Predicing Sock Marke Index Trading Using Neural Neworks C. D. Tilakarane, S. A. Morris, M. A. Mammadov, C. P. Hurs Cenre for Informaics and Applied Opimizaion School of Informaion Technology and Mahemaical Sciences Universiy of Ballara, PO Box 663, Ballara, Vicoria, Ausralia (cilakarane@sudens., s.morris@, m.mammadov@, c.hurs@)ballara.edu.au Absrac This sudy forecass rading signals of he Ausralian All Ordinary Index (AORD), one day ahead. These forecass were based on he curren day s relaive reurn of he Close price of he US S&P 5 Index, he UK FTSE Index, French CAC 4 Index and German DAX Index as well as he AORD. The forecasing echniques examined were feedforward and probabilisic neural neworks. Performance of he neworks was evaluaed by using classificaion/misclassificaion rae and rading simulaions. For boh evaluaion crieria, feedforward neural neworks performed beer. Trading simulaions suggesed ha he prediced rading signals are useful for shor erm raders.. Inroducion A majoriy of previous sudies have aimed a specially predicing he price levels of he sock marke indices. However, some recen sudies have suggesed ha rading sraegies guided by forecass on he direcion of price change may be more effecive and may lead o higher profis []. During he las few decades here has been growing ineres in applicaions of arificial neural neworks for predicing sock reurns [2]. The mos commonly used neural neworks o predic he rading signals are he feedforward neural neworks (FNN) and probabilisic neural nework (PNN). Many sudies in his area have assessed he predicabiliy of heir mehods bu have inadequaely considered model profiabiliy. Predicabiliy does no necessarily imply profiabiliy. Profi depends no only on he accuracy of he forecass bu also on he rading sraegy used and magniude of he ransacion coss [3]. Timely decisions mus be made which resul in buy signals when he marke is low and sell signals when he marke is high [4]. The resuls from rading are also useful in idenifying beer models when he predicive performances are no significanly differen. There are four sraegies used in lieraure: (i) buy sock index, or buy reasury bills, (ii) buy sock index, or shor sock index, (iii) buy sock index, or say ou of he marke, and (iv) selec he bes/wors performing socks o form porfolios [2].
To compare he predicion performance of he backpropagaion neural nework wih hose of linear regression and random walk models, Qi and Maddala [3] used he proporion of imes ha he upward or downward movemens of he excess sock reurns of he S&P 5 index are correcly prediced. Their resuls showed ha he predicabiliy of neural neworks ouperform oher wo ools. However, linear regression forecass ouperformed hose relaing o he neural nework by means of profiabiliy. In heir sudy based on he predicion of he KLCI index of he Kuala Lumpur Sock Exchange, Yao e al. compared he predicion performance of backpropagaion neural neworks wih ha of ARIMA models [5]. They evaluaed he predicion performance by means of several measuremens including percenage of direcional correcness as well as a buy and sell rading sraegy. In boh cases neural neworks performed beer. Some oher sudies (such as [6] and [7]) focused on predicing he direcion (up and down) of financial marke indices showed ha neural nework is a beer opion o classify he fuure direcion (rend) of he indices. A sudy done by Kim and Chun [8] compared he predicion performance of an arrayed probabilisic neural nework wih ha of recurren neural nework. This sudy suggesed ha former is beer in all perspecives (classificaion rae and misclassificaion rae). They employed hese echniques o predic he direcion for he fracional change in Singapore sock price index. In heir sudy, Chen e al. aemped o model and predic he direcion of reurn of marke index of he Taiwan Sock Exchange [9]. Direcional forecas was done by PNNs and he performance of he PNN forecas was compared wih ha of he generalised mehods of movemens (GMM) wih Kalman filer. Resuls showed ha PNN forecass ouperform hose from GMM. Moreover, he forecass were applied o wo rading sraegies. Empirical resuls showed ha he PNN-based invesmen sraegies obained higher reurns. Leung e al. [] evaluaed he effeciveness of classificaion models for predicing he direcion of sock marke indices by means of number of correc forecas (hi rae) and rae of reurn obained from index rading. They used he ools, PNN, linear discriminan analysis, logi and probi models o predic he direcion (upward or downward rend) of monhly reurns of he US S&P 5 Index, he UK FTSE Index and Japanese Nikkei 225 Index. Resuls corresponding o he US S&P 5 Index and he UK FTSE Index suggesed ha PNN is a beer classificaion ool by means of he hi rae and he rae of reurn. However, he resuls obained from he Japanese Nikkei 225 Index did no agree wih his. All he above sudies based on various financial indices focus on classificaion of fuure values ino wo caegories (up or down) which corresponding o he buy and sell signals. Also none of hese sudies compare he predicion performance of PNN wih mulilayer feedforward neural neworks (FNN). 2
