Mutual Fund Performance Evaluation System Using Fast Adaptive Neural Network Classifier

Transcription

1 Fourh nernaonal Conference on Naural Compuaon uual Fund Performance Evaluaon Sysem Usng Fas Adapve Neural Nework Classfer Kehluh Wang Szuwe Huang Y-Hsuan Chen Naonal Chao ung Unversy Naonal Chao ung Unversy Chung Hua Unversy Absrac Applcaon of fnancal nformaon sysems requres nsan and fas response for connually changng marke condons. he purpose of hs paper s o consruc a muual fund performance evaluaon model ulzng he fas adapve neural nework classfer (FANNC, and o compare our resuls wh hose from a backpropagaon neural neworks (BPN model. n our expermen, he FANNC approach requres much less me han he BPN approach o evaluae muual fund performance. RS s also superor for FANNC. hese resuls hold for boh classfcaon problems and for predcon problems, makng FANNC deal for fnancal applcaons whch requre massve volumes of daa and roune updaes.. nroducon uual funds are popular nvesmen vehcles n he modern world. o evaluae a fund s performance, numerous measures have been devsed. For example, he Sharpe ndex [7], Jenson ndex [0] and reynor ndex [22] are all used wdely n he marke, and many nvesors place grea mporance on a fund s rankng n hese measures. However, evaluaons for muual funds are mosly made perodcally n weeks or even n monhs, makng useful only for comparng hsorcal performance. o cach up wh he fas changng marke condons, an evaluaon sysem should be able o updae new saus consanly and whenever a reques by he user. eanwhle, alhough hese ndces are frequenly adoped for performance evaluaons, hey do no provde predcve varables, and so canno be used drecly n forecasng superor muual funds. o address hs problem, researchers have explored varous approaches. n parcular, evaluaon mehods based upon arfcal neural neworks (ANN have been he focus of sgnfcan developmen, as he forecasng and calculang ables of ANN are superor o radonal algorhms n many respecs [5,20,5]. Backpropagaon neural neworks (BPN s an ANN model wdely used n fnance wh a supervsed neural nework whch can analyze connuous daa [9]. Udo [23] dscusses a BPN model beer n bankrupcy classfcaon han sascal mehods. Davalos, Gra and Chow [6] ulze BPN o predc he bankrupcy rsk of major US ar carrers, whle Surkan and Sngleon [2] use BPN o mprove bond rang. ul-layer perceprons (LP s appled o predc muual fund performance by ndro, Jang, Pauwo and Zhang [9] and hey subsequenly oban beer forecasng resul n blended funds, bu no for growh funds. Ahn, Cho and Km [] propose a hybrd nellgen sysem ha predcs he falure of frms based on pas fnancal performance daa by combnng a rough se approach wh LP. Lam [4] nvesgaes he ably of backpropagaon neural neworks o negrae fundamenal and echncal analyss for fnancal performance predcon. Alhough BPN s commonly appled n fnancal sudes, has some lmaons he ranng cos s frequenly oo hgh, local mnma ofen mslead he resul, and onlne learnng s mpossble. here are oher ypes of ANN models desgned for classfcaon problems whch elmnae he drawbacks of BPN, such as he Self Organzaon ap (SO [2,6] and Adapve Resonance heory (AR [4] famles. Unlke BPN, hese ypes of neural models can be raned quckly and can classfy a new unknown paern whou accurae nformaon. However, mos of hem are unsupervsed models, a characersc whch lms her applcaons n fnancal felds. FANNC s a new approach o neural neworks derved by Zhou, Chen and Chen [24]. s algorhm seems parcularly suable for nsan and fas response o he connually changng fnancal marke condons. he mehod s based on adapve resonance heory and feld heory. AR can perform onlne learnng and work under a non-saonary world. he Coulomb poenal model for elecrosac forces provdes he bass for he feld heory approach o arfcal neural neworks. enables one-pass learnng and can perform real-me supervsed learnng a hgh speed. FANNC s a four-layer srucured neural nework wh he archecure llusraed n Fgure. he funcon of he feedback connecons s o ransfer an acve sgnal o /08 $ EEE DO 0.09/CNC

