Working Paper Series Brasília n. 184 Apr p. 1-60

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2 ISSN CGC.38.66/-5 Working Papr Sris rasília n. 84 Apr. 9 p. -6

3 Working Papr Sris Editd by sarch Dpartmnt Dpp Editor: njamin Miranda Tabak Editorial Assistnt: Jan Soia Moita Had o sarch Dpartmnt: Carlos Hamilton Vasconclos Araújo [email protected] Th anco Cntral do rasil Working Paprs ar all valuatd in doubl blind rr procss. production is prmittd only i sourc is statd as ollows: Working Papr n. 84. Authorizd by Mário Msquita, Dputy Govrnor or Economic Policy. Gnral Control o Publications anco Cntral do rasil Scr/Surl/Dimp SS Quadra 3 loco Ediício-Sd º andar Caixa Postal rasília DF razil Phons: and Fax: [email protected] Th viws xprssd in this work ar thos o th authors and do not ncssarily rlct thos o th anco Cntral or its mmbrs. Although ths Working Paprs otn rprsnt prliminary work, citation o sourc is rquird whn usd or rproducd. As opiniõs xprssas nst trabalho são xclusivamnt dos autors não rltm, ncssariamnt, a visão do anco Cntral do rasil. Ainda qu st artigo rprsnt trabalho prliminar, citação da ont é rqurida msmo quando rproduzido parcialmnt. Consumr Complaints and Public Enquiris Cntr anco Cntral do rasil Scr/Surl/Diat SS Quadra 3 loco Ediício-Sd º subsolo rasília DF razil Fax: Intrnt: http//

4 havior Financ and Estimation isk in Stochastic Portolio Optimization José Luiz arros Frnands * Juan Ignacio Pña ** njamin Miranda Tabak *** Th Working Paprs should not b rportd as rprsnting th viws o th anco Cntral do rasil. Th viws xprssd in th paprs ar thos o th authors and do not ncssarily rlct thos o th anco Cntral do rasil. Abstract Th objctiv o this papr is twoold. Th irst is to incorporat mntal accounting, loss-avrsion, asymmtric risk-taking bhavior, and probability wighting in a multi-priod portolio optimization or individual invstors. Whil ths bhavioral biass hav prviously bn idntiid in th litratur, thir ovrall impact during th dtrmination o optimal asst allocation in a multi-priod analysis is still missing. Th scond objctiv is to account or th stimation risk in th analysis. Considring 6 daily indx stock data ovr th priod rom 995 to 7, w mpirically valuat our modl ATE havior sampl Adjustd Tchniqu against th traditional Markowitz modl. Kywords: havior, Portolio Optimization, sampling JEL Classiication: G, G. * Univrsidad Católica d rasília and anco Cntral do rasil Grência-Excutiva d isco da Ára d Política Montária ** Dpartamnto d Economía d la Emprsa, Univrsidad Carlos III d Madrid, España. *** Univrsidad Católica d rasília and anco Cntral do rasil Dpartamnto d Estudos Psquisas 3

5 In a standard asst allocation procdur, onc th risk tolranc, constraints, and inancial goals ar st, th output is givn by a man-varianc optimization Markowitz, 95; Fldman and isman,. Unortunatly this procdur is likly to ail or individuals, who ar suscptibl to bhavioral biass. For instanc, in rspons to shorttrm markt movmnts and to th dtrimnt o th long-trm invstmnt plan, th individual invstor may rquir his asst allocation to b changd. Frnands t al. [7] suggst that arly liquidation o a long trm invstmnt may b th caus o momntum. In trms o motional biass, svral mpirical studis Tvrsky and Kahnman, 99 hav shown that, whn daling with gains, agnts ar risk-avrs, but whn choics involv losss, agnts ar risk-sking asymmtric risk-taking bhavior. Morovr, in a wid varity o domains, popl ar signiicantly mor avrs to losss than thy ar attractd to sam-sizd gains. Loss-avrsion Schmidt and Zank, 5 is a rlvant psychological concpt that has bn importd to inancial and conomic analysis, and it rprsnts th oundation o prospct thory. Th currnt paradigm o individual bhavior in inanc thory is basd on xpctd utility maximization and risk-avrsion, which has bn undr attack in rcnt yars du to its dscriptiv inaccuracy. Exprimntal psychologists hav dmonstratd that popl systmatically dviat rom th choic prdictions th classical paradigm implis as individuals ar typically biasd. havioral biass can roughly b groupd in two catgoris: cognitiv and motional, though both typs yild irrational dcisions. caus cognitiv biass huristics lik anchoring, availability, and rprsntativ biass stm rom aulty rasoning, bttr inormation and advic can otn corrct thm. Convrsly, motional biass, such as rgrt and loss-avrsion, originat rom impulsiv lings or intuition, rathr than conscious rasoning, and ar hardly possibl to corrct. Lo t al. [5] invstigatd svral possibl links btwn psychological actors and trading prormanc, inding that subjcts whos motional raction to montary gains and losss was mor intns on both th positiv and ngativ sid xhibitd signiicantly wors trading prormanc. Shrin [5] posits that th portolios slctd by invstors whos choics conorm to prospct thory will dir in ky aspcts rom th portolios slctd by invstors whos choics conorm to xpctd utility thory. Th gnral charactr o bhavioral portolios is that thy atur a combination o scuritis that ar vry sa 4

6 with scuritis that ar vry risky, with th ovrall portolio ailing to b wll divrsiid. In this sns, an optimal solution to th asst allocation problm should guid invstors to mak dcisions that srv thir bst intrst. This could b th rcommndation o an asst allocation that suits th invstor s natural psychological prrncs motional biass, vn though it may not maximiz xpctd rturn or a givn lvl o risk. Mor simply, a clint s bst practical allocation may b a slightly undr-prorming long-trm invstmnt program to which th invstor can comortably adhr. From a man-varianc optimization prspctiv, bhavioral invstors slct portolios that ar stochastically dominatd. This dos not man that th individual invstors ar irrational in any sns: it is not irrational or popl to anticipat motional ractions and tak thm into account whn making dcisions that try to adjust thir choics to thir prrncs. Howvr, portolio managrs lack th guidlins ncssary or incorporating ths biass during th procss o dtrmining asst allocation. W addrss this issu by valuating whthr managrs should modrat th way clints naturally bhav to countract th cts o bhavioral biass so that thy can it a prdtrmind asst allocation or thy should crat an asst allocation that adapt to clints biass, so that clints can comortabl adhr to th und. In gnral trms, prospct thory and its lattr vrsion cumulativ prospct thory Kahnman and Tvrsky, 979, 99 posits our novl concpts in th ramwork o individuals risk prrncs. First, invstors valuat assts according to gains and losss and not according to inal walth mntal accounting. Scond, individuals ar mor avrs to losss than thy ar attractd to gains loss-avrsion. Third, individuals ar risk-sking in th domain o losss and risk-avrs in th domain o gains asymmtric risk prrnc. Finally, individuals valuat xtrm probabilitis in a way that ovrstimats low probabilitis and undrstimats high probabilitis probability wighting unction. This study, as ar as w know, is th irst to considr all thos aspcts in th ramwork o portolio choic. Thr ar conlicting rsults in th inanc litratur on how prior outcoms act th risk-taking bhavior o invstors in subsqunt priods. Loss-avrsion would prdict that tradrs with proitabl mornings would rduc thir xposur to atrnoon risk, trying to avoid losss and thus guaranting th prvious gains Wbr and Zuchl, 3. Odan [998] and Wbr and Camrr [998] hav shown that invstors ar mor willing to sll stocks that trad abov th purchas pric winnrs than stocks that trad blow purchas pric losrs a phnomnon trmd th disposition ct 5

7 Schrin and Statman, 985. oth works intrprtd this bhavior as vidnc o dcrasd risk-avrsion atr a loss, and incrasd risk-avrsion atr a gain. Th standard xplanation or th prvious bhavior is basd on prospct thory, and particularly on th act that individuals ar risk-sking in th domain o losss and riskavrs in th domain o gains asymmtric risk prrnc. Howvr, anothr stram o th litratur ound th opposit bhavior. Thalr and Johnson [99] nam th hous-mony ct, th bhavior o incrasing risk apptit atr a gain. arbris t al. [] prsnt a modl whr invstors ar lss lossavrs atr a gain whil thy bcom mor loss-avrs atr prior losss. Our proposd modl addrsss and clariis th prvious contradiction btwn hous-mony and disposition ct. Dspit th vast litratur conirming th bhavioral biass associatd with prospct thory, th considration o all thos biass in an asst allocation ramwork is still missing. arbris and Huang [] and arbris t al [] us loss-avrsion and mntal accounting Thalr, 999 to xplain aspcts o stock pric bhavior, but do not mploy th ull prospct thory ramwork and don t xamin optimal asst allocation. nartzi and Thalr [995] considr prospct thory to solv th quity prmium puzzl whn invstors ar loss-avrs and valuat thir portolios myopically with a horizon o approximatly on yar. Thy also suggst an optimal allocation in quitis rom 3% to 55%. Magi [5] uss bhavioral prrncs to numrically solv a simpl modl o intrnational portolio choic, providing a possibl xplanation or th quity hom bias puzzl, th tndncy o individual invstors to prr its hom-country stocks dspit th gratr prormanc o orign stocks. Davis and Satchll [4] provid a solution or th optimal quity allocation, and xplor mor thoroughly th cumulativ prospct thory paramtr spac that is consistnt with obsrvd quity allocations givn a inancial markt s rturns distributions ovr a on-month horizon. Shrin [5] considrs htrognous invstors to s th impact o bhavioral concpts in th ramwork o asst pricing. Th irst main goal o this study is to incorporat mntal accounting, lossavrsion, asymmtric risk-taking, disposition ct, and probability wighting in portolio optimization in a multi-priod stting or individual invstors. W provid a solution or th asst allocation problm, taking into account all bhavioral biass associatd with prospct thory and using a utility unction suggstd in Giorgi t. al., 4 consistnt with both th xprimntal rsults o Tvrsky and Kahnman, and also 6

8 with th xistnc o quilibrium. W also shd mor light on th issu o how prior outcoms act subsqunt risk-taking bhavior, invstigating th invstor s risk-taking bhavior ollowing a ris, or a all, in th pric o th risky asst. In lin with prospct thory, invstors driv utility rom luctuations in th valu o thir inal walth. In our ramwork, thr is a inancial markt on which two assts ar tradd. A risklss asst, also calld a bond, and a risky asst, also calld a stock undr th assumption o normally distributd rturns or th risky asst. As w ar modling th dcision making procss o an individual invstor, short-slling is not allowd. In ach priod w considr two priods, th invstor chooss th wight o his ndowmnt to b invstd in th risky asst, in ordr to maximiz his utility prospct thory basd. W assum that th invstor acts myopically in a sns that h dosn t discount long-trm wlar whn valuating his utility, and that th rrnc point rlativ to which h masurs his gains and losss or th irst priod is his initial ndowmnt. Although all agnts solv th sam maximization problm in th irst priod, th scond priod dcision dpnds on th rrnc point rlativ to which th agnt masurs th scond priod outcoms gains or losss. W considr two possibl rrnc points: th initial walth or th currnt walth, and analyz both cass. St- Amour [6] valuats houshold portolios and his rsults rval that rrncs ar strongly rlvant and stat-dpndnt. Anothr wll-known issu in asst allocation problms, using Markowitz optimization, is that th output is strongly drivn by th risk/rturn stimation, which usually gnrats vry unstabl portolios. Th most amous problm with this tchniqu is th substitution problm, whr two assts with th sam risk but slightly dirnt xpctd rturns. Th optimizr would giv all th wight to th asst with th highr xpctd rturn, lading to a vry unstabl asst allocation. Th scond goal o this chaptr is to incorporat stimation risk in th portolio allocation bhavioral problm. cnt litratur has trid to ovrcom th prvious problm o lading to unasibl portolios. Th main ocus o thos modls is to ind out how to crat ralistic portolios considring that th valus usd or risk and rturn ar not dtrministic but instad just stimats thy ar stochastic. It should b notd that th misspciication o xpctd rturns is much mor critical than that o variancs Zimmr and Nidrhausr, 3. 7

