Investor Sentiment and the Asset Pricing Process Extension of an Existing Model

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1 Joural of Appled Busess ad Ecoomcs Ivesor Seme ad he Asse Prcg Process Exeso of a Exsg Model Doa G. Vlad Seo Hll Uversy Commo aspecs of huma behavor, lke overcofdece or mscocepos updag belefs, mgh fluece marke behavor. We exed a exsg sgle-asse overlappg geerao model by cosderg wo correlaed rsky asses for whch ose raders may form dffere belefs. Whe he secod correlaed rsky asse was roduced he model, he asymmerc effec from posve/egave shfs seme was cossely reduced. Thus, a heorecal corbuo ha hs sudy brgs o he exsg leraure s ha good/bad ews has a asymmerc effec o he asse prcg process. INTRODUCTION May researchers have aemped o exame heorecally ad emprcally he Effce Marke Hypohess (EMH) ad perhaps he mos well kow advocae of dffere levels of marke effcecy s Fama (970, 99). However, some ecoomss have red o solve some of he explcable pheomea lke he Jauary Effec or he Day-of-he-Week Effec. Because researchers have bee uable o expla dffere scearos of marke effcecy, hey seem o accep (a leas a ac way) he exsece of some rraoal forces affecg he marke. Ths paper res o expla how commo aspecs of mscocepos mgh fluece he marke behavor. As Schller (000) meoed, deparures from marke effcecy ca have egave effecs for fuure geeraos; ay msallocao of resources hrough marke overvaluao akes resources away from oher eedy secors of he ecoomy. The goal s o ppo some of he hdde facors ha gude he marke a specfc dreco, o aalyze hem, ad o fer possble judgmes for fuure marke behavor. Rece leraure combes all hese rraoal, uusual flueces o a aggregae erm, vesor seme, ha should be able o expla some of he observed aomales asse reurs or marke volaly. For example, De Bod ad Thaler (985) foud ha people overreaced o ews; her choces dd o sasfy Bayes' rule: "dvduals ed o overwegh rece formao ad uderwegh pror (or base rae) daa" (p. 793) ad hey esed he predcve power of he overreaco pheomeo.

2 Summers (986) aalyzed wheher he sock marke reflecs fudameal values raoally, ad he cocluded ha was hard o defy some ypes of marke effcecy by usg sadard mehods. Fama ad Frech (996) argued ha he aomales are relaed ad proposed a hree-facor model o expla hem. The model appeared o accou for he cross-secoal volaly reurs ad he log-ru reurs reversals, bu could o expla he shor-erm reurs' couao. A eresg ssue ha has receved a lo of aeo s he exe o whch speculaors acos affec he asse prces. I he pas, researchers were cofde ha ay desablzg aco by speculaors could be offse by a oppose aco from raoal vesors. However, more rece research shows ha raoal vesors work o brg asse prces closer o fudameals, bu hey cao succeed due o rsk averso o ose raders upredcable acos. DeLog, Shlefer, Summers, ad Waldma (990) developed a overlappg geerao model ad showed ha ose raders ( rraoal vesors ) do affec asse prces, ad cera codos ca ear hgher expeced reurs. Oe psychologcal characersc of dvduals geeral ad of vesors parcular s overcofdece (Dael, Hrshlefer, & Subrahmayam, 998). Ths characersc presumably geeraes hgh forecas errors hrough overesmao of prvae formao. Usg psychologcal suppor explag people s behavor, Shlefer, Barbers, ad Vshy (998) bul a model of vesor seme ha could expla boh uderreaco ad overreaco pheomea. Rece sudes facal behavor recogze he lms of arbrage, ad Dael, Hrshlefer, ad Teoh (00) poed ou some psychologcal facors ha may affec decso-makg processes: self-arbuo (arbue he success ad blame he bad luck whe falure), selfdecepos, emoo-based judgmes, framg effecs, ad meal accoug. Brow ad Clff (00) separaed vesor seme o a suoal ad a dvdual oe. I addo, usg he Seme Idex daa, Lee e.al (00) showed ha seme s a prced rsk facor (p. 8). The purpose of hs paper s o exed he sgle-asse heorecal aalyss DeLog e. al. (990) model o allow for wo correlaed rsky asses for whch ose raders may have dffere belefs. The heorecal model shows ha he presece of a secod rsky asse reduces he asymmerc effec from posve/egave shfs seme. THE THEORETICAL FRAMEWORK We exed he wo-perod sgle-asse overlappg geerao model (DeLog e. al., 990) by cosderg wo-correlaed rsky asses for whch vesors may form dffere belefs. Asses - The safe asse ( s ), perfec elasc supply; s prce s ormalzed a - Two rsky asses ( u ad u ), o elasc supply; her prces are ad respecvely. - Each asse pays he same dvdeds: r (o fudameal rsk s assumed). Ivesors p p

