MARKET ORGANIZATION AND THE PRICES OF FINANCIAL ASSETS*

Transcription

1 The Mancheser School Supplemen MARKET ORGANIZATION AND THE PRICES OF FINANCIAL ASSETS* by GEORGE M. CONSTANTINIDES Universiy of Chicago and NBER Several empirical regulariies in he prices of financial asses are a odds wih he predicions of sandard economic heory. I address hese regulariies and explore he exen o which hey are resolved in he conex of wo markes organized in very differen ways. The firs seing is a neoclassical economy wih incomplee markes and heerogeneous agens. Marke incompleeness naurally arises because of he non-exisence of markes in which consumers or households can co-insure idiosyncraic income shocks for obvious moral hazard reasons. The second seing is an overlapping generaions economy wih hree generaions in which he young generaion is consrained from borrowing and invesing in equiies. The borrowing consrains naurally arise because human capial alone does no collaeralize major loans in modern economies for reasons of moral hazard and adverse selecion. Inroducion Several empirical regulariies in he prices of financial asses are a odds wih he predicions of sandard economic heory. I address hese regulariies and explore he exen o which hey are resolved in he conex of wo very differen economic seings. The firs seing is a neoclassical economy wih incomplee markes and heerogeneous agens. Marke incompleeness naurally arises because of he non-exisence of markes in which consumers or households can co-insure idiosyncraic income shocks for obvious moral hazard reasons. The second seing is an overlapping generaions (OLG) economy wih hree generaions in which he young generaion is consrained from borrowing and invesing in equiies. The borrowing consrains naurally arise because human capial alone does no collaeralize major loans in modern economies for reasons of moral hazard and adverse selecion. I begin wih an overview of he empirical regulariies in he prices of financial asses ha are a odds wih he predicions of sandard economic heory. The aggregae equiy reurn, he long-erm bond reurn and he reurns of various subclasses of financial asses are oo large, oo variable and oo predicable. One such regulariy ha has received a lo of aenion in he lieraure is he equiy risk premium puzzle. I is he inabiliy of he * I hank he paricipans a he Money Macro and Finance 2005 Annual Conference for valuable feedback. I remain responsible for errors. Journal compilaion 2006 Blackwell Publishing Ld and The Universiy of Mancheser Published by Blackwell Publishing Ld, 9600 Garsingon Road, Oxford OX4 2DQ, UK, and 350 Main Sree, Malden, MA 0248, USA.

2 2 The Mancheser School Table The Long-run Expeced Premium in he USA Sample mean premium Mean annual growh of Price dividends Price earnings Price book equiy Premium adjused for Price dividends Price earnings Price book equiy Source: Rober Shiller s websie (hp:// and Vuoleenaho (2000). neoclassical economic heory o reconcile he hisorically large realized premium of sock marke reurn over he risk-free rae wih is low covariabiliy wih aggregae consumpion growh. In Table, I repor he sample mean premium of he annual arihmeic aggregae equiy reurn over he risk-free rae. I proxy he aggregae equiy reurn wih he S&P Composie Index reurn. I proxy he annual risk-free rae wih he rolled-over reurn on hree-monh Treasury bills and cerificaes. The sample mean premium is 5.85 per cen over he period , and 5.6 per cen over he period The sample mean premium is 7.80 per cen over he period , and 7.30 per cen over he period These sample means are large even when I ake ino accoun he recen sock marke decline. In Table 2, I repor he equiy premium across counries. The sample means are large across mos counries. Is i possible ha he sample mean of he equiy premium oversaes he uncondiional mean premium? Over he period , he price dividend raio increased by a facor of 4.6 and he price earnings raio by a facor of 2.5. Over he period , he price dividend raio increased by a facor of 3.9 and he price earnings raio increased by a facor of 2.6. One may consider adjusing downwards he sample mean esimae of he uncondiional mean reurn on equiy. The size of he adjusmen ough o relae o he perceived cause of he increase of hese financial raios. In he year 998, 52 per cen of he US adul populaion held equiy eiher direcly or indirecly, compared wih 36 per cen of he adul populaion in 989. This equiizaion has been brough abou by he increased accessibiliy of informaion on he sock marke, elecronic rading, he growh of muual funds, he growh of defined-conribuion pension plans The increase in hese financial raios should be inerpreed wih cauion. The increase in he price dividend raio is due in par o an increase in share repurchases and a decrease in he fracion of dividend-paying firms.

3 Marke Organizaion and Prices of Financial Asses 3 Table 2 The Long-erm Expeced Premium across Counries, Counry Mean equiy reurn Treasury bill reurn Mean equiy premium Annualized growh of price dividends raio Adjused mean equiy premium Ausralia Belgium Canada Denmark France Germany Ireland Ialy Japan The Neherlands Souh Africa Spain Sweden Swizerland NA NA UK USA source: Dimson e al. (2002). Germany, years excluded; Swizerland since 9.

