away from best prices we might expect an incoming buy-side order to add more depth, typically at best prices. When DEPTHLOCATIONASK is large, by contrast, we would expect bid-side orders to remove depth. Analogous reasoning would apply for ask-side messages. Thus, we predict that the coefficient on DEPTHLOCATIONBID (DEPTHLOCATIONASK) should be positive (negative) in our model when the dependent variable is BIDTYPE. Opposite signs are expected for these variables when the dependent variable is ASKTYPE. We similarly distinguish trading activity according to whether the observed number of contracts transacted in the previous five seconds was buyer-initiated or seller-initiated. We define variables RECENTBUYS and RECENTSELLS, accordingly. Although we have observed that trading is correlated through time, we have no prior on how recent trading activity should be expected to affect new adjustments to the limit order book. Rather, according to microstructure theories, it is typically derived that orders in the book are placed such that traders placing those orders are indifferent to transacting at the limit price, conditional on having that price be filled by an incoming order. Table 5A presents the ordered logit results for the variable BIDTYPE. Table 5B presents the results for ASKTYPE. We describe only the results for bid-side messages as the results for ask-side messages are nearly perfectly symmetric. Across all three horizons, our estimated coefficients are nearly always statistically significant and are of the sign consistent with our