2 each successve layer n order o mplemen compeon and resonance. fourh layer (oupu layer hrd layer (hdden layer second layer (hdden layer frs layer (npu layer Fgure FANNC archecure FANNC ncorporaes he concep of he aracng basn, represened n feld heory as he elecrc feld produced by he raned nsance. Each second-layer un defnes an aracng basn by he responsve ceners and he responsve characersc wdhs of he Gaussan weghs conneced wh hem. hese second-layer uns are used o classfy npus nernally, whle he hrd-layer uns are used o classfy oupus nernally. n hs sudy, we adop FANNC o evaluae muual fund performance and compare he resuls wh hose from BPN. npu and oupu nsances are dscussed n secon 2. he ranng process and he resuls are provded n secon 3. n secon 4, we compare and analyze he resuls. Secon 5 concludes. 2. Preparng npu and Oupu nsances 2. Raw daa preparaon he muual funds lsed n awan Economc Journal (EJ daabase are used as npu nsances for our expermen. n order o ge some dealed nformaon from he sample funds, we selec hree hsorcal perods: , and so he concerns of confdenaly abou he daa wll no arse. Raw daa colleced from hese nsances are hen calculaed o provde he npu varables for our models. n he followng secons hese daa are processed perod by perod. 2.2 npu nsances any facors ha affec muual fund performance such as he sze of he muual fund and some of he manager s characerscs have been suded n pror leraure [2,3]. n hs sudy, we focus on he manager s momenum sraeges and herdng behavor as he npu varables appled n FANNC and BPN omenum sraeges omenum nvesors buy socks ha were pas wnners and sell socks ha were pas losers [8]. On measurng he momenum, Grnbla, Sherdan and Wermers [7] sugges he followng equaon: ( k w, w, R (, k+ where w, s he porfolo wegh on secury a dae, R s he reurn of secury (,,N from dae, k + k o dae k +, wh k as he lag ndex. he wo mos recen benchmark daes are represened by k and k 2. hey may be he major facors ha affec he momenum of he fund. We refer as lag- momenum (L and 2 as lag-2 momenum (L2. Furhermore, we can decompose he L no buy and sell pars. he equaons are: (2 B S ( w w,, ( R, w > w,, (3 w < w,, ( w w,, ( R, We subrac he mean from he reurn n order o have measures ha approach zero under no momenum nvesng. Smlar o he lag- momenum measures, he buy and sell pars of he lag-2 momenum measure are: B ( w w ( R (4 2,,, 2 S w > w,, (5 ( w w ( R,,, w > w,, Herdng behavor Herdng behavor s a rade endency n whch muual fund managers buy and sell he same socks n he same perod. Recenly nsuonal herdng behavor aracs some neress n academcs as well as n professonals [,8]. here are hree measuremens of herdng behavor. he frs one s unsgned herdng measure (UH presened by Lakonshok, Shlefer, and Vshny [3]. UH measures he average endency of all managers eher o buy or o sell a parcular sock a he same me. Namely, UH p E p (6,,, where p, equals he proporon of he muual funds ha purchase sock durng quarer, and p, he expeced value of p,, s he mean of p, over all socks durng quarer. UH can no dfferenae a manager s herdng beween sellng and buyng he socks. Grnbla, Sherdan and Wemers [7] propose he sgned herdng measure (SH whch provdes an ndcaon of wheher a fund s 480

