Improving Technical Trading Systems By Using A New MATLAB based Genetic Algorithm Procedure

Transcription

1 4h WSEAS In. Conf. on NON-LINEAR ANALYSIS, NON-LINEAR SYSTEMS and CHAOS, Sofia, Bulgaria, Ocober 27-29, 2005 (pp29-34) Improving Technical Trading Sysems By Using A New MATLAB based Geneic Algorihm Procedure + STEPHANOS PAPADAMOU and ++ GEORGE STEPHANIDES + Deparmen of Economics Universiy of Thessaly ++ Deparmen of Applied Informaics Universiy of Macedonia 7.5 Km Thessalonikis Asvesohoriou, Dios 3, Posal Code 5700 GREECE Absrac: - Recen sudies in financial markes sugges ha echnical analysis can be a very useful ool in predicing he rend. Trading sysems are widely used for marke assessmen however parameer opimizaion of hese sysems has adoped lile concern. In his paper, o explore he poenial power of digial rading, we presen a new MATLAB ool based on geneic algorihms, which specializes in parameer opimizaion of echnical rules. I uses he power of geneic algorihms o generae fas and efficien soluions in real rading erms. Our ool was esed exensively on hisorical daa of a UBS fund invesing in Emerging sock markes hrough a specific echnical sysem. Resuls show ha our proposed GATradeTool ouperforms commonly used, non-adapive, sofware ools wih respec o he sabiliy of reurn and ime saving over he whole sample period. Key-Words: - financial markes; predicion; geneic algorihms; non-linear echnical rules Inroducion The developmen of new sofware echnology and he appearance of new sofware environmens (e.g. MATLAB) provide he basis for solving difficul financial problems in real ime. MATLAB s vas buil-in mahemaical and financial funcionaliy, he fac ha i is boh an inerpreed and compiled programming language and is plaform independence make i well suied for financial applicaion developmen. There have been many sudies in he lieraure concerning he profiabiliy of echnical analysis ([] [2] [3] [4] [5] [6] [7] [8]). However he majoriy of hese sudies have ignored he issue of parameer opimizaion, leaving hem open o criicism of daa snooping and he possibiliy of survivorship bias ([9], [0]). Tradiionally researchers used ad hoc specificaion of rading rules. They use a defaul popular configuraion or randomly ry ou few differen parameers and selec he bes wih crieria based on reurn mainly. A firs rial [] in implemening a new MATLAB based oolbox for compuer aided echnical rading presened weak poins in he opimizaion procedure. When he daa ses are large and you would like o re-opimize your sysem ofen and you need a soluion as soon as possible, hen ry ou all he possible soluions and ge he bes one would be a very edious ask. In our days, analyss are ineresed o ge a few good soluions as fas as possible raher han he globally bes soluion. The globally bes soluion does exis, bu i is highly unlikely ha i will coninue o be he bes one. Geneic algorihms (GAs) are beer suied since hey perform random searches in a srucured manner and converge very fas o populaions of near opimal soluions. The GA will give you a se (populaion) of good soluions. The aim of his sudy is o show how geneic algorihms, a class of algorihms in evoluionary compuaion, can be employed o improve he performance and he efficiency of compuerized rading sysems. I is no he purpose here o provide heoreical or empirical jusificaion for he echnical analysis. We demonsrae our approach in a paricular forecasing ask based on he Emerging Sock Markes. 2 Problem Formulaion The las years, here is a growing ineres in GA use in financial economics bu so far here has been lile research concerning auomaed rading. To our knowledge he firs published paper linking geneic algorihms o invesmens was from Bauer e al [2]. Bauer [3] in his book Geneic Algorihms and Invesmen sraegies offered pracical guidance concerning how GAs migh be used o develop aracive rading sraegies based on fundamenal

