Algorithmic Trading in Foreign Exchange Based on Order Flow

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1 AlgorithmicTradinginForeignExchangeBased onorderflow Mat IndependentResearchProjectsinAppliedMathematics 6 th February2009 HelsinkiUniversityofTechnology DepartmentofEngineeringPhysicsandMathematics TuomasNummelin 62832W

2 1. ExecutiveSummary Thegoalofthisstudywastoconstructasimplifiedsimulationmodelforforeign exchangeandtotesttheperformanceoftradingalgorithms.someofthetested algorithmsusetheinformationfromorderflowandthegoalwastoseewhether significant insight is gained from this it. After rigorous analysis it could be deemed that the utilisation of order flow information does benefit the algorithms. However, the results depend on how the information is used. Differences in performance are evident. The performances of algorithms vary fromamediocreandstableperformancelackingtheexceptionalhighprofits,toa performance altering much from the top profits to the largest loses. It is also noteworthythatthedifferentalgorithmsperformedwell,withbothasimulation data set and with a real daily data set. This information encourages us to seek betterwaystoutilizetheorderflowdata. 2.MotivationandBackgroundforResearch Thefocusofthisstudyisonautomatedtradinginforeignexchange(forex,FX). Focusingonamicrostructure basedorderflowwehopetoenhanceautomated trading in FX markets. In order to adapt the microstructure view to automated trading, we first look at the FX market and the FX spot rate determination models, examining microstructure based models, and determine whether they canbeusedinautomatedtradingornot.thisisthefirstpartofthisstudywhile thequantitativeanalysisofthechosenmodelimplementationisthesecondone. Theforeignexchangemarketisacashinter bankorinter dealermarket,which isthebiggestandmostliquidmarketintheworld.theaveragedailyturnoverin traditional FX markets has grown by 69% since April 2004, to $3.2 trillion in April2007(BIS,TriennalCentralBankSurvey2007).Howevertherecentcrisis infinancialmarketshasaneffectinfxmarketaswell,butitisstilltooearlyto say what are the lasting consequences for market. Although the potential markets and technical improvements in information and communication technologies (ICT) the FX markets have turned in to actual 24/7 real time electronicmarketsusingelectronictradingsystemstobeveryattractivemarket. Theuseofautomatedtradingsystemshasincreased( itisestimatedthataround25%automatedtradingin2008doesalltradeinfx markets. 2

3 3. ForeignExchangeMarket:BriefOverviewAboutModels&Market Traditionally,themodelsforFXspotratehavebeenextensivelybasedonmacro exchange models, which pay little attention to how actual trading in the FX marketiscarriedout,eventhoughmacroeconomicmodelsdotakeintoaccount such factors as GDP, monetary politics, etc. These models have been used to modelmediumtolongterm(afewmonthstoyears)developmentsinfxrates. However, these models have little or no prediction power in the short term (MeeseandRogoff1983,1997).Theimplicitassumptionincorporatedinmacro modelsisthatthedetailsoftrading(i.e.whoquotescurrencypricesandhowthe trade takes place) are unimportant to exchange rate changes over months and quartersorlonger.incontrast,micromodelsexaminehowinformationrelevant tothespotpriceofthecurrencyisreflectedinthespotexchangerateviatrading process. Based on this microstructure, the trading process is not an ancillary marketactivitythatcanbeignoredwhenconsideringexchangeratebehaviour. Instead, the trading process can be seen as a crucial factor in the process that determinesthefxspotrate. TheFXmarketconsistsoftwosegments;theinterbankmarketandthecustomer market.theadvancementsintradingtechnologyhavereshapedthestructureof the FX market; the electronic brokers in interbank markets and the internet trading for customers have been the main driving factors of the restructuring (Rime).Intheinterbankmarket,tradingiseitherdirect(bilateralortakingplace between dealers) or brokered (interdealer trades). Prior to the Internet revolution,customerstradedwiththebank.however,nowadayscustomershave thepossibilitytotradethroughelectronicbrokeringsystemswhichhavebecome thedefactosystemsoftoday.therefore,weshouldconsidercustomersasthe ultimate end users of currency. Customers can be broadly defined as being central banks, governments, importers and exporters of goods, financial institutions,likehedgefunds,andprivateindividuals.themarketiscentralised unlikebeforetheictimprovementswhenthefxmarketwasdecentralisedcall market. The fundamental nature of currency trading (i.e. due different time zones there exists a continuous need to recognize the value of different currencies)ledtothedecentralisedandcontinuousmarket. 4. MicrostructureModels Marketmicrostructureisapartoffinanceconcerningindetailshowthetrading ofassetsoccursinthemarkets.themainfocusofmicrostructuremodelsishow the trading process affects asset prices, quotes, transaction costs, volumes and tradingbehaviour.theearliestmicrostructuremodelsfocusedonmacroaspect ofthemarketsandconsideredlongtermeconomicalscaleissuesinthemarkets. However until the s the microstructure models have not been seen as veryprominentinshort termexchangerateprediction.onerelevantfactisthat the ICT technology has made it possible to record detailed data about transactions in the markets and give researchers the needed empirical data to develop models. However, it is still today one drawback of microstructure modelsthattheyneedtohavesufficientdatatovalidation.thedevelopmentin microstructuremodelshasbeenfastandprofitable. 3