3 - Raoal vesors ( ) have raoal expecaos (have a accurae percepo of he dsrbuo of reurs from holdg he rsky asse). - Irraoal vesors or ose raders ( ) msperceve he expeced prce of he rsky asse by a depede decally dsrbued radom varable: where * ρ N ( ρ, ), () ρ ρ s ose rader s mspercepo, ρ s he mea (a average bewee opmsm ad pessmsm), ad ρ s he varace of ose raders mspercepos per u of he rsky asse. - Irraoal vesors have dffere mscocepos of he expeced prces of he rsky asses: βρ for asse ad βρ for asse ( β ad β are parameers). - The umber of rraoal vesors s µ ad he umber of raoal vesors s ( µ ). Assumpos - The resources o be vesed are exogeously gve, so here s o frs-perod cosumpo ad o labor supply decso. - The oly decso ha vesors have o make s o choose a porfolo whe youg (frs perod), based o her belefs. Each age s uly fuco s a CARA of wealh whe old: ( γ ) ω U = e, () where γ s he coeffce of absolue rsk averso ad w s he expeced fal wealh. Assumg ormally dsrbued reurs, maxmzg U s equvale o maxmzg: w γ w, (3) where w s he average of wealh ad w s oe perod ahead varace of wealh. a) Raoal vesors choose he amou λ of he rsky asse u ad he amou λ of he rsky asse ad maxmze: u 0 λ 0 λ, p,,, p p p E( U ) = c [ r E p p ( r)] c [ r E p p ( r)] γ[( λ ) ( λ ) ρ λ λ ] where, p = E {[ p E ( p )] } (5..) ad, p = E{[ p E ( p )] } (5..) are he expeced varace of p. p ad b) Nose raders choose he amou λ p. (4) ρ s he correlao coeffce bewee p ad of he rsky asse u ad he amou λ of he rsky asse u ad maxmze: E( U ) = c λ [ r E p ( p β ρ )( r)] c λ [ r E p (6) ( p )( )] [( ) ( ) ] 0 0 βρ r γ λ, p λ, p ρλ, p λ, p

4 Equlbrum prces I he secod geerao, ages sell he safe asse for cosumpo goods o he ew youg. They also sell rsky asses: u for p ad u for p. Marke Clearg Codos ( ) = R ( ) = R µλ µ λ µλ µ λ where R s he supply of asse u ad R s he supply of asse u. Subsue for ages demads for he rsky asses ad solve for p ad ρ ρ p = p ( ) µ β β ρ γ ( ρ ) R ( ρ ) r p% ρ p% ( r) ρ ρ p = p µ ( β β ) ρ γ ( ρ ) R ( ρ ) r p% ρ p% ( r) where =, p ; =, p ; p% = Ep ; p% = Ep. p : (7..) (7..) Cosder oly seady sae equlbrum by mposg ha ucodoal dsrbuos of p be equal o he dsrbuos of p ad p respecvely: Ep = p µ ρ β ρ ) (8..) ( Ep = p µρ ( βρ) (8..) The solve for p ad p explcly: p = µβ ρ γ r r [ R ρ R ] (9..) γ p µβ ρ r r ρ R R ] = [ I boh (9..) p ad p, p equaos, oly he secod erm s varable, so oe-sep-ahead varace of p ad p are fucos of he cosa varace of oe-geerao of ose raders mscocepos, ρ : β µ ρ ( ) =, = = (0..) p p r