4 4 The Mancheser School and demographic changes. Oher regime shifs include he adven of he echnology/media/elecoms new economy and changes in he axaion of dividends and capial gains. Explanaions of he price increase ha rely on economic models ha are less han fully raional include culural and psychological facors and ap ino he rich and burgeoning lieraure on behavioral economics and finance. In Consaninides (2002), I discussed how one may process his informaion and adjus he sample mean esimae of he uncondiional mean premium by subracing he mean annual growh of he price dividend raio. In Table, I repor he mean annual growh of various financial raios. Even if I subrac he enire mean annual growh of he price dividend raio, price earnings raio or price book equiy raio from he sample mean, he adjused esimae of he uncondiional mean premium is large. Any adjusmen wih he average growh of he financial raios sill leaves he uncondiional mean premium large and in need of an economic explanaion. In Table 2, I repor he mean annual growh of he price dividend raio across counries and he corresponding adjusmen of he mean equiy premium. Again, he uncondiional mean premium is large and in need of an economic explanaion. The neoclassical economic model parsimoniously links he reurns of all asses o per capia consumpion growh hrough he Euler equaions of consumpion. 2 According o he heory, he risk premia of financial asses are explained by heir covariance wih per capia consumpion growh. However, per capia consumpion growh covaries oo lile wih he reurns of mos classes of financial asses. Aemps o leverage he low covariabiliy ypically backfire, implying ha he observed risk-free rae is oo low and has oo low variance. I discuss in some deph he aggregae equiy puzzle because i exemplifies many of he problems ha arise in aemping o explain he premium of any subclass of financial asses. The covariance of per capia consumpion growh wih he aggregae equiy reurn is posiive. The raional model explains why he aggregae equiy premium is posiive. However, he covariance is ypically one order of magniude lower han wha is needed o explain he premium. Thus, he equiy premium is a quaniaive puzzle. 3 The equiy premium puzzle is robus. One may address he problem by esing he Euler equaions of consumpion or by calibraing he economy. 2 See Meron (973), Rubinsein (976), Lucas (978) and Breeden (979). 3 Grossman and Shiller (98), Hansen and Singleon (982), Ferson and Consaninides (99), Hansen and Jagannahan (99) and many ohers esed and rejeced he Euler equaions of consumpion. Mehra and Presco (985) calibraed an economy o mach he process of consumpion growh. They demonsraed ha he uncondiional mean annual premium of he aggregae equiy reurn over he risk-free rae is, a mos, 0.35 per cen. This is oo low, no maer how one esimaes he uncondiional mean equiy premium. Weil (989) sressed ha he puzzle is a dual puzzle of he observed oo high equiy reurn and oo low risk-free rae.

5 Marke Organizaion and Prices of Financial Asses 5 Eiher way, i is a puzzle. In calibraing an exchange economy, he model canno generae he firs and second uncondiional momens of he equiy reurns. In esing and rejecing he Euler equaions of consumpion, one absracs from he marke clearing condiions. Variaions in he assumpions on he supply side of he economy do no resolve he puzzle. The challenge is a dual puzzle of he equiy premium ha is oo high and he risk-free rae ha is oo low relaive o he predicions of he model. In calibraing an economy, he sraegy of increasing he risk aversion coefficien in order o lever he effec of he problemaic low covariance of consumpion growh wih equiy reurns increases he prediced risk-free rae and aggravaes he risk-free rae puzzle. In esing he Euler equaions of consumpion, he rejecions are sronges when he risk-free rae is included in he se of es asses. Several generalizaions of essenial feaures of he model have been proposed o miigae is poor performance. They include alernaive assumpions on preferences; 4 rare bu disasrous marke-wide evens; 5 disored beliefs and learning; 6 incomplee markes; 7 marke imperfecions; 8 and liquidiy risk. 9 They also include a beer undersanding of daa problems such as limied paricipaion of consumers in he sock marke; 0 emporal aggregaion; and he survival bias of he US capial marke. 2 The low covariance of he growh rae of aggregae consumpion wih equiy reurns is a major sumbling block in explaining he mean aggregae equiy premium and he cross-secion of asse reurns, in he conex of a represenaive-consumer economy wih ime-separable preferences. Mankiw and Shapiro (986) found ha he marke bea ofen explains asse reurns beer han he consumpion bea does. Over he years, a number of differen economic models have been proposed ha effecively increase he covariance of equiy reurns wih he growh rae of aggregae consumpion, by proxying 4 For example, Abel (990), Consaninides (990), Epsein and Zin (99), Ferson and Consaninides (99), Braun e al. (993), Benarzi and Thaler (995), Campbell and Cochrane (999), Boldrin e al. (200), Cagei e al. (2002) and Bansal and Yaron (2004). 5 For example, Mehra and Presco (988), Riez (988), Danhine and Donaldson (999) and Barro (2005). 6 Danhine and Donaldson (999), Cecchei e al. (2000), Guidolin (2004) and Weizman (2005). 7 For example, Bewley (982), Mehra and Presco (985), Mankiw (986), Consaninides and Duffie (996), Heaon and Lucas (996), Soresleen e al. (200, 2004), Brav e al. (2002), Krebs (2002), De Sanis (2004) and Jacobs and Wang (2004). 8 For example, Aiyagari and Gerler (99), Danhine e al. (992), He and Modes (995), Bansal and Coleman (996), Heaon and Lucas (996), Daniel and Marshall (997), Consaninides e al. (2002), Guvenen (2005) and Parker and Julliard (2005). 9 See Alvarez and Jermann (200) and Lusig (2004). 0 For example, Mankiw and Zeldes (99), Brav and Geczy (995), Aanasio e al. (2002), Brav e al. (2002) and Vissing-Jorgensen (2002). See Heaon (995), Lynch (996) and Gabaix and Laibson (200). 2 See Brown e al. (995). However, Jorion and Goezmann (999, Table 6) found ha he average real capial gain rae of a US equiies index exceeds he average rae of a global equiies index ha includes ha boh markes have and have no survived by merely per cen per year.

6 6 The Mancheser School he growh rae of aggregae consumpion wih he sock marke reurn in he Euler equaions of consumpion. 3 Many of hese generalizaions conribue in par owards our beer undersanding of he economic mechanism ha deermines he pricing of asses. I refer he reader o he exbooks by Campbell e al. (997) and Cochrane (200); and he aricles by Cochrane and Hansen (992), Kocherlakoa (996), Cochrane (997), Campbell (200, 2003), Consaninides (2002) and Mehra and Presco (2003). 2 An Overview of he Neoclassical Economic Model I begin wih he sandard assumpions of he neoclassical economic model, as i adaped in finance. There are I consumers i, i =,...,I, each consuming c unis of he consumpion good in period and having von Neumann Morgensern preferences [ ( )] () i E U c,..., c, c,... 0 i 0 i i + There are J capial asses, j =,...,J, raded by he consumers in perfec markers and having reurns R j,+ beween periods and +. Uiliy maximizaion by he ih consumer in rading he jh asse a ime yields he following Euler equaion of consumpion beween periods and + : E U c i i U + c i i + R j, + = 0 (2) In he sandard heory, preferences are ypically specialized o be ime separable as E 0 = 0 β ui( c i ) (3) wih consan subjecive discoun facor b. There is no empirical jusificaion for his specializaion of preferences. In any case, wih ime-separable preferences as in equaion (3), he Euler equaion of consumpion simplifies ino he following equaion: 3 Friend and Blume (975) explained he mean equiy premium wih low relaive risk aversion coefficien by assuming a single-period economy in which he end-of-period consumpion ineviably equals he end-of-period wealh. In he Epsein and Zin (99) model, even hough he preferences are defined over consumpion alone, he sock marke reurn eners direcly in he Euler equaions of consumpion. Bakshi and Chen (996) inroduced a se of preferences defined over consumpion and wealh he spiri of capialism ha also have he effec of inroducing he sock marke reurn in he Euler equaions of consumpion.