4 AmajordevelopmentinmicrostructuremodelinginFXwasachievedin1999, when Evans and Lyons (Evans and Lyons, 1999) presented their paper about orderflowandexchangeratedynamics.theyintroducedasimplemodel,which captured the high R 2 statistics in daily DM/USD and YEN/USD spot rate dynamics. The overall fit of the model is striking, compared to the traditional macro models, with R 2 statistics of 64% and 45% for the DM and YEN respectively. It is remarkable that the model captures the essentials from the macropointofviewaswellasthemicropointofview.themodelconsidersthat allmacroinformation(i.e.interestrate)isconsideredpublicinformation.private ornon publicinformation(i.e.orderflow)isbasedmainlyonmicroindicators. Theinformationprocessoraggregationoftheprivateinformationisembedded intheorderflowwhichisthesourceofinformationdiffusioninthemodel.even thoughthemodelisbetterthantraditionalmacroeconomicmodels,itstillisfar from perfect. To some extent, models with roughly 50% R 2 statistics can be regardedasgoodmodelsinthefieldoffx. The rationale behind order flow was analysed more closely and developed further by Evans and Lyons in 2004 (Evans and Lyons, 2004). This time they took a different approach to exchange rate predictions; they focused on information sets and the diffusion of these sets in the markets. Their model is basedonrationalexpectations(rationalexpectationsandportfolioshiftmodels canbeseenastwoofthemostusedmodelideasinmicrostructure).thesumof presentvaluesofthemeasuredmacroeconomicfundamentalsandfundamentals whicharenotexplainedwithmacroeconomicfundamentals,i.e.microstructure measures,formarelationforthepredictionofexchangerate.thekeyempirical findings of their paper include transaction flows, forecasts of future macro variables,suchasoutputgrowth,moneygrowth,andinflation.transactionflows generally forecast these macro variables better than spot rates do. Transaction flowsforecastfuturespotrates,andthoughflowsconveynewinformationabout future fundamentals, much of this information is still not captured in the spot ratesonequarterlater.thesefindingsindicatethatorderflowhasasignificant roleinexchangeratepredictionthroughseveraldifferentchannels. A different point of view to market dynamics comes from Bacchetta and Van Wincoop (2004). Their model is based on heterogeneous information of standard dynamic monetary model for exchange rate determination. Their findings support the idea that heterogeneous information and different risk attitude through market makers disconnect changes in exchange rate from macro fundamentals in the short run and the value of the order flow as the distributorofprivateinformation. Danielson and Payne (2002) analyse the forecasting power of order flow in differenttimehorizonsandfoundthattheorderflowhassignificantmeaningin exchange rate forecasting. They examine different currency pairs and crossreferencetheirfindingswithothercurrencypairscloselyrelatedtotheoriginal pairs orderflows. EvansandLyons(2005)takeamoredetailedlookatorderflowsandseparate order flows in different segments and find that order flows based on 4