This sudy proposes a novel idea of classifying sock marke rading signals ino hree classes. Is objecive is o forecas he rading signals: Buy, Hold and Sell, of he Ausralian All Ordinary Index (AORD) one day ahead. Such forecass are useful o shor erm raders. I is worh holding shares if here is no significan rise or drop in he price index. Therefore, from he pracical poin of view, i is imporan o consider he hold caegory. Considering hese hree classes complicaes he classificaion problem as hese classes creae imbalance in he daa disribuion. Usually he hold class is dominaing while oher wo classes are small. This sudy employs FNN and PNN o classify he nex day s relaive reurn of he AORD, hereby faciliaing he comparison of he predicion performance of hese wo ypes of neural nework. The oher imporance of his sudy is he usage of he inermarke influences from he major global sock marke indices o forecas he rading signals of he AORD. Recen sudies have shown ha he inermarke influences enhance he predicion accuracy [, 2, 3]. Lieraure shows ha he previous day s Close prices of he US S&P 5 Index (GSPC), he UK FTSE Index (FTSE), French CAC 4 Index (FCHI), and German DAX Index (GDAXI) as well as he ha of he AORD influence he curren day s Close of he AORD [4, 5]. Therefore, his sudy also uses he curren day s relaive reurns of he Close prices of he above markes o idenify he nex day s rading signals of he AORD. The efficiency of he neural neworks as a echnique o predic he rading signals is sudied by applying wo differen crieria. Firs, he problem of classifying rading signals as Buy, Hold, and Sell. The classificaion resuls are measured by classificaion/misclassificaion raes. Second, a simple and very pracical rading simulaion o evaluae wheher he raders can gain profis by using he prediced rading signals, is considered. The ouline of he paper is as follows: Secion 2 discuses he mehodology used in his sudy. I includes a descripion of classificaion echniques and he proposed rading simulaions. Secion 3 describes he daa used for experimens. Secion 4 presens he resuls relevan o predicion and rading simulaions ogeher wih heir inerpreaions. Finally Secion 5 concludes he paper and proposes direcions fuure research could ake. 2. Mehodology This sudy classified he nex day s relaive reurn of he Close price of he AORD ino hree classes: (i) Buy, (ii) Hold and (iii) Sell, based on he curren day s relaive reurns of he Close 3
prices of he GSPC, FTSE, FCHI, GDAXI as well as ha of he AORD (Secion ). Le Y(+) be he prediced relaive reurn of he nex day s (+) Close price of he AORD. This sudy uses he following crierion o idenify he rading signals which corresponding o he hree classes: Buy if Y ( + ).5 Hold if.5< Y ( + ) <.5 Sell if Y ( + ).5 () The echniques used were FNN and PNN. These neworks were rained wih wo ses of inpus: () curren day s (day ) relaive reurns of he Close prices of he US and he hree European markes as inpus (se ); (2) curren day s relaive reurns of he Close prices of he US and he hree European markes ogeher wih ha of AORD as inpus (se 2). Since he influenial paerns vary wih he ime he analysis was performed for a number of moving windows [6]. 2. Forecasing wih FNN Three-layered FNNs were rained 5 imes using Levenberg-Marquard algorihm. The above menioned wo ses of inpus were considered when raining he neworks. These neworks oupu he nex day s relaive reurn of he AORD which was subsequenly classified ino he hree classes of ineres according o Equaion (). The average numbers of classificaions/misclassificaions ino differen classes were calculaed. This procedure was repeaed for six moving windows each of size hree rading years. Each window consiss of 768 cases. The mos recen % of daa was used for esing. The nex mos recen 2% of daa was used for validaion while he remaining 7% was used for raining. Each ime he saring poin was shifed by one year o ge he saring poin of he nex window. Always, hree neurons were used for he hidden layer while he learning rae and momenum were fixed a.3 and. respecively [6]. 2.2 Forecasing wih PNN PNNs were also rained for he same six moving windows. For each window he mos recen % of daa was used for esing while he remaining 9% was used for raining. Neworks oupu he class ( Buy, Hold, or Sell ) relevan o he nex day s Close price of AORD. Neworks were rained wih boh ses of inpus. The join disribuion of he inpu variables was assumed o be Gaussian. The parameers of he disribuion were esimaed by using he raining daa. The average sandard deviaion of he individual inpu variables was considered as he sandard deviaion of he join disribuion. The cos of misclassificaion for each class was assumed o be equal. 4