3 followng he crowd or gong agans he crowd for a parcular sock durng he specfed perod. SH,, UH, E[, UH, ] (7 where, s an ndcaor for buy or sell herdng. s defned as follows:, 0 f p, < E p,, f p, > E p, and he muual fund s a buyer of sock durng quarer, or f ( p, > E p, and he fund s a seller of sock., f p, > E p, and he muual fund s a seller of sock durng quarer, or f ( p, > E p, and he fund s a buyer. SH, s se o be zero f fewer han 0 funds rade sock durng perod. f he number of funds radng sock s small, no meanngful way can ndcae wheher he fund s herdng or no. Fnally, he herdng measure of a muual fund (FH s hen calculaed by subsung he sgned herdng measure n place of he sock reurn n equaon (. n FH ( w w,, SH (8, where w, s he proporon of he funds radng sock durng quarer. 2.3 Oupu nsances We use wo ses of oupu nsances n our performance evaluaon models o sudy he classfcaon capably and he predcve power of FANNC. n he former case, he oupu s he Sharpe ndex calculaed for he same perod n whch he momenum and herdng measures are deermned. We denoe hs as he classfcaon case. n he laer case, we use as he oupu nsance he Sharpe ndex calculaed for he nex monh rgh afer he perod for momenum and herdng measures. s labeled he predcon case. he oupu nsances are calculaed as follows: Classfcaon Sharpe ndex: R Sharpe ndex f (9 Predcon Sharpe ndex, + R f (0 Sharpe ndex where R : he average monhly reurn for fund n he, calculaon perod. + R : he reurn of fund for he monh afer he calculaon perod. R f : he average monhly rsk-free rae represened by he -year CD rae of commercal bank. : he sandard devaon of he reurn of he fund over he calculaon perod. 3. ranng and esng Process All he npu and oupu nsance pars dscussed n he las secon are dvded no wo pars. 80% of hem are used for ranng and 20% are for esng. 3. Backpropagaon neural neworks We apply Neural Connecon by SPSS o mplemen he backpropagaon neural neworks (BPN algorhm. Before ranng he nework, we frs se he sop creron, learnng coeffcen and momenum coeffcen. For sop creron, we lm he maxmum epochs o 3000 mes as our expermen ndcaes ha he roo mean square (RS sablzes by hs me. o deermne he learnng and momenum coeffcens, he sofware ess several pars and chooses he mos effecve one auomacally afer ranng. n hs sudy, hs opmzaon process resuls n a value of 0. for he learnng coeffcen and a value of 0.9 for he momenum coeffcen. Nex, we decde he acvaon funcon. he sofware offers us wo choces: sgmod funcon or hyperbolc angen funcon. Afer ranng and esng, we fnd no remarkable dfferences beween he wo and we choose he sgmod funcon as s wdely used n he leraure of BPN. o enhance he accuracy of BPN, we normalze he npu and oupu nsances by he sandard normalzaon mehod. x μ f ( x ( where x s he normalzed varable, μ s he mean of x, and s he sandard devaon of x. n a manner smlar o he denfcaon of he learnng and momenum coeffcens, he sofware deermnes he number of layers and nodes auomacally. also adjuss he nework srucure accordng o he npu and oupu nodes. n hs sudy, he archecure we oban s a 7-4- nework. When we npu he nsances no nework, he feedng sequence and he selecon of esng nsances are arranged randomly. Afer he ranng, he sofware repors he RS whch s calculaed from nsances. 3.2 FANNC As here s no commercal package readly avalable o 48

