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Precedence rules in matching algorithms
Journal Pre-proof Precedence Rules in Matching Algorithms Richard Haynes, Esen Onur
PII:
S2405-8513(19)30074-1
DOI:
https://doi.org/10.1016/j.jcomm.2019.100109
Reference:
JCOMM 100109
To appear in:
Journal of Commodity Markets
Received Date: 10 October 2019 Accepted Date: 22 October 2019
Please cite this article as: Haynes, R., Onur, E., Precedence Rules in Matching Algorithms, Journal of Commodity Markets, https://doi.org/10.1016/j.jcomm.2019.100109. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. Published by Elsevier B.V.
Precedence Rules in Matching Algorithms∗† Richard Haynes‡
Esen Onur§
October 31, 2019 ABSTRACT Markets with time priority rules incentivize efforts to increase trading speeds. In particular, revenues resulting from liquidity provision due to discrete pricing can often accrue to the fastest traders, those who can hold favorable queue positions. We examine the impact of precedence rules for a single market that switched to a first-in-first-out (FIFO) matching algorithm from one primarily based on prorata. Due to a technology issue, in May 2015 the two year Treasury futures contract unexpectedly switched from partially pro-rata to FIFO for several days. We study the effects of this switch through a difference-in-difference comparison with a related futures contract that had no change in priority rules. We find that compared to FIFO, orders placed later in time are significantly more profitable under pro-rata. However, the lower profitability of earlier orders in the queue under pro-rata matching causes prices to be less efficient under pro-rata rules. Secondary results find that order sizes and cancellations increase under pro-rata. While analyzed using the Treasury futures market, our findings are applicable to commodity futures as well, where both FIFO and pro-rata are widely used.
Keywords: Precedence Rules, FIFO, Pro-Rata, K-Algo
∗
The research presented in this paper was co-authored by Richard Haynes and Esen Onur, CFTC employees who wrote this paper in their official capacities. The analyses and conclusions expressed in this paper are those of the authors and do not reflect the views of other members of the Office of CFTC Chief Economist, other Commission staff, or the Commission itself. † Authors would like to acknowledge the contributions of Terrence Hendershott and Charles M. Jones to the analysis presented in the paper during their time as consultants with the CFTC. Declarations of interest: none ‡ Commodity Futures Trading Commission; [email protected] § Commodity Futures Trading Commission; [email protected]
I. Introduction The matching rules of financial markets determine which orders trade and at what price. Historically, floor based markets were based on a mixture of objective and subjective criteria in determining who traded with whom; placement on the floor, pre-existing relationships, and inventory levels could all affect whether a given trade occurred or not. The automation of financial markets has, among other things, increased the importance of one factor, the speed of response. Traders who can observe and react faster to public information can cancel mis-priced old orders or execute against orders that have not yet reacted to the information, i.e., orders that are mispriced when they execute due to changes in market conditions after submission (see Budish, Cramton and Shim (2015)). This speed advantage, however, can differ from market to market. In markets where orders are prioritized relative to when they were received, speed can be a primary factor; in others, orders may face different prioritization rules, potentially leading to a larger order getting filled before a faster order. In this paper, we empirically study how the rules of trading impact various market quality measures, such as price discovery and price efficiency. Profitability in liquidity provision increases the importance of secondary precedence rules for orders at the same price. Most markets use price priority as the primary characteristic, which ensures that orders with the most competitive price get to trade first. Given that a minimum tick size ensures discrete prices, however, there are often multiple orders at the best price. Markets specify how trades are allocated among orders at the best price. The procedures for allocating trades at a given price level are referred to as secondary precedence rules. Most markets use time as the secondary precedence rule, making the queue of the orders at the best price operate in a first-in-first-out (FIFO) manner. Under FIFO, orders at the top of the queue are more likely to trade
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and more likely to trade with smaller orders. Smaller orders are less likely to be informed orders Kyle (1985) and Glosten (1987). Hence, because speed increases the likelihood of avoiding adverse selection, faster traders are incentivized under FIFO rules. We study the impact of switching to FIFO from a more pro-rata algorithm where resting orders of the same size receive equal priority regardless of when they arrive.1 The switch from pro-rata to FIFO occurred unexpectedly in the 2-year Treasury futures contract on May 11-12, 2015.2 In constrast, other Treasury futures contracts, including the 30-year, did not change algorithm on those days. This allows us to conduct a difference-in-difference analysis where the 30-year contract controls for changes in market condition. Changes in the 2-year contract relative to the 30-year contract thus measure the impact of the change in precedence rules. Precedence rules have not been widely studied. In a model with free entry, Glosten (1998) studies FIFO and pro-rata precedence rules.3 Pro-rata provides incentives for traders to place orders even when the queue is already long because the later arriving orders enjoy the same priority, after controlling for size, as earlier orders. Under FIFO, later orders must wait for all earlier orders to execute. This means that, controlling for order size, the marginal value of adding an order at the end of the queue is higher in pro-rata than FIFO, leading to longer order queues under pro-rata. We find empirical support for this prediction. Furthermore, we find support for the economic mechanism which leads to greater depth under pro-rata: orders earlier in the queue are more profitable and execute more often under FIFO than under pro-rata.4 1
As explained later in more detail, the precedence rule for 2-year Treasury futures is not exactly pro-rata. For brevity, we refer to it as pro-rata in the rest of the paper. 2 Pro-rata and FIFO are both used for commodity contracts. See Appendix for more detailed information. 3 Glosten (1998) also analyzes more general secondary precedence rules which depend on the quantities of orders. Pro-rata is a special case where all orders of the same quantity have the same precedence. 4 Field and Large (2008) in addition show that depth can be higher under pro-rata for a second reasons - traders with a desired quantity to execute have an incentive to overquote. For example, a trade wanting to trade 100 contacts will place an order for 1,000 contracts if the trader believes that
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While pro-rata’s incentives encourage the placement of orders when the queue is already long, pro-rata discourages the placement of orders when the queue is short. Short queues in pro-rata markets are likely signals that the levels of adverse selection are high (and thus the marginal value of placing an order is low). Because of this, orders that remain in the queue are likely to suffer from adverse selection and lead to unprofitable trades; those in the queue should cancel and wait for the price movement. This can lead to higher frequencies of price changes due to this cancellation activity, changes that are often reversed. This increased frequency of price reversals imply a less efficient price discovery process. We find evidence that prices are less efficient under pro-rata, as evidenced by a high level of price reversal events. The paper proceeds as follows. Section II describes in detail the change in precedence rules we are studying. Section III presents an overview of the related literature. Section IV describes the data used in our analysis and presents some descriptive statistics. Section V presents our main analysis and results. Section VI concludes.
II. Background On May 10th, 2015 (a Sunday), the Chicago Mercantile Exchange (CME) determined that the algorithm designed to match orders in the 2-year Treasury futures contract was not working as expected. The algorithm the CME uses for matching aggressive and passive trades in the 2-year contract is known as a ”K” algorithm. This algorithm is a mixture of first-in, first-out (FIFO) and pro-rata components (40% FIFO, 60% pro-rata), where pro-rata matching is based on a price, quantity precedence rule. In addition to this weighting of pro-rata and FIFO components, the K-algorithm gives additional preference to the first order at a new price point. That first order must his fill rate will be 10 percent.
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be filled (up to a pre-specified amount) before any other executions; once the initial fill is complete, the FIFO/pro-rata balance becomes active. For brevity’s sake, we will refer to this hybrid matching approach for the 2-year as a ”pro-rata” matching algorithm, highlighting that it is primarily, but not fully, a pro-rata mechanism. Generally, pro-rata matching algorithms are used in markets where price volatility is lower than average. For instance, Eurodollar (short-term interest rates) also use pro-rata matching algorithms, as do many commodity spread markets 5 . Because this hybrid algorithm was not working properly on May 10th, the CME put out a public announcement that evening stating that for the following day, May 11th, the 2-year contract would be traded using a 100 % FIFO algorithm, the algorithm used for most of the other Treasury futures contracts. At the end of May 11, after unsuccessfully trying to switch the matching engine back to pro-rata, the CME put out another public notice that precedence rules on May 12th would also be FIFO. Starting on May 13th, precedence rule returned to the traditional pro-rata algorithm. This unanticipated shift provided an exogenous test on how matching algorithms may affect liquidity provision, as well as the dynamics of price discovery and price efficiency. In addition, because many Treasury futures contracts (including the 5-year, the 10-year and the 30-year, which trade on a FIFO basis) were unaffected, we are able to incorporate difference-indifference tests into our analysis. We hypothesize a few market changes due to the change in precedence rules. Because the pro-rata matching algorithm puts lower value on queue position relative to FIFO markets, the marginal value of adding a new passive order to the end of a long queue is higher in pro-rata markets. In a pro-rata market, this order has a high likelihood of a partial fill even for the first aggressive order; in contrast, in a FIFO market the order would need to wait until all orders placed prior to it execute. In contrast, because the 5
See the Appendix for a detailed information on different markets and their matching algorithms.
