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Working Paper Series No. 204 March 2005

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The comovement of US and German bond markets

T. Engsted and C. Tanggaard

The comovement of US and

German bond markets

Tom Engsted and Carsten TanggaardThe Aarhus School of Business, Fuglesangs alle 4, DK-8210 Aarhus V.

E-mails: tom@asb.dk (Engsted); cat@asb.dk (Tanggaard). February 2005.

Abstract

We use a vector-autoregression, with parameter estimates cor-rected for small-sample bias, to decompose US and German un-expected bond returns into three ’news’ components: news aboutfuture inflation, news about future real interest rates, and newsabout future excess bond returns (term premia). We then cross-country correlate these news components to see which compo-nent is responsible for the high degree of comovement of US andGerman bond markets. For the period 1975-2003 we find thatinflation news is the main driving force behind this comovement.When news is coming to the US market that future US inflationwill increase, there is a tendency that German inflation will alsoincrease. This is regarded bad news for the bond market in bothcountries whereby bond prices are bid down leading to immediatenegative return innovations and changing expectations of futureexcess bond returns. Thus, comovement in expected future infla-tion is the main reason for bond market comovement.

Keywords: International bond markets, VAR-model, returnvariance decomposition, small-sample bias, bootstrap simulation.JEL codes: C32, E43, E44, F21, F36, G12, G15.

1 Introduction

It is well-established that bond markets in di erent countries tend tomove together, i.e. bond yields and returns are positively correlatedacross countries. A number of earlier studies have used cointegrationanalysis to document this fact, e.g. Hafer et al. (1997). Long-term

Comments from seminar participants at the Aarhus School of Business, andparticipants at the International Bond and Debt Market Integration Conference inDublin, are gratefully acknowledged.

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interest rates seem to be cointegrated across countries, indicating thatinternational bond markets are linked together. These cointegrationanalyses do not, however, examine comovement in the underlying fac-tors determining bond yields. Ilmanen (1995) suggests a number of fac-tors determining international bond returns, and he finds that a smallset of global (world) factors accounts for the predictable variation inbond returns and their cross-country correlation. In particular, wealth-dependent risk-aversion of bond investors appears to be an importantsource of the international comovement. Barr and Priestley (2004) alsofind that bond returns in di erent countries are predictable over time,and based on an international CAPM they find that 70 percent of thevariation in expected returns is due to world risk factors while the re-maining 30 percent is due to local country-specific risk factors. Theyinterpret this result as indicating that national bond markets are onlypartially integrated into world markets. Driessen et al. (2003) use alinear factor model and principal components analysis to analyze in-ternational bond returns, and they find that the positive correlation ofbond returns is driven by the positive correlation between the levels ofthe term structures across countries.1

In the present paper we approach the international comovement ofbond markets from a di erent angle. We do not search for plausibleunderlying factors that can explain the comovement, or test specificinternational asset pricing models. Instead, we make use of the returnvariance decompositions developed by Campbell and Ammer (1993) andEngsted and Tanggaard (2001): we decompose excess bond return in-novations in each country into three ’news’ components: news aboutfuture long-term inflation, news about future real interest rates, andnews about future excess bond returns (term premia). We then use avector-autoregressive (VAR) model to compute these news and innova-tion components. The VAR model contains variables from each country,and we measure international bond market linkages by cross-countrycorrelating the VAR-generated news and innovation components. Theappealing feature of our approach is that, apart from a linearization er-ror, the return variance decomposition holds as a dynamic identity, i.e.from the way bond returns are defined unexpected excess bond returnscan always be stated in terms of changes in expectations (’news’) of fu-ture inflation, real interest rates, and term premia. Thus, these threenews components jointly comprise all possible underlying economic fac-tors governing the variation in bond returns.

1An obvious economic candidate for this level factor is the rate of inflation. Aswill become clear, our analysis explicitly investigates the importance of expectedinflation in explaining international bond market comovement.

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Our analysis is close in spirit to the analysis in Sutton (2000). Hesuggests a method for examining whether comovement in long-term bondyields can be explained in terms of comovement in short-term interestrates (in accordance with the Expectations Theory), or is rather a con-sequence of comovement in term premia across countries. He finds thatterm premia at the long end of the term structure are both time-varyingand positively correlated across countries. Sutton’s analysis has somerestrictive features that distinguishes it from our analysis. First, Suttonassumes that term premia and interest rates are independent. Second,his approach does not make it possible to identify the separate e ects onbond yield comovement from inflation and real interest rates. Finally,his analysis is based on computation of ’perfect foresight’ long-term in-terest rates, which reduces the e ective sample-size dramatically. Ourapproach, by contrast, makes no assumptions on the relation betweenterm premia and interest rates, identifies the separate e ects from infla-tion and real interest rates, and uses a low-order VAR model to computeexpected values which implies no large reduction in the e ective samplesize.Recently it has been documented that in VAR models the traditional