5 heterogeneouscustomerscarrymoreinformationaboutthefuturevaluesofthe fundamentalswhencustomersfocusedonlong terminvestments. The central banks have also been keen to understand the FX market microstructurefromtheregulatorypointofviewandalsoinextremesituations, where interventions are needed, to understand the possible impacts (Vitale P, 2006).Theresearchareaofthemicrostructureandorderflowbasedmodelsin FXisapromisingresearchfieldinthenearfuture.Itcanbenotedthatthepoint of view has expanded slightly towards the Hidden Markov Processes that are seen as a new, very prominent, but loosely microstructure based method to predictexchangerates. 5. AutomatedTradingwithInformationfromMicrostructureModels In this section we consider, which improvements are possible in automated trading with the help of better understanding of the market microstructure. In chapter5.1,wedefinethesimulationmarketmodel,whichisusedtomodelfx market. 5.1 SimulationModelforFXMarket Thesimulationmodelisaportfolioshiftmodel,wherethesourceofthevariation in exchange rates is based on shifts in portfolio balance of the customers. The modelisbasedontheworkofevansandlyons(1999).thismodelwaschosen asthebasisofthesimulationbecauseofitssimplicityandthefactthatnomodel has performed consistently better in exchange rate prediction in all time horizons.sincethemainpointofthisstudyistodevelopatradingalgorithm,the use of this simplified model for markets seems reasonable. A simulation model based on rational expectations could have been an alternative approach. However, the alternative approach was discarded because it would have led to theuseofimpracticalestimations. The portfolio shifts are not common knowledge at the time of occurrence. Commonknowledgeisknowntoeveryoneinthemarkets(e.g.currentexchange rateandeveryoneknowsthateveryoneknowsthateveryoneknowsadinfinum). The shifts are large enough that the clearing of the market requires rate adjustments of the spot rate. The fact that a portfolio shift is not common knowledgeatthetimeofoccurrenceservesasaninitiatingsourceoforderflow. Whenacustomerplacesprivate(notpublicallyobserved)quotestodealerswho trade among themselves in the interdealer markets to share the resulting inventory risk. The market learns about the initial portfolio shifts through interdealer trading. Though it can be considered common practice that dealers donotholdovernightrisks.theinventoryrisksaresharedwiththepublic.the inventoryriskisnotdefinedindetail.itisusedasconceptinpotentiallossdue the inventory, which adjust the actions of traders. The public s demand for foreign currency assets has to be less than perfectly elastic because if the currency assets are imperfect substitutes, price adjustments are required to clear the market. Innovations in the model are considered in two parts; public information(standardmacrofundamentals)andnon public,privateinformation 5

6 inportfolioshifts.however,themodeldoesnottakeintoaccounttheunderlying sourceoftheseportfolioshifts. LetusconsiderapureexchangeeconomywithTtradingperiods.Theeconomy hastwoassets;risklessandriskywithstochasticpayoffrepresentingthefx.the payoft+1periodsinthefx,denotedf,iscomposedofaseriesofincrementsrt, observed before trading in each period. This flow of realised increments represents publicly available macro economic information (e.g. interest rate changes). T+1 F r t, r t ~ N (0,Σ t ) i.i.d (1) t=1 ThesimulatedFXmarketismodelledasadecentraliseddealershipmarketwith Ndealersindexedbyi,andcontinuumofnon dealercustomersindexedbyzin interval[0,1].withineachtradingperiodthreeroundsoftradingaredone.inthe first round, dealers trade with customers(the public), i.e. receive the customer order flow, which carries the information about the portfolio shifts of those customers.inthesecondround,dealerstradeamongthemselvesininterdealer market to share the resulting inventory risk. In the third round, dealers trade again,butthistimewiththepublictoshareriskmorebroadly. Figure1.Timingoftheperiod Nextweconsiderthedifferentroundsoftrading. 6

7 Round1 At the beginning of each period t in round 1, all market participants observe rt period stincrementforpayoff.basedonrtandallotheravailableinformation (both public and private information) each dealer chooses simultaneously an independent price with which he/she agrees to sell and buy any amount of currencytohis/hercustomers.wedenotedealer priceforround1fordealerias Pi1.Dealer priceisamappingfromrtandallotherinformationtorealnumbers. Themappingisdefinedbydealerpreferences.ThevalueofPi1canbethesame among multiple trades but it does not have to be. Every dealer receives net customerordersinthevalueofci1thatisexecutedbyeachdealer squoteprice Pi1. ci1 <0 denotes net customer sales (dealer purchases). Each net customer order ci1 is independent across dealers. Customer net orders are distributed independentlyfromri1.customerorderrealisationsaredistributedci1~n(0,σc1). These initial customer orders can be seen as preferred bilateral customer transactions.thesecustomerordersrepresenttheportfolioshiftsonthepartof the non dealer public information and the realisation of these orders is not publicallyobserved. Round2 Round 2 is the interdealer trading round. In the beginning of the round, each dealer independently and simultaneously chooses his/her price with which he/sheiswillingtobuyandsellanyamountamongthedealers.theinterdealer pricepi2fortraderiisamappingofpi1andci1torealnumbers.theseinterdealer quotes are observable and available to all dealers in the market. Then each dealer independently trades on the other dealers quotes. The orders on the same quoting price are equally distributed among the dealers who are quoting thatprice.letti2denotethe(net)interdealertradeinitiatedbydealeriinround 2.Attheendofround2,alldealersobservethenetinterdealerorderflowfrom thatperiod N Δx = T i 2 (2) i=1 Equation (2) is the interdealer order flow and it is observed without noise, though adding noise to the equation does not affect the estimates. FX market interdealerorderflowisrecorded,becausedealer dealertradesareobservable. However,customer dealertradesarenotpublicallyobserved.thesignalsofthe customerorderflowareembeddedintheinterdealerorderflowandthesignals fromtheformercanbeobservedtosomeextent. Round3 In round 3 dealers share the inventory risk with the non dealer public. The simulation model is derived from the Evans and Lyons (1999) model, which 7