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relative value of being at the front of the queue is lower, the probability of cancellation at the front of the queue is higher, potentially increasing adverse selection for short queue lengths. Given the relative value of adding a new order to a long queue (and a short queue) in pro-rata versus FIFO markets, we propose two related hypotheses: H1: The average short-term revenue of passive orders, as a function of queue position, is flatter for pro-rata markets relative to FIFO markets. H2: The variance in order book depth is higher for pro-rata markets relative to FIFO markets. In addition to these two hypotheses on liquidity provision, we anticipate that the level of price efficiency in a market will change as matching algorithms are adjusted. Because short queues are less attractive in pro-rata markets, price adjustments are likely to come more quickly and more often in a pro-rata market, conditional on there being a short queue. This leads us to a further, third hypothesis focusing on the relative price efficiency of these two algorithms. H3: The probability of a price reversal (e.g. a trade price increase following a trade price decrease) is higher in a pro-rata market than in a FIFO market. The combination of these three hypotheses highlights at least one component of the cost-benefit comparison between these two market structures. Because the marginal value of the next order, in a relatively long queue, is higher in pro-rata than in FIFO, liquidity provision is also likely to be higher in pro-rata than in FIFO markets. For large traders, who require significant market depth for efficient risk transfer, this additional depth in the book is of value. In contrast, short queues in pro-rata markets tend to last for a shorter period than they do in FIFO markets, leading to ”inefficient” price movements which are eventually reversed. This balance between the top and bottom ends of the depth distribution illustrate the trade-off between these two matching algorithms.
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III. Related Literature While there is an extensive literature on markets operating a central limit order book with price time precedence rules (FIFO), there is little research on markets with prorata precedence rules. Similar to the markets we analyze, Frino, Hill and Jarnecic (2000) analyzes market changes after the CME modified the precedence rules in the Eurodollar futures contract from FIFO to pro-rata in 1998. They find that this change did not have a significant impact on the liquidity in the market. Similarly, two other papers study the changes in the precedence rules at the London International Financial Futures and Options (LIFFE) exchange. Lepone and Yang (2012) analyzes the impact on the market when LIFFEs matching algorithm changed its precedence rules from a mixed price-time pro-rata algorithm to a pure quantity pro-rata algorithm in 20015. They find that this change had an adverse effect on the liquidity in the market, namely order book depth decreased and bid-ask spread widened. Another study, (Aspris et al. 2015) analyzes how the market is affected when LIFFE decided to switch to a pro-rata algorithm with some time priority in 2007. They do not find any significant changes on market quality as a result of changes in precedence rules. However, in line with our findings, Aspris et al. (2015) do find that the trading environment changes as a result of the rule change in 2007. They find that under pure pro-rata matching algorithms, traders strategically over-size their orders. More importantly, they conclude that market participants optimize their trading and quoting decisions based on the matching algorithm adopted by the exchange, a result which lines up with our main findings. Janecek and Kabrhel (2007) offers a comparison of pro-rata matching algorithms with price time priority; the authors find that FIFO motivates narrower spreads, but discourages other orders from joining the queue. They also find that orders sitting on the book will be smaller under FIFO. In comparison, they find pro-rata to moti-
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vate other orders to join the queue with large limit orders, leading to increased market depth. They also note that the pro-rata algorithm does not motivate bid ask spread to be narrower. Janecek and Kabrhel (2007) also offer a summary of the rules used by international derivatives exhanges. On the theoretical side, Field and Large (2008) present a model analyzing the effects of pro-rata matching in one-tick markets, similar to those in futures markets. The authors postulate that market participants rationally choose to over-quote under prorata precedence rules. The paper also finds that since traders have the incentive to over-quote, cancellation rates under pro-rata precedence rules are higher. Degryse and Karagiannis (2019) present a theoretical model where they compare the price-time priority rule with a different kind of priority rule, one that follows a pricebroker-time (PBT) priority. The latter is generally used in a number of Canadian and Nordic markets compared to the former that is used in the U.S. markets. They find that under the PBT rule, fill rates are higher when tick size is large and smaller when tick size is small. Similarly, they also show that investor welfare is higher with PBT when tick size is large but lower when tick size is small. Finally, Glosten (1998) posits a theoretical analysis of precedence rules and find that markets will have greater depth when quoted quantity plays a role in precedence rules. Comparing time and quantity precedence rules, Glosten (1998) suggests cases when the bid-ask spread can is the same between these two precedence rules but market depth is higher in pro-rata.
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IV. Data and Summary Statistics A. Description of the Data The analysis below is based on order book data sourced from the Chicago Mercantile Exchange (CME). We analyze the 2-year U.S. Treasury futures market, the market where the unexpected switch of precedence rules occurred, as well as the 30-year Treasury futures as the control. The CME publicly provides a real-time summary of bids and offers at the top ten price levels. For each price level, market participants are able to see how many orders are at that price, as well as the total quantity at that price. In addition to this, the CME provides, at special request, more detailed regulatory order data to the U.S. Commodity Futures Trading Commission. This more detailed data set provides detailed information about every order-related message sent to the exchange, including new orders, modifications of orders, and cancellations of orders. In addition to each order’s price and quantity, this regulatory data set also identifies the participant who entered the order. Our sample goes from May 4th, 2015 until May 15th, 2015, a two week set of dates which straddles the two-day matching algorithm change.
B. Summary Statistics Tables I and II provide an overview of daily liquidity provision for the two focal contracts. Table I provides a distributional summary of the size of all passive orders placed in the book for that contract, on that day. Table II provides a distributional summay of the aggregate top of the book depth (best ask plus best bid) for each day and each contract. Because pro-rata markets prioritize large passive orders over small passive orders, we expect the distribution of passive order sizes would shift lower during the period when the two year contract was traded using a FIFO algorithm. In addition, because the marginal
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value of adding an order to the back of the queue in pro-rata markets is higher than that for FIFO markets, the distribution of order book depth should also be lower for the FIFO algorithms. We find both of these effects in the tables. During the two-day period of interest, 95% of passive orders in the two year market were for 115 (Monday) or 105 (Tuesday) or fewer contracts; in contrast, for the days where the pro-rata algorithm was active, this cutoff was never less than 150. Similarly the standard deviation of order size was roughly 70 contracts during the key two-day period, significantly lower than during the regular pro-rata precedence days. Note that the 30-year Treasury futures market does not display any significant change during the two-week period, indicating that the changes observed in the two year contract were not due to changes in the fundamentals. As demonstrated in table II, order book depth trends show a similar pattern, with the top of the distribution significantly lower during the two days relative to the rest of the panel. In addition to this, the standard deviation of depth is also lower, highlighting that small order book depth is less likely when FIFO priority rules are used. This second finding corraborates our earlier hypothesis that, where the marginal value of adding a quote to a long queue is higher in pro-rata, the marginal value of adding a quote to a short queue is lower. As a result of these dynamics, the queue distribution for FIFO markets is tighter than for pro-rata markets. These results coincide with Hypothesis 2.