2.3 Trading Sraegies This sudy assumes ha a he beginning of each period, he rader has some amoun of money as well as a number of shares. Furhermore, i is assumed ha he value of money in hand and he value of shares in hand are equal. Each period consiss of successive 76 rading days. Two ypes of rading sraegies were used in his sudy: () response o he prediced rading signals which migh be a Buy, Hold or a Sell signal (rading sraegy ); (2) do no paricipae in rading bu hold he iniial shares in hand and keep he money in hand unil he end of he period (rading sraegy 2). The second sraegy was used as a benchmark. 2.3. Firs rading sraegy This sudy assumes index can be raded as a securiy in is own righ. Le he value of he iniial money in hand be M. The number of shares a he beginning of he period, S = M P, where P is he Close price of he AORD on he day before he saring day of he period. Also le M, S, P, VS be he money in hand, number of shares, Close price of he AORD, value of shares holding on he day (=, 2,, T), respecively. This sraegy assumes ha always a fixed amoun of money is used in rading regardless of he rading signal is Buy or Sell. Le his fixed amoun be denoed as F and be equal o M L, L >. In he calculaions L =, 2,, is considered. When L =, F equals o M, when L = 2, F equals o 5% of M and so on. Le and s be he number of shares buy and he number of shares sell a day, respecively. b Suppose he rading signal a he beginning of he day is a Buy signal. Then he rader spends F = min{ F, M } amoun of money o buy a number of shares a a rae of he previous day s Close price. M M F F min{ F, M } (2) =, = S b = S Suppose he rading signal is a Hold signal, hen; F P b (3) = + (4) VS = S P (5) = M M (6) S (7) = S VS = S P (8) 5
Le he rading signal a he beginning of he day is a Sell signal. Then he rader sells S = min{ ( F P ), S } amoun of shares. s = S S = min{( F P ), S } (9), M () = M + S P S = () S s VS = S P (2) I should be noed ha a Buy signal ha immediaely follows anoher Buy signal will be reaed as a Hold signal. Also, if all shares have been sold, a Sell signal is ignored. 2.3.2 Second Trading Sraegy In his case he rader does no paricipae. Therefore, M, = M and S = S for all =, 2,, T. However, he value of he shares changes wih he ime and herefore, he value of shares a day, VS = S P. 2.3.3 Rae of Reurn A he end of he period (day T) he oal value of money and shares in hand; for he firs rading sraegy, for he second rading sraegy, TC = M + S P (3) T TC = M + S The rae of reurn (R%) for each rading period is calculaed as below; T T P T (4) TC 2M R % = (5) 2M 3. Daa and Daa Pre-processing The daa se consiss of daily relaive reurns of he Close prices four influenial sock markes and he AORD, from 2nd July 997 o 3h December 25. The seleced influenial markes are:. US S&P 5 Index (GSPC) 2. UK FTSE Index (FTSE) 3. French CAC 4 Index (FCHI) 4. German DAX Index (GDAXI) 6
Since differen sock markes are closed on differen holidays, he regular ime series daa ses considered have missing values. If no rading ook place on a paricular day, he rae of change of price should be zero. Therefore, he missing values of he Close price were replaced by he corresponding Close price of he las rading day. Relaive Reurns, of he daily Close price of he sock marke indices were used for he analysis. P( ) P( ) RR ( ) = (6) P( ) where and are he relaive reurn and he Close price of a seleced index on day, respecively. Reurns are preferred o price, since reurns for differen socks are comparable on equal basis. The sudy period was divided ino six moving windows, each of lengh hree rading years (3 256 days). These six windows were considered for analysis. The mos recen % of daa (he las 76 rading days) in each window was accouned for ou of sample predicions. I is worh noing ha he opening and closing imes for many of he various markes do no coincide. For example, he Ausralian, French and German markes have all closed by he ime he US markes open. 4. Resuls and Inerpreaions 4. Disribuion of Classes in Tes Samples Firsly, he disribuion of ou of sample daa among he hree classes was invesigaed. Table shows he disribuion of he acual Buy, Hold and Sell signals wihin he es sample (he las 76 days) of each window. Table : Disribuion daa belongs o es samples (percenages of daa in each class are also shown in brackes) Window Number Class (Buy) Class 2 (Hold) Class 3 (Sell) 2 (26.32%) 4 (52.63%) 6 (2.5%) 2 2 (26.32%) 44 (57.89%) 2 (5.79%) 3 23 (3.26%) 38 (5.