Financial Data Mining Using Genetic Algorithms Technique: Application to KOSPI 200

Transcription

1 Fiacial Daa Miig Usig Geeic Algorihms Techique: Applicaio o KOSPI 200 Kyug-shik Shi *, Kyoug-jae Kim * ad Igoo Ha Absrac This sudy ieds o mie reasoable radig rules usig geeic algorihms for Korea Sock Price Idex 200 (KOSPI 200) fuures. We have foud radig rule which would have yielded he highes reur over a cerai ime period usig hisorical daa. Simulaed resuls of buyig ad sellig of radig rules were ousadig. These prelimiary resuls sugges ha geeic algorihms are promisig mehods for exracig profiable radig rules. Key words: daa miig, sock marke predicio, radig rule exracio, geeic algorihms 1. Iroducio learig. Previous sudies o his issue sugges ha arificial ielligece echiques such as arificial eural Over he las decades, here has bee much research ieress direced a udersadig ad predicig fuure. Amog hem, o forecas price movemes i sock markes is a major challege cofroig ivesors, speculaor ad busiesses. I heir ques o forecas he markes, hey assume ha fuure occurreces are based a leas i par o prese ad pas eves ad daa. However, fiacial ime series are amog he 'oisies' ad mos difficul sigals o forecas. While rule-based echologies improved dramaically, may of sock marke applicaios were less ha successful. For his reaso, he red oward auomaic learig sysems is paricularly evide i he fiacial services secor. Advaces i chaos heory provide he heoreical jusificaio for cosrucig oliear models, which is ypically he goal i machie eworks (ANN) have more freque chaces o deec oliear paers i sock marke (Ahmadi, 1990; Kamijo & Taikawa, 1990; Kimoo e al., 1990; Yoo & Swales, 1991). ANN, however, has a drawback ha he users of he model ca o readily comprehed he fial rules. I his paper, we propose daa miig approach usig geeic algorihms (GAs) o solve he kowledge acquisiio problems ha are ihere i cosrucig ad maiaiig rule-based applicaios for sock marke. Alhough here are a ifiie umber of possible rules by which we could rade, bu oly a few of hem would have made us a profi if we had bee followig hem. This sudy ieds o fid good ses of rules which would have made he mos moey over a cerai hisorical period. This paper is orgaized as follows. The followig secio provides a brief descripio of prior research o Graduae School of Maageme Korea Advaced Isiue of Sciece ad Techology

2 sock marke applicaios usig arificial ielligece echiques. Secio 3 describes he characerisics of GAs. Secio 4 explais he rule exracio mehods usig GAs. Secio 5 ad 6 repor he experimes ad empirical resuls of Korea sock marke applicaio. The fial secio discusses he coclusios ad fuure research issues. 2. Sock Marke Applicaios Usig Arificial Ielligece Techiques Kimoo e al. (1990) used several learig algorihm ad predicio mehod for he Tokyo sock exchage prices idex (TOPIX) predicio sysem. This sysem used modular eural ework ha leared he relaioships bewee various facors. The oupu of his sysem was he bes imig for whe o buy ad sell socks. They execued simulaio of buy ad sell socks o evaluae he effec of sysem. I his sudy, vecor curve, ur-over raio, foreig exchage rae ad ieres rae were used as ipu variables. Tradig profi usig his sysem revealed more ha ha of Buy ad hold sraegy. Kamijo ad Taikawa (1990) classified he chagig paer of TOPIX o riagle paer by use of cadlesick char. They have leared hese paers usig he recurre eural ework. The es se of riagle was accuraely classified i 15 ou of 16 experimes. Ahmadi (1990) ried o es he Arbirage pricig heory (APT) by ANN. This sudy used backpropagaio eural ework wih geeralized dela rule o lear relaioship bewee he reur of idividual socks ad marke facors. Yoo ad Swales (1991) performed predicio usig mixed qualiaive ad quaiaive daa. Qualiaive daa i his research was iformaio abou cofidece, ecoomic facors, ew producs ad expeced loss, ec. from he Forue 500 ad Busiess Week s Top Quaiaive daa was obaied from he firm s aual repor o he sock holders. The archiecure of eural ework model was a four-layered ework. Afer he experime, hey compared he resuls of arificial eural ework ad muliple discrimia aalysis (MDA) ad foud ha he eural ework model ouperformed MDA approach i predicio of he sock price. Lee e al. (1989) developed he iellige sock porfolio maageme sysem (ISPMS). They aemped o build exper sysems aided by opimizaio echiques. There were wo idepede exeral relaioal daabases. Oe provided he curre iformaio abou idividual socks ad he ohers provided he seleced hisorical isace of ivesme. I his sudy, par of kowledge was geeraed by machie learig ad he oher was derived from he expers opiio. Idividual ivesors displayed persoal preferece via he preferece revelaio sysem. To associae he qualiaive facors i he kowledge ad preferece base (KPB) wih quadraic programmig (QP) model, he facors i he KPB should be ierpreed as decisio variables or addiioal cosrais i he QP model. This sudy demosraed he capaciy of he sysem o correcly predic wheher he price will be up, dow or susaied o bewee 68% ad 82%. Trippi ad DeSieo (1992) execued daily predicio of up ad dow direcio of S&P 500 Idex Fuures usig ANN. Geeraig a composie recommedaio for he curre day's posiio. Ipu variables i his sudy were echical variables for he wo-week period o he radig day, ope, high, low, close price, ope price ad he price fifee miues afer he marke opeig of he curre radig day. The oupu variable was log or shor recommedaio. They performed composie rule geeraio procedure o geerae rules for combiig oupus of eworks. They repored predicio accuracy was 45.3% %.