V. Analysis of the Change A. Changes in Market Statistics As discussed above, the change in matching algorithm occurred on May 11th and May 12th of 2015. After this period, the system returned to normal and the 2-year treasury futures reverted back to using a pro-rata matching algorithm, with no other Treasury
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contract affected. We continue our analysis of changes due to the algorithm swtich by moving from market-level information to individual order and trade information. We begin by analyzing changes in average trade sizes. As implied by the precedence rules, aggressive orders in FIFO markets trade fully against the first limit order before executing against any others. As a result, average trade size increases during the two days of change, as expected. Figure 1 captures this change, with average trade size increasing from 5 contracts to over 15 contracts on May 12th. As the right hand panel in figure 1 indicates, there is no major change in average trade sizes in the control market. Similarly, as a result of FIFO rules, an aggressive order ends up transacting against fewer resting orders in the book. This results in a lower number of transactions, as observed in figure 2. Generally, the number of trades on these two days is roughly a third of what we observe in this market on normal days. Related to these two changes are effects on order fill rates, conditional on partial fill. When the matching algorithm switched to FIFO, aggressive orders were no longer broken up into multiple pieces, to be matched with multiple passive orders, so partial fills of an order should be proportionally larger. In contrast, fewer passive orders will be matched against any individual aggressive order in a FIFO market. Controlling for order resting times, the fill percentage of passive orders, conditional on at least a partial fill, should therefore be higher in the FIFO market. Figure 3 shows on the average conditional fill percentage of an order. We highlight a few points. First, we observe fill ratios to be quite different between the 2-year and 30-year treasury futures markets. While the fill ratios in the former market are around 60 percent, they are around 90 percent in the latter market. Additionally, fill ratios in 2-year treasury futures jumps to the levels of the 30-year during the change, indicating market participants experienced significantly higher fill ratios during the change, conditional on being filled. The prior results highlighted a few effects of the algorithm change that were at least 10
partially ”mechanical” in nature. We move from this set of results to a few dependent on the choices made by individual market participants. Field and Large (2008) posits that market participants will have the incentive to ”over-quote” in the pro-rata market, expecting to trade only a small proportion of their order. In figure 4, we look at the average size of new passive orders for each day in our sample. Though the average size of these new orders does not appear to change significantly, like the market depth results we see that the top end of the distribution has been truncated. This result indicates that a subset of accounts, perhaps those who tend to post orders with sizes at the top end of the distribution, potentially adjust their quoting behavior under the new conditions.
B. Changes in Revenue and Price Efficiency We now move to the two primary topics of interest in the comparison of pro-rata and FIFO algorithms: queue position value and price efficiency. We have noted in the charts above the relatively tight order book distribution in FIFO markets. We have hypothesized that this is due to the fact that the cut-off between the queue position with positive marginal value and negative marginal value experiences relatively low variance. In contrast, this dividing line has much higher variance in the pro-rata case. Figure 5 charts the average short term (30 second) revenue associated to a given queue position. In order to calculate this revenue, the first execution for each passive order is compared to the mid-market price 30 seconds after this initial execution. A positive revenue is assigned when this mid-market price is ”in the direction” of the prior trade (i.e. a price move down for sells, a price move up for buys) and negative when the mid-market price is in the opposing direction. Queue positions are assigned to partially or fully executed trades using the time of initial order placement. Revenues are then averaged across all passive orders with a given queue position, for a given matching algorithm and day;
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these average revenues are shown in the figure, with the y-axis scaled by the size of the bid-ask spread. As hypothesized, the distribution of revenue by queue position is significantly flatter for the period when the pro-rata algorithm is active relative to the time when FIFO is used. Although revenue values are relatively monotonic for both algorithms, where the short term revenue for queue positions 1-50 are well above 0 under pro-rata, for FIFO markets revenue is already close to 0 by queue position 10. Because time priority is given to the order with queue position 1 under both algorithms, revenue for this queue position is almost identical under both regimes. This graphical summary is further validated in a regression of trade revenue against a set of market characteristics; the results of the regression are shown in Table III. The regression highlights a number of expected general findings: 1) that passive orders are generally ”profitable” in the short term relative to the future mid-market price, 2) that revenue falls as queue position increases and 3) that revenue per contract is relatively higher in the lower volatility 2-year contract than the 30-year contract. In addition to these general findings, the regression provides some diff-in-diff results as shown in the interaction terms. The key term of interest is the triple interaction, which considers how revenue changes for a given queue position in the 2-year contract during the period of the FIFO change. We see that revenue is significantly lower (and statistically significant) for a given queue position in the FIFO market, and this difference increases as position increases. Our regression generates economically significant results. While the first order in the queue experiences only a small drop (4.4%) in revenue on average after pro-rata changes to FIFO, the order occupying the tenth position under the pro-rata rules generate on average two times the revenue of an order occupying the same queue position under FIFO rules. These regressions coincide with our Hypothesis 1 above, that the revenue distribution is flatter for pro-rata markets. Aggregating across coefficients, 12
we find that once the 2-year contract trades under a FIFO algorithm, there is little statistical difference between the 2-year and the 30-year contract. Table IV provides a regression overview focused on Hypothesis 3. The regression is a logit regression with a binary dependent variable indicating whether a trade price change is followed by a trade price change in the opposite direction (an event we refer to as a ”price reversal”). For markets with high levels of price efficiency (such as those that follow a martingale), the probability of a price reversal should fall around 50 percent. The regression provides an overview of how these probabilities adjust across contracts and matching algorithms. We see, first, that price reversals are much more likely to occur in the wide tick, low volatility 2-year futures contract, before including additional controls. Furthermore, price reversals are less likely the longer the time since the prior price change, or the higher the amount of trading volume since the last price change. This indicates that the more ”established” a price level is, the less likely subsequent trading will move against that price change; this effect is stronger for the FIFO-based 30-year contract. Finally, the included interaction terms allow us to identify whether the matching algorithm affects price reversal probabilities over and above the other controls. We see that the change had a significant effect on the 2-year contract reversal probability, reducing the occurence of reversals by around 10%. This confirms Hypothesis 3 above, that FIFO markets tend to have fewer price reversals, in part due to the lower probability of short queues.
VI. Conclusion Most liquid financial markets involve an electronic centralized limit order book or similar automated medium of trade. While there are many differences across these markets (e.g. the settlement price procedure or the means of accessing the limit order book), one of the 13
most important differences for traders is the precedence rules for trade matching. These precedence rules define which types of orders are incentivized for early vs late matching, and thus what types of traders will be most successful in using the markets. These incentive structures can therefore result in more macro effects on the quality of a given market, including the level and speed of price discovery, the distribution of revenue, as well as the level of price efficiency. In order to more clearly identify these market quality effects, we analyze an unexpected change in matching rules due to a technical error in the matching engine of the 2-year Treasury futures market. This unexpected change lasted for two days and provides a natural experiment to observe how precedence rules affect market quality relative to other, unchanged markets. Overall, we find that as a result of the change from pro-rata to FIFO, revenue is significantly lower for positions later in the queue, implying a clear distinction in revenue for different queue positions. As a result, the variance in queue length (and thus order book depth) in pro-rata markets is higher. Compared to FIFO, we observe longer periods with much higher order book depth, but also other periods with lower order book depth as well. In addition, prices appear to be more efficient under FIFO rules, exhibiting fewer reversals than in the case of the prorata market. In sum, although order book depth may increase due to pro-rata rules on average, this greater order book depth can come paired with the possibility of increased variance in depth and some reduction in price efficiency.
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References Aspris, Angelo, Sean Foley, Drew Harris, and Peter O’Neill. 2015. “Time Prorata Matching: Evidence of a Change in LIFFE STIR Futures.” Journal of Futures Markets, 35(6): 522–541. Budish, Eric, Peter Cramton, and John Shim. 2015. “The high-frequency trading arms race: Frequent batch auctions as a market design response.” The Quarterly Journal of Economics, 130(4): 1547–1621. Degryse, Hans, and Nikolaos Karagiannis. 2019. “Priority Rules.” Working Paper. Field, Jonathan, and Jeremy Large. 2008. “Pro-rata matching and one-tick futures markets.” CFS Working Paper. Frino, Alex, Amelia Hill, and Elvis Jarnecic. 2000. “An empirical analysis of price and time priority and pro rata trade execution algorithms in screen-traded markets.” The Journal of Derivatives, 7(4): 41–48. Glosten, Lawrence R. 1987. “Components of the bid-ask spread and the statistical properties of transaction prices.” The Journal of Finance, 42(5): 1293–1307. Glosten, Lawrence R. 1998. “Precedence Rules.” Unpublished manuscript. Janecek, Karel, and Martin Kabrhel. 2007. “Matching algorithms of international exchanges.” Citeseer. Kyle, Albert S. 1985. “Continuous auctions and insider trading.” Econometrica: Journal of the Econometric Society, 1315–1335. Lepone, Andrew, and Jin Young Yang. 2012. “The impact of a pro-rata algorithm on liquidity: Evidence from the NYSE LIFFE.” Journal of Futures Markets, 32(7): 660–682.
