ESTIMATION OF RETURN ON INVESTMENT IN SHARE MARKET THROUGH ANN

ESTIMATION OF RETURN ON INVESTMENT IN SHARE MARKET THROUGH ANN K.S.Ravicandran, P.Tirunavukarasu 2, R. Nallaswamy 3, R.Babu 4 Scl f Cmputing, SASTRA Deemed University, Tanjavur 63 402, Tamil Nadu, India. 2 Department f Matematics, Sri Angalaman Cllege f Engineering & Tecnlgy, Siruganr, Tricy, Tamil Nadu, India. 3 Department f Matematics and Cmputer Applicatins, Natinal Institute f Tecnlgy, Tricy, Tamil Nadu, India. 4 Sanmuga Plytecnic Cllege, Tanjavur- 63 402, Tamil Nadu, India ABSTRACT Te stck market is ne f te mst ppular investing places because f its expected ig prfit. Traditinally, tecnical analysis apprac, tat predicts stck prices based n istrical prices and vlume, basic cncepts f trends, price patterns and scillatrs, is cmmnly used by stck investrs t aid investment decisins. Advanced intelligent tecniques, ranging frm pure matematical mdels and expert systems t fuzzy lgic netwrks, ave als been used by many financial trading systems fr investing and predicting stck prices. In recent years, mst f te researcers ave been cncentrating teir researc wrk n te future predictin f sare market prices by using Neural Netwrks. But, in tis paper we newly prpse a metdlgy inwic te neural netwrk is applied t te investr s financial decisin making t invest all type f sares irrespective f te ig / lw index value f te scripts, in a cntinuus time frame wrk and furter it is furter extended t btain te expected return n investment trug te Neural Netwrks and finally it is cmpared wit te actual value. Te prpsed netwrk as been tested wit stck data btained frm te Indian Sare Market BSE Index. Finally, te design, implementatin and perfrmance f te prpsed neural netwrk are described. Keywrds: Indian Stck Market, Neural Netwrks, Decisin Making, Crrelatin and Regressin analysis. INTRODUCTION Frm te beginning f time it as been man s cmmn gal t make is life easier. Te prevailing ntin in sciety is tat wealt brings cmfrt and luxury, s it is nt surprising tat tere as been s muc wrk dne n ways t predict te markets t increase suc wealt. Varius tecnical, fundamental, and statistical indicatrs ave been prpsed and used wit varying results. Hwever, n ne tecnique r cmbinatin f tecniques as been successful enug t cnsistently "beat te market". Traditinally, tecnical analysis apprac [4, 6, 7, 8], tat predicts stck prices based n istrical prices and vlume, te Dw Tery, basic cncepts f trends, price patterns and scillatrs, is cmmnly used by stck investrs t aid investment decisins. Advanced intelligent tecniques ranging frm pure matematical mdels and expert systems [5, 7] t neural netwrks [, 2, 3, 8, 9, 0, ] ave als been used by many financial trading systems fr stck predictin. Ultimately, mst f te researcers ave derived te varius metdlgies fr predicting future sare market prices using artificial neural netwrk [. But, in tis paper te neural netwrk cncept is used t calculate te return n investment and finally it is cmpared wit te actual value. In Indian Sare Market, te index f BSE increases r decreases depending upn te perfrmance f te varius sub-indexes, namely, BSEIT, BSEED, BSEFMCG, BSEHC, BSECG, TECH, BSEPSU, BANKEX, AUTO, METAL, and OILGAS. Tese sub-indexes are dented by te decimals t and in te later part f tis paper, we dente tese numbers are script numbers. Based n te available data, [6] te ranking f varius sub-indexes is establised and based n te ranking, we invest te amunt invariably t all type f sares and te expected 44