OLS parameter estimates may be severely biased in small samples, andthat this bias may seriously distort statistics generated from the VAR,see e.g. Bekaert et al. (1997). For this reason we use the analytical biasformula from Pope (1990) to correct the VAR parameter estimates forsmall-sample bias. In addition, we use standard bootstrap techniquesto compute small-sample standard errors and confidence intervals of theVAR generated statistics.We apply our suggested procedure on monthly data from the US and

German bond markets over the period 1975-2003. Our most importantempirical results can be summarized as follows. First, there is significantpredictable variation in one-month excess bond returns in both countries.Second, there are important spillover e ects from the US market to theGerman market, but only limited spillover e ects the opposite way, andone-month excess bond returns in the US and Germany show a contem-poranous positive correlation of 0.54, indicating that bond markets inthe two countries are closely linked together. Third, inflation news is themain driving force behind this comovement. When news is coming tothe US market that future US inflation will increase, there is a tendencythat German inflation will also increase. This is regarded bad news forthe bond market in both countries whereby bond prices are bid downleading to immediate negative return innovations and changing expec-tations of future excess bond returns. Thus, in contrast to the resultsreported by Sutton (2000) where comovement in term premia is found

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to be the main reason for bond market comovement, our results suggestthat expected future inflation is the main reason. Finally, our results aremostly robust to changes in the lag-length of the VAR and to changesin the sample periods.The rest of the paper is organized as follows. In section 2 we present

the basic bond return variance decomposion based on a VAR-model,and we briefly describe the procedures for bias-adjustment of the VARparameter estimates and the bootstrap simulations. Section 3 reportsthe empirical results, and o ers some thoughts on the possible causes forinflation news comovement. Finally, in section 4 we relate our findingsto some other recent findings in the literature.

2 A VAR-based variance decomposition of bond re-

turns

In section 2.1 we present the basic excess bond return innovation formulathat will form the basis for the subsequent empirical work. In section 2.2we decribe how we construct the return variance decomposition based ona vector-autoregression. Finally, in section 2.3 we explain the procedureused to bias-correct the VAR parameter estimates, and the bootstraptechnique used to compute small-sample standard errors and confidenceintervals of the VAR generated statistics.

2.1 The excess bond return innovation formula

Campbell and Ammer (1993) derive an expression for the unexpectedexcess return on an -period zero-coupon bond. According to this ex-pression the one-period return on an -period zero-coupon bond in ex-cess of the short-term interest rate can be decomposed into changes inexpectations of three variables -1 periods into the future: inflation,real interest rates, and excess bond returns. However, often zero-couponyields on long bonds do not exist many years back, so one will have towork with yields on coupon bonds. In Engsted and Tanggaard (2001)we use the log-linearized formula for the return on a long-term couponbond in Shiller and Beltratti (1992) to derive an excess return innovationexpression similar to the one in Campbell and Ammer (1993), but fora coupon bond instead of a zero-coupon bond. The expression looks asfollows:

+1 +1 = ( +1 )X=1

( +1+ +1+ +1+ ) (1)

where +1 is the nominal one-period log gross bond return from to +1in excess of the continuously compounded nominal one-period interest

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rate, +1 is the inflation rate from to + 1, +1 is the one-periodlog real interest rate from to + 1, is the conditional expectationsoperator based on information at time , and is constant slightly lessthan one.2

Expression (1) shows that unexpected excess bond returns must bedue to ’news’ (i.e. changes in expectations) coming to the market abouteither future inflation, future real interest rates, or future excess returns(or a combination of the three). News that either inflation, real interestrates, or excess returns will be higher (lower) in the future, will lead toan immediate drop (increase) in excess bond returns.The expression is a dynamic accounting identity with no economic

theory imposed; it is derived from the definition of the linearized one-period return on a long-term coupon bond, so apart from the lineariza-tion error, it holds by construction. Excess bond return innovations canalways be decomposed into changes in expectations of future inflation,real rates, and excess returns. Thus, empirical analysis of the volatil-ity of the bond market based on (1) is not conditional on a particulareconomic model for the bond market. However, it is illustrative andinformative to ask what traditional economic theories for bond yieldsimply for equation (1). For example, the Fisher Hypothesis states thatnominal bond yields move one-for-one with expected inflation so that exante real rates are constant. This implies that the ’news about futurereal rates’ component in (1), ( +1 )

P=1 +1+ , will be zero.

