IIMK/WPS/121/FIN/2013/07. Abhilash S. Nair 1

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1 IIMK/WPS/2/FIN/203/07 EXISTENCE OF CAPITAL MARKET EQUILIBRIUM IN THE PRESENCE OF HERDING AND FEEDBACK TRADING Abhilsh S. Nir Assistnt Professor, Indin Institute of Mngement Kozhikode, IIMK Cmpus PO, Kozhikode , emil:

2 EXISTENCE OF CAPITAL MARKET EQUILIBRIUM IN THE PRESENCE OF HERDING AND FEEDBACK TRADING This pper ttempts to estblish the existence of equilibrium, in n sset mrket inhbited by two representtive investors with different risk versions. In order to cpture heterogeneity in informtion nd welth, the pper segments the investor popultion into two: (i) Individul investors nd (ii) Institutionl investors. Bsed on prior literture, the present study posits tht Institutionl investors demonstrte rtionl intentionl herding nd positive feedbck trding (buy when the mrkets rise nd sell when it flls) nd individul investors demonstrte negtive feedbck trding (vice vers). In other words, when the mrkets re (monotoniclly) incresing, institutionl investors, expecting the trend to continue would buy more, thus demonstrting decresing bsolute risk version. Similrly, when the mrket is (monotoniclly) decresing he will try to stem his loss s soon s possible, demonstrting incresing bsolute risk version. Such n investment behvior is cptured in power utility function. Further, negtive feedbck trding by individul investors implies tht when mrket is (monotoniclly) incresing individul investors, expecting the trend to reverse, would sell. Thus demonstrting incresing bsolute risk version. And when the mrkets re (monotoniclly) decresing, they would hold on to their investments expecting better times to come, thus depicting decresing bsolute risk version. Such investment behvior is cptured by qudrtic utility function. Given their welth nd investment behvior, the two investor groups would trde with ech other such tht the mrket clers. To the best of our knowledge this is the first pper tht proposes sset pricing model tht not only llows for behviourl bises but lso for heterogeneous gents who re ffected differently by these bises. This pper estblishes the bounds for the bsolute risk version function nd the shdow rte of interest t which the two investor groups will lend money to ech other to enble trding nd mrket clering. For resonble endowments nd presumed behviourl bises s implied by the chosen utility function, numericl exmple t the end of this pper shows tht the mrket clering interest rte (t which the investors would lend to nd borrow from ech other) occurs between 5.5% nd 28.05%. Key Words: Heterogenous Agents, Herding, Feed bck trding, shdow rte of interest. JEL Clssifiction: G2, C62, D53 INTRODUCTION Since Shrpe (965), Lintner (966) nd Mossin (967), there hve been lot of ttempts to rrive t more ccurte sset pricing models. While the initil Asset Pricing Models (APMs) ssumed tht ll investors in the mrket hve the sme expected returns nd these re constnt cross time. The Stochstic Discount Fctor (SDF) pproch to sset pricing tries to relx this ssumption. The initil SDF 2 bsed APMs ssumed tht ll mrket prticipnts hve equl ccess to informtion, equl welth nd thus similr ssessment of risk nd expected returns. Given this ssumption, the sid SDF bsed APMs llowed for time vrition in expected 2 SDF is the discounted rtio of mrginl utility (of representtive investor) t time t+ to tht t time t 2