9 Jorion [986] ors a simpl mpirical ays stimator that should outprorm th sampl man in th contxt o a portolio. His main ida is to slct an stimator with avrag minimizing proprtis rlativ to th loss unction th loss du to stimation risk. Instad o th sampl man, an stimator obtaind by shrinking th mans toward a common valu is proposd th avrag rturn or th minimum varianc portolio, which should lad to dcrasd stimation rror. Similar to Jorion, Kmp t al [] assums that th prior man is idntical across all risky assts. Howvr, Kmp s modl considrs stimation risk as a scond sourc o risk, dtrmind by th htrognity o th markt and givn by th standard dviation o th xpctd rturns across risky assts. lack and Littrman [99] postulat that th considration o th global CAPM Capital Asst Pricing Modl quilibrium can signiicantly improv th usulnss o asst allocation modls, as it can provid a nutral starting point or stimating th st o xpctd xcss rturns rquird to driv th portolio optimization procss. Horst t al. [] propos a nw adjustmnt in man-varianc portolio wights to incorporat th stimation risk. Th adjustmnt amounts to using a psudo risk-avrsion, rathr than th actual risk-avrsion, which dpnds on th sampl siz, th numbr o assts in th portolio, and th curvatur o th man-varianc rontir. Th psudo risk-avrsion is always highr than th actual on and this dirnc incrass with th uncrtainty in th xpctd rturn stimations. Manhout [4] also considrs an adjustmnt in th coicint o risk-avrsion to insur th invstor against som ndognous worst cas. Finally, Michaud [998] suggsts portolio sampling as a way to allow an analyst to visualiz th stimation rror in traditional portolio optimization mthods, and Shrr [] posits that sampling rom a multivariat normal distribution a paramtric mthod trmd Mont Carlo simulation is a way to captur th stimation rror. Markowitz and Usmn [3] compard th traditional approach to rsampling and thir rsults support th lattr. Frnands t al. [8] valuat svral asst allocation modls and suggst that rsampling mthods typically or th bst rsults. This study prsnts a novl approach ATE havioral sampl Adjustd Tchniqu to incorporat bhavioral biass and stimation risk into man-varianc portolio slction. In a papr clos to ours, Vlck [6] proposs a modl to valuat portolio choic with loss-avrsion, asymmtric risk-taking bhavior, and sgrgation o risklss opportunitis. His indings suggst that th changs in portolio wights crucially dpnd on th rrnc point and th ratio btwn th rrnc point and th 8

10 currnt walth, and thus indirctly on th prormanc o th risky asst. Our work dirs rom his study as w xplicitly considr all novl aspcts o prospct thory: mntal accounting, loss-avrsion, asymmtric risk-taking bhavior, and probability wighting unction. W also valuat th inicincy cost o th bhavioral biass and considr a mor gnral orm or th risky asst rturn procss, including stimation risk in th analysis. Considring daily quity data rom th priod rom 995 to 7, w mpirically valuat our modl in comparison to th traditional Markowitz modl. Our rsults support th us o ATE as an altrnativ or dining optimal asst allocation and posit that a portolio optimization modl may b adaptd to th individual biass implid in prospct thory. Th rmaindr o this papr contains th ollowing sctions. Sction A discusss th bhavioral biass considrd and dscribs our modl proposing th bhavioral rsampling adjustd tchniqu ATE. Sction prsnts th mpirical study, dscribing th data and implmntation, and providing th rsults. Sction C concluds th rsarch by rviwing th main achivmnts. A Th havioral Modl W prsnt a two priod s modl or portolio choic in a stylizd inancial markt with only two assts, whr th invstor s prrncs ar dscribd by cumulativ prospct thory as suggstd by Kahnman and Tvrsky [979] and Tvrsky and Kahnman [99]. In our ramwork, thr is a inancial markt in which two assts ar tradd. A risklss asst, also calld th bond, and a risky asst, th stock. Lt us considr th rturn o th stock in ach priod givn by th ollowing procss: n, with n ~ N,. Th riskr bond yilds a sur rturn o. W assum that th tim valu o th mony is positiv, i.. that intrst rats ar non-ngativ. Th prrncs o th invstor ar basd on changs in walth and ar dscribd by prospct thory. W assum that h owns an initial ndowmnt, W normalizd to montary unit, and that h arns no othr incom. Th agnt invsts a proportion o his walth in th stock and - in th bond. Sinc w want to modl th individual invstor s bhavior, w assum that short slling is not allowd. W also assum that th invstor acts myopically, and th rrnc point rlativ to which h 9

11 masurs his gains and losss in th irst priod is his initial walth. Thn, th prcivd gain or loss in th nd o th irst priod is givn by: x ΔW x x [ W W ] n Eq. W As pointd out in Vlck [6] th choic procss undr prospct thory starts with th diting phas, ollowd by th valuation o ditd prospcts, and inally th altrnativ with th highst valu is chosn. During th diting phas, agnts discriminat gains and losss. Thy also prorm additional mntal adjustmnts in th original probability unction p x, dining th probability wighting unction p. asd on xprimntal vidnc, individuals adjust th liklihood o outcoms such that small probabilitis ar ovrwightd and larg probabilitis ar undrwightd. W will considr th probability wighting unction, as in Giorgi t al. [4] givn by: p, Eq. γ p γ γ p p γ whr γ is th adjustmnt actor. Th ollowing graph compars th valus o p and p, considring γ Figur In th valuing phas, th agnts attach a subjctiv valu to th gambl. Lt us assum th valu unction proposd by Giorgi t al. [4], as ollows: v x x, x, i i x x < Eq. 3 whr is th coicint o absolut risk prrnc, > > maks th valu unction stpr in th ngativ sid loss-avrsion, and x is th chang in walth or wlar, rathr than inal stats mntal accounting, as proposd by Kahnman and Tvrsky [979]. Also, th valu unction is concav abov th rrnc point and convx blow it asymmtric risk prrnc. It is usul to considr th prvious orm or th valu unction bcaus o th xistnc o a CAPM quilibrium 3 and th ability to rach constant coicints o risk prrnc. Th prvious ormulation is also

12 supportd by th laboratory rsults rom osh-domènch and Silvstr [3]. Th ollowing graph indicats vx whn.88,.5 and Kahnman and Tvrsky suggstd valus Figur In our two-priod modl or portolio choic, th invstor chooss a wight in th risky asst to maximiz his xpctd utility V. His prrncs ar basd on changs in his walth x and ar dscribd by prospct thory. Th total xpctd valu h addrsss to a givn choic o is givn by: d V v x x dx Eq. 4 dx whr v x is th prospct valu o th outcom x, and x is th wightd cumulativ probability associatd with that outcom. Prospct thory is a dscriptiv thory, postulating that, in comparing altrnativs, th invstor will choos th altrnativ that maks V as high as possibl. Lt us thn valuat th invstor s problm in ach priod. A. First Priod In th irst priod, th agnt s problm consists o dining th allocation o his initial walth btwn th two assts tradd in th inancial markt. H maximizs his utility in t by allocating a raction,, o his initial walth 4, W, in th risky asst and - in th riskr asst. W considr that th invstor is a myopic optimizr in th sns that h taks into account only th irst priod rsult. For multi-priod horizons, th choics at arlir dats impact th rrnc points at latr dats. This atur allows or complx modling. Howvr, as pointd out in Shrin [5], prospct thory is a thory about invstors who ovrsimpliy, and so, assuming that individuals ar sophisticatd nough to prciv th link btwn thir currnt choics and utur rrnc points is somthing unrasonabl. W also constrain short slling, as it is common or individual invstors modls. Thus, his problm can b givn by d maxv v x x dx dx Eq. 5

13 Lt us mak th ollowing drivation: n x. arranging th trms in x, w gt n x. W call and C. Thn, Cn x, and so x > implis C n >. Thn, 6 Eq. ˆ C C C C C V n d n d C V n d n d C C V n d n d V x d x d V dx x dx d x v V C C nc C nc C nc C nc C Cn C Cn x x Whr, or th last stp, w usd 5 : z x z x d φ φ ˆ Obsrv that, i w wr considring a standard utility unction risk-avrsion ovr all possibl outcoms, th valu would b givn by: C S V Eq. 7 Morovr, th partial drivativs o V Eq. 6 ar:

14 3 [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] Eq. 9 } ] [ { Eq. 8 ]} ˆ [ { V V As a consqunc, th ollowing proprtis hold 6, i > V ; ii V or or ; iii < V or >. Equations 6 and 7 clarly yild dirnt wights or th risky asst, considring th rmaining paramtrs ixd. Thus, it is possibl to valuat th cost o inicincy associatd with th bhavioral biass as compard to th standard utility solution. [ ] [ ] Eq. Cost PT PT S S whr S is th risky asst wight givn by th standard utility maximization problm, and PT is th stock wight as dind in our modl. Proposition. Th optimal asst allocation in t, or th risky asst * is such that maximizs th valu unction givn by: C C C C C V C whr: [ ] * * and * C. I w wr considring a standard utility unction, th optimal allocation in t, or th risky asst would thn b givn by:

15 * Lt us irst considr standard valus or th modl s paramtrs 7. Th riskr rat quals th historical annual rturn o th US thr-month Trasury ill.73%. Th quity xpctd rturn and volatility quals th historical avrag o th MSCI global quity indx and its standard dviation 7.6% and.98%. Th adjustmnt actor in th probability wighting unction quals γ.9. Th coicint o risk-avrsion quals 3. Also, as suggstd by Kahnman and Tvrsky,.5 and. Th individual s valus prospct thory and standard as a unction o th prcntag o his walth invstd in th risky asst ar givn in Figur 3. Th individual invstor is xpctd to choos th allocation in th risky asst which maximizs his xpctd valu Figur As can b obsrvd rom th graph, using a standard utility unction, th allocation in th risky asst approachs % thta or which th valu unction rachs its maximum, whil using prospct thory utility, th invstor should allocat 8% o his walth in th stock 8. Th shaps o th graphs ar dirnt, notably or larg allocations in th stock. Th valu unction using standard utility is qual to or gratr than th on or prospct utility. Th rason or this dirnc coms rom th act that in prospct thory, ngativ outcoms ar pnalizd mor as ar risky portolios bcaus individuals ar loss-avrs >. In th loss-avrsion litratur vidnc suggsts that individuals ar around twic mor snsitiv to losss than thy ar attractd to sam siz gains. For small allocations in stocks, th prospct o losss bcoms lss likly and th valu unctions tnd to coincid. latd to th ct o probability wighting, i w st γ, thus cancling out its ct, w rach th ollowing Figur rprsnting th valu unction: Figur