5 β µ, ρ p p ( r) Cosequely, he fal equaos for p = = = (0..) r r( r) p ad p are as follows: γµ ρ = µβ ρ [ β ρ β β R ] (..) R p = µβ ρ ( ) [ r γµ ρ ρ r r ββr β R ] (..) Aleravely, a ecoomy wh oly oe rsky asse, he soluo for sgle prce p s: γµ ρ p = µρ r r( r) (.3.) The frs erm each of he equaos.. ad.. gves he fudameal value of oe, ad he remag hree erms expla he effec of ose raders mscocepos o he prces of he wo rsky asses. Cosequely, whe ρ coverges o zero, asse prces coverge o her fudameals. The flucuaos he wo prces of he rsky asses are revealed by he secod erm he equaos.. ad..: oe geerao of opmsc ose raders wll crease he asse s prce; he hgher he umber of ose raders, he hgher he equlbrum prce wll be. The oppose suao s rue for he pessmsc ose raders case. For he hrd erm he equaos.. ad.., sce ρ s o zero, oe geerao of ose raders wll be, o average, opmsc or pessmsc. Ths, ur, wll devae he equlbrum prces above/below her fudameals. These fdgs are smlar o DeLog, Shlefer, Summers, ad Waldma s (990) fdgs: The Prce Pressure Effec, because pus upward/dowward pressure o he rsky asses prce more ha would oherwse be absece of mscocepos. My corbuo o he exsg research comes from aalyzg he las erm of equaos.. ad.. The las erm he prcg formula (equaos.. ad..) proves ha arbrage cao elmae he prce volaly, due o upredcably he ose raders behavor he ear fuure. Cosequely, raoal vesors are wllg o hold he rsky asse oly f hey are compesaed for he rsk ha fuure pessmsc ose raders could duce. Ths s he Space Effec ha he ose raders creae: ose raders fuure belefs are ucera ad uceray makes he rsky asse rsker ad creases s reur. Overall, he roduco of he secod correlaed rsky asse he model makes a dfferece he fal prce equaos. For example, whe vesors are opmsc abou fuure reurs o boh asses, ad assumg ha fuure prces are posvely correlaed ( β, β, ad ρ equaos.. ad..), he devao of prce above each asse s fudameal value s smaller ha ha a sgle-asse case (equao.3). For he oppose suao, whe vesors are pessmsc abou fuure reurs o boh asses, ad assumg ha fuure prces are posvely correlaed ( β, β 0, ρ equaos.. ad.), he devao of prce below 0 each asse s fudameal value s greaer ha ha sgle-asse case. Ths oucome s 0

6 cosse wh some emprcal fdgs abou he asymmerc effec ha good/bad ews has o marke volaly. CONCLUSIONS I he heorecal par of hs paper I exeded a sgle-asse overlappg-geerao model by cosderg wo correlaed rsky asses for whch ose raders mgh form dffere belefs. Cosse wh DeLog e. al (990), I foud ha vesors mscocepos have a log-ru effec he asse prcg process. A heorecal corbuo ha hs sudy brgs o he exsg leraure s ha good/bad ews has a asymmerc effec o he asse prces process. Ths heorecal resul s cosse wh prevous emprcal fdgs ha bad ews creaes hgher volales ha good ews of he same magude. I cocluso, here s heorecal evdece favor of seme measures as sgfca varables o expla he sock s excess reurs; hs resul s cosse wh he Capal Asse Prcg Model s predco. Based o emprcal evdece abou marke aomales, commo sese suggess cosderg some less ha fully raoal explaaos o accou for reurs paer. O he oher had, models cosderg mperfec raoaly approaches are o very lkely o be geerally acceped. Cosequely, he ssue s o fd some ou of sample predcve explaaos wh several emprcal applcaos. REFERENCES Brow, G. & Clff, M. (00). Ivesor Seme ad he Near-Term Sock Marke. Workg paper. Uversy of Norh Carola, Chapel Hll. Dael, K., Hrshlefer, D. & Subrahmayam, A. (998). Ivesor Psychology ad Secury Marke uder- ad Overreacos. Joural of Face, 53, Dael, K., Hrshlefer, D. & Teoh, S. (00). Ivesor psychology capal markes: evdece ad polcy mplcaos. Joural of Moeary Ecoomcs, 49, De Bod, W. & Thaler, R. (985). Does he Sock Marke Overreac? Joural of Face, 40, De Log, J., Shlefer, A., Summers, L. & Waldma, R. (990). Nose Trader Rsk Facal Markes. Joural of Polcal Ecoomy, 98, Eugee Fama (970). Effce Capal Markes: A Revew of Theory ad Emprcal Work. Joural of Face, 5, Eugee Fama (99). Effce Capal Markes: II. Joural of Face, 46, Eugee Fama (988). Permae ad Temporary Compoes of Sock Prces. Joural of Polcal Ecoomy, 96,

7 Fama, E. & Frech, K. (996). Mulfacor Explaaos of Asse Prcg Aomales. Joural of Face, 5, Fama, E. & Frech, K. (993). Commo rsk facors he reurs o socks ad bods. Joural of Facal Ecoomcs, 33, Lee, W., Jag, C. & Idro, D. (00). Sock marke volaly, excess reurs, ad he role of vesor seme. Joural of Bakg & Face, 6, Seyhu, N. (990). Overreaco or Fudameals: Some Lessos from Isders Respose o he Marke Crash of 987. Joural of Face, 45, Shller, Rober (000). Irraoal Exuberace. Prceo Uversy Press. Shlefer A., Barbers N. & Vshy R. (998). A model of vesor seme. Joural of Facal Ecoomcs, 49, Summers, L.(986). Does he Sock Marke Raoally Reflec Fudameal Values? Joural of Face, 4, I would lke o hak Dr. Sajal Lahr for hs helpful suggesos, gudace, ad coued suppor.