The Importance of Low Latency to Order Book Imbalance Trading Strategies
David Byrd, Sruthi Palaparthi, Maria Hybinette, Tucker Hybinette Balch
TThe Importance of Low Latency to Order Book ImbalanceTrading Strategies
David Byrd [email protected] of Interactive ComputingGeorgia Institute of TechnologyAtlanta, Georgia
Sruthi Palaparthi [email protected] of Computer ScienceUniversity of GeorgiaAthens, Georgia
Maria Hybinette [email protected] of Computer ScienceUniversity of GeorgiaAthens, Georgia
Tucker Hybinette Balch [email protected] of Interactive ComputingGeorgia Institute of TechnologyAtlanta, Georgia
ABSTRACT
There is a pervasive assumption that low latency access to an ex-change is a key factor in the profitability of many high-frequencytrading strategies. This belief is evidenced by the “arms race” under-taken by certain financial firms to co-locate with exchange servers.To the best of our knowledge, our study is the first to validate andquantify this assumption in a continuous double auction marketwith a single exchange similar to the New York Stock Exchange. Itis not feasible to conduct this exploration with historical data inwhich trader identity and location are not reported. Accordingly, weinvestigate the relationship between latency of access to order bookinformation and profitability of trading strategies exploiting that in-formation with an agent-based interactive discrete event simulationin which thousands of agents pursue archetypal trading strategies.We introduce experimental traders pursuing a low-latency orderbook imbalance (OBI) strategy in a controlled manner across thou-sands of simulated trading days, and analyze OBI trader profit whilevarying distance (latency) from the exchange. Our experiments sup-port that latency is inversely related to profit for the OBI traders,but more interestingly show that latency rank , rather than absolutemagnitude, is the key factor in allocating returns among agentspursuing a similar strategy.
KEYWORDS simulation, finance, market, strategy, artificial, intelligence, multia-gent, latency
It is commonly understood that execution speed is essential for asuccessful high-frequency trading (HFT) strategy. In
High Frequency Trading: A Practical Guide , Irene Aldridge observes that “High-frequency trading relies on fast, almost instantaneous, executionof orders” and that “even a secondâĂŹs worth of delay inducedby hesitation or distraction on the part of a human trader cansubstantially reduce the systemâĂŹs profitability” [1]. Althoughthere is a well-developed body of financial literature around suchstrategies, works that rely on analysis of historical market datacannot reliably quantify the precise, continuous benefit of specificlatency levels to a strategy. Publicly available market informationdoes not identify individual actors or provide a mechanism to revealthe latency of an actor’s order execution after a trading decisionhas been reached, so it is not feasible to use such data to infer theimportance of latency for such strategies.To address this problem, we employ an agent-based interactivediscrete event simulation to construct a market with nanosecondprecision to fully account for agent computational delay and com-munication latency. We experiment within that simulated marketto assess the effect of low latency on overall agent returns for atypical high-frequency strategy. As far as we know, this is the firstpublished study to directly and quantitatively assess the impact ofvariable latency on a trader’s profit.Our work specifically focuses on market microstructure, or mak-ing short-term directional trading decisions based on observedquotes. Richard Lyons divides this group of High Frequency Trad-ing (HFT) strategies in two sets [16], both relating to mismatchesin supply and demand: • Inventory effects pertaining to a market maker absorbinginventory and attempting to dissipate risk. • Portfolio balance effects in which the order flow producesa more lasting impact. a r X i v : . [ q -f i n . T R ] J un avid Byrd, Sruthi Palaparthi, Maria Hybinette, and Tucker Hybinette Balch We introduce a group of experimental agents following a strategyfrom the first category, inventory effects, and investigate the effectof absolute and relative latency on the profitability of each suchagent.
Our work draws from prior lines of financial research in marketmicrostructure trading and latency arbitrage, and computationalresearch in discrete event simulation and agent-based modeling.Here we describe some of the important prior work in each area.