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Instrument Two Year
Thirty Year
Date 5/4/2015 5/5/2015 5/6/2015 5/7/2015 5/8/2015 5/11/2015 5/12/2015 5/13/2015 5/14/2015 5/15/2015 5/4/2015 5/5/2015 5/6/2015 5/7/2015 5/8/2015 5/11/2015 5/12/2015 5/13/2015 5/14/2015 5/15/2015
Median 20 11 12 20 20 20 20 25 25 25 2 2 2 2 2 2 2 2 2 3
Standard Dev. 551 244 240 90 376 70 71 150 542 224 14 9 10 9 9 10 11 10 10 10
Top 10 % 130 100 91 88 100 80 80 130 225 130 11 10 10 10 11 11 12 12 10 10
Top 5 % 300 190 179 150 200 115 105 300 1111 300 17 15 15 15 17 17 18 17 17 17
Table I: Passive Order Quantity Table I reports a distributional summary of the size of all passive orders placed on the book for each day in our sample, for both contracts. The two days with the change in precedence rules are highlighted in red.
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Instrument Two Year
Thirty Year
Date Median 5/4/2015 10,637 5/5/2015 8,265 5/6/2015 7,878 5/7/2015 6,471 5/8/2015 8,746 5/11/2015 8,202 5/12/2015 7,450 5/13/2015 6,673 5/14/2015 11,504 5/15/2015 7,486 5/4/2015 269 5/5/2015 212 5/6/2015 216 5/7/2015 186 5/8/2015 168 5/11/2015 240 5/12/2015 210 5/13/2015 182 5/14/2015 220 5/15/2015 277
Standard Dev. 5,824 4,739 5,511 3,178 12,477 1,257 1,680 4,325 14,368 5,058 81 71 80 58 56 95 73 63 83 109
Top 10 % 15,668 12,584 12,603 9,700 10,469 9,717 9,515 9,616 19,349 9,610 367 308 303 261 233 350 300 260 308 409
Top 5 % 18,527 14,092 14,767 11,906 22,973 10,347 10,739 11,963 41,245 12,500 415 350 360 295 265 421 348 301 352 467
Table II: Total Top-of-Book Depth Table II reports a distributional summary of the aggregation of the top of the book depth for the bid side and the ask side for each day in our sample, for both contracts. The two days with the change in precedence rules are highlighted in red.
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Table III: Passive Trading Revenue Regression Passive Trading Revenue Regression Variable
Coefficient
P-value
Constant Original Queue Position 2-Year Futures Dummy Position x 2-Year Futures Position x 2-Year Futures x Change
0.058 -0.005 0.196 0.003 -0.011
<.0001 <.0001 <.0001 .0085 <.0001
Number of Observations Adj-R2
383,641 0.001
Table III reports estimates of the regression of revenue on queue position, 2-year treasury futures market dummy and interactive terms including the change in precedence rules of the matching algorithm.
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Table IV: Price Reversal Probability Regression Price Reversal Probability Regression Variable
Coefficient
P-value
Constant 2-Year Futures Dummy Algorithm Change Dummy Volume Since Price Change Time Since Price Change (x10000) 2-Year Futures x Change 2-Year Futures x Volume 2-Year Futures x Time (x1000)
0.314 0.534 -0.034 -0.003 -0.006 -0.108 0.002 0.006
<.0001 <.0001 0.038 <.0001 0.785 0.046 <.0001 0.049
Number of Observations Pseudo R2
66,738 0.028
Table IV reports estimates of the regression of probability of price reversal on 2-year treasury futures market dummy, dummy on the change in the precedence rules of the matching algorithm, volume since price change, time since price change and interactive terms.
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Figure 1: Average Trade Size
Figure 1 presents the average trade size per day for the 2-year treasury futures and 30-year treasury futures contracts.
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Figure 2: Number of Trades
Figure 2 presents the number of transactions per day for the 2-year treasury futures and 30-year treasury futures contracts.
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Figure 3: Fill Ratios
Figure 3 presents the daily average percentage of orders filled for the 2-year treasury futures and 30-year treasury futures contracts.
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Figure 4: Size of New Orders
Figure 4 presents the daily distribution of the size of passive new orders for the 2-year treasury futures contract.
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Figure 5: Distribution of Revenue
Figure 5 presents the average revenue distribution for the 2-year treasury futures contract during regular times (change = 0) and also during the days of the algorithm change (change = 1). Revenue is measured as the percentage of the tick and x-axis shows the position of the order in the queue conditional on execution.
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A. Matching Algorithms Used by Different Contracts Exchanges prefer to use FIFO, Pro-rata, or K-Algo matching algorithms for different contracts. Additionally, there are more nuances to how transactions are allocated to different limit orders, such as maximum and minimum allocations set for the top order (the first order in the queue).6 In tables A1 and A2 we present an abbreviated version of matching algorithm detailes used in grain and oilseeds, livestock, commodity indexes, softs, and the two-year and 30-year treasury futures markets.7
6
For an excellent description of how algorithms in CME grain futured determine which trades are filled, see https://ksugrains.wordpress.com/2018/05/16/how-algorithms-in-cme-grainfutures-determine-which-trades-are-filled-k-state-ag-economics/. 7 For a complete list, go to https://www.cmegroup.com/globex/files/globex-product-referencesheet.xls
25
Residual Allocation
Pro-rata Minimum Allocation
Pro-rata Percent Allocation
FIFO Percent Allocation
Top Order Allocation Maximum
Top Order Allocation Minimum
Top Order Percent Allocation
Instrument
Algorithm
Table A1: Matching Algorithms Used by Different Markets - Grains, Oilseeds, and Livestock
Grains and Oilseeds (CBOT) 26
Corn Futures
K
100%
1
100
40%
60%
1
Leveling
Oats Futures
K
100%
1
100
40%
60%
1
Leveling
Rough Rice Futures
K
100%
1
100
40%
60%
1
Leveling
Soybean Futures
K
100%
1
100
40%
60%
1
Leveling
Soybean Meal Futures
K
100%
1
100
40%
60%
1
Leveling
Soybean Oil Futures
K
100%
1
100
40%
60%
1
Leveling
Wheat Futures
K
100%
1
100
40%
60%
1
Leveling
KC Hard Red Winter (HRW) Wheat Futures
K
100%
1
50
40%
60%
1
FIFO
Black Sea Wheat Futures
K
100%
1
100
40%
60%
1
Leveling
Livestock (CME) Feeder Cattle Futures
K
100%
Lean Hog Futures
K
100%
Live Cattle Futures
K
100%
Residual Allocation
Pro-rata Minimum Allocation
Pro-rata Percent Allocation
FIFO Percent Allocation
Top Order Allocation Maximum
Top Order Allocation Minimum
Algorithm
Instrument
Top Order Percent Allocation
Table A2: Matching Algorithms Used by Different Markets - Commodity Indexes, Softs, U.S. Treasury Futures
Commodity Indexes (CME) 27
S&P-GSCITM Excess Return Index Futures
F
BTIC on S&P-GSCITM Excess Return Index Futures
Q
S&P-GSCITM Commodity Index Futures
F
BTIC on S&P-GSCITM Commodity Index Futures
Q
100% 100%
100% 100%
100%
100%
Softs (NYMEX) Cocoa Futures
F
100%
Coffee Futures
F
100%
Cotton Futures
F
100%
Sugar #11 Futures
F
100%
U.S. Treasury Futures (CBOT) 2-Year U.S. Treasury Note Futures
K
U.S. Treasury Bond Futures
F
100%
1
19999
40% 100%
60%
1
Leveling
PII:
S2405-8513(19)30074-1
DOI:
https://doi.org/10.1016/j.jcomm.2019.100109
Reference:
JCOMM 100109
To appear in:
Journal of Commodity Markets
Received Date: 10 October 2019 Accepted Date: 22 October 2019
Please cite this article as: Haynes, R., Onur, E., Precedence Rules in Matching Algorithms, Journal of Commodity Markets, https://doi.org/10.1016/j.jcomm.2019.100109. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. Published by Elsevier B.V.
