Why does the correlation between stock and bond returns vary over time?

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1 Why does he correlaion beween sock and bond reurns vary over ime? Magnus Andersson a,*, Elizavea Krylova b,**, Sami Vähämaa c,*** a European Cenral Bank, Capial Markes and Financial Srucure Division b European Cenral Bank, Invesmen Division c Universiy of Vaasa, Deparmen of Accouning and Finance November 5, 2004 Absrac This paper examines he impac of inflaion and economic growh expecaions and perceived sock marke uncerainy on he ime-varying correlaion beween sock and bond reurns. The resuls indicae ha sock and bond prices move in he same direcion during periods of high inflaion expecaions, while epochs of negaive sock-bond reurn correlaion seem o coincide wih he lowes levels of inflaion expecaions. Furhermore, consisenly wih he fligh-oqualiy phenomenon, he resuls sugges ha high sock marke uncerainy leads o a decoupling beween sock and bond prices. Finally, i is found ha he sock-bond reurn correlaion is virually unaffeced by economic growh expecaions. Keywords: sock-bond reurn correlaion, dynamic condiional correlaion, macroeconomic expecaions, implied volailiy JEL classificaion: G10, E44 We are graeful o Seppo Pynnönen, Paul Söderlind, and seminar paricipans a he European Cenral Bank for helpful discussions and commens. The views expressed in his paper are hose of he auhors and should no be inerpreed as reflecing he views of he European Cenral Bank. * Address: European Cenral Bank, Kaisersrasse 29, DE Frankfur am Main, Germany. Tel.: Fax: address: ** Address: European Cenral Bank, Kaisersrasse 29, DE Frankfur am Main, Germany. Tel.: Fax: address: *** Corresponding auhor. Address: Universiy of Vaasa, P.O. Box 700, FIN Vaasa, Finland. Tel.: Fax: address:

2 Why does he correlaion beween sock and bond reurns vary over ime? Absrac This paper examines he impac of inflaion and economic growh expecaions and perceived sock marke uncerainy on he ime-varying correlaion beween sock and bond reurns. The resuls indicae ha sock and bond prices move in he same direcion during periods of high inflaion expecaions, while epochs of negaive sock-bond reurn correlaion seem o coincide wih he lowes levels of inflaion expecaions. Furhermore, consisenly wih he fligh-oqualiy phenomenon, he resuls sugges ha high sock marke uncerainy leads o a decoupling beween sock and bond prices. Finally, i is found ha he sock-bond reurn correlaion is virually unaffeced by economic growh expecaions. Keywords: sock-bond reurn correlaion, dynamic condiional correlaion, macroeconomic expecaions, implied volailiy JEL classificaion: G10, E44

3 2 1. Inroducion This paper examines he impac of macroeconomic expecaions and perceived sock marke uncerainy on he ime-varying correlaion beween sock and bond reurns. Undersanding he dynamics of he ime-varying relaionship beween sock and bond markes is imporan for several reasons. Asse allocaion and risk managemen sraegies ha assume a consan relaionship beween sock and bond reurns may be improved by properly aking ino accoun he observed ime-variaion in he correlaion beween hese wo asse classes. A beer undersanding of he ime-varying co-movemens beween sock and bond markes may also be useful for moneary policy purposes. Alhough cenral banks do no have specific price arges for financial asses such as bonds or socks, moneary policy auhoriies are using he informaion conained in he prices of hese asses o gauge, for insance, marke paricipans growh and inflaion expecaions. Hence, he sock-bond reurn correlaion esimaes may offer policymakers useful complemenary informaion o deermine wheher markes are changing heir views on inflaion or economic aciviy prospecs. The relaionship beween sock and bond reurns has received considerable aenion in he lieraure. Shiller and Belrai (1992) documen a srong posiive (negaive) correlaion beween changes in sock prices and long-erm bond prices (yields). They argue ha his posiive correlaion is caused by he common discoun rae effec. Also Campbell and Ammer (1993) find a posiive, albei low, correlaion beween sock and bond reurns. However, boh Shiller and Belrai (1992) and Campbell and Ammer (1993) implicily assume ha he relaionship beween sock and bond prices remains consan over ime. More recenly, several sudies have shown ha he correlaion beween sock and bond reurns exhibis considerable ime-variaion (see e.g., Gulko, 2002; Cappiello, Engle and Sheppard, 2003; Ilmanen, 2003; Connolly, Sivers and Sun, 2004; Jones and Wilson, 2004; Li, 2004). Alhough sock and bond prices, in general,

