Interest rates and asset prices: A primer

Transcription

1 Ineres raes and asse prices: A primer Rober Barsky and Theodore Bogusz Inroducion and summary Economic commenaors ofen asser ha major asse price booms and buss are closely associaed wih variaions in he erms of borrowing o fund risky asse purchases. One imporan narraive focuses on changes in borrowing coss arising from variaion in he riskless ineres rae, which may resul from a variey of causes noably cenral bank policy acions in he shor run and changes in world saving and associaed capial flows over a longer horizon. For example, Allen and Gale (2000) conend ha so-called bubble episodes ypically begin wih financial liberalizaion or a conscious decision by he cenral bank o increase lending. Afer a period of perhaps several years, hese auhors coninue, he cenral bank s policy sance ighens, ineres raes rise, and he bubble collapses. Greenspan (200) also noes a connecion beween ineres raes and asse prices bu sresses he role of global savings paerns and oher deerminans of long-erm raes raher han he shor-erm policy raes ha are mos closely conneced o he acions of cenral bankers. 2 Wha does economic heory have o say abou he exen o which exogenous changes in shor-erm and/or long-erm riskless raes ough o affec asse prices, and by wha channels? In his aricle, we examine he implicaions of hree key heoreical models of asse booms and buss, focusing on a variey of channels hrough which ineres raes migh affec real asse prices. Afer providing a bi of empirical moivaion via a brief look a daa from Japan s sock and land price boom and bus of 985 9, we sudy implicaions of he cenral model of radiional asse pricing, in which price is simply expeced discouned fuure dividends. Here he focus is on he way in which he riskless ineres rae affecs he fundamenal value of asses. Leverage does no play a cenral role because of he celebraed Modigliani Miller heorem, which says ha he oal value of iles o an asse s payoffs is independen of how hey are divided ino deb and equiy claims. Using firs he simple Gordon formula, and hen Campbell and Shiller s log-linearized dynamic Gordon model, we derive quaniaive implicaions for he effecs of innovaions in he shor-erm rae on an asse ha could be hough of as land or he sock of an unlevered firm. The key resul of his perfec markes model is ha he exen o which increases in he riskless ineres rae lower fundamenal asse values is an increasing funcion of he persisence of shor-erm ineres raes and a decreasing funcion of he risk premium. This observaion has imporan implicaions for debaes over wheher or no cenral banks are likely o cause Rober Barsky is a senior economis and research advisor and Theodore Bogusz is a senior associae economis in he Economic Research Deparmen of he Federal Reserve Bank of Chicago. 204 Federal Reserve Bank of Chicago Economic Perspecives is published by he Economic Research Deparmen of he Federal Reserve Bank of Chicago. The views expressed are he auhors and do no necessarily reflec he views of he Federal Reserve Bank of Chicago or he Federal Reserve Sysem. Charles L. Evans, Presiden; Daniel G. Sullivan, Execuive Vice Presiden and Direcor of Research; Spencer Krane, Senior Vice Presiden and Economic Advisor; David Marshall, Senior Vice Presiden, financial markes group; Daniel Aaronson, Vice Presiden, microeconomic policy research; Jonas D. M. Fisher, Vice Presiden, macroeconomic policy research; Richard Heckinger, Vice Presiden, markes eam; Anna L. Paulson, Vice Presiden, finance eam; William A. Tesa, Vice Presiden, regional programs; Lisa Barrow, Senior Economis and Economics Edior; Helen Koshy and Han Y. Choi, Ediors; Ria Molloy and Julia Baker, Producion Ediors; Sheila A. Mangler, Ediorial Assisan. Economic Perspecives aricles may be reproduced in whole or in par, provided he aricles are no reproduced or disribued for commercial gain and provided he source is appropriaely credied. Prior wrien permission mus be obained for any oher reproducion, disribuion, republicaion, or creaion of derivaive works of Economic Perspecives aricles. To reques permission, please conac Helen Koshy, senior edior, a or Helen.Koshy@chi.frb.org. ISSN Federal Reserve Bank of Chicago 39