Similarly, the Expectations Theory of the term structure says that thelong-term bond yield is given as expected future short rates plus a time-invarying term premium. This implies that expected excess bond returnsare constant so that the ’news about future excess returns’ component,( +1 )

P=1 +1+ , is zero. Thus, if both the Expectations The-

ory and the Fisher Hypothesis hold, inflation news is the only source ofvariation in excess bond return innovations. However, these economictheories will not hold exactly (and according to many empirical studiesnot even approximately), so in general variation in bond returns will becaused by all three news components in (1).Equation (1) holds for each country, so we will use a VAR model, to

be described in more detail in the next sub-section, containing variablesfrom the US and German bond markets to estimate the components in(1) for each country, and we will then cross-country correlate the com-ponents to see whether the high positive correlation of US and Germanbond returns is caused mainly by high positive correlation of inflation

2 is defined as = exp( ), where is the mean nominal yield to maturity onthe long coupon bond, see Shiller and Beltratti (1992) and Engsted and Tanggaard(2001).

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news, real interest rate news, or term premia news.In order to simplify the notation, we write (1) as

e +1 = e +1 e +1 e +1 , = (2)

where denotes either US (us) or Germany (ge), and e +1 +1

+1 e +1 ( +1 )P

=1 +1+ e +1 ( +1 )P

=1 +1+

and e +1 ( +1 )P

=1 +1+ .

2.2 The VAR-based return variance decomposition

In order to compute each of the components in (2) based on availabledata samples, we need an econometric time-series model that can be usedto estimate the conditional expectations of returns, inflation, and inter-est rates. The standard choice is a linear VAR containing excess bondreturns and real interest rates, and possibly other variables with predic-tive power for returns and real rates. The VAR needs to include and

in order to be able to compute e +1, e +1, e +1 and e +1. Simi-larly, and are needed in the VAR in order to compute e +1 ande +1. Note that only three of the four components in (2) are computeddirectly from the VAR; the last component is computed as a residualto make sure that (2) holds exactly. Thus, e +1, e +1, and e +1 arecomputed directly, and the remaining component e +1 is computed ase +1 = e +1 e +1 e +1.

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Our benchmark VAR model contains the following variables, col-lected in the vector : = ( , , , , , )0. is the’spread’ between the long-term bond yield and the short-term interestrate in country .4 We include this variable because many previousstudies have found that the long-short spread has significant predictive

3In Campbell and Ammer (1993) the VAR model does not include excess bondreturns directly. Instead, the first-di erence of the nominal short-term interest rateand the spread between the long-term and short-term interest rates are included, andthe excess return innovation is then computed from these two variables. Campbelland Ammer include as a state variable in the VAR, which makes it possible tocompute the real interest rate news component directly. In addition, by combining thereal interest rate with the first-di erence of the nominal interest rate, the inflationnews component can be computed. Finally, the excess return news component iscomputed as a residual from the other components using the dynamic identity. InEngsted and Tanggaard (2001) we show that Campbell and Ammer’s procedure onlyworks for zero-coupon bonds. For coupon bonds it will be necessary to include excessbond returns directly in the VAR, and then compute the inflation news componentas a residual.

4Specifically, is defined as = (1 )1, where is the log of the

nominal long-term bond yield in country and is the continuously compundednominal short-term interest rate in country (see Shiller and Beltratti, 1992).

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ability for bond returns. The first-order VAR model for is written as(higher-order models are easily handled using the companion form)

+1 = + +1 (3)

where is the VAR parameter matrix and is the vector of errorterms.5 From (3) the VAR estimate of +1 +1 is +1. Similarly,the VAR estimate of ( +1 ) +1+ is +1. Thus, by defining rowselection vectors 1 , 1 , 2 , and 2 that pick out, respectively, thefirst, second, third, and fourth element of , VAR estimates of each ofthe components in (2) are given as

e +1 = 1 +1 = (4)

e +1 = 1 ( ) 1+1 = (5)

e +1 = 2 ( ) 1+1 = (6)

e +1 = e +1 e +1 e +1 = (7)

where the VAR residuals and parameter estimates are inserted in +1

and , respectively. Note that the inflation news component, e +1, iscomputed as a residual from the dynamic identity. This implies that wedo not have to include inflation directly as a state variable in the VAR,which is quite appealing because monthly inflation in both the US andGermany shows strong seasonal variation.6

From (2) it follows that

(e )= (e ) + (e ) + (e ) +2 (e e ) + 2 (e e ) + 2 (e e ) (8)

We calculate the relative magnitude of each of the news componentsby computing the variances and covariances in (8) and then normalizeby (e ). The covariances, however, make these measures di cultto interpret. Thus, we also measure the relative magnitudes by orthog-onalizing (using a Cholesky decomposition) the components and thencompute the 2 values in regressions of e +1 onto each of the orthog-onalized components. The sum of the 2 values then add up to one,

5All variables in the VAR are measured in deviation from their unconditionalmeans.