return n investment is calculated trug Neural Netwrks and finally tese values are tested wit te actual value. Te prpsed netwrk as been tested wit stck data btained frm te Indian Sare Market Index BSE. Te paper is rganized as fllws. Sectin 2 prvides te infrmatin related t neural netwrk and its learning rule (back prpagatin) fr predicting sub sectrs investment in stck market. Sectin 3 cvers te determinatin f te ptimum number f iteratins needed t get te ptimum return n investment trug te prpsed netwrk. Te return n investment in te sare market tat is btained trug te neural netwrk and cmpared wit te actual values are discussed in sectin 4. Te merits f te present prblem using neural netwrks are discussed in sectin 5 and finally te cnclusin is given in sectin 4. Sectin2.ARTIFICIAL NEURAL NETWORK Befre te age f cmputers, peple traded stcks and cmmdities primarily n intuitin. As te level f investing and trading grew, peple searced fr tls and metds tat wuld increase teir gains wile minimizing teir risk. Statistics, tecnical analysis, fundamental analysis, Time series analysis, cas tery and linear regressin are all used t attempt t predict and benefit frm te market s directin. Nne f tese tecniques as been prved t be te cnsistently crrect predictin tl tat is desired, and many analysts argue abut te usefulness f many f te appraces. Hwever, tese metds are presented as tey are cmmnly used in practice and represent a base-level standard fr wic neural netwrks suld utperfrm. Als, many f tese tecniques are used t preprcess raw data inputs, and teir results are fed int neural netwrks as input. Sme f te related wrk are given belw. A neural netwrk is a cmputer prgram tat recgnizes patterns and is designed t take a pattern f data and generalize frm it. An essential feature f tis tecnlgy is tat it imprves its perfrmance n a particular task by gradually learning a mapping between inputs and utputs. Tere are n set rules r sequence f steps t fllw in generalizing patterns f data. Te netwrk is designed t learn a nnlinear mapping between te input and utput data. Generalizatin is used t predict te pssible utcme fr a particular task. Tis prcess invlves tw pases knwn as te training pase (learning) and te testing pase (predictin). Regressin mdels ave been traditinally used t mdel te canges in te stck markets. Multiple regressin analysis is te prcess f finding te least squares predictin equatin, testing te adequacy f te mdel, and cnducting tests abut estimating te values f te mdel parameters, Mendenall et al. [9]. Hwever, tese mdels can predict linear patterns nly. Te stck market returns cange in a nnlinear pattern suc tat neural netwrks are mre apprpriate t mdel tese canges. Studies ave swn tat back prpagatin netwrks may be used fr predictin in financial market analysis. Refenes et al. [20] cmpared regressin mdels wit a back prpagatin netwrk bt using te same stck data. In cmparisn wit regressin mdels back prpagatin prved t be a better predictr. Te results swed tat te Mean Squared (MSE) fr te neural netwrk was lwer tan te Multiple Linear Regressin (MLR) mdel. Te MSE fr te netwrk was 0.044 and te MSE fr te MLR mdel was 0.38 suc tat te neural net prved t be mre effective in learning te training data tan te MLR. Fr te test data, wic was different frm te training data, te neural netwrk MSE was 0.066 wic is als lwer tan te MLR MSE f 0.28. Accrding t Refenes et al. [20] neural netwrks are capable f making better predictin in capturing te structural relatinsip between a stck s perfrmance and its determinant factrs mre accurately tan MLR mdels. Kryzanwski et al. [2] using Bltzmann macine trained an artificial neural netwrk wit 49 test cases f psitive (rise in te stck price) and negative (fall in te stck price) returns fr te years 987-989 and cmpared tis t training te netwrk wit psitive, neutral (uncanged stck price), and negative returns fr te same 49 test cases fr te years 987-989. Te netwrk predicted 72% crrect results wit psitive and negative returns. Hwever te netwrk predicted nly 46% crrect results wit psitive, neutral, and negative returns. If stck market return fluctuatins are affected by teir recent istric beavir, Tang [22] neural netwrks wic can mdel suc tempral infrmatin alng wit spatial infrmatin in te stck market canges can prve t be better predictrs. Te canges in a stck market can ten be learned better using netwrks wic emply a feedback mecanism t cause sequence learning. 45