8 focusesondailyexchangerateprediction.however,muchshortertimeperiods (minutes) are considered in our simulation. In their paper Evans and Lyons (1999)consideredround3asanovernightrisksharinground.Althoughinthe minuteconceptround3isstillarisksharinground,itisalsomorespeculative. Initially, each dealer simultaneously and independently quotes a price Pi3 at which he/she agrees to buy and sell any amount. These quotes are observable and available to the public. The number of customers is large compared to the number of dealers, implying that the public s capability to bear risk is greater than that of dealers. Therefore dealers set the prices according to the public s willingness to bear the inventory imbalance risk. In the concept of daily trade, therearenoovernightnetpositionsfordealerswhereasintheminuteconcept the imbalance risk can be seen as the unbearable exposure to exchange rate variation. Typically this means that each dealer has limited currency positions, whicharesettokeeprisksacceptable.theseround3pricesareconditionedby the round 2 interdealer order flow. The interdealer order flow informs the dealersofthesizeofthetotalinventorythatthepublicneedstoabsorbinorder to achieve stock equilibrium. Knowing the size of the total inventory that the public needs to absorb is not sufficient for determining the price for round 3. Dealers need to know the risk bearing capability of the public (normal assumptionisthatitislessthaninfinite).givennegativeexponentialutility,the public s total demand for risky assets in round 3, denoted by c3, is a linear functionofitsexpectedreturnthatisconditionalonpublicinformation: c 3 = γ( E[ P 3,t+1 Ω 3 ] P 3,t ) (3) Wherethepositivecoefficientγcapturestheaggregaterisk bearingcapacityof the public, and Ω3 is the public information available at the time of trading in round3. Equilibrium Thedealer sproblemisdefinedoverfourchoicevariables,thethreepricequotes Pi1, Pi2, and Pi3, and the dealer s interdealer trade Ti2 (the latter being a component of x, the interdealer order flow). The more detailed reasoning of Bayes Nash Equilibrium in Evans and Lyons (1999) leads to optimal trading strategyhavingthepricedifferenceinperiodtandt 1as Δp t = r t + λδx t (4) Where λ is a positive constant. The fact that this price change includes the innovationinpayoffsrtone for oneisunsurprising.theλ xtermistheportfolio shift term. The no arbitrage conditions ensures that, within a given round, all dealersquoteacommonprice.giventhatalldealersquoteacommonprice,this priceisnecessarilyconditionedoncommoninformationonly.eventhoughrtis common information in the beginning of round 1, the order flow xt is not observed until the end of round 2. The price for round 3 trading, P3, therefore reflects the information in both r and x. Interdealer order flow carries the signalsfrominitialportfolioshifts,ifitisassumedthatthedealers tradeisbased on initial customer order flow and in that sense interdealer order flow communicatestheinitialportfolioshiftsinthemarket.however,theaggregated 8