16 Not that th amount optimally invstd by th bhavioral invstor in th risky asst dcrass to 48%, and so probability wighting tnds to incras th risk apptit. Kahnman and Tvrsky [979] suggst that th ovrwighting o low probabilitis has an ambiguous ct on risk-taking, as it can induc risk-avrsion in th domain o losss, and risk-sking in th domain o gains. In our cas, th ovrstimation o th xtrm positiv outcoms probabilitis, shown in Figur 3, is inducing invstors to tak mor risk. Howvr, dspit th cts o loss-avrsion and probability wighting, vn i w considr and γ, kping constant th rmaining paramtrs, th valu unctions wouldn t coincid, as can b sn in Figur 5: Figur oth modls would prdict that th invstor should allocat % o his ndowmnts in th stock. Howvr, th valu unctions ar dirnt bcaus, in prospct thory, individuals ar risk-sking in th loss domain asymmtric risk prrnc. Thus, thy would b mor comortabl in allocating a gratr part o thir walth in th risky asst. Th prospct valu unction is gratr than th standard utility unction. Obsrv that th ct o th asymmtric risk prrnc gos in th opposit dirction o loss-avrsion and probability wighting. Whn w diminish th coicint o risk prrnc.5 in both utility unctions, w rduc th ct o asymmtry, and so th valu unctions ar much closr, as can b sn in th ollowing igur Figur Th cts o th bhavioral biass can thus b summarizd as ollows: lossavrsion rducs risk-taking, and asymmtric risk-taking bhavior inducs risky attituds. Probability wighting has an ambiguous ct on risk. Our intuition is that, in th long run, as th valu unction paramtrs ar changing, ths biass tnd to cancl out, liminating th icincy loss originatd by ach bias. That is why w argu that human biass do not nd to b modratd to rach an icint invstmnt stratgy. Th 5

17 xprimntal rsults o lavatskyy and Pogrbna [6] rval that th ct o lossavrsion is largly nutralizd by th ovrwighting o small probabilitis and undrwighting o modrat and high probabilitis. In ordr to vriy proprty i, Lt us valuat V whil changing and kping constant th othr paramtrs considring 5%. Figur 7 prsnts th graph which indicats that ovr all positiv valus o, th slop o V is positiv. Th valu unction is incrasing in. Thus, whn th risky asst has a highr xpctd rturn, ctris paribus implis a highr valu or th invstor: Figur Considring proprtis ii and iii, Lt us valuat V whil changing and kping constant th othr paramtrs considring 5%. Figur 8 prsnts th graph indicating that ovr all positiv valus o, th slop o V is ngativ, whil or, th slop is null. Whn tnds to ininity, th slop tnds to null. Th valu unction is dcrasing in. Th intuition is that, i th volatility o th risky asst is highr, or th sam allocation, this implis a highr probability o losss rducing th valu o th prospct. In lin with traditional rational invstor, bhavioral individuals also prr highr rturn and lowr risk; mainly bcaus thy ar risk-avrs in th gain domain and also lossavrs Figur Now lt us valuat th valus o whn w chang th riskr rat and th xpctd rturn o th risky asst. Sinc many paramtrs ar involvd, it is not possibl to ind closd orm solutions or. Thror, w prsnt numrical rsults or th optimal allocation o walth in t. Figur 9 prsnts th rsults or % < < 5% and < 6%. Th rmaining paramtrs ar ixd.98%, 3,.5, < and Figur 9 6

18 As xpctd, whn th risky asst ors mor attractiv rturns, th agnt gradually invsts mor in th stock. Whn th stock is vry attractiv, th invstor chooss to allocat his ntir walth in th risky asst. Thus, w obsrv that is incrasing in and dcrasing in. Also, whn is highr, th changs in du to a variation in ar smoothr, bcaus in ths cass losss ar lss likly and w approach th standard utility solution. Whn is lowr, th changs in du to a variation in ar mor abrupt, giving ris to xtrm portolio allocations. I w considr that is not known with crtainty, th rsulting portolio would b vry unstabl. Goms [3], in a modl with loss-avrs invstors, has ound that individuals will not hold stocks unlss th quity prmium is quit high. W can valuat th xpctd cost o inicincy rlatd to th bhavioral biass associatd to th prospct thory unction, or th sam paramtrs considrd in th prvious analysis, using quation. Th rsult is prsntd in Figur, and its orm is du to th act that, in standard utility unction, th invstor is willing to tak mor risk than with th loss-avrs prospct utility. Th cost is du to th act that th xpctd rturn o th stock is gratr than th bond, and th standard utility invstor is allocating a gratr part o his walth in th risky asst than th prospct utility individual. Thus, th cost is incrasing in. Howvr, it is worth noting that th prvious cost is basd on xpctd rturns, which ar stochastic in practic. Th ral cost can just b obsrvd at th nd o th irst priod with th ralization o th stock s rturn. An important insight can b mad rom Figur in trms o th bst practic or asst allocation. As long as th riskr rat is lowr and th xpctd rturn o th stock is highr, th optimal allocation should modrat th invstor s biass in ordr to rach a bttr prormanc. On th othr hand, i th risk prmium is lowr, th modration is lss rlvant, and th optimal allocation may adapt to th individual s biass Figur

19 W can also analyz th chang in th allocation o th stock whn w vary th loss-avrsion in th risk-taking bhavior. Th rsult is shown in Figur, or < < 4. Obsrv that, as long as th invstor is much mor avrs to losss than h is attractd to gains, th allocation in th risky asst is lowr. Whn. 5, th allocation in th risky asst corrsponds to 8%, as prviously mntiond Figur Dimmock[5] has alrady shown that a highr lvl o loss-avrsion lads to lowr quity xposur, and htrognity in th coicint o loss-avrsion has th ability to xplain puzzling aturs o houshold inancial bhavior. A. Scond Priod In ordr to valuat th scond priod allocation choic o th invstor, Lt us kp som paramtrs ixd:.98, 3,.5 and. Atr th invstor has mad his irst priod dcision in t, th stat o natur ralizs in t, whn h is acd with his scond priod problm. Again, h must allocat his walth in th two possibl assts in th inancial markt, bond and stock, to maximiz his utility. Lt us considr th sam normal distribution or th rturn o th risky asst. Th invstor s walth position at t quals his position in t plus th rturn o his portolio in th scond priod. Whil all agnts solv th sam maximization problm in th irst priod, in th scond priod, it will dpnd on th rrnc point to which h masurs his gains and losss in th ramwork o prospct thory. In our modl, thr ar two candidats or th invstor s rrnc point at t : his initial walth at t W or his walth at th nd o th irst priod, t W. I h masurs his gains and losss rlativ to his walth at t his currnt walth, h trats ach gain and loss sparatly. On th othr hand, i h considrs his initial walth as th rrnc point, h adds up th outcoms gains and losss, that is, h nts his positions. Th prvious distinction is rlvant in prospct thory. Th valu unction is concav in th domain o gains and convx in th loss domain asymmtric risk bhavior. First, Lt us considr as th invstor s rrnc point his currnt walth at t. In this cas, th maximization problm h will solv in th scond priod is th sam as th on or th irst priod. Thus, w can stat th ollowing proposition. 8

20 * Proposition. Th optimal asst allocation in t, or th risky asst, i th agnt masurs his gains and losss rlativ to his currnt walth, is such that maximizs th * sam valu unction o th irst priod. * W can obsrv that an individual who masurs his gains and losss rlativ to his currnt walth is actually solving th sam maximization problm in ach priod. That is why th allocation in th risky asst might b th sam. This is not surprising; as h is not using past inormation to updat his blis about th assts, his prrncs ar similarly unactd. Nxt, lt us analyz th invstor s maximization problm i h valuats his gains and losss rlativ to his initial walth. I h has an initial walth position o W and his walth riss in th irst priod to W and alls in th nxt priod to W 5, h valus his position at t as a gain o 5, and not as a gain o ollowd by a loss o 5. In th scond priod, th agnt s problm consists o dining th allocation o his walth W btwn th two assts tradd in th inancial markt. H maximizs his utility in t by allocating a raction,, o his walth W in th risky asst and - in th risklss asst. As w did in th irst priod analysis, w also constrain short slling. d maxv v x x dx dx Lt us mak th ollowing drivation: x W [ n ] W and W W [ ], whr priod. So x W [ ] is th rturn o th stock in th irst [ n ] arranging th trms in x and considring W, w gt x [ n ] Lt us call [ ] [ ] ] [. 9

21 and C Thn, x Cn, so x > implis n >. Thn, C V C C C C C C Eq. * Proposition 3. Th optimal asst allocation in t, or th risky asst, i th agnt masurs his gains and losss rlativ to his initial walth, is such that it maximizs th valu unction givn by: whr: V C C C C * * W [ ], W [ ] C C * [ ] C, is th amount allocatd in th risky asst in th irst priod, and is th obsrvd rturn o th risky asst in th prvious priod. Obsrv that th valu unction to b maximizd is clos to th on o th irst priod, but with changs in th paramtrs and C, which account or th prvious priod outcom gain or loss. As w ar intrstd in th invstor s risk-taking bhavior atr ralizing a gain or a loss, lt us valuat th valus o whn w chang th total rturn obtaind in th irst priod. call that th total rturn rom t to t tot, dpnds both on his allocation choic in t and on th ralizd rturn o th risky asst. tot * * Lt us thn, valuat considring th ralizd rturn o th stock in th irst priod varying ovr th ollowing rang: * < <. W prsnt numrical * rsults or th optimal allocation o walth,, at t. Th rmaining paramtrs ar ixd 7.6%,.98, 3, W,.5 and. Figur shows th rsults. call that th optimal allocation in th risky asst or th irst priod, considring th prvious paramtrs, is 8%. Thus, w nd to vriy whthr th

22 allocation in th stock in th scond priod is gratr or lowr than 8%, indicating gratr or lowr risk apptit, rspctivly. First, obsrv that, or a total rturn in th irst priod qual to zro no gains/losss, th situation rplicats th sam ramwork th invstor acd in th irst priod. Thn w rach th sam optimal allocation in th * risky asst or tot implis 8% Figur Considr th surroundings o th nt valu tot. I th invstor xprincs a gain in th irst priod, th modl prdicts that h should optimally invst lss in th risky asst in th scond priod. This bhavior prvails up to th point whr th loss-avrsion ct is lss pronouncd. On th othr hand, i a loss is obsrvd in th irst priod, h should tak mor risk in th ollowing priod, allocating a gratr part o his walth in th stock. This prdiction is in lin with svral xprimnts, which hav shown that disposition ct dominats hous-mony in dynamic sttings Wbr and Zuchl 3. Whn th invstor xprincs a gain in th irst priod, h tnds to rduc his risk apptit in ordr to guarant th prvious outcom. On th othr hand, i h xprincs a loss in th irst priod, h will incras his bts on stocks, trying to avoid th prvious loss. In th modl, th pattrn holds or th whol gain domain; howvr, in th loss domain, high losss in th irst priod induc lss risk apptit in th scond priod. Th intuition is that i th invstor is acing a hug loss, th loss avrsion ct will dominat th risk-sking bhavior, inducing a rduction in th optimal allocation in th stocks. Whn w valuat th xpctd cost Eq. o th bhavioral inicincy in th scond priod as a unction o th rturn o th risky asst in th irst priod Figur 3, it is possibl to obsrv that, dpnding on th prvious outcom, th cost can b incrasing or dcrasing. I th valu or is such that it implis a small loss in th irst priod, th cost is vn ngativ, which mans that th xpctd rturn in th scond priod undr prospct thory is gratr than th on associatd with standard utility. This is rlatd to a gratr risk apptit o th prospct thory individual atr a loss, implying a gratr allocation in th stock, which has a gratr xpctd rturn. I indicats a gain in th irst priod, thn th cost is positiv onc th allocation in th stock or th standard utility invstor is gratr than or th prospct utility individual.