6The seasonal pattern is slightly changing over time in both countries, so we couldnot account for it by simply including seasonal dummies in the VAR.

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so each individual 2 number can be interpreted as the fraction of thereturn innovation variance explained by that particular news component.

2.3 Small-sample bias-correction and the bootstrap

technique

OLS estimates of VAR parameters are biased in small samples and hencethe news and innovation components (4) to (7) are also biased. Oneway to correct for this bias is to use Monte Carlo procedures, as ine.g. Bekaert et al. (1997) and Engsted and Tanggaard (2001), by ei-ther assuming normally distributed VAR errors or by using bootstraptechniques to resample the original VAR residuals, i.e. use the empiricalsmall-sample distribution of the errors. An alternative is to use the an-alytical bias formula derived by Pope (1990). Based on a higher-orderTaylor series expansion, Pope derives the following formula for the bias,, in VAR models like (3):

= + ( 3 2)

where is

= [( ) 1 + ( 2) 1 +X

( ) 1] (0) 1

and ( ) = 0

+ , are the eigenvalues of , is the conditionalvariance of , and is the sample size.As seen, the approximation error in the bias formula vanishes at

the rate 3 2 which is at least as fast as in standard Monte Carlo orbootstrap bias-adjustment. In our empirical analysis we will use Pope´sbias-adjustment procedure.We use bootstrap simulation to compute small-sample standard er-

rors and equal-tailed confidence intervals of the VAR generated statistics,i.e. variance and covariance ratios, correlation coe cients and 2 valuesfrom the regressions with the orthogonalized components.7 Basically,Bose’s (1988) and Kilian’s (1998) resampling technique is used with thespecial feature that residuals are resampled from the bias-adjusted VARsystem.

7We report equal-tailed confidence intervals in addition to standard errors sincethe statistics may have non-symmetric finite-sample distributions. Thus, confidenceintervals summarize better than standard errors the distribution of the point es-timates. See Davison and Hinkley (1997) for definitions of bootstrap confidenceintervals.

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3 Empirical results

The data to be used in the empirical analysis are from the InternationalMonetary Fund, International Financial Statistics. Monthly US andGerman data for long-term government bond yields were collected forthe period July 1975 to February 2003. From these yields log one-monthholding period returns, +1, were computed using the formula +1 =

+1 + , where is the log of the nominal yield to maturity onthe long bond ( ), = exp( ) is the mean nominal yield overthe sample, and is a linearization constant (see Shiller and Beltratti(1992) and Engsted and Tanggaard (2001)).8 Excess log bond returns,

+1, were then computed by subtracting from +1 the continuouslycompounded short term interest rate, taken to be the 1-month interestrate on government Treasury bills. Real interest rates were computedby subtracting the monthly inflation rate from the short term nominalinterest rate. Finally, the yield spread, , was obtained as described infootnote 4.The correlation between US and German monthly excess bond re-

turns, and , over the period 1975 to 2003, is +0.54 which indicatesa quite high degree of comovement of US and German bond markets.In order to investigate in more detail the nature of this comovement weestimate a comprehensive VAR model containing excess bond returns,real interest rates, and yield spreads for each country, cf. section 2.2.Table 1 reports the results from a one-lag VAR model. First, we see thatexcess bond returns are highly positively autocorrelated in both coun-tries: the coe cient to in the +1 equations is positive and stronglysignificant. Second, lagged domestic real interest rates significantly pre-dict excess bond returns in both countries. Third, none of the laggedGerman variables significantly predict US excess bond returns, whereaslagged US excess returns strongly predict German excess bond returns.Similarly, US variables serve as good predictors for German real interestrates and yield spreads, while German variables generally have no pre-dictive power for US real rates or yield spreads, except for in the +1

equation. These results indicate significant predictable time-variation inUS and German bond returns, and that there are important spillovere ects from the US market to the German market, but not vice versa.Based on the VAR parameter estimates in Table 1, we next com-

pute the innovation and news components as in equations (4) to (7).Table 2 reports the variance decomposition of these components. Asseen, in both countries the news about future inflation component, e ,is clearly the dominating factor behind movements in excess bond return

8The values of are: = 0 9932; = 0 9944.

