S tock price has been found to provide important

Transcription

1 Why Are Sock Marke Reurns Correlaed wih Fuure Economic Aciviies? Hui Guo S ock price has been found o provide imporan informaion abou fuure economic aciviies. Fama (98) Fischer and Meron (984) and Barro (99) among many ohers documen a posiive relaion beween sock marke reurn and subsequen growh in invesmen and oupu. These findings are consisen wih raional expecaions asse pricing models in which sock price is equal o he sum of discouned fuure cash flows or dividends. An unexpeced increase in he sock price indicaes ha (i) fuure dividend growh is higher and/or (ii) fuure discoun raes are lower han previously anicipaed. Given ha he dividend is an imporan componen of gross domesic produc (GDP) and is also likely o be posiively correlaed wih he oher componens of GDP he sock price increase may merely reflec higher expeced fuure oupu. On he oher hand lower discoun raes are associaed wih higher invesmen and herefore higher oupu. Moreover recognizing a imevarying risk premium Leau and Ludvigson (2b) show ha he q heory of invesmen implies an imporan relaion beween he expeced sock marke reurn and invesmen. Tha is lower expeced sock marke reurn implies lower fuure sock price and higher fuure capial cos; accordingly invesmen falls over long horizons. The analysis above shows ha sock reurns are correlaed wih fuure economic aciviies hrough differen channels. In his paper I address he relaive imporance of hese mechanisms by using Campbell and Shiller s (988) mehod o decompose excess sock marke reurn e M ino hree pars: expeced reurn E e M ; a shock o he expeced fuure reurn Hui Guo is an economis a he Federal Reserve Bank of S. Louis. William Bock provided research assisance. 22 The Federal Reserve Bank of S. Louis. M+ = ( E E ) ρ e and a shock o he expeced fuure dividend growh 2 M+ = ( E E ) ρ d I find ha a posiive shock o he expeced fuure dividend growh is associaed wih higher fuure GDP growh. Conrary o he convenional wisdom however dividend shocks are raher weak predicors for economic aciviies. For example heir forecasing power concenraes on he nex four quarers of which dividend shocks explain only abou 2 percen of variaions in GDP growh. I find similar resuls for he GDP componens as well. In conras he expeced reurn especially and shocks o he expeced fuure reurn exhibi srong predicive abiliy for economic aciviies. However heir predicive paerns are quie differen: while shocks o he expeced fuure reurn are posiively (negaively) correlaed wih fuure invesmen over shor (long) horizons he expeced reurn is negaively (posiively) correlaed wih fuure invesmen over shor (long) horizons. As a resul he forecasing power of excess sock marke reurn is considerably compromised. For example i explains essenially no variaions in one-quarer-ahead invesmen growh while he hree componens oinly accoun for 4 percen. Also excess sock marke reurn explains only 2 percen of variaions in he nex hree years invesmen growh compared wih 3 percen by he hree componens. Inuiively a posiive innovaion in he dividend indicaes greaer fuure economic growh. However he forecasing power of dividend shocks is moderae because my decomposiions show ha hey accoun for only a small porion of variaions in excess sock marke reurn. The relaion beween he expeced reurn E e M and fuure invesmen According o he q heory of invesmen a negaive shock o discoun raes should increase sock price and invesmen simulaneously. However Lamon (2) argues ha here are ineremporal shifs in hese relaionships because of lags beween invesmen decisions and invesmen expendiures. His resuls help explain why according o he daa sock reurn is negaively correlaed wih conemporaneous invesmen and posiively correlaed wih subsequen invesmen. 2 Acually here is an exra erm: he shock o he real risk-free rae ( E E ) ρ rf +. = However Campbell and Ammer (993) find ha i accouns for very few variaions in excess sock marke reurn. For simpliciy I assume ha is value is zero in his paper. ;. MARCH/APRIL 22 9

2 Guo R EVIEW is consisen wih Leau and Ludvigson (2b) who show ha he wo variables are negaively correlaed in he shor run and are posiively correlaed in he long run. Similarly because he shock o he expeced fuure reurn a period M+ = ( E E ) ρ e is negaively correlaed wih he expeced reurn a period + E e M+ i should also be negaively correlaed wih invesmen in he long run even hough he wo are posiively correlaed in he shor run. In oher words an appreciaion in sock price may imply eiher an increase or decrease in fuure invesmen depending on wheher such an appreciaion in price is due o (i) a negaive shock o he expeced fuure reurn or (ii) o he fac ha he sock price is expeced o be high. 3 My resuls herefore explain why he predicive power of sock marke reurns is raher limied as argued by many auhors (e.g. Sock and Wason 999). Laer in he aricle I discuss he sock marke reurn predicabiliy and hen decompose excess sock marke reurns. I show forecasing abiliy of hese componens for fuure economic aciviies and hen offer conclusions. STOCK MARKET RETURN PREDICTABILITY In he pas wo decades financial economiss have documened mouning evidence agains he random walk hypohesis of sock price. For example Campbell Lo and MacKinlay (997) provide evidence ha dividend yield and he sochasically derended risk-free rae conain informaion abou fuure sock price movemens. 45 Leau and Ludvigson (2a) find ha flucuaions in he consumpion-wealh raio are srong predicors of fuure sock marke reurns. Moreover Guo (22) shows ha pas sock marke variance has significan predicive abiliy as well; and ineresingly such predicive abiliy is grealy enhanced if he consumpion-wealh raio is also included in he forecasing equaion. Table replicaes some resuls of he predicabiliy of sock marke reurn documened in he early lieraure. The informaional variables include lagged excess sock marke reurn e M ; he dividend yield dp ; he sochasically derended risk-free rae rrel ; he consumpion-wealh raio cay ; and pas sock marke variance σ 2 M. I use quarerly daa from 953:Q o 2:Q4 and Appendix A provides deails abou ha daa. The firs five rows presen he univariae regression resuls. I find ha while rrel cay and σ 2 M forecas one-quarer-ahead excess sock marke reurn e M and dp ener he forecasing equaion insignificanly. Row 6 is he regression resul of excess sock marke reurn on all he informaional variables excep σ 2 M. Again rrel and cay are boh saisically significan and he adused R 2 is abou 2 percen. I add σ 2 M as an addiional regressor o he mulivariae regression in row 7. Consisen wih Guo (22) rrel cay and σ 2 M are highly significan and he adused R 2 umps o 2 percen! The subsanial improvemen in he forecasing abiliy is explained by he fac ha while σ 2 M and cay are negaively correlaed hey boh ener he excess sock marke reurn equaion wih a posiive sign. To summarize evidence suggess ha a large porion of variaions in excess sock marke reurn is predicable. I wan o emphasize ha sock price predicabiliy does no necessarily conradic he sock marke efficiency hypohesis. This poin is clearly demonsraed in Meron s (973) ineremporal capial asse pricing model (ICAPM) which can be summarized by equaion (a): 2 M + M + MF + (a) Ee = γeσ + λeσ. The condiional excess sock marke reurn E e M+ (defined as he difference beween he condiional sock marke reurn E r M+ and he risk-free rae r f+ ) is a linear funcion of is condiional variance E σ 2 M+ and is covariance wih invesmen opporuniies E σ 2 MF+. The coefficien γ is a measure of relaive risk aversion and he coefficien λ is a funcion of he model s underlying parameers. I call he firs erm of equaion (a) he risk componen and he second erm he hedge componen. I is well known ha sock marke variance is serially correlaed in he daa; also here is no paricular reason o believe ha he covariance beween excess 3 A simple model developed by Guo (2) makes his poin clear. If he condiional sock marke reurn is proporional o he risk he auhor shows ha excess sock marke reurn is posiively correlaed wih lagged sock marke variance and is negaively correlaed wih curren variance. Given ha sock marke variance is negaively correlaed wih fuure oupu he posiive relaion beween excess reurn and lagged variance weakens he forecasing power of he former. His model herefore explains why sock marke variance drives ou reurn in forecasing GDP growh as documened by Campbell e al. (2). 4 The sochasically derended risk-free rae is he risk-free rae less is average over he las four quarers. 5 Leau and Ludvigson (2a) find ha he dividend yield loses is forecasing abiliy when he sample period is exended o he laer 99s a resul I reproduce laer in he paper. 2 MARCH/APRIL 22

3 FEDERAL RESERVE BANK OF ST. LOUIS Guo Table Forecasing Quarerly Excess Sock Marke Reurn Row e M dp rrel cay σ 2 M R (.54) 2.9. (.459) ( 3.929) (3.2) (2.825) (.658) (.254) ( 4.783) (3.86) (.569) (.537) ( 4.3) (5.579) (5.249) NOTE: This able repors he ordinary leas-squares (OLS) regression resuls of excess sock marke reurn e M+ on informaional variables including he lagged excess sock marke reurn e M ; he dividend yield dp ; he sochasically derended risk-free rae rrel ; he consumpion-wealh raio cay ; and he realized sock marke variance σ 2 M. Newey-Wes (987) correced sandard errors are used o calculae he saisics which are repored in parenheses. The daa are quarerly and span from 953:Q o 2:Q4. See Appendix A for a descripion of he daa. sock marke reurns and invesmen opporuniies is consan or ha is coefficien is zero. In general he expeced sock marke reurn is no consan and sock marke reurns are predicable. While he early lieraure has emphasized he risk componen Guo (2) shows ha he hedge componen is also imporan in undersanding he ime-varying equiy premium in a limied sock marke paricipaion model. As shown in equaion (b) he equiy premium also has wo componens in he model developed by Guo (2) 6 : (b) 2 M + f f f Ee M + + σ E γeσ MC + + r + min { r + r2 + } 2 where E σ MC+ is he covariance beween he shareholder s consumpion growh and sock marke reurns and r+ f and r2+ f are he shareholder s and he non-shareholder s shadow risk-free raes respecively. While he firs erm γ E σ MC+ is proporional o he risk componen in equaion (a) he second erm r+ f min{r+r f 2+} f can be hough of as a liquidiy premium because i reflecs he fac ha he shareholder canno use socks o hedge he income risks because of he consrains of limied sock marke paricipaion. Moreover such a liquidiy premium is small (large) when he sock price is high (low); herefore i is posiively correlaed wih he dividend yield. Ineresingly Guo (2) also predics ha when he dividend yield is low sock marke variance should be negaively correlaed wih he dividend yield. Thus given ha he consumpion-wealh raio is equivalen o he dividend yield in Guo (2) his model well explains he empirical evidence documened in Table. 7 6 The variance erm 2 σ M E + 2 on he lef-hand side of equaion (b) is he adusmen for Jensen s inequaliy. 7 Campbell Lo and MacKinlay (997) explain ha he dividend yield forecass sock marke reurns because i can be wrien as a funcion of expeced fuure excess sock marke reurn and dividend growh. Similarly Leau and Ludvigson (2a) show ha he consumpionwealh raio is also a funcion of expeced fuure excess sock marke reurn and consumpion growh. The wo variables herefore are equivalen in an exchange economy (e.g. Guo 2). Despie heir close heoreical link he consumpion-wealh raio demonsraes much sronger predicive power han he dividend yield does possibly because he former is a beer measure of is heoreical counerpar han he laer is. MARCH/APRIL 22 2

4 Guo R EVIEW A DECOMPOSITION OF EXCESS STOCK MARKET RETURN Given srong evidence of sock reurn predicabiliy in his secion I adop Campbell and Shiller s (988) log-linearizaion mehod o decompose excess sock marke reurn ino hree pars: expeced reurn a shock o he expeced fuure reurn and a shock o he expeced fuure dividend growh. The advanages of his approach are racabiliy and accuracy. The coninuously compounded sock marke reurn r M is defined as (2) rm = log( PM + DM ) log( PM ) where P M is he sock price a he end of period and D M is he dividend paid ou during period. Throughou his paper I use upper case o denoe he level and lower case o denoe he log. Using a firs-order Taylor expansion around he seady sae of he log dividend price raio d p equaion (2) can be rewrien as a firs-order difference equaion for he sock price: (3) r k+ ρp p + ( ρ) d M M M M where ρ = + exp( d p) k = log( ρ) ( ρ)log( ). ρ Campbell Lo and MacKinlay (997) repor ha he annual dividend yield is abou 4 percen in he hisorical daa. Accordingly I se ρ o.99 for he quarerly daa in his paper. Solving equaion (3) forward and imposing he ransversaliy condiion lim ρ M + = P he sock price can be wrien as a funcion of fuure dividend flows and discoun raes: k (4) pm = + ρ [( ρ) dm + rm + ]. ρ = Equaion (4) is simply an accouning ideniy which also holds ex ane: k (5) pm = + E ρ [( ρ) dm + rm + ]. ρ = Subsiuing equaion (5) ino equaion (3) I hen decompose he realized excess sock marke reurn ino hree pars: expeced reurn a shock o he expeced fuure dividend growh and a shock o he expeced fuure reurn. (6) r E r = ( E E ) ρ d ( E E ) ρ r For he excess sock marke reurn e M+ = r M+ r f+ where r f+ is he real risk-free rae I can rewrie equaion (6) as (7) e E e = M M ( E E )( ρ d ρ r ρ e ). M M M + M + = = M + f + M + = = = I assume ha x x 2 x n are n sae variables ha predic excess sock marke reurn and he vecor X =[e M x x 2 x n ] follows a firs order vecor auoregression (VAR) process (8) X = A+ BX + ε where A is an (n+) by vecor of consans B is an (n+) by (n+) coefficien marix and ε is an (n+) by vecor of whie noise. Then he expeced excess sock marke reurn E e m is equal o e B X where e is an n by vecor [ ]. As shown in Appendix B he shock o he expeced fuure reurn M+ = ( E E ) ρ e is equal o e ρb(i ρb) ε where I is an (n+) by (n+) ideniy marix. Campbell and Ammer (993) find ha he shock o he expeced fuure real riskfree rae f+ = ( E E ) ρ r accouns for very few variaions in excess sock marke reurn. For simpliciy I assume ha is value is zero; and herefore he shock o he expeced fuure dividend growh M+ = ( E E ) ρ d is approximaely equal o e M E e M e ρb (I ρb) ε. Furhermore I denoe he shock o he expeced fuure reurn M+ = ( E E ) ρ e. 22 MARCH/APRIL 22

5 FEDERAL RESERVE BANK OF ST. LOUIS Guo Table 2 Vecor Auoregression of Excess Sock Marke Reurn e M dp rrel cay σ 2 M R 2 e M (.569) (.537) ( 4.3) (5.579) (5.249) dp ( 2.83) (76.929) (5.3) ( 4.9) ( 5.894) rrel (.975) (.26) (4.3) (.529) (.42) cay ( 6.9) (.559) (.684) (25.93) (.668) σ 2 M (.4) (.88) (.929) ( 2.93) (5.274) NOTE: This able repors he ordinary leas-squares (OLS) regression resuls of he VAR sysem specified by equaion (8). Newey-Wes (987) correced sandard errors are used o calculae he saisics which are repored in parenheses. The daa are quarerly and span from 953:Q o 2:Q4. See Appendix A for a descripion of he daa. Table 3 Summary Saisics e M E e M η e η d Panel A: Mean and sandard error Mean Sandard error Panel B: Covariance and correlaion e M E e M η e η d NOTE: This able repors he mean sandard error covariance (lower riangle of Panel B in bold) and correlaion (upper riangle of Panel B) of he excess sock marke reurn in is hree componens. The decomposiion is based on he VAR esimaion repored in Table 2. by η e and he shock o he expeced fuure dividend growh M+ = ( E E ) ρ d by η d. Noe η e and η d are orhogonal o E e M by definiion. Table 2 repors he ordinary leas-squares (OLS) esimae of he VAR sysem specified in equaion (8). The sae variables include all he forecasing variables used in Table. I adop a VAR () specificaion because i is consisen wih he Schwarz Bayesian informaion crierion and he Akaike informaion crierion. One ineresing observaion is ha he coefficien on is own lag is prey large for dp rrel and cay whereas i is only.38 for σ 2 M. Therefore unlike oher forecasing variables σ 2 M capures relaively high-frequency variaions in excess sock marke reurn. Summary saisics for excess sock marke reurn e M and is hree componens are repored in Table 3. By consrucion shocks o he expeced fuure reurn η e and shocks o he expeced fuure dividend growh η d boh have zero means. How- MARCH/APRIL 22 23

6 Guo R EVIEW Figure Realized Excess Sock Marke Reurn Figure 2 Expeced Excess Sock Marke Reurn ever he sandard error of η e is almos wice as large as ha of η d. The expeced reurn E e M has he same mean as bu a much smaller sandard error han ha of e M. Moreover he covariance beween η e and e M is abou 66 percen of he variance of e M while i is 22 percen for E e M and 2 percen for η d. Similarly η e has he larges correlaion coefficien wih e M followed by E e M and η d. Therefore η e and E e M accoun for he vas maoriy of variaions in e M while η d is relaively unimporan in explaining sock price movemens. In oher words sock price is no sensiive o he dividend news. My resuls are consisen wih hose repored in he early lieraure (e.g. Campbell and Shiller 988) alhough he wo papers adop differen forecasing variables. Figures hrough 4 plo excess sock marke reurn and is hree componens wih he shaded areas indicaing recessions he daes of which were deermined by he Naional Bureau of Economic Research. Figure shows ha sock price seems o decrease (increase) a he beginning (end) of recessions. However i flucuaes dramaically over ime and displays lile business cycle paern. This assessmen is consisen wih he convenional skepicism abou sock price as a leading indicaor. The picure is quie differen for he expeced reurn. Figure 2 shows ha he expeced reurn always increases during recessions and decreases during expansions. In only wo occasions namely he second quarer of 962 and he fourh quarer of 987 were he sharp increases in he expeced reurn no associaed wih recessions. In he firs case he economy slowed down significanly in he following quarers. In he second case he expeced reurn was driven up solely by he dramaic increase in sock marke 24 MARCH/APRIL 22

7 FEDERAL RESERVE BANK OF ST. LOUIS Guo Figure 3 Shock o he Expeced Fuure Reurn Figure 4 Shock o he Expeced Fuure Dividend Growh variance because of he Ocober sock marke crash which was unusual and shor-lived. My findings of a srongly cyclical expeced reurn should no be a surprise because forecasing variables such as he consumpion-wealh raio he sochasically derended risk-free rae and pas sock marke variance all display srong business cycle paerns. In conras Figures 3 and 4 show ha shocks o he expeced fuure reurn and shocks o he expeced fuure dividend growh do no move in andem very much wih business cycles. STOCK MARKET RETURNS AND FUTURE ECONOMIC ACTIVITIES Excess sock marke reurn e M is high because (i) i is expeced o be high or E e M is high (ii) here is a negaive shock o he expeced fuure reurn or η e is high or (iii) here is a posiive shock o he expeced fuure dividend growh or η d is high. In his secion I analyze he relaive imporance of hese componens in forecasing economic aciviies. Fixed Privae Nonresidenial Invesmen Table 4 repors he long-horizon regression resuls of he fixed privae nonresidenial invesmen growh on excess sock marke reurn and is hree componens. 8 For horizon H he dependen variable is he invesmen growh rae from ime + o ++H. Row shows ha excess sock marke reurn e M is always posiively correlaed wih fuure invesmen growh. Is predicive power as measured by he adused R 2 firs increases hen decreases and peaks a four quarers a which i 8 I obain qualiaively similar resuls if I also include he lagged dependen variable as a regressor. MARCH/APRIL 22 25

8 Guo R EVIEW Table 4 Forecasing Fixed Nonresidenial Invesmen Growh Forecas horizon Row Regressor e M (.4) (2.82) (3.4) (3.25) (2.6) (.2) [.] [.4] [.8] [.6] [.2] [.] 2 E e M ( 2.2) (.4) (.77) (3.72) (4.2) (3.8) [.2] [.] [.4] [.4] [.4] [.9] 3 η e (.62) (2.59) (2.26) (.35) (.) (.67) [.2] [.7] [.3] [.] [.] [.] 4 η d (.8) (.42) (.76) (2.2) (.67) (.8) [.] [.] [.] [.] [.] [.] 5 η e +η d (.42) (2.92) (2.75) (.23) (.48) (.34) [.] [.5] [.5] [.] [.] [.] 6 E e M ( 2.9) (.9) (.83) (3.89) (4.4) (3.7) η e (.58) (2.8) (2.56) (.9) (.74) (.45) η d (.97) (.47) (.87) (2.47) (.65) (.6) [.4] [.5] [.8] [.5] [.3] [.9] LR NOTE: This able repors he ordinary leas-squares (OLS) regression resuls of real fixed nonresidenial invesmen growh on excess sock marke reurn and is hree componens. Newey-Wes (987) correced sandard errors are used o calculae he saisics which are repored in parenheses. The adused R 2 is repored in brackes. LR he saisic of log-likelihood raio es of equal coefficiens in row 6 has a χ 2 disribuion wih wo degrees of freedom and is criical value a he 5 percen significance level is The daa are quarerly and span from 953:Q o 997:Q4 because of he leads in he dependen variable. The decomposiion is based on he VAR esimaion repored in Table 2. See Appendix A for a descripion of he daa. explains 8 percen of variaions in fuure invesmen growh. In row 2 he expeced reurn E e M is negaively correlaed wih he nex wo quarers invesmen growh and he correlaion urns posiive as he forecasing horizon increases. Is predicive power concenraes a relaively long horizons and peaks around wo o hree years a which i explains abou 4 percen of variaions in invesmen growh. As shown in row 3 shocks o he expeced fuure reurn η e also forecas invesmen growh; however heir predicive paerns are quie differen from hose of E e M. In paricular η e is posiively correlaed wih fuure invesmen growh over shor horizons and he correlaion urns negaive as he forecasing horizon increases. Moreover is predicive power concenraes a relaively shor horizons and peaks a wo quarers a which i explains abou 7 percen of variaions in invesmen growh. In conras row 4 shows ha he shock o he dividend η d does no conain much informaion abou fuure invesmen growh. The correlaion beween he wo is no saisically significan unil he forecasing horizon increases o 2 years and hen i becomes insignifican again a longer forecasing horizons. A is peak η d explains only percen of variaions in he invesmen growh rae. Moreover row 5 shows ha he oal shock η e +η d displays a similar predicive paern o ha of η e. Therefore he forecasing power of sock marke reurn mainly comes from he expeced reurn and shocks o he expeced 26 MARCH/APRIL 22

9 FEDERAL RESERVE BANK OF ST. LOUIS Guo Table 5 Forecasing Nondurable Consumpion and Service Growh Forecas horizon Row Regressor e M (2.6) (2.56) (3.27) (2.4) (.83) (.) [.5] [.5] [.5] [.] [.] [.] 2 E e M (.27) (.59) (.73) (.77) (.) (.58) [.] [.] [.] [.] [.] [.] 3 η e (3.4) (2.67) (.97) (.49) (.93) (.23) [.7] [.5] [.3] [.] [.] [.] 4 η d (.72) (.68) (.94) (.7) (.24) (.42) [.] [.] [.] [.] [.] [.] 5 η e +η d (2.76) (2.5) (2.66) (.96) (.4) (.26) [.6] [.4] [.4] [.] [.] [.] 6 E e M (.33) (.64) (.79) (.8) (.2) (.58) η e (2.92) (2.58) (2.4) (.76) (.7) (.3) η d (.4) (.34) (.68) (.) (.65) (.) [.6] [.5] [.4] [.] [.] [.] LR NOTE: This able repors he ordinary leas-squares (OLS) regression resuls of real nondurable consumpion growh which is measured by (nondurable + service shoes clohes) on excess sock marke reurn and is hree componens. Newey-Wes (987) correced sandard errors are used o calculae he saisics which are repored in parenheses. The adused R 2 is repored in brackes. LR he saisic of log-likelihood raio es of equal coefficiens in row 6 has a χ 2 disribuion wih wo degrees of freedom and is criical value a he 5 percen significance level is The daa are quarerly and span from 953:Q o 997:Q4 because of he leads in he dependen variable. The decomposiion is based on he VAR esimaion repored in Table 2. See Appendix A for a descripion of he daa. fuure reurn while he informaion conen of dividend shocks is raher limied. These resuls are no a surprise because dividend shocks accoun for a relaively small porion of variaions in excess sock marke reurns as shown in Table 3. Alhough excess sock marke reurn and fuure invesmen growh are posiively correlaed a all horizons he forecasing abiliy of excess sock marke reurn is considerably compromised because of differen predicive paerns beween he expeced reurn and shocks o he expeced fuure reurn. This poin is clearly demonsraed in row 6 of Table 4 which shows he mulivariae regression resuls of invesmen growh on he hree componens of excess sock marke reurn. I find ha he coefficiens of he expeced reurn and shocks o he expeced fuure reurn have opposie signs over boh shor and long horizons as in he univariae regressions. Also he adused R 2 in row 6 is much higher han is counerpar in row. Moreover he las line of row 6 repors he log-likelihood raio es of he null hypohesis ha he hree componens have he same coefficien which is overwhelmingly reeced in mos cases. To summarize I find ha he dividend shock of excess sock marke reurn provides lile informaion abou fuure invesmen. Also he expeced reurn and shocks o he expeced fuure reurn display quie differen predicive paerns. Togeher my resuls sugges ha he forecasing power of MARCH/APRIL 22 27

10 Guo R EVIEW Table 6 Forecasing Durable Consumpion Growh Forecas horizon Row Regressor e M (3.43) (5.96) (4.72) (3.5) (.45) (.72) [.9] [.9] [.2] [.2] [.] [.] 2 E e M (2.5) (3.27) (3.8) (4.6) (3.) (.53) [.3] [.] [.6] [.4] [.5] [.] 3 η e (2.63) (4.8) (2.9) (.99) (.67) (.3) [.5] [.7] [.] [.] [.] [.] 4 η d (.6) (.2) (2.3) (.42) (.8) (.74) [.] [.] [.2] [.] [.] [.] 5 η e +η d (2.95) (4.88) (3.25) (.92) (.79) (.52) [.5] [.] [.3] [.] [.] [.] 6 E e M (2.78) (3.73) (4.23) (4.69) (3.8) (.52) η e (2.98) (4.74) (2.89) (.89) (.7) (.3) η d (.85) (2.48) (2.7) (.23) (.4) (.93) [.9] [.2] [.2] [.3] [.4] [.] LR NOTE: This able repors he ordinary leas-squares (OLS) regression resuls of real durable consumpion growh on excess sock marke reurn and is hree componens. Newey-Wes (987) correced sandard errors are used o calculae he saisics which are repored in parenheses. The adused R 2 is repored in brackes. LR he saisic of log-likelihood raio es of equal coefficiens in row 6 has a χ 2 disribuion wih wo degrees of freedom and is criical value a he 5 percen significance level is The daa are quarerly and span from 953:Q o 997:Q4 because of he leads in he dependen variable. The decomposiion is based on he VAR esimaion repored in Table 2. See Appendix A for a descripion of he daa. excess sock marke reurn is raher limied alhough i is a forward-looking variable. Nondurable Consumpion and Service Hall (978) documens a posiive relaionship beween sock price and fuure consumpion (nondurable and service) growh which is a odds wih he permanen income hypohesis. Hall inerpres his resuls as consumpion adusing o capial gain wih lags. In row of Table 5 I confirm Hall s resuls and show ha excess sock marke reurn e M forecass consumpion growh up o eigh quarers. 9 Is predicive power peaks around four quarers wih an adused R 2 of abou 5 percen. Row 2 shows ha he informaion conen of excess sock marke reurn does no come from he expeced reurn E e M which does no forecas consumpion growh a any horizons. This finding is consisen wih early evidence ha consumpion is no sensiive o ineres rae changes or ha he elasiciy of iner-emporal subsiuion is small. Ineresingly dividend shocks η d do no explain fuure consumpion growh eiher as shown in row 4. Therefore all he predicive power of excess sock marke reurn comes from shocks o he expeced fuure reurn η e. As shown in row 3 η e forecass con- 9 In Table 5 I exclude shoes and clohes from he nondurable consumpion. 28 MARCH/APRIL 22

11 FEDERAL RESERVE BANK OF ST. LOUIS Guo Table 7 Forecasing Fixed Residenial Invesmen Growh Forecas horizon Row Regressor e M (4.55) (4.49) (3.69) (.64) (.24) (.37) [.2] [.9] [.9] [.] [.] [.] 2 E e M (4.69) (5.93) (7.2) (3.4) (.89) (.7) [.6] [.24] [.28] [.4] [.5] [.] 3 η e (3.67) (2.9) (.2) ( 2.55) (.34) (.44) [.6] [.4] [.] [.2] [.] [.] 4 η d (.68) (.94) (.49) (.36) (.7) (.23) [.] [.] [.] [.] [.] [.] 5 η e +η d (3.5) (3.2) (.7) ( 3.8) (.58) (.68) [.8] [.5] [.] [.] [.] [.] 6 E e M (4.84) (6.7) (7.55) (3.2) (.86) (.7) η e (3.73) (2.95) (.8) ( 2.92) (.42) (.53) η d (.53) (.72) (.87) (.27) (.64) (.56) [.24] [.29] [.28] [.5] [.5] [.] LR NOTE: This able repors he ordinary leas-squares (OLS) regression resuls of real fixed residenial invesmen growh on excess sock marke reurn and is hree componens. Newey-Wes (987) correced sandard errors are used o calculae he saisics which are repored in parenheses. The adused R 2 is repored in brackes. LR he saisic of log-likelihood raio es of equal coefficiens in row 6 has a χ 2 disribuion wih wo degrees of freedom and is criical value a he 5 percen significance level is The daa are quarerly and span from 953:Q o 997:Q4 because of he leads in he dependen variable. The decomposiion is based on he VAR esimaion repored in Table 2. See Appendix A for a descripion of he daa. sumpion growh up o four quarers. The associaed adused R 2 peaks a a one-quarer horizon indicaing ha consumpion acually reacs o capial gain/ loss quickly. Again he oal shock η e +η d exhibis very similar predicive paerns o hose of η e. Consumpion reacs differenly o η d and η e for wo possible reasons. Firs dividend shocks accoun for a relaively small porion of variaions in excess sock marke reurn as repored in Table 3. Second Table 4 also shows ha η e has a much larger sandard error han η d has. In oher words here is greaer uncerainy associaed wih shocks o he expeced fuure reurn han wih shocks o dividends. As a resul consumers reac wih more cauion o η e han o η d. Consisen wih he second hypohesis I find ha consumpion reacs conemporaneously o dividend shocks bu no shocks o he expeced reurn. Anoher ineresing observaion is ha unlike nonresidenial invesmen row 6 shows ha he adused R 2 in he mulivariae regressions is no subsanially higher han is counerpar in row. Also he null hypohesis ha he hree componens have he same coefficien is no reeced by he log-likelihood raio es in any cases. Durable Consumpion and Fixed Residenial Invesmen Table 6 repors he regression resuls of durable consumpion. Excess sock marke reurn e M is MARCH/APRIL 22 29

12 Guo R EVIEW Table 8 Forecasing GDP Growh Forecas horizon Row Regressor e M (3.2) (4.9) (4.36) (3.4) (2.6) (.66) [.7] [.4] [.3] [.3] [.] [.] 2 E e M (.76) (2.46) (3.27) (3.48) (3.) (2.45) [.2] [.7] [.6] [.4] [.8] [.5] 3 η e (2.35) (2.82) (.97) (.72) (.7) (.73) [.4] [.5] [.] [.] [.] [.] 4 η d (.5) (.9) (2.87) (.87) (.64) (.83) [.] [.] [.2] [.] [.] [.] 5 η e +η d (2.67) (3.55) (2.92) (.27) (.9) (.43) [.4] [.8] [.3] [.] [.] [.] 6 E e M (.88) (2.65) (3.5) (3.73) (3.6) (2.49) η e (2.63) (3.3) (2.56) (.3) (.39) (.53) η d (.6) (2.57) (3.49) (2.3) (.58) (.74) [.6] [.5] [.2] [.5] [.8] [.4] LR NOTE: This able repors he ordinary leas-squares (OLS) regression resuls of real GDP growh on excess sock marke reurn and is hree componens. Newey-Wes (987) correced sandard errors are used o calculae he saisics which are repored in parenheses. The adused R 2 is repored in brackes. LR he saisic of log-likelihood raio es of equal coefficiens in row 6 has a χ 2 disribuion wih wo degrees of freedom and is criical value a he 5 percen significance level is The daa are quarerly and span from 953:Q o 997:Q4 because of he leads in he dependen variable. The decomposiion is based on he VAR esimaion repored in Table 2. See Appendix A for a descripion of he daa. posiively correlaed wih he fuure durable consumpion growh a all horizons. However is forecasing power concenraes over relaively shor horizons and peaks a wo quarers wih an adused R 2 of 9 percen. The predicive paern is also quie differen among is hree componens. The expeced reurn E e M is posiively correlaed wih fuure durable consumpion growh a all horizons and is forecasing power peaks a one year wih an adused R 2 of 6 percen. In conras shocks o he expeced fuure reurn η e are posiively correlaed wih fuure durable consumpion over shor horizons and he correlaion urns negaive as he horizon increases. Their predicive power peaks a wo quarers wih an adused R 2 of 7 percen. Again I find ha he forecasing power of dividend shocks η d is raher limied: I peaks around one year wih an adused R 2 of percen. Also he forecasing power of oal shocks η e +η d displays similar paerns o hose of η e. Because of heir differen predicive paerns row 6 shows ha he oin forecasing power of he hree componens of excess sock marke reurn is larger han is counerpar in row especially over long horizons. Also he null hypohesis ha he hree componens have he same coefficien is overwhelmingly reeced in many cases. Table 7 repors he regression resuls of fixed residenial invesmen which are qualiaively similar o hose of durable consumpion as repored in Table 6 (alhough i is no discussed in deail here). 3 MARCH/APRIL 22

13 FEDERAL RESERVE BANK OF ST. LOUIS Guo To summarize I find ha durable consumpion and fixed residenial invesmen show many similariies o fixed nonresidenial invesmen. This finding is no a surprise because durable consumpion and fixed residenial invesmen can be hough of as invesmen in home producions. However here is one noable difference. I is well known ha durable consumpion and fixed residenial invesmen end o lead fixed nonresidenial invesmen. Gomme Kydland and Ruper (2) have emphasized his feaure of he daa in business cycle modeling. In my paper his is refleced by he fac ha durable consumpion and fixed residenial invesmen end o respond o excess sock marke reurn and is componens much faser han fixed nonresidenial invesmen does. GDP Table 8 repors he regression resuls of GDP. Excess sock marke reurn e M is posiively correlaed wih fuure GDP growh over all horizons and is predicive power peaks a wo quarers wih an adused R 2 of 4 percen. Is componens however display quie differen predicive paerns. The expeced reurn E e M is also posiively correlaed wih fuure GDP growh a all horizons and is predicive power peaks a wo years wih an adused R 2 of 6 percen. In conras shocks o he expeced fuure reurn η e are posiively correlaed wih fuure GDP growh a shor horizons and he correlaion urns negaive as forecasing horizons increase. Their predicive power peaks a wo quarers wih an adused R 2 of 5 percen. Ineresingly dividend shocks are always posiively correlaed wih fuure GDP growh; however heir predicive power is weak as I find for he GDP componens above. No surprisingly row 6 shows ha he oin predicive power of he hree componens is much sronger han is counerpar in row especially over long horizons. Also he null hypohesis ha he hree componens have he same coefficien is reeced in many cases. CONCLUSION In his paper I firs summarize recen evidence agains he random walk hypohesis of sock price. Using pos-world War II daa I find ha over 2 percen of variaions in quarerly excess sock marke reurn are explained by pas sock marke variance and oher informaional variables. I hen analyze he predicive power of excess sock marke reurn for economic aciviies by decomposing i ino hree pars: expeced reurn shocks o he expeced fuure reurn and shocks o he expeced fuure dividend. I find ha sock price is no sensiive o dividend news and herefore he dividend componen has lile predicive power for GDP and is componens. In conras he expeced reurn and shocks o he expeced fuure reurn especially he former are srong predicors for economic aciviies. However heir predicive paerns are quie differen especially over long horizons. Togeher my resuls explain why he predicive power of sock marke reurns is raher limied. REFERENCES Barro Rober J. The Sock Marke and Invesmen. Review of Financial Sudies 99 3() pp Campbell John Y. and Shiller Rober J. The Dividend-Price Raio and Expecaions of Fuure Dividends and Discoun Facors. Review of Financial Sudies 988 pp and Ammer John. Wha Moves he Sock and Bond Markes? A Variance Decomposiion for Long-Term Asse Reurns. Journal of Finance March () pp ; Lo Andrew W. and MacKinlay A. Craig. The Economerics of Financial Markes. Princeon: Princeon Universiy Press 997. ; Leau Marin; Malkiel Buron G. and Xu Yexiao. Have Individual Socks Become More Volaile? An Empirical Exploraion of Idiosyncraic Risk. Journal of Finance February 2 56() pp Fama Eugene F. Sock Reurn Real Aciviy Inflaion and Money. American Economic Review Sepember 98 7(4) pp Fisher Sanley and Meron Rober C. Macroeconomics and Finance: The Role of he Sock Marke. Carnegie- Rocheser Conference Series on Public Policy pp Gomme Paul; Kydland Finn E. and Ruper Peer. Home Producion Mees Time o Build. Journal of Poliical Economy Ocober 2 9(5) pp Guo Hui. Limied Sock Marke Paricipaion and Asse Prices in a Dynamic Economy. Working Paper 2-3A Federal Reserve Bank of S. Louis 2. MARCH/APRIL 22 3

14 Guo R EVIEW. Sock Marke Reurns Volailiy and Fuure Oupu. Working paper Federal Reserve Bank of S. Louis 2.. Undersanding he Risk-Reurn Tradeoff in he Sock Marke. Working Paper 22-A Federal Reserve Bank of S. Louis 22. Hall Rober E. Sochasic Implicaions of he Life Cycle- Permanen Income Hypohesis: Theory and Evidence. Journal of Poliical Economy (6) pp Lamon Owen A. Invesmen Plans and Sock Reurns. Journal of Finance December 2 55(6) pp Leau Marin and Ludvigson Sydney. Consumpion Aggregae Wealh and Expeced Sock Reurns. Journal of Finance June 2a 56(3) pp and. Time-Varying Risk-Premia and he Cos of Capial: An Alernaive Implicaion of he q Theory of Invesmen. Journal of Moneary Economics 2b (forhcoming). Meron Rober C. An Ineremporal Capial Asse Pricing Model. Economerica pp On Esimaing he Expeced Reurn on he Marke: An Exploraory Invesigaion. Journal of Financial Economics December 98 8(4) pp Newey Whiney K. and Wes Kenneh D. A Simple Posiive Semi-Definie Heeroskedasiciy and Auocorrelaion Consisen Covariance Marix. Economerica May (3) pp Schwer G. William. Indexes of U.S. Sock Prices from 82 o 987. Journal of Business July 99 63(3) pp Sock James H. and Wason Mark W. Business Cycle Flucuaions in U.S. Macroeconomic Time Series in J. Taylor and M. Woodford eds. Handbook of Macroeconomics Vol. A. Amserdam: Elsevier 999 pp Appendix A DATA DESCRIPTION Sock Marke Reurn and Is Forecasing Variables Consumpion-Wealh Raio: cay Source: < economis/leau/daa.hml>. S&P 5 Dividend Yield: dp Las four-quarer dividends divided by sock price using S&P 5 socks. Source: Haver Analyics (2). Sochasically Derended Risk-Free Rae: rrel Risk-free rae less is las four-quarer average or 4 rrel = rf rf k 4 k= where r f is he nominal risk-free rae. I consruc he quarerly nominal risk-free rae by summing up he monhly rae wihin each quarer. Source: CRSP Cener for Research in Securiy Prices. Graduae School of Business The Universiy of Chicago 22. Used wih permission. All righs reserved. < Excess Sock Marke Reurn: e M Value-weighed sock marke reurn less he nominal risk-free rae. Source: CRSP. Sock Marke Variance: σ M Sum of he squared deviaion of daily excess sock marke reurn for is quarerly average or σ τ 2 M = ( em τ e M τ ) = where e Mτ is he daily excess sock marke reurn and e M is is average in quarer. The daily riskfree rae is assumed o be equal o he monhly rae divided by he number of rading days. Source: I use he daily marke reurn consruced by Schwer (99) before July and use he daily valueweighed marke reurn (VWRET) from CRSP hereafer; he nominal monhly risk-free rae is also from CRSP. Following Campbell e al. (2) I downweigh sock marke variance during he 987 sock marke crash. Naional Accouns Daa Source: Bureau of Economic Analysis. 32 MARCH/APRIL 22

15 FEDERAL RESERVE BANK OF ST. LOUIS Guo Appendix B DERIVATION OF THE SHOCK TO THE EXPECTED FUTURE RETURN From equaion (8) i is sraighforward o show ha (B) E X = A+ BA+ L+ B A+ B X and (B2) E X = A+ BA+ L+ B A+ B X. Then (B3) + + ( E E ) ρ X = ρ [ A+ BA+ L+ B A+ B X A BA L B A B X ] = = ρ [ B ( X X ) B A] = ρ [ BA+ Bε BA] = ρbi ( ρb) ε. Because e M is he firs row of X (B4) ( E E ) ρ e = = = = e ( E E ) ρ X = M + = + = e ρb( I ρb) ε MARCH/APRIL 22 33

16 Guo R EVIEW 34 MARCH/APRIL 22