23 Figur W can conclud that or losss in th irst priod, th optimal allocation should adapt to th individual s biass to rach bttr prormanc as th cost coms out to b ngativ in this domain. For gains in th prvious outcom, th allocation should modrat th biass obsrv a positiv valu or th xpctd cost. For xtrm losss in th irst priod, th allocation should also modrat th invstor s biass. I w accumulat th cost rsults in priods and, w gt th graph rprsntd in Figur 4. It indicats that, or a ngativ stock rsult in th irst priod, or vn a slightly positiv on, th prospct thory individual outprorms th standard utility invstor. And so, th allocation stratgy should b adaptd to th individual biass. Th prvious rsults should b takn with car as thy rr to xpctd valus. In sction A.3., w provid a mor robust comparison, taking into account th prormanc o thos individuals in an out-o-sampl analysis Figur A.3 Multi-Priod Analysis I w xtnd th two-priod analysis to a multi-priod on, by analogy, i th invstor considrs his currnt walth as th rrnc to which h masurs his gains/losss, h will solv th sam maximization problm or ach priod and th optimal asst allocation is givn as in proposition. In this situation, th agnt acts myopically, just considring th ollowing priod possibl gain/loss. In gnral, this rsult implis a smallr stock allocation i compard to a standard utility invstor, gnrating an xpctd cost associatd to th prospct thory biass. On th othr hand, i th individual s rrnc point is his initial walth or his walth in som momnt in tim t t, th allocation is dind as in proposition 3, but now considring th prvious outcom as th total rturn obtaind by him rom t or rom t t to th currnt tim. As discussd in th two-priod modl, th allocation in th risky asst will dpnd on th prvious gains/losss, and can b gratr or smallr than th on chosn by th standard utility invstor. Obsrv that th standard utility invstor always chooss th sam allocation in th risky asst, no mattr what th

24 rrnc point, as nithr his dcisions nor his blis ar actd by prvious outcoms. A.4 sampling In sctions A., A. and A.3 w alrady valuatd th optimal asst allocation undr prospct thory prrncs and considring mntal accounting, loss-avrsion, asymmtric risk-taking bhavior, and probability wighting. Howvr, thr is still an important issu in portolio optimization missing: stimation rror. Up to now, whn solving th invstor s problm, w considrd th xpctd rturn known with crtainty, which is not th cas in rality spcially in mrging markts whr th uncrtainty is highr. Th assumd rturn or th risky asst is just an stimat, and so th ral valu can b dirnt. This problm is rlvant in any modl o portolio optimization and is crucial undr prospct thory, whr or lowr valus o th riskr rat, a slightly incras in th risk prmium o stocks can lad to xtrm allocations. I th ral rturn o th risky asst is lowr, th liklihood o acing a loss is gratr and should signiicantly rduc th valu o that prospct. In an attmpt to ovrcom this stimation problm, Michaud [998] proposd th rsampling tchniqu. Portolio sampling allows an analyst to visualiz th stimation rror in traditional portolio optimization mthods. Suppos that w stimatd both th varianc and th xcss rturn by using N obsrvations. It is important to not that th point stimats ar random variabls and so anothr sampl o th sam siz rom th sam distribution would rsult in dirnt stimats. Shrr [] suggsts that sampling rom a multivariat normal distribution a paramtric mthod trmd Mont Carlo simulation is a way to captur th stimation rror. In this sns, rturn and varianc would just b th xpctd valus or a multivariat normal distribution. I w just considr two assts, th probability dnsity unction or a multivariat normal distribution would b givn by. y rpating th sampling procdur n tims, w gt n nw sts o optimization inputs, and thn a dirnt icint allocation. Th rsampld wight or a portolio would thn b givn by n samp i n i 3

25 Th rsampld portolios should rlct a gratr divrsiication mor assts ntr in th solution than th classical man-varianc icint portolio, and should also xhibit lss suddn shits smooth transitions in allocations as rturn rquirmnts chang. oth charactristics ar dsirabl or invstors. cnt litratur has shown unambiguous rsults in avor o rsampld portolios in out-o-sampl analysis Pawly, 5; Markowitz and Usmn, 3; Wol, 6; Jiao, 3. Howvr, Harvy t al. [6], valuating ays vs. rsampling mthods, posit that th choic o risk-avrsion drivs th rsults. Kohli [5] concluds that, dspit th act that thr ar no conclusiv advantags or disadvantags o using rsampling as a tchniqu to obtain bttr rturns, rsampld portolios do sm to or highr stability and lowr transaction costs, two crucial aturs or long trm invstors choics. W thn propos th ATE havior sampl Adjustd Tchniqu as a novl mthodology to din asst allocation, which incorporats bhavioral idas and rsampling tchniqus into portolio optimization, thus adapting to th individual s prrncs. In this cas, th optimal asst allocation should b givn by th prvious propositions and or 3, dpnding on th rrnc point, but th procdur should b prormd svral tims or dirnt xpctd stock rturns givn by a multivariat normal distribution. Th inal allocation is thn givn by th xpctd risky asst allocation. Th procdur can b summarizd as ollows 9 Stp : Estimat varianc-covarianc and rturn rom th historical inputs. Stp : sampl rom inputs cratd in Stp by taking n draws rom th input distribution. Th numbr o draws rlcts th dgr o uncrtainty in th inputs. Calculat nw varianc-covarianc and rturn rom sampld sris. Estimation rror will rsult in stimations that ar dirnt rom thos obtaind in Stp. Stp 3: Calculat th optimal allocation or inputs dind in Stp, using th appropriat propositions and or 3, dpnding on th rrnc point considrd. Stp 4: Atr rpating Stps and 3 many tims, calculat avrag portolio wights. This is th ATE portolio allocation. 4

26 In th nxt sction, w provid an mpirical analysis comparing th ATE allocation prormanc to a standard utility allocation.. Empirical Study. Data and Implmntation Our tsts ar basd considring daily data rom 6 countris MSCI stock indics and riskr rats, plus th MSCI World Indx, or th priod rom April 4 th, 995 to January 5 th, 7. Dvlopd countris and mrging markts razil, Chil, South Arica, South Kora, Taiwan, Thailand, Turky wr includd in th analysis in ordr to ind gnralizabl rsults. Th total rturn tim sris ar calculatd on ach country s currncy and also in US-Dollars. Thus, w ar considring both currncy hdgd and unhdgd invstors. Tabl I prsnts som dscriptiv statistics o ach markt considrd, or th whol sampl priod Tabl I From th tabl, w vriy a risk prmium associatd with th stock markt, both considring th valus in ach country s currncy and in USD, with th man rturn o stocks bing highr than th on o th corrsponding riskr rat. Lt us irst considr th valus in ach country s currncy. Th avrag annualizd rturn o th riskr rat varid rom.5% Japan to 39.54% Turky, whil or th stock indx, it rangs rom.76% Thailand to 47.84% Turky. Th annualizd volatility standard dviation o th stock markt varid rom.976% World Indx to 45.7% Turky. As xpctd, mrging markts tnd to b mor volatil than dvlopd markts. Whil in razil, South Kora, Thailand, and Turky th volatility was abov 3 %, in countris lik Unitd Kingdom and Unitd Stats, its valu was clos to 6%. In trms o skwnss and kurtosis, usual rsults appar, indicating that daily stock indx rturns ar ngativ skwd and hav xcss kurtosis gratr than 3. Finally, Tabl prsnts th annualizd Sharp atio, which was gratr in dvlopd markts around.35 than mrging markts.9. Our rsults ar in lin with prvious litratur which givs.34 as an stimation o th long-trm Sharp atio or th U.S. conomy. 5

27 Whn w considr th valus in USD, say in th prspctiv o a US basd intrnational invstor who dosn t currncy hdg his invstmnts, w ind similar rsults. Th avrag daily rturn in USD is clos to th on in th country s currncy, which is vidnc o th man rvrting aspct o th orign xchang markt. Howvr, th standard dviation in USD is slightly gratr than th on in th country s currncy, as th ormr includs both stock markt risk and currncy risk th volatility o th orign xchang rat. In trms o skwnss and kurtosis, th prvious rsults rmain. Howvr, now th Sharp atios do not prsnt rlvant dirncs among mrging and dvlopd markts or instanc it is.43 or razil and.4 or th Unitd Stats. Thus it sms that mrging stock markts ar lss intrsting or domstic invstors than or orign unhdgd invstors. Nxt w analyz th prormanc o th ollowing optimization stratgis: an invstor with a standard utility prrnc - STU; an invstor with prospct utility prrnc, with rrnc point givn by his currnt walth PTU; an invstor with prospct utility prrnc, with rrnc point givn by his walth in th prvious priod CPT; an invstor with a standard utility prrnc rsampld STU; an invstor with prospct utility prrnc, with rrnc point givn by his currnt walth rsampld ATEa; and an invstor with prospct utility prrnc, with rrnc point givn by his walth in th prvious priod rsampld ATEb. Th utility unction paramtrs ar ixd 3,.5 and. W vary th stimation priod p in an out-o-sampl analysis. Th paramtrs ar stimatd using daily rturn obsrvations o th past p days. W din th icint portolio and hold it or th nxt months, thn r-stimat th paramtrs and adjust th portolio wights. To judg th inancial prormanc o th stratgis, w comput thir avrag rturn and mpirical Sharp atios... sults Th Sharp atios o th dirnt stratgis ar prsntd in Tabl II or th World Indx and or th total priod rom 995 to 7, considring p 6 months,,, and 4 yars, and varying rom months to yar. W ar valuating th dirnt stratgis or a US basd intrnational stock invstor. Th riskr rat considrd was th 3 month T-ill Tabl II

28 In gnral, w can stat that th rsampld modls ord bttr rsults or a short slling constraind invstor. It is an xpctd rsult as rsampld modls tak into account th stimation risk, gnrating a mor divrsiid portolio which tnds to outprorm in out-o-sampl studis. Th highst Sharp atio was rachd by th ATEb modl or an stimation priod o yars and valuation priod o yar.465. On avrag rsampld modls incras th Sharp atio in around., whn compard to th dtrministic ons. Also, whil th STU invstor sms to outprorm PTU, it dosn t happn with CPT. I w considr just th total rturn obtaind by ach stratgy, w ind th rsults prsntd in Tabl III. In this cas, it s possibl to inr an inicincy cost rlatd to th bhavioral invstors, who tnd to undrprorm th rsults o th standard utility invstor in around bps. Howvr i tak into account th incrmnt in risk a risk adjustd masur lik Shap atio, th inicincy disappars Tabl III asd on th prvious rsults, w can stat that rsampld modls tnd to outprorm traditional modls. Also, thr is no clar advantag o standard utility invstors ovr bhavioral prospct thory invstors at last to th CPT invstor. Lvy and Lvy [4] rachd a similar rsult, positing that th practical dirncs btwn prospct thory and traditional man-varianc thory ar minor. In this sns, bhavioral biass should not b modratd, nor should standard modls b adaptd to includ bhavioral biass. Whn w tak into account ach markt sparatly, w ind th rsults prsntd in Tabl IV in ach country s currncy. Considring ach country individually, thr s no clar dominanc o a singl stratgy. sampld modls tnd to outprorm traditional modls in mrging markts obsrv th rsults or razil, Chil, South Arica, South Kora, Taiwan, Thailand and Turky, whr th uncrtainty ovr th risk/rturn stimation is highr Tabl IV In trms o th comparison btwn th standard and th prospct utility invstor, gnrally th ormr dosn t outprorm th lattr, indicating no clar 7

29 dominanc o th traditional rational modl. In this sns, thr is no nd or modrating th bhavioral biass as dscribd by prospct thory, as no xtra inancial icincy is gaind. Gnrally spaking, an intrsting inding is th act that all prvious allocation modls outprorm th % risky stratgy. Th Sharp atio o th % stock stratgy was.383 whil all rsampld modls rachd, on avrag, a rsult abov.59. Finally, i w tak into account th valus in USD and so considring that th invstor is acing orign xchang risk, w rach th rsults prsntd in Tabl V Tabl V Again, th rsults indicat a dominanc o rsampld modls in mrging markts, whil or dvlopd countris, no clar dominanc can b sn. Th traditional rational modl dos not outprorm th bhavioral ons. Finally, all six dynamic modls add valu or th invstor whn compard to a % stock invstd individual. Obsrv that th Sharp atio ound or th dirnt markts both in th country s currncy and in USD ar notably highr than th ons prsntd in Tabl. Summing up, rsampld modls, which tak into account stimation risk, tnd to outprorm dtrministic modls, notably or mrging markts whr th uncrtainty o th xpctd rturn stimation is highr. Morovr, prospct thory utility invstors don t rach wors rturns i compard to th traditional rational ons, which indicats no nd or addrssing bias modration in th portolio allocation. C. Conclusions This study had two objctivs: irst to incorporat mntal accounting, lossavrsion, asymmtric risk-taking bhavior, and probability wighting in portolio optimization or individual invstors; and scond to tak into account th stimation risk in th analysis. Considring daily indx stock data rom 6 countris ovr th priod rom 995 to 7, w mpirically valuatd our modl ATE havior sampl Adjustd Tchniqu against th traditional Markowitz. Svral stimation and valuation priods wr usd and w also considrd a orign xchang hdgd and an unhdgd stratgy. 8