9 information about portfolio shifts is absorbed into the market and the price is adjusted based on known information about the relation between interdealer orderflowandsubsequentpriceadjustments.thisprocessofinformationflow takesafiniteamountoftime. For simulation purposes we define empirical implementation of the price differenceequation: * Δp t = β 1 Δ( i t i i ) + β 2 Δx t +η t (5) where ptisthechangeinthelogspotexchangeratefromtheendofperiodt 1 totheendofperiodt, (it it*)isthechangeintheovernightinterestdifferential fromperiodt 1toperiodt(*denotesforeigncurrency),and xistheorderflow fromtheendofperiodt 1totheendofperiodt(negativesigndenotesnetsales ofthehomecurrency). Theovernightinterestrateisthemacrofundamentalofthemodel.Itisassumed to bring all macro information into the model. In the simulation market the empiricalpricingrelationisusedtoadjustexchangerate,accordingly Δp t = ln S t ln S t 1 (6) S t = S t 1 e Δp t wherestisthespotexchangerate. In the simulation market, order flow has three components, two of which are basedontradingalgorithms,andonewhichisacombinedorderflowfromother dealersinthemarket.therelativesizesoftheorderflowscangreatlyinfluence thedynamicsofthemarketandthiscanbeseenasoneinterestingfactorinthe simulation model. The simulation market model is based on an equilibrium model,whereitisassumedthatunlessshiftsoccurintheportfoliosbalanceon the market, it tends to stay in equilibrium state. The non algorithmic dealers order flows in period i are assumed to be normally distributed, because it is assumed that each dealer s customer order flow is independently normally distributed. This assumption is based on the model assumption of round 2 tradingstrategies.inround2,thedealerstradesomefractionofcustomerorder flow as their interdealer market flow, which leads to a sum distribution, which can be modeled as a normal distribution (N(0,σ 2 )). The normal distribution parameters can be seen as average values of the periodic values of the whole market. Hence he simulation market model is based on market orders, if we generalise the concept of limit orders. We can see that the limit orders can be seenasapartoftheorderflowinaperiod,justlikethemarketordersinthat period. However, the limit orders could give a more detailed view of the buying/selling pressure of the market. In certain cases, when the triggering condition for a limit order is met, the limit order can be executed in the same wayasamarketorder.limitorderscanbeconsideredtobufferthechangesin exchangerate. 9

10 Figure2Overviewofsimultationmodel Figure 2 shows the components of simulation model and some basic relationships between components. In addition customers are added to algorithms.however,thosecustomersarenotexplicitlymodeledinsimulation. Algorithms are assumed to take customers in account as algorithms try to maximizetheirownprofit. 5.2 TradingAlgorithmBasedonMicrostructureKnowledge. InordertoanalysemicrostructurebasedalgorithmsinFXmarket,wetestthree different kinds of models. Recursive reinforced learning (RRL) based model is not truly dependent on understanding the microstructure of the market. However, to some extent it can be regarded as the algorithm that is based on microstructure ideology. A more detailed description of RRL can be found in ExploringAlgorithmsforAutomatedFXTrading ConstructingaHybridModel Mat Seminar on Case Studies in Operations Research, Spring The fundamentalideaoftherrlisalsousedinthesecondmicrostructurealgorithm, whichisforthemostpartofsimilarconstructiontotherrl.inprinciple,ittries to model the order flow using the RRL to achieve reasonable predictions of exchange rate movements. The third model is a combination of the basic RRL andsomedirectlyorderflowbasedindicator(and/orflowitself). The order flow RRL algorithm is fundamentally similar to the normal RRL algorithm,whichusesreturnsindecisionfunction.intheorderflowmodel,the algorithm uses differences in the order flow to predict the order flow in the future.therationalebehindtheattempttopredictorderflowandthatwayform adecisionoftheshort/longpositionistheideaofthestrongdependenceofthe 10

11 spotexchangerateandorderflow.however,therelationbetweenspotrateand orderflowisnotasevidentastherelationbetweenreturnsandspotrate.inthe orderflowalgorithmthedecisionestimateismainlybasedonadaptive,moving averageofthedifferencesinorderflow. F t = tanh(uf t 1 + v 0 o t + v 1 o t 1 +K+ v m o t m + w) (7) where ot s are differences in order flow at t, i.e. how much cumulative buying/selling pressure is changed in time t, Ft is the decision and u, vi, w are systemparameters. Togeneralisedecisionsandtoensuredifferentiabilityofthedecision,hyperbolic tangent is used. Even though the function is continuous, decisions are discrete and achieve three different positions; long, neutral and short ([1,0, 1]). Continuousdecisionscouldbeusedtomeasurethestrengthoftheimpact,which is based on the variation of the exchange rate. The differentiability of the decisionfunctionisimportantwhenconsideringgradient basedoptimizationof system parameters. The wealth of the trader is defined as the sum of periodic increments. W T = T R t=1 t ( ) (8) R t = µ F t 1 r t δ F t F t 1 wherewtisthewealthofthetrader,rtistheperiodicincrementinwealth,µ>0 isthetradingpositionsize,δisthetransactioncost,andrtisthereturninperiod t. Tomeasuretheperformanceofthealgorithm,autilityfunctionofthetraderis definedasafunctionofwealthandprofit(wt,rt).strictlyspeakingthemeasure of the performance is not a utility function in the conventional sense. The differentialratio,likethesharperatio,isusedasaperformancemeasureforthe algorithm.anotherpossiblemeasureisthesterlingratio.thedifferentialratiois usedtocapturethemarginalutilityofthertineachperiod.inthealgorithmthe downsized deviation, which is based on the Sterling ratio, is used as the risk adjustedperformancemeasureforthesystemparameterupdate. Sterling ratio = Downsizeddeviationratiois DDR t = Average(R t ) DD T, DD T = 1 T T t=1 Annual Average Re turn Maximum Drawn Down (9) { } 2 min R t,0 1/2 (10) InordertousetheDDRintherecurrentlearning,ithastobedifferentiated.The learning is defined as the gradient of the utility with respect to the system parameters. 11