Recurrent netwrks use te back prpagatin learning metdlgy. Te main difference between a feed frward back prpagatin netwrk and a recurrent netwrk is te existence f a feedback mecanism in te ndes f te recurrent netwrk. Tis feedback mecanism facilitates te prcess f using te infrmatin frm te previus pattern alng wit te present inputs. Cpy-back/Cntext units are used t integrate te previus pattern int te fllwing r a later input pattern, Mrgan et al. [23]. Tis ability f recurrent netwrks in learning spatitempral patterns makes tem suitable fr te stck market return predictin prblem. Back prpagatin netwrks are independent f te sequence in wic te inputs are presented wereas te recurrent netwrks take int accunt te sequence. Tus te recurrent netwrks represent te idea f predicting stck market returns n te basis f recent istry mre clsely [24-27]. Since n training ccurs during testing, a pattern is matced wit its clsest learned training pattern (independently) and te crrespnding utput is generated. Hence, if tere was n training after week 48 and we test te netwrk fr week 59, it will be matced wit te learned data set fr weeks l-48 and maybe week 37 will be used t predict te utput fr week 59 --intrinsically assuming tat week 36 befre week 37 is a gd representative f week 58 preceding week 59. Altug, tis is ideally wat we pe t ccur, tere is n guarantee tat te neural netwrks will use tis relatinsip. It may use ter learned infrmatin based n te data. very pwerful cmputatinal tl, aving te ability t learn and t generalize frm examples t prduce meaningful slutins t prblems even in case f errneus r incmplete data. Neural netwrks ave widely been used in sare market predictin and frecasting f te varius sare price predictins, as well as fr time series mdeling. Mst ften feed-frward netwrks, wic emply a sliding windw ver a sequence f data (i.e., t induce te functin in ANN arcitecture, using a set f lder recrds as inputs and a single utput as te target value f te netwrk), are used fr time series mdeling. Altug, in general, nn-linear, aut-regressive time series mdeling is difficult tan linear mdels, yet wit te ANN apprac suc a restrictin des nt apply. Similarly, in cntrast t te aut-regressive and mving average metds, ANNs are nnparametric data driven appraces tat can capture nnlinear data structures witut prir assumptin abut te underlying relatinsip in a particular prblem. Besides, ANNs are mre general and flexible mdeling and analysis tls fr frecasting applicatins, capable f finding nnlinear structures, as well as linear nes. In fact, linear autregressive (AR) mdels are special cases f ANNS witut idden ndes. Fr an explanatry r casual frecasting prblem, te inputs t an ANN are usually te independent r predictr variables []. Te functinal relatinsip estimated by te ANN can be written as: Y = F (x, x 2, x 3, x n ) Te predictin accuracy f a netwrk alng wit additinal infrmatin available frm recent istry f a stck market can be used t make effective stck market prtfli recmmendatins [28]. 2. NN cncepts and its terminlgy T mdel cmplex prcess in many pysical systems, te use f Artificial Neural Netwrk (ANN) as been extensively in use in recent times. As a branc f artificial intelligence, tis rbust and versatile tl is being mdeled after te uman neurlgical system, cnsisting f a series f neurns (te basic cmputing elements), intercnnected tgeter t allw recgnitin f incidents tat ave ad a similar pattern t te current input. Especially fr pattern recgnitin and functin apprximatin, ANN, equipped wit parallel distributed prcessing arcitecture, is well recgnized as a () Were x, x 2, x 3, x n are n