2 FIGURE Japanese discoun rae and real sock price percen index Nikkei 225 index deflaed by consumer price index, all iems excep food and energy (righ axis) Nominal discoun rae (lef axis) Source: Haver Analyics. large cycles in real asse prices by varying policy raes. In order o have such effecs in his sandard model, cenral bankers mus be able o creae highly persisen changes in real policy raes pu differenly, hey mus exer major effecs on real long-erm ineres raes. Moneary heory, however, suggess ha he abiliy of cenral banks o effec permanen changes in real raes is limied (Shiller, 980). 3 These wo observaions in combinaion sugges ha cenral banks also have limied abiliy o creae booms and buss in real asse markes. While radiional asse-pricing heory focuses on fundamenals discouned fuure real cash flows here are alernaive heories in which marke imperfecions play an imporan role. One such model, originaing wih Allen and Gale (2000) and developed more fully in Barlevy (204), is based on he idea ha speculaors borrow (wihou sufficien collaeral) from banks in order o buy risky asses. Banks are unable o differeniae beween enrepreneurs ha are safe o lend o and speculaors ha defaul if he payoff from he asse is disappoining. In his model, he price is pushed above is (social) fundamenal value because of he defaul opion. We inroduce a borrowing limi (a haircu in finance erminology) and show ha is magniude impacs he size of he bubble. In he one-period model we skech explicily, he ineres rae affecs boh he fundamenal value and he size of he bubble, bu he channel for he laer is essenially he same as ha for he fundamenal value. In he Allen Gale Barlevy model unlike he fundamenal valuaion model leverage is absoluely essenial; here is no Modigliani Miller heorem. Furher, he model s indispensable consrain on shor sales makes i a model of limis o arbirage, in he sense of Shleifer and Vishny (997). We consider anoher model in his class he naural buyers model, based in our case (as in Miller, 977; Geanakoplos, 200; and Simsek, 203) on heerogeneous beliefs, he naural buyers being hose mos opimisic abou he dividend payou of he asse. In general, he naural buyers borrow in order o leverage heir purchases of he asse. Increasing he effecive demands of he naural buyers raises he equilibrium price, an effec ha may be limied by high ineres raes and possible credi consrains. This resuls in an asse price ha is deermined by a combinaion of beliefs, ineres raes, and borrowing limis. In paricular, we use a simple model from Barsky and Bogusz (203) o illusrae he channels hrough which he ineres rae can affec he asse price in his sor of model. The significan new ineres 40 4Q/204, Economic Perspecives

3 FIGURE 2 Yearly ineres rae changes label Change in Bank of Japan discoun rae Change in long-erm real bond yields Change in long-erm nominal bond yields Sources: Barsky (20), able 2., and sources cied herein. rae channel ha his sor of model adds o he mix is wha migh be called an affordabiliy effec. Higher borrowing coss may make i impossible for collaeralconsrained naural buyers o fully roll over loans used o buy he asse, and he resuling drop in cash in he marke necessiaes a lower level of he asse price. 4 A key quesion is wheher he models incorporaing limis o arbirage migh produce larger effecs of emporary ineres rae changes on asse prices han are seen in he perfec markes model. Though we by no means rule ou ha possibiliy, he simple examples ha we consruc do no have his propery. In he imperfec markes models we presen, he effecs of ineres raes on asse prices never exceed he effecs on fundamenal value. Empirical moivaion: Japanese sock prices, Figure is a ime-series plo of he raw monhly daa on he Bank of Japan s nominal discoun rae and he Nikkei 225, perhaps he bes-known index of Japanese sock prices, divided by he core consumer price index (all iems, excep food and energy). The plo shows ha he discoun rae halved beween lae 985 and early 987. As he discoun rae fell from 5 o 2.5, he Nikkei 225 increased by 50 percen. From March 987 