Lawrence Harris described three types of stylized traders relevantto market microstructure trading: [7](1)
Liquidity traders are uninformed traders whose executiontimelines are externally motivated by a client demand or aneed to modify cash holdings.(2)
Informed traders are those who have specific, private in-formation they believe correlates with short term price move-ment, which must be acted on quickly.(3)
Value-motivated traders have an exogenous opinion on astock’s true worth and are motivated to buy or sell at specificprices that represent significant deviations from that value.Harris further identifies informed traders as aggressive , utilizingmarket orders or limit orders near the spread to ensure their privateinformation is monetized before its expiration. Value-motivatedtraders are characterized as more passive , placing limit orders farfrom the spread to execute only if the order flow reaches theirnotion of a fair price.Our study includes simulated versions of these three stylizedstrategies. We construct an environment of informed traders andvalue-motivated traders that serve as “background” market agentsthen, under various conditions, evaluate the performance of a par-ticular kind of liquidity trader which attempts to predict short-termprice changes using an order book imbalance (OBI) indicator.Bloomfield et al constructed experimental markets to test someof Harris’s predictions, finding that informed traders take liquiditywhen the gap between current prices and those suggested by theirtime-sensitive information is high, but provide liquidity when thatgap is low [3]. This provides empirical support for our simulatedliquidity traders’ belief that a large amount of liquidity provisionnear the spread indicates impending directional movement.
Wah and Wellman have previously studied latency arbitrage witha simulated two-market model plus public price quotes from anNBBO (National Best Bid and Offer) provider [22]. They found thatthe presence of a high frequency trading (HFT) agent arbitragingthe two markets negatively impacted the surplus achieved by othertraders in excess of the amount it obtained for itself. The latencyarbitrageur did improve order execution speed (a common defenseof HFT activity) but actually caused a wider bid-ask spread.Our work examines a different aspect of latency arbitrage, in-troducing multiple competing liquidity traders which pursue a low-latency strategy with a single exchange. We focus on the re-lationship between absolute and relative communication latencylevels and the profitability of each liquidity trader.
We conduct our experiments in an event driven framework builton a discrete event simulation (DES) system kernel. Under a DESmodel, the system changes state only at the edges of discrete pointsin time. Conventional approaches to DES are either time driven(synchronous) or event driven (asynchronous).In time driven (or time “stepped”) systems, progress is drivenby incrementally advancing time, which is typically representedby a global counter. The counter is increased by a fixed amount,the minimum resolution, and then events that have a time stampmatching the current counter are processed. One disadvantage oftime stepped simulation is the wasting of computation time on stepsduring which no activity takes place. For example, when exploringhigh frequency trading (HFT), it might be important to allow agentsto act with nanosecond time resolution. If the counter is at time t after some agent places an order, and the next agent will act justfifty microseconds later, the system will have to sequentially checkfor activity at time steps t + t + some next scheduled event. Under this model, each time an agentacts, it will schedule its next action through a priority queue in thesystem kernel.To revisit the above HFT example in the event driven context,when an agent places an order at time t and the next agent willact fifty microseconds later, the kernel’s event priority queue willhave time stamp t + t to t + he Importance of Low Latency to Order Book Imbalance Trading Strategies limitation that it does not support the implementation of complexcustom trading strategies. Our system uses an agent based model (ABM), formed by a set ofautonomous agents that interact with their environment, includingother agents, to achieve their objectives. Agent based modeling andsimulation (ABMS) has been successfully employed in a variety ofapplication domains [17] such as social science [2], computationaleconomics [21], and marketing [19]. We follow prior work in thearea by modeling a stock market based on the behavior of individualinvestors [14] represented as strategic trading agents. Agent-basedfinancial markets have been shown to be effective for dynamicsituations in which investor behavior must change in response tothe environment [13].Some notable agent-based simulators from the literature areSwarm [18], MASON [15], and Player/Stage [6]. There are alsosimulators like SASSY [8] that support large numbers of agentsthrough an optimistic parallel kernel. While our system is not aparallel simulation kernel we draw inspiration from their designand currently support many thousands of agents.