7 Marke Organizaion and Prices of Financial Asses 7 ui c i c i E β ( ) u( c ) c + + i i i j R, + = (4) In he sandard heory, he model is ypically furher specialized by assuming ha he marke is complee. There is lile, if any, empirical jusificaion for his assumpion eiher. In his essay, I relax his assumpion, considering insead an incomplee marke, and explore is implicaions in he pricing of financial asses. In any case, under he assumpion of marke compleeness, he equilibrium in his heerogeneous-consumer economy is isomorphic in is pricing implicaions o he equilibrium in a represenaive-consumer economy. For our purposes, marke compleeness implies ha here exiss a period uiliy funcion u(c ) of per capia consumpion C I Σi Ι = c i, such ha we may replace he I consumer-specific Euler equaions (4) wih he following Euler equaion of consumpion of he represenaive consumer: E uc C β ( + ) + uc C R j, + ( ) = (5) I is ofen assumed ha he period uiliy funcion is of he power form, u(c ) = ( - A) - (C ) -A, wih consan relaive risk aversion (RRA) coefficien A. Wih power uiliy, he Euler equaion (5) furher simplifies ino he following: C E β + C A Rj, + = (6) An advanage of he assumpion ha he period uiliy funcion is of he power form is ha per capia consumpion appears in he Euler equaion only as per capia consumpion growh, C +/C, which may be saionary even if he consumpion level is non-saionary. In empirical work and calibraion, per capia consumpion growh in he Euler equaion (6) is ofen aken o be he aggregae consumpion growh, where he aggregae consumpion is aken from he Naional Income and Produc Accouns. However, he aggregae consumpion repored by he Naional Income and Produc Accouns is he sum oal over all households, irrespecive of wheher hese households are marginal in he equiies and bond markes or no. Leaving aside he limied sock marke paricipaion by households, I condiion down he Euler equaion (6) ino uncondiional form and linearize i under he assumpion ha he logarihm of he consumpion growh and he logarihm of asse reurns are bivariae normally disribued:

8 8 The Mancheser School ln E[ Ri, + ] E[ lnri, + ]+ var ( lnri, + ) 2 C+ = ln + A E β ln C 2 C+ A var ln 2 C + C+ A cov ln R i, +,ln C I ake he difference of he linearized Euler equaions for he marke reurn and for he risk-free rae and find ha he uncondiional mean equiy premium is equal o he produc of he RRA coefficien of he represenaive consumer and he covariance of he marke reurn wih per capia consumpion growh: 4 C+ ln E[ RM, + ] ln E[ RF, + ]= A cov ln RM, +, ln C (8) I also find ha he risk-free rae is equal o he sum of he subjecive discoun rae (-ln b) and he produc of he RRA coefficien and he mean growh rae in consumpion, less one-half he produc of he squared RRA coefficien and he variance of consumpion growh: C+ C+ ln E[ RF, + ]= ln + A E ln A var ln C 2 β 2 C (9) The elasiciy of subsiuion in consumpion is defined as he increase in expeced consumpion growh for a uni increase in he risk-free rae, ψ E[ ln( C+ C) ] ln E[ RF, +]. Wih ime-separable preferences and consan RRA coefficien, equaion (9) implies ha he produc of he RRA coefficien and he elasiciy equals one, RRA y =. In erms of he elasiciy, equaion (9) may be wrien as C+ C+ ln E[ RF, + ]= ln + E ln var ln C β 2 2 C (0) ψ ψ Wih ime-separable preferences and consan RRA coefficien, equaions (9) and (0) are inerchangeable. 5 (7) 4 I make use of he propery ha he risk-free rae R F,+ is known a ime. The condiional covariance cov [ln R F,+, (ln C +/C )] is zero and herefore he uncondiional covariance cov[ln R F,+, ln(c +/C )] is approximaely zero. 5 Wih ime-separable preferences ha allow a variable RRA coefficien, u(c ) = ( - A) - (C - K) -A, equaion (9) is replaced by C+ K C+ K ln E[ RF, + ]= ln + A E ln A var ln C K 2 β 2 C K I is sill he case ha A y ª. However, A no longer equals he RRA coefficien and he produc RRA y need no equal one. Also, wih ime-non-separable preferences, such as