2 4h WSEAS In. Conf. on NON-LINEAR ANALYSIS, NON-LINEAR SYSTEMS and CHAOS, Sofia, Bulgaria, Ocober 27-29, 2005 (pp29-34) informaion. These echniques can be easily exended o include oher ypes of informaion such as echnical and macroeconomic daa as well as pas prices. According o [4], geneic algorihm is an appropriae mehod o discover echnical rading rules. Fernandez-Rodriguez e al [5] by adoping geneic algorihms opimizaion in a simple rading rule provide evidence for successful use of GAs from he Madrid Sock Exchange. Some oher ineresed sudies are [6] presened a new geneicalgorihm-based sysem and applied i o he ask of predicing he fuure performances of individual socks; [7] and [8] applied geneic programming o foreign exchange forecasing and repored some success. One of he complicaions in GA opimizaion is ha he user mus define a se of parameers such as he crossover rae, he populaion size and he muaion rae. According o De Jong s [9] who sudied geneic algorihms in funcion opimizaion good GA performance requires high crossover probabiliy (inversely proporional o populaion size), and a moderae populaion size. Goldberg [20] sugges ha a se of parameers ha works well across many problems is crossover parameer = 0.6, populaion size = 30 and muaion parameer = Bauer [2] performed a series of simulaions on financial opimizaion problems and confirmed he validiy of Goldberg s suggesions. In he presen sudy we will perform a limied simulaion sudy by esing various parameer configuraions for he rading sysem esed. We will also provide evidence for he GA proposed by comparing our ool wih oher sofware ools. 2. Mehodology Our mehodology is conduced in several seps. Firsly, we have o implemen our rading sysem based on echnical analysis. In developing a rading sysem, you need o deermine when o ener and when o exi he marke. If he rader is in he marke he binary variable F is equal o one oherwise is zero. As posiion raders we base he majoriy of our enry and exi decisions on daily chars by consrucing a rend following indicaor (Dimbea). This indicaor calculaes he deviaion of curren prices from is moving average of θ lengh. The indicaors used in our rading sysem can be formalized as below: Close MovAv ( Close, θ ) () Dimbea = MovAv ( Close, θ ) where Close is he closing price of he fund a ime and funcion MovAv calculaes he simple moving average of he variable Close wih ime lengh θ. θ MovAv (, ) Close θ = Close, = θ i, θ +,..., Ν (2) θ i= 0 Our rading sysem consiss of wo indicaors, he Dimbea indicaor and he Moving Average of Dimbea given by he following equaion. θ 2 = θ 2 θ +,..., Ν (3) MovAv ( Dimbea, θ 2 ) = θ 2 i= 0 Dimbea If MovAv(Dimbea,θ2) cross upward he Dimbea hen ener long ino he marke (i.e. buy signal). If MovAv(Dimbea,θ2) cross-downward hen close he long posiion in he marke (i.e. sell signal). Secondly, we have o opimize our rading sraegy. I is well known ha maximizing objecive funcions such as profi or wealh can opimize rading sysems. The mos naural objecive funcion for a risk-insensiive rader is profi. In our sofware ool we consider muliplicaive profis. Muliplicaive profis are appropriae when a fixed fracion of accumulaed wealh ν>0 is invesed in each long rade. In our sofware no shor sales are allowed and he leverage facor is se fixed a ν=, he wealh a ime T is given by he following formula: T ( T ) o = = Close / Close i W = W ( + F r ) { δ F F } (4), where r ( ) is he reurn realized for he period ending a ime, δ are he ransacion coss and F is he binary dummy variable indicaing a long posiion or no (i.e. or 0). The profi is given by subracing from he final wealh he iniial wealh, PT = W ( T ) W0. Opimizing a sysem involves performing muliple ess while varying one or more parameers (θ, θ2) wihin he rading rules. The number of ess can quickly grow enormous (Measock has a maximum of 32,000 ess). In he FinTradeTool [], here is no limi however he ime processing depends on he compuer sysem used. In his paper we invesigae he possibiliy of solving he opimizaion problem by using geneic algorihms. Geneic Algorihms (GAs) ha were developed by Hollands [2] consiue a class of search, adapaion and opimizaion echniques based on he principles of naural evoluion. Geneic Algorihms lend hemselves well o opimizaion problems since hey are known o exhibi robusness and can offer significan advanages in soluion mehodology and opimizaion performance. GAs differ from oher opimizaion and search procedures in some ways. Firsly, hey work wih a coding of he parameer se, no he parameers hemselves. Therefore GAs, 2