30 Our rsults support th us o ATE as an altrnativ or dining optimal asst allocation and posit that a portolio optimization modl may b adaptd to th individual biass implid in prospct thory. havioral biass don t sm to rduc icincy whn w considr a dynamic stting. This rsult is robust or dirnt dvlopd and mrging markts. Also, th prvious optimization modls add valu or th individual invstor whn compard to a naiv % risky stratgy. As urthr xtnsions o th prsnt rsarch, w suggst th inclusion o svral risky assts in th analysis. In this cas, th issu o multipl mntal accounting is a crucial issu to addrss th problm. An invstor who valuats vry scurity in thir own mntal account will not ncssarily viw additional scuritis as rdundant, which dramatically incrass th complxity o th problm. W also lav unanswrd th qustion o how individuals arriv at th undrlying rturn distribution. That is th modl abov is a proposd mchanism or how individuals might transorm a givn probability distribution assumd to b an accurat rprsntation o th undrlying distribution into dcision wights. Onc w introduc uncrtainty, it can induc individual biass, subjctivity and rror. Thr is vidnc that popl display considrabl ovrconidnc whn askd to provid a subjctiv assssmnt o a probability distribution 3. Morovr, it is qustionabl whthr th wightings providd by CPT truly rlct th procss by which individuals valuat continuous probability distributions. Anothr suggstion is an analysis i th Sharp atio is an appropriat prormanc masur whn considring bhavioral invstors. Is th volatility capturing all th rlvant risk or th individual bhavioral invstor? Th considration o stimation rror in th Sharp atio stimation is also lt or a urthr rsarch. Th agnt who masurs his gains and losss always rlativ to his actual walth solvs th sam maximization problm ach priod, thror slcting a ix-mix stratgy. An opn qustion rmains, i a ix-mix stratgy, whr th invstor st a ixd proportion o stocks and bonds or his portolio, can b th caus o th disposition ct. 9

31 rncs AEIS, Nicholas and Ming HUANG,, Mntal accounting, loss avrsion, and individual stock rturns, Journal o Financ, LVI 4, pp AEIS, Nicholas, HUANG, Ming and Tano SANTOS,, Prospct Thory and Asst Prics, Quartrly Journal o Economics, CXVI, pp ENATZI, Shlomo, and ichard THALE, 995, Myopic Loss Avrsion and th Equity Prmium Puzzl, Quartrly Journal o Economics, Vol., No., LACK, Fishr and obrt LITTEMAN, 99, Global Portolio Optimization, Financial Analysts Journal, 48, 5, pp LAVATSKYY, Pavlo and Ganna POGENA, 6, Myopic Loss Avrsion visitd: th Ect o Probability Distortions in Choic Undr isk. IEW Working Papr No. 49 Availabl at SSN: OSCH-DOMÈNECH, Antoni and Joaquim SILVESTE, 3, lctions on Gains and Losss: A X X 7 Exprimnt, Working Papr, Univrsitat Pompu Fabra and Univrsity o Caliornia at Davis. DAVIES, Grg and Stphn SATCHELL, 4, Continuous Cumulativ Prospct Thory and Individual Asst Allocation, Cambridg Working Paprs in Economics, 467. DIMMOCK, Stphn G., 5, Loss-Avrsion and Houshold Portolio Choic. Availabl at SSN: FELDMAN, David and Haim EISMAN,, Simpl Construction o th Eicint Frontir, Forthcoming, Europan Financial Managmnt. FENANDES, Jos L.., ONELAS, Jos. H., and Marclo TAKAMI, 8, Incorporating Markt and Crdit isk in Stochastic Portolio Optimization, Icai Journal o Financial isk Managmnt, Vol. 5, No., pp FENANDES, Jos, Augusto HASMAN and Ignacio PEÑA, 7, isk Prmium: Insights ovr th Thrshold, Availabl at SSN: Forthcoming in Applid Financial Economics. FENANDES, José, PEÑA, Juan I., TAAK, njamin and José ONELAS, 7, Prossional Portolio Managrs, A Stting or Momntum Stratgis, Availabl at SSN: GIOGI, Enrico, HENS, Thorstn and Haim LEVY, 4, Existnc o CAPM Equilibria with Prospct Thory Prrncs, National Cntr o Comptnc in 3

32 sarch Financial Valuation and isk Managmnt, Working Papr No. 85, pp. -4. GOMES, Francisco J., 3, Portolio Choic and Trading Volum with Loss Avrs Invstors. EFA 663. Availabl at SSN: or DOI:.39/ssrn HAVEY, Campbll, LIECHTY, John and Mrrill LIECHTY, 6, ays vs. sampling: A match, Availabl at SSN: HOST, Jnk, OON, Frans and as WEKE,, Incorporating Estimation isk in Portolio Choic, CntE Working Papr No. 65. Availabl at SSN: JIAO, Wi, 3, Portolio sampling and Eicincy Issus, Mastr Thsis Prsntd at Humboldt-Univrsity o rlin. JOION, Philipp, 986, ays-stin Estimation or Portolio Analysis, Th Journal o Financial and Quantitativ Analysis, Vol., No. 3, pp KAHNEMAN, Danil and Amos TVESKY, 979, Prospct Thory: An Analysis o Dcision Undr isk, Economtrica. Vol. 47, No., March, pp KEMPF, Alxandr, KEUZEG, Klaus and Christoph MEMMEL,, How to Incorporat Estimation isk into Markowitz Optimization, Oprations sarch Procdings, rlin t al.. KOHLI, Jasraj, 5, An Empirical Analysis o sampld Eicincy, Thsis submittd to th Faculty o th Worcstr Polytchnic Institut. LEVY, H., and M. LEVY, 4, Prospct Thory and Man-Varianc Analysis, viw o Financial Studis, Vol. 7, No. 4, pp LO, Andrw, EPIN, Dmitry and rtt STEENAGE, 5, Far and Grd in Financial Markts: A Clinical Study o Day-Tradrs, Working Papr. MAENHOUT, Pascal, 4, obust Portolio uls and Asst Pricing, viw o Financial Studis, 7, 4, pp MAGI, Alssandro, 5, Financial Dcision-making and Portolio Choic undr havioral Prrncs: Implications or th Equity Hom ias Puzzl. Availabl at SSN: MAKOWITZ, Harry and Nilur USMEN, 3, sampld Frontirs vrsus Dius ays: An Exprimnt, Journal o Invstmnt Managmnt, vol., no. 4 Fourth Quartr, pp

33 MAKOWITZ, Harry. 95. Portolio Slction. Th Journal o Financ, Vol. 7, No., March, pp MICHAUD, ichard, 998, Eicint Asst Managmnt, oston, MA: Harvard usinss School Prss. ODEAN, Trranc, 998, Ar Invstors luctant to aliz thir Losss, Th Journal o Financ, Vol. 53, No. 5, Octobr, PAWLEY, Mark, 5, sampld Man-Varianc Optimization and th Dynamic Natur o Markts, Papr prsntd at th binnial 5 conrnc o th Economic Socity o South Arica. SCHMIDT, Ulrich, and Horst ZANK, 5, What is Loss Avrsion? Th Journal o isk and Uncrtainty, Vol. 3, No., SHEFIN, Hrsh and M. STATMAN, 985. Th Disposition Ect to sll winnrs too arly and rid losrs too long. Journal o Financ, Vol. 4, No. 3, pp SHEFIN. Hrsh, 5, A havioral Approach to Asst Pricing, Elsvir Acadmic Prss. SHEE, rnd,, Portolio sampling: viw and Critiqu, Financial Analysts Journal, Vol. 58, No. 6, pp St-AMOU, Pascal, 6, nchmarks in Aggrgat Houshold Portolios. Swiss Financ Institut sarch Papr No. 7-9 Availabl at SSN: THALE, ichard H., 999, Mntal accounting mattrs, Journal o havioral Dcision Making,, pp THALE, ichard H., and Eric J. JOHNSON, 99, Gambling with th Hous-mony and Trying to rak Evn: Th Ects o Prior Outcoms on isky Choic, Managmnt Scinc, Vol. 36, TVESKY, Amos, and KAHNEMAN, Danil, 99. Advancs in prospct thory: cumulativ rprsntation o uncrtainty, Journal o isk and Uncrtainty. Vol. 5, No. 4, VLCEK, Martin, 6, Portolio Choic with Loss Avrsion, Asymmtric isk-taking havior and Sgrgation o isklss Opportunitis, Swiss Financ Institut, sarch Papr Sris, N WEE, Martin and Colin CAMEE, 998, Th Disposition Ect in Scuritis Trading: An Exprimntal Analysis, Journal o Economic havior and Organization, Vol. 33, No.,

34 WEE, Martin, and Hiko ZUCHEL, 3, How do Prior Outcoms Act isk Attitud? Univrsität Mannhim, Working Papr, vrsion: Fbruary. WOLF, Michal, 6, sampling vs. Shrinkag or nchmarkd Managrs, Institut or Empirical sarch in Economis, Univrsity o Zurich, Working Papr Sris, No. 63. ZIMME, Christian and at NIEDEHAUSE, 3, Dtrmining an Eicint Frontir in a Stochastic Momnts Stting, Univrsidad d São Paulo, Dpartamnto d Administração, Working Papr Sris Nº 3/. 33

35 Footnots:. Tvrsky and Kahnman s Cumulativ Prospct Thory CPT [99] combins th concpts o loss-avrsion and a non linar rank dpndnt wighting o probability assssmnts.. Exprimnts suggst a valu o γ btwn.8 and.9 Tvrsky and Kahnman, Undr Cumulatd Prospct Thory CPT with Tvrsky and Kahnman [99] spciications, quilibria do not xist as at last on invstor can ininitly incras his utility by ininitly lvraging th markt portolio th utility indx is almost linar or larg staks, whil th Scurity Markt Lin Thorm holds Giorgi t al., W will considr th invstor s initial walth quals to. 5. This last drivation is valid or th cas whr γ. 6. S Appndix or th proos. 7. Th riskr rat, th xpctd rturn o th risky asst and th volatility o th risky asst wr calculatd, using daily data, ovr th priod rom 995 and 7. Th rsults wr annualizd. 8. Davis and Satchll [4] ound that th avrag proportion in domstic and orign quitis o larg pnsion unds in 993 was 83% in th UK, which is in lin with th prospct thory rsults. 9. This mthodology is an adaptation o th on proposd in Michaud [998].. Th only xcption is Thailand whr th Sharp atio is ngativ bps.%.. A t-tst ovr th Sharp atio dirncs ord a signiicant rsult with a p- valu o.. 3. Thir subjctiv distribution is too tightly cntrd on thir stimatd man. 34

36 35 Appndix : Proos o th Valu Function Proprtis W want to prov that th ollowing proprty hold: i > V ; Th partial drivativ o V Eq. 6 is givn by: [ ] [ ] [ ] [ ] Eq. 8 ]} [ { V as [ ] [ ] [ ] [ ] ] [ > so, > V Now, lt s prov proprtis ii and iii ii V or or ; iii < V or >. Th partial drivativ o V Eq. 6 is givn by: [ ] [ ] [ ] [ ] } ' ] [ { ` V It ollows:, V using that, - and ' Lt us considr [ ], V, or >. W show that, <.