Precedence Rules in Matching Algorithms∗† Richard Haynes‡
Esen Onur§
October 31, 2019 ABSTRACT Markets with time priority rules incentivize efforts to increase trading speeds. In particular, revenues resulting from liquidity provision due to discrete pricing can often accrue to the fastest traders, those who can hold favorable queue positions. We examine the impact of precedence rules for a single market that switched to a first-in-first-out (FIFO) matching algorithm from one primarily based on prorata. Due to a technology issue, in May 2015 the two year Treasury futures contract unexpectedly switched from partially pro-rata to FIFO for several days. We study the effects of this switch through a difference-in-difference comparison with a related futures contract that had no change in priority rules. We find that compared to FIFO, orders placed later in time are significantly more profitable under pro-rata. However, the lower profitability of earlier orders in the queue under pro-rata matching causes prices to be less efficient under pro-rata rules. Secondary results find that order sizes and cancellations increase under pro-rata. While analyzed using the Treasury futures market, our findings are applicable to commodity futures as well, where both FIFO and pro-rata are widely used.
Keywords: Precedence Rules, FIFO, Pro-Rata, K-Algo
∗
The research presented in this paper was co-authored by Richard Haynes and Esen Onur, CFTC employees who wrote this paper in their official capacities. The analyses and conclusions expressed in this paper are those of the authors and do not reflect the views of other members of the Office of CFTC Chief Economist, other Commission staff, or the Commission itself. † Authors would like to acknowledge the contributions of Terrence Hendershott and Charles M. Jones to the analysis presented in the paper during their time as consultants with the CFTC. Declarations of interest: none ‡ Commodity Futures Trading Commission; [email protected] § Commodity Futures Trading Commission; [email protected]
I. Introduction The matching rules of financial markets determine which orders trade and at what price. Historically, floor based markets were based on a mixture of objective and subjective criteria in determining who traded with whom; placement on the floor, pre-existing relationships, and inventory levels could all affect whether a given trade occurred or not. The automation of financial markets has, among other things, increased the importance of one factor, the speed of response. Traders who can observe and react faster to public information can cancel mis-priced old orders or execute against orders that have not yet reacted to the information, i.e., orders that are mispriced when they execute due to changes in market conditions after submission (see Budish, Cramton and Shim (2015)). This speed advantage, however, can differ from market to market. In markets where orders are prioritized relative to when they were received, speed can be a primary factor; in others, orders may face different prioritization rules, potentially leading to a larger order getting filled before a faster order. In this paper, we empirically study how the rules of trading impact various market quality measures, such as price discovery and price efficiency. Profitability in liquidity provision increases the importance of secondary precedence rules for orders at the same price. Most markets use price priority as the primary characteristic, which ensures that orders with the most competitive price get to trade first. Given that a minimum tick size ensures discrete prices, however, there are often multiple orders at the best price. Markets specify how trades are allocated among orders at the best price. The procedures for allocating trades at a given price level are referred to as secondary precedence rules. Most markets use time as the secondary precedence rule, making the queue of the orders at the best price operate in a first-in-first-out (FIFO) manner. Under FIFO, orders at the top of the queue are more likely to trade
1
and more likely to trade with smaller orders. Smaller orders are less likely to be informed orders Kyle (1985) and Glosten (1987). Hence, because speed increases the likelihood of avoiding adverse selection, faster traders are incentivized under FIFO rules. We study the impact of switching to FIFO from a more pro-rata algorithm where resting orders of the same size receive equal priority regardless of when they arrive.1 The switch from pro-rata to FIFO occurred unexpectedly in the 2-year Treasury futures contract on May 11-12, 2015.2 In constrast, other Treasury futures contracts, including the 30-year, did not change algorithm on those days. This allows us to conduct a difference-in-difference analysis where the 30-year contract controls for changes in market condition. Changes in the 2-year contract relative to the 30-year contract thus measure the impact of the change in precedence rules. Precedence rules have not been widely studied. In a model with free entry, Glosten (1998) studies FIFO and pro-rata precedence rules.3 Pro-rata provides incentives for traders to place orders even when the queue is already long because the later arriving orders enjoy the same priority, after controlling for size, as earlier orders. Under FIFO, later orders must wait for all earlier orders to execute. This means that, controlling for order size, the marginal value of adding an order at the end of the queue is higher in pro-rata than FIFO, leading to longer order queues under pro-rata. We find empirical support for this prediction. Furthermore, we find support for the economic mechanism which leads to greater depth under pro-rata: orders earlier in the queue are more profitable and execute more often under FIFO than under pro-rata.4 1
As explained later in more detail, the precedence rule for 2-year Treasury futures is not exactly pro-rata. For brevity, we refer to it as pro-rata in the rest of the paper. 2 Pro-rata and FIFO are both used for commodity contracts. See Appendix for more detailed information. 3 Glosten (1998) also analyzes more general secondary precedence rules which depend on the quantities of orders. Pro-rata is a special case where all orders of the same quantity have the same precedence. 4 Field and Large (2008) in addition show that depth can be higher under pro-rata for a second reasons - traders with a desired quantity to execute have an incentive to overquote. For example, a trade wanting to trade 100 contacts will place an order for 1,000 contracts if the trader believes that
2
While pro-rata’s incentives encourage the placement of orders when the queue is already long, pro-rata discourages the placement of orders when the queue is short. Short queues in pro-rata markets are likely signals that the levels of adverse selection are high (and thus the marginal value of placing an order is low). Because of this, orders that remain in the queue are likely to suffer from adverse selection and lead to unprofitable trades; those in the queue should cancel and wait for the price movement. This can lead to higher frequencies of price changes due to this cancellation activity, changes that are often reversed. This increased frequency of price reversals imply a less efficient price discovery process. We find evidence that prices are less efficient under pro-rata, as evidenced by a high level of price reversal events. The paper proceeds as follows. Section II describes in detail the change in precedence rules we are studying. Section III presents an overview of the related literature. Section IV describes the data used in our analysis and presents some descriptive statistics. Section V presents our main analysis and results. Section VI concludes.
II. Background On May 10th, 2015 (a Sunday), the Chicago Mercantile Exchange (CME) determined that the algorithm designed to match orders in the 2-year Treasury futures contract was not working as expected. The algorithm the CME uses for matching aggressive and passive trades in the 2-year contract is known as a ”K” algorithm. This algorithm is a mixture of first-in, first-out (FIFO) and pro-rata components (40% FIFO, 60% pro-rata), where pro-rata matching is based on a price, quantity precedence rule. In addition to this weighting of pro-rata and FIFO components, the K-algorithm gives additional preference to the first order at a new price point. That first order must his fill rate will be 10 percent.
3
be filled (up to a pre-specified amount) before any other executions; once the initial fill is complete, the FIFO/pro-rata balance becomes active. For brevity’s sake, we will refer to this hybrid matching approach for the 2-year as a ”pro-rata” matching algorithm, highlighting that it is primarily, but not fully, a pro-rata mechanism. Generally, pro-rata matching algorithms are used in markets where price volatility is lower than average. For instance, Eurodollar (short-term interest rates) also use pro-rata matching algorithms, as do many commodity spread markets 5 . Because this hybrid algorithm was not working properly on May 10th, the CME put out a public announcement that evening stating that for the following day, May 11th, the 2-year contract would be traded using a 100 % FIFO algorithm, the algorithm used for most of the other Treasury futures contracts. At the end of May 11, after unsuccessfully trying to switch the matching engine back to pro-rata, the CME put out another public notice that precedence rules on May 12th would also be FIFO. Starting on May 13th, precedence rule returned to the traditional pro-rata algorithm. This unanticipated shift provided an exogenous test on how matching algorithms may affect liquidity provision, as well as the dynamics of price discovery and price efficiency. In addition, because many Treasury futures contracts (including the 5-year, the 10-year and the 30-year, which trade on a FIFO basis) were unaffected, we are able to incorporate difference-indifference tests into our analysis. We hypothesize a few market changes due to the change in precedence rules. Because the pro-rata matching algorithm puts lower value on queue position relative to FIFO markets, the marginal value of adding a new passive order to the end of a long queue is higher in pro-rata markets. In a pro-rata market, this order has a high likelihood of a partial fill even for the first aggressive order; in contrast, in a FIFO market the order would need to wait until all orders placed prior to it execute. In contrast, because the 5
See the Appendix for a detailed information on different markets and their matching algorithms.