3 4h WSEAS In. Conf. on NON-LINEAR ANALYSIS, NON-LINEAR SYSTEMS and CHAOS, Sofia, Bulgaria, Ocober 27-29, 2005 (pp29-34) can easily handle he binary variables. Secondly, GAs search from a populaion of poins, no a single poin. Therefore GAs can provide a se of globally opimal soluions. Finally, GAs use only objecive funcion informaion, no derivaives or oher auxiliary knowledge. Therefore GAs can deal wih he non-coninuous and non-differeniable funcions ha are acually exised in a pracical opimizaion problem. 2.. Proposed GATradeTool In GATradeTool, Geneic Algorihm operaes on a populaion of candidae soluions encoded. Each decision variable in he parameer se is encoded as a binary sring and hese are concaenaed o form a chromosome. I begins wih a randomly consruced populaion of iniial guesses. These soluion candidaes are evaluaed in erms of our objecive funcion (equaion 4). In order o obain opimaliy each chromosome exchanges informaion by using operaors (i.e. crossover and muaion 2 ) borrowed from naural geneic o produce he beer soluion. The objecive funcion (equaion 4) is used o provide a measure how individuals have performed in he problem domain. In our case, he mos fied individuals will have he highes numerical value of he associaed objecive funcion. The finess funcion ransforms he raw objecive funcion values ino non-negaive figures of meri for each individual. The ool suppors he offseing and scaling mehod [20] and he linear-ranking algorihm [22]. Following genior selecion mehod [23] we ranked all individuals of a populaion according o performance based on reurn. Beer performers replaced he poor performers. These candidaes were allowed o paricipae in he crossover and possible muaion. The procedure ha recombines promising candidaes in order o creae he nex generaion is known as crossover. Finally random muaions [3] are inroduced in order o avoid local opima. These seps were repeaed unil a well-defined crierion is saisfied. 3 Problem Soluion In his secion, we apply our mehodology in a UBS Muual Fund invesing in emerging sock markes. The daa analyzed consiss of 2800 observaions on daily closing prices of ha fund for he period /5/98 25/6/04. The opimizaion period is defined beween /5/98 o 25/6/03. The opimized sysem was evaluaed hrough he exended period 25/6/03 o 25/6/04. The opimizaion problem is se as o deermine he opimal lenghs of Dimbea indicaor and is moving average for he simple Dimbea model ha will maximize profis. Firsly, he effec of differen GA parameer configuraions will be sudied. More specifically we are ineresed o measure he effec of he populaion size and he crossover parameer in he performance of he geneic algorihm based opimizaion procedure. According o previous research recommendaions [20], [2], [24], he populaion size should be equal o 30 and he crossover rae should be 0,6 (defaul values). The number of ieraions was se o 300 for all simulaions. Secondly, we compared he soluions of opimizaion problem conduced by differen sofware ools in order o measure he validiy of he GATradeTool proposed. Table provides he GA opimizaion resuls for differen size of populaions. The firs row of he able shows he bes parameers for he Dimbea indicaor and he moving average of Dimbea. In order o measure he effec of he populaion size in he bes soluion we examine a series of differen saisics. The soluion wih he maximum and minimum reurn, he average reurn, he sandard deviaion of hese soluions, he ime needed for convergence of he algorihm, and an efficiency index calculaed by dividing max reurn soluion by he sandard deviaion of soluions. By looking in able we can say ha as long as you increase he populaion size he bes and he average soluions are higher. However, afer a populaion size of 30 he performance decreased. In order o ake ino consideraion he compuaional coss involved since increase in populaion size, we calculae he ime needed for solving he problem. Low populaion size leads o low performance and low compleion ime. According o he efficiency index he bes soluion is ha given by he populaion size 20. Table Populaion Size Effec Table 2 gives he resuls of he geneic opimizaion procedure by alering he crossover rae beween and 0.2 for he populaion size seleced from previous able (i.e. 20). The srucure of his able is he same like he previous one. For example, when