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innovations. Var(e ) is much higher than Var(e ) and Var(e ), and thedominant covariance term also involves e . By looking at the orthogo-nalized components we see that inflation news accounts for 85 percentof the variation in unexpected excess bond returns in the US and 69percent in Germany (both statistically significant), while news about fu-ture real interest rates is completely unimportant, both statistically andeconomically. News about future excess returns (term premia) is alsostatistically insignificant, but accounts for an economically importantpart of the variation (14 percent in the US and 29 percent in Germany),although still much less than the inflation news component. These re-sults are in fact quite similar to the results documented by Campbelland Ammer (1993) for the US. They also find that inflation news is themost important factor driving US bond returns.Since US and German bond returns are highly positively correlated,

and since news about future long-term inflation seems to be the mostimportant force behind movements in bond returns in both the US andGermany, we expect that e and e are also highly positively corre-lated. This is confirmed in Table 3, which reports pairwise correlations ofall computed innovation and news components. e and e have a pos-itive correlation of 0.74. Excess return news, and to a lesser extent realinterest rate news, are also highly cross-country correlated, but sincethese components are much less important in explaining bond returnvariability in the two countrries, the overall conclusion must be that themain reason for the high degree of comovement of US and German bondmarkets is a high degree of comovement of inflation news. Another note-worthy result to be seen in Table 3 is that in both countries the inflationnews component is highly negatively correlated with both the return in-novation component, e, and with the return news component, e . Thismeans that news that inflation is going to increase in the future is badnews for the bond markets in both the short and long term.The results reported in Tables 1 to 3 are based on a VAR model with

one lag. Diagnostic tests (not reported) do not show signs of misspec-ification, i.g. there are no strong indications of autocorrelation in theVAR residuals. However, in order to investigate the robustness of theresults, we also estimate a two-lag VAR model, and we split the sampleperiod 1975-2003 into two sub-samples (1975-1989 and 1989-2003) andcarry out the whole analysis with these shorter data samples. Table 4summarizes the main results.9

9We only report the variance decompositions based on the orthogonalized com-ponents, and we only report the cross-country correlations of the three news compo-nents. Furthermore, we do not report the bootstrapped standard errors and confi-dence intervals. The full set of results are available from the authors upon request.

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First, we see that increasing the lag-length to two does not in anysubstantive way change the results. Thus the results are robust to thelag-length of the VAR. Second, the finding that inflation news is themost important part of bond return volatility remains true when thesample is split into sub-periods, although the relative magnitude of e issmaller in the sub-periods compared to the whole sample period. How-ever, there seems to be an interesting change in the relative importanceof e and e from the early period to the more recent period: in the1975-1989 period real interest rate news is completely unimportant inboth countries, whereas excess return news is non-negligible, especiallyin Germany. But in the 1989-2003 period the relative importance ofthese two news components change; now real interest rate news becomesnon-negligible while the excess return news component becomes quitesmall. Third, both e and e remain highly positively cross-countrycorrelated in the sub-periods and, in fact, the correlations increase overtime. By contrast, the correlation between e and e changes from pos-itive to negative when we go from the early period to the later period.However, since US and German bond returns are still highly positivelycorrelated in the 1989-2003 period, and since excess return news is quiteunimportant in this sub-period, the implication of the above findingsmust be that comovement in real interest news cannot be responsiblefor the positive bond return correlation over the period 1989-2003; in-stead comovement in inflation news must be the explanation, just as weconcluded for the whole period 1975-2003.The main conclusion from our analysis is that inflation news is the

main driving force behind movements in both the US and German bondmarket, and that this inflation news component shows a high degree ofcross-country correlation which generates a high degree of comovementof the two markets. When news is coming to the US market that futureUS inflation will increase, there is a tendency that German inflationwill also increase. This is regarded bad news for the bond market inboth countries whereby bond prices are bid down leading to immediatenegative return innovations and changing expectations of future excessbond returns.The results reported above indicate that inflation has a strong role to

play in explaining bond return movements within countries and acrosscountries. Term premia (excess returns) also have some role to play(especially if we focus on the period before 1990), but not nearly to thesame extent as inflation. Thus, our results to some extent conflict withthose reported by Sutton (2000). He measures the extent to which bondmarket comovement can be explained in terms of comovement of shortterm nominal interest rates and term premia, respectively, but he does

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not attempt to isolate the e ects from inflation and real interest rates.He finds that term premia comovement is the most important factorbehind the comovement of international long-term interest rates. Ourresults, by contrast, imply only a minor role for term premia comovementand instead refer most of the comovement to comovement in inflationnews.We leave to future research the question of what then generate co-

movement in inflation news across countries. But naturally the increas-ing globalization and international trade, and the gradual elimination ofbarriers to trade between the US and Europe during the last 30 years,have contributed to a common development in inflation rates acrosscountries. Hence, inflation in di erent countries to a large extent re-spond to a set of global factors in addition to country-specific factors,and this implies that investors in bond markets in di erent countriesrevise their inflation expectations in response to the same kind of news.The identification of those global factors that generate common move-ment in inflation rates across countries marks an interesting topic forfuture research.