9 Marke Organizaion and Prices of Financial Asses 9 Empirically, he covariance of per capia consumpion growh wih he marke reurn is low and canno generae he mean equiy premium, as in equaion (8), wih a reasonable value of he RRA coefficien. If one assumes a sufficienly high value of he RRA coefficien in order o generae a realisic mean premium, he Euler equaion of consumpion wih respec o he risk-free rae, equaion (9), now generaes a risk-free rae ha is much higher han he hisorically observed risk-free rae. Thus, he puzzle is a dual puzzle ha he observed mean equiy premium is oo high and he risk-free rae is oo low. 6 These are bu wo of he implicaions of he Euler equaions (5) ha are a odds wih he daa in boh empirical work and calibraion. In he nex secion, I relax he assumpion of marke compleeness and explore is ramificaions in beer undersanding he equiy premium, he risk-free rae and he Euler equaions of consumpion. 3 Incomplee Markes and Idiosyncraic Income Shocks In economic recessions, invesors are exposed o he double hazard of sock marke losses and job loss. Invesmen in equiies no only fails o hedge he risk of job loss bu accenuaes is implicaions. Invesors require a hefy equiy premium in order o be induced o hold equiies. The argumen hinges on he fac ha he marke for job-loss insurance is incomplee. Moral hazard impedes he developmen of unemploymen insurance markes and exan unemploymen compensaion provides inadequae proecion for invesors wealhy enough o be significan players in he financial markes. For example, wih job-loss insurance, an increase by per cen in he probabiliy of job loss merely manifess iself as a per cen decrease in per capia consumpion growh a risk ha is oo small o generae he observed equiy premium. Job loss is bu one example of idiosyncraic income shocks ha have he poenial o generae a sizable equiy premium. The observed correlaion of per capia consumpion growh wih sock reurns is low. Over he years, I have grown skepical of how meaningful an economic consruc per capia consumpion is, and how hard we should push per capia consumpion o explain reurns. Per capia consumpion is a meaningful economic concep only if he marke is complee or effecively habi-forming preferences, and sae-non-separable preferences as in Epsein Zin (99), he produc RRA y need no equal one. Wih Epsein Zin (99) preferences, he riskfree rae is given by equaion (0) in erms of he elasiciy and no by equaion (9) in erms of he RRA coefficien. 6 Noe ha he risk-free rae is decreasing in he RRA coefficien for sufficienly high value of his coefficien. However, i akes an absurdly high value of he RRA coefficien o lower he risk-free rae in his way.

10 0 The Mancheser School so. 7 Any ime ha we model he household secor by a represenaive consumer and proxy consumpion wih per capia (or aggregae) consumpion, we suppress he poenially major economic impac of uninsurable idiosyncraic income shocks. I begin o formalize hese ideas wih he observaion ha, in he compeiive equilibrium of a complee marke economy, heerogeneous households allocae heir consumpion in a way ha hey equalize, sae by sae, heir marginal rae of subsiuion. Negishi (960) poined ou ha he same consumpion allocaion is aained when a social planner maximizes he judiciously weighed sum of he households uiliy funcions. For his resul o hold, he weigh of each household s uiliy funcion is chosen o be inversely proporional o he Lagrange muliplier of he budge consrain of he respecive household. The claim follows from he observaion ha he households firs-order condiions are idenical o he firs-order condiions of a social planner. Consaninides (982) furher showed ha he social planner s problem can be spli ino wo subproblems. 8 In he firs subproblem, one consrucs an increasing and concave uiliy funcion ou of he social planner s weighed sum of he households uiliy funcions. In he second subproblem, he social planner maximizes he above-consruced uiliy funcion and ends up allocaing consumpion a each sae equal o he oal consumpion allocaed a ha sae in he heerogeneous-household economy. This implies ha he equilibrium in a heerogeneous-household, full-informaion economy is isomorphic in is pricing implicaions o he equilibrium in a represenaivehousehold, full-informaion economy, if households have von Neumann Morgensern preferences. The srong assumpion of marke compleeness is indirecly buil ino asse pricing models in finance and neoclassical macroeconomic models hrough he assumpion of he exisence of a represenaive household. Bewley (982), Mehra and Presco (985) and Mankiw (986) suggesed he poenial of enriching he asse-pricing implicaions of he represenaivehousehold paradigm, by relaxing he assumpion of complee markes. 9 Consaninides and Duffie (996) found ha incomplee markes subsanially enrich he implicaions of he represenaive-household model. Their main resul is a proposiion demonsraing, by consrucion, he exisence of household income processes, consisen wih given aggregae income and dividend processes, such ha equilibrium equiy and bond price processes mach he given equiy and bond price processes. 7 The marke is effecively complee when all households have preferences ha imply wo-fund separaion. 8 See also he discussion in an unpublished earlier draf of Mehra and Presco (985). 9 There is an exensive lieraure on he hypohesis of complee consumpion insurance. See Cochrane (99), Mace (99), Alonji e al. (992) and Aanasio and Davis (997).

11 Marke Organizaion and Prices of Financial Asses The saring poin in he Consaninides and Duffie (996) heory is he I J Euler equaions () of individual consumpion by he I consumers for he J asses, specialized for preferences ha imply consan relaive risk aversion: E[ β gi A, + Ri, + ]= i =,..., I j =,..., J () The consumpion growh of he ih consumer is gi, + c i + c i and he RRA coefficien is A. The poin of deparure from sandard heory is he recogniion ha marke incompleeness rules ou he sep of replacing he Euler equaions () by he Euler equaion (6) of he represenaive consumer. A sochasic discoun facor (SDF), or pricing kernel, is defined as any random variable m + wih he following propery: E[ m+ Rj, + ]= j =,..., I (2) Therefore, equaion () saes ha each consumer s marginal rae of subsiuion, βg i, +, is a valid SDF. A I sum he I J Euler equaions () across households and obain he expression I { } i= E β I gi A + Rj+ j J,, = =,..., (3) Equaion (3) saes ha he weighed sum of he consumers marginal rae of subsiuion is a valid SDF also: m β I g, (4) + I = { i A + } i= I expand equaion (4) as a Taylor series up o cubic erms and obain he following approximaion for he SDF: I AA ( + ) g m g A i + = + + I, { + β g 2 AA ( + ) ( A+ 2) I 6 i= + I i, + i= g g (5) The erm g+ I Σ i I = gi, + is he sample mean of he consumpion growh rae across consumers; I i I 2 Σ = ( gi, + g+ ) is he squared coefficien of variaion of he consumpion growh rae across consumers; and I i I 3 Σ = ( gi, + g+ ) is a measure of he skewness of he cross-secional variaion of consumpion growh. The heory requires ha he idiosyncraic income shocks have hree properies in order o explain he reurns on financial asses. Firs, hey mus