4
relative value of being at the front of the queue is lower, the probability of cancellation at the front of the queue is higher, potentially increasing adverse selection for short queue lengths. Given the relative value of adding a new order to a long queue (and a short queue) in pro-rata versus FIFO markets, we propose two related hypotheses: H1: The average short-term revenue of passive orders, as a function of queue position, is flatter for pro-rata markets relative to FIFO markets. H2: The variance in order book depth is higher for pro-rata markets relative to FIFO markets. In addition to these two hypotheses on liquidity provision, we anticipate that the level of price efficiency in a market will change as matching algorithms are adjusted. Because short queues are less attractive in pro-rata markets, price adjustments are likely to come more quickly and more often in a pro-rata market, conditional on there being a short queue. This leads us to a further, third hypothesis focusing on the relative price efficiency of these two algorithms. H3: The probability of a price reversal (e.g. a trade price increase following a trade price decrease) is higher in a pro-rata market than in a FIFO market. The combination of these three hypotheses highlights at least one component of the cost-benefit comparison between these two market structures. Because the marginal value of the next order, in a relatively long queue, is higher in pro-rata than in FIFO, liquidity provision is also likely to be higher in pro-rata than in FIFO markets. For large traders, who require significant market depth for efficient risk transfer, this additional depth in the book is of value. In contrast, short queues in pro-rata markets tend to last for a shorter period than they do in FIFO markets, leading to ”inefficient” price movements which are eventually reversed. This balance between the top and bottom ends of the depth distribution illustrate the trade-off between these two matching algorithms.
5
III. Related Literature While there is an extensive literature on markets operating a central limit order book with price time precedence rules (FIFO), there is little research on markets with prorata precedence rules. Similar to the markets we analyze, Frino, Hill and Jarnecic (2000) analyzes market changes after the CME modified the precedence rules in the Eurodollar futures contract from FIFO to pro-rata in 1998. They find that this change did not have a significant impact on the liquidity in the market. Similarly, two other papers study the changes in the precedence rules at the London International Financial Futures and Options (LIFFE) exchange. Lepone and Yang (2012) analyzes the impact on the market when LIFFEs matching algorithm changed its precedence rules from a mixed price-time pro-rata algorithm to a pure quantity pro-rata algorithm in 20015. They find that this change had an adverse effect on the liquidity in the market, namely order book depth decreased and bid-ask spread widened. Another study, (Aspris et al. 2015) analyzes how the market is affected when LIFFE decided to switch to a pro-rata algorithm with some time priority in 2007. They do not find any significant changes on market quality as a result of changes in precedence rules. However, in line with our findings, Aspris et al. (2015) do find that the trading environment changes as a result of the rule change in 2007. They find that under pure pro-rata matching algorithms, traders strategically over-size their orders. More importantly, they conclude that market participants optimize their trading and quoting decisions based on the matching algorithm adopted by the exchange, a result which lines up with our main findings. Janecek and Kabrhel (2007) offers a comparison of pro-rata matching algorithms with price time priority; the authors find that FIFO motivates narrower spreads, but discourages other orders from joining the queue. They also find that orders sitting on the book will be smaller under FIFO. In comparison, they find pro-rata to moti-
6
vate other orders to join the queue with large limit orders, leading to increased market depth. They also note that the pro-rata algorithm does not motivate bid ask spread to be narrower. Janecek and Kabrhel (2007) also offer a summary of the rules used by international derivatives exhanges. On the theoretical side, Field and Large (2008) present a model analyzing the effects of pro-rata matching in one-tick markets, similar to those in futures markets. The authors postulate that market participants rationally choose to over-quote under prorata precedence rules. The paper also finds that since traders have the incentive to over-quote, cancellation rates under pro-rata precedence rules are higher. Degryse and Karagiannis (2019) present a theoretical model where they compare the price-time priority rule with a different kind of priority rule, one that follows a pricebroker-time (PBT) priority. The latter is generally used in a number of Canadian and Nordic markets compared to the former that is used in the U.S. markets. They find that under the PBT rule, fill rates are higher when tick size is large and smaller when tick size is small. Similarly, they also show that investor welfare is higher with PBT when tick size is large but lower when tick size is small. Finally, Glosten (1998) posits a theoretical analysis of precedence rules and find that markets will have greater depth when quoted quantity plays a role in precedence rules. Comparing time and quantity precedence rules, Glosten (1998) suggests cases when the bid-ask spread can is the same between these two precedence rules but market depth is higher in pro-rata.
7
IV. Data and Summary Statistics A. Description of the Data The analysis below is based on order book data sourced from the Chicago Mercantile Exchange (CME). We analyze the 2-year U.S. Treasury futures market, the market where the unexpected switch of precedence rules occurred, as well as the 30-year Treasury futures as the control. The CME publicly provides a real-time summary of bids and offers at the top ten price levels. For each price level, market participants are able to see how many orders are at that price, as well as the total quantity at that price. In addition to this, the CME provides, at special request, more detailed regulatory order data to the U.S. Commodity Futures Trading Commission. This more detailed data set provides detailed information about every order-related message sent to the exchange, including new orders, modifications of orders, and cancellations of orders. In addition to each order’s price and quantity, this regulatory data set also identifies the participant who entered the order. Our sample goes from May 4th, 2015 until May 15th, 2015, a two week set of dates which straddles the two-day matching algorithm change.
B. Summary Statistics Tables I and II provide an overview of daily liquidity provision for the two focal contracts. Table I provides a distributional summary of the size of all passive orders placed in the book for that contract, on that day. Table II provides a distributional summay of the aggregate top of the book depth (best ask plus best bid) for each day and each contract. Because pro-rata markets prioritize large passive orders over small passive orders, we expect the distribution of passive order sizes would shift lower during the period when the two year contract was traded using a FIFO algorithm. In addition, because the marginal
8
value of adding an order to the back of the queue in pro-rata markets is higher than that for FIFO markets, the distribution of order book depth should also be lower for the FIFO algorithms. We find both of these effects in the tables. During the two-day period of interest, 95% of passive orders in the two year market were for 115 (Monday) or 105 (Tuesday) or fewer contracts; in contrast, for the days where the pro-rata algorithm was active, this cutoff was never less than 150. Similarly the standard deviation of order size was roughly 70 contracts during the key two-day period, significantly lower than during the regular pro-rata precedence days. Note that the 30-year Treasury futures market does not display any significant change during the two-week period, indicating that the changes observed in the two year contract were not due to changes in the fundamentals. As demonstrated in table II, order book depth trends show a similar pattern, with the top of the distribution significantly lower during the two days relative to the rest of the panel. In addition to this, the standard deviation of depth is also lower, highlighting that small order book depth is less likely when FIFO priority rules are used. This second finding corraborates our earlier hypothesis that, where the marginal value of adding a quote to a long queue is higher in pro-rata, the marginal value of adding a quote to a short queue is lower. As a result of these dynamics, the queue distribution for FIFO markets is tighter than for pro-rata markets. These results coincide with Hypothesis 2.