3 Duke ad Log (1993) also execued daily predicio of Germa Goverme Bod Fuures usig feed-forward back-propagaio eural ework. I his sudy, hey used opeig rage (obaied from he highes ad lowes bids a he ope), highes, lowes price, closig price, volume of raders, ope Ieres, idusrial producio, cosumer prices, curre accou balace, uemployme raes, shor ad log erm ieres raes, wholesale price idex, M3 combied supply ad bechmark bod yield as ipu variables. The followig day's closig price was oupu. A predicio (Kigdom ad Feldma, 1995), credi evaluaio (Walker e al, 1995) ad budge allocaio (Packard, 1990). The mai idea of GAs is o sar wih a populaio of soluios o a problem, ad aemp o produce ew geeraios of soluios which are beer ha he previous oes. GAs operae hrough a simple cycle cosisig of he followig four sages: iiializaio, selecio, crossover, ad muaio (Davis, 1991; Wog ad Ta, 1994). Figure 1 shows he basic seps of geeic algorihms. resul of he ework's predicios as compared o he acual moveme was 53.94%. Choi e al. (1995) performed daily predicio of up/dow direcio of S&P 500 Idex Fuures. They used ope, high, low, close price, movig average, echical Problem represeaio Iiialize he populaio idicaors like ROC (rae of chage), RSI (relaive sregh idex), Marke Breakdow as ipu variables. Calculae fiess Their predicio accuracy was 62.5% i es se ad 63.8% i whole daa. Perform selecio 3. Geeic Algorihms (GAs) Perform crossover GAs are search algorihm based o he mechaics of Perform muaio aural selecio ad geeics ad hey combie survival of he fies amog srig srucures o form a search algorihm (Davis,1991; Goldberg, 1989; Hollad, 1975). GAs have bee demosraed o be effecive ad robus i searchig very large spaces i a wide rage of applicaios (Coli, 1994; Davis, 1991, Fogel, 1993; Goldberg, 1989; Ha e al, 1997; Klimasauskas, 1992; Koza, 1993). GAs are paricularly suiable for muli-parameer opimizaio problems wih a objecive fucio subjec o umerous hard ad sof cosrais. The fiacial applicaio of GAs is growig wih successful applicaios i radig sysem (Coli, 1994; Deboeck, 1994), sock selecio (Mahfoud ad Mai, 1995), porfolio selecio (Rua, 1993), bakrupcy Check covergece Figure 1. Basic seps of geeic algorihms I he iiializaio sage, a populaio of geeic srucures (called chromosomes) ha are radomly disribued i he soluio space, is seleced as he sarig poi of he search. These chromosomes ca be ecoded usig a variey of schemes icludig biary srigs, real umbers or rules. Afer he iiializaio sage, each chromosome is evaluaed usig a user-defied fiess fucio. The goal of he fiess fucio is o umerically ecode he performace of he chromosome. For real-