3 returns. The lter SDF bsed APMs llowed for heterogeneity in informtion, welth, risk ssessment nd hence expected returns, such s: (i) APMs with gents who re constrined for resources (Constntinides nd Duffie, 996) nd (ii) APMs with gents who re constrined for informtion (Admti, 985). Though the heterogeneous gent APMs re closer to how the mrkets work in relity, these models ssume tht investors re rtionl under ll circumstnces. Recently, this ssumption hs come under hevy criticism from the behviorists who rgue tht there exists nonstndrdized investor behviour which is driven by irrtionlity. In other words, the investor my not ct rtionlly under ll circumstnces. The present pper, while ttempting to sty within the Arrow-Debreu frmework, tries to incorporte two of the cognitive bises, identified in existing literture: (i) Herding nd (ii) Feedbck Trding in the investment behviour of mrket prticipnts. Bsed on recent literture, it hs been conjectured tht s compred to institutionl investors, individuls re less informed nd more vulnerble to psychologicl bises (Kniel et. l., 2008, Brber nd Oden, 2008). Accordingly, the pper segments investor popultion into two: (i) Individul investors nd (ii) Institutionl investors nd posits tht while institutionl investors demonstrte rtionl intentionl herding nd positive feedbck trding (Nofsinger nd Sis, 999), individul investors demonstrte negtive feedbck trding (Shefrin nd Sttmn, 985). Such investment behvior, demonstrted by institutionl nd individul investors, is cptured by specifying power (institutionl investor) nd qudrtic (individul investor) utility function. When these two investor types trde competitively by borrowing nd lending money to ech other, the lloction of welth fluctutes rndomly between them. The chllenge here is to find the shdow rte of interest (t which the two investors borrow nd lend) such tht equilibrium sset price exists. To our knowledge this is the first pper ttempting to build in rtionl herding nd feedbck trding into rtionl sset pricing models. For resonble endowments nd presumed behviourl bises s implied by the chosen utility function, numericl exmple t the end of this pper shows tht the mrket clering interest rte (t which the investors would lend to nd borrow from ech other) occurs between 5.5% nd 28.05%. BACKGROUND TO THE STUDY As stted erlier, in order to cpture heterogeneity in informtion nd resources, the present pper segments the investor popultion into two: (i) Individul investors nd (ii) Institutionl investors. These two ctegories of investors differ in their investment behvior primrily on the following premises: 3

4 (i) Agent principl reltion: Institutions mnge funds provided to them by investors. Since the people who mnge the funds re not the people who own them, the likelihood of gency problem is very high. One proposed solution is to link the fund mngers compenstion to its performnce. However, in doing so, gents my t times tke decisions tht my not be in the best interest of owners (Guerrieri nd Kondor, 2009). In the cse of individul investor since the owner nd mnger of funds is the sme individul, there is no gency problem. (ii) Legl Environment: As compred to individul investors, institutionl investors fce reltively stricter regultory environment with regrd to cpitl requirements, redemptions, investment strtegies etc. (iii) Liquidity nd trnsction cost: Institutionl investors churn their portfolio much more frequently s compred to individuls (Schwrtz nd Shpiro, 992). Hence, they would be more sensitive to trnsction costs, especilly if the sset is not liquid. The response of individul nd institutionl investors to new informtion would differ bsed on their ccess to informtion nd their vulnerbility to psychologicl bises. The pper llows for (rtionl intentionl) herding nd feedbck trding. (i) Herding: It is witnessed when group of investors trde in the sme wy over period of time. Herding cn be purely ccidentl becuse of rrivl of correlted informtion to independently cting investors. Such herding is clled spurious herding (Bhikchndni nd Shrm, 200). Herding cn lso be intentionl evolving from interctive observtion of ctions nd pyoffs of other mrket prticipnts. Two lterntive explntion of such intentionl herding re:. Investor Psychology: Intentionl herding my be driven by psychologicl fctors such s tendency mong investors to conform their investment choice to others. Thus, investors my tke similr investment choices becuse they converse with ech other nd wnt to conform (Shiller, 995) or becuse they observe ech others investment choices (Bhikchndni et. l., 992). b. Rtionlity: In the presence of symmetry in informtion vilbility nd processing cpbility, some investors my feel tht they re better off (rtionl) by imitting nother investor (Devenov nd Welch, 996). Such behvior is more prominent in cses where performnce pprisl of the investment professionl is reltive to how his industry peers hve performed. While, the less ble professionl my try to imitte the better professionl, it hs been seen tht even the ble investment professionl would choose to follow investment decision of the mjority of his peers even if it is suboptiml to preserve his reputtion in the job mrket (Schrfstein nd Stein, 990). This ide is premised on ssumption tht dmge to 4