12 2 The Mancheser School be uninsurable. If here exiss a complee se of markes, he equilibrium of a heerogeneous-household, full-informaion economy is isomorphic in is pricing implicaions o he equilibrium of a represenaive-household, fullinformaion economy and household consumpion growh canno do beer han aggregae consumpion growh in explaining he reurns. To see his, noe ha, if a complee se of markes exiss, hen he heerogeneous households are able o equalize, sae by sae, heir marginal raes of subsiuion. In paricular, for any sae s a ime + here exiss a sae-specific bu consumer-independen parameer l s such ha g i, = g = l s, i =,...,I. The SDF in equaion (5) simplifies ino m = βg + + A or, equivalenly, ino 20 A (6) C+ m + = β (7) C Therefore, if here exiss a complee se of markes, he equilibrium of a heerogeneous-household, full-informaion economy is isomorphic in is pricing implicaions o he equilibrium of a represenaive-household, fullinformaion economy and household consumpion growh canno do beer han aggregae consumpion growh in explaining he reurns. Second, he heory requires ha he idiosyncraic income shocks be persisen. If he shocks are ransien, hen households can smooh heir consumpion by borrowing or by drawing down heir savings. 2 Third, he condiional variance, or some higher momen of he income shocks, mus be counercyclical. In equaion (5), he SDF is monoone increasing in he condiional variance. If he condiional variance is counercyclical, hen he SDF is counercyclical and covaries negaively wih he marke reurn, even hough aggregae consumpion has low covariance wih he marke reurn. In principle, his negaive covariaion gives rise o an equiy premium ha is absen in a complee marke. Even if he condiional variance is no counercyclical, he cyclical or counercyclical behavior of some higher momen of he income shocks may generae a high equiy 20 When here is a complee se of markes, equaion (7) follows from he fac ha, for any sae s, C C + I i I = c i + = = λ = g I c i I i s + = I expec ha he SDF given by equaion (7) is less suscepible o observaion error han he SDF given by equaion (6). 2 Aiyagari and Gerler (99) and Heaon and Lucas (996) found ha consumers facing ransien shocks come close o he complee markes rule of complee risk sharing even wih ransacion coss and/or borrowing coss, provided ha he supply of bonds is no resriced o an unrealisically low level.

13 Marke Organizaion and Prices of Financial Asses 3 premium. For example, in equaion (5), he SDF is monoone decreasing in he condiional skewness. If he condiional skewness is cyclical, hen he SDF is counercyclical and covaries negaively wih he marke reurn, giving rise o an equiy premium. A good example of a major uninsurable income shock is job loss. Job loss is uninsurable because unemploymen compensaion is inadequae. Layoffs have persisen implicaions on household income, even hough he laidoff workers ypically find anoher job quickly. 22 Lay-offs are counercyclical as hey are more likely o occur in recessions. Recall ha he main resul in Consaninides and Duffie (996) is a proposiion demonsraing, by consrucion, he exisence of household income processes, consisen wih given aggregae income and dividend processes, such ha equilibrium equiy and bond price processes mach he given equiy and bond price processes. The proposiion implies ha he Euler equaions of household (bu no necessarily of per capia) consumpion mus hold. Furhermore, since he given price processes have embedded in hem whaever predicabiliy of reurns by he price dividend raios, dividend growh raes and oher insrumens ha he researcher cares o ascribe o reurns, he equilibrium price processes have his predicabiliy buil ino hem by consrucion. The firs implicaion of he heory is an explanaion of he counercyclical behavior of he equiy risk premium: he risk premium is highes in a recession because he sock is a poor hedge agains he uninsurable income shocks, such as job loss, ha are more likely o arrive during a recession. The second implicaion is an explanaion of he uncondiional equiy premium puzzle: even hough per capia consumpion growh is poorly correlaed wih socks reurns, invesors require a hefy premium o hold socks over shor-erm bonds because socks perform poorly in recessions, when he invesor is mos likely o be laid off. In principle, I may direcly es he I J sysem of Euler equaions () of household consumpion. In he USA, he bes available disaggregaed consumpion daa are provided by he Deparmen of Labor Saisics Consumer Expendiure Survey (CEX) of quarerly consumpion of seleced households (no individual consumers). In pracice, he direc es is difficul because household consumpion daa are repored wih subsanial error. Brav e al. (2002) provided empirical evidence on he imporance of uninsurable idiosyncraic income risk on pricing. They pu forh a series of 22 The empirical evidence is sensiive o he model specificaion. Heaon and Lucas (996) modeled he income process as univariae and provided empirical evidence from he Panel Sudy on Income Dynamics (PSID) ha he idiosyncraic income shocks are ransiory. Soresleen e al. (200) modeled he income process as bivariae and provided empirical evidence from he PSID ha he idiosyncraic income shocks have a highly persisen componen ha becomes more volaile during economic conracions. Soresleen e al. (2004) corroboraed he laer evidence by sudying household consumpion over he life cycle.