4 3 end o move in he same direcion, recen sudies have also documened susained periods of negaive correlaion. Surprisingly lile is known abou he driving forces behind his ime-varying correlaion beween sock and bond reurns. One macroeconomic variable ha, in heory, may affec he sock-bond reurn correlaion is inflaion. An increase in expeced inflaion ends o raise discoun raes, and hence, is ineviably bad news for he bond markes. However, he impac of increasing inflaion on sock prices is ambiguous, as boh he expeced fuure cash flows and he discoun raes are likely o be affeced. Ilmanen (2003) uses US daa o examine he impac of inflaion on he correlaion beween sock and bond reurns, and finds ha a high levels of inflaion, changes in he discoun raes dominae he changes in cash flow expecaions, hereby inducing a posiive sock-bond reurn correlaion. Li (2004) examines he impac of uncerainy abou expeced long-erm inflaion on sock-bond reurn correlaion, and shows ha greaer concerns abou fuure inflaion end o resul in sronger co-movemens beween socks and bonds. Apar from he fundamenal changes in he macroeconomic environmen, also financial marke dynamics and changes in marke paricipans assessmen abou risk may have an imporan impac on he relaionship beween sock and bond reurns. For insance, in periods of financial marke urbulence, he equiy risk premium demanded by he invesors o hold sock may increase relaive o he erm premium for bonds. This may cause so-called fligh-oqualiy porfolio shifs from he sock markes o he bond markes, leading o some divergence in he reurns beween hese wo asse classes. Gulko (2002) focuses on he sock-bond correlaions around sock marke crashes, and shows ha he periods of negaive sock-bond correlaion end o coincide wih sock marke crashes. In a similar vein, Connolly e al. (2004) sugges ha opion-implied sock marke volailiy is a good indicaor of financial marke urmoil. They find ha bond reurns end o be high (low) relaive o sock reurns during days when implied sock marke volailiy is high (low).

5 4 The purpose of his paper is o examine how inflaion and economic growh expecaions and perceived sock marke uncerainy affec he correlaion beween sock and bond reurns. The main conribuion of his paper is he focus on he impac of expecaions. The use of inflaion and economic growh expecaions, insead of he acual hisorical values, may be considered more appropriae, as he sock and bond prices should reflec marke paricipans expecaions of fuure values of hese fundamenals. In addiion, his paper exends he lieraure by joinly examining he impacs of macroeconomic expecaions and expeced sock marke uncerainy on he sock-bond reurn correlaion. Following Connolly e al. (2004), volailiy esimaes exraced from opion prices are used o assess sock marke uncerainy. Finally, his paper conribues o he lieraure by applying recen echniques proposed by Engle (2002) o measure he ime-varying correlaion beween sock and bond reurns. The empirical findings repored in his paper demonsrae ha he correlaion beween sock and bond reurns varies considerably over ime. Using daa from he Unied Saes and Germany, we show ha he sock-bond correlaions in boh counries are posiive mos of he ime, alhough susained periods of negaive correlaion are also observed. Our findings also demonsrae ha he sock-bond correlaion may change subsanially, and urn from posiive o negaive, in very shor periods of ime. Ineresingly, he sock-bond correlaions in he US and Germany exhibi raher similar paerns over ime, as for insance he periods of negaive correlaion seem o coincide. Furhermore, our empirical findings indicae ha expeced inflaion is posiively relaed o he ime-varying correlaion beween sock and bond reurns. Sock and bond prices end o move in he same direcion during periods of high inflaion expecaions, while epochs of negaive sock-bond correlaion seem o coincide wih he lowes levels of inflaion expecaions. The empirical findings also demonsrae ha expeced sock marke uncerainy, as measured by implied volailiy, is negaively relaed o he sock-bond correlaion. In paricular, he resuls srongly indicae ha high sock marke uncerainy leads o a decoupling beween

6 5 sock and bond prices. This finding is consisen wih he fligh-o-qualiy phenomenon. Finally, we are unable o find any sysemaic relaionship beween economic growh expecaions and sock-bond reurn correlaions. The remainder of his paper is organised as follows. Secion 2 describes he daa used in he empirical analysis. The sock-bond reurn correlaion measures used in his paper are presened in Secion 3. Secion 4 discusses he behaviour of he sock-bond reurn correlaions over ime. The empirical findings on he impac of inflaion and growh expecaions and expeced sock marke uncerainy on he sock-bond reurn correlaions are repored in Secion 5. Finally, Secion 6 provides concluding remarks. 2. Daa The empirical analysis in his paper is performed using daily daa on US and German sock and bond reurns. The US sock reurns are calculaed from he S&P 100 index, while he DAX index is applied o calculae he German sock reurns. The sock index daa used in he analysis are obained from Reuers. The bond reurns for boh he US and Germany are exraced from he benchmark 10-year governmen bond price indices. 1 The bond price indices are aken from Thomson Financial Daasream. The sample period used in he analysis spans from January 1991 o April 2004 for he Unied Saes and from January 1994 o April 2004 for Germany. The impac of macroeconomic expecaions on he sock-bond reurn correlaion is examined using monhly daa on inflaion and growh expecaions. We use expeced growh raes of he US and German consumer price indices (CPI) and real gross domesic producs (GDP) over he nex 12 monhs. The daa on hese macroeconomic expecaions are obained from Consensus 1 The analysis was also conduced using 2-year governmen bond price indices. However, since he sockbond reurn correlaions are virually similar regardless of he mauriy of he bonds, we only repor resuls based on 10-year bonds.