%) 5 (9.74%) 4 2 (5.79%) 56 (73.68%) 8 (.53%) 5 (4.47%) 59 (77.63%) 6 ( 7.9%) 6 2 (27.63%) 4 (52.63%) 5 (9.74%) The noiceable feaure in he daa disribuion is ha in each window, 5% or more signals are coming from he Hold class (Table ) wih his signal accouning for over 7% in he 4 h and he 5 h windows. 7
4.2 Classificaion Resuls Table 2 and Table 3 show he average raes of classificaion and misclassificaion (over six windows) relaing o he resuls obained from FNN and PNN respecively. These raes indicae he paerns of classificaion/misclassificaion of daa belong o a class. Classificaion rae indicaes he proporion of correcly classified signals o a paricular class ou of he oal number of acual signals in ha class whereas, misclassificaion rae indicaes he proporion of incorrecly classified signals from a paricular class o anoher class ou of he oal number of acual signals in he former class. From a rader s poin of view, he misclassificaion of a Hold signal o Buy class or Sell class is a more serious misake han misclassifying a Buy signal or a Sell signal as a Hold signal. The reason is in he former case a rader will loses he money by aking par in an unwise invesmen while in he laer case he/she only lose he opporuniy of making a profi, bu no moneary loss. The mos serious misakes are he misclassificaion of Buy signal o Sell signal and vice versa. Table 2: Average Classificaion/Misclassificaion raio for wo ypes of inpus for he resuls Acual Class obained by FNN Average Classificaion/Misclassificaion Raio for Inpu Se Average Classificaion/Misclassificaion Raio for Inpu Se 2 Prediced Class Prediced Class Buy Hold Sell Buy Hold Sell.223.777..23.769. 2.42.896.62.37.9.62 3..822.78..8444.56 As expeced Hold class shows higher classificaion rae irrespecive of he inpu se (Table 2). When he FNNs were rained wih he firs inpu se (wihou AORD), on average, 22%, and 8% signals were correcly classified o Buy and Sell classes, respecively. On average, 78% of Buy signals and 82% of Sell signals were misclassified as Hold signals. Alhough hese figures are large, he consequence of such misclassificaion is no crucial. The percenage of signals misclassified from Hold class o Buy and Sell classes were relaively small. Also here were no misclassificaions ino non-coniguous classes (ha is no Buy signals were misclassified as Sell signals and vice versa). The FNNs rained wih second se of inpus also gave similar resuls. 8
Table 3: Average Classificaion/Misclassificaion raio for wo ypes of inpus for he resuls Acual Class obained by PNN Average Classificaion/Misclassificaion Raio for Inpu Se Average Classificaion/Misclassificaion Raio for Inpu Se 2 Prediced Class Prediced Class Buy Hold Sell Buy Hold Sell.47.853..55.845. 2.2.93.49.25.93.45 3..84.59..84.59 The PNNs also show resuls similar o he FNNs (Table 2 and Table 3). The percenages of signals correcly classified o Hold class were slighly higher han he case of he FNNs while hose corresponding o Buy class were slighly lower han in he case of he FNNs. However, as wih he FNNs, he PNNs also do no show serious misakes such as misclassificaion of Buy signals o Sell signals and vice versa (Table 3). Having observed no serious misclassificaions, boh he FNNs and he PNNs give hope ha raders can be benefied from he predicions obained. As a resul of lower classificaion rae corresponding o Buy class, he PNNs may yield lower profis han he FNNs. However, rading simulaions needed o be performed o clarify hese maers. 4.3 Trading Simulaions Differen rading simulaions were performed on he predicion resuls obained from he neural nework is presened. Table 4 presens he oal number of Buy and Sell signals prediced by he FNNs and he PNNs, rained wih wo inpu ses. The percenage of correcly prediced Buy ( Sell ) signals ou of he oal number of Buy ( Sell ) signals wihin each window are also shown wihin brackes. For many cases, boh ypes of neworks prediced Buy and Sell signals correcly wih an accuracy rae more han 5% (Table 4). However, he PNNs missed many rading signals and did no predic any signals in he las wo windows. Boh ype of neworks show beer predicion performance when hey were rained wih he firs se of inpus. This sudy considered differen proporions of money o respond o he rading signals. In oher words, when calculaing he rae of reurn, i was assumed he rader buy or sell shares ha worh he full amoun of money in hand a he beginning, half of his money, one hird of his money and so on. Figures and Figure 2 depic how he average rae of reurn (over 6 windows) changes 9