14 4 The Mancheser School candidae SDFs: he marginal rae of subsiuion of he represenaive consumer as in equaions (6) or (7); he Taylor series expansion of he SDF up o quadraic erms; he Taylor series expansion of he SDF up o cubic erms, as in equaion (5); and a log-linearized expansion of he SDF. They esimaed he RRA coefficien and esed he se of Euler equaions of household consumpion on he premium of he value-weighed and he equally weighed marke porfolio reurn over he risk-free rae and on he premium of value socks over growh socks. 23 Brav e al. (2002) did no rejec he Euler equaions of household consumpion wih RRA coefficien beween 2 and 4 when he candidae SDF is he Taylor series expansion of he SDF up o cubic erms, as in equaion (5). An RRA coefficien beween 2 and 4 is economically plausible. They rejeced he Euler equaions of household consumpion wih any value of he RRA coefficien when he Taylor series expansion of he SDF does no include he cubic erms. This implies ha, in addiion o he mean and variance, he skewness of he cross-secional disribuion is imporan in explaining he equiy premium. They also found ha he log-linearized expansion of he SDF fails o explain he premia, possibly because he loglinearizaion downplays he effec of ouliers. These resuls emphasize he role of he higher momens of he cross-secional disribuion in explaining he premia. Krebs (2002) provided a heoreical jusificaion as o why i is possible ha neiher he variance nor he skewness bu higher momens of he crosssecional disribuion are imporan in explaining he equiy premium. He exended he Consaninides and Duffie (996) model by inroducing rare idiosyncraic income shocks ha drive consumpion close o zero. In his model, he condiional variance and skewness of he idiosyncraic income shocks are nearly consan over ime. Despie his, Krebs demonsraed ha he original proposiion of Consaninides and Duffie remains valid, i.e. here exis household income processes, consisen wih given aggregae income and dividend processes, such ha equilibrium equiy and bond price processes mach he given equiy and bond price processes. Essenially, he provided a heoreical jusificaion as o why i may be hard o empirically deec he rare bu caasrophic shocks in he low-order cross-secional momens of household consumpion growh. Jacobs and Wang (2004) expanded he se es asses used by Brav e al. (2002) o he se of he 25 Fama French size and value porfolios and provided addiional empirical evidence on he imporance of uninsurable idiosyncraic income risk on pricing. They found ha a wo-facor asse pricing 23 In relaed sudies, Jacobs (999) sudied he PSID daabase on food consumpion; Cogley (2002) and Vissing-Jorgensen (2002) sudied he CEX daabase on broad measures of consumpion; Jacobs and Wang (2004) sudied he CEX daabase by consrucing synheic cohors; and Ai-Sahalia e al. (2004) insrumened he household consumpion wih he purchases of cerain luxury goods.

15 Marke Organizaion and Prices of Financial Asses 5 model, wih he mean and cross-secional variance of he household consumpion growh rae as facors, significanly ouperforms he capial asse pricing model in explaining he cross-secion of asse reurns. Korniois (2005) invesigaed he poenial incompleeness of he marke across US saes while assuming complee consumpion insurance wihin each sae. He esed he Euler equaion of consumpion for each sae, where sae consumpion is proxied by he annual sae-wide sales a reail esablishmens. He found ha a facor-pricing model ha recognizes his incompleeness wih he cross-secional variance of he sae consumpion as a facor has modes success in explaining he cross-secion of asse reurns. He also found ha a facor-pricing model ha simulaneously recognizes his incompleeness and nonlinear exernal habi beer explains he cross-secion of asse reurns. 4 Borrowing Consrains in an OLG Economy In his secion, I explore he impac of borrowing consrains in he conex of he OLG model inroduced in Consaninides e al. (2002) and address is implicaions on he risk-free rae and he equiy premium. The demographic srucure of an OLG economy is a naural seing in which o address he impac of borrowing consrains. The model has hree generaions in which he young generaion is consrained from borrowing and invesing in equiies. Borrowing consrains arise because human capial alone does no collaeralize major loans in modern economies for reasons of moral hazard and adverse selecion. There has been considerable confusion in he lieraure as o he sense in which an OLG economy differs from an Arrow Debreu economy. As Gaenakoplos (987) makes clear, he basic difference is ha in an OLG economy here is no marke clearing a infiniy, irrespecive of wheher he marke is complee or incomplee. The paricular OLG economy ha I discuss is incomplee. However, i is he borrowing consrain ha drives he main resuls and no he marke incompleeness or he lack of marke clearing a infiniy. Indeed, he limied paricipaion in he borrowing consrained economy generaes a plausible mean equiy premium while he borrowing unconsrained version of he same economy generaes a negligible mean equiy premium. In he Consaninides e al. (2002) economy, consumers live for hree periods. In he firs period, a period of human capial acquisiion, consumers receive a relaively low endowmen income. In he second period, consumers are employed and receive wage income subjec o large uncerainy. In he hird period, consumers reire and consume he asses accumulaed in he second period. The key feaure is ha he bulk of he fuure income of he young consumers is derived from heir wages forhcoming in heir middle

16 6 The Mancheser School age, while he fuure income of he middle-aged consumers is derived primarily from heir savings in equiy and bonds. The young would like o inves in equiy, given he observed large equiy premium. However, hey are unwilling o decrease heir curren consumpion in order o save by invesing in equiy, because he bulk of heir lifeime income is derived from heir wages forhcoming in heir middle age. They would like o borrow, bu he borrowing consrain prevens hem from doing so. Human capial alone does no collaeralize major loans in modern economies for reasons of moral hazard and adverse selecion. The model explains why many consumers do no paricipae in he sock marke in he early phase of heir life cycle. The fuure income of he middle-aged consumers is derived from heir curren savings in equiy and bonds. Therefore, he risk of holding equiy and bonds is concenraed in he hands of he middle-aged saving consumers. This concenraion of risk generaes he high equiy premium and he demand for bonds, in addiion o he demand for equiy, by he middleaged. 24 The model recognizes and addresses simulaneously, a leas in par, he equiy premium, he limied paricipaion in he sock marke and he demand for bonds. Consaninides e al. (2002) calibraed he model o mach he following eigh arges: he average share of income going o labor; he average share of income going o he labor of he young; he average share of income going o ineres on governmen deb; he coefficien of variaion of he 20-year wage income of he middle-aged; he coefficien of variaion of he 20-year aggregae income; he 20-year auocorrelaion of he labor income; he 20-year auocorrelaion of he aggregae income; and he 20-year cross-correlaion of he labor income and he aggregae income. Since he lengh of one period in his model is 20 years, for all securiies (equiy, bond or consol), he annualized mean reurn is defined as he mean of (20) - ln(20-year holding period reurn); and he annualized sandard deviaion of he reurn is defined as he sandard deviaion of (20) -0.5 ln(20-year holding period reurn). In Table 3 I reproduce he firs panel of Table in Consaninides e al. (2002). 25 The borrowing consrain decreases he mean reurn of he 20-year or consol bond by abou a facor of 2. This observaion is robus o he calibraion of he correlaion and auocorrelaion of he labor income of he middleaged wih he aggregae income. The borrowing consrain goes a long way, alhough no all he way, owards resolving he risk-free rae puzzle. If he 24 See also he discussion in he relaed papers by Bodie e al. (992), Jagannahan and Kocherlakoa (996), Berau and Haliassos (997) and Soresleen e al. (200). 25 The RRA coefficien is se a 6; he coefficien of variaion of he (20-year) aggregae income is se a 0.20; he coefficien of variaion of he (20-year) wages is se a 0.25; he auocorrelaion of aggregae income, he auocorrelaion of wages, and he correlaion of aggregae income and wages are all se a 0.. The consol bond is in posiive ne supply and he one-period (20-year) bond is in zero ne supply.