independent variables and y is a dependent variable. In tis sense, te neural netwrk is functinally equivalent t a nnlinear regressin mdel. Fr an extraplative r time series prblem, n te ter and, inputs are typically te past bservatins f te series and te utput is te future value. Te functin mapping perfrmed by te ANN is as fllws: Y t+ = F (y t, y t-, y t-2,, y t-n ) (2) Were y t is te bservatin at time t. Tus te ANN is equivalent t te nnlinear autregressive mdel alng te series. Fr a time series prblem, a training pattern cnsists f a fixed number f lagged bservatins f te series. Tere are N bservatins y, y 2, y 3,, y N 46

in te training set and if ne-step-aead frecasting is required, ten using an ANN wit n input ndes, we ave N-n training patterns. Te first training pattern will be cmpsed f y, y 2, y 3,, y n as inputs and Y n+ as te target utput. Te secnd training pattern will cntain y, y 2, y 3,, y n+ as inputs and Y n+2 as te desired utput. Finally, te last training pattern will be y N-n, y N-n+,, y N- fr inputs and y N fr te target utput. Typically, least- squares based bjective functin r cst functin t be minimized during te training prcess is: N 2 E= ( y i a i ) 2 i= n+ (3) were a i is te utput f te netwrk and ½ is included t simplify te expressin f derivatives cmputed in te training algritm. Mst f te envirnmental and water resurces applicatins f ANN ave used feed-frward netwrks fr functin apprximatin. Wile a majrity f tem used te back-prpagatin training algritm, a few f tem attempted ter algritms. Te general structure f a feedfrward neural netwrk is swn in Fig.. Te ndes in an input layer receive te inputs f te mdel and tey flw trug te netwrk and prduce utputs at ndes in te utput layer. Te wrking principle f feed-frward neural netwrk is available elsewere [2]. Matematically, a tree-layer neural netwrk wit I input ndes, J idden ndes in a single idden layer, and K utput ndes, can be expressed as: J I j k O pk = f w jk f 2 wij x pi + b + b2 j= i=, k,2,..., K (4) activatin functin as te frm f: f ( x) = + e x (5) Te linear activatin functin as te frm f ( x) = x (6) In tis study sigmid functin is used fr f 2 and te linear functin is applied fr f. Te sigmid functins (wic plts like curves) nrmally ave a tendency t pus te value f f(x) t te extremes (binary in te case f lgistic sigmid; biplar in te case f tan functin). Tus te sigmid functins are mre suitable fr classificatin prblems. Wen cntinuus utputs are expected, as in te case f time series mdeling, sigmid functins are nt a gd cice. Tere are several ter activatin functins used in many ter studies, wever, tis wrk did nt analyze te suitability f activatin functins fr sare market price predictins. Linear autregressive mdels assume te predictin equatin t be a linear cmbinatin f a fixed number f previus data in te time series. Including a nise term, it can be written as were O Pk is te utput frm te k t nde f te utput layer f te netwrk fr te P t vectr (data pint); X Pi is te input at te i t nde f input layer frm p t vectr (data pint); w jk t te cnnectin weigt between j nde f te idden layer and k t nde f te utput layer (Fig. ); w ij is te cnnectin weigt between i t nde f te input layer and j t nde f te j b k b 2 idden layer; and and are bias terms; and f(.) and f 2 (.) are activatin functins. Te lgistic sigmid functin, a cmmnly used is p x( t) = α ix( t i) + ξ ( t) ` i= = F L (x(t-),x(t-2),,x(t-p)) + ξ (t) 47