To test the hypothesis that lower communication latency with anexchange will correlate with higher trading period profits for orderbook imbalance (OBI) liquidity traders, we construct an agent-basedinteractive discrete event simulation using components describedin Background and Related Work. The simulation provides a Kernelwhich enforces the proper flow of time and through which all inter-agent communication must occur, and the simulation environmentrepresents a modern electronic stock market in which numerousstrategic trading agents place bids and offers with a single exchangeagent.
Volumes P r i c e s Bid SideAsk SideMid Price Spread Ask PriceBid Price
Limit order to sell is addedto the queue
Figure 1: Example illustrating liquidity provisioned to alimit order book.
At the core of our simulated market is an exchange agent whichaccepts orders to buy (bid prices) and sell (ask prices) specified quantities of various securities. Such orders may optionally containan additional limit price which prohibits transaction at any lessadvantageous price for the submitting agent. Orders with a limitprice, called limit orders , may not immediately transact, and willinstead be recorded into the limit order book for the relevant securityas shown in Figure 1, to await future transaction if a matching ordershould arrive. Orders without a limit price, called market orders ,have no such restriction and will always transact immediately atthe best currently available price.As the limit order book consists of all unfulfilled orders to trans-act a security, the limit prices and quantities of visible bid and askorders can be interpreted as some representation of the supply anddemand for the security at one moment in time. Measurable aspectsof the limit order book include: the spread , or the distance betweenthe highest bid and lowest ask price; the available liquidity , or thetotal volume of shares on offer; and the distribution of that liquidity,in particular whether it is concentrated near or far from the spread,and whether it is significantly greater on one side of the book thanthe other.Our simulated limit order book follows an order matching pro-cess similar to the Nasdaq exchange in the United States. That is,an arriving order to buy will transact with the lowest priced askorder already in the limit order book. If the arriving order is to sell,it will transact with the highest priced bid order instead. If thereare multiple orders in the limit order book at the same price, theoldest order will be transacted. All transactions happen at the limitprice of the order already in the limit order book, not the arrivingorder.
Our simulated market is not a simple backtest constructed fromstatic historical data, but rather a dynamic and interactive one inwhich many agents participate in pursuit of profit, each able todirectly impact market pricing and other agents through its actions.To this end we employ a population of stylized strategy agentsdivided into several families inspired by the work of LawrenceHarris [7]: value-motivated traders, informed traders, and liquiditytraders. The first two represent our “background” trading popula-tion, which we do not alter or manipulate, and the third representsour experimental population.Both of our representative background agent strategies obtainnoisy observations of an exogenous price-time series, sometimescalled the fundamental series, that represents the “true value” ofa stock independent of current market price fluctuations. Theseobservations over time influence an internal value belief that dif-fers per agent according to the update of a Bayesian process asconstructed by Wah et al [23]. In summary, assume a backgroundagent, arriving at the market via a Poisson process, wakes at time t and receives observation o t . It updates an estimate of the currentfundamental value ˜ r t and that estimate’s variance ˜ σ t :˜ r t ′ ← ( − ( − κ ) δ ) ¯ r + ( − κ ) δ ˜ r t ′ (1)˜ σ t ′ ← ( − κ ) δ ˜ σ t ′ + − ( − κ ) δ − ( − κ ) σ s (2)where t ′ is agent’s previous wake time, δ = t − t ′ , κ is the funda-mental mean