17 Marke Organizaion and Prices of Financial Asses 7 Table 3 The Implicaions of Borrowing Consrains in an OLG Economy Borrowing consrained Borrowing unconsrained Mean equiy reurn Sd of equiy reurn Mean bond reurn Sd of bond reurn Mean premium over bond 3.4. Sd of premium over bond Mean consol reurn Sd of consol reurn Mean premium over consol Sd of premium over consol Correlaion of wages and dividend Correlaion of wages and premium young were able o borrow, hey would do so and purchase equiy; he borrowing aciviy of he young would raise he bond reurn, hereby exacerbaing he risk-free rae puzzle. Second, he mean equiy premium over he 20-year or consol bond is abou 4 per cen. This is saisfacory given ha long-erm bond reurns ypically command a premium over he shor-erm risk-free rae. This premium drasically decreases when he borrowing consrain is relaxed. If he young were able o borrow, he increase in he bond reurn would induce he middle-aged o shif heir porfolio holdings in favor of he bond; he increase in he demand for equiy by he young and he decrease in he demand for equiy by he middle-aged work in opposie direcions; on balance, he effec would be o increase he reurn on boh equiy and he bond while simulaneously shrinking he equiy premium. Third, he correlaion of he labor income of he middle-aged and he equiy premium over he 20-year bond is much smaller in absolue value han he exogenously imposed correlaion of he labor income of he middle-aged and he dividend. Thus, equiy is aracive o he young because of he large mean equiy premium and he low correlaion of he premium wih he wage income of he middle-aged, hereby corroboraing anoher imporan dimension of he model. In equilibrium, i urns ou ha he correlaion of he wage income of he middle-aged and he equiy reurn is low. 26 The young consumers would like o inves in equiy because equiy reurn has low correlaion wih heir fuure consumpion, if heir fuure consumpion is derived from heir fuure wage income. However, he borrowing consrain prevens hem from purchasing equiy on margin. Furhermore, since he young consumers are relaively poor and have an incenive o smooh heir ineremporal 26 The low correlaion of he wage income of he middle-aged and he equiy reurn is a propery of he equilibrium and obains for a wide range of values of he assumed correlaion of he wage income of he middle-aged and he dividend.

18 8 The Mancheser School consumpion, hey are unwilling o decrease heir curren consumpion in order o save by invesing in equiy. Therefore, he young choose no o paricipae in he equiy marke. Finally, he borrowing consrain lowers he sandard deviaion of he annualized, 20-year equiy and bond reurns. However, he sandard deviaion of he equiy reurn and paricularly he sandard deviaion of he bond reurn remain high. 5 Concluding Remarks I examined he observed asse reurns and conclude ha he evidence does no suppor he case for abandoning he raional economic model. I argued ha he sandard model is grealy enhanced by relaxing some of is assumpions. In paricular, I argued ha we go a long way owards addressing marke behavior by recognizing ha consumers face uninsurable and idiosyncraic income shocks, e.g. he loss of employmen. The prospec of such evens is higher in economic downurns and his observaion akes us a long way owards undersanding boh he uncondiional momens of asse reurns and heir variaion along he business cycle. I also argued ha we should accoun for borrowing consrains. In his conex, life cycle consideraions are imporan and are ofen overlooked in finance. Borrowing consrains become imporan when placed in he conex of he life cycle. The ficiious represenaive consumer ha holds all he sock marke and bond marke wealh does no face credible borrowing consrains. Young consumers, however, do face credible borrowing consrains. I raced heir impac on he equiy premium, he demand for bonds who holds bonds if he equiy premium is so high? and on he limied paricipaion of consumers in he capial markes. Has he equiy premium puzzle been resolved? I do no hink so. However, he pursui of an explanaion has helped us broaden he scope of our invesigaion in several imporan ways. We are now ineresed in undersanding he mean, higher momens, covariabiliy and predicabiliy of he reurn of differen classes of financial asses. A he macro level, we sudy he shor-erm risk-free rae, he erm premium of long-erm bonds over he risk-free rae and he aggregae equiy premium of he sock marke over he risk-free rae. A he micro level, we sudy he premium of individual sock reurns and of classes of socks, such as he small-capializaion versus large-capializaion socks, he value versus growh socks and he pas losing versus winning socks. Our pursui has led us o sudy a broader class of preferences, evoluion of sae variables, beliefs and learning mechanisms, marke incompleeness, marke imperfecions and noions of liquidiy han hose embedded in he sandard neoclassical model. Our pursui has also helped us gain a beer undersanding of daa problems such as limied paricipaion of