37 36 Suppos that or som * and * >, *, >. Sinc, is continuous, [ ], lim < and, lim or all >, w can assum without loss o gnrality that * > is a local maxima o *,. W comput th partial drivativ o with rspct to. W hav [ ] [ ] [ ] [ ] 4 - ` ', Lt η thn [ ] [ ] { } *,, η η η η whr [ ] [ ] * η. Morovr, or,, * < > η η and or,, * > < < η η. It ollows that * * / > η is th uniqu maximum/minimum o, and sinc or * >,, > and or *,,, * < < < is a minimum. This contradicts th xistnc o * and * local maxima o *, such that * *, >. Hnc,, < and thror, < V. Also,, lim or > sinc [ ] [ ] [ ] [ ] lim lim And [ ] ' lim

38 Tabls Tabl I Dscriptiv Statistics This Tabl provids dscriptiv statistics or th sampl o world markts. For ach markt w prsnt, th avrag risk r rat, th man, standard dviation, skwnss, and kurtosis o stock rturns, as wll as th Sharp atio annualizd valus. Th valus ar prsntd in th countris currncy and also in USD. Th risk r rat usd to calculat th Sharp atio in USD is th 3 month UST ill rat or all markts. Currncy USD isk Fr Man Std. Skw Kurt Sharp atio Man Std. Skw Kurt Sharp atio T-ill 3 month 'Australia' 'Austria' 'lgium' 'razil' 'Canada' 'Chil' 'Dnmark' 'Finland' 'Franc' 'Grmany' 'Irland' 'Italy' 'Japan' 'Nthrlands' 'Norway' 'Portugal' 'SouthArica' 'SouthKora' 'Spain' 'Swdn' 'Switzrland' 'Taiwan' 'Thailand' 'Turky' UnitdKingdom' 'UnitdStats' World Indx Tabl II Sharp atios This Tabl prsnts th Sharp atio o th icint portolio gnratd by ach stimation modl. Th Sharp atio is calculatd by dividing th xcss rturn obsrvd by th standard dviation. STU PTU CPT STU ATEa ATEb 6m-m m-6m y-6m y-6m y-6m y-y y-y y-y man

39 Tabl III Avrag Total turn This Tabl prsnts th Avrag Total turn o th icint portolio gnratd by ach stimation modl. STU PTU CPT STU ATEa ATEb 6m-m m-6m y-6m y-6m y-6m y-y y-y y-y man Tabl IV Sharp atios This Tabl prsnts th Sharp atio o th icint portolio gnratd considring an stimation priod o yar and valuation priod o 6 months in ach country s currncy. Th Sharp atio is calculatd by dividing th xcss rturn obsrvd by th standard dviation. STU PTU CPT STU ATEa ATEb 'Australia' 'Austria' 'lgium' 'razil' 'Canada' 'Chil' 'Dnmark' 'Finland' 'Franc' 'Grmany' 'Irland' 'Italy' 'Japan' 'Nthrlands' 'Norway' 'Portugal' 'SouthArica' 'SouthKora' 'Spain' 'Swdn' 'Switzrland' 'Taiwan' 'Thailand' 'Turky' UnitdKingdom' 'UnitdStats' World Indx'

40 Tabl V Sharp atios This Tabl prsnts th Sharp atio o th icint portolio gnratd considring an stimation priod o yar and valuation priod o 6 months valus in USD. Th Sharp atio is calculatd by dividing th xcss rturn obsrvd by th standard dviation. STU PTU CPT STU ATEa ATEb 'Australia' 'Austria' 'lgium' 'razil' 'Canada' 'Chil' 'Dnmark' 'Finland' 'Franc' 'Grmany' 'Irland' 'Italy' 'Japan' 'Nthrlands' 'Norway' 'Portugal' 'SouthArica' 'SouthKora' 'Spain' 'Swdn' 'Switzrland' 'Taiwan' 'Thailand' 'Turky' UnitdKingdom' 'UnitdStats' World Indx'

41 Figurs,,8,6 pip p,4,,,4,6,8, Figur Cumulativ probability wighting unction or γ.8.,5 -,5 - -,5,5,5 -,5 - -,5 Figur Prospct thory valu unction or.88,.5 and 4

42 .6.5 Vpt Vs.4.3 V % Figur 3 Prospct valu and standard utility valu as unction o.6.5 Vpt Vs.4.3 V % Figur 4 Prospct valu and standard utility valu as unction o 4

43 .7.6 Vpt Vs V % Figur 5 Prospct valu and standard utility valu as unction o..8 Vpt Vs.6.4 V % Figur 6 Prospct valu and standard utility valu as unction o 4

44 V Figur 7 Prospct valu as unction o.5..5 V Figur 8 Prospct valu as unction o 43

45 r Figur 9 Optimal quity allocation in th irst priod as unction o and r. 5 Cost r Figur Expctd cost in th irst priod as unction o and r. 44

46 Figur Optimal quity allocation in th irst priod as unction o. 45

47 tot Figur Optimal quity allocation in th scond priod as unction o th total rturn obtaind in th irst priod Cost Figur 3 Expctd cost in th scond priod as unction o th quity rturn obtaind in th irst priod. 46

48 Acum Cost Figur 4 Expctd cumulativ cost in th scond priod as unction o th quity rturn obtaind in th irst priod. 47

49 anco Cntral do rasil Trabalhos para Discussão Os Trabalhos para Discussão podm sr acssados na intrnt, no ormato PDF, no ndrço: Working Papr Sris Working Paprs in PDF ormat can b downloadd rom: Implmnting Inlation Targting in razil Jol ogdanski, Alxandr Antonio Tombini and Sérgio ibiro da Costa Wrlang Política Montária Suprvisão do Sistma Financiro Nacional no anco Cntral do rasil Eduardo Lundbrg Montary Policy and anking Suprvision Functions on th Cntral ank Eduardo Lundbrg 3 Privat Sctor Participation: a Thortical Justiication o th razilian Position Sérgio ibiro da Costa Wrlang 4 An Inormation Thory Approach to th Aggrgation o Log-Linar Modls Pdro H. Albuqurqu 5 Th Pass-Through rom Dprciation to Inlation: a Panl Study Ilan Goldajn and Sérgio ibiro da Costa Wrlang 6 Optimal Intrst at uls in Inlation Targting Framworks José Alvaro odrigus Nto, Fabio Araújo and Marta altar J. Morira 7 Lading Indicators o Inlation or razil Marcll Chauvt 8 Th Corrlation Matrix o th razilian Cntral ank s Standard Modl or Intrst at Markt isk José Alvaro odrigus Nto 9 Estimating Exchang Markt Prssur and Intrvntion Activity Emanul-Wrnr Kohlschn Anális do Financiamnto Extrno a uma Pquna Economia Aplicação da Toria do Prêmio Montário ao Caso rasiliro: Carlos Hamilton Vasconclos Araújo nato Galvão Flôrs Júnior A Not on th Eicint Estimation o Inlation in razil Michal F. ryan and Stphn G. Ccchtti A Tst o Comptition in razilian anking Márcio I. Nakan Jul/ Jul/ Jul/ Jul/ Jul/ Jul/ Jul/ Sp/ Sp/ Nov/ Mar/ Mar/ Mar/ 48

50 3 Modlos d Prvisão d Insolvência ancária no rasil Marcio Magalhãs Janot 4 Evaluating Cor Inlation Masurs or razil Francisco Marcos odrigus Figuirdo 5 Is It Worth Tracking Dollar/al Implid Volatility? Sandro Cansso d Andrad and njamin Miranda Tabak 6 Avaliação das Projçõs do Modlo Estrutural do anco Cntral do rasil para a Taxa d Variação do IPCA Srgio Aonso Lago Alvs Evaluation o th Cntral ank o razil Structural Modl s Inlation Forcasts in an Inlation Targting Framwork Srgio Aonso Lago Alvs 7 Estimando o Produto Potncial rasiliro: uma Abordagm d Função d Produção Tito Nícias Tixira da Silva Filho Estimating razilian Potntial Output: a Production Function Approach Tito Nícias Tixira da Silva Filho 8 A Simpl Modl or Inlation Targting in razil Paulo Springr d Fritas and Marclo Koury Muinhos 9 Uncovrd Intrst Parity with Fundamntals: a razilian Exchang at Forcast Modl Marclo Koury Muinhos, Paulo Springr d Fritas and Fabio Araújo Crdit Channl without th LM Curv Victorio Y. T. Chu and Márcio I. Nakan Os Impactos Econômicos da CPMF: Toria Evidência Pdro H. Albuqurqu Dcntralizd Portolio Managmnt Paulo Coutinho and njamin Miranda Tabak 3 Os Eitos da CPMF sobr a Intrmdiação Financira Sérgio Mikio Koyama Márcio I. Nakan 4 Inlation Targting in razil: Shocks, ackward-looking Prics, and IMF Conditionality Jol ogdanski, Paulo Springr d Fritas, Ilan Goldajn and Alxandr Antonio Tombini 5 Inlation Targting in razil: viwing Two Yars o Montary Policy 999/ Pdro Fachada 6 Inlation Targting in an Opn Financially Intgratd Emrging Economy: th Cas o razil Marclo Koury Muinhos 7 Complmntaridad Fungibilidad dos Fluxos d Capitais Intrnacionais Carlos Hamilton Vasconclos Araújo nato Galvão Flôrs Júnior Mar/ Mar/ Mar/ Mar/ Jul/ Abr/ Aug/ Apr/ May/ May/ Jun/ Jun/ Jul/ Aug/ Aug/ Aug/ St/ 49

51 8 gras Montárias Dinâmica Macroconômica no rasil: uma Abordagm d Expctativas acionais Marco Antonio onomo icardo D. rito 9 Using a Mony Dmand Modl to Evaluat Montary Policis in razil Pdro H. Albuqurqu and Solang Gouvêa 3 Tsting th Expctations Hypothsis in th razilian Trm Structur o Intrst ats njamin Miranda Tabak and Sandro Cansso d Andrad 3 Algumas Considraçõs sobr a Sazonalidad no IPCA Francisco Marcos. Figuirdo obrta lass Staub 3 Criss Cambiais Ataqus Espculativos no rasil Mauro Costa Miranda 33 Montary Policy and Inlation in razil 975-: a VA Estimation André Minlla 34 Constraind Discrtion and Collctiv Action Problms: lctions on th solution o Intrnational Financial Criss Arminio Fraga and Danil Luiz Glizr 35 Uma Dinição Opracional d Estabilidad d Prços Tito Nícias Tixira da Silva Filho 36 Can Emrging Markts Float? Should Thy Inlation Targt? arry Eichngrn 37 Montary Policy in razil: marks on th Inlation Targting gim, Public Dbt Managmnt and Opn Markt Oprations Luiz Frnando Figuirdo, Pdro Fachada and Sérgio Goldnstin 38 Volatilidad Implícita Antcipação d Evntos d Strss: um Tst para o Mrcado rasiliro Frdrico Pchir Goms 39 Opçõs sobr Dólar Comrcial Expctativas a spito do Comportamnto da Taxa d Câmbio Paulo Castor d Castro 4 Spculativ Attacks on Dbts, Dollarization and Optimum Currncy Aras Aloisio Araujo and Márcia Lon 4 Mudanças d gim no Câmbio rasiliro Carlos Hamilton V. Araújo Gtúlio. da Silvira Filho 4 Modlo Estrutural com Stor Extrno: Endognização do Prêmio d isco do Câmbio Marclo Koury Muinhos, Sérgio Aonso Lago Alvs Gil illa 43 Th Ects o th razilian ADs Program on Domstic Markt Eicincy njamin Miranda Tabak and Eduardo José Araújo Lima Nov/ Nov/ Nov/ Nov/ Nov/ Nov/ Nov/ Dz/ Fb/ Mar/ Mar/ Mar/ Apr/ Jun/ Jun/ Jun/ 5