5 reputtion in the job mrket, due to potentil filure, outweighs the expected benefits from potentilly successful investment decision (Grhm, 999). In the present study we consider only rtionl intentionl herding. (ii) Feedbck trding: Feedbck trding occurs due to high correltion between current investment decision nd pst return performnce of the sset. If the investor trdes in the sme direction s the pst return performnce, then he is clled positive feedbck trder, while if he trdes in the opposite direction then he is clled negtive feedbck (contrrin) trder (De Bondt nd Thler, 985; Bowmn nd Iverson, 998; Jegdeesh nd Titmn, 200; Kng et. l., 2002; Antonious et. l., 2005). Fundmentlly, feedbck trding behvior is bsed on the premise tht informtion (Privte/Public) tkes time to get impounded into stock prices either becuse it is privte informtion or becuse the qulity of the informtion is suspect. Hence, initil prices (when new informtion is initilly bsorbed in stock price) tend to produce directionl ptterns (trends) for certin periods of time. Feedbck trding behvior is n outcome of investor psychology. For exmple, positive feedbck trding my exist becuse of the following behviorl bises: () The investor gives more weightge to more recent informtion s compred to older informtion (Representtion heuristic); (b) the investor my be conservtive in updting his beliefs in response to new informtion. Resultntly, new informtion would only grdully get reflected in stock prices (Conservtism Bis), thus producing directionl ptterns in trde (Brberis et. l. 998); (c) Investor my trde ggressively fter hving executed profitble trde. In other words, he my exhibit overconfidence in his investment choice following successful trde (Overconfidence Bis) (Oden, 998). Further, negtive feedbck trding my be cused by the reluctnce of people to sell stocks whose performnce in the recent pst hs been poor nd to sell stocks whose performnce hs been good (Disposition Effect) (Shefrin nd Sttmn, 985). Accordingly, the present study posits the following: (i) Rtionl intentionl herding is relevnt only in the cse of institutionl investors since they tend to hve more symmetric informtion s compred to individuls nd lso becuse, their lbour mrket reputtion is linked to the performnce of their investment. (ii) Though, feedbck trding is witnessed mong both the investor groups (institutionl nd individul), prior literture sttes tht while institutionl investors exhibit positive feedbck trding (Nofsinger nd Sis, 999), individul investors demonstrte negtive feedbck trding (Shefrin nd Sttmn, 985). 5

6 THE MODEL The cpitl mrket of our model economy consists of two types of investors: (i) Institutionl investors nd (ii) Individul investors. To mp their investment behvior two seprte utility functions re specified. Institutionl Investor: If the institutionl investor demonstrtes herding nd positive feedbck trding then, when the mrket outlook (expected pyoff) is positive nd the sset prices re expected to go up, becuse he expects pst trends to continue, he would invest more money in the mrket. Thus, demonstrting decrese in his bsolute risk version during n uptrend in sset prices. Similrly, when the when mrket outlook is gloomy, he will try to stem his loss s soon s possible, thus demonstrting n increse in bsolute risk version during downtrend in the mrket. Such negtive reltion of bsolute risk version coefficient γ with expected pyoff is cptured by power utility function ( ) c U c = (where, C>0 nd γ 0<<). Individul Investor: If the individul investor demonstrtes negtive feedbck trding then, when the mrket outlook is positive nd sset prices re incresing, he tends to book profits pretty soon nd exit, thus demonstrting n increse in his bsolute risk version during n uptrend in the mrket. Similrly, when the mrket outlook is gloomy, he tends to hold on to the sset in the hope tht it will be profitble in the future. By doing so, he demonstrtes reduction in his bsolute risk version during downtrend in the mrket. Such positive reltion of bsolute risk version coefficient with expected pyoff is cptured in qudrtic * * b * utility function, 2 U 2( c ) = c c, where b <. * 2 c The two investors consume single good nd hve ccess to two investment opportunities: (i) They cn invest in stocks in such wy tht their investment is linerly homogenous to cpitl with the expected returns following Gussin distribution with prmeters nd. They cn borrow/ lend cpitl with ech other t rte, which vries endogenously over time. Nottions Let w * be the welth of the individul investor; w be the welth of institutionl investor. Sy, s is the ggregte welth in n economy i.e. s = w * + w. Let x * nd x be the proportion of welth of the individul nd institutionl investor respectively tht is invested in risky ssets. And let c * nd c be the consumption rtes of individul nd institutionl investors respectively. 6