unil April 989, he ineres rae remained consan a 2.5 percen, is lowes level prior o he deep recession ha followed he Nikkei s collapse. During his period, he Nikkei 225 increased a furher 50 percen. From one perspecive, his suggess he possibiliy ha he low ineres rae environmen was fueling an asse boom. An alernaive perspecive migh emphasize he fac ha sock prices coninued o rise rapidly wihou a furher lowering of he discoun raes. For a period of several monhs in 989, he ineres rae and asse price rose ogeher, an indicaion ha he relaionship beween ineres raes and asse prices is complex and inconsisen wih unidimensional causaliy in eiher direcion. As he discoun rae rose by a furher.75 percenage poins beween lae 989 and he middle of 990, sock prices declined by more han a hird. These rae increases in 989 and 990 correspond raher closely wih he collapse of he Nikkei. In paricular, we see from figure ha he sharp rise in he discoun rae from 4.25 percen o 5.25 percen Federal Reserve Bank of Chicago 4

4 in February 990 corresponds o a drop of 4 log poins in he real Nikkei ha same monh. This, compounded by subsequen drops in he Nikkei as well as in various indexes of land and housing prices earned Yasushi Mieno (righly or wrongly) he disincion of being called he governor who pricked Japan s bubble economy. 5 From mid-99 hrough he middle of he subsequen year, he discoun rae fell seadily as he sock price coninued o decline. Thus, figure illusraes he Allen Gale noion of a so-called bubble ha begins in an environmen of falling policy raes and ends in a period characerized by sharp rae increases, bu i also indicaes ha he relaionship beween ineres raes and real asse prices is complex and requires a heoreical framework o faciliae meaningful discussions regarding causaliy. We urn now o he quesion of wha heories migh be relevan and wha hey migh each us. How do ineres raes affec fundamenals? As noed in he inroducion, he long-erm rae feaures heavily in discussions of ineres rae effecs on asse prices. While only he discoun rae is under he direc conrol of he cenral bank, figure 2 illusraes via a bar graph he associaion in annual daa beween changes in he basic discoun rae, nominal and real long-erm raes, and he Nikkei. In 986, he Bank of Japan (BOJ) cu is discoun rae by 200 basis poins. In 987, he discoun rae was reduced by anoher 50 basis poins. The discoun rae was increased sharply in 989 and 990. Figure 2 shows ha BOJ aleraions of he nominal discoun rae were associaed wih changes in boh nominal and real long-erm bond yields. We now urn o a consideraion of several models ha migh shed ligh on he effec of shor- and longerm ineres raes on asse prices. The mos orhodox accoun of he impac of ineres rae changes on asse prices focuses on he effec on he fundamenal value of he asse he expecaion of he asse s sream of fuure cash flows discouned by an appropriae discoun facor ha we will call ρ. For now, we assume his is consan over ime, hough we will relax his laer. More precisely, if P is he fundamenal real asse price a ime and D +i is he real dividend or service flow received by he asse holder a ime + i, hen D+ i P = E. ( i + ) i= ρ Because of he uncerain naure of he cash flows from real asses, hey should be discouned no a he riskless ineres rae r, bu a a higher rae ha includes a risk premium ha we will call θ. 6 Thus, he full discoun rae ρ is he sum of he riskless ineres rae r (which is he primary focus of his aricle) and he risk premium ρ = r + θ. I is boh convenien and revealing o represen he presen value formula heurisically in a compac form known universally as he Gordon formula, D P = ρ g, or in erms of he asse price, D D P = =. 