V. Analysis of the Change A. Changes in Market Statistics As discussed above, the change in matching algorithm occurred on May 11th and May 12th of 2015. After this period, the system returned to normal and the 2-year treasury futures reverted back to using a pro-rata matching algorithm, with no other Treasury
9
contract affected. We continue our analysis of changes due to the algorithm swtich by moving from market-level information to individual order and trade information. We begin by analyzing changes in average trade sizes. As implied by the precedence rules, aggressive orders in FIFO markets trade fully against the first limit order before executing against any others. As a result, average trade size increases during the two days of change, as expected. Figure 1 captures this change, with average trade size increasing from 5 contracts to over 15 contracts on May 12th. As the right hand panel in figure 1 indicates, there is no major change in average trade sizes in the control market. Similarly, as a result of FIFO rules, an aggressive order ends up transacting against fewer resting orders in the book. This results in a lower number of transactions, as observed in figure 2. Generally, the number of trades on these two days is roughly a third of what we observe in this market on normal days. Related to these two changes are effects on order fill rates, conditional on partial fill. When the matching algorithm switched to FIFO, aggressive orders were no longer broken up into multiple pieces, to be matched with multiple passive orders, so partial fills of an order should be proportionally larger. In contrast, fewer passive orders will be matched against any individual aggressive order in a FIFO market. Controlling for order resting times, the fill percentage of passive orders, conditional on at least a partial fill, should therefore be higher in the FIFO market. Figure 3 shows on the average conditional fill percentage of an order. We highlight a few points. First, we observe fill ratios to be quite different between the 2-year and 30-year treasury futures markets. While the fill ratios in the former market are around 60 percent, they are around 90 percent in the latter market. Additionally, fill ratios in 2-year treasury futures jumps to the levels of the 30-year during the change, indicating market participants experienced significantly higher fill ratios during the change, conditional on being filled. The prior results highlighted a few effects of the algorithm change that were at least 10
partially ”mechanical” in nature. We move from this set of results to a few dependent on the choices made by individual market participants. Field and Large (2008) posits that market participants will have the incentive to ”over-quote” in the pro-rata market, expecting to trade only a small proportion of their order. In figure 4, we look at the average size of new passive orders for each day in our sample. Though the average size of these new orders does not appear to change significantly, like the market depth results we see that the top end of the distribution has been truncated. This result indicates that a subset of accounts, perhaps those who tend to post orders with sizes at the top end of the distribution, potentially adjust their quoting behavior under the new conditions.
B. Changes in Revenue and Price Efficiency We now move to the two primary topics of interest in the comparison of pro-rata and FIFO algorithms: queue position value and price efficiency. We have noted in the charts above the relatively tight order book distribution in FIFO markets. We have hypothesized that this is due to the fact that the cut-off between the queue position with positive marginal value and negative marginal value experiences relatively low variance. In contrast, this dividing line has much higher variance in the pro-rata case. Figure 5 charts the average short term (30 second) revenue associated to a given queue position. In order to calculate this revenue, the first execution for each passive order is compared to the mid-market price 30 seconds after this initial execution. A positive revenue is assigned when this mid-market price is ”in the direction” of the prior trade (i.e. a price move down for sells, a price move up for buys) and negative when the mid-market price is in the opposing direction. Queue positions are assigned to partially or fully executed trades using the time of initial order placement. Revenues are then averaged across all passive orders with a given queue position, for a given matching algorithm and day;
11
these average revenues are shown in the figure, with the y-axis scaled by the size of the bid-ask spread. As hypothesized, the distribution of revenue by queue position is significantly flatter for the period when the pro-rata algorithm is active relative to the time when FIFO is used. Although revenue values are relatively monotonic for both algorithms, where the short term revenue for queue positions 1-50 are well above 0 under pro-rata, for FIFO markets revenue is already close to 0 by queue position 10. Because time priority is given to the order with queue position 1 under both algorithms, revenue for this queue position is almost identical under both regimes. This graphical summary is further validated in a regression of trade revenue against a set of market characteristics; the results of the regression are shown in Table III. The regression highlights a number of expected general findings: 1) that passive orders are generally ”profitable” in the short term relative to the future mid-market price, 2) that revenue falls as queue position increases and 3) that revenue per contract is relatively higher in the lower volatility 2-year contract than the 30-year contract. In addition to these general findings, the regression provides some diff-in-diff results as shown in the interaction terms. The key term of interest is the triple interaction, which considers how revenue changes for a given queue position in the 2-year contract during the period of the FIFO change. We see that revenue is significantly lower (and statistically significant) for a given queue position in the FIFO market, and this difference increases as position increases. Our regression generates economically significant results. While the first order in the queue experiences only a small drop (4.4%) in revenue on average after pro-rata changes to FIFO, the order occupying the tenth position under the pro-rata rules generate on average two times the revenue of an order occupying the same queue position under FIFO rules. These regressions coincide with our Hypothesis 1 above, that the revenue distribution is flatter for pro-rata markets. Aggregating across coefficients, 12
we find that once the 2-year contract trades under a FIFO algorithm, there is little statistical difference between the 2-year and the 30-year contract. Table IV provides a regression overview focused on Hypothesis 3. The regression is a logit regression with a binary dependent variable indicating whether a trade price change is followed by a trade price change in the opposite direction (an event we refer to as a ”price reversal”). For markets with high levels of price efficiency (such as those that follow a martingale), the probability of a price reversal should fall around 50 percent. The regression provides an overview of how these probabilities adjust across contracts and matching algorithms. We see, first, that price reversals are much more likely to occur in the wide tick, low volatility 2-year futures contract, before including additional controls. Furthermore, price reversals are less likely the longer the time since the prior price change, or the higher the amount of trading volume since the last price change. This indicates that the more ”established” a price level is, the less likely subsequent trading will move against that price change; this effect is stronger for the FIFO-based 30-year contract. Finally, the included interaction terms allow us to identify whether the matching algorithm affects price reversal probabilities over and above the other controls. We see that the change had a significant effect on the 2-year contract reversal probability, reducing the occurence of reversals by around 10%. This confirms Hypothesis 3 above, that FIFO markets tend to have fewer price reversals, in part due to the lower probability of short queues.
VI. Conclusion Most liquid financial markets involve an electronic centralized limit order book or similar automated medium of trade. While there are many differences across these markets (e.g. the settlement price procedure or the means of accessing the limit order book), one of the 13
most important differences for traders is the precedence rules for trade matching. These precedence rules define which types of orders are incentivized for early vs late matching, and thus what types of traders will be most successful in using the markets. These incentive structures can therefore result in more macro effects on the quality of a given market, including the level and speed of price discovery, the distribution of revenue, as well as the level of price efficiency. In order to more clearly identify these market quality effects, we analyze an unexpected change in matching rules due to a technical error in the matching engine of the 2-year Treasury futures market. This unexpected change lasted for two days and provides a natural experiment to observe how precedence rules affect market quality relative to other, unchanged markets. Overall, we find that as a result of the change from pro-rata to FIFO, revenue is significantly lower for positions later in the queue, implying a clear distinction in revenue for different queue positions. As a result, the variance in queue length (and thus order book depth) in pro-rata markets is higher. Compared to FIFO, we observe longer periods with much higher order book depth, but also other periods with lower order book depth as well. In addition, prices appear to be more efficient under FIFO rules, exhibiting fewer reversals than in the case of the prorata market. In sum, although order book depth may increase due to pro-rata rules on average, this greater order book depth can come paired with the possibility of increased variance in depth and some reduction in price efficiency.
14
References Aspris, Angelo, Sean Foley, Drew Harris, and Peter O’Neill. 2015. “Time Prorata Matching: Evidence of a Change in LIFFE STIR Futures.” Journal of Futures Markets, 35(6): 522–541. Budish, Eric, Peter Cramton, and John Shim. 2015. “The high-frequency trading arms race: Frequent batch auctions as a market design response.” The Quarterly Journal of Economics, 130(4): 1547–1621. Degryse, Hans, and Nikolaos Karagiannis. 2019. “Priority Rules.” Working Paper. Field, Jonathan, and Jeremy Large. 2008. “Pro-rata matching and one-tick futures markets.” CFS Working Paper. Frino, Alex, Amelia Hill, and Elvis Jarnecic. 2000. “An empirical analysis of price and time priority and pro rata trade execution algorithms in screen-traded markets.” The Journal of Derivatives, 7(4): 41–48. Glosten, Lawrence R. 1987. “Components of the bid-ask spread and the statistical properties of transaction prices.” The Journal of Finance, 42(5): 1293–1307. Glosten, Lawrence R. 1998. “Precedence Rules.” Unpublished manuscript. Janecek, Karel, and Martin Kabrhel. 2007. “Matching algorithms of international exchanges.” Citeseer. Kyle, Albert S. 1985. “Continuous auctions and insider trading.” Econometrica: Journal of the Econometric Society, 1315–1335. Lepone, Andrew, and Jin Young Yang. 2012. “The impact of a pro-rata algorithm on liquidity: Evidence from the NYSE LIFFE.” Journal of Futures Markets, 32(7): 660–682.