7 Assuming tht the dynmics of ggregte welth in n economy re governed by n Ito process, they cn be specified s: α σ * ds = ( s c c ) dt + sdz Welfre Optimum nd Existence of Equilibrium Given tht this study posits power nd qudrtic utility function for institutionl nd individul investors respectively, to ttin (preto) optiml welfre, weighted verge of the two investors utility is to be mximized. Sy nd (-) re the weights ssocited with the utility functions of institutionl nd individul investors respectively nd is the discount fctor, the eqution for welfre optim cn be stted s: b c E e c c + dt 2 γ () γ ρt * *2 mx * 0 [( λ)( ) λ( )] c, c 0 where, 0 < λ <, 0 < γ < nd ρ > 0 subject to ds = s c c dt + sdz S S t * ( α ) σ given 0 nd 0. Necessry Condition A necessry condition for mximizing the previous eqution is tht there exists function v(s), the undiscounted bellmn function such tht the Hmilton Jcobi Bellmn eqution (herefter HJB), the first order conditions nd the trnsverslity conditions t infinity re stisfied. The HJB for eqution () cn be written s: b c 0 ( λ)( c c ) + λ( ) ρv + v ( αs c c ) + v σ s 2 γ 2 γ * *2 * 2 2 (2) t optimum: v s = c = bc γ * ( ) λ ( λ)( ) λ γ * v ( s) ( ) nd c ( ) c = = v ( s) b b( λ) (3) nd trnsverslity condition is ρt lim E e v ( s ) s = 0 (4) T 0 T T Substituting the optiml vlues of c nd c * in the HJB nd differentiting with respect to s gives: 7

8 v s v s v s s λ γ v ( s) v s 2 2 s v s 2 s 0 = ρ ( ) + ( ) α + ( )[ α ] + ( ) γ + ( ) σ v ( s) b b( λ) 2 (5) Defining p s the mrginl utility of welth, p p( s ) v ( s ), eqution (5) cn be written s: t t t (6) λ γ ρ = ρ p + p [ α s ] + p σ s + pα + p σ s ρ b b( λ) 2 Defining the shdow rte of interest for the welfre problem s: eqution (6) could be written s: 2 rt r( st ) = pα + p σ s ( ) γ λ p ρ r p = p [ α s ] + p σ s p b b( λ) (7) The right hnd side of eqution (7), is the conditionlly expected chnge in mrginl utility of welth p. By simple ppliction of Ito s lemm, the chnge in p cn be expressed s: ( ) 2 dp( s) = p ds + p ds 2 λ γ p where, ds = [ αs ] dt + σ sdz p b b( λ) ρt nd lim E e p s = 0 T (8) 0 T T λ γ p 2 2 dp ( s) = p [ αs ] dt p σsdz p σ s dt + + p b b( λ) 2 α r = ( ρ r) pdt pdzt σ (9) For the optiml solution to exist, the quntum of present welth in the economy should be equl to the sum of the discounted future welth (Detiled proof given in Appendix ). 8