4 4h WSEAS In. Conf. on NON-LINEAR ANALYSIS, NON-LINEAR SYSTEMS and CHAOS, Sofia, Bulgaria, Ocober 27-29, 2005 (pp29-34) crossover rae is one, he GA found ha he Dimbea(203,79) had he bes performance of 26,39% profi. The second row given he ime needed o reach he opimal soluion. The nex rows give saisics on he evoluion process. All configuraion sudied appear o converge o near opimal soluions, producing large posiive profis. In order o assess he appropriaeness of a specific crossover rae, since he models have differen iniial populaions (i.e. iniial se of random numbers, he iniial condiions) and find differen opimal soluions we will examine he sabiliy of he average by using he sandard deviaion measure. We can see ha he mos sable average populaion finess appears for a crossover rae of 60%, his confirms he configuraion suggesed in he lieraure. (populaion size 80, crossover rae 0,6). I can be observed ha he maximum reurn has a posiive rend. I appears o be relaively sable afer 50 generaions and moves in he range beween.2 and (ie. 20%-00% reurn). For he minimum finess no paern seems o exis. For he average populaion reurn a clear upward rend can be found in he firs 80 generaions, his is an indicaion ha he overall finess of he populaion improves over ime. Concerning he volailiy of he soluions, sandard deviaion of soluions afer an increase in he firs generaions sabilizes in a range beween 0.3 and 0.6 providing evidence of a sable and efficien se of soluions. Table 2 Crossover Effec By looking a Table 3 you can compare he resuls of opimizaion of our rading sysem by using hree differen sofware ools. The firs row gives he resul for he GATradeTool agains he Measock and he FinTradeTool. Our proposed sofware ool (GATradeTool) can solve he opimizaion problem very fas wihou any specific resricions abou he number of oal ess. The maximum number of es ha can be performed in Measock sofware is The FinTradeTool needs much more ime in order o find he opimal soluion. The soluion provided by he GATradeTool, is closed o he opimal soluion of he FinTradeTool. Fig.2 Evoluion of saisics over 300 generaions Figure 3 provides a hree dimensional plo of he opimum soluions given by he GATradeTool. In axes x and y we have he parameers θ, θ2 for he dimbea indicaor and is moving average. Axis 2 shows he reurn of he Dimbea rading sysem for he seleced opimum parameers. As can be easily undersood our ool provides an area of opimum soluions in conras wih he FinTradeTool ha provides only he bes soluion. Table 3 Comparison of differen sofware ools Sofware Opimised Parameers Toal Compleion Opimisaion Evaluaion Tool (Dimbea,MovAv(DimBea)) Tess Time Period Reurn Period Reurn (minues) (/5/98-25/6/03) (25/6/03-25/6/04) GATradeTool (72,35) - 7,57 2,% 6,5% FinTradeTool (75,29) ,5 26,4%,7% Measock (60,) ,3 6,9% 4,5% The rading sysems wih he opimum parameers ha have been found in period /5/98-25/6/03 were esed in he evaluaion period 25/6/03-25/6/04. The performance of our rading sysem has been increased in all sofware ools. However, he cos of ime has o be considered very seriously (column 4). Figure 2 depics he evoluion of he maximum, minimum and average reurn across he 300 generaions for he Dimbea rading sysem Fig.3 A 3-D Plo of he opimum area 4 Conclusion Our main objecive in his paper is o illusrae ha he new echnology of MATLAB can be used in

5 4h WSEAS In. Conf. on NON-LINEAR ANALYSIS, NON-LINEAR SYSTEMS and CHAOS, Sofia, Bulgaria, Ocober 27-29, 2005 (pp29-34) order o implemen a geneic algorihm ool ha can improve opimizaion of echnical rading sysems. Our experimen resuls show ha GATradeTool can improve digial rading by providing quickly a se of near opimum soluions. Concerning he effec of differen GA parameer configuraions, we found ha an increase in populaion size can improve performance of he sysem. The parameer of crossover rae does no affec seriously he qualiy of he soluion. By comparing he soluions of he opimisaion problem conduced by differen sofware ools, we found ha he GATradeTool can perform beer, by providing very fas a se of opimum soluions ha presen a consisency in all over he evaluaion period. Finally, i would be ineresing for furher research o es a series of differen sysems in order o see he correlaion beween geneic algorihm and sysem performances. In our days of frequen changes in financial markes he researchers and raders can easily es heir specific sysems in GATradeTool by changing only he funcion ha produce he rading signals. References: [] Jegadeesh, N. and Timan, S., Reurns