4 world applicaios of opimizaio mehods such as GAs, he choice of he fiess fucio is he mos criical sep. The maig coveio for reproducio is such ha would have yielded he mos profi had i bee used o rade socks o a give se of hisorical daa, firsly, we develop radig rules of his geeral form: oly he high scorig members will preserve ad propagae heir worhy characerisics from geeraios o geeraio ad hereby help i coiuig he search for a opimal soluio. The chromosomes wih high performace may be chose for replicaio several imes whereas poor-performig srucures may o be chose a all. Such a selecive process causes he bes-performig chromosomes i he populaio o occupy a icreasigly larger proporio of he populaio over ime. Crossover causes o form a ew offsprig bewee wo radomly seleced 'good pares'. Crossover operaes by swappig correspodig segmes of a srig IF he idicaor 1 is GREATER THAN OR EQUAL TO (LESS THAN) X1, AND he idicaor 2 is GREATER THAN OR EQUAL TO (LESS THAN) X2, AND he idicaor 3 is GREATER THAN OR EQUAL TO (LESS THAN) X3, AND he idicaor 4 is GREATER THAN OR EQUAL TO (LESS THAN) X4, AND he idicaor 5 is GREATER THAN OR EQUAL TO (LESS THAN) X5, THEN buy, ELSE sell represeaio of he pares ad exeds he search for ew soluio i far-reachig direcio. The crossover occurs oly wih some probabiliy (he crossover rae). There are may differe ypes of crossover ha ca be performed: he oe-poi, he wo-poi, ad he uiform ype (Syswerda,1989). Muaio is a GA mechaism where we radomly choose a member of he populaio ad chage oe radomly chose bi i is bi srig represeaio. Alhough he reproducio ad crossover produce may ew srigs, hey do o iroduce ay ew iformaio io he populaio a he bi level. If he mua member is feasible, i replaces he member which was muaed i he populaio. The presece of muaio esures ha he probabiliy of reachig ay poi i he search space is ever zero. 4. Tradig Rule Exracio Alhough here are a ifiie umber of possible rules by which we could rade, i seems ha oly a few of hem would have made a profi. To fid he rule ha There are five codiios ha are evaluaed for each radig day. If he all of five codiios are saisfied, he he model will produce buy sigal o ha day, oherwise i will sugges sell. X1 o X5 deoes he cuoff values. The cuoff values rage from 0 o 1, ad represe he perceage of he daa source's rage. For example, if RSI (relaive sregh idex) rages from 0 o 100, he a cuoff value of 0.0 would mach a RSI of 0, a cuoff value of 1.0 would mach a RSI of 100, ad a cuoff value of 0.5 would mach a RSI of 50. This allows he rules o refer o ay daa source, regardless of he values i akes o. We cosider addiioal flexibiliy regardig he idicaor compoe of he rule srucure such as oday s value, las day s value, ad chage sice he las day s value. Traslaig his i is full form, for example, would yield he followig saeme: IF TODAY S VALUE of ROC is GREATER THAN OR EQAUAL TO 30.0, AND CHANGE SINCE THE LAST DAY S VALUE of RSI is LESS THAN 60.0,