9 / γ ρt λ pt t pt b b λ p0s0 = E0 e p dt () 0 ( ) where the dynmics of the totl welth in the economy will be governed by / γ λ p ds = α s dt + σ sdz pt b b( λ) (2) Given tht the undiscounted Bellmn function v(s) exists nd is strictly incresing, concve nd twice differentible one cn define the ggregte utility of consumption in the mrket u(x) s: b λ u ( x) = λ c c + c 2 ( γ ) * *2 γ mx( )[ ] ( ) c *, c * subject to c + c = x (3) Bsed on this definition of ggregte utility in the mrket, the conditions necessry for n optiml solution to exist cn be rrived t. In other words, the bounds for the bsolute risk version function s well s the shdow rtes of interest such tht the mrket clers nd n optiml solution exists, cn be rrived t. The sid bounds for the bsolute risk version function is given s (Proof elborted in Appendix 2) u ( x) x c( x) >< >< [ + ] u ( x) c( x) c( x) bc( x) γ (4) Thus, the Bellmn function v(s) would lso stisfy similr property (Dums, 989) v ( s) x c( x) Therefore, >< >< [ + ] v ( s) c( x) c( x) bc( x) γ We will use this result to rrive t the bounds in which the shdow rte of interest of lending nd borrowing should move so tht the mrket clers nd the equilibrium exists. v ( s) 2 we know r( s) = α + σ s v ( s) By (4) we cn sy tht 9

10 v ( s) x c( x) s >< + s >< [ ] s + v ( s) b( x) c( x) c( x) α σ α σ γσ α Or x c( x) s >< r( s) >< [ ] s + bc( x) c( x) c( x) 2 2 α σ γσ α The two extreme vlues would be obtined when the individul or institutionl investors hold ll the welth. A Numericl Exmple Sy the ggregte consumption in n economy is 00 units nd the optiml consumption for the individul investors is 30 units. The economy is inhbited by two investors (i) individul nd (ii) institutionl. The individul investor s investment behvior is mpped by specifying * * *2 qudrtic utility function U ( c ) = 0* c 0.04* c nd the institutionl investor s investment behvior is mpped by specifying power utility function ( 0.3) c U ( c) =. ( 0.3) Assume tht the return per unit of cpitl invested in this economy follows Gussin distribution with fixed men α (=20%) nd stndrd devition σ (=30%). Assume lso tht the proportion of welth with the individul investor is 0.5. Bsed on the bounds derived bove, the mrket clering rte of interest t which the two investors would borrow from nd lend to ech other will be 5.5% nd 28.05%.[5.5%<(resp. >) r <(resp. >) 28.05%. This mrket clering rte cn lso be used to clculte the equity premium. CONCLUSION In this pper, we hve given simple proof of existence of mrket equilibrium in n sset mrket inhbited by two types of gents: (i) Institutionl Investors nd (ii) Individul investors. By ssuming tht the institutionl investor is chrcterized by power utility nd the individul investor is chrcterized by qudrtic utility, the pper tries to incorporte two irrtionl investment behviorl (i) Herding nd (ii) Feedbck trding into the sset pricing model. This pper estblishes tht given tht the risk version coefficients of heterogeneous representtive gents re in certin bounds we cn rrive t the shdow rte of interests t which these gents would lend to /from ech other such tht the mrket clers. The equilibrium pricing so rrived t would djust for existence of herding nd feedbck trding mongst mrket prticipnts. Thus, in simple terms it cn be sid tht the study tries to generlize the existence of equilibrium price even when investment behvior is irrtionl. 0

11 However, some comments re in order. First of ll, the choice of qudrtic utility constrins the utility function to be vlid only till b<(/c * ), but we feel tht it is more importnt to cpture the behviorl bises in individul investor decision mking nd for most prcticl purposes this is t best scling issue. Secondly, the choice of qudrtic utility to represent the individul investor behvior leds to n equilibrium sset pricing prtil differentil eqution tht does not hve closed form solution. We gin feel tht this is the trdeoff tht we mke to cpture the behviourl bis in individul investor s decision mking process. Finlly, there is gin lot of heterogeneity mong individul investors bsed on whether they re high net worth individuls or otherwise. There is lso lot of heterogeneity in the cse of institutionl investors depending on their size nd skill. This pper does not del with this issue. However solution to this problem cn be rrived t in similr fshion (three or four gent problems) nevertheless bit more complicted.