reversion parameter, and σ s is the shock variance of avid Byrd, Sruthi Palaparthi, Maria Hybinette, and Tucker Hybinette Balch the fundamental process. Having now accounted for interveningtime, the agent applies its new observation o t to obtain an estimateof the current fundamental value and that estimate’s variance:˜ r t = σ n σ n + ˜ σ t ′ ˜ r t ′ + ˜ σ t ′ σ n + ˜ σ t ′ o t (3)˜ σ t = σ n ˜ σ t ′ σ n + ˜ σ t ′ (4)where σ n is the agent’s observation noise. With updated estimates˜ r t and ˜ σ t , the agent can compute ˆ r t , the final fundamental value r T as estimated at current time t :ˆ r t ← ( − ( − κ ) T − t ) ¯ r + ( − κ ) T − t ˜ r t (5)where ¯ r is the fundamental mean, and random perturbations areassumed to take on a mean value of zero. This estimate of the finalfundamental value represents the agent’s belief about what thestock price should be at the close of the trading day. It uses thisvalue to inform its decisions concerning limit price, trade direction,aggressiveness of trading posture, and so on.Value-motivated traders tend to place limit orders away from thespread, intending to transact only if prices reach a level consistentwith their private value beliefs plus a required level of surplus.We represent this style of trading with a common variation ofthe Zero Inteligence (ZI) trader as described by Wah et al [23],which estimates the final fundamental value as explained above.Each ZI trader is constructed with a random vector of incrementalprivate values placed on the acquisition or release of one additionalunit of stock, given the agent’s current holding, which is appliedas an offset to the estimated final fundamental value. If q max isthe holding limit, then the preferences for trading agent i are theelements θ qi in: Θ i = ( θ − q max + i , . . . , θ i , θ i , . . . , θ q max i ) (6)where q is the quantity of stock currently held. Θ i is drawn ran-domly from N( , σ PV ) , where σ PV is a selected experimental pa-rameter. The values are sorted in descending order ensuring dimin-ishing returns on private value offsets. The ZI trader places limitorders in a random direction (buy/sell) but selects limit prices suchthat transacted orders will always produce an expected surplus tothe agent.Informed traders are represented by a class of agents taking onthe role of an arbitrageur. These agents are broadly similar to theZI agents, as they also make noisy observations of a fundamentalvalue and construct a belief about the “true” worth of a stock. Theinformed traders, however, always place a directional order thatwill profit from a reversion of the order flow to the fundamental.Based on market conditions, these agents may place orders in oneof two postures: aggressively with market orders or limit ordersthat cross over the spread, or passively with limit orders that do notcross the spread. The supply and demand information they injectto the order flow should be predictive of short-term price movesdue to their approximately correct exogenous observations. Liquidity traders have no opinion about the “correct” value of astock. They participate in anticipation of profit by observing the order flows in the market for clues that suggest short-term pricemovement arising from the market microstructure itself. We injecta population of liquidity traders as our experimental agents ofchange, observing their impact on the market, and altering theircommunication latency to the exchange to understand the effectthis has on the profitability of their strategy. In keeping with thespirit of liquidity trading, these agents are unable to observe theexogenous price-time series (fundamental) used by the backgroundtraders. Our specific choice of liquidity trader follows an orderbook imbalance (OBI) strategy which continuously tracks whatproportion of total liquidity near the spread is on the buy side ofthe limit order book: I = (cid:205) b ∈ B V b (cid:205) o ∈ O V o (7)where B is the set of visible bid orders, O is the set of all visibleorders, and V represents the share volume of a particular order. Forexample, when the indicator I = .