(7) If p previus sequence elements are taken, ne speaks f an AR(p) mdel f time series. Finding an apprpriate AR(p) mdel means csing an apprpriate and estimating te cefficients α trug tecniques like least i squares ptimizatin prcedures. Tis tecniques, altug rater pwerful, is naturally limited, since it assumes a linear relatinsip amng sequence elements. It becmes clear tat a feed frward neural netwrk can replace te linear functin F L in equatin (7) by an arbitrary nn-linear functin F NN as in equatin (8). x(t) = F NN (x(t -),x(t - 2),...,x(t p))+ ξ (t) Tis nn-linear functin can be estimated based n samples frm te series, using ne f te well-knwn learning r ptimizatin tecniques like back prpagatin r cnjugate gradient. Making F NN dependent n p previus elements is identical t using p input units being fed wit p adjacent sequence elements. Tis input is usually referred t as a time windw, since it prvides a limited view n part f te series. Nn-linear autregressive mdels are ptentially mre pwerful tan linear nes in tat tey can mdel muc mre cmplex underlying caracteristics f te series. (8) OP O Pk OPK k K Output Layer w w k w K wj j J w jk w jk w Jk wj w JK Hidden Layer w w j wi w J w ij wij wi w Ij w IJ i I Input Layer xp xpi x PI Fig. Tree-layer feed-frward neural netwrk arcitecture 2.2 Selectin f Activatin Functin Suitable activatin functin fr te Hidden Units is needed t intrduce nn-linearity int te netwrk, wic gives te pwer t capture nnlinear relatinsip between input and utput. Tree cmmnly used activated functins are lgistic, linear, tan. Since te expected utput is a cntinuus variable (nt a classificatin prblem wit unbunded functin), linear activatin functin (g(x)) is used (in-stead f lgistic sigmidal r. tan functins mstly used 48

fr classificatin prblems and fr biplar utput ranges, i.e., between - and +). Te frm f te linear activatin functin is as belw: g(x) = x g'(x) = 3. DETERMINATION OF OPTIMUM NUMBER OF ITERATION learning by te netwrk is cmputed by a factr called learning rate. In standard backprpagatin, t lw a learning rate makes te netwrk learn very slwly and t ig a learning rate makes te weigts and bjective functin diverge, leading t n learning at all. In te present case, since te training is cntinues (nn-batc type), te training rate can be maintained cnstant trugut te training. back prpagatin wit mmentum can be viewed as gradient descent wit smting. T stabilize te weigt trajectry by making te weigt cange a cmbinatin f te gradientdecreasing term plus a fractin f te previus weigt cange, a specific mmentum parameter is selected in any ANN arcitecture. Te rate f Te effect f number f iteratin n errrs (at different learning rates and mmentum parameters) fr varying number f idden ndes were studied and presented in Tables ( A t D) fr eac sub sectrs like BSEIT, BSECD and s n. Table : Te effect f learning rate, mmentum parameter, number f idden ndes and iteratin n errrs A: Learning Rate(LR)/ (MP) 0.0 50000 0 5000 Learning Rate(LR) 0.0 20 9000 30 0000 40 iteratin 0000 0.05 0. 0.5 0.9 40000 5000 8000 0000 0000 40000 0.008 5000 7500 0000 0000 5000 0.008 5000 0.008 7000 0.008 8000 0.008 0000 0.008 000 6000 6000 4000 3000 0.008 B: Learning Rate(LR)/ (MP) 0.0 0.05 0. 0.5 0.9 50000 0 20000 Learning Rate(LR) 0.05 20 40000 30 70000 40 iteratin 90000 75000 0.008 20000 30000 70000 0.008 85000 90000 20000 0.008 25000 60000 0.008 80000 0.008 000 0.0054 5000 0.008 8000 0.008 0000 0.008 50000 000 000 000 000 5000 0.005 0.008 49

C. Learning Rate(LR)/ (MP) 0.0 0.05 0. 0.5 0.9 000 0 5000 Learning Rate(LR) 0. 20 50000 30 25000 0.008 40 iteratin 25000 65000 0.03 5000 0.008 50000 0.007 20000 0.006 25000 0.007 65000 30000 0.005 50000 0.005 20000 0.007 25000 0.006 000 30000 0.005 50000 0.005 20000 0.005 25000 0.007 000 000 000 000 000 0.006 D. Learning Rate(LR)/ (MP) 0.0 0.05 0. 0.5 0.9 000 0 000 Learning Rate(LR) 0.7 20 000 30 000 40 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 Based n te analyses in te tables (A t D) it was fund tat te minimum number f iteratin fr different number f ndes suld be 000 fr minimum errrs. Te learning rate is mre tan 0.7 wit respect t iger mmentum parameters are diverges. Hence, if we assign te value f te learning parameters is less tan 0.7 at any mmentum values ten te minimum errr is btained trug neural netwrks. And als we predict tat at wat level eac sub sectrs t penetrate and influences t increase r decrease f te sare market index. Te fllwing bar diagram sws te percentage f influences f eac sub sectr t increase / decrease te sare market index. 50