12 du T dθ = T t=1 du T dr t dr t df t df t dθ + dr t df t 1 df t 1 dθ (11) Usinggradientlearningwithlearningrateρ,theadjustmentoftheparametersis Δθ = ρ du (θ ) T (12) dθ Note that due to the inherit recurrence of the total derivatives, the entire sequence depends on the previous time periods. To correctly compute the learning in a time sequence, we have to compute in a recursive manner. The learningequationhasaform Δθ t = ρ dd t dr t dr t df t df t dθ t + dr t 12 df t 1 df t 1 (13) dθ t 1 wheredtisadifferentialofddr. The other algorithm, which uses direct information from the order flow, is a hybrid algorithm that uses a combination of the decision suggested by normal RRL algorithm and order flow based moving averages. In the simulations we decidedtousethemovingaverageofthefivelastobservations.thedecisionis basedonheuristictestsoftheperformanceofthealgorithm.however,itcanbe reasoned that if the intraday trading happens with high frequency, then the 5 minute time marginal can be seen as a practical time period. The algorithm combinestheinformationfromvarioussubalgorithmpartsandmakesdecisions basedonthatinformation.themostobviousadvantageofthisalgorithmisthat by combining information from multiple sources, it reduces the risk of biased onesourcedecision.inthishybridalgorithm,theorderflowpartdeterminesthe possible future direction of the spot exchange rate, if we accept the positive correlationassumptionbetweentheorderflowandspotnominalexchangerate. TheRRLpartgivesestimatesnotonlyoftheamountofchangeinspotexchange rate,butalsosomeestimateofthedirection. ThecombinedmodeloftheRRLandorderflowismorepromisingthantheuse of direct RRL based on the order flow algorithm. The decision function in RRL made it possible for us to utilise order flow more accurately, though different functionalformswerethoughtandtested. 6. QuantitativeAnalysisofthePerformance The quantitative analysis is performed with simulated data and to some extent withrealdailydata(evansandlyons(1999)).eventhoughusingthedailydata somewhat changes the nature of the trading, which is done by algorithms, the algorithmsareunrelatedtothetimediscretionofthemarkettime. Tomeasuretheperformanceofthealgorithms,threemeasuresareused;profit, Sharpe ratio, and daily ranking, which is made by ranking analysed algorithms bythedailyprofit(profitmadeindailytradingtakingplacebetween i.e.in480minutes).sharperatioisdefinedas