52 44 Estrutura Comptitiva, Produtividad Industrial Libração Comrcial no rasil Pdro Cavalcanti Frrira Osmani Tixira d Carvalho Guillén 45 Optimal Montary Policy, Gains rom Commitmnt, and Inlation Prsistnc André Minlla 46 Th Dtrminants o ank Intrst Sprad in razil Tarsila Sgalla Aanasi, Priscilla Maria Villa Lhacr and Márcio I. Nakan 47 Indicadors Drivados d Agrgados Montários Frnando d Aquino Fonsca Nto José Albuqurqu Júnior 48 Should Govrnmnt Smooth Exchang at isk? Ilan Goldajn and Marcos Antonio Silvira 49 Dsnvolvimnto do Sistma Financiro Crscimnto Econômico no rasil: Evidências d Causalidad Orlando Carniro d Matos 5 Macroconomic Coordination and Inlation Targting in a Two-Country Modl Eui Jung Chang, Marclo Koury Muinhos and Joanílio odolpho Tixira 5 Crdit Channl with Sovrign Crdit isk: an Empirical Tst Victorio Yi Tson Chu 5 Gnralizd Hyprbolic Distributions and razilian Data José Fajardo and Aquils Farias 53 Inlation Targting in razil: Lssons and Challngs André Minlla, Paulo Springr d Fritas, Ilan Goldajn and Marclo Koury Muinhos 54 Stock turns and Volatility njamin Miranda Tabak and Solang Maria Gurra 55 Componnts d Curto Longo Prazo das Taxas d Juros no rasil Carlos Hamilton Vasconclos Araújo Osmani Tixira d Carvalho d Guillén 56 Causality and Cointgration in Stock Markts: th Cas o Latin Amrica njamin Miranda Tabak and Eduardo José Araújo Lima 57 As Lis d Falência: uma Abordagm Econômica Aloisio Araujo 58 Th andom Walk Hypothsis and th havior o Forign Capital Portolio Flows: th razilian Stock Markt Cas njamin Miranda Tabak 59 Os Prços Administrados a Inlação no rasil Francisco Marcos. Figuirdo Thaís Porto Frrira 6 Dlgatd Portolio Managmnt Paulo Coutinho and njamin Miranda Tabak Jun/ Aug/ Aug/ St/ Sp/ St/ Sp/ Sp/ Sp/ Nov/ Nov/ Nov/ Dc/ Dz/ Dc/ Dz/ Dc/ 5

53 6 O Uso d Dados d Alta Frqüência na Estimação da Volatilidad do Valor m isco para o Ibovspa João Maurício d Souza Morira Eduardo Facó Lmgrubr 6 Taxa d Juros Concntração ancária no rasil Eduardo Kiyoshi Tonooka Sérgio Mikio Koyama 63 Optimal Montary uls: th Cas o razil Charls Lima d Almida, Marco Aurélio Prs, Graldo da Silva Souza and njamin Miranda Tabak 64 Mdium-Siz Macroconomic Modl or th razilian Economy Marclo Koury Muinhos and Srgio Aonso Lago Alvs 65 On th Inormation Contnt o Oil Futur Prics njamin Miranda Tabak 66 A Taxa d Juros d Equilíbrio: uma Abordagm Múltipla Pdro Calhman d Miranda Marclo Koury Muinhos 67 Avaliação d Métodos d Cálculo d Exigência d Capital para isco d Mrcado d Cartiras d Açõs no rasil Gustavo S. Araújo, João Maurício S. Morira icardo S. Maia Clmnt 68 al alancs in th Utility Function: Evidnc or razil Lonardo Soriano d Alncar and Márcio I. Nakan 69 r-iltrs: a Hodrick-Prscott Filtr Gnralization Fabio Araújo, Marta altar Morira Arosa and José Alvaro odrigus Nto 7 Montary Policy Surpriss and th razilian Trm Structur o Intrst ats njamin Miranda Tabak 7 On Shadow-Prics o anks in al-tim Gross Sttlmnt Systms odrigo Pnaloza 7 O Prêmio pla Maturidad na Estrutura a Trmo das Taxas d Juros rasiliras icardo Dias d Olivira rito, Anglo J. Mont'Alvrn Duart Osmani Tixira d C. Guilln 73 Anális d Componnts Principais d Dados Funcionais uma Aplicação às Estruturas a Trmo d Taxas d Juros Gtúlio orgs da Silvira Octavio ssada 74 Aplicação do Modlo d lack, Drman & Toy à Prciicação d Opçõs Sobr Títulos d nda Fixa Octavio Manul ssada Lion, Carlos Albrto Nuns Cosnza César das Nvs 75 razil s Financial Systm: silinc to Shocks, no Currncy Substitution, but Struggling to Promot Growth Ilan Goldajn, Kathrin Hnnings and Hlio Mori Dz/ Fv/3 Fb/3 Fb/3 Fb/3 Fv/3 Fv/3 Fb/3 Fb/3 Fb/3 Apr/3 Maio/3 Maio/3 Maio/3 Jun/3 5

54 76 Inlation Targting in Emrging Markt Economis Arminio Fraga, Ilan Goldajn and André Minlla 77 Inlation Targting in razil: Constructing Crdibility undr Exchang at Volatility André Minlla, Paulo Springr d Fritas, Ilan Goldajn and Marclo Koury Muinhos 78 Contornando os Prssupostos d lack & Schols: Aplicação do Modlo d Prciicação d Opçõs d Duan no Mrcado rasiliro Gustavo Silva Araújo, Claudio Hnriqu da Silvira arbdo, Antonio Carlos Figuirdo, Eduardo Facó Lmgrubr 79 Inclusão do Dcaimnto Tmporal na Mtodologia Dlta-Gama para o Cálculo do Va d Cartiras Compradas m Opçõs no rasil Claudio Hnriqu da Silvira arbdo, Gustavo Silva Araújo, Eduardo Facó Lmgrubr 8 Dirnças Smlhanças ntr Paíss da América Latina: uma Anális d Markov Switching para os Ciclos Econômicos d rasil Argntina Arnildo da Silva Corra 8 ank Comptition, Agncy Costs and th Prormanc o th Montary Policy Lonardo Soriano d Alncar and Márcio I. Nakan 8 Cartiras d Opçõs: Avaliação d Mtodologias d Exigência d Capital no Mrcado rasiliro Cláudio Hnriqu da Silvira arbdo Gustavo Silva Araújo 83 Dos Inlation Targting duc Inlation? An Analysis or th OECD Industrial Countris Thomas Y. Wu 84 Spculativ Attacks on Dbts and Optimum Currncy Ara: a Wlar Analysis Aloisio Araujo and Marcia Lon 85 isk Prmia or Emrging Markts onds: Evidnc rom razilian Govrnmnt Dbt, 996- André Soars Louriro and Frnando d Holanda arbosa 86 Idntiicação do Fator Estocástico d Dscontos Algumas Implicaçõs sobr Tsts d Modlos d Consumo Fabio Araujo João Victor Isslr 87 Mrcado d Crédito: uma Anális Econométrica dos Volums d Crédito Total Habitacional no rasil Ana Carla Abrão Costa 88 Ciclos Intrnacionais d Ngócios: uma Anális d Mudança d gim Markoviano para rasil, Argntina Estados Unidos Arnildo da Silva Corra onald Otto Hillbrcht 89 O Mrcado d Hdg Cambial no rasil: ação das Instituiçõs Financiras a Intrvnçõs do anco Cntral Frnando N. d Olivira Jun/3 Jul/3 Out/3 Out/3 Out/3 Jan/4 Mar/4 May/4 May/4 May/4 Maio/4 Dz/4 Dz/4 Dz/4 53

55 9 ank Privatization and Productivity: Evidnc or razil Márcio I. Nakan and Danila. Wintraub 9 Crdit isk Masurmnt and th gulation o ank Capital and Provision quirmnts in razil a Corporat Analysis icardo Schchtman, Valéria Salomão Garcia, Srgio Mikio Koyama and Guilhrm Cronmbrgr Parnt 9 Stady-Stat Analysis o an Opn Economy Gnral Equilibrium Modl or razil Mirta Nomi Sataka ugarin, obrto d Gos Ellry Jr., Victor Goms Silva, Marclo Koury Muinhos 93 Avaliação d Modlos d Cálculo d Exigência d Capital para isco Cambial Claudio H. da S. arbdo, Gustavo S. Araújo, João Maurício S. Morira icardo S. Maia Clmnt 94 Simulação Histórica Filtrada: Incorporação da Volatilidad ao Modlo Histórico d Cálculo d isco para Ativos Não-Linars Claudio Hnriqu da Silvira arbdo, Gustavo Silva Araújo Eduardo Facó Lmgrubr 95 Commnt on Markt Disciplin and Montary Policy by Carl Walsh Maurício S. ugarin and Fábia A. d Carvalho 96 O qu É Estratégia: uma Abordagm Multiparadigmática para a Disciplina Anthro d Moras Mirlls 97 Financ and th usinss Cycl: a Kalman Filtr Approach with Markov Switching yan A. Compton and Jos icardo da Costa Silva 98 Capital Flows Cycl: Stylizd Facts and Empirical Evidncs or Emrging Markt Economis Hlio Mori Marclo Koury Muinhos 99 Adquação das Mdidas d Valor m isco na Formulação da Exigência d Capital para Estratégias d Opçõs no Mrcado rasiliro Gustavo Silva Araújo, Claudio Hnriqu da Silvira arbdo, Eduardo Facó Lmgrubr Targts and Inlation Dynamics Srgio A. L. Alvs and Waldyr D. Arosa Comparing Equilibrium al Intrst ats: Dirnt Approachs to Masur razilian ats Marclo Koury Muinhos and Márcio I. Nakan Judicial isk and Crdit Markt Prormanc: Micro Evidnc rom razilian Payroll Loans Ana Carla A. Costa and João M. P. d Mllo 3 Th Ect o Advrs Supply Shocks on Montary Policy and Output Maria da Glória D. S. Araújo, Mirta ugarin, Marclo Koury Muinhos and Jos icardo C. Silva Dc/4 Dc/4 Apr/5 Abr/5 Abr/5 Apr/5 Ago/5 Aug/5 Aug/5 St/5 Oct/5 Mar/6 Apr/6 Apr/6 54

56 4 Extração d Inormação d Opçõs Cambiais no rasil Eui Jung Chang njamin Miranda Tabak 5 prsnting oommat s Prrncs with Symmtric Utilitis José Alvaro odrigus Nto 6 Tsting Nonlinaritis twn razilian Exchang ats and Inlation Volatilitis Cristian. Albuqurqu and Marclo Portugal 7 Dmand or ank Srvics and Markt Powr in razilian anking Márcio I. Nakan, Lonardo S. Alncar and Fabio Kanczuk 8 O Eito da Consignação m Folha nas Taxas d Juros dos Empréstimos Pssoais Eduardo A. S. odrigus, Victorio Chu, Lonardo S. Alncar Tony Takda 9 Th cnt razilian Disinlation Procss and Costs Alxandr A. Tombini and Srgio A. Lago Alvs Fators d isco o Sprad ancário no rasil Frnando G. ignotto Eduardo Augusto d Souza odrigus Avaliação d Modlos d Exigência d Capital para isco d Mrcado do Cupom Cambial Alan Cosm odrigus da Silva, João Maurício d Souza Morira Myrian atriz Eiras das Nvs Intrdpndnc and Contagion: an Analysis o Inormation Transmission in Latin Amrica's Stock Markts Anglo Marsiglia Fasolo 3 Invstigação da Mmória d Longo Prazo da Taxa d Câmbio no rasil Srgio ubns Stancato d Souza, njamin Miranda Tabak Danil O. Cajuiro 4 Th Inquality Channl o Montary Transmission Marta Arosa and Waldyr Arosa 5 Myopic Loss Avrsion and Hous-Mony Ect Ovrsas: an Exprimntal Approach José L.. Frnands, Juan Ignacio Pña and njamin M. Tabak 6 Out-O-Th-Mony Mont Carlo Simulation Option Pricing: th Join Us o Importanc Sampling and Dscriptiv Sampling Jaqulin Trra Moura Marins, Eduardo Saliby and Josét Florncio dos Santos 7 An Analysis o O-Sit Suprvision o anks Proitability, isk and Capital Adquacy: a Portolio Simulation Approach Applid to razilian anks Thodor M. arnhill, Marcos. Souto and njamin M. Tabak 8 Contagion, ankruptcy and Social Wlar Analysis in a Financial Economy with isk gulation Constraint Aloísio P. Araújo and José Valntim M. Vicnt Abr/6 Apr/6 May/6 Jun/6 Jun/6 Jun/6 Jul/6 Jul/6 Jul/6 Ago/6 Aug/6 Sp/6 Sp/6 Sp/6 Oct/6 55