7 The Gordon formula is de- ρ g r + θ g rived when ρ and g are consan over ime, bu wha we are ineresed in, of course, is he effec of changes in r. Differeniaing he Gordon formula will give he correc answer for he effec of unanicipaed and permanen changes in r. If, on he oher hand, r follows a sochasic process oher han a random walk, a somewha more complicaed approximae formula is required (see below). Le us begin wih he effec on P of a permanen change in he riskless rae r. We have d log(p) =. dr r + θ g This derivaive becomes large as g ges close o r + θ. Thus, he presence of he risk premium θ pus a damper on he exen o which a change in r can affec he fundamenal asse price. Since θ has hisorically been quie large (Mehra and Presco, 985), he dampening effec due o he presence of he risk premium is quaniaively imporan, and i will subsanially reduce he effec of changes in he ineres rae. So far, we have focused on permanen changes in r. When r follows a sochasic process ha renders ineres rae changes less han permanen, i remains rue ha he presence of he risk premium reduces he effec on asse prices of changes in he riskless rae. In addiion, however, he effec on he fundamenal value of a shock o r is furher reduced relaive o he case when r is shocked permanenly. 8 A way o see his is o work wih he log-linear approximaion o he Gordon formula ha holds when required raes of reurn and dividend growh raes are nonconsan over ime bu follow saionary sochasic processes (he Campbell Shiller dynamic Gordon growh model; see Campbell, Lo, and MacKinlay, 997, pp ). 42 4Q/204, Economic Perspecives

5 The formula reads p k i + E d j r j γ [( γ) ], γ j= 0 where γ = and μ d p is he populaion + exp( µ d p) mean of he log dividend price raio. Here, he lowercase p refers o he log of he price. Because our concern is wih he role of he ineres rae, i will prove useful o define p r i γ r++ j, he par of j= 0 his expression for he log-linearized asse price ha depends on curren and expeced fuure shor-erm ineres raes. Campbell, Lo, and MacKinlay (997) offer as an example he special case in which E[ r+ ] = r + x wih x = φx + ξ. In his insrucive example, we have p r r x = +. γ γφ This provides a saisfying framework in which o discuss he role of he persisence of ineres rae disurbances. We see immediaely ha he effec of an ineres rae shock on he fundamenal price is increasing in he persisence parameer ϕ and he discoun facor γ (in fac hey appear compleely symmerical). Noe ha ϕ measures he persisence of innovaions in he ineres rae. As ϕ goes o one, we effecively replicae he permanen shocks o r associaed wih he simple Gordon formula shown a he beginning of his secion. 9 The inuiion for he imporance of ineres rae persisence is raher sraighforward. The asse is presumed o be long lived, yielding cash flows for many years o come. A highly persisen increase in he ineres rae raises he rae a which even cash flows ha are expeced o arrive far in he fuure are discouned, reducing significanly he presen value of he sum oal of expeced fuure cash flows. A ransiory increase in he ineres rae, on he oher hand, affecs only he presen value of cash flows expeced o arrive in he near fuure. How abou he role of he risk premium? Since he discoun facor γ is inversely relaed o he mean dividend price raio (which in urn is increasing in he average risk premium), his can be regarded as he reappearance in he dynamic conex of he earlier poin ha a large risk premium pus a damper on he effec of an ineres rae innovaion on he asse price. The inuiive reason is ha a higher baseline required reurn shorens he duraion of he asse and reduces he imporance of ineres raes in he more-disan fuure. How persisen would ineres rae shocks have needed o be o raionalize he rise in he Nikkei beween 985 and 986 enirely in erms of he drop in he discoun rae? Translaing he persisence parameer ϕ ino he half-life of he ineres rae response o an exogenous shock of he appropriae magniude and loosely calibraing o he Japanese financial daa from his period sugges ha he required degree of persisence corresponds o a half-life of abou 3 years. If he change in he ineres rae came from a moneary policy shock, his half-life is far oo large o be plausible. If insead of a shock o he policy rae we were dealing wih a drop in ineres raes due o long-erm capial flows, 3 years migh be a quie reasonable half-life. Thus i maers a grea deal where ineres rae shocks come from. Conrary o firs impressions, in he perfec markes presen value model wih raional expecaions moneary policy does no seem o be a good candidae for explaining he large swings in he Nikkei during