4 mplemen FANNC, we use C++ o program he algorhm. here are seven varables o be deermned n FANNC: responsve cener θ j, responsve characersc wdh α j, responsve cener adjusmen sep δ, bas, he leakage compeon hreshold n he second layer, he ouer layer smlary conrol coeffcen Err, and he nner layer smlary conrol coeffcen Errc u. When a new node n he second layer s generaed, s relaed responsve cener s se o he value of npu componen n curren nsance under ranng, and he responsve characersc wdh s se o be he defaul value, When hs value ncreases slghly, he predcve ably of he nework wll ncrease; however, excessve ncrease n he responsve characersc wdhs wll decrease he predcve ably. he value for responsve cener adjusmen sep, δ, affecs he learnng speed of he nework and usually adops a value beween 0 and.0. n hs paper, we choose he value o be 0.0. he leakage compeon hresholds n he second layer, Err and Errc u play smlar roles, as boh deermne how many new nodes wll be generaed n a raned nework. When Err ncreases, he nework ends o adjus s θj and α j nsead of generang new nodes n he second and he hrd layers. ncreasng Errc u wll ncrease he probably ha only one new node s appended o he second layer and decrease he probably ha wo new nodes are appended o he second and he hrd layers smulaneously. he number of he nodes n he second and he hrd layers deermnes he predcably of he model and s ably o memorze he raned nsances. n general, he predcably wll decrease and he error from memorzng wll ncrease when he node number ncreases. Zhou, e. al. [24] sugges ha he leakage compeon hreshold be 0.8 and he maxmum permssble error 0.. he archecure of FANNC s composed of seven npu uns and one oupu un. he hdden layer uns are generaed dynamcally. n hs research, we ulze he regresson funcon of FANNC o evaluae he muual fund performance. Lke n BPN, npu and oupu nsances are normalzed by he sandard procedure. eanwhle, feedng sequence and he selecon of esng nsances are arranged randomly. BPN. able he resuls of Classfcaon es Sample number FANNC BPN Perod ranng esng RS me* RS me* < < < *ncludng ranng me and esng me. Uns are n seconds. able 2 he resuls of predcon es Sample number FANNC BPN Perod ranng esng RS me* RS me* < < < *ncludng ranng me and esng me. Uns are n seconds. RS from FANNC s sgnfcanly lower han hose from BPN, ypcally by a facor of wo or hree. As for processng me, FANNC consumes less han one second, whle BPN requres a leas 6 seconds. hs dfference n process me wll only become more sgnfcan as he number of samples ncreases. Fgure 2 depcs he scaer dagram of classfcaon RS. os of he pons are dsrbued around he 45 degree lne. However, we see ha he pons from FANNC are more concenraed and closer o 45 degree lne when compared wh he resuls generaed by BPN. hs mples ha he FANNC approach has hgher accuracy n Sharpe ndex classfcaon han he BPN approach. hese resuls are smlar n he predcon case, as shown n fgure 3. Lke before, FANNC pons are more concenraed and closer o 45 degree lne. n addon o he advanages n me consumpon and RS accuracy, FANNC s superor o BPN for fnancal applcaons n oher aspecs as well. Frs, FANNC s equpped wh a real-me learnng capably. When we oban a new nsance, re-ranng s no necessary, so n pracce, we can use he algorhm o monor a dynamc daabase. When he daabase s changed, he nework wll check wheher he new nsance can be classfed by any exsng aracon basn. f no, wll creae a new one. eanwhle, f he raned nework fals o classfy a new npu, can memorze and reclassfy laer afer more nsances are avalable. 4. Resul Comparson able and able 2 provde he comparson of RS and he processng me beween he FANNC approach and he BPN approach. For boh he classfcaon case and he predcon case, FANNC s clearly superor o 482