5 AND LAST DAY S VALUE of Sochasic %D is LESS THAN 51.0, AND LAST DAY S VALUE of A/D Oscillaor is LESS THAN 12.5, AND TODAY S VALUE of Sochasic %K is LESS THAN 75.9, THEN buy ELSE sell are he cell values of Table 1. The varyig parameers geerae a umber of combiaios of our geeral rules. The ask of defiig a fiess fucio is always applicaio specific. I his case, he objecive of he sysem is o fid a radig rule which would have yielded he highes reur over a cerai ime period. We apply he radig profi o he fiess fucio for his sudy. Above rule srucure is summarized i Table 1. I Table 1, which daa meas daa source he rule refers o, ad modifier meas a modifier value ha deermies if he value iself should be examied, or if he las day's value or he chage sice he las day should be examied. There has bee much debae regardig he developme of radig sysem usig hisorical daa. We agree ha he fuure is ever exacly like he pas, however, a commo ivesme approach is o employ sysems ha would probably have worked well i he pas ad ha seem o have a reasoable chace of doig well i he fuure. So, we defie a goal of he sysem as fidig a rule which would have yielded he highes reur over a cerai ime period. I seig up he geeic opimizaio problem, we eed he parameers ha have o be coded for he problem ad a objecive or fiess fucio o evaluae he performace of each srig. The parameers ha are coded 5. Daa ad Variables The research daa used i his sudy is KOSPI 200 (Korea sock price idex 200) from May 1996 hrough Ocober KOSPI 200 is he uderlyig idex of KOSPI 200 fuure which is he firs derivaive isrume i Korea sock marke. Fuures are he sadard forms ha decide he quaiy ad price i he cerified marke (radig place) a cerai fuure poi of ime (delivery dae). Geeral fucios of fuures marke are supplyig iformaio abou fuure price of commodiies, fucio of speculaio ad hedgig (Kolb & Hamada, 1988). Beig differe from he spo marke, fuures marke does o have coiuiy of price daa. Tha is because fuures marke has price daa by corac. So, i fuures marke aalysis, eares corac daa mehod is maily used ad icorporaed i his research. We colleced a sample of 660 radig days. Table 1. The geeral srucure of radig rule Rule umber Descripio Which daa IND IND i1 IND i2 IND i3 IND i4 IND Ij (i=1,,, j = cod. i5 umber) Less ha / greaer 1= Less ha / 2= greaer ha or 1 or 2 1 or 2 1 or 2 1 or 2 1 or 2 ha or equal o equal o Cuoff value Cuoff X X 1 X 2 X 3 X 4 X j (j = cod. umber) 5 Modifier 1,2 or 3 1,2 or 3 1,2 or 3 1,2 or 3 1,2 or 3 1= oday s value, 2= las day s, 3= chage sice he las day

6 Table 2 Techical idicaors (adaped from Achelis, 1995 ad Kolb & Hamada, 1988) Name Descripio Formulas Sochasic %K Sochasic %D Momeum ROC A/D Oscillaor Dispariy (5 days) CCI OSCP The Sochasic Oscillaor compares where a securiy s price closed relaive o is price rage over a give ime period. The Sochasic Oscillaor compares where a securiy s price closed relaive o is price rage over a give ime period. The Momeum idicaor measures he amou ha a securiy s price has chaged over a give ime spa. The Price Rae-of-Chage (ROC) idicaor displays he differece bewee he curre price ad he price x periods ago. The A/D Oscillaor measures he accumulaio ad disribuio of marke power. The Dispariy meas he disace of curre spo price ad movig average. The Commodiy Chael Idex (CCI) measures he variaio of a securiy s price from is saisical mea. The Price Oscillaor shows he differece bewee wo movig averages of a securiy s price. RSI The RSI is price followig oscillaor ha rages from 0 o 100. C L 100 H L 1 i= 0 %K i C C 4 C C H H C MA 100 C L ( M SM ) ( D ) MA MA MA i = 0 1 i = 0 Up Dw Noe) C: Closig price, L: Low price, H: High price, Volume: Tradig volumes MA: Movig average of price, M : ( H + L + C ) 3 SM : D : i = 1 i = 1 M M i + 1 i + 1 SM May previous sock marke aalyses have used echical or fudameal idicaor. I geeral, fudameal idicaors are mosly used for log-erm red aalysis while echical idicaors are used for shorerm paer aalysis. I his research, we use he echical idicaors as ipu variables. We choose 9 echical idicaors o arrow he se of variables. The oal available idicaors used o search radig rules are echical idicaors such as Sochasic %K, Sochasic %D, Momeum, ROC (rae of chage), A/D Oscillaor