his period. Limis-o-arbirage models wih a nonrivial role for leverage Risk-shifing models In he previous secion, we examined he effec of ineres raes on fundamenals. Our analysis shows ha large flucuaions in asse prices due o exogenous ineres rae movemens canno be explained enirely hrough fundamenals. However, a number of asse-pricing models deviae from he sandard Gordon model. One such model is he moneary bubble model we dismissed in he inroducion. In his secion, we will examine wo asse-pricing models ha may yield more dramaic resuls. In boh he risk-shifing and heerogeneiy models, he price depends no only on fundamenals, bu also on he abiliy of agens o borrow funds. I seems plausible ha ineres raes may have a larger effec in hese models. We skech here a simple one-period version of a model proposed by Allen and Gale (2000) and analyzed in a much richer conex by Barlevy (204). This variey of model arises from he moral hazard ha is induced when some agens are able o buy risky asses largely wih borrowed money and defaul in one or more lowpayou saes, shifing he risk o lenders. In hese models, here is ypically a kind of bubble, in he sense ha he price of he risky asse rises above is social valuaion due o he subsidy implicily received by he borrower as a resul of he opion o defaul. One quesion we will ask is wheher a sufficienly high riskless ineres rae can pop he bubble. Federal Reserve Bank of Chicago 43

6 Suppose ha here is a good sae ha occurs wih probabiliy q, in which he asse pays a high liquidaing dividend of H a he end of he period. Wih probabiliy q, a bad sae occurs in which he asse pays nohing a all. In he benchmark model, he asse is purchased by agens ha we will call speculaors, enirely wih funds borrowed from agens ha we will call banks. Speculaors pay back he loan in he good sae and defaul in he bad one. Banks canno idenify speculaors because hey are pooled wih a hird se of agens ha we (following Barlevy, 204) call enrepreneurs. Though hey would no lend o recognizable speculaors, in he pooling equilibrium hese risk-neural banks earn an expeced reurn jus high enough o compensae for he riskless rae r yielded by an ouside aciviy. The one elemen we add o he exising models is a borrowing limi measured in erms of a margin or haircu h, so ha speculaors can borrow only B = ( h) P per uni of he risky asse priced a P. The (social) fundamenal value F of he asse is qd / ( + r). Wih free enry o he pool of speculaors, he price of he asse will be his fundamenal value plus he expeced value of he subsidy ( q) B. Thus we have he equilibrium condiion qd P = + ( q)( h) P. ( + r) The soluion for he asse price, herefore, is P = qd [ + r ( q)( h) ]. No surprisingly, in he case in which he enire asse purchase can be funded by borrowing (ha is, when D h = 0), his collapses o P = ( + r). The speculaor is willing o pay up o he full presen value of he dividend in he good sae, because in he bad sae he purchase price is effecively refunded. This capures he inuiion in he popular descripion of moral-hazardfilled financial ransacions as heads I win, ails you lose. Noe ha in his zero-haircu case, he level of D he bubble is ( q), ha is, he price + r D ( + r) minus he fundamenal qd. Alhough one migh + r imagine ha a sufficienly high ineres rae would deer poenial speculaors and cause he price o rever o is fundamenal level, his is no he case in he model described. These expressions show ha a rise in he ineres rae lowers he magniude of he bubble componen in exacly he same proporion ha i lowers he fundamenal value. However, here is anoher somewha unexpeced channel by which a rise in he ineres rae can burs he bubble. Recall ha he speculaor is able o borrow only because in he conex of a pooling equilibrium lenders canno disinguish him from a producive enrepreneur. If he ineres rae rises above he marginal efficiency of invesmen, he enrepreneurs will drop ou of he loan marke, revealing he ideniies of he speculaors o he banks and leaving hem unable o borrow. Naural-buyer (heerogeneous beliefs) models Anoher way o analyze he possible role of leverage in major asse price flucuaions is wih a model in which