7 6 Economics. Every monh, Consensus Economics surveys abou 600 economiss for heir forecass regarding fuure macroeconomic developmens. The average forecass of his survey are used o measure inflaion and economic growh expecaions. The expecaions daa are published on he second Monday of each monh and consis of year-on-year growh expecaions for he curren and he nex year. In order o obain a comparable and consisen ime-series of inflaion and real GDP growh expecaions, he expecaions for he curren year and he nex year are weighed ogeher o measure 12-monh ahead expecaions m 12 m = (1) E 12, EC, + E N, where E 12, denoes he 12-monh ahead expecaions of a cerain macroeconomic variable a ime, E C, and E N, denoe he ime expecaions of he macroeconomic variable for he curren and he nex year, respecively, and m is he number of remaining monhs during he curren year. To examine he impac of expeced sock marke uncerainy on he sock-bond reurn correlaion, we use implied volailiies exraced from he prices of sock index opions. Opionimplied volailiy may be regarded as he marke paricipans forecas of he fuure volailiy of he underlying asse over he remaining life of he opion conrac. Provided ha marke paricipans are raional, implied volailiy should incorporae all he available informaion ha is relevan for forming expecaions abou he fuure volailiy. Therefore, implied volailiy is widely regarded as he bes available esimae of marke uncerainy. To capure sock marke uncerainy, we use he VIX and VDAX implied volailiy indices, consruced by he Chicago Board Opions Exchange (CBOE) and he Deusche Börse, respecively. These implied volailiy indices are obained from Reuers. VIX is calculaed from he S&P 100 index opions as he average eigh near-erm and close-o-money call and pu opions. The implied volailiies of hese S&P 100 index opions are weighed ogeher o creae a single implied volailiy esimae, which represens he expeced sock marke volailiy over

8 7 he nex 30 days. 2 Correspondingly, he VDAX is calculaed from DAX index opions by weighing ogeher implied volailiies of near-erm and close-o-money call and pu opions. The VDAX has a consan mauriy of 45 days, hereby represening he expeced sock marke uncerainy over he nex 1½ monhs. 3. Measuring he correlaion beween sock and bond reurns We use wo mehods o measure he ime-varying correlaion beween sock and bond reurns: (i) a simple rolling window sample correlaion, and (ii) he dynamic condiional correlaion (DCC) model proposed by Engle (2002). The simples mehod o capure he ime-variaion of he sock-bond reurn correlaion is o compue sample correlaion coefficiens based on a rolling window of sock and bond reurns. In his paper, a monhly esimae of he correlaion beween sock and bond reurns is compued for he 15 h day of each monh using he reurns of he previous 22 rading days. More formally, he 22-day rolling window correlaion is calculaed by dividing he equally weighed covariance esimae over he las 22 rading days by he square roo of he produc of he wo 22-day variance esimaes ρˆ = i= i= 1 S, i, 22 2 S, i i= 1 r r r B, i r 2 B, i (2) where r S, and r B, denoe he sock and bond reurns on day, respecively. Alhough he rolling window correlaion esimae is uerly simple o esimae, i capures, a leas o some exen, he ime-variaion and clusering of he sock-bond reurn correlaion. However, his correlaion 2 For addiional deails on implied volailiy indices, see e.g. Fleming e al. (1995), Blair e al. (2001), and Graham e al. (2003).

9 8 esimae also has some severe drawbacks, as he rolling esimaes can no adequaely measure he dynamics of cross-reurn linkages. In paricular, due o he equal weighing of he reurn observaions in Equaion (2), he correlaion esimaes adjus raher slowly o new informaion. Addiionally, unusually small or large reurn observaions will no gradually diminish over ime, bu insead lead o jumps in he correlaion esimaes when hese observaions fall ou of he window. Moreover, since correlaion esimaes depend on marke volailiy, hey may conain an upward bias over periods of marke sress (see e.g., Forbes and Rigobon, 2002). An alernaive mehod applied in his paper o model he ime-varying co-movemens beween sock and bond reurns in he dynamic condiional correlaion (DCC) model proposed by Engle (2002). DCC is a simplified mulivariae generalized auoregressive condiional heeroskedasiciy (GARCH) model. DCC has he flexibiliy of univariae GARCH models, bu i sill provides parsimonious correlaion specificaions wihou he compuaional difficulies of mulivariae GARCH models. In his paper, he ime-varying covariance beween sock and bond reurns is assumed o be given by he following DCC(1,1) model r i, = γ i + φ i ri, 1 + ε i, σ i, = ωi + α iε i, 1 + βσ i, 1 (3) σ ij, = σ ij + α ( z z σ ) + β( σ σ ) i, 1 j, 1 ij ij, 1 ij where r i, denoes he reurn on asse i a ime, σ i, is he condiional volailiy of asse i a ime, σ ij, is he ime condiional covariance beween asses i and j, z i, = ri, / σi,, and σ ij is he uncondiional expecaion of he cross produc z i, z j,. A furher descripion of he DCC model and he esimaion procedure is provided in Appendix 1. (inser Table 1 abou here)

10 9 The maximum likelihood esimaes of he DCC model given by Equaion (3) are repored in Table 1. As can be seen from he able, he esimaed DCC(1,1) models appear saisically highly significan for boh he US and Germany. For boh counries, he sum of he α and β esimaes in he condiional covariance equaion is less han uniy, and consequenly he esimaed models preserve mean-reversion of sock-bond reurn correlaion. 4. How does he correlaion beween sock and bond reurns behave over ime? Descripive saisics of he rolling window and condiional sock and bond reurn correlaion esimaes for he Unied Saes and Germany are repored in Table 2. On average, he sockbond correlaions in boh counries are posiive, wih mean correlaion esimaes of abou 0.14, regardless of he esimaion mehod used. The correlaions have ranged from 0.87 o 0.80 in he US and from 0.71 o 0.88 in Germany. Ineresingly, he median correlaion esimaes are much higher for he US han for Germany. I can also be noed from Table 2 ha in erms of means and medians, he rolling window and dynamic condiional correlaion esimaes seem raher similar o each oher. Moreover, virually similar correlaion esimaes for boh economies were obained when 2-year governmen bond indices were used insead of 10-year bonds. Therefore, hese resuls are no repored in he paper. (inser Table 2 abou here) Developmens of he sock-bond reurn correlaions in he US and Germany are ploed in Figures 1 and 2. Several ineresing feaures emerge from hese figures. Alhough he correlaions in boh counries are posiive on average, i is apparen ha he relaion beween sock and bond reurns has been raher unsable over ime, and also susained periods of negaive correlaion can be observed. For boh counries, he correlaions have been consanly

11 10 posiive unil November 1997, whereas during 1998 and afer auumn 2000 he correlaions appear o be mosly negaive. Moreover, Figures 1 and 2 indicae ha he sock-bond correlaion may change subsanially in very shor periods of ime. For insance, in Ocober 1997 he condiional sock-bond correlaion in he US was abou 0.52, bu already one monh laer in November he correlaion had dropped o This may pose challenges for asse allocaion and risk managemen procedures. (inser Figures 1 and 2 abou here) I may also be noed from Figures 1 and 2 ha he condiional and rolling window sockbond reurn correlaions exhibi a very similar paern over ime. However, as expeced, he rolling window correlaion esimaes appear o be considerably more erraic han he condiional correlaions produced by he DCC model. Also, DCC esimaes should accoun for he changes in volailiy, and hereby be free from he poenial upward bias during periods of financial urmoil. In order o faciliae comparison of he behaviour of sock-bond reurn correlaions across counries, he condiional correlaion esimaes for he US and Germany are overlapped in Figure 3. Ineresingly, he sock-bond reurn correlaions in he US and Germany exhibi raher similar paerns, hereby suggesing ha some common facors may deermine he ime-varying relaion beween he wo main asse classes. For boh counries, he sock-bond correlaion was posiive unil November 1997, and hen suddenly dropped o levels below zero for a shorperiod during he lae 1997 and early The correlaions in boh counries again became posiive in March 1998, bu fell back o negaive levels already in he summer of During he excepionally opimisic growh period from spring 1999 unil summer 2000, he sock-bond correlaions were soundly posiive. Afer he sock marke correcion sared in March 2000, he correlaions boh in he Unied Saes and Germany became less posiive and sared o wander

12 11 a levels close o zero. The correlaions for boh economies hen urned negaive in early 2001 and sayed below zero levels hroughou 2002 and early During he laer par of 2003 and early 2004 he correlaions have become less negaive, coinciding wih he rebound in sock markes. (inser Figure 3 abou here) 5. Why does he sock-bond reurn correlaion vary over ime? The preceding analysis evidenly demonsraes ha he relaion beween bond and sock reurns varies considerably over ime. Agains his background, i is of ineres o examine wha facors may cause his ime-variaion in he correlaion beween sock and bond reurns. A priori, he poenial deerminans of he ime-varying sock and bond reurn correlaion may be deduced from he asse pricing heory, which posulaes ha he price of an asse equals he presen value of all fuure cash flows from he asse discouned a an appropriae discoun rae. Hence, he price of a sock S a ime can be expressed as he discouned sum of all expeced fuure dividends + = 1 G S E D (4) =1 1 + Y + ERP where D denoes dividends, Y is he governmen bond yield, G is he expeced growh rae of he dividends, and ERP is he equiy risk premium demanded by invesors. Correspondingly, he ime price of a governmen bond B can be wrien as he discouned sum of all fuure coupon paymens and he face value of he bond B T = E = 1 C (1 + Y ) + FC (1 + Y ) T T (5)

13 12 where C denoes coupon paymen and FC is he face value of he bond. The governmen bond yield Y, used as he discoun rae, reflecs expecaions abou fuure shor-erm raes and he required bond risk premium demanded by invesors for holding longer-erm bonds. According o he Fisher decomposiion, he nominal governmen bond yield Y may be decomposed ino a real ineres rae componen and a compensaion for he expeced inflaion over he remaining life of he bond. Moreover, Y may also include a erm premium, which invesors demand for holding longer (i.e. more risky) asses. Consequenly, he nominal governmen bond Y yield can be expressed as r e Y = + π + θ (6) n Y n n where Y n denoes he n period nominal bond yield, r Yn is he n period real ineres rae, e πn is he expeced inflaion rae over n periods, and θ denoes he erm premium. Since long-erm real ineres raes should, in heory, be closely linked o long-erm real growh expecaions, Equaion (6) suggess ha nominal governmen bond yields are decisively deermined by growh and inflaion expecaions. 3 In paricular, higher (lower) growh and/or inflaion expecaions should lead o higher (lower) bond yields. Consequenly, given Equaion (5), i is apparen ha bond prices should be negaively relaed o growh and inflaion expecaions. The impac of growh and inflaion expecaions on sock prices is raher ambiguous. Rising inflaion or growh expecaions may have no impac on sock prices, if he discoun raes and expeced growh rae of he dividends are equally affeced by rising inflaion and growh expecaions. Neverheless, in case of elevaed inflaion expecaions, he discoun rae effec 3 The link beween economic aciviy and he real ineres rae daes back o Fisher (1907), who showed ha he real ineres rae is deermined by a raio of opimal fuure consumpion o opimal curren consumpion. This raio, including he discoun facor adjusmen, is he marginal rae of iner-emporal subsiuion reflecing agens preferences, and he presence of he discoun facor ensures ha he real rae of ineres exceeds real consumpion growh in he long run.

14 13 may ouweigh he changes in expeced fuure dividends, and hence, high inflaion expecaions end o have a negaive impac on sock prices (see e.g., Ilmanen, 2003). Also relaive changes in he equiy risk premium and he erm premium of long-erm bonds may significanly affec he ime-varying relaion beween socks and bond reurns. The erm and equiy risk premiums ulimaely depend on he asse s perceived risk characerisics and on invesors risk aversion. For insance, during periods of financial marke urbulence invesors end o become more risk averse, hereby promping shifs of funds ou of he sock marke ino safer asse classes, such as long-erm governmen bonds. These so-called fligh-o-qualiy episodes may be inerpreed as an increase in he equiy risk premium and a decrease in he bond erm premium. Consequenly, i may be expeced ha sock and bond prices move in he opposie direcion during periods of marke urmoil. To examine how inflaion and growh expecaions and perceived sock marke uncerainy affec he relaionship beween sock and bond reurns, we calculae he average sock-bond reurn correlaions in 12 differen subsamples, which are creaed based on he levels of CPI growh expecaions, real GDP growh expecaions, and sock marke volailiy expecaions. The average sock-bond reurn correlaions in he quanile subsamples are repored in Table 3. As can be seen from he able, expeced inflaion appears o be posiively relaed o he correlaion beween sock and bond reurns. Panel A of Table 3 shows ha he average sockbond reurn correlaion in he Unied Saes is abou 0.30 during periods in which he expeced inflaion is in he highes quarile. Similarly, Panel B shows ha in Germany, he correlaion has also been highly posiive, abou 0.39, during periods of high expeced inflaion. On he conrary, during periods in which he expeced inflaion is in he lowes quarile, he correlaions beween sock and bond reurns in boh counries are negaive, being abou in he US and in Germany. The boosrapped 95 % confidence inervals for he mean correlaion esimaes (repored in parenheses) sugges ha he observed differences in sock-bond reurn correlaions beween differen quanile subsamples are saisically highly significan.

15 14 (inser Table 3 abou here) Turning he focus ono he impac of growh expecaions on sock-bond correlaions, Table 3 shows no clear paerns. Regardless of he level of growh expecaions, sock-bond correlaions in boh counries are consisenly posiive, wihou any sysemaic differences beween differen subsamples. For insance, he correlaion in he US is mos posiive during periods of lowes growh expecaions, while in Germany sock-bond correlaion appears o be highes on medium levels of growh expecaions. Consequenly, no inferences abou he impac of growh expecaions on he ime-varying correlaion beween sock and bond reurns can be drawn from Table 3. Finally, Table 3 clearly demonsraes ha expeced sock marke uncerainy, as measured by implied volailiy, is negaively relaed o he correlaion beween sock and bond reurns. Panel A shows ha he average sock-bond reurn correlaion in he US is abou during periods of high sock marke uncerainy, and sricly posiive, 0.38, during periods in which implied volailiy is in he lowes quarile. Correspondingly, Panel B shows a similar paern for he German sock-bond correlaion. During periods of sock marke sress, sock-bond correlaion is negaive, -0.15, while during periods of low marke uncerainy he correlaion is highly posiive, The boosrapped 95 % confidence bounds sugges ha hese differences in sock-bond reurn correlaions beween differen subsamples are saisically significan. To furher examine he impac of inflaion and growh expecaions and perceived sock marke uncerainy on he correlaion beween sock and bond reurns, we regress he sock-bond reurn correlaion esimaes on he expeced growh rae of consumer prices, expeced growh rae of real gross domesic produc, and implied sock marke volailiy. A poenial difficuly in regressing sock-bond reurn correlaion esimaes is ha he correlaion coefficien is, by definiion, resriced o he range [-1, +1], whereas he righ hand side of he regression is no resriced o produce values wihin his range. In order o make he dependen variable

16 15 unresriced, a generalized logi ransformaion is applied o ransform he range of correlaion esimaes o [-, + ]. Consequenly, he following regression model is esimaed 1+ ρ log = α + β1cpi i + β 2GDP i + β3iv 1 + ε (7) 1 ρ where ρ denoes he correlaion beween sock and bond reurns a ime, CPI is he expeced growh rae of consumer price index, GDP is he expeced growh rae of real gross domesic produc, IV is he implied sock marke volailiy, and i is eiher 0 or 1 depending on wheher conemporaneous or lagged impacs of expeced inflaion and growh on sock-bond correlaion are examined. The Ljung-Box saisic indicaes significan serial correlaion in he residuals of he regressions, and hence AR(p) erms are added o he regression specificaions. To ascerain wheher he explanaory variables used in he regression are saionary, he augmened Dickey-Fuller and Phillips-Perron uni roo ess are performed. The lag lengh used in he ess is decided based on he Schwarz informaion crierion. The resuls of he uni roo ess are repored in Table 4. As can be seen from he able, he uni roo ess indicae ha all explanaory variables, excep he expeced growh rae of he German CPI, are saionary, as he null hypohesis of a uni roo can be soundly rejeced for hese ime-series. Given ha he here is considerable evidence for saionariy of inflaion raes (see e.g., Rose, 1988; Lai, 1997; Lee and Wu, 2001), i is assumed in he subsequen analysis ha he expeced growh rae of he German CPI is saionary. 4 (inser Table 4 abou here) 4 Moreover, since he main objecive of he Deusche Bundesbank and he European Cenral Bank has been o deliver low and sable inflaion, he inflaion expecaions may be expeced o wander around he inflaion arge, if he policy objecive is considered credible among he marke paricipans.

17 16 The regression resuls for he Unied Saes are repored in Table 5. In Panel A, he rolling window sock-bond reurn correlaion is used as he dependen variable, whereas in Panel B he dependen variable is he dynamic condiional correlaion. The esimaion resuls indicae ha expeced inflaion is posiively relaed o sock-bond reurn correlaion. In all four regression specificaions, he esimaed coefficien for CPI is posiive. However, he coefficiens are significan only when he rolling window correlaion is used as he dependen variable. The resuls in Table 5 also demonsrae ha expeced sock marke uncerainy has a negaive impac on he correlaion beween sock and bond reurns, as he esimaed coefficien for implied volailiy is negaive, and saisically significan a he one percen level in all four regression specificaions. Finally, i can be noed from Table 5 ha he esimaed coefficiens for expeced growh are always negaive, bu none of he four coefficien esimaes appears saisically significan. (inser Table 5 abou here) Table 6 repors he regression resul for he German sock-bond reurn correlaions. Panel A indicaes ha all he explanaory variables have an impac on he sock-bond correlaion. Consisenly wih he resuls repored in Table 5, he esimaed coefficiens for implied volailiy are negaive and saisically significan a he one percen level, hereby suggesing ha high sock marke uncerainy ends o move sock and bond prices ino opposie direcions. The resuls repored in Panel A also show ha inflaion expecaions are posiively relaed o sockbond correlaions, as he coefficien esimaes are posiive and saisically highly significan. Finally, he resuls demonsrae negaive, albei only weakly significan, relaion beween growh expecaions and sock-bond correlaions. In Panel B of Table 5, he dynamic condiional sock-bond reurn correlaion is used as he dependen variable. The signs of all coefficien esimaes are consisen wih he esimaes repored in Panel A, being negaive for

18 17 implied volailiy and growh expecaions and posiive for inflaion expecaions. However, only he coefficien of conemporaneous growh expecaion appears saisically significan, and only a he en percen level. (inser Table 6 abou here) Overall, he regression resuls for he Unied Saes and Germany are very similar. These resuls srongly indicae ha expeced inflaion is posiively relaed o he correlaion beween sock and bond reurns. The esimaed coefficiens for expeced growh rae of he CPI are always posiive, and appear saisically significan in four regressions specificaions. Since bond prices should be negaively relaed o inflaion expecaions, our findings sugges ha high inflaion expecaions have a larger impac on he discoun raes han on he expeced fuure dividends, hereby causing a negaive relaion beween sock prices and inflaion expecaions, and consequenly a posiive relaion beween inflaion expecaions and sock-bond reurn correlaion. Furhermore, he esimaed coefficiens for implied volailiy are negaive in all eigh regression specificaions, and in mos cases he coefficiens are saisically significan a he one percen level. Hence, he esimaion resuls srongly indicae ha high sock marke uncerainy ends o lead o a decoupling beween sock and bond prices. This finding is consisen wih he fligh-o-qualiy phenomenon. Finally, he esimaed coefficiens for expeced growh are always negaive. However, he coefficiens are saisically significan only in wo of he regressions, and only a he en percen level. 6. Conclusions This paper examines he impac of macroeconomic expecaions and perceived sock marke uncerainy on he correlaion beween sock and bond reurns. Our empirical findings demonsrae ha he correlaion beween sock and bond reurns varies considerably over ime.

19 18 Using daa from he Unied Saes and Germany, we find ha he sock-bond correlaions in boh counries are posiive mos of he ime, alhough susained periods of negaive correlaion are also observed. Ineresingly, he sock-bond correlaions in he US and Germany exhibi raher similar paerns over ime, as for insance he periods of negaive correlaion seem o coincide. Furhermore, our findings demonsrae ha he sock-bond correlaion may change subsanially, and urn from posiive o negaive, in very shor periods of ime. These rapid changes in he relaionship beween sock and bond markes may pose challenges for asse allocaion and risk managemen procedures. Our empirical findings indicae ha expeced inflaion is posiively relaed o he imevarying correlaion beween sock and bond reurns. Sock and bond prices end o move in he same direcion during periods of high inflaion expecaions, while epochs of negaive sockbond reurn correlaion seem o coincide wih he lowes levels of inflaion expecaions. The empirical findings also demonsrae ha expeced sock marke uncerainy, as measured by implied volailiy, is negaively relaed o he correlaion beween sock and bond reurns. In paricular, our resuls srongly indicae ha high sock marke uncerainy leads o a decoupling beween sock and bond prices. This finding is consisen wih he so-called fligh-o-qualiy phenomenon. Finally, we are unable o find any sysemaic relaionship beween economic growh expecaions and sock-bond reurn correlaions.

20 19 Appendix 1. Le r F 1 N(0, H ) denoe an n-dimensional condiional mulivariae normal process wih zero expecaions and a condiional covariance marix H = E ( r r '). To avoid unnecessary 1 expansion, we ge rid of he equaion for mean in a GARCH process and assume ha r are already derended and demeaned residuals. DCC model, being a generalisaion of Bollerslev s (1990) consan condiional correlaion model, shares he same condiional correlaion esimaor H = D R D. where D = diag } is a diagonal marix of ime-varying sandard deviaions of he residuals { h i, of he mean equaion of univariae GARCH models 2 2 h i, = E 1( ri, ), ri, = hi, ε i, where ε i, WN(0,1) are sandardised disurbances. In conras o he consan condiional correlaion model, he correlaion marix R = ( ε ε ') is now allowed o be ime-dependen. E 1 Engle (2002) proposed o find he elemens of D-marix from he univariae GARCH models and o formulae he dynamic covariance srucure as a following GARCH process q ij, = ρij + α( ε i, 1ε j, 1 ρij ) + β( qij, 1 ρij ) where ρij is he uncondiional correlaion of ε i, and j, ε and ρ ij, = q ij, / qii, q jj,. Thus, he condiional correlaions ρ ij, depend on he common GARCH parameers, α and β, and on he uncondiional correlaions. Then, he ime-varying correlaion marix is given by R = diag Q ) Q diag( Q ). ( If he sum of posiive coefficiens α and β is less han one, he esimaed model will preserve o be mean-revering. The covariance marix Q = ) is a weighed average of a posiive ( q ij, semi-definie and a posiive-definie marices, and hus i is posiive-definie.

21 20 The log-likelihood esimaor 1 L = 2 T = 1 ( n log(2π) + log D R D + r ' D 1 R 1 D r ) 1 r can be decomposed in wo pars, which depend on volailiy and on condiional correlaion T L = L vol + L cor, L vol = ( n log(2π) + log D + r ' D rr ) and 2 = 1 T 1 1 L cor = (log R + ε ' R ε r ε ' ε r ). 2 = 1 As suggesed by Engle (2002), i can be esimaed in a wo-sep procedure. Taking ino accoun ha D has a diagonal form, he volailiy-dependen par of he likelihood funcion L vol is he sum of separaely esimaed n likelihood funcions for individual GARCH models, which are esimaed in he firs sep. Given he maximising values of variances obained from he firs sep, he dynamic condiional correlaions are esimaed in he second sep.

22 21 References Barsky, R. (1987). The Fisher hypohesis and he forecasabiliy and persisence of inflaion. Journal of Moneary Economics, 19, Blair, B., Poon, S.-H., & Taylor, S. (2001). Forecasing S&P 100 volailiy: he incremenal informaion conen of implied volailiies and high frequency index reurns. Journal of Economerics, 105, Bollerslev, T. (1990). Modeling he coherence in shor-run nominal exchange raes: a mulivariae generalized ARCH model. Review of Economics and Saisics, 72, Campbell, J., & Ammer, J. (1993). Wha moves he sock and bond markes? A variance decomposiion for long-erm asse reurns. Journal of Finance, 48, Cappiello, L., Engle, R., & Sheppard, K. (2003). Asymmeric dynamics in he correlaions of global equiy and bond reurns. European Cenral Bank Working Paper Series, No Connolly, R., Sivers, C., & Sun, L. (2004). Sock marke uncerainy and he sock-bond reurn relaion. Journal of Financial and Quaniaive Analysis, forhcoming. Engle, R. (1982). Auoregressive condiional heeroscedasiciy wih esimaes of he variance of Unied Kingdom inflaion. Economerica, 50, Engle, R. (2002). Dynamic condiional correlaion: a simple class of mulivariae generalized auoregressive condiional heeroskedasiciy models. Journal of Business and Economic Saisics, 20, Fisher, I. (1907). The Rae of Ineres. New York, Macmillan. Fleming, J., Osdiek, B., & Whaley, R. (1995). Predicing sock marke volailiy: a new measure. Journal of Fuures Markes, 15, Forbes, K., & Rigobon, R. (2002). No conagion, only inerdependence: Measuring sock marke comovemens. Journal of Finance, 57, Gulko, L. (2002). Decoupling. Journal of Porfolio Managemen, 28,

23 22 Graham, M., Nikkinen, J., & Sahlsröm, P. (2003). Relaive imporance of scheduled macroeconomic news for sock marke invesors. Journal of Economics and Finance, 27, Ilmanen, A. (2003). Sock-bond correlaions. Journal of Fixed Income, 13, Jones, C., & Wilson, J. (2004). The changing naure of sock and bond volailiy. Financial Analyss Journal, 60, Lai, K. (1997). On he disparae evidence on rend saionariy in inflaion raes: a reappraisal. Applied Economics Leers, 4, Lee, H.-Y., & Wu, J.-L. (2001). Mean reversion of inflaion raes: evidence from 13 OECD counries. Journal of Macroeconomics, 23, Li, L. (2004). Macroeconomic facors and he correlaion of sock and bond reurns. Proceeding of he 2004 American Finance Associaion Meeing. MacDonald, R., & Murphy, P. (1989). Tesing for he long run relaionship beween nominal ineres raes and inflaion using coinegraion echniques. Applied Economics, 21, Shiller, R., & Belrai, A. (1992). Sock prices and bond yields. Journal of Moneary Economics, 30, Rose, A. (1988). Is he real ineres rae sable? Journal of Finance, 43,

24 23 Table 1. Maximum likelihood esimaes of he DCC(1,1) model. The able repors he maximum likelihood esimaes of he following DCC(1,1) model: γ + φ r + r i, = i i i, 1 εi, σi, = ωi + αiεi, 1 + βσi, 1 ( z z σ ) + β( σ σ ) σij, = σij + α i, 1 j, 1 ij ij, 1 ij where r i, denoes he reurn on asse i a ime, σ i, is he condiional volailiy of asse i a ime, σ ij, is he ime condiional covariance beween asses i and j, z i, = ri, / σi,, and σ ij is he uncondiional expecaion of he cross produc z i, z j,. Unied Saes Germany Esimae -sa. Esimae -sa. γ STOCK *** ** γ BOND ** φ STOCK φ BOND *** ω STOCK ** *** ω BOND *** *** α STOCK *** *** α BOND *** *** β STOCK *** *** β BOND *** *** α *** *** β *** *** *** significan a he 0.01 level ** significan a he 0.05 level * significan a he 0.10 level

25 24 Table 2. Descripive saisics of sock-bond reurn correlaions. The able repors descripive saisics of he monhly rolling window correlaion (RWC) and dynamic condiional correlaion (DCC) esimaes beween sock and bond reurns. US RWC US DCC German RWC German DCC Mean Median Minimum Maximum Sandard Deviaion Skewness Kurosis No. of Observaions

26 25 Table 3. Sock-Bond reurn correlaions and economic expecaions. The able repors average correlaions beween sock and bond reurns in monh for subsamples creaed by soring inflaion expecaions (CPI), real GDP growh expecaions, and sock marke volailiy expecaions (IV) in monh -1. The boosrapped 95 % confidence inervals for he correlaion esimaes are repored in parenheses. Panel A: US sock-bond reurn correlaion Quanile CPI GDP IV 75 h -100 h ( ) ( ) ( ) 50 h -75 h ( ) ( ) ( ) 25 h -50 h ( ) ( ) ( ) 0-25 h ( ) ( ) ( ) Panel B: German sock-bond reurn correlaion Quanile CPI GDP IV 75 h -100 h ( ) ( ) ( ) 50 h -75 h ( ) ( ) ( ) 25 h -50 h ( ) ( ) ( ) 0-25 h ( ) ( ) ( )

27 26 Table 4. Uni roo ess. The able repors Augmened Dickey-Fuller (ADF) and Phillips-Perron (PP) uni roo ess for he inflaion expecaions (CPI), real GDP growh expecaions, and sock marke volailiy expecaions (IV). The lag lengh for he uni roo ess is decided based on he Schwarz informaion crierion. ADF p-value PP p-value US CPI US GDP US IV German CPI German GDP German IV

28 27 Table 5. US sock-bond reurn correlaions. The repored resuls are based on he following regression specificaions: 1+ ρ log = α + β1cpi i + β 2GDP i + β3iv 1 + ε 1 ρ where ρ denoes he correlaion beween sock and bond reurns a ime, CPI is he expeced growh rae of consumer price index, GDP is he expeced growh rae of real gross domesic produc, IV is he implied sock marke volailiy, and i is eiher 0 or 1. Panel A: Rolling window correlaion Esimae -sa. Esimae -sa. Consan CPI ** GDP CPI * GDP IV *** *** AR(1) *** *** AR(2) *** *** Adjused R F-sa *** *** No. of observaions Panel B: Dynamic condiional correlaion Esimae -sa. Esimae -sa. Consan CPI GDP CPI GDP IV *** *** AR(1) *** *** Adjused R F-sa *** *** No. of observaions *** significan a he 0.01 level ** significan a he 0.05 level * significan a he 0.10 level

29 28 Table 6. German sock-bond reurn correlaions. The repored resuls are based on he following regression specificaions: 1+ ρ log = α + β1cpi i + β 2GDP i + β3iv 1 + ε 1 ρ where ρ denoes he correlaion beween sock and bond reurns a ime, CPI is he expeced growh rae of consumer price index, GDP is he expeced growh rae of real gross domesic produc, IV is he implied sock marke volailiy, and i is eiher 0 or 1. Panel A: Rolling window correlaion Esimae -sa. Esimae -sa. Consan CPI ** GDP * CPI *** GDP IV *** *** AR(1) *** Adjused R F-sa *** *** No. of observaions Panel B: Dynamic condiional correlaion Esimae -sa. Esimae -sa. Consan CPI GDP * CPI GDP IV AR(1) *** *** Adjused R F-sa *** *** No. of observaions *** significan a he 0.01 level ** significan a he 0.05 level * significan a he 0.10 level

30 29 Figure 1. US sock-bond reurn correlaions. 1 RWC DCC Jan-91 Jan-93 Jan-95 Jan-97 Jan-99 Jan-01 Jan-03

31 30 Figure 2. German sock-bond reurn correlaions. 1 RWC DCC Jan-94 Jan-96 Jan-98 Jan-00 Jan-02 Jan-04

32 31 Figure 3. US and German sock-bond reurn correlaions. 1 U.S. Germany Jan-91 Jan-93 Jan-95 Jan-97 Jan-99 Jan-01 Jan-03

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