12 Appendix : Proof of necessry condition for existence of Welfre optim Lemm: A necessry condition for the optiml solution (while mximizing the weighted verge of the two investors utility) to exist is tht there exists function p(s) (the mrginl utility of welth) defining process such tht the quntum of present welth in the economy is equl to the sum of discounted future welth: / γ ρ t λ pt 0 0 = 0 0 t pt b b( λ ) p s E e p dt where, the dynmis co totl welth in the economy is governed by stochstic process: / γ λ p ds = α s dt + σ sdz pt b b( λ) Proof: Given the dynmics of totl welth ds nd the mrginl utility of welth dp(s) one cn define stochstic differentil eqution (SDE) mpping the dynmics of the co movement of p nd s i.e. d ( ps) = pdst + sdpt + dstdpt (A..) Substituting ds t nd dp t from eqution 8 nd 9 we get γ λ p α r d( ps) = [ ρ ps p[ ] dt + ps[ σ ] dz p b b( λ) σ (A..2) Tking expecttions on both sides of eqution A..2, we get λ p γ E[ d( ps)] = E ρ ps p[( ) ( )] dt p b b( λ) (A..3) Now, we hve liner Ordinry Differentil Eqution (ODE) nd integrting this with respect to boundry condition in eqution 8, gives 2

13 / γ ρ t λ p t t pt b b λ p0s0 = E 0 e p dt 0 ( ) (A..4) Appendix 2: Bounds for bsolute risk version coefficient nd the shdow rte of interest. Lemm: Assuming tht the undiscounted Bellmn function, if it exists, is strictly incresing, concve nd twice differentible, the bounds for Arrow-Prtt bsolute risk version u ( x) coefficient,, nd the shdow rte of interest, r(s) (Such tht the mrket clers, is u ( x) given by: u ( x) x c( x) >< >< [ + ] u ( x) c( x) c( x) bc( x) γ 2 2 x c( x) nd, α σ s >< r( s) >< α γσ s[ + ] c ( x ) c ( x ) bc ( x ) Proof: We know tht the ggregte utility of consumption in the mrket is given by: b λ u x = c c + c γ ( ) * *2 mx( λ)[ ] ( ) c, c * 2 ( γ ) Let c+c * =x nd substitute c * =x-c(x), where c(x) is the optiml c for given x. We now hve mximiztion problem similr to b λ f ( x, c x ) = [ ( x c( x)) ( x c( x)) ] + [ c( x)] 2 γ 2 ( ) ( λ ) Prtil derivtive of u(x) with respect to the first rgument, c * (x), gives: u ( x)=(- λ)[ - b( x - c( x))] (A.2.) nd u ( x) = ( λ) b( c ( x)) (A.2.2) Therefore, the coefficient of bsolute risk version is given s: γ 3

14 - u ( x) b( c ( x)) = u ( x) bx + bc( x) (A.2.3) Further, the prtil derivtive of u(x) with respect to the second rgument, c(x) gives: = λ + + λ - u ( x) (- )( b( x - c( x)) c( x) γ (A.2.4) At optimum, u ( x) = 0, Therefore we cn sy tht And, bsed on eqution A.2., we cn sy tht u ( x) = λc( x) γ γ Further, u ( x) = γλc( x) c ( x) Thus, the coefficient of bsolute risk version cn be written s: u ( x) c ( x) = γ u ( x) c( x) (A.2.5) (- λ)( ( - ( )) λ ( ) - b x c x = c x γ To rrive t the bounds for the coefficient of bsolute risk version, first ssume tht u ( ) x < where, b > 0 & 0 x c( x) u ( x) b Bsed on eqution A.2.3, we cn sy tht b(- c ( x)) < - bx + bc( x) Therefore, c ( x) x c( x) > + c( x) c( x) c( x) b( x) x c( x) Since x > 0 nd 0 x c( x) we cn sy tht 0 < < b c( x) bc( x) c ( x) x c( x) Therefore, > γ > γ [ + ] c( x) c( x) c( x) bc( x) Similrly, if we ssume u ( x) > 0, then it cn be shown tht u ( x) 4