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Instrument Two Year
Thirty Year
Date 5/4/2015 5/5/2015 5/6/2015 5/7/2015 5/8/2015 5/11/2015 5/12/2015 5/13/2015 5/14/2015 5/15/2015 5/4/2015 5/5/2015 5/6/2015 5/7/2015 5/8/2015 5/11/2015 5/12/2015 5/13/2015 5/14/2015 5/15/2015
Median 20 11 12 20 20 20 20 25 25 25 2 2 2 2 2 2 2 2 2 3
Standard Dev. 551 244 240 90 376 70 71 150 542 224 14 9 10 9 9 10 11 10 10 10
Top 10 % 130 100 91 88 100 80 80 130 225 130 11 10 10 10 11 11 12 12 10 10
Top 5 % 300 190 179 150 200 115 105 300 1111 300 17 15 15 15 17 17 18 17 17 17
Table I: Passive Order Quantity Table I reports a distributional summary of the size of all passive orders placed on the book for each day in our sample, for both contracts. The two days with the change in precedence rules are highlighted in red.
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Instrument Two Year
Thirty Year
Date Median 5/4/2015 10,637 5/5/2015 8,265 5/6/2015 7,878 5/7/2015 6,471 5/8/2015 8,746 5/11/2015 8,202 5/12/2015 7,450 5/13/2015 6,673 5/14/2015 11,504 5/15/2015 7,486 5/4/2015 269 5/5/2015 212 5/6/2015 216 5/7/2015 186 5/8/2015 168 5/11/2015 240 5/12/2015 210 5/13/2015 182 5/14/2015 220 5/15/2015 277
Standard Dev. 5,824 4,739 5,511 3,178 12,477 1,257 1,680 4,325 14,368 5,058 81 71 80 58 56 95 73 63 83 109
Top 10 % 15,668 12,584 12,603 9,700 10,469 9,717 9,515 9,616 19,349 9,610 367 308 303 261 233 350 300 260 308 409
Top 5 % 18,527 14,092 14,767 11,906 22,973 10,347 10,739 11,963 41,245 12,500 415 350 360 295 265 421 348 301 352 467
Table II: Total Top-of-Book Depth Table II reports a distributional summary of the aggregation of the top of the book depth for the bid side and the ask side for each day in our sample, for both contracts. The two days with the change in precedence rules are highlighted in red.
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Table III: Passive Trading Revenue Regression Passive Trading Revenue Regression Variable
Coefficient
P-value
Constant Original Queue Position 2-Year Futures Dummy Position x 2-Year Futures Position x 2-Year Futures x Change
0.058 -0.005 0.196 0.003 -0.011
<.0001 <.0001 <.0001 .0085 <.0001
Number of Observations Adj-R2
383,641 0.001
Table III reports estimates of the regression of revenue on queue position, 2-year treasury futures market dummy and interactive terms including the change in precedence rules of the matching algorithm.
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Table IV: Price Reversal Probability Regression Price Reversal Probability Regression Variable
Coefficient
P-value
Constant 2-Year Futures Dummy Algorithm Change Dummy Volume Since Price Change Time Since Price Change (x10000) 2-Year Futures x Change 2-Year Futures x Volume 2-Year Futures x Time (x1000)
0.314 0.534 -0.034 -0.003 -0.006 -0.108 0.002 0.006
<.0001 <.0001 0.038 <.0001 0.785 0.046 <.0001 0.049
Number of Observations Pseudo R2
66,738 0.028
Table IV reports estimates of the regression of probability of price reversal on 2-year treasury futures market dummy, dummy on the change in the precedence rules of the matching algorithm, volume since price change, time since price change and interactive terms.
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Figure 1: Average Trade Size
Figure 1 presents the average trade size per day for the 2-year treasury futures and 30-year treasury futures contracts.
20
Figure 2: Number of Trades
Figure 2 presents the number of transactions per day for the 2-year treasury futures and 30-year treasury futures contracts.
21
Figure 3: Fill Ratios
Figure 3 presents the daily average percentage of orders filled for the 2-year treasury futures and 30-year treasury futures contracts.
22
Figure 4: Size of New Orders
Figure 4 presents the daily distribution of the size of passive new orders for the 2-year treasury futures contract.
23
Figure 5: Distribution of Revenue
Figure 5 presents the average revenue distribution for the 2-year treasury futures contract during regular times (change = 0) and also during the days of the algorithm change (change = 1). Revenue is measured as the percentage of the tick and x-axis shows the position of the order in the queue conditional on execution.
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A. Matching Algorithms Used by Different Contracts Exchanges prefer to use FIFO, Pro-rata, or K-Algo matching algorithms for different contracts. Additionally, there are more nuances to how transactions are allocated to different limit orders, such as maximum and minimum allocations set for the top order (the first order in the queue).6 In tables A1 and A2 we present an abbreviated version of matching algorithm detailes used in grain and oilseeds, livestock, commodity indexes, softs, and the two-year and 30-year treasury futures markets.7
6
For an excellent description of how algorithms in CME grain futured determine which trades are filled, see https://ksugrains.wordpress.com/2018/05/16/how-algorithms-in-cme-grainfutures-determine-which-trades-are-filled-k-state-ag-economics/. 7 For a complete list, go to https://www.cmegroup.com/globex/files/globex-product-referencesheet.xls
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Residual Allocation
Pro-rata Minimum Allocation
Pro-rata Percent Allocation
FIFO Percent Allocation
Top Order Allocation Maximum
Top Order Allocation Minimum
Top Order Percent Allocation
Instrument
Algorithm
Table A1: Matching Algorithms Used by Different Markets - Grains, Oilseeds, and Livestock
Grains and Oilseeds (CBOT) 26
Corn Futures
K
100%
1
100
40%
60%
1
Leveling
Oats Futures
K
100%
1
100
40%
60%
1
Leveling
Rough Rice Futures
K
100%
1
100
40%
60%
1
Leveling
Soybean Futures
K
100%
1
100
40%
60%
1
Leveling
Soybean Meal Futures
K
100%
1
100
40%
60%
1
Leveling
Soybean Oil Futures
K
100%
1
100
40%
60%
1
Leveling
Wheat Futures
K
100%
1
100
40%
60%
1
Leveling
KC Hard Red Winter (HRW) Wheat Futures
K
100%
1
50
40%
60%
1
FIFO
Black Sea Wheat Futures
K
100%
1
100
40%
60%
1
Leveling
Livestock (CME) Feeder Cattle Futures
K
100%
Lean Hog Futures
K
100%
Live Cattle Futures
K
100%
Residual Allocation
Pro-rata Minimum Allocation
Pro-rata Percent Allocation
FIFO Percent Allocation
Top Order Allocation Maximum
Top Order Allocation Minimum
Algorithm
Instrument
Top Order Percent Allocation
Table A2: Matching Algorithms Used by Different Markets - Commodity Indexes, Softs, U.S. Treasury Futures
Commodity Indexes (CME) 27
S&P-GSCITM Excess Return Index Futures
F
BTIC on S&P-GSCITM Excess Return Index Futures
Q
S&P-GSCITM Commodity Index Futures
F
BTIC on S&P-GSCITM Commodity Index Futures
Q
100% 100%
100% 100%
100%
100%
Softs (NYMEX) Cocoa Futures
F
100%
Coffee Futures
F
100%
Cotton Futures
F
100%
Sugar #11 Futures
F
100%
U.S. Treasury Futures (CBOT) 2-Year U.S. Treasury Note Futures
K
U.S. Treasury Bond Futures
F
100%
1
19999
40% 100%
60%
1
Leveling