5, liquidity is equally distributedbetween the two sides of the book, and when I = . I > . + H or I < . − H , where H is a configurable entry threshold, and exits thedirectional trade based on a trailing stop at configurable distance D applied to the same indicator (not the midpoint stock price). Theorder book depth (level) L at which to consider liquidity provisionto be a positively-correlated signal is also a configurable parameter. We conducted two primary experiments for analysis in this work.Both experiments utilize a simulated market containing a singleexchange with a limit order book mechanism accepting offers totransact shares of a single security. The experimental market ispopulated with 1,000 background traders, split evenly between thevalue-motivated and informed trader types described in Approach.Every trading agent is configured with a minimum communi-cation latency to the exchange. When a message is scheduled fortransmission, the time sent is the agent’s current time plus a de-lay that accounts for the computational complexity of the agent’sstrategy. The time received will be scheduled for the time sent plusthe minimum communication latency plus a random factor drawnfrom a realistic network “jitter” model.For those agents requiring an exogenous price-time series, weemployed a sparse mean-reverting fundamental as described inByrd [4]. This mathematical series is a continuous form of thediscrete mean reverting process described in Wah et al [23] withthe addition of a second variance process which is applied at lowerfrequency but greater magnitude to represent infrequent “newsshocks” that can change a trader’s belief about the proper valuationof the stock.We conducted a preliminary experiment in which we added tenOBI liquidity traders, as previously described, to the backgroundpopulation with random latency and no particular control, andsimulated hundreds of different market days. Figure 2 comparesthe absolute latency of OBI traders to their profit at market close,with each grey data point representing one trader’s result for onefull market day. We find a strong inverse Pearson correlation of r = − . he Importance of Low Latency to Order Book Imbalance Trading Strategies Figure 2: Profit vs absolute latency of liquidity (OBI) traders. gap in the plot at low latency values, with a cluster of positiveprofit agents and a cluster of negative profit agents, and virtuallyno agents with profit close to zero. A desire to understand this gapmotivated the design of our two subsequent experiments.
In the first experiment, the described background agents were geo-graphically situated around the United States relative to the locationof the New York Stock Exchange. The minimum communicationlatency of each individual background agent was drawn from auniform distribution of 21 µs (roughly the other side of Manhattan)to 13 ms (around Seattle, Washington).To the background population, we added ten order book im-balance (OBI) liquidity traders following the previously describedindicator strategy. One liquidity trader, serving as a control, wasalways placed at the minimum latency permitted to backgroundagents and eight were randomly distributed in the same range asthe background agents. The final liquidity trader is considered theexperimental agent for Experiment 1, for which the geographiclocation (latency) is systematically varied to measure its impact onthe returns of all liquidity traders. All OBI liquidity traders used anentry threshold of H = .
17, a trailing stop distance of D = . L = ns ) to Seattle,Washington (approx. 13 ms ). Each of twenty random market days (i.e.different exogenous price-time fundamental series) were repeatedwith the experimental agent varied among the thirty positions tominimize unintended perturbations in the market process. We thusobtained 6,000 full-day observations of the latency and profitabilityrelationship of an OBI liquidity trader. Results.
For this experiment, we logged the absolute latency of eachliquidity trader along with its marked-to-market profit at the endof each trading day.
Figure 3: Profit of experimental liquidity trader for thirtylevels of absolute latency (log scale) across twenty marketdays. Blue line represents fixed-latency control liquiditytrader.
Figure 3 is a box-plot representation of the relationship betweenlog-scale latency in nanoseconds and final profit for the singleexperimental liquidity trader at each tested location. The meanprofit per tested latency is marked with a tick, the box extentsmark one standard deviation, and the whiskers mark two standarddeviations. Recall that a control liquidity trader (blue line) is alwaysplaced at the minimum permitted latency outside of colocation in aneffort to explain the zero profit gap in the preliminary experiment.We can see that the experimental agent is consistently profitablewhen it is co-located, and performs quite poorly when far fromthe exchange, consistent with the earlier result. As hoped, thecombination of a control agent and systematic latency variationdid add interpretive value beyond the preliminary experiment.Let X be the experimental liquidity trader with latency L X andprofit P X , and C be the control liquidity trader with fixed latencyfixed latency L C and profit P C . We now note two new observations.First, ∀ L X < L C : P X ⊥ L X . That is, once the absolute latency ofthe experimental trader is lower than that of the control trader, itslatency does not affect its profit. Second, as soon as L X > L C thereis an immediate transfer from P X to P C . Discussion.
These results together suggest that latency rank amongthe competing liquidity agents is more significant to profit outcomesthan absolute latency values. This could explain the gap in thepreliminary plot: Depending on whether some other agent waseven closer to the exchange, a given low latency trader might seevery different results. However, we cannot support this claim basedsolely on Experiment 1, because the location of the other liquiditytraders (non-experimental, non-control) on each market day is notconsidered.