4 Concluding remarks

In this paper we have analyzed the comovement of US and Germanbond returns over the period 1975-2003 using VAR based return variancedecompositions similar to the ones in Campbell and Ammer (1993) andEngsted and Tanggaard (2001).While the results reported in this paper contrast with some of the

results reported in the earlier literature (e.g. Sutton, 2000), our find-ings complement the findings in other recent studies. Our finding ofpredictable variation in US and German bond returns and that commonmovement in inflation news is the main factor behind the comovement ofthe bond markets in the two countries, complement Barr and Priestley’s(2004) finding that most of the variation in international bond returns isdue to world (global) risk factors rather than to country-specific factors.Furthermore, our analysis suggests a natural explanation for Dreissenet al.’s (2003) finding that positive correlation between the levels of theterm structures across countries accounts for the positive correlation ofinternational bond returns: the level of the term structure is most nat-urally determined by the rate of inflation, so cross-country correlationof inflation news will cause cross-country correlation of term structurelevels.Of course, further analysis will be needed in order to explain the

precise reasons for common movements in inflation news over time, andthat the correlation seems to have increased recently (c.f. Table 4). We

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leave that for future research.

5 References

Barr, D.G., and R. Priestley (2004): Expected returns, risk andthe integration of international bond markets. Journal of InternationalMoney and Finance 23, 71-97.Bekaert, G., R.J. Hodrick, and D.A. Marshall (1997): On biases in

tests of the expectations hypothesis of the term structure of interestrates. Journal of Financial Economics 44, 309-348.Bose, A. (1988): Edgeworth correction by bootstrap in autoregres-

sion. Annals of Statistics 16, 1709-1722.Campbell, J.Y., and J. Ammer (1993): What moves the stock and

bond markets? A variance decomposition for long term asset returns.Journal of Finance 48, 3-37.Davison, A.C., and D.V. Hinkley (1997): Bootstrap Methods and

Their Applications. Cambridge University Press.Driessen, J., B. Melenberg, and T. Nijman (2003): Common fac-

tors in international bond returns. Journal of International Money andFinance 22, 629-656.Engsted, T., and C. Tanggaard: The Danish stock and bond markets:

comovement, return predictability and variance decomposition. Journalof Empirical Finance 8, 243-271.Hafer, R.W., A.M. Kutan, and S. Zhou (1997): Linkage in EMS term

structures: evidence from common trends and transitory components.Journal of International Money and Finance 16, 595-607.Ilmanen, A. (1995): Time-varying expected returns in international

bond markets. Journal of Finance 50, 481-506.Kilian, L. (1998): Small-sample confidence intervals for impulse re-

sponse functions. Review of Economics and Statistics 80, 218-230.Pope, A.L. (1990): Biases of estimators in multivariate non-gaussian

autoregressions. Journal of Time Series Analysis 11, 249-258.Shiller, R.J., and A. Beltratti (1992): Stock prices and bond yields:

can their comovement be explained in terms of present value models?Journal of Monetary Economics 30, 25-46.Sutton, G.D., (2000): Is there excess comovement of bond yields

between countries? Journal of International Money and Finance 19,363-376.

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6 Tables

+1 +1 +1 +1 +1 +1

.368 .002 .002 .169 .013 -.001

(.062) (.004) (.001) (.051) (.005) (.000)

[.248, .491] [-.006, .010] [.001, .003] [.068, .268] [.004, .023] [-.002, .000]

1.657 .564 .007 .837 .056 .005

(.755) (.047) (.009) (.629) (.061) (.004)

[.145, 3.12] [.474, .660] [-.009, .025] [-.391, 2.09] [-.062, .176] [-.004, .013]

2.479 -.098 .950 2.184 .293 .039

(1.859) (.115) (.021) (1.553) (.148) (.010)

[-1.15, 6.24] [-.317, .142] [.914, .996] [-.973, 5.30] [.000, .590] [.020, .060]

-.129 -.003 -.001 .248 -.011 .001

(.072) (.005) (.001) (.061) (.006) (.000)

[-.272, .009] [-.012, .006] [-.002, .001] [.133, .368] [-.022, .001] [.000, .002]