15 c ( x) x c( x) < γ < γ [ + ] c( x) c( x) c( x) bc( x) Thus, the bounds for the bsolute risk version coefficient of the investors is given s: ( ) ( ) u x [ x >< >< γ + c x ] u ( x) c( x) c( x) bc( x) (A.2.6) To rrive t the bounds for the shdow rte of interest, it would be resonble to ssume tht the Bellmn function v(s) would stisfy similr property s in eqution A.2.6 (Dums, 989). ( ) ( ) Therefore, v s [ x >< >< γ + c x ] v ( s) c( x) c( x) bc( x) As expressed in eqution 7, the shdow rte of interest for the welfre optimum is given by: v ( s) 2 r( s) = α + σ s v ( s) Bsed on A.2.6, the bounds for the shdow rte of interest cn be rrived t s: 2 v ( s) 2 2 x c( x) α σ s >< α + σ s >< α γσ s[ + ] v ( s) c( x) c( x) bc( x) 2 2 x c( x) α σ s >< r( s) >< α γσ s[ + ] c ( x ) c ( x ) bc ( x ) 5

16 REFERENCES Admti, A., 985, A Noisy Rtionl Expecttions Equilibrium for Multiple Asset Securities Mrkets. Econometric, 53, pp Antoniou, A., Koutmos, G. nd Pericli, A., 2005, Index Futures nd Positive Feedbck Trding: Evidence from Mjor Stock Exchnges. Journl of Empiricl Finnce, 2, pp Brberis, N., Shleifer, A. nd Vishny, R., 998, A Model of Investor Sentiment. Journl of Finncil Economics, 49, pp Brber, B. M., nd Oden T., 2008, All tht glitters: The effect of ttention nd news on the buying behvior of individul nd institutionl investors. Review of Finncil Studies 2, pp Bikhchndni S. nd Shrm S., 200, Herd Behviour in Finncil Mrkets. IMF Stff Ppers, 47, pp Bikhchndni, S., Hirshleifer, D. nd Welch, I., 992, A Theory of Fds, Fshion, Custom, nd Culturl Chnge s Informtionl Cscdes. Journl of Politicl Economy, 00, pp Bowmn, R., Iverson, D., 998, Short-Run Overrection in the New Zelnd Stock Mrket. Pcific-Bsin Finnce Journl, 6, pp Constntinides, G. M., nd D. Duffie, 996, Asset pricing with heterogeneous consumers. Journl of Politicl Economy 04, pp De Bondt, W.F.M. nd Thler, R.H., 985, Does the Stock Mrket Overrect? Journl of Finnce, 40, pp Devenow, A. nd Welch, I., 996, Rtionl Herding in Finncil Economics. Europen Economic Review, 40, pp Dums, B., 989, Two-Person Dynmic Euilibrium in the Cpitl Mrket. The Review of Finncil Studies, 2, pp Grhm, J.R., 999, Herding Among Investment Newsletters: Theory nd Evidence. Journl of Finnce, 54, pp Guerrieri, V nd Kondor, P, 2009, Fund Mngers, Creer Concerns, nd Asset Price Voltility. NBER Working Pper No Jegdeesh, N. nd Titmn, S., 200, Profitbility of Momentum Strtegies: An Evlution of Alterntive Explntions. Journl of Finnce, 56, pp Kng, J., Liu, M-H nd Ni, S.X., 2002, Contrrin nd Momentum Strtegies in the Chin Stock Mrket: Pcific-Bsin Finnce Journl, 0, pp Kniel, R., Gideon S, nd Titmn, S., 2008, Individul investor trding nd stock Returns. Journl of Finnce, 63, pp