o Buying Winners and Selling Losers: Implicaions for Sock Marke Efficiency, Journal of Finance, Vol.48, No., 993, pp [2] Lehmann, B. N., Fad, maringales, and marke efficiency, Quarerly Journal of Economics, Vol.05, 990, pp [3] Werner, F.M., Bond, D. and Thaler, R., Furher Evidence on Invesor Overreacion and Sock Marke Seasonaliy, Journal of Finance, Vol.42, No.3,987, pp [4] Menkhoff, L. and Schlumberger, M., Persisen Profiabiliy of Technical Analysis on Foreign Exchange Markes? BNL Quarerly Review, Vol.93, 995, pp [5] Brock, W., Lakonishok, J. and LeBaron, B., Simple echnical rading rules and he sochasic properies of sock reurns, Journal of Finance, Vol.47, 992, pp [6] Allen, H. L. and Taylor, M. P., The use of echnical analysis in he foreign exchange marke, Journal of Inernaional Money and Finance, Vol., 992, pp [7] Cheung, Y. W. and Wong, C. Y. P., The Performance of Trading Rules on Four Asian Currency Exchange Raes. Mulinaional Finance Journal, Vol., 997, pp [8] Papadamou, S. and Tsopoglou, S., Invesigaing he profiabiliy of Technical Analysis Sysems on foreign exchange markes, Managerial Finance, Vol.27, No.8, 200, pp [9] Lo, A.W. and MacKinlay, A.C., When are conrarian profis due o sock marke overreacion? Review of Financial Sudies, Vol.3, 990, pp [0] Brown, S., W. Goezmann and S. Ross, Survival, Journal of Finance, Vol.50, 995, pp [] Papadamou, S. and Sephanides, G., A New Malab-Based Toolbox For Compuer Aided Dynamic Technical Trading, Financial Engineering News, Vol. May/June, No.3, [2] Bauer, R. J. and G. E. Liepins, Geneic Algorihms and Compuerized rading sraegies, In Exper Sysems in Finance, edied by D.E. O Leary and P.R. Wakins, Amserdam, The Neherlands: Elsevier Science Publishers, 992. [3] Bauer, R. J. Jr., Geneic Algorihms and Invesmen Sraegie, New York, John Wiley & Sons, Inc, 994. [4] Allen, F. and Karjalainen, R., Using geneic algorihms o find echnical rading rules, Journal of Financial Economic, Vol. 5, 999 pp [5] Fernández-Rodríguez, F., González-Marel, C. and Sosvilla-Rivero, S., Opimisaion of Technical Rules by Geneic Algorihms: Evidence from he Madrid Sock Marke, Working Papers 200-4, FEDEA (fp://fp.fedea.es/pub/papers/200/d200-4.pdf) [6] Mahfoud, S. and Mani, G., Financial Forecasing Using Geneic Algorihms, Journal of Applied Arificial Inelligence,Vol.0,No.6, 996, pp [7] Neely, C., Weller, P. and Dimar, R., Is echnical analysis in he foreign exchange marke profiable? A geneic programming approach, in Dunis, C. & Rusem, B.(ed.), Proceedings, Forecasing Financial Markes: Advances for Exchange Raes, Ineres Raes and Asse Managemen, London, 997. [8] Oussaidene, M., Chopard, B., Pice, O. and Tomassini, M., Pracical aspecs and experiences Parallel geneic programming and is applicaion o rading model inducion, Journal of Parallel Compuing, Vol.23, No.8, 997, pp [9] De Jong, K., An Analysis of he behavior of a class of Geneic Adapive Sysems, Ph.D. diss., Universiy of Michigan, Universiy Microfilms No , 975.

6 4h WSEAS In. Conf. on NON-LINEAR ANALYSIS, NON-LINEAR SYSTEMS and CHAOS, Sofia, Bulgaria, Ocober 27-29, 2005 (pp29-34) [20] Goldberg, D. E., Geneic Algorihms in Search, Opimizaion and Machine Learning, Addison- Wesley, 989. [2] Holland, J.H., Adapaion in naural and arificial sysem, Universiy of Michigan Press, 975. [22] Baker, J. E., Adapive Selecion Mehods for Geneic Algorihms, In Proceedings of he firs Inernaional Conference on Geneic Algorihms, 985, pp. 0-. [23] Whiley, D., The Genior algorihm and selecion pressure: why rank-based allocaions of reproducive rials are bes In Proceedings of he hird Inernaional Conference on Geneic Algorihms, 989, pp [24] Markellos, R.N., Backesing rading sysems, Journal of Compuaional Inelligence in Finance, Vol.5, No. 6, 997, pp Foonoes Arihmeic single-poin crossover, involves randomly cuing wo srings a he same randomly deermined sring posiion and hen swapping he ail porions. Crossover exends he search for new soluions in farreaching direcions. 2 Muaion is a geneic operaion ha occurs wih low frequency and alers one characer in a paricular sring posiion. For example a 0 in a sring could be alered o, or vice versa, hrough muaion. Acknowledgemens: This research paper was par of he posdocoral research of Dr. S. Papadamou ha has been funded by IKY Greek Sae Scholarships Foundaion.