wih differen proporions of money as well as he benchmark sraegy. Figure and Figure 2 are corresponding o he resuls obained from he FNNs and he PNNs, respecively. Table 4: Disribuion of Buy and Sell signals relaing o he resuls obained from FNNs and PNNs (percenages of correc signals are shown in brackes) Window Inpu Se Inpu Se 2 Number FNN PNN FNN PNN Buy Sell Buy Sell Buy Sell Buy Sell 2 (67%) 2 (67%) 5 (8%) 2 (58%) (64%) 4 (57%) 7 (7%) 2 (58%) 2 6 (67%) 6 (33%) 6 (83%) 8 (38%) 5 (8%) 5 (4%) 7 (7%) 7 (43%) 3 (64%) (5%) (73%) 6 (67%) (6%) 7 (57%) (8%) 6 (67%) 4 3 (%) (%) 3 (%) (%) 5 (%) (%) 6 2 (%) 2 (%) 9 8 7 Rae of Reurn 6 5 4 3 2 Benchmark / /9 /8 /7 /6 /5 /4 /3 /2 Trading Sraegy Inpu Se (w ihou AORD) Inpu Se 2 (w ih AORD) Figure : Average rae of reurn versus rading sraegy for he resuls obained from FNNs Figure indicaes ha when more money involves in rading he profi gain increases. When he money involves in rading is 5% or less, he profis generaed is he same for he FNNs rained wih he firs inpu se and he FNNs rained wih he second inpu se. However, he rading
which involves he full amoun of money iniially in he hand, gives subsanially higher profis in he case of he firs inpu se (wihou AORD). 7 6 Rae of Reurn 5 4 3 2 Benchmark / /9 /8 /7 /6 /5 /4 /3 /2 Trading Sraegy Inpu Se (w ihou AORD) Inpu Se 2 (w ih AORD) Figure 2: Average rae of reurn versus rading sraegy for he resuls obained from PNNs Figure 2 also implies ha he profi gain increases when more money involves in rading. Irrespecive of he proporion of money used in rading, he profi gain relaing o he PNNs rained wih he second inpu se almos he same as hose relaing o he PNNs rained wih he firs inpu se. Boh Figure and Figure 2 sugges ha he highes profi can be gained when he full amoun of money iniially in hand involves in rading. For he corresponding proporion of money involved in rading, he signals prediced by he FNNs always gave higher profis han hose prediced by he PNNs. The highes profi was obained when he FNNs were rained wih he second inpu se which includes he previous day s (day ) relaive reurn of he AORD. However, furher analysis needs o be carried ou o decide wheher adding he previous day s relaive reurn of AORD helps improve predicion accuracy. Irrespecive of he nework ype and he inpu se, he maximum rae of reurn of each window was obained when he full amoun of money involved in rading. Table 5 shows he maximum rae of reurn obained for each window.
Window Maximum rae of Maximum rae of reurn for he firs rading sraegy number reurn for he second FNN PNN rading sraegy Inpu se Inpu se 2 Inpu se Inpu se 2 (Benchmark).48% 9.459% 8.5757% 3.464% 2.289% 2 4.4693% 8.7695% 7.632% 7.785% 8.6736% 3.3297% 7.224% 7.54% 8.2424% 8.2424% 4.9952% 4.245% 4.245% 3.5767% 3.5767% 5 5.649%.8493%.8493% - - 6 2.6287% 8.5929% 6.7227% - - For boh ses of inpus, he highes he lowes maximum raes of reurn corresponding o he FNNs are.8493% and 4.245%, respecively. The highes and he lowes maximum raes of reurn obained by he PNNs rained wih he firs inpu se are 8.2424% and 3.464%, respecively. The corresponding values relaed o he PNNs rained wih he second inpu ses are 8.6736% and 2.289%, respecively. By considering he resuls obained from he proposed rading sraegies, i can be suggesed ha a rader can make subsanial profis (wihin abou hree and half monhs) by responding o he rading signals prediced by his sudy. Furhermore, he predicion performance of he FNNs seems o be beer han ha of PNNs. 5. Conclusions and Furher Sudies According o he resuls obained from he rading simulaions, he prediced rading signals are useful o he shor erm raders. FNN performed beer han PNN by means of predicion evaluaion wih classificaion/misclassificaion rae as well as rading simulaions. The resuls of his sudy may be furher improved by adding wo exra classes which denoes he srong buy and srong sell signals. An example for idenificaion crierion of raining signals could be as follows; Srong Buy if Y ( + ).7 Buy if.5 Y ( + ) <.7 Hold if.5< Y ( + ) <.5 (7) Sell if.5 Y ( + ) >.7 Srong Sell if Y ( + ).7. 2
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