In the second experiment, ten liquidity traders were again addedto the background agent population. This time, all agents wererandomly situated with a latency ranging from exchange colocation(333 ns ) to Seattle, Washington (13 ms ), with the intent to examine avid Byrd, Sruthi Palaparthi, Maria Hybinette, and Tucker Hybinette Balch latency rank independent of absolute latency. Without the needto resimulate the same market day for control, this experimentwas conducted across 600 different market days, producing again6,000 observations of OBI liquidity trader latency and profit. Theexperiment was otherwise similar to Experiment 1. Figure 4: Profit of multiple trials with liquidity traders dis-tributed randomly, identified by latency rank order withineach trial. Lower rank traders are closer to the exchange.
Results.
For Experiment 2, the latency rank of each liquidity traderwas logged along with the marked-to-market profit at the endof each trading day. For example, the liquidity trader closest tothe exchange on a given day would be latency rank 1, the secondclosest rank 2, and so on. Absolute latency was also logged forvisualization purposes. In Figure 4, we present a box-and-whiskerplot of aggregated profit by latency rank among the OBI liquidityagents.Over the course of a simulated trading day, without considerationof absolute latency, the liquidity trader closest to the exchangereceives mean and std marked-to-market profit of $2,681.04 and$1,389.37. The second closest liquidity trader receives mean and stdprofit of $-3,297.30 and $1,661.30, and the liquidity trader furthestfrom the exchange received mean and std profit of $-24,473.64 and$-6,449.97. This supports the notion that latency rank is the keyfactor driving the allocation of profit within this trading strategypopulation.However, there is a potential confounding factor. It could bethe case that liquidity trader latency distributions were such thatthe lowest ranked agent was also always close to the exchange inabsolute terms. A different look at the data will help to clarify this.In Figure 5, we plot end of day profit against log-scale nanosec-ond latency, with the addition of a zero profit line. Each pointrepresents one liquidity trader’s result for one simulated marketday, and each point is color-coded according to that trader’s latencyrank for that simulated market day, with red being rank 1, bluebeing rank 2, and so on. Ranks 6-10 are aggregated into a singleblack grouping. Because this plot shows both absolute latency andlatency rank together, we can see that the nearest liquidity trader(red) on a given market day does well even when situated very farfrom the exchange, and liquidity agents in ranks 2 and 3 performpoorly even when relatively near the exchange.
Figure 5: Profit of multiple trials with liquidity traders dis-tributed randomly showing ranked and absolute latency.
Discussion.
Taking Figures 4 and 5 together, we can clearly statethat: The liquidity trader closest to the exchange rarely loses money,and the second closest liquidity trader rarely makes money, regard-less of their absolute distance from the exchange.Our initial concern regarding the preliminary experiment’s zero-profit gap proved correct. While there was a strong inverse correla-tion between absolute latency and profit, this was not the primaryfactor influencing strategy returns. Profitability was rather deter-mined by the ordinal latency rank among agents pursuing a similarlow-latency strategy.
CONCLUSION
Using a realistic agent based market simulation, we explored theeffect of latency on the profitability of a strategy that depends onperishable information. We constructed an environment consistingof thousands of background trading agents into which we could in-ject low latency liquidity traders acting on an order book imbalanceindicator.Through a preliminary experiment, we observed a strong in-verse correlation between the absolute latency and profitability ofliquidity traders. We systematically investigated this through twocontrolled experiments and found that the result of the preliminaryexperiment was not sufficiently explanatory. While the correlationis real, the actual determining factor in profitability was the ordinalrank of latency among the population of liquidity traders.Regardless of absolute distance, we found that the closest liq-uidity trader was substantially more profitable than agents evenslightly further away, and was the only consistently net profitableliquidity trader. These observed winner-take-all outcomes amongtraders pursuing the same time-sensitive strategy would seem tojustify the apparent “arms race” to achieve the minimum possiblelatency to an exchange when engaging in market microstructuretrading.
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