13 S T = mean R t (14) var R t wherertisthereturnintimet. Thesimulationsaredonewithasetofsimulationparameters,wherethespread for the day is The spread is large, but can be seen in highly volatile markets (i.e. RUB). Half of the used spread is used as the transaction cost for trading. High spreads, like the one used, should encourage algorithms to do fewer trades during the day. Large spreads are also used to encourage gaining differencesinsimulationresults.thetestedalgorithmshaveeachapproximately 5% share of the total order flow of the market. The algorithms can be seen to represent major players in the market (10 th largest overall currency trader by volume in May 2008 did have about a 3% share of the overall volume (EuromoneyFXsurvey)).Theparametersthatdefinetherelationbetweenorder flowandspotexchangeratearetheorderofmagnitudeofthenetorderflowof 10 million, which will cause a 1% change in spot rate according to the buying pressureofthedemand.themagnitudeoftherelationisoverestimatedtofind possible changes in exchange rate. Based on this, the volatility of the market is high. In the simulation, the spot exchange rate is updated every minute. However,themacropartoftheexchangeratepredictionisupdatedonlyevery 200 minutes (about once in every 3 hours). It can be seen that the changes in macrofundamentalshavealowerfrequency. The model parameters in RRL based algorithms can greatly affect the performanceofthealgorithm.weshouldkeepthisinmindwhenconsideringthe performanceofrrl basedalgorithms.themodelparameters,likethelearning rate and numbers of differences that is used in the moving average part of the decision function, will greatly affect the performance of the algorithm. In the simulation,therrlmodelparametersareheuristicallychosenandhaveahigh likelihood of not being the optimal ones. The choice of the optimal model parameters for RRL based algorithms can be seen as one of the drawbacks of usingthesealgorithms 7. Results The simulation results are based on simulation runs of the simulation trading day (480 min = 8 hour trading day) to obtain statistically significant results. It took a total of two days to compute these simulation runs. First we lookattheresultswithoutanyfilteringorremovalofbiasedobservations.then ten best and ten worst daily results are removed from each algorithm s result. Toanalysetheperformanceofthealgorithm,theKruskal Wallisnon parametric one way analysis of variance test (Gibbons, J. D) is performed. The common descriptivestatisticsoftheprofitsare: 13

14 Table1.Profitsofthedifferentalgorithms.(Profitsaremeasuredaspercentsand1meansthat the equity of the dealer has not changed during the day. Exceptionally high magnitude of 10 3 profits or loses are explained by the simulation spot exchange rate, which gives a slight possibilitytogainunrealisticallyhugevariationsinexchangerate.) InTable1weseethedescriptivestatisticsofalgorithms.,theRRL+orderflow indicatorandrrlperformedwell.however,theorderflowbasedrrlhadthe highest overall result when there was no removal of the 10 best daily results. Thehighestresultwasintheorderofmagnitudeof1e+6.However,thiskindof resultwascausedbyexceptionalvariationoftheexchangerate.thefluctuation ofexchangerateisaninheriteffectofthechosenmodelparameters,whichwere chosentoencourageexchangeratevariation.itis,however,noteworthythatthe RRL+orderflowindicatorhasalsothebiggeststandarddeviation.Thiscanbe seen as an undesirable characteristic for a good algorithm. On the other hand, RRLseemstoperformaveragelywitharathersmallstandarddeviation. Figure3Box WhiskerPlotoftheprofits.(1istheorderflowRRL,2isRRL,3isRRL+orderflow indicator) 14

15 BasedontheKurskal Wallistest,wecanrejectthenullhypothesisofthesame median of all three algorithm s profits with confidence of 95%. By continuing testing, we can see that even the medians of the RRL and RRL + order flow indicator differ from each other. We can conclude that the RRL + order flow indicatorseemstooutperformtheothers. Table2.Sharperatiodescriptivestatistics Figure4Sharperatios(Ratiosofeachindividualsimulationdaysortedindescendingorder) Table 2 and in Figure 4 show that the order flow RRL performs both exceptionally well and very poorly with respect to the Sharpe ratio. This is especially evident in Figure 4 where the line of the order flow RRL is very S shapedwhencomparedtotheotheralgorithms.weseethattherrlstaysrather flat with respect to the Sharpe ratio and therefore its performance is steady, if not the most profitable. RRL + order flow indicator seems to perform well in general,butdoeshavesomebaddays.tosummarize,wecanconcludethatrrl+ order flow indicator is in a class of its own in general. The RRL performs most steadily. The order flow RRL does have some remarkable days, but the overall performanceisnotgood. 15

16 Figure5Dailyrankingofthealgorithms(Fromleft:numberonerankings,numbertworankings, numberthreerankings) Figure 5 shows that RRL + order flow indicator captures most of the top rankings. RRL has a consistent performance and ranks number two in most of thedays.orderflowrrlseemstobetheoptionwiththeweakestperformance. 16