.197 .131 .008 1.536 .209 -.005

(.714) (.045) (.008) (.585) (.056) (.004)

[-1.26, 1.56] [.046, .220] [-.009, .024] [.357, 2.67] [.096, .317] [-.013, .003]

.459 -.030 -.019 .306 -.606 .955

(2.544) (.159) (.028) (2.058) (.200) (.014)

[-4.75, 5.40] [-.348, .283] [-.079, .032] [-3.74, 4.32] [-.997, -.207] [.929, .985]

2 .128 .366 .879 .214 .116 .941(.000) (.000) (.000) (.000) (.000) (.000)

Notes: The table reports bias-adjusted VAR parameter estimates (in bold),

with bootstrap standard errors in parentheses and bootstrap 95% equal-tailed

confidence intervals in brackets. The number of bootstrap simulation runs is

10,000. The number in parenthesis under the 2 value is the p-value for joint

significance tests of the explanatory variables.

Table 1: VAR parameter estimates, July 1975 - February 2003

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US bonds German bondsShares ofVar(e ) 2.929 (1.046) [0.005, 3.966] 3.768 (1.377) [-0.155, 5.154]

Var(e ) 0.011 (0.007) [-0.010, 0.016] 0.013 (0.011) [-0.020, 0.022]

Var(e ) 0.722 (0.827) [-1.838, 1.189] 1.438 (1.143) [-2.016, 2.300]

2Cov(e e ) -0.101 (0.117) [-0.291, 0.184] -0.152 (0.182) [-0.420, 0.302]

2Cov(e e ) -2.596 (1.826) [-4.038, 2.803] -4.146 (2.470) [-6.319, 3.168]

2Cov(e e ) 0.043 (0.099) [-0.184, 0.221] 0.091 (0.158) [-0.284, 0.352]

2(e ) 0.849 (0.136) [0.755, 1.282] 0.690 (0.135) [0.530, 1.056]2(e ) 0.008 (0.059) [-0.194, 0.015] 0.020 (0.097) [-0.310, 0.039]2(e ) 0.144 (0.136) [-0.242, 0.266] 0.290 (0.152) [-0.041, 0.530]

Notes: The table presents the results of the variance decomposition (8), where

each variance and covariance component has been normalized by Var(e) Thenumbers in bold are point estimates based on the bias-adjusted VAR para-

meter estimates, with bootstrap standard errors in parentheses; the numbers

in brackets are bootstrap 95% equal-tailed confidence intervals. The number

of bootstrap simulation runs is 10,000.

Table 2: Variance decomposition of bond returns, July 1975 -February 2003

15

e e e ee 1

e 0.657 1(0.191)

[0.472, 1.194]

e 0.182 0.245 1(0.156) (0.408)

[-0.091, 0.509] [-0.382, 1.098]

e -0.921 -0.895 -0.288 1(0.118) (0.049) (0.294)

[-1.325, -0.877] [-1.013, -0.825] [-0.961, 0.174]

e 0.504 0.117 0.044 -0.355

(0.038) (0.159) (0.138) (0.104)

[0.430, 0.579] [-0,177, 0.440] [-0.221, 0.321] [-0.618, -0.208]

e 0.706 0.879 0.248 -0.864

(0.156) (0.184) (0.379) (0.114)

[0.583, 1.185] [0.779, 1.480] [-0.342, 1.067] [-1.205, -0.771]

e 0.419 0.168 0.505 -0.359

(0.150) (0.489) (0.335) (0.354)

[0.199, 0.769] [-0.588, 1.089] [0.093, 1.346] [-1.200, 0.116]

e -0.720 -0.613 -0.205 0.737

(0.099) (0.205) (0.299) (0.111)

[-1.040, -0.649] [-1.117, -0.327] [-0.844, 0.301] [0.568, 1.000]

Table 3: Correlations of innovations and news components, July 1975- February 2003

Table continues on next page.

16

Table 3 continued :

e e e ee 1

e 0.496 1(0.152)

[0.300, 0.894]

e 0.160 0.341 1(0.128) (0.446)

[-0.060, 0.445] [-0.247, 1.331]

e -0.831 -0.893 -0.351 1(0.119) (0.039) (0.340)

[-1.214, -0.750] [-0.972, -0.821] [-1.157, 0.126]Notes: The numbers in bold are correlation coe cients based on the bias-

adjusted parameter estimates. The numbers in parentheses and brackets are

bootstrap standard errors and 95% equal-tailed confidence intervals, respec-

tively, based on 10,000 simulation runs.

