NEURAL NETWORKS AND INVESTOR SENTIMENT MEASURES FOR STOCK MARKET TREND PREDICTION

NEURAL NETWORKS AND INVESTOR SENTIMENT MEASURES FOR STOCK MARKET TREND PREDICTION SALIM LAHMIRI Deparmen of Compuer Science, UQAM, Monreal, Canada ABSTRACT Sof compuing mehods and various senimen indicaors are employed o conduc ou-of-sample predicions of he fuure sign of he sock marke. In paricular, we assess he performance of he probabilisic neural nework (PNN) agains he back-propagaion neural nework (BPNN) in predicing echnology socks and NYSE up and down moves. Geneic algorihms (GA) are employed o opimize he opologies of he BPNN. Our resuls from Granger causaliy ess show srong evidence ha all sock are srongly relaed o a leas one of he senimen variables. In addiion, he resuls from simulaions show ha he GA-BPNN is more capable of disinguishing beween marke ups and downs han he PNN. Finally, he simulaions show ha rading given decision rules (for example; buy sock if prediced reurn is higher han a given hreshold) yields o higher accuracy han predicing he sock marke ups and downs. Keywords: Arificial Inelligence, Classificaion, Sock Marke 1. INTRODUCTION Large profis can be earned by rading in sock markes. Therefore, invesors are highly ineresed in forecasing he fuure rend of sock marke indices and sock prices. The purpose of predicion is o reduce uncerainy associaed o invesmen decision making. However, forecasing sock markes is a challenging ask since he dynamics of he marke are very complex and nonlinear. For insance, many facors affec he sock marke such as business and economic condiions, poliical evens and invesor s expecaions. There is an abundan heoreical and empirical lieraure exploring he economics and he behaviour of sock markes. For insance, empirical finance has documened ha radiional asse-pricing which are based on saisical mehods such as he capial asse pricing model [1][2], he asse pricing model [3], and iner-emporal capial asse pricing model [4] all fail o explain and predic fuure sock. On he oher hand, behavioural finance provides an alernaive heory regarding financial markes. Based on experimenal psychology lieraure, behavioural finance considers ha cogniive biases could affec asse prices. Indeed, invesor senimen and limied arbirage are he main argumens on which he heory of behavioural finance relies. In paricular, he heory of invesor s senimen saes ha invesors make invesmen decisions according o heir senimens (emoions) insead of following a fully raional process. Then, sock prices could be affeced by senimen (irraional behaviour). Many papers in he field of behavioural finance documen he effec of senimen on sock markes [5-8]. Oher sudies invesigae he role of senimen variables in he predicion of sock and financial fuures. For example, [9-11] find ha senimen measures help predic on fuures. On he oher hand, [10] concludes ha invesor senimen may have significan effecs on he cross-secion of sock prices. In addiion, Baker and Wang [11] show ha he forecasing power of senimen measures is exremely limied once pas are included as predicors. Based on he invesor psychology, he behavioural finance lieraure has proposed many proxies of invesors senimen, including invesors surveys [12-14], invesor mood [15][16], muual fund flows [16][17], rading volume [17][19], reail invesor rades [20][21], and closed-end fund discoun [22-24] among ohers. In he previous works [5-24] linear saisical regressions were used o model and predic sock marke wih invesor senimen using in-sample daa. In his sudy we consider he problem of sock marke rend predicion. Indeed, predicing sock marke rends is a classificaion problem ha caegorizes markes as up and down moves, which is easier han he price variaion predicion as in [5-24]. 1