17 Figure 6 Results from real daily data (top panel: blue = exchange rate, green dashed = order flow.restofthepanels:pink=orderflowrrl,greendashed=rrl,bluedash dot=rrl+order flowindicator) WecanseeanoteworthytrendinFigure6.TheorderflowRRLoutperformsthe restofthealgorithms.thisismainlyduetothemorecautiousnatureoftherrl +orderflowindicator,whichcanbeseeninthedecisionspanel(figure6.thierd panelfromthetop),wheretherearemanyzerodecisionsmadebyrrl+order flow. Looking at the Sharpe ratio panel, we can see that order flow RRL algorithmatalltimesperformswellandthatotheralgorithmsperformhorribly. In order to gain more realistic and statistically correct results, more genuine minute data would have been needed. The parameterisation of the RRL based algorithmscanalsobeseenasarelevantfactor,sincethemodelparametersfor RRL were chosen to represent a volatile simulation market. The effects of the parameters are most clearly seen in the RRL + order flow indicator algorithm; thealgorithmistoocarefulandthereforemakestoomanyzerodecisions(figure 6, third panel). However, since limited genuine data was available for the RRL modelparameters,wewereunabletochoosetheminanymorespecifiedway. 8. LimitationsoftheSimulation The simulation is somewhat simplified. We were forced to determine some simulation parameters, namely parameters for distributions of the order flow, size of the market, and segmentation of the different algorithms. From the algorithm point of view, one limiting factor was the choice of the model parameters. The lack of a limit order book can be seen as a hindrance in the simulationmodel.therealisticimplementationofalimitorderbookisdifficult, because in order to define it realistically, we would need to know the traders strategiesofusingtousethelimitorderbook.thereareseveralwaystousethe 17

18 limit order book; it can be used as a risk control method as well as in an opportunisticway.thesimulationwasbasedononlyalimitednumberofagents andtherestofagentpopulationwasmodeledonlywithdistributions. 9. Conclusions TheuseoftheorderflowinformationandbetterunderstandingoftheFXmarket help develop better trading algorithms. However, the efficient utilisation of the gained information seems to be hard. The hybrid algorithms are the most promising approach to construct a well performing algorithmic trader. The better understanding of the market microstructure helps us to develop more accurate indicators and hence, to improve algorithmic trading. Based on the simulations presented in this paper, the order flow information helps us to developbetteralgorithmictraders.however,constructinganefficientalgorithm remainsachallenge.algorithmsimplementedliketherrlareblackboxmodels. These algorithms are very sensitive to model parameter changes. The prospect of RRL based algorithms being able to learn to pick certain features in the FX marketandtomakedefeasibledecisionsbasedonthosefeaturesispromising.in order to gain better and more accurate results, genuine minute based data is needed. It might be available in some time in the future mainly because of the advances in algorithms and the transition to use electrical broker systems(e.g. EBS). The next logical research challenge is to develop an even better and detailed understandingofthemarketmicrostructure.afterthatwemightseetheuseof new kinds of algorithms, e.g. Hidden Markov process based algorithms, which areusedwithsuccessinspeechrecognition.inthefutureitisinterestingtosee whethertheuseofalgorithmictradingwillalterthedynamicsofthemarketand exchangerateprocess,ornot. 18

19 10. References MarkP.Austin,GrahamBates,MichaelA.H.Dempster,VascoLeemans and Stacy N William, 2004, Adaptive systems for foreign exchange trading, QuantitativeFinanceVolume4(August2004)C37 C45 PhilippeBacchettaandEricvanWincoop,2006, CanInformationHeterogeneity Explain the Exchange Rate Determination Puzzle?, The American Economic Review, AmericanEconomicAssociation,vol.96(3),pages ,June. JonDanielsson,RichardPayne,JinhuiLuo,2002,ExchangeRateDetermination andinter MarketOrderFlowEffects ( pdf)( ) Martin D. D. Evans and Richard K. Lyons, 1999, Order flow and exchange rate dynamics( Martin D. D. Evans and Richard K. Lyons, 2001, Order flow and exchange rate dynamics, ( ( ) MartinD.D.EvansandRichardK.Lyons,2004,ExchangeRateFundamentalsand OrderFlow ( pdf)( ) MartinD.D.EvansandRichardK.Lyons,2007,ExchangeRateFundamentalsand OrderFlow,( MartinD.D.EvansandRichardK.Lyons,2005,ANewMicroModelofExchange RateDynamics,( Martin D. D. Evans and Richard K. Lyons, 2005, Understanding Order Flow ( html)( ) Martin D. D. Evans, Richard K. Lyons,2005, MEESE ROGOFF REDUX: ( ( ) Martin D. D. Evans, Richard K. Lyons, 2005, Understanding Order Flow ( html)( ) MartinD.D.Evans,2008,OrderFlowsandTheExchangeRateDisconnectPuzzle ( J.D.Gibbons,1985,NonparametricStatisticalInference,2ndedition,M.Dekker. 19

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