7 (accumulaio / disribuio oscillaor), Dispariy 5 days, CCI (commodiy chael idex), OSCP (price oscillaor) ad RSI (relaive sregh idex). The descripio ad formulas of echical idicaors are preseed i Table Experimeal Resul To fid he profiable radig rules, we apply GAs model proposed i he previous secio. We use 500 chromosomes i he populaio for his sudy. The crossover ad muaio raes are chaged o preve he oupu from fallig io he local opima. The crossover rae rages ad he muaio rae rages for his experime. These processes are doe by he geeic algorihms sofware package Evolver 4.0, called from a Excel macro. We exrac hree radig rules by geeic search process. The derived rules are aleraively good radig rules alhough here is mior differece i simulaed performace. Each of rules cosiss of five codiios referrig ipu facors. The descripios of rules derived are illusraed i Table 3. Tradig profi eared from simulaio resuls are summarized i Table 4 ad Figure 2. While he uderlyig we could fid rules ha would have yielded he high level of profi had i bee used o rade socks o a give se of hisorical daa. The rules derived by learig raiig daa usig GAs are applied validaio (holdou) samples o verify he effeciveess of he proposed approach. While he uderlyig idex decreased abou 19% durig he validaio period (Jauary 1998 Ocober 1998), he radig sraegies followed by he derived rules ear 13% o 26% of radig profi durig he period. These prelimiary resuls demosrae ha GAs are promisig mehods for exracig profiable radig rules. Their success is due o heir abiliy o lear oliear relaioships amog he ipu variables. Addiioal advaage of his approach is ha he model geeraes comprehesible rules while ANN has a drawback ha he users ca o readily comprehed he fial rules. These rules ca serve as approximae explaaios of how he various echical idicaors relaed o fuure sock marke reurs. However, radig rules geeraed by GAs produce predicios oly whe he rules are fired. Each of he rules exraced produces predicios less ha 20% of ime. We may hik ha GAs do o produce predicios whe he marke is early equally likely o move i eiher direcio. idex decreased more ha 58% durig he raiig period, Table 3. Tradig rules geeraed Rule umber Rule 1 Rule 2 Rule 3 Descripio of rules If yeserday s AD OSC is greaer ha or equal o 0.329, AND chage i ROC is less ha 0.667, AND RSI is less ha 0.642, AND yeserday s %D is less ha 0.733, AND Dispariy5 is less ha 0.755, THEN buy he sock, Else sell or hold. If yeserday s AD OSC is greaer ha or equal o 0.343, AND chage i ROC is less ha 0.641, AND RSI is less ha 0.604, AND yeserday s %D is less ha AND Dispariy5 is less ha 0.778, THEN buy he sock, Else sell or hold. If yeserday s AD OSC is greaer ha or equal o 0.343, AND chage i ROC is less ha 0.641, AND RSI is less ha 0.618, AND yeserday s %D is less ha 0.695, AND Dispariy5 is less ha 0.778, THEN buy he sock, Else sell or hold.

8 Tradig Sraegy Table 4. The profi of buyig ad sellig simulaios Traiig period (May 1996 November 1997) Accumulaed amou (assume iiial ivesme of 10,000 wo) Validaio period (Jauary 1998 Ocober, 1998) Followig Buy & Hold 4,167 wo (-58.3%) 8,105 wo (-19.0%) Followig he rule se 1 14,938 wo (49.4%) 11,314 wo (13.1%) Followig he rule se 2 13,237 wo (32.4%) 12,641 wo (26.4%) Followig he rule se 3 13,252 wo (32.5%) 12,641 wo (26.4%) * US$1 = 1,400 wo (approximae) Simulaio resuls (raiig) Simulaio resuls (validaio) Amou Amou Tradig days Rule1 Rule2 Rule3 Buy & Hold Figure 2. Performace of simulaios Tradig day Rule1 Rule2 Rule3 Buy & Hold Cocludig Remarks verifyig ad ehacig radig rules usig curre daa i Korea fuure marke. This sudy ieds o mie reasoable radig rules usig GAs for Korea Sock Price Idex 200 (KOSPI 200) Referece fuures. We have foud hree aleraive good rules which would have yielded he high reur over a cerai ime period. Simulaed resuls of buyig ad sellig of radig rules were ousadig. These prelimiary resuls sugges ha GAs are promisig mehods for exracig profiable radig rules. However, he fuure is ever exacly like he pas. Alhough he radig sysems ha have worked well i he pas seem o have a reasoable chace of doig well i he fuure, we eed a more exesive validaio process. Sice he eire hisory of Korea fuure marke is less ha 2 ad half years, we have difficuly i doig ou-of-sample validaios i his sudy. We are workig owards Achelis, S. B., Techical Aalysis from A o Z, Probus Publishig, Ahmadi, H., Tesabiliy of he arbirage pricig heory by eural eworks, Proceedigs of he IEEE Ieraioal Coferece o Neural Neworks, 1990, pp Choi, J. H., Lee M. K. ad Rhee M. W., Tradig S&P 500 sock idex fuures usig a eural ework, Proceedigs of he Third Aual Ieraioal Coferece o Arificial Ielligece Applicaios o Wall Sree, 1995, pp