There have already been sudies looking a he direcion or rend of movemens of sock markes using BPNN [25-27] and PNN [28-33]. However, none of hese sudies provide a comparaive evaluaion of differen inelligen classificaion echniques regarding he abiliy o predic he sign of socks and index using senimen measures as inpus. Our conribuion is o use senimen measures in he predicion of daily rend of individual socks in ou-of-sample daa from he US echnology secor and sock marke index using neural neworks wih senimen indicaors. We rely on he echnology secor because invesors are srongly ineresed in invesing in high-echnology companies in he US and Europe since he lae 1999s and he lieraure does no conain work ha explores hese companies wih sof compuing echniques and using indicaors relaed o invesor psychology. The well known back-propagaion neural nework (BPNN) is geneically opimized o predic he up and down moves of socks, and i performance is compared o hose of he probabilisic neural nework (PNN). The BPNN is a feed-forward nework inroduced by Rumelhar [33]. Given inpu oupu pairs, he sysem is rained using back propagaion gradien descen wih momenum, and consequenly adjused o approximae any non-linear funcion, which make he sysem powerful in classificaion problems. On he oher hand, he PNN was proposed by Spech [34]. I is buil based upon he Bayesian mehod of classificaion. Indeed, he PNN employs Bayesian decision-making heory based on an esimae of he probabiliy densiy of he daa. The main advanage of he Bayesian mehod is o be able o classify a new sample wih he maximum probabiliy of success given a large raining se using prior knowledge [35]. The PNN combines he simpliciy, speed and ransparency of radiional saisical classificaion models and he compuaional power and flexibiliy of backpropagaed neural neworks [36]. According o Kim and Chun [37], PNN ouperforms back-propagaion in discovering local paerns in ime series, paricularly in he absence of noise. The res of he paper is organized as follows. Secion 2 describes he mehodology. Secion 3 oulines he simulaion resuls. Secion 4 concludes he paper. 3rd 2000 o December 31s 2008. The firs 80% observaions of he daa are used for raining and he remaining 20% is used for esing. For each company and he equiy index i, he reurn ime series are compued according o: R i, log( p i, ) log( p i, 1 ) where p is he closing price and is ime scrip. Figure 1 shows he reurn series..1.0 -.1 -.2 -.3 -.4.06.04.02.00 -.02 -.04 -.06 -.08 Apple Reurns General Elecric Reurns.12.08.04.00 -.04 -.08.03.02.01.00 -.01 -.02 -.03 -.04 -.05 Cisco Reurns NYSE Reurns Figure 1: Reurn series In his sudy, four measures of invesor senimen are used o predic fuure sock marke. The firs measure is he Volailiy Index (VIX) of he Chicago Board Opions Exchange [38] which is an esimae of he implied volailiy of S&P 500 index opions. The VIX is viewed as a fear index; ha is high (low) levels indicae bearish (bullish) senimen [10]. The second measure is he Sae Sree's Invesor Confidence Index (ICI) [39] ha measures he aiude of invesors o risk. Figure 2 exhibis he VIX and he ICI ime series. 120 100 80 60 40 20 2. METHODOLOGY In his sudy we uilize US daily ime series for he of hree companies (Apple, Cisco, and General Elecric) from he echnology secor and one equiy index (NYSE) from January 0 ICI VIX Figure 2: ICI, and VIX series 2

According o Hirshleifer [40], a lack of accurae informaion and greaer uncerainy abou socks leads o psychological biases. Moreover, Greaer informaion uncerainy is highly relaed o fuure sock [41]. Harris [42] and Godek [43] sugges ha he uncerainy abou he sock price should be esimaed using sock volailiy and rading aciviy. Indeed, senimen is relaed o high volailiy [8]. Consequenly, he log of volume series (Figure 3) and measures of he volailiy of reurn series are considered in our sudy as he hird and he fourh senimen indicaors respecively. In he nex sep, series are modeled by ARMA processes and APARCH models o esimae and exrac volailiy series. 8.5 8.0 7.5 7.0 6.5 6.0 8.8 8.4 8.0 7.6 7.2 6.8 6.4 Apple log-volume General Elecric log-volume 8.5 8.0 7.5 7.0 6.5 10.5 10.0 9.5 9.0 8.5 8.0 7.5 Cisco log-volume NYSE log-volume Figure 3: Log-volume series 2.1 Volailiy modeling and exracion To esimae he volailiy of socks and marke, he following mehodology is employed. Assuming ha R i, follows an ARMA(p,q) process, he condiional variance is modelled using he asymmeric power GARCH model APARCH (m,n) inroduced by Granger and Engle [44]. Firs, he mean equaion is esimaed: p q R i, s i R i i i i, 1, 1, 1 1, 1, 1 2 i, ~ 0, i, To idenify 1 he degrees p and q, we make use of he Akaike informaion crierion (AIC) and Schwarz crierion (SC) compued as follows [45]: AIC 2 T 2k T SC 2 T ( k logt ) T 21 log(2 ) log( ˆ ˆ T ) s s where k and T are respecively he number of coefficiens and sample size used for esimaion and is he error erm from he mean equaion. The APARCH (m,n) model is given by he following variance equaion: s, s m n s, js, j j1 i1 s, i s, i T s, i s, i where is he power parameer of he sandard deviaion and is a parameer ha capures asymmery effec up o a given order. In his sudy, is se o 1. The model APARCH is esimaed wih errors following a generalized exponenial disribuion (GED) which is inroduced by Subboin [46]. For insance, [47][48] found ha he ou-ofsample performance for he GARCH family models is worse wih normal disribuion. The orders m and n were arbirarily se o 1 and he obained parameers (,,,) are all saisically and highly significan 2. The APARCH (m,n) model provides hree ineresing advanages. The power parameer of he sandard deviaion can be esimaed wihin he variance equaion raher han imposed. Squared power ransformaion may lead o a sub-opimal model when he daa is non-normally disribued [49]. Moreover, he power erm is suiable o model volailiy clusering -low volailiy periods followed by high volailiy periods- by changing he imporance of he ouliers [50]. Finally, he volailiy series used are hose exraced from he APARCH (m,n) equaion. They are shown in Figure 4..0024.0020.0016.0012.0008.0004.0000.00035.00030.00025.00020.00015.00010.00005.00000 Apple Volailiy General Elecric Volailiy.0012.0010.0008.0006.0004.0002.0000.00028.00024.00020.00016.00012.00008.00004.00000 Cisco Volailiy NYSE Volailiy Figure 4: Volailiy series 1 The parameers (p,q,,,) are no repored, bu are available upon reques. 2 They are no repored, bu are available upon reques. 3

The five inpus (senimen indicaors) are firs seleced afer running Granger causaliy ess [51]. The Granger causaliy es allows considering only inpus which have a highly saisical causal effec on fuure sock. The es is based on bivariae regressions of he form: y y,0 x,0 y y,1 1 x x x,1 1... y y, k k... x x, k k x x,1 1 y y,1 1... x x, k k... y y, k k where and represen Gaussian disurbances. Then, F-saisics are compued as he Wald saisics for he join hypohesis: 1 2... k 0 The F-saisics allows esing wheher he coefficiens on he lagged x s are saisically significan in explaining he dependan y. In his sudy, he number of lags, k, was arbirarily se o 5. Table 1 provides he obained resuls for he Granger causaliy es for each sock. Only saisically significan inpus are repored. Table 1 Summary of pairwise Granger causaliy ess Null Hypohesis F-Sa Probabiliy Apple Volailiy does no Granger Cause VIX does no Granger Cause Cisco Volume does no Granger Cause VIX does no Granger Cause General Elecric VIX does no Granger Cause NYSE 3.98117 0.00134 2.07191 0.05609 3.4265 0.00435 3.29944 0.00568 6.65516 3.70E-06 ICI does no Granger Cause 2.42607 0.03337 Volailiy does no Granger Cause 9.18499 1.20E-08 VIX does no Granger Cause 5.01435 0.00014 2.2 The BPNN The BPNN inroduced by [33] has feed forward connecions and uses he back-propagaion algorihm opimized based on he gradiens mehod. The opology of he nework consiss of hree layers: an inpu layer, a hidden layer, and an oupu layer. All nodes of a layer are conneced o all he nodes in he nex higher layer. On he oher hand, here are no connecions among neurons in he same layer. Acivaion funcions are used in he hidden layers o inroduce non-lineariy ino he nework o approximae non-linear funcions. Indeed, i is he non-lineariy ha makes he BPNN powerful. The sigmoid funcions such as he logisic and hyperbolic angen funcions, and he Gaussian funcion are he sandard choices. The raining of a BPNN involves hree sages: he feedforward of he inpu raining paern, he calculaion and back-propagaion of he error, and he adjusmen of he weighs. In paricular, he adapaion of he weighs is derived based on he gradien descen mehod and error backpropagaion o minimize he error funcion E given by: E 0.5 k j 2 ( d j y j ) j 1 Here, y j and d j are respecively he acual and he desired oupu in each node j and k is he number of oupu neurons. The error is hen back-propagaed by he gradien descen hrough he nework by adjusing he new weighs according o his equaion: W ( ) E W W ( 1) Where W is he weigh change a ime and he parameers and are respecively he learning rae and he momenum coefficien. This laer, makes he convergence faser and he raining more sable. 2.3 The PNN Unlike he back-propagaion neural neworks, he probabilisic neural nework [34] requires only a single presenaion of each paern. The PNN employs an exponenial acivaion funcion raher han he sigmoid funcion ha is commonly used in he MLP. Then, a PNN can idenify nonlinear decision boundaries ha approach he Bayes opimal [52]. The basic nework opology consiss of four layers. The firs layer is he inpus layer. In he second layer, he probabiliy densiy funcion (PDF) of each group of paerns is direcly esimaed from he se of raining samples using [53] window approximaion mehod. The hird layer performs he summaion of all PDFs. Finally, he Bayesian decision is made in he fourh layer. In sum, he nework srucure of PNN is similar o back-propagaion neural nework; bu he main difference is ha he ransfer funcion is replaced by exponenial funcion and all raining samples are sored as weigh vecors. For insance, he PDF is assumed o follows a Gaussian disribuion. Then, 4

he PDF for a feaure vecor X o be of a cerain caegory A is given by: m 0.5 p p 1 2 f A X 1 2 m exp X X Ai X X Ai 2 i1 Where, p is he number of paerns in X, m is he number of he raining paerns of caegory A, i is he paern number, and σ is he smoohing facor of he Gaussian curves used o consruc he PDF. The value of σ is opimized during raining based on he cleares separaion of classes wih he highes classificaion rae [54-58]. 2.4 Geneic algorihms A geneic algorihm [59-62] was used o auomaically opimize he archiecures of he neworks. GA was used for hree reasons. Firs, he archiecural design is crucial o he success of a nework s informaion processing capabiliies [62]. Second, geneic search provides an advanage over exper experience in building neural neworks and also over consrucive and desrucive algorihms [63-64]. Finally, geneic algorihms allow he convergence speed of arificial neural neworks o be faser because of he search muliple iniial saes and he effec of muaion operaions [64]. The process of a geneic algorihm is ieraive and consiss of he following seps 3 : 1. Creae an iniial populaion of genoypes, i is a geneic represenaion of neural neworks, and nework archiecures are randomly seleced. 2. Train and es he neural neworks o deermine how fi hey are by calculaing he finess measure of each rained nework i. The finess funcion is calculaed as: fi 1 MSE i, where MSE is he mean squared error. 3. Compare he finess of he neworks and keep he bes op 10 for fuure use. 4. Selec beer neworks from each compleed populaion by applying he selecion operaor. 5. Refill he populaion back o he defined size. 6. Mae he genoypes by exchanging genes (feaures) of he neworks. 7. Randomly muae he genoypes according o a given probabiliy. 8. Reurn back o sep 2 and coninue his process unil sopping crieria (RMSE<) is reached. The iniial parameers of he BPNN o be opimized are described in Table 2. 3 Deailed comprehension of geneic algorihms is given in [62]. Table 2 Iniial parameer space of he geneic algorihm Hidden layers Neurons by each hidden layer Maximum 8 Acivaion funcions Linear, sigmoid, hyperang Size of iniial populaion 30 Selecion 0.50% Refill Cloning Maing Tail swap Muaions Random exchange a 0.25% Number of passes 20 Learning rae parameer range 0.4 Momenum rae parameer range 0.3 Sopping crierion 10 generaions Noes: sigmoid funcion is defined as sigmoid 1 1 e, anh e e e e hyperang funcion is defined as In order o predic he fuure rends of socks and he NYSE, he following model is approximaed using neural neworks: y i, f ( R i, 1, R i, 2, S i, 1 ) where R 4 is, S is a marix of senimen indicaors seleced following he Granger causaliy es, is an unknown funcion o be approximaed, y is he fuure rend, is ime scrip and i is he series o be modeled. All inpus (R and S) are sandardized o help he inelligen sysems o converge efficienly according o he following he ransformaion given by: x 2 x Maxx Minx Max x Minx The oupu is defined as follows: y i, 0 if R i, 0;1 if R i, 0 The previous definiion means ha he rading sraegy is buying sock if is prediced fuure reurn is posiive (fuure sock price is expeced o increase) and selling sock if is prediced fuure reurn is negaive (fuure sock price is expeced o fall). The ou-of-sample daily predicions were conduced and he predicion accuracy was measured. The accuracy is calculaed based on he number of correc classificaions (Hi Raio). The highes neural oupu of he nework indicaes he caegory or class he daa record falls ino. For example, 100% accuracy is where all records are properly classified and 0% accuracy is where none are properly classified. 4 Fuure rends are prediced wih pas reurn a -1 and -2 since all reurn series follows an ARMA(2,2) process. Indeed, all auoregressive coefficiens up o order wo were found o be saisically significan. 5

3. RESULTS AND DISCUSSION Firs of all, he Granger causaliy ess shows srong evidence ha senimen variables saisically cause shifs in sock. This is consisen wih [12][13] findings. Table 3 presens he correc classificaion raes from he wo sysems. In erms of predicion accuracy, he GA- BPNN has he highes hi raio (55.75%) in predicing he sign of fuure reurn, while he bes hi raio obained by PNN is 52.83%. On he oher hand, he lowes hi raios were 48.14% and 53.32% obained by PNN and GA-BPNN respecively. As a resul, he GA-BPNN ouperforms he PNN in all socks including he NYSE. Alhough he predicion accuracy is low, he overall resuls are ineresing since some previous sudies repored ha sock prices are approximaely close o he random walk process and; consequenly; an accuracy of 56% in he predicions is a saisfying resul for sock forecasing [65-68]. Table 3: Ou-of-sample classificaion accuracy in % PNN GA-BPNN Apple 51.95 55.75 Cisco 48.14 54.34 GE 52.30 54.69 NYSE 49.96 53.32 According o empirical behavioural finance, high impulsiviy invesors and invesors wih high confidence in he fuure are more likely o ake financial risks [69][70]. Among many possible reasons for fuure risk aking is fully subsiuable socks o purchase. Indeed, in many siuaions invesors ac as if hey exrapolae a posiive price rend by overbuying winners [71]. In addiion, invesors who exrapolae rends in sock prices are likely o follow a momenum invesmen sraegy and buy winners [72][73]. In paricular, if momenum invesmen sraegy is adoped hen invesors are more likely o buy shares ha have a higher value [74]. Then, in order o improve he predicion of he fuure rend in echnology socks and he NYSE, a rading rule is defined o buy socks. For insance, he oupu is defined according o hree sraegies as follows: Sraegy.1: y i, 0 if R i, 1%;1 if R i, 1% Sraegy.2: y i, 0 if R i, 1.5%;1 if R i, 1.5% Sraegy.3: y i, 0 if R i, 2%;1 if R i, 2% The previous oupu definiions allow invesigaing he relaionship beween rading rules (buying he sock if he expeced rend is up more han s %) and he performance of he neural nework sysems. The forecasing performance of each rained sysem was compared and analyzed depending on he rading sraegy. The resuls obained from simulaions are given in Table 4. Table 4 Classificaion accuracy (in %) given rading rules Sysems GB GB GB PNN PNN PNN Rules 1% 1.50% 2% 1% 1.50% 2% Apple 82.65 86.36 94.60 80.97 86.27 94.51 Cisco 84.60 91.33 95.31 83.36 90.09 94.16 GE 92.39 96.55 98.67 91.59 96.02 98.41 NYSE 97.79 98.67 99.47 97.52 98.58 99.38 GB is GABPNN. The simulaions show ha he performance of he sysems improves when he rading rules are considered. The lowes and he highes hi raios for he PNN are 82.65% and 99.47%. On he oher hand, lowes and he highes hi raios for he GA-BPNN are 80.97% and 99.38%. The lowes hi raios are obained wih Apple given 1% decision rule and he highes hi raio is obained wih NYSE given 2% decision rule. Recall ha he lowes and highes accuracy raes obained when he rading rule is 0% are respecively 48.14% for he PNN and 53.32% for he GA-BPNN. Then, a predicive sysem based on defined decision rules (buy sock if prediced up is more han s %) performs much beer han a predicive sysem ha predics boh fuure direcions: up and down. Moreover, he performance of he sysems increases wih he rading rules: an increase in he decision rule leads o an improvemen in he performance of he sysems. Finally, he simulaions confirm ha he GA-BPNN is suiable for sock marke rend predicion han he PNN since i achieves higher accuracy in all socks and all sraegies. Previous sudies have shown ha PNN provide good classificaion raes han radiional BPNN in many differen applicaions [75][76]. However, our findings show he superioriy of GA- BPNN over PNN. Indeed, he PNN has a fixed opology and; on he oher hand; he opology of he BPNN is opimized using geneic algorihms in his sudy. This could explain why BPNN ouperforms he PNN. Thus, he role of geneic algorihm is 6