Prbability f influencing BSE Index Prbability 0.8 0.6 0.4 0.2 Series 0 2 3 4 5 6 7 8 9 0 Script Numbers Figure 2 represents te bar diagram fr influencing scripts twards te Increment / Decrement f BSE Index. 4. ANN MODELING OUTPUT Te ANN mdel (develped based n te training data) wit 26 idden ndes (mnlayer) was fund t sw te least errr, wen cmpared wit te testing data, tereby resulting in maximum capture f te actual trend bserved in te field wit respect t te Indian BSE index. Fig. 3 sws te predictability f te ANN mdel in predicting te sare market price and Fig. 4 te crrelatin between actual BSE and predicated BSE btained by te mdel (swing a significantly ig crrelatin cefficient f abut 0.989). Predictability f Expected Return n Investment by different ANN Arcitectures Return n Investment 0000 8000 6000 4000 2000 0 5 9 372252933374 Series Series2 Time ( Assrted) Figure 3 : Series - Actual and Series 2 - Expected 5

8000.00 6000.00 Actual 4000.00 2000.00 2000.00 3000.00 4000.00 5000.00 6000.00 7000.00 8000.00 9000.00 Expected Figure 4, represents te Crrelatin between te actual and expected Return On Investment 5. BENEFITS Mst f te benefits in te articles depend n te prblem dmain and te NN metdlgy used. A cmmn cntributin f NN applicatins is teir ability t deal wit uncertain and rbust data. Terefre, NN can be efficiently used in stck markets, t predict te expected return n investment. It can be seen frm a cmparative analysis tat te Back prpagatin algritm as te ability t predict wit greater accuracy tan ter NN algritms, n matter wic data mdel was used. Te variety f data mdels tat exist in te papers culd als be cnsidered a benefit, since it sws NNs flexibility and efficiency in situatins wen certain data are nt available. It as been prven tat NN utperfrm classical frecasting and statistical metds, suc as multiple regressin analysis [0] and discriminant analysis. Wen jined tgeter, several NNs are able t predict values very accurately, because tey can cncentrate n different caracteristics f data sets imprtant fr calculating te utput. Analysis als sws te great pssibilities f NN metdlgy in varius cmbinatins wit ter metds, suc as expert systems. Te cmbinatin f te NN calculating ability based n euristics and te ability f expert systems t prcess te rules fr making a decisin and t explain te results can be a very effective intelligent supprt in varius prblem dmains [2]. 6 CONCLUSIONS Te studies reveal a ig ptential f ANN in predicting te return n investment in te sare market. Already, we knw te evaluatin f te return n investment in te sare market trug any ne f te traditinal tecniques [, 2, 3, 4, 5] (mstly statistical metds like time series analysis, mving averages etc.,) is tedius, expensive and a time-taking prcess. Again, te return n investment in sare market is always uncertain and ambiguity in nature, s tat n traditinal tecniques will give te accurate r apprpriate slutin. Hence, a nn-traditinal mdel wuld be f immense elp fr estimating te predictin n te return n investment accurately and tis metd gives better slutin always. Tis metd f predicting return n investment will elp furter t investigate tat te mdel can be extended t ANFIS (Artificial Neural Fuzzy Inference System), wic is based n te linguistic rules tat te fuzzy system culd design a rule and tese rules will be furter refined wit te elp f neural netwrks. REFERENCE [] Refenes, A.N., Zapranis, A., Francis, G., Stck Perfrmance Mdeling Using Neural Netwrks: A Cmparative Study wit Regressin Mdels, Neural Netwrks, vl. 7, N. 2, 994, pp. 375-388. 52

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