57 9 A Cntral d isco d Crédito no rasil: uma Anális d Utilidad d Inormação icardo Schchtman Forcasting Intrst ats: an Application or razil Eduardo J. A. Lima, Flip Luduvic and njamin M. Tabak Th ol o Consumr s isk Avrsion on Pric igidity Srgio A. Lago Alvs and Mirta N. S. ugarin Nonlinar Mchanisms o th Exchang at Pass-Through: a Phillips Curv Modl With Thrshold or razil Arnildo da Silva Corra and André Minlla 3 A Noclassical Analysis o th razilian Lost-Dcads Flávia Mourão Graminho 4 Th Dynamic lations btwn Stock Prics and Exchang ats: Evidnc or razil njamin M. Tabak 5 Hrding havior by Equity Forign Invstors on Emrging Markts arbara Almanni and José nato Haas Ornlas 6 isk Prmium: Insights ovr th Thrshold José L.. Frnands, Augusto Hasman and Juan Ignacio Pña 7 Uma Invstigação asada m amostragm sobr qurimntos d Capital para isco d Crédito no rasil icardo Schchtman 8 Trm Structur Movmnts Implicit in Option Prics Caio Ibsn. Almida and José Valntim M. Vicnt 9 razil: Taming Inlation Expctations Aonso S. vilaqua, Mário Msquita and André Minlla 3 Th ol o anks in th razilian Intrbank Markt: Dos ank Typ Mattr? Danil O. Cajuiro and njamin M. Tabak 3 Long-ang Dpndnc in Exchang ats: th Cas o th Europan Montary Systm Srgio ubns Stancato d Souza, njamin M. Tabak and Danil O. Cajuiro 3 Crdit isk Mont Carlo Simulation Using Simpliid Crditmtrics Modl: th Joint Us o Importanc Sampling and Dscriptiv Sampling Jaqulin Trra Moura Marins and Eduardo Saliby 33 A Nw Proposal or Collction and Gnration o Inormation on Financial Institutions isk: th Cas o Drivativs Gilnu F. A. Vivan and njamin M. Tabak 34 Amostragm Dscritiva no Aprçamnto d Opçõs Européias através d Simulação Mont Carlo: o Eito da Dimnsionalidad da Probabilidad d Exrcício no Ganho d Prcisão Eduardo Saliby, Srgio Luiz Mdiros Pronça d Gouvêa Jaqulin Trra Moura Marins Out/6 Oct/6 Nov/6 Nov/6 Nov/6 Nov/6 Dc/6 Dc/6 Dc/6 Dc/6 Jan/7 Jan/7 Mar/7 Mar/7 Mar/7 Abr/7 56

58 35 Evaluation o Dault isk or th razilian anking Sctor Marclo Y. Takami and njamin M. Tabak 36 Idntiying Volatility isk Prmium rom Fixd Incom Asian Options Caio Ibsn. Almida and José Valntim M. Vicnt 37 Montary Policy Dsign undr Compting Modls o Inlation Prsistnc Solang Gouva Abhijit Sn Gupta 38 Forcasting Exchang at Dnsity Using Paramtric Modls: th Cas o razil Marcos M. Ab, Eui J. Chang and njamin M. Tabak 39 Slction o Optimal Lag Lngth incointgratd VA Modls with Wak Form o Common Cyclical Faturs Carlos Enriqu Carrasco Gutiérrz, inaldo Castro Souza and Osmani Tixira d Carvalho Guillén 4 Inlation Targting, Crdibility and Conidnc Criss aal Santos and Aloísio Araújo 4 Forcasting onds Yilds in th razilian Fixd incom Markt Jos Vicnt and njamin M. Tabak 4 Criss Anális da Corência d Mdidas d isco no Mrcado rasiliro d Açõs Dsnvolvimnto d uma Mtodologia Híbrida para o Expctd Shortall Alan Cosm odrigus da Silva, Eduardo Facó Lmgrubr, José Albrto bllo aranowski nato da Silva Carvalho 43 Pric igidity in razil: Evidnc rom CPI Micro Data Solang Gouva 44 Th Ect o id-ask Prics on razilian Options Implid Volatility: a Cas Study o Tlmar Call Options Claudio Hnriqu da Silvira arbdo and Eduardo Facó Lmgrubr 45 Th Stability-Concntration lationship in th razilian anking Systm njamin Miranda Tabak, Solang Maria Gurra, Eduardo José Araújo Lima and Eui Jung Chang 46 Movimntos da Estrutura a Trmo Critérios d Minimização do Erro d Prvisão m um Modlo Paramétrico Exponncial Caio Almida, omu Goms, André Lit José Vicnt 47 Explaining ank Failurs in razil: Micro, Macro and Contagion Ects Adriana Soars Sals and Maria Eduarda Tannuri-Pianto 48 Um Modlo d Fators Latnts com Variávis Macroconômicas para a Curva d Cupom Cambial Flip Pinhiro, Caio Almida José Vicnt 49 Joint Validation o Crdit ating PDs undr Dault Corrlation icardo Schchtman May/7 May/7 May/7 May/7 Jun/7 Aug/7 Aug/7 Ago/7 Sp/7 Oct/7 Oct/7 Out/7 Oct/7 Out/7 Oct/7 57

59 5 A Probabilistic Approach or Assssing th Signiicanc o Contxtual Variabls in Nonparamtric Frontir Modls: an Application or razilian anks obrta lass Staub and Graldo da Silva Souza 5 uilding Conidnc Intrvals with lock ootstraps or th Varianc atio Tst o Prdictability Eduardo José Araújo Lima and njamin Miranda Tabak 5 Dmand or Forign Exchang Drivativs in razil: Hdg or Spculation? Frnando N. d Olivira and Waltr Novas 53 Aplicação da Amostragm por Importância à Simulação d Opçõs Asiáticas Fora do Dinhiro Jaqulin Trra Moura Marins 54 Idntiication o Montary Policy Shocks in th razilian Markt or ank srvs Adriana Soars Sals and Maria Tannuri-Pianto 55 Dos Curvatur Enhanc Forcasting? Caio Almida, omu Goms, André Lit and José Vicnt 56 Escolha do anco Dmanda por Empréstimos: um Modlo d Dcisão m Duas Etapas Aplicado para o rasil Sérgio Mikio Koyama Márcio I. Nakan 57 Is th Invstmnt-Uncrtainty Link ally Elusiv? Th Harmul Ects o Inlation Uncrtainty in razil Tito Nícias Tixira da Silva Filho 58 Charactrizing th razilian Trm Structur o Intrst ats Osmani T. Guilln and njamin M. Tabak 59 havior and Ects o Equity Forign Invstors on Emrging Markts arbara Almanni and José nato Haas Ornlas 6 Th Incidnc o srv quirmnts in razil: Do ank Stockholdrs Shar th urdn? Fábia A. d Carvalho and Cyntia F. Azvdo 6 Evaluating Valu-at-isk Modls via Quantil grssions Wagnr P. Gaglianon, Luiz nato Lima and Olivr Linton 6 alanc Sht Ects in Currncy Criss: Evidnc rom razil Marcio M. Janot, Márcio G. P. Garcia and Waltr Novas 63 Sarching or th Natural at o Unmploymnt in a Larg lativ Pric Shocks Economy: th razilian Cas Tito Nícias Tixira da Silva Filho 64 Forign anks Entry and Dpartur: th rcnt razilian xprinc Pdro Fachada 65 Avaliação d Opçõs d Troca Opçõs d Sprad Européias Amricanas Giuliano Carrozza Uzêda Iorio d Souza, Carlos Patrício Samanz Gustavo Santos aposo Oct/7 Nov/7 Dc/7 Dz/7 Dc/7 Dc/7 Dz/7 Jan/8 Fb/8 Fb/8 Fb/8 Fb/8 Apr/8 May/8 Jun/8 Jul/8 58

60 66 Tsting Hyprinlation Thoris Using th Inlation Tax Curv: a cas study Frnando d Holanda arbosa and Tito Nícias Tixira da Silva Filho 67 O Podr Discriminant das Opraçõs d Crédito das Instituiçõs Financiras rasiliras Clodoaldo Aparcido Annibal 68 An Intgratd Modl or Liquidity Managmnt and Short-Trm Asst Allocation in Commrcial anks Wnrsamy amos d Alcântara 69 Mnsuração do isco Sistêmico no Stor ancário com Variávis Contábis Econômicas Lucio odrigus Caplltto, Elisu Martins Luiz João Corrar 7 Política d Fchamnto d ancos com gulador Não-nvolnt: sumo Aplicação Adriana Soars Sals 7 Modlos para a Utilização das Opraçõs d dsconto plos ancos com Cartira Comrcial no rasil Sérgio Mikio Koyama Márcio Issao Nakan 7 Combining Hodrick-Prscott Filtring with a Production Function Approach to Estimat Output Gap Marta Arosa 73 Exchang at Dynamics and th lationship btwn th andom Walk Hypothsis and Oicial Intrvntions Eduardo José Araújo Lima and njamin Miranda Tabak 74 Forign Exchang Markt Volatility Inormation: an invstigation o ral-dollar xchang rat Frdrico Pchir Goms, Marclo Yoshio Takami and Vinicius atton randi 75 Evaluating Asst Pricing Modls in a Fama-Frnch Framwork Carlos Enriqu Carrasco Gutirrz and Wagnr Piazza Gaglianon 76 Fiat Mony and th Valu o inding Portolio Constraints Mário. Páscoa, Myrian Ptrassi and Juan Pablo Torrs-Martínz 77 Prrnc or Flxibility and aysian Updating Gil illa 78 An Economtric Contribution to th Intrtmporal Approach o th Currnt Account Wagnr Piazza Gaglianon and João Victor Isslr 79 Ar Intrst at Options Important or th Assssmnt o Intrst at isk? Caio Almida and José Vicnt 8 A Class o Incomplt and Ambiguity Avrs Prrncs Landro Nascimnto and Gil illa 8 Montary Channls in razil through th Lns o a Smi-Structural Modl André Minlla and Nlson F. Souza-Sobrinho Jul/8 Jul/8 Jul/8 Jul/8 Jul/8 Ago/8 Aug/8 Aug/8 Aug/8 Dc/8 Dc/8 Dc/8 Dc/8 Dc/8 Dc/8 Apr/9 59

61 8 Avaliação d Opçõs Amricanas com arriras Monitoradas d Forma Discrta Giuliano Carrozza Uzêda Iorio d Souza Carlos Patrício Samanz 83 Ganhos da Globalização do Capital Acionário m Criss Cambiais Marcio Janot Waltr Novas Abr/9 Abr/9 6