17 Lintner, J., 965, The Vlution of Risky Assets nd the Selection of Risky Investments in Stock Portfolios nd Cpitl Budgets. Review of Economics nd Sttistics, 47, pp Mossin, J, 966, Equilibrium in Cpitl Asset Mrket. Econometric, 34, pp Nofsinger, J., nd Richrd W. Sis, 999. Herding nd Feedbck Trding by Institutionl nd Individul Investors. Journl of Finnce, 54, pp Oden, T., 998, Volume, Voltility, Price nd Profit when All Trders re bove Averge. Journl of Finnce, 53, pp Schrfstein, D.S. nd Stein, J.C., 990, Herd Behviour nd Investment. Americn Economic Review, 80, pp Schwrtz, R. nd Shpiro,J., 992, The Chllenge of Institutionliztion of the Equity Mrket, in Recent Developments in Finnce, Sunders, A. ed. (New York Slomon Center, New York: 992). Shrpe, W., 964, Cpitl Asset Prices: A Theory of Mrket Equilibrium under Conditions of Risk. Journl of Finnce, 9, pp Shefrin, H. nd Sttmn, M., 985, The Disposition to Sell Winners too Erly nd Ride Losers too Long. Journl of Finnce, 40, pp Shiller, R. J., 995, Converstion, Informtion nd Herd Behvior. Americn Economic Review, 85, pp

18 Indin Institute of Mngement Kozhikode Type of Document: (Working Pper/Cse/ Teching Note, etc.) WORKING PAPER Title: Ref. No.: IIMK/WPS/2/FIN/203/07 EXISTENCE OF CAPITAL MARKET EQUILIBRIUM IN THE PRESENCE OF HERDING AND FEEDBACK TRADING Author(s): Institution(s) Assistnt Professor Indin Institute of Mngement Kozhikode IIMK Cmpus PO Abhilsh S. Nir Kozhikode, Kerl Phone: emil: Subject Ares: Finnce Accounting & Control Subject Clssifiction Codes, if ny: Supporting Agencies, if ny: Supplementry Informtion, if ny: Abstrct: Reserch Grnt/Project No.(s): Dte of Issue: Mrch 203 Number of Pges: 6 This pper ttempts to estblish the existence of equilibrium, in n sset mrket inhbited by two representtive investors with different risk versions. In order to cpture heterogeneity in informtion nd welth, the pper segments the investor popultion into two: (i) Individul investors nd (ii) Institutionl investors. Bsed on prior literture, the present study posits tht Institutionl investors demonstrte rtionl intentionl herding nd positive feedbck trding (buy when the mrkets rise nd sell when it flls) nd individul investors demonstrte negtive feedbck trding (vice vers). In other words, when the mrkets re (monotoniclly) incresing, institutionl investors, expecting the trend to continue would buy more, thus demonstrting decresing bsolute risk version. Similrly, when the mrket is (monotoniclly) decresing he will try to stem his loss s soon s possible, demonstrting incresing bsolute risk version. Such n investment behvior is cptured in power utility function. Further, negtive feedbck trding by individul investors implies tht when mrket is (monotoniclly) incresing individul investors, expecting the trend to reverse, would sell. Thus demonstrting incresing bsolute risk version. And when the mrkets re (monotoniclly) decresing, they would hold on to their investments expecting better times to come, thus depicting decresing bsolute risk version. Such investment behvior is cptured by qudrtic utility function. Given their welth nd investment behvior, the two investor groups would trde with ech other such tht the mrket clers. To the best of our knowledge this is the first pper tht proposes sset pricing model tht not only llows for behviourl bises but lso for heterogeneous gents who re ffected differently by these bises. This pper estblishes the bounds for the bsolute risk version function nd the shdow rte of interest t which the two investor groups will lend money to ech other to enble trding nd mrket clering. For resonble endowments nd presumed behviourl bises s implied by the chosen utility function, numericl exmple t the end of this pper shows tht the mrket clering interest rte (t which the investors would lend to nd borrow from ech other) occurs between 5.5% nd 28.05%. Key Words/Phrses: Heterogenous Agents, Herding, Feed bck trding, shdow rte of interest. 8