Table 3: Correlations of innovations and news components, July 1975- February 2003

17

1975-2003

1975-1989

1989-2003

US GE US GE US GEVAR(1):

2(e ) .849 .690 .707 .529 .551 .5162(e ) .008 .020 .020 .011 .393 .3862(e ) .144 .290 .270 .459 .056 .098(e e ) .737 .760 .965(e e ) .505 .771 -.987(e e ) .879 .846 .992

VAR(2):2(e ) .851 .737 .715 .604 .521 .4042(e ) .032 .026 .011 .003 .340 .4582(e ) .117 .237 .273 .392 .140 .138(e e ) .732 .759 .990(e e ) .608 .896 -.994(e e ) .851 .894 .997

Notes: "VAR( )" denotes a VAR model with lags. The precise sample

periods are: July 1975 - February 2003; July 1975 - March 1989; April 1989

- February 2003.

Table 4: Robustness check: di erent lag-lengths and sub-sampleanalyses

18

List of CAF’s Working Papers 2003 -

141. P. Raahauge (January 2003), Empirical rationality in the stock market. 142. F. Bec and A. Rahbek (January 2003), Vector equilibrium correction models with non-linear

discontinuous adjustments. 143. P. Reinhard Hansen and A. Lunde (February 2003), Testing the significance of calendar

effects. 144. P. Reinhard Hansen and A. Lunde (February 2003), Consistent preordering with an estimated

criterion function, with an application to evaluation and comparison of volatility models.

145. C. Christiansen, T. Engsted, S. Jakobsen and C. Tanggaard (February 2003), An empirical

study of the term structure of interest rates in Denmark, 1993-2002. in: J. Batten, T. Fetherston, and P. Szilagyi, ed., European Fixed Income Markets: Money, Bond, and Interest Rate Derivatives, John Wiley & Sons.

146. C. Christiansen, T. Engsted, S. Jakobsen and C. Tanggaard (February 2003), A chapter on the

Danish bond market. in J. Batten, T. Fetherston, and P. Szilagyi, ed.," European Fixed Income Markets: Money, Bond, and Interest Rate Derivatives, John Wiley & Sons.

147. M. Shin Jensen and M. Svenstrup (March 2003), Efficient control variates and strategies for

Bermudan swaptions in a Libor market model. 148. B.M. Bibby, I.M. Skovgaard and M. Sørensen (March 2003), Diffusion-type models with given

marginal and autocorrelation function.(to appear in Bernoulli) 149. K.L. Bechmann and P. Løchte Jørgensen (March 2003), The value and incentives of option-

based compensation in Danish listed companies (Journal of Derivatives Accounting, vol. 1(1), pp 99-109).

150. G. Peskir (April 2003), On the American option problem.(to appear in Math. Finance) 151. L. Kelly, E. Platen and M. Sørensen (May 2003), Estimation for discretely observed diffusions

using transform functions.(to appear in J. Appl. Prob.) 152. O.E. Barndorff-Nielsen and N. Shephard (May 2003), Power and bipower variation with

stochastic jumps. 153. G. Peskir (May 2003), The Russian option: Finite horizon. (to appear in Financae Stoch.) 154. A. Frino, V. Mollica and T. Walter (July 2003), Asymmetric price behaviour surrounding

block trades: A market microstructure explanation.

155. K. Stegenborg Larsen and M. Sørensen (July 2003), Diffusion models for exchange rates in a target zone.

156. D. Koulikov (August 2003), Modeling sequences of long memory non-negative covariance

stationary random variables. 157. H. Schmidli (August 2003), Modelling PCS options via individual indices. 158. M. Bladt and M. Sørensen (September 2003), Statistical inference for discretely observed

Markov processes. 159. O.E. Barndorff-Nielsen and N. Shephard (November 2003), Econometrics of testing for jumps

in financial economics using bipower variation. 160. M. Ørregaard Nielsen (November 2003), Spectral Analysis of fractionally cointegrated

systems. (Economics Letters 83, 225-231). 161. M. Ørregaard Nielsen, (November 2003), Local empirical spectral measure of multivariate

processes with long range dependence.(Stochastic Processes and Their Applications, 109, 145-166.)

162. C. Christiansen (November 2003), Volatility-spillover effects in European bond markets. 163. D. Koulikov (December 2003), Long memory ARCH(•) models: specification and quasi-

maximum likelihood estimation. 164. K. Bechmann (December 2003), Short sales, price pressure, and the stock price response to

convertible bond calls (forthcoming Journal of Financial Markets). 165. M.Y. An, B.J. Christensen and N. Datta Gupta (December 2003), On pensions and retirement:

bivariate mixed proportional hazard modelling of the joint retirