INVESTOR SENTIMENT AND BOND RISK PREMIA

Transcription

1 INVESTOR SENTIMENT AND BOND RISK PREMIA Ricardo Laborda a*, Jose Olmo b a Cenro Universiario de la Defensa. Zaragoza (Spain) b Economics Division, School of Social Sciences. Universiy of Souhampon Absrac This aricle sudies he saisical significance of he se of marke senimen variables proposed by Baker and Wurgler (2006) o predic he risk premium on U.S. sovereign bonds. We show ha hese variables can be summarized in one single marke senimen facor similar in spiri o he single-reurn forecasing facor proposed by Cochrane and Piazzesi (2005). Our findings reveal ha his facor has predicive power beyond ha conained in he yield curve and benchmark macroeconomic facors. The predicive power of his variable is ime-varying, exhibiing more relevance during recession periods. Keywords: Bond risk premia; Forward prices; Invesor senimen; Boosrap sandard errors; Wald ess. JEL Classificaion: E4; G11; G12. *Corresponding Auhor: Ricardo Laborda. rlaborda@unizar.es. Phone: Cenro Universiario de la Defensa de Zaragoza. Academia General Miliar. Cra. Huesca s/n Zaragoza. Spain. Ricardo Laborda acknowledges financial suppor from CreaValor Research Group financed by DGA-FSE and Jose Olmo from he Spanish Governmen hrough projec MICINN ECO

2 1. Inroducion The expecaions heory of he erm srucure of ineres raes saes ha long yields are he average of fuure expeced shor yields. This heory implies ha he expeced excess reurns on bonds should no be forecasable. Despie prominen effors o provide empirical suppor o his heory is failure is largely documened in many sudies. Thus, Fama and Bliss (1987) and Campbell and Shiller (1991) using he forward-spo rae differenial and he slope of he yield curve as predicor variables repor evidence on he exisence of ime-varying risk premiums in US bond markes implying ha excess reurns have a predicable componen. Cochrane and Piazzesi (2005) find furher evidence on predicabiliy using a en-shaped linear combinaion of five forward raes, which succeed a predicing he one-year excess reurn of he n-year bond (n=2 5) wih an R 2 higher han 35% in mos cases. These findings imply ha condiional expecaions of excess reurns on US governmen bonds across mauriies can be expressed in erms of forward raes observed a ime. Cochrane and Piazzesi (2005) inroduce his single-reurn facor ha appears o be counercyclical and canno be enirely explained by he level, slope and curvaure of he yield curve. Dahlquis and Hasselof (2011) exend Cochrane and Piazzesi (2005) resuls o inernaional bond markes by allowing for he exisence of a local facor ha is posiively associaed wih he slope of local yield curves and a global facor correlaed wih he US bond risk premia, and ha have significan forecasing power for inernaional bond reurns. Recen lieraure has documened he exisence of facors ha link he counercyclical behavior of bond risk premia wih expeced excess reurns on US governmen bonds a he highes (lowes) levels during recession (expansion) periods, o variables no direcly exraced from he yield curve. Ludvigson and Ng (2009) find ha real and inflaion facors, consruced from dynamic facor analysis o 132 monhly economic series, have imporan forecasing power for fuure excess reurns on US governmen bonds above and beyond he predicive power conained in forward raes and yield spreads. The macro facors proposed by hese auhors combined wih he Cochrane and Piazzesi facor reach an R 2 higher han 40% across mauriies and also display a counercyclical behaviour, implying ha bond risk premia is ied o a compensaion required by he invesor for bearing risks relaed o recessions. Cooper and Priesly (2009) find ha he oupu gap also has predicive power for excess bond reurns beyond ha of he erm srucure. Duffie (2011) documens he presence of a 2

3 facor ha appears o be relaed o shor-run flucuaions in economic aciviy. This facor has an almos impercepible effec on he cross secion of yields bu has a srong forecasing power for fuure shor-erm ineres raes and excess bond reurns. Bond prices are also affeced by subjecive invesors beliefs on he sae of he economy. I is surprising however he absence of empirical sudies assessing he impac of invesor senimen for explaining and predicing bond risk premia. This is no he case for asse markes, hus, Baker and Wurgler (2006) show ha invesor senimen disproporionaely affecs securiies whose valuaions are highly subjecive and are difficul o arbirage away. They find ha when beginning-of-period proxies for invesor senimen are low, subsequen reurns are relaively high on small socks, young socks, high volailiy socks, unprofiable socks, non-dividend-paying socks, exreme-growh socks and disressed socks, suggesing ha such socks are relaively underpriced in low-senimen saes. When senimen is high, on he oher hand, he paerns largely reverse, suggesing ha hese caegories of socks are relaively overpriced in his sae. Baker and Wurgler (2006) define an invesor senimen index as he firs principal componen of he correlaion marix of six variables underlying proxies for senimen. These proxies, orhogonalized o several macroeconomic variables, are: 1) he closedend fund discoun, which is he average difference beween he ne asse value of closed-end sock fund shares and heir marke prices. 2) NYSE share urnover, based on he raio of repored share volume o average shares lised from he NYSE Fac Book. 3) he number of IPOs. 4) he average firs-day reurns. 5) he share of equiy issues in oal equiy and deb issues, which is a measure of financing aciviy and 6) he dividend premium. The aim of his paper is o invesigae ino he relaionship beween marke senimen variables and he exisence of a risk premium in bond markes. More specifically, our ineres is in assessing he saisical predicive power of invesor senimen for describing bond risk premia a differen mauriies. To do his, we exend he mehodology proposed by Cochrane and Piazzesi (2005) and Ludvigson and Ng (2009) by incorporaing a senimen facor consruced from he se of variables inroduced in Baker and Wurgler (2006) reflecing marke senimen. Our main conribuion is o documen empirically a posiive relaionship beween invesor senimen variables and expeced excess bond reurns ha is beyond and above he informaion conained in he erm srucure of bonds and macroeconomic facors. The in-sample regressions show an R 2 ha reaches nearly 50% for some mauriies and 3

4 sample periods giving suppor o he exisence of an invesor senimen facor in bond risk premia especially relevan for shorer mauriies. The ou-of-sample evidence also shows he ouperformance of he augmened model ha includes invesor senimen variables compared o he resriced model especially afer periods of very high senimen. We also find empirical evidence on he relaionship beween shor and long mauriy bonds condiional on invesor senimen, in paricular we observe ha high invesor senimen, which is mean revering, favours he excess reurns on long mauriy bonds over he one-year bond. As a byproduc of our analysis, we formalize he exisence of a senimen forecasing facor ha adds o he single-reurn forecasing facor based on he erm srucure of ineres raes and originally proposed in Cochrane and Piazzesi (2005) and he macroeconomic facor inroduced by Ludvigson and Ng (2009). We do his by implemening saisical ess o assess he differences in explanaory power beween unresriced and resriced versions of regression models exploring he relaionship beween he ses of variables describing macroeconomic fundamenals and marke senimen, respecively, and he excess reurn on US governmen bonds wih mauriies beween 2 and 5 years. Our resuls for he period Augus 1965 o December 2007 show overwhelming saisical evidence on he exisence of single facors ha summarize macroeconomic fundamenals and marke senimen in a similar way as he single reurn-forecasing facor does. We finally carry ou several robusness exercises o assess he reliabiliy of our resuls. In paricular, we repea he analysis using an alernaive daabase of US yields consruced by Gurkaynack, Sack and Wrigh (2006) ha conains mauriies longer han five years. The resuls of his analysis suppor our empirical findings. This aricle fills he absence of academic work on he effec of invesor senimen on governmen bond pricing. A noable excepion o his gap is Baker and Wurgler (2012). These auhors analyze he relaionship beween senimen and he comovemen beween governmen bonds and bond-like socks, characerized as being long maure, low volailiy, profiable, from dividend-paying firms and ha are neiher high growh nor disressed. Using monhly excess porfolio reurns, hese auhors find ha when he invesor senimen index is high and subsequen reurns on bond-like socks are expeced o ouperform speculaive socks, bond reurns are also expeced o be posiive. Baker and Wurgler (2012) also argue ha an explanaion for he predicabiliy paerns hey documen should joinly be based on shocks o real cash 4

5 flows, shocks o discoun raes and ime-varying invesor senimen ha is linked o marke risk aversion. Nayak (2010) also explores he impac of invesor senimen on corporae bond yield spreads, finding ha corporae bonds appear underpriced (wih high yields and spreads) when beginning-of-period senimen is low, and overpriced (wih low yields and spreads) when beginning-of-period senimen is high. Under (over) priced bonds, especially he low raed, in low (high) invesor senimen periods have subsequen lower (higher) yield spreads. Invesor senimen appears o be linked o biases in he projecions of fuure cash flows and especially o he assessmen of he oulook of risk, which is a key ingredien of he relaive demand of socks vs. bonds. According o he senimen index proposed by Baker and Wurgler (2006), high invesor senimen periods are associaed o high equiy issuances in an overpriced sock marke, increasing number of IPOs wih high average firs day reurns, high NYSE share urnover and decreasing closed-end funds discoun. These marke characerisics deermine bull sock markes and invesors high risk-appeie. These periods are usually characerized by increasing ineres raes and he presence of less risk averse invesors willing o demand highly risky asses vs. safe asses, as governmen bonds. However, when he opimism revers o he hisorical mean, he marke proceeds o correc absolue and relaive mispricing, and especially in disressed imes he safey offered by US sovereign deb riggers he fligh o qualiy form he riskies asses (socks and high yield bonds) o he safes asses. High invesor senimen periods anicipae high ex-pos bond excess reurns as a consequence of a poserior inward movemen of he forward ineres rae curve, reflecing an increasing risk aversion. Consumpion based models can explain ime varying risk aversion using a habi specificaion model. Campbell and Cochrane (1999) show ha when consumpion is high relaive o some rend or he recen pas, invesors risk aversion and he corresponding risk premia increase, negaively affecing risky asse prices. The model developed by Campbell and Cochrane (1999) displays a counercyclical behaviour of he Sharpe raio linked o he behaviour of he business cycle ha can be reconciled wih he behaviour of ineres raes, using a precauionary saving explanaion. When consumpion is low relaive o he habi, invesors are no willing o assume risks and save more in order o build up asses agains he even ha omorrow migh be even worse. This precauionary desire o save drives down ineres raes. These resuls sugges ha he main channel for he ransmission of marke senimen, which is formed using variables from he equiy marke, ino bond reurns is hrough nominal ineres 5

6 raes. Indeed, he sock can be viewed as a long-erm bond plus cash flow risk, so any variable ha forecass sock reurns can also poenially forecas bond reurns and vice versa. We hypohesize ha low (high) invesor senimen periods are relaed o excepionally high (low) invesor risk aversion periods and decreasing (increasing) ineres raes, which induce he reversion of absolue and relaive mispricing. The aricle is srucured as follows. Secion 2 lays ou he economeric framework and discusses he differen mehodologies o explain he risk premia on bond reurns. In Secion 3 we formalize he exisence of a macroeconomic and a senimen forecasing facor ha add o he single-reurn forecasing facor based on he erm srucure of annual implici forward raes. To do his we implemen he saisical ess discussed in Cochrane and Piazzesi (2005). Secion 4 presens he in-sample resuls of he one-year-ahead predicive regressions from he differen economeric specificaions. This secion also discusses differen robusness measures o provide empirical suppor o he findings. These robusness measures include an ou-of-sample rolling window, which also evaluaes he economic relevance of including he invesor senimen facor o explain bond risk premia hrough a very simple asse allocaion process, and an alernaive choice of daabase conaining US yields wih mauriy longer han five years. Secion 5 concludes. 2. Economeric framework: Bond reurns This secion discusses he mehodology proposed by Cochrane and Piazzesi (2005) and Ludvigson and Ng (2009) for consrucing heir single-reurn forecasing facors. We accommodae his wo-sage regression procedure o define a new marke senimen facor given by an opimal linear combinaion of variables relaed o he invesor senimen index discussed in Baker and Wurgler (2006). Le n p be he log price of an n-year zero-coupon bond a ime. We use parenheses o disinguish mauriy from exponeniaion in he superscrip. The log yield is n n y = - 1/n p (1) Under no-arbirage condiions, he coninuously compounded forward raes saisfy ha n1 n f = p -p n 1 n (2) 6

7 We consider he sraegy of buying an n-year zero coupon bond a ime and selling i as an n-1 year bond a ime +1. The reurn on his sraegy afer one period is n n1 n r 1 = p 1 -p (3) and he excess reurn obained from subsracing he yield on he one-year bond is n n n1 n (1) (1) 1=r1- = (4) rx y p p y Furher, afer some algebra, he bond price can be expressed as: wih f 0 1 (1) p n-1 n jj1 =- f j =0 (5) y, ha can be used o subsiue prices away from (3). The excess reurn can be wrien as rx n-1 n-1 n jj1 j1j 1= f f 1 j=1 j=1 (6) Excess reurns depend on he se of presen forward raes and he corresponding se of nex year forward raes wih mauriies decreased by one year. Assuming raional expecaions, he deviaions from he expecaions hypohesis of he erm srucure should be explained by he presence of a bond risk premia defined as where E. E. n-1 n-1 n jj1 j1j E rx 1 = f E f 1 j=1 j=1 (7) denoes he mahemaical expecaion condiional on, he sigma-algebra conaining he se of all available informaion a ime. We use overbars o denoe averages across mauriies. Thus, rx =1/4 5 n rx 1 (8) n=2 denoes he average excess reurn on an equally-weighed porfolio of bonds wih mauriies beween wo and five years. Cochrane and Piazzesi (2005) sudy he predicive power of he erm srucure of ineres raes for explaining he one year excess reurns in (6). These auhors find ha a linear combinaion of five forward spreads explains beween 30% and 35% of he variaion in nex year s excess reurns on bonds wih mauriies ranging from wo o five years. The regression specificaion proposed by hese auhors is a wo-sep procedure. Firs, hey esimae a regression of he average (across mauriy) excess reurn on all forward raes, 7

8 rx y f f f f u (9) (1) = where u is he error erm of he regression. Second, hey use he fied values from his regression, denoed hereafer as CP, as an excess bond reurn predicor for all mauriies: rx = b CP = b ( y f f f f ) (10) ( n) ( n) (1) ( n) 1 n 1 n Cochrane and Piazzesi (2005) denominae CP as he single reurn-forecasing facor and observe a en-shaped form for he regression parameers in (9). These auhors formalize he exisence of his facor by deploying a baery of saisical ess assessing he predicive power of his facor compared o ha of he unresriced regression rx = y f f f f (11) ( n) (1) ( n) The resriced model is equivalen o seing he resricion = b n. We also consider he role of macroeconomic variables wih saisical power o explain variaion on he bond risk premia. This is done by running predicive regressions of bond excess reurns on he Ludvigson and Ng (2009) six-facor model ha minimizes he BIC crierion for he forecasing regressions of excess bond reurns across differen specificaions. This vecor of regressors is a subse of he se of dynamic facors found in Ludvigson and Ng (2009) ha summarize he informaional conen on 132 monhly economic series. These auhors propose wo differen bu relaed specificaions of he risk premium and use he same wo-sage procedure as in Cochrane and Piazzesi (2005) o consruc a macroeconomic facor analogous o he single-reurn forecasing facor. The firs regression model akes his form: rx F F F F F F (12) wih v 1 he error erm of he regression. These auhors inerpre he firs facor, F 1, as a real facor relaed o employmen, producion, capaciy uilizaion and new manufacuring orders; he second facor, F 2, is linked o several ineres rae spreads; he hird and fourh facors, F 3 and F 4, are inflaion facors relaed o nominal ineres raes and he eighh facor, F 8, is a sock marke facor. The second specificaion of he predicive regression model proposed by hese auhors also considers he CP facor. In his specificaion he facor F 2 is highly correlaed wih ineres rae spreads and is 8

9 informaion abou he bond risk premia is subsumed in he CP facor, being dropped from he regression model ha becomes rx = b CP b LN (13) ( n) ( n) 1 n, CP n, LN 1 wih LN defined as he fied values from (12) bu wih he variable F 2 dropped from he regression model. In his paper, we augmen hese models by including variables relaed o he invesor senimen index (S ) consruced in Baker and Wurgler (2006) and discussed above. Following he sraegy developed by Cochrane and Piazzesi (2005) and Ludvigson and Ng (2009) we consruc a synheic variable, BW hereafer, ha defines a new facor reflecing invesor senimen. This predicive facor is defined as he projecion of rx on S, S 2 and S, wih S a senimen index ha is orhogonal o a sample of macroeconomic facors seleced by Baker and Wurgler (2006), S 2 is he square of he senimen variable and reflecs he magniude of he underlying senimen and S ha measures he variaion in senimen. More specifically, he senimen facor is obained from he following regression: rx = 0 1 S + 2 S S + 1 (14) wih 1 he error erm of his regression. The senimen facor BW = rx allows us o exend he model in Ludvigson and Ng by incorporaing invesor senimen for predicing he risk premium on bond reurns. The proposed model is n n rx = b CP b LN b BW (15) 1 ncp, nln, nbw, 1 wih n 1 he error erm of he regression. 3. Facors for predicing bond risk premia This secion describes he daa used in our empirical analysis of he risk premium on US sovereign bond reurns and assesses he saisical validiy of single facor models proxying informaion on sovereign bond markes, macroeconomic condiions and marke senimen raher han unresriced versions assigning differen coefficiens o each of he regressors in a long mulivariae predicive regression model difficul o inerpre in erms of he above facors. 9

10 3.1. Daa We use he Fama-Bliss daase available from he Cener for Research in Securiies Prices (CRSP) and conains observaions on one- hrough five-year zero-coupon US Treasury bond prices covering he period beween Augus 1965 and December We consruc daa on excess bond reurns, yields, and forward raes, as described above. Annual reurns are consruced by coninuously compounding monhly reurn observaions. We use he esimaed macro facors available a Sydney Ludvigson s web page (hp:// o esimae he LN facor and he index S available a Jeffrey Wurgler page (hp://pages.sern.nyu.edu/~jwurgler/). [Inser Figures 1 and 2 abou here] Figure 1 plos he senimen index ha lines up wih he anecdoal accouns of bubbles and crashes over he period 1965 and 2007 discussed in Baker and Wurgler (2006), along wih shaded NBER recessions daes. Table 1 presens he correlaion marix beween he excess bond reurns, rx (n=2,,5) and he explanaory variables () n 1 used in regression (15). To obain some insigh ino he correlaion beween he excess bond reurns and he senimen facor we have broken down he underlying senimen variables. All he explanaory facors are welve-monh lagged. The Cochrane and Piazzesi facor, CP, and he Ludvigson and Ng (2009) macro facor, LN, are posiively correlaed o fuure excess bond reurns wih levels larger han 40%. S and S 2 are also posiively correlaed o fuure excess bond reurns and S is srongly negaively correlaed o fuure excess bond reurns. Ineresingly, invesor senimen variables are almos uncorrelaed, and S and S are posiively and negaively relaed o he CP and LN facors, respecively. The variable S 2 is almos uncorrelaed wih he CP and LN facors. As expeced, he invesor senimen index is posiively correlaed wih he ineres rae variables, (1) y, 1 2 f, 2 3 f, 3 4 f and 4 5 f, reaching values abou 0.30 in he considered sample period. Figure 2 shows ha he 10 year moving average correlaion beween he invesor senimen index and he US Fed rae is posiive, increasing especially in high invesor senimen periods. Periods of high invesor senimen seem o be associaed wih lowering invesor risk aversion and a higher desire o borrow agains he fuure, ha drives up ineres raes. Our main focus is on he 10

11 unusually high invesor senimen periods ha could convey valuable informaion abou fuure US excess governmen bond reurns beyond he informaion embedded in he yield curve and macro facors. [Inser Table 1 abou here] 3.2. Tesing he single reurn-forecasing facors One of he main conribuions of Cochrane and Piazzesi (2005) is o show ha he same se of regressors explains he variaion on excess bond reurns for all mauriies. These auhors also discuss saisical ess o disenangle he efficiency loss incurred by using a single facor insead of he full se of regressors. Table 2 repors he esimaes of boh unresriced and resriced models corresponding o he CP facor for he period Augus 1965 o December The resuls are very similar o hose found by Cochrane and Piazzesi (2005) for a sample ending on To formalize hese findings Cochrane and Piazzesi (2005, p. 156) deploy wo saisical ess: a J T es o assess wheher he momen condiions imposed for he esimaion of he unresriced model are violaed by he resriced version of he model and a Wald es of he join parameer resricions implied by he resriced model. The resuls of hese ess validae he use of he resriced model defining he CP facor. The p-values of he asympoic and boosrap versions of he ess can be found as an online appendix. We follow he mehodology described by hese auhors and show ha he single senimen facor esimaed from (14) is also a reliable represenaion of he se of variables reflecing invesor senimen. Table 3 repors he esimaes of he unresriced and resriced versions of he model ha only considers invesor senimen. The resuls sugges a posiive and linear effec of he senimen variable ha increases wih mauriy. The variable reflecing differences in marke senimen has a negaive effec on he excess reurns suggesing ha a posiive one-year invesor senimen momenum implies a drop in bond risk premia. The R 2 coefficiens are beween and and decrease wih he ime o mauriy. The resriced model reveals ha here is an overall posiive effec beween marke senimen and bond risk premia ha increases wih ime o mauriy. Boh ables presen he Hansen and Hodrick (1983) asympoic sandard errors and he boosrap sandard errors derived from assuming a VAR(12) model for 11

12 he one-year yield, see Cochrane and Piazzesi (2005, Secion C.2 of online Appendix) available a hp:// The repored differences in sandard error esimaes beween OLS and GMM and boosrap echniques sugges ha sandard esimaion mehods no considering he presence of overlapping daa can be inadequae for modelling annual excess reurns when using monhly frequency daa. These auhors also discuss Newey and Wes (1987) asympoic sandard errors in order o accoun nonparamerically for he presence of heeroscedasiciy and serial correlaion in he errors. For sake of space he resuls for he Newey-Wes case wih 18 lags are only repored for he Wald and J ess. For he res of regression analyses hese sandard errors are no repored alhough are available from he auhors upon reques. Table 4 presens he es saisics and p-values for he J T es and Wald ess discussed above. Following Cochrane and Piazzesi (2005), his is done for differen lags of he regressor variables, wih i=0 denoing he regressors one-year lagged, i=1 denoing he regressors 13 monhs lagged and so on. The resuls reveal some discrepancies beween he asympoic and boosrap ess, and also beween he es saisics obained using he correcion by Newey-Wes and he no overlapping mehod. Overall, boh ypes of ess in Table 4 reveal ha he loss in predicive power is no saisically significan and validae he use of he facor BW o proxy marke senimen. [Inser Tables 2, 3 and 4 abou here] Figure 3 shows he paern of he regression coefficiens. The op panel presens unresriced esimaes of he model parameers for each mauriy. The boom panel presens resriced parameers obained from he wo-sep procedure. These chars also provide graphical evidence on he similariy beween he unresriced and resriced regression models. The main senimen variables wih forecasing power are S (indexed by 1in he x axis) and S (indexed by 3 in he x axis). [Inser Table 5 and Figure 3 abou here] For compleeness, Table 5 presens he esimaes of he unresriced and resriced versions of he prediced regression model proposed by Ludvigson and Ng 12