19 Marke Organizaion and Prices of Financial Asses 9 consumers in he sock marke, emporal aggregaion and survival biases. In my eclecic discussion of hese issues, I hope o have convinced he reader ha he organizaion of he markes, specifically marke incompleeness and borrowing consrains in he life cycle, provide a promising vanage poin from which o sudy he prices of asses and heir reurns boh heoreically and empirically. References Abel, A. B. (990). Asse Prices Under Habi Formaion and Caching Up wih he Joneses, American Economic Review, Papers and Proceedings, Vol. 80, pp Ai-Sahalia, Y., Parker, J. A. and Yogo, M. (2004). Luxury Goods and he Equiy Premium, Journal of Finance, Vol. 59, pp Aiyagari, R. S. and Gerler, M. (99). Asse Reurns wih Transacions Coss and Uninsured Individual Risk, Journal of Moneary Economics, Vol. 27, pp Alonji, J. G., Hayashi, F. and Kolikoff, L. J. (992). Is he Exended Family Alruisically Linked?, American Economic Review, Vol. 82, pp Alvarez, F. and Jermann, U. J. (200). Quaniaive Asse Pricing Implicaions of Endogenous Solvency Consrains, Review of Financial Sudies, Vol. 4, pp Aanasio, O. P. and Davis, S. J. (997). Relaive Wage Movemens and he Disribuion of Consumpion, Journal of Poliical Economy, Vol. 04, pp Aanasio, O. P., Banks, J. and Tanner, S. (2002). Asse Holding and Consumpion Volailiy, Journal of Poliical Economy, Vol. 0, pp Bakshi, G. and Chen, Z. (996). The Spiri of Capialism and Sock Marke Prices, American Economic Review, Vol. 86, pp Bansal, R. and Coleman, J. W. (996). A Moneary Explanaion of he Equiy Premium, Term Premium, and Risk-free Rae Puzzles, Journal of Poliical Economy, Vol. 04, pp Bansal, R. and Yaron, A. (2004). Risks for he Long Run: a Poenial Resoluion of Asse Pricing Puzzles, Journal of Finance, Vol. 59, pp Barro, R. J. (2005). Rare Evens and he Equiy Premium, Working Paper, Harvard Universiy. Benarzi, S. and Thaler, R. H. (995). Myopic Loss Aversion and he Equiy Premium Puzzle, Quarerly Journal of Economics, Vol. 0, pp Berau, C. C. and Haliassos, M. (997). Precauionary Porfolio Behavior from a Life-cycle Perspecive, Journal of Economic Dynamics and Conrol, Vol. 2, pp Bewley, T. F. (982). Thoughs on Tess of he Ineremporal Asse Pricing Model, Working Paper, Norhwesern Universiy. Bodie, Z., Meron, R. C. and Samuelson, W. F. (992). Labor Supply Flexibiliy and Porfolio Choice in a Life Cycle Model, Journal of Economic Dynamics and Conrol, Vol. 6, pp Boldrin, M., Chrisiano, L. J. and Fisher, J. D. M. (200). Habi Persisence, Asse Reurns, and he Business Cycle, American Economic Review, Vol. 9, pp Braun, P. A., Consaninides, G. M. and Ferson, W. E. (993). Time Nonseparabiliy in Aggregae Consumpion: Inernaional Evidence, European Economic Review, Vol. 37, pp

20 20 The Mancheser School Brav, A. and Geczy, C. C. (995). An Empirical Resurrecion of he Simple Consumpion CAPM wih Power Uiliy, Working Paper, Universiy of Chicago. Brav, A., Consaninides, G.M. and Geczy, C. C. (2002). Asse Pricing wih Heerogeneous Consumers and Limied Paricipaion: Empirical Evidence, Journal of Poliical Economy, Vol. 0, pp Breeden, D. T. (979). An Ineremporal Asse Pricing Model wih Sochasic Consumpion and Invesmen Opporuniies, Journal of Financial Economics, Vol. 7, pp Brown, S. J., Goezmann, W. N. and Ross, S. (995). Survival, Journal of Finance, Vol. 50, pp Cagei, M., Hansen, L. P., Sargen, T. and Williams, N. (2002). Robusness and Pricing wih Uncerain Growh, Review of Financial Sudies, Vol. 5, pp Campbell, J. Y. (200). Asse Pricing a he Millennium, Journal of Finance, Vol. 55, pp Campbell, J. Y. (2003). Consumpion-based Asse Pricing, in G. M. Consaninides, M. Harris and R. Sulz (eds), Financial Markes and Asse Pricing: Handbook of he Economics of Finance, Vol. B, Handbooks in Economics 2, Amserdam, Norh-Holland, pp Campbell, J. Y. and Cochrane, J. H. (999). By Force of Habi: a Consumpionbased Explanaion of Aggregae Sock Marke Behavior, Journal of Poliical Economy, Vol. 07, pp Campbell, J. Y., Lo, A. W. and MacKinlay, A. C. (997). The Economerics of Financial Markes, Princeon, NJ, Princeon Universiy Press. Cecchei, S. G., Lam, P. and Mark, N. (2000). Asse Pricing wih Disored Beliefs: Are Equiy Reurns Too Good o Be True?, American Economic Review, Vol. 90, pp Cochrane, J. H. (99). A Simple Tes of Consumpion Insurance, Journal of Poliical Economy, Vol. 99, pp Cochrane, J. H. (997). Where is he Marke Going? Uncerain Facs and Novel Theories, Economic Perspecives (Federal Reserve Bank of Chicago), Vol. 2, pp Cochrane, J. H. (200). Asse Pricing, Princeon, NJ, Princeon Universiy Press. Cochrane, J. H. and Hansen, L. P. (992). Asse Pricing Exploraions for Macroeconomics, in O. J. Blanchard and S. Fischer (eds), NBER Macroeconomics Annual, Cambridge, MA, MIT Press. Cogley, T. (2002). Idiosyncraic Risk and he Equiy Premium: Evidence from he Consumer Expendiure Survey, Journal of Moneary Economics, Vol. 49, pp Consaninides, G. M. (982). Ineremporal Asse Pricing wih Heerogeneous Consumers and wihou Demand Aggregaion, Journal of Business, Vol. 55, pp Consaninides, G. M. (990). Habi Formaion: a Resoluion of he Equiy Premium Puzzle, Journal of Poliical Economy, Vol. 98, pp Consaninides, G. M. (2002). Raional Asse Prices, Journal of Finance, Vol. 57, pp Consaninides, G. M. and Duffie, D. (996). Asse Pricing wih Heerogeneous Consumers, Journal of Poliical Economy, Vol. 04, pp Consaninides, G. M., Donaldson, J. B. and Mehra, R. (2002). Junior Can Borrow: a New Perspecive on he Equiy Premium Puzzle, Quarerly Journal of Economics, Vol. 7, pp Daniel, K. and Marshall, D. (997). The Equiy Premium Puzzle and he Risk-free Rae Puzzle a Long Horizons, Macroeconomic Dynamics, Vol., pp