agens have heerogeneous beliefs abou fundamenals. Opimiss face collaeral consrains limiing heir abiliy o borrow, and pessimiss face shor-sales consrains limiing heir abiliy o sell he risky asse o he opimiss. Here, we examine a simple and highly sylized one-period model of heerogeneous beliefs borrowed from Barsky and Bogusz (203). The model incorporaes wo ypes of agens, opimiss and pessimiss, and wo goods, a final consumpion good called coconus and a coconu-yielding asse called rees. Opimiss and pessimiss each receive an endowmen of coconus and rees. In equilibrium, opimiss buy rees from he pessimiss using coconus, some of which are borrowed from he pessimiss. A he end of he period, rees yield coconus and agens consume. Opimiss and pessimiss differ in heir beliefs abou he number of coconus ha rees will yield a he end of he period, and pessimiss which migh be hough of as money marke funds ha canno afford o break he buck addiionally have a paricular concern wih avoiding he downside risk associaed wih defauls on loans ha hey make. Aside from purchasing rees, agens can always sore coconus o earn a riskless reurn f. They can also ake ou loans a he ineres rae r. We define he following variables: S i is agen i s sorage; b i is he amoun borrowed; q i is he quaniy of rees purchased (negaive if he rees are sold); E (Y) refers o agen i s expeced yield of rees a he end of he period; and T i refers o agen i s iniial endowmen of rees. The opimisic agens (i = ), which migh be hough of as hedge funds, are risk neural and hus have expeced uiliy U = s ( + f) b (+r)+e [Y](q i + T i ). The money marke agens are principally concerned wih avoiding losses resuling from heir lending and 44 4Q/204, Economic Perspecives

7 FIGURE 3 Ineres rae shock price V b + r V s + r quaniy will charge haircus sufficien o render he loans riskless. Thus, in addiion o he budge consrain and he nonnegaive sorage consrain faced by boh kinds of agens, he borrower faces he collaeral consrain b i Lj( Ti + qi ), where L + r j is he wors sae of he world from he pessimiss poin of view. Since even in he wors sae of he world he lender is paid in full, loans are enirely riskless, and his ensures ha he reurn on sorage will be equal o he ineres rae in equilibrium. There are wo channels hrough which movemens in he ineres rae affec asse prices in his model. Which channel he ineres rae innovaion operaes hrough depends on wha se of consrains are binding. The firs way a rise in he ineres rae affecs he price is by reducing he fundamenal value of boh he opimiss and he pessimiss, since he perceived fundamenal can be wrien as E ( Y) i. This channel is relevan in + r wo differen scenarios. The firs is he case in which he shor-sales consrain binds for he pessimiss bu he collaeral consrain does no bind for he opimiss. In his scenario, he price of he asse will be he opimiss fundamenal value. The oher scenario is when he shor-sales consrain doesn bind, bu he collaeral consrain does bind. In his scenario, he price of he asse will be he pessimiss fundamenal value. Wih he righ consrains, however, ineres rae movemens can have rich effecs in a heerogeneiy model hrough an enirely differen mechanism. When collaeral consrains bind alongside shor-sales consrains, a scenario we refer o as cash in he marke, he rise in he ineres rae ighens he borrowing consrain shown above and reduces he affordabiliy of he asse o he opimiss. Since he opimiss are able o borrow less han hey were before he ineres rae increase, he equilibrium asse price mus fall. I follows ha no maer wha combinaions of consrains are binding, a rise in he ineres rae will reduce he asse price. Figure 3 illusraes he response equilibrium price o an exogenous ineres rae shock. Here, he red line corresponds o he opimiss demand curve and he blue line corresponds o he pessimiss supply curve. Noe ha he opimiss can afford o pay heir full valuaion up o a cerain quaniy of he risky asse. This makes heir demand curve horizonal. A a cerain poin, he collaeral consrain begins o bind, and he opimiss demand curve is ben downward. The supply curve has a similar srucure. As long as he pessimiss are he marginal holders of he risky asse, he price will be heir valuaion and he supply curve is horizonal. However, once he Federal Reserve Bank of Chicago 45

8 pessimiss hi heir shor-selling consrain and no longer hold any of he risky asse, he rees can sell a a price above he pessimiss beliefs abou he rees fundamenal value. The dashed line corresponds o he supply and demand curves under a higher ineres rae han before. Looking a he buyers demand curve, we see here are wo effecs of he ineres rae. Firs, i lowers fundamenals, since he opimiss valuaion is EY ( ). + r However, here is an addiional effec of increasing he ineres rae, which is o lower he amoun of lending he pessimiss are willing o do. Noe ha while leverage is a sine qua non for nonrivial resuls in Allen and Gale (2000) and Barlevy (204), he naural-buyers model has conen even in is absence. When he binding consrains are such ha he equilibrium price is one of he agens full valuaion of he asse, here need no be any leverage a all. However, changes in he degree of leverage make he naural-buyers model a rich framework for sudying large credi-induced movemens in asse prices. Cash-in-he-marke pricing is, of course, a resul of leverage and he forces consraining i, and here he degree o which he opimis is able o lever himself has a crucial role o play. In he cash-in-he-marke region, we can also derive an expression for he effec (in logs) of a change in he ineres rae on he asse price when he buyer is collaeral consrained: d ln(p) = dr ( n( r). + + )( + r) b Here, n is he raio of risk capial o borrowing, which b in his model is he inverse of a measure of leverage. This says he effec of an ineres rae change on price is increasing in leverage. No surprisingly, he effec of ineres rae movemens on asse prices is larger when a greaer fracion of he asse is paid for wih borrowed funds. Thus, he heerogeneiy model is suggesive of wo ways ha exogenous ineres rae movemens migh cause flucuaions in asse prices: one hrough fundamenals and anoher hrough he affordabiliy channel. I is someimes argued ha he fire sales resuling from he sudden inabiliy of naural buyers o roll over he loans needed o fund heir posiions can cause drops in asse prices ha grealy exceed fundamenals, and Geanakoplos (200) consrucs a raher complex edifice wih his propery. In our oneperiod model, however, i is no hard o see ha he effec of he ineres rae on marke price never exceeds is effec on he fundamenal value as perceived by eiher he opimiss or pessimiss. For example, in he cash-in-he-marke region, he effec on he marke price approaches he fundamenal effec only as he haircu approaches zero and he asse is funded enirely hrough borrowing. Conclusion We have discussed several models in which exogenous changes in he riskless ineres rae, collaeral consrains, or boh have poenially major effecs on real asse prices. We began wih models in which credi consrains are absen and riskless ineres raes impac asse prices hrough heir effecs on fundamenal value. We found ha in order o have large effecs on fundamenal real asse prices, large changes in he shor-erm ineres rae have o be highly persisen. In addiion, we showed ha he presence of a subsanial risk premium also pus a damper on he effecs of ineres rae changes on fundamenals. We hen moved o models wih limis o arbirage, in which he exen o which agens are able o purchase risky asses on margin is a key deerminan of asse prices. The simple models we sudied did no sugges ha he asse price effecs of ineres rae changes are subsanially larger in his conex han in he classic model based on fundamenals. Geanakoplos (200), in he elaborae fire-sales model menioned earlier, is able o generae collapses in asse prices in excess of hose jusified by worsened fundamenals in response o cerain sequences of bad news ha necessiae deleveraging. I appears possible, bu by no means cerain, ha some of he same consideraions could raionalize large responses of asse prices o changes in ineres raes. We are invesigaing his furher in ongoing research. 46 4Q/204, Economic Perspecives