13 (2009). These resuls illusrae he imporance of considering LN for predicing he risk premium on bond reurns. Ineresingly, all facors are saisically significan excep F 3, an inflaion facor relaed o ineres raes. The R 2 oscillaes beween 0.22 for bonds wih mauriy in wo years and for bonds wih five year mauriy. 4. Predicive regressions for bond risk premia This secion analyses he bond risk premia predicive performance of he differen ses of facors: forward ineres raes, macroeconomic variables and invesor senimen summarized in hree single reurn-forecasing facors as discussed above. The dynamics of hese facors and he bond excess reurns, shown in Figure 4, reveal srong comovemens beween he facors during some periods bu absence of correlaion during oher marke episodes. The senimen index facor exhibis he lowes variabiliy wihin he facors and he CP facor he highes variabiliy. [Inser Figure 4 abou here] 4.1 In-sample predicive performance Our aim in his secion is o empirically assess he gains of considering marke senimen in he predicive regression model. Tables 6 and 7 presen he resuls from insample forecasing regressions. In paricular, Table 6 presens resuls from in-sample forecasing regressions of he general form (15) for wo-, hree-, four-, and five- year bond excess reurns using he whole sample. In order o assess he relaive imporance of each facor over differen periods, in-sample forecasing regressions esimaes are repored in Table 7 for differen subsamples. The choice of hese evaluaion samples is aken from Cochrane and Piazzesi (2005, Appendix, Table A.8) and coincides wih periods marked by differen inflaion dynamics over several decades 1.The resuls highligh he predicive role of each of he facors over he differen periods under sudy. The CP facor is srongly saisically significan and forecass expeced excess bond reurns across differen mauriies wih an adjused R 2 larger han 30%. The loadings CP of expeced excess bond reurns on he CP facor increase smoohly wih 1 Unrepored Chow ess, see Chow (1960), show overwhelming saisical evidence of he exisence of wo regimes across subsamples. The p-values are zero in mos cases and for boh he unresriced and resriced models. 13

14 mauriy. The conribuion of he LN facor o he predicive model adds an R 2 of abou 10%, he LN facor is more relevan for shorer mauriies. The coefficien corresponding o he Ludvigson and Ng facor is highly significan across mauriies and increases wih mauriy. Tables 6 and 7 also repor he esimaes of he regression model for he average excess reurn over he four mauriies. For hese cases we also repor he marginal conribuions of each facor o he R 2 saisic. For he full sample, in Table 6, we observe an increase of 8% in explanaory power beween he basic model and he version incorporaing he macroeconomic facor. The analysis for differen subsamples in Table 7 reveals significan differences in he imporance of LN over he evaluaion period. This is paricularly noorious for he highly inflaionary period January December [Inser Tables 6 and 7 abou here] The above empirical analysis provides mixed resuls on he empirical relevance of he marke senimen variables. Ineresingly, he gain in predicive power depends very much on he evaluaion period. The analysis of he full sample reveals marginal gains obained from including he senimen facor. This can be also observed from he marginal conribuion of he variables o he R 2 of he regression on he average excess reurn over mauriies. On he oher hand, for he period Augus December 1969 he gain in R 2 is very significan, achieving for example an increase of 14% for he average excess reurn. During his period, coinciding wih a hump in he marke senimen index as shown in Figure 1, his facor has a negaive and very significan effec on he bond risk premia ha is observed across mauriies. Similar findings are noed over he periods January December 1979 and January December The explanaory power of he exended model is remarkable over he las period. The R 2 achieves values higher han 40% for some mauriies. In conras o he 1970 decade he senimen facor has a posiive effec on he risk premia. For oher periods where he marke senimen index does no flucuae much, see Figure 1, he influence of his facor is no relevan. During hese periods bond risk premia is beer explained by financial marke facors and macroeconomic fundamenals. The analysis for he res of subsamples sudied in Cochrane and Piazzesi (2005) is also found in Table 7. 14

15 4.2 Robusness checks This secion provides some robusness checks o assess he exisence of an invesor senimen facor wih power o predic excess bond reurns on US governmen bonds. The ou-of-sample forecasing performance of he regression models is very imporan o es he parsimony of he differen regression specificaions. To assess he relaive ou-of-sample predicabiliy we carry ou wo exercises. Firs, we compue he mean square predicion error of he unresriced and resriced models, denoed MSPE u and MSPE r, respecively; and second, we es he saisical significance of hese differences by implemening he Diebold and Mariano (1995) predicive abiliy es. This ou-of-sample es is useful o assess he relaive meri of wo or more forecas alernaives by comparing he predicive abiliy of compeing forecass, given a general loss funcion, in our case we use he MSPE. The null hypohesis corresponds o equal predicive abiliy and rejecion of he null corresponds o he superior predicive abiliy of one mehod over he oher. In our case, rejecion of he null hypohesis is inerpreed as a beer ou-of-sample performance of he exended model ha considers marke senimen agains he reduced model only considering CP and LN facors. To evaluae he ou-of-sample performance of he models, we consider rolling regressions of 120 monhs esimaed using he large-sample Hansen and Hodrick sandard errors and he boosrap counerpars, and covering differen subperiods of he full evaluaion sample. The iniial esimaion period spans he period Augus 1965 o December 1979 and considers daa on bond excess reurns over January 1980 o December 1989 as he ou-of-sample period for model evaluaion. The second period is consruced from moving forward all he relevan daa en years ahead. Thus, he insample esimaion period covers Augus 1975 o December 1989 and he ou-of-sample covers January 1990 o December The las period is defined by he inerval Augus 1985 o December 1999 and considers he remaining eigh years of daa for ouof-sample evaluaion. The values of MSPE r and MSPE u in Table 8 shed ineresing findings. The firs subsample uses he inflaionary period Augus December 1979 for esimaing he coefficiens of he predicive regression model. The MSPE is slighly larger for he unresriced model han for he resriced version. Alhough he difference is small in relaive erms i is saisically significan for he excess reurn on bonds wih mauriies beween hree and five years. The marke senimen facor overreacs o he inflaionary 15

16 period impeding a good performance of he model ou of sample compared o he resriced model. The magniude of he forecasing error for his period is also larger han for he oher wo subsamples. In conras, for he second subsample he resuls are reversed; he MSPE is smaller for he unresriced model and he magniude of he forecasing error is also smaller during his period. During his period, he regression model exended wih he marke senimen facor ouperforms he simple model given by he CP and LN facors. The unresriced model also ouperforms he resriced version in erms of MSPE during he las subsample. However, he difference in he magniude of he loss funcion beween models is no sufficienly large o be able o rejec he null hypohesis of superior predicive abiliy. [Inser Table 8 abou here] We also evaluae he ou-of-sample performance of he economeric models hrough an analysis of heir economic imporance using a very simple asse allocaion process ha srenghens he saisical resuls provided by he Diebold and Mariano es. Following Cochrane and Piazzesi (2005), we calculae he cumulaive profis or rading rule profis for boh he unresriced and resriced model corresponding o he n-year () n bonds wih n=2,3,4,5. The rading rule uses he forecas 1 of a posiion which is subjec o he ex-pos reurn ( n) 1 Erx o recommend he size rx. The cumulaive profis of he rading rule sraegies, in Figures 5 o 8, illusrae he superior performance of he unresriced model in he second and hird subsamples considered above, especially for he hree-, four- and five- year bonds. [Inser Figures 5 o 8 abou here] The las robusness exercise consiss on assessing wheher hese findings are also suppored for longer mauriies. To do his we use an alernaive daabase of US yields consruced by Gurkaynack, Sack and Wrigh (2006) ha conains mauriies up o hiry years a daily frequencies. The counerpars of Tables 3 and 6 are repored in Tables 9 and 10. The analysis for subsamples is repored as an online appendix. The resuls are in line wih our previous findings. The parameer esimaes corresponding o each facor are increasing wih respec o he ime o mauriy of he bond excep he effec of 16

17 S in he unresriced model ha decreases wih mauriy. The senimen index BW evaluaed over he full sample period, covering he period Augus 1972 o December 2007, see Tables 9 and 10, is more relevan for shorer mauriies. The coefficien of deerminaion is raher sable across mauriies. Neverheless, as shown in Secion 4.1 he senimen index gains relevance in periods of high senimen, especially if i is no highly correlaed wih he CP facor. Thus, he analysis of BW over subsamples confirms ha he saisical significance of marke senimen is cyclical, being paricularly relevan for periods characerized by high inflaion dynamics as he decade of Marke senimen is also highly significan during he las period analyzed spanning from 2000 o 2007, where he forecasing power of he CP facor diminishes. This period corresponding o he grea moderaion is characerized by low inflaion, low nominal ineres raes and buoyan equiy markes. [Inser Tables 9 and 10 abou here] 5. Conclusion Recen lieraure has focused on he imporance of marke senimen in empirical asse pricing. To capure his effec, Baker and Wurgler (2006) define an index consruced from he firs principal componen of he correlaion marix of a vecor of proxies for invesor senimen. These auhors find ha waves of invesor senimen disproporionaely affec securiies wih valuaions ha are highly subjecive and difficul o arbirage. This paper has shifed he focus o bond markes. Our empirical analysis obained from a long sample on US bond daa covering he las four decades reveal ha he dynamics of invesor senimen conain informaion for explaining bond risk premia, above and beyond ha conained in he yield curve and macro facors used in he lieraure. Furher, he ou-of-sample performance of our pricing model ha adds he invesor senimen facor o he single reurn-forecasing facors of Cochrane and Piazzesi (2005) and Ludvigson and Ng (2009) is superior o sandard benchmark models. The conribuion of marke senimen o explaining variaions on bond excess reurns is more imporan for periods of high senimen. These findings, along wih exising evidence on he relevance of invesor senimen in asse markes, sugges ha marke senimen has a prominen role for 17

18 explaining sysemaic deviaions in bond prices relaed o waves of marke opimism and pessimism such as he fligh o qualiy phenomenon beween socks and bonds. Invesors require a higher premium on socks han bonds when marke senimen is low and a lower premium when marke senimen is high. This mechanism operaes hrough he choice of bonds compared o socks in disress episodes ha increases heir relaive demand and depresses he corresponding ex-pos reurn. Similarly, he choice of socks compared o bonds in periods of high senimen increases is relaive demand and depresses is ex-pos reurn. Invesor senimen also reflecs marke expecaions on fuure ineres rae dynamics and moneary policy ha are affecing he relaive performance of he one-year bond vs. longer mauriy bonds. In paricular, low senimen in he marke signals fuure increases in ineres raes ha depress ex-pos reurns on long mauriy bonds vs. he one year bond; similarly, high senimen signals expecaions of lower fuure ineres raes ha reflec increases in ex-pos reurns on long mauriy bonds vs. he one year bond. 18

19 References [1] Baker, M., and Wurgler, J., 2006, Invesor Senimen and he Cross Secion of Sock Reurns, Journal of Finance, 61 (4), [2] Baker, M., and Wurgler, J., 2012, Comovemen and Predicabiliy Relaionships beween Bonds and he Cross-Secion of Socks, Review of Asse Pricing Sudies, 2 (1), [3] Brand M., Sana Clara P., Valkanov, R., 2009, Parameric Porfolio Policies Exploiing he Characerisics in he Cross Secion of Equiy Reurns, Review of Financial Sudies, 22, [4] Campbell, J. Y., Cochrane, J. H., 1999, By Force of Habi: A consumpion-based Explanaion of Aggregae Sock Marke Behavior, Journal of Poliical Economy, 107, [5] Campbell, J. Y., Shiller, R. J., 1991, Yield spreads and Ineres Rae Movemens: A Bird's Eye View, Review of Economic Sudies, 58, [6] Chow, G. C., 1960, Tess of Equaliy Beween Ses of Coefficiens in Two Linear Regressions, Economerica, 28 (3), [7] Cochrane, J. H., and Piazzesi, M., 2005, Bond Risk Premia, American Economic Review, 95(1), [8] Cooper, I., and Priesly, R., 2009, Time-Varying Risk Premiums and he Oupu Gap, Review of Financial Sudies, 22 (7), [9] Dahlquis, M., and Hasselof, H., 2011, Inernaional Bond Risk Premia, Swiss Finance Insiue Research Paper, [10] Diebold, F.X. and Mariano, R.S., 1995, Comparing Predicive Accuracy. Journal of Business and Economic Saisics, 13, [11] Duffie, G., 2011, Informaion in (and no in) he Term Srucure, Review of Financial Sudies, 24, [12] Fama, E.F., and Bliss, R.R., The Informaion in Long-Mauriy Forward Raes, American Economic Review, 1987, 77(4), [13] Gurkaynak, R.S., Sack, B., and Wrigh, J.H., 2006, The U.S. Treasury Yield Curve: 1961 o he Presen. Finance and Economics Discussion Series. WP Federal Reserve Board, Washingon, D.C. [14] Hansen, L. P., and Hodrick, R. J. Risk Aversion Speculaion in he Forward Foreign Exchange Marke: An Economeric Analysis of Linear Models, in Jacob Frenkel, ed., Exchange raes and inernaional macroeconomics. Chicago: Universiy of Chicago Press,

20 [15] Ludvigson, S.C., and Ng, S., 2009, Macro Facors in Bond Risk Premia, The Review of Financial Sudies, 22(12), [16] Nayak, S. 2010, Invesor Senimen and Corporae Bond Yield Spreads, Review of Behavioral Finance, 2, [17] Newey, W. K., and Wes, K. D., 1987, A Simple, Posiive Semidefinie, Heeroskedasiciy and Auocorrelaion Consisen Covariance Marix, Economerica, 55,

21 Tables and Figures Table 1. Correlaion of excess bond reurns and explanaory variables. (2) (3) (4) (5) rx 1 rx 1 rx 1 rx 1 CP LN S 2 S S rx 1 (2) 1 rx (3) 1 rx (4) 1 rx (5) 1 CP LN S S S Noes: The able repors correlaions of excess bond reurns on he 12 monh lagged variables used in eqn 15, ( n) breaking down he underlying invesor senimen facor ino he variables ha define i (eqn. 14). The variable rx 1 is he excess reurn on he n-year Treasury bond. CP is he Cochrane and Piazzesi (2005) facor ha is a linear combinaion of five forward raes (eqn. 9). LN is he Ludvigson and Ng macro facor (2009) ha is a combinaion of five facors esimaed by he mehod of principal facor applied o a panel of of daa wih 132 individual series (eqn 12 wih F 2 dropped). S is he invesor senimen variable defined in Baker and Wurgler (2006) which is a combinaion of six proxies for senimen and S is he annual change of S. The sample spans he period 1965:8 2007:12. 21

22 Table 2. Esimaes of he Cochrane and Piazzesi model (2005). Unresriced model. ( n) ( n) rx = y f f f f coef small coef small coef small coef small n β 0 β 1 β 2 β 3 β 4 β 5 R 2 95% confidence χ 2 (5) [ ] (0.68) (0.16) (0.38) (0.31) (0.20) (0.19) (0.84) (0.30) (0.50) (0.40) (0.29) (0.27) [ ] (1.25) (0.30) (0.61) (0.50) (0.39) (0.31) (1.51) (0.53) (0.89) (0.70) (0.53) (0.50) [ ] (1.72) (0.43) (0.77) (0.63) (0.64) (0.41) (2.02) (0.71) (1.19) (0.93) (0.93) (0.68) [ ] (2.14) (0.53) (0.90) (0.72) (0.61) (0.51) (2.48) (0.88) (1.47) (1.15) (0.87) (0.84) Resriced model. Two sep procedure. 1) Esimaes of he reurn forecasing model. rx y f f f f u = λ 0 λ 1 λ 2 λ 3 λ 4 λ 5 R 2 95% confidence inerval χ 2 (5) coef [ ] small (1.43) (0.35) (0.65) (0.54) (0.42) (0.35) (1.70) (0.60) (1.01) (0.79) (0.60) (0.57) 2) Individual bond regressions. ( n) ( n) rx = b ( y f f f f ) 1 n bn gmm small R2 95% confidence inerval 0.46 (0.03) (0.02) 0.29 [ ] 0.87 (0.02) (0.02) 0.32 [ ] 1.23 (0.01) (0.01) 0.35 [ ] 1.43 (0.04) (0.03) 0.32 [ ] Noes: The unresriced model repors esimaes from OLS regressions of excess bond reurns on he forward raes. The dependen variable n rx is he excess reurn on he n-year Treasury bond. Hansen and Hodrick and boosrap 1 sandard errors are repored in parenheses. The resriced model repors esimaes from OLS regressions of excess bond reurns on he CP facor. The sample spans he period 1965:8 2007:12. 22

23 Table 3. Esimaes of he invesor senimen model. Unresriced model, n 2 n S 2 S 3 S rx 1 n β 0 β 1 β 2 β 3 R 2 95% confidence inerval χ 2 (3) coef small coef small coef small coef small [ ] 9.42 (0.33) (0.28) (0.17) (0.04) (0.23) (0.38) (0.17) (0.07) [ ] 8.44 (0.60) (0.49) (0.28) (0.07) (0.41) (0.69) (0.31) (0.14) [ ] 7.05 (0.85) (0.65) (0.38) (0.11) (0.56) (0.95) (0.42) (0.20) [ ] 7.32 (1.03) (0.78) (0.46) (0.14) (0.68) (1.15) (0.51) (0.24) Resriced model. Two sep procedure. 1) Esimaes of he reurn forecasing model. 0 1 rx S S S R 2 95% confidence inerval coef [ ] 7.78 small (0.70) (0.55) (0.32) (0.08) (0.47) (0.79) (0.35) (0.16) χ 2 (3) rx 1 bn 0 1 S 2 S 3 S 1 2) Individual bond regressions. n 2 n bn gmm small R2 95% confidence inerval 0.56 (0.05) (0.07) 0.14 [ ] 0.94 (0.04) (0.05) 0.12 [ ] 1.18 (0.03) (0.03) 0.10 [ ] 1.31 (0.07) (0.10) 0.08 [ ] Noes: The unresriced model repors esimaes from OLS regressions of excess bond reurns on he invesor senimen variables. The dependen variable n rx is he excess reurn on he n-year Treasury bond. S 1 is he invesor senimen variable defined in Baker and Wurgler (2006) and S is he annual change of S. Hansen and Hodrick sandard errors and boosrap sandard errors are repored in parenheses. The resriced model repors esimaes from OLS regressions of excess bond reurns on he BW facor. The sample spans he period 1965:8 2007:12. 23

24 Table 4. GMM ess of he invesor senimen model. NW, 18 No overlap Simple S Small Sample Lag i Tes χ 2 p-value χ 2 p-value χ 2 p-value χ 2 p-value 0 J T Wald J T Wald J T Wald Noes: J T and Wald ess proposed by Cochrane and Piazzesi (2005) of he invesor senimen model agains he unresriced model. The 5 percen criical values for all he ess is

25 Table 5. Esimaes of he Ludvigson and Ng macro facor model (2009). rx F F F F F Unresriced model, n 3 ( n) n β 0 β 1 β 2 β 3 β 4 β 5 R 2 95% confidence inerval χ 2 (5) coef [ ] 34.9 small (0.26) (0.20) (0.02) (0.05) (0.16) (0.09) (0.13) (0.28) (0.02) (0.07) (0.21) (0.14) coef [ ] 31.2 small (0.47) (0.35) (0.03) (0.11) (0.30) (0.18) (0.22) (0.51) (0.03) (0.12) (0.31) (0.25) coef [ ] small (0.66) (0.46) (0.04) (0.17) (0.45) (0.25) (0.31) (0.71) (0.05) (0.17) (0.52) (0.34) coef [ ] 26.8 small (0.81) (0.56) (0.05) (0.21) (0.56) (0.31) (0.37) (0.85) (0.06) (0.21) (0.63) (0.42) Resriced model. Two sep procedure. 1) Esimaes of he reurn forecasing model. 0 rx F F F F F R % confidence inerval χ 2 (5) coef [ ] small (0.55) (0.39) (0.03) (0.14) (0.37) (0.21) (0.25) (0.58) (0.04) (0.14) (0.44) (0.28) 2) Individual bond regressions. n rx b F F F F F ) ( ) 3 ( n ) 1 n bn gmm small R2 95% confidence inerval 0.55 (0.02) (0.06) 0.22 [ ] 0.93 (0.01) (0.04) 0.19 [ ] 1.19 (0.02) (0.01) 0.16 [ ] 1.32 (0.03) (0.01) 0.14 [ ] Noes: The unresriced model repors esimaes from OLS regressions of excess bond reurns on he Ludvigson and n rx Ng macro facors (2009). The dependen variable 1 is he excess reurn on he n-year Treasury bond. Hansen and Hodrick and boosrap sandard errors are repored in parenheses. The resriced model repors esimaes from OLS regressions of excess bond reurns on he LN facor. The sample spans he period 1966:7 2007:12. 25

26 Table 6. Regressions of monhly excess bond reurns on lagged facors. n CP LN BW R 2 95% confidence inerval Parial R 2 Coef [ ] (0.07) (0.07) small (0.10) (0.14) Coef [ ] (0.07) (0.07) (0.12) small (0.10) (0.15) (0.23) Coef [ ] (0.14) (0.14) small (0.19) (0.25) Coef [ ] (0.14) (0.13) (0.22) small (0.20) (0.28) (0.43) Coef [ ] (0.20) (0.18) small (0.26) (0.34) Coef [ ] (0.20) (0.18) (0.30) small (0.26) (0.39) (0.60) Coef [ ] (0.26) (0.21) small (0.32) (0.41) Coef [ ] (0.25) (0.21) (0.36) small (0.32) (0.47) (0.73) Noes: The able repors esimaes from OLS regressions of excess bond reurns on he lagged variables named in row 1. The dependen variable is he excess reurn on he n-year Treasury bond. CP is he Cochrane and Piazzesi (2005) facor ha is a linear combinaion of five forward raes. LN is he Ludvigson and Ng macro facor (2009) ha is a combinaion of six facors esimaed by he mehod of principal facor applied o a panel of of daa wih 132 individual series. BW is he invesor senimen facor (see eqn. 14) ha is a linear combinaion of variables relaed o he senimen index defined in Baker and Wurgler (2006). Hansen and Hodrick sandard errors and boosrap sandard errors are repored in parenheses. The sample spans he period 1965:8 2007:12. 26

27 Table 7. Regressions of monhly excess bond reurns on lagged facors. Subsample analysis. 1965:8-1969:12 N CP LN BW R 2 Parial R 2 Coef (0.02) (0.19) Coef (0.14) (0.22) (0.24) Coef (0.11) (0.22) Coef (0.11) (0.28) (0.25) Coef (0.17) (0.38) Coef (0.24) (0.46) (0.48) Coef (0.21) (0.53) Coef (0.42) (0.62) (0.79) :1-1979:12 N CP LN BW R 2 Parial R 2 Coef (0.09) (0.14) Coef (0.11) (0.09) (0.10) Coef (0.15) (0.25) Coef (0.18) (0.15) (0.18) Coef (0.19) (0.31) Coef (0.23) (0.18) (0.22) Coef (0.25) (0.38) Coef (0.29) (0.25) (0.30) :1-2007:12 N CP LN BW R 2 Parial R 2 Coef (0.17) (0.11) Coef (0.12) (0.09) (0.18) Coef (0.34) (0.13) Coef (0.27) (0.19) (0.32) Coef (0.47) (0.10) Coef (0.39) (0.26) (0.40) Coef (0.56) (0.07) Coef (0.48) (0.33) (0.48)