imporan in opimizing he BPNN archiecure and achieving higher performance. This is consisen wih [62]. Also, he reason ha GA-BPNN ouperforms he PNN in his sudy is ha PNN is sensiive o noisy daa such as financial ime series. Finally, i is imporan o menion ha faser han GA-BPNN wih similar classificaion accuracy for up rend deecion, he PNN would be more appropriae in real ime applicaions when rading sraegies are considered. 4. CONCLUSION Predicing sock marke rends is a classificaion problem ha caegorizes markes as up and down moves, which is easier han price predicion. There are several neural nework archiecures and saisical mehods o perform classificaion asks. In his paper, wo differen neural nework archiecures are used o predic fuure rends of he NYSE and hree socks from he echnology secor. The neural neworks are he Back-Propagaion neural neworks (BPNN) and he Probabilisic Neural Nework (PNN). Geneic algorihms (GA) are used o opimize he opology of he BPNN. Invesor senimen measures are used as inpus o he neural neworks. Firs, Granger causaliy ess are applied o idenify which measures are saisically relaed o each company and equiy marke index. Similar o prior sudies, our findings show ha individual sock are highly relaed o he senimen of he invesor according o Granger causaliy ess. Second, sof compuing echniques arificial neural neworks - are employed o model and predic he fuure sign of sock and he marke. The simulaions show ha he GA-BPNN is suiable for sock marke rend predicion han he PNN since i achieves higher accuracy in all socks and in all sraegies. According o financial heory, invesors seek o maximize heir final wealh. And, according o empirical behavioural finance; when a momenum invesmen sraegy is adoped invesors are more likely o buy shares ha have a higher value. Therefore, i is ineresing o design inelligen sysems o predic fuure up rends based on suiable rading rules. The resuls show ha rading given decision rules (buy a sock if prediced reurn is higher han a given hreshold) yields o higher accuracy han rading on he basis of prediced rend up or less han 0%. For fuure research i is suggesed o compare he predicion accuracy of neural neworks sysems and suppor vecor machines (SVM). More imporanly, i is suggesed o design and implemen an ensemble sysem. In addiion, i would be ineresing o ake ino accoun boh economic variables and echnical indicaors along wih senimen measures o predic sock marke fuure rends. REFRENCES: [1] W.F. Sharpe. Capial asse prices: A heory of marke equilibrium under condiions of risk. Journal of Finance 19 (1964), 425-442. [2] J. Linner. The valuaion of risk asses and he selecion of risky invesmens in sock porfolios and capial budges. Review of Economics and Saisics 47 (1965), 13-37. [3] S. Ross. The Arbirage Theory of Capial Asse Pricing. Journal of Economic Theory 13 (1976), 341-360. [4] R.C. Meron. An Ineremporal Capial Asse Pricing Model. Economerica 41 (1973), 867-887. [5] J.B. De Long, A. Shleifer, L.H Summers and R.J Waldmann. Noise rader risk in financial markes, Journal of Poliical Economy 98 (1990), 703-738. [6] K.L. Fisher and M. Saman. Invesor Senimen and Sock Reurns. Financial Analyss Journal 56 (2000), 16-23. [7] M. Baker and J. Wurgler. Invesor Senimen and he Cross-Secion of Sock Reurns. Naional Bureau of Economic Research,Working Papers 10449, 2004. [8] M. Baker and J. Wurgler. Invesor Senimen and he Cross-Secion of Sock Reurns. Journal of Finance 61 (2006), 1645-1680. [9] R.S. Neal and S.M. Whealey. Adverse selecion and bid-ask spreads: Evidence from closed-end funds. Journal of Financial Markes 1 (1998), 121-149. [10] D.P. Simon and A. Roy. Wiggins III. S&P Fuures Reurns and Conrary Senimen Indicaors. The Journal of Fuures Markes 21 (2001), 447 462. [11] C. Wang. Invesor Senimen and Reurn Predicabiliy in Agriculural Fuures Markes. The journal of Fuures Markes 21 (2001), 929-952. [12] G.W. Brown and M.T Cliff. Invesor Senimen and Asse Valuaion. Journal of Business 78 (2005), 405 40. [13] M. Lemmon and E. Porniaguina. Consumer Confidence and Asse Prices: Some Empirical Evidence. Review of Financial Sudies 19 (2006), 1499 1529. 7

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