5 Oupu BPN -0.5 arge Fgure 2 RS n classfcaon case, Oupu FANN arge C Fgure 3 RS n predcon case, Concluson FANNC he purpose of hs paper s o consruc a flexble and responsve muual fund performance evaluaon sysem ulzng FANNC, and compare he resuls wh hose from BPN based model. FANNC s a newly developed neural nework whch combnes he feaures of AR and feld heory. n our expermen, FANNC no only requres sgnfcanly less me o evaluae muual fund performance han he BPN approach bu also has a superor RS record. hese resuls hold for boh classfcaon problems and predcon problems. Furhermore, he algorhm n FANNC assures fas processng me and easy on-lne learnng, hus makng FANNC deal for fnancal applcaons nvolvng massve volumes of daa and roune updaes. 6. References []. Ahn, B. S., S.S. Cho and C.Y. Km (2000, he negraed ehodology of Rough Se heory and Arfcal Neural Nework for Busness Falure Predcon, Exper Sysems wh Applcaons, 8, pp [2]. Brown, S.J. and W.N. Goezmann (995, Performance Perssence, Journal of Fnance, 4, pp [3]. Carhar,.. (997, On Perssence n uual Fund Performance, Journal of Fnance, 52, pp [4]. Carpener, G..A. and S. Grossberg (987, A assvely Parallel Archecure for a Self-Organzng Neural Paern Recognon achne, Compuer Vson, Graphcs, and mage Processng, 37, pp [5]. Chang, W.C. and G.W. Baldrdge (995, "A Neural Nework Approach o uual Fund Ne Asse Value Forecasng." Omega. November 995. p [6]. Davalos, S., R.D. Gra and G. Chow (999, he applcaon of neural nework approach o predcng bankrupcy rsks facng major US ar carrers: , Journal of Ar ranspor anagemen, 5, pp [7]. Grnbla,.,. Sherdan and R. Wermers (995, omenum nvesmen Sraeges, Porfolo Performance, and Herdng: A Sudy of uual Fund Behavor, he Amercan Economc Revew, 85(5, pp [8]. Hameed, A. and Y. Kusnad, (2002, omenum Sraeges: Evdence from Pacfc Basn Sock arkes, Journal of Fnancal Research, Vol. 25, pp [9]. ndro, D.C., C.X. Jang, B.E. Pauwo and G.P. Zhang (999 Predcng uual Fund Performance Usng Arfcal Neural Neworks, he nernaonal Journal of anagemen Scence, Vol.27, pp [0]. Jensen,. C. (968, he Performance of uual Funds n he Perod, Journal of Fnance, 23, pp []. Km, K. A. and J. R. Nofsnger, (2005, nsuonal Herdng, Busness Groups, and Economc Regmes: Evdence from Japan, Journal of Busness, Vol. 78, no.. [2]. Kohonen,. (989, Self-organzaon and Assocave emory, Sprnger-Verlag Press, Breln. [3]. Lakonshok, J., A. Shlefer and R. Vshny (992, he mpac of nsuonal radng on Sock Prce, Journal of Fnancal Economcs, 32, pp [4]. Lam.. (2004, Neural nework echnques for fnancal performance predcon: negrang fundamenal and echncal analyss, Decson Suppor Sysems, 37, pp [5]. Ray, P. and V. Vna, (2004, "Neural Nework odels for Forecasng uual Fund Ne Asse Value", 8h Capal arkes Conference, ndan nsue of Capal arkes Paper [6]. Serrano-Cnca, C. (996, Self Organzaon Neural Neworks for Fnancal Dagnoss, Decson Suppor Sysem, 7, pp [7]. Sharpe, W. F (966, uual Fund Performance, Journal of Busness, 39, pp [8]. Sas, R. W., (2004, nsuonal Herdng, he Revew of Fnancal Sudes, Vol. 7, No., pp [9]. Smh, K.A. and J. Gupa (2000, Neural Nework n Busness: echnques and Applcaons for he Operaon Researcher, Compuers and Operaon Research, 27, pp [20]. Sern, H. S. (996, Neural Neworks n Appled Sascs, echnomercs, 38, pp [2]. Surkan, A. J., and J.C. Sngleon (989, Neural Neworks for Bond Rang mproved by ulple Hdden Layers, JCNN-89, pp [22]. reynor, J. L. (965, How o Rae anagemen of nvesmen Funds, Harvard Busness Revew, (3, pp [23]. Udo G., (993, Neural Nework Performance on Bankrupcy Classfcaon Problem., Compuer and ndusral Engneerng, 25, pp [24]. Zhou, Z., S. Chen and Z. Chen, (2000, FANNC: Fas Adapve Neural Nework Classfer, Knowledge and nformaon Sysem, 2, pp