9 NOTES We use he erm bubble as i appears in popular discourse wihou necessarily adoping he academic crierion ha asse prices depar from fundamenals during hese episodes. 2 Similar argumens appear in a number of speeches by former Federal Reserve Board Chair Ben Bernanke, available on he websie of he Board of Governors of he Federal Reserve Sysem, 3 Shiller s paper is now 35 years old. Ye his hypohesis 3 (ha here is a policy effeciveness inerval beyond which anicipaed moneary policy canno force real ineres raes o depar from he naural rae) is fully consisen wih curren New Keynesian dynamic sochasic general equilibrium (DSGE) models. The lengh of his inerval depends on he degree of price and wage rigidiy and can be as shor as a few monhs or as long as several years. See also Sanley Fischer s inroducion o he volume in which Shiller s paper is found (Fischer, 980). 4 An addiional alernaive heory of asse pricing ha warrans menion, bu is no aken up furher in his aricle, is he sandard model of raional bubbles. The simples exbook version describes an asse wih no fundamenal value ha rades a a posiive price only because of he self-fulfilling raional expecaion ha he asse can be resold o someone else in he fuure. The only resricion on he asse price is ha i mus offer he marke reurn by growing a he expeced rae of ineres. Thus, hese models deermine only he growh rae of he asse price, no is level, a poin acknowledged bu unforunaely underplayed in a prominen recen paper by Galí (204). Galí argues unconvincingly in our view ha raising ineres raes may well exacerbae raher han miigae bubbles. Since a saisfacory resoluion of his and oher policy quesions requires deermining asse price levels, we do no discuss his model furher. 5 Mayumi Osuma, 202, Mieno, governor who pricked Japan s bubble economy, dies, Bloomberg, April 8, available a 6 This premium, which compensaes for sysemaic risk, is ypically represened as a covariance beween he asse s ex pos reurn and he reurn on a broad index, such as he marke porfolio or aggregae consumpion. 7 Noe ha i is necessary ha ρ > g, or he above presen value will be infinie. There is an exensive echnical lieraure abou possible worlds in which his condiion does no hold. 8 The remainder of his paragraph, as well as he nex one, draws heavily on Barsky s (20) chaper on he Japanese bubble. 9 To see his, noe ha dpr dlog( P ) = = =. dx γ exp( μ ) ρ g dr d p Federal Reserve Bank of Chicago 47

10 REFERENCES Allen, F., and D. Gale, 2000, Bubbles and crises, Economic Journal, Vol. 0, No. 460, January, pp Barlevy, G., 204, A leverage-based model of spec ulaive bubbles, Journal of Economic Theory, Vol. 53, Sepember, pp Barsky, R., 20, The Japanese asse price bubble: A heerogeneous approach, in K. Hamada, A. K Kashyap, and D. E. Weinsein, eds., Japan s Bubble, Deflaion, and Long-erm Sagnaion, Cambridge, MA: MIT Press. Barsky, R., and T. Bogusz, 203, Bubbles and leverage: A simple and unified approach, Federal Reserve Bank of Chicago, working paper, No , November. Campbell, John Y., A. W. Lo, and A. C. MacKinlay, 997, The Economerics of Financial Markes, Princeon, NJ: Princeon Universiy Press. Fischer, S., 980, Inroducion, in Raional Expecaions and Economic Policy, S. Fischer (ed.), Chicago: Universiy of Chicago Press, pp. 3. Galí, Jordi, 204, Moneary policy and raional asse price bubbles, American Economic Review, Vol. 04, No. 3, March, pp Geanakoplos, J., 200, The leverage cycle, in NBER Macroeconomics Annual 2009, Vol. 24, pp. 65, Chicago: Universiy of Chicago Press. Greenspan, A., 200, The crisis, Brookings Papers on Economic Aciviy, Spring, pp Mehra, R., and E. C. Presco, 985, The equiy premium: A puzzle, Journal of Moneary Economics, Vol. 5, No. 2, March, pp Miller, E. M., 977, Risk, uncerainy, and divergence of opinion, Journal of Finance, Vol. 32, No. 4, Sepember, pp Shiller, R. J., 980, Can he Fed conrol real ineres raes?, in Raional Expecaions and Economic Policy, S. Fischer (ed.), Chicago: Universiy of Chicago Press, pp Shleifer, A., and R. W. Vishny, 997, The limis of arbirage, Journal of Finance, Vol. 52, No., March, pp Simsek, A., 203, Belief disagreemens and collaeral consrains, Economerica, Vol. 8, No., January, pp Q/204, Economic Perspecives