9 Coli, A. M., Geeic algorihms for fiacial modelig, I Deboeck, G.J. (Eds.), Tradig O The Edge, New York: Joh Wiley, 1994, pp Davis, L., Hadbook of geeic algorihms, Va Nosrad Reihold, NY, Deboeck, G. J., Usig GAs o opimize a radig sysem, I Deboeck, G.J (Eds.), Tradig O The Edge. New York: Joh Wiley, 1994, pp Duke, L.S. ad Log, J., Neural ework fuures radig - A feasibiliy sudy, Adapive Iellige Sysems, Elsevier Sciece Publishers, Fogel, D. B., Applyig evoluioary programmig o seleced ravelig salesma problems, Cybereics ad Sysems, Vol.24, No.1, Goldberg, D. E., Geeic Algorihms i Search, Opimizaio ad Machie Learig, MA : Addiso- Wesley, Ha, I., Jo, H. ad Shi, K. S., "The hybrid sysems for credi raig," Joural of he Korea Operaios Research ad Maageme Sciece Sociey, 22(3), pp , Hollad, J. H., Adapaio i aural ad arificial sysems, A Arbor: The Uiversiy of Michiga Press, Kamijo, K. ad Taigawa, T., Sock price paer recogiio: A recurre eural ework approach Proceedigs of he IEEE Ieraioal Joi Coferece o Neural Neworks, 1990, pp Kimoo, T., Asakawa, K., Yoda, M. ad Takeoka, M., Sock marke predicio sysem wih modular eural eworks, Proceedigs of he IEEE Ieraioal Joi Coferece o Neural Neworks, 1990, pp Kigdom, J. ad Feldma, K., Geeic algorihms No.01-95, Search Space Ld. Lodo, Klimasauskas, C. C., Hybrid euro-geeic approach o radig algorihms, Advaced Techology for Developers, Vol.1, No.7, Kolb, R. W. ad Hamada, R. S., Udersadig Fuures Markes, Sco, Forema ad Compay, Koza, J., Geeic programmig, Cambridge: The MIT Press, Lee, J. K., Kim, H. S. ad Chu S. C., Iellige sock porfolio maageme sysem, Exper Sysems, Vol. 6, No. 2, 1989, pp Mahfoud, S. ad Mai, G., "Geeic algorihms for predicig idividual sock performace," Proceedigs of he 3rd Ieraioal Coferece o Arificial Ielligece Applicaios o Wall Sree, pp , Packard, N., "A geeic learig algorihm for he aalysis of complex daa," Complex Sysems, 4, 1990, pp Rua, E., "Experimes wih opimal sock screes," Proceedigs of he 3rd Ieraioal Coferece o Arificial Ielligece Applicaios o Wall Sree, 1993, pp Syswerda, G., Uiform crossover i geeic algorihms, I Schaffer, J.D. (Eds.), Proc. 3 rd I.Cof. Geeic Algorihms. Sa Maeo, CA: Morga Kaufma, Trippi, R. R. ad DeSieo D., Tradig equiy idex fuures wih a eural ework, The Joural of Porfolio Maageme, Walker, R., Haasdijk, E. ad Gerres, M., "Credi evaluaio usig a geeic algorihm," I Cooailake, S. ad Treleave, P. (Eds.), Iellige Sysems for Fiace ad Busiess, Chicheser, Joh Wiley, 1995, pp for bakrupcy predicio, Search Space Research Repor,

10 Wog, F. ad Ta, C., Hybrid eural, geeic ad fuzzy sysems, I Deboeck, G.J. (Eds.), Tradig O The Edge. New York: Joh Wiley, 1994, pp Yoo, Y. ad Swales G., Predicig sock price performace: A eural ework approach, Proceedigs of he IEEE 24 h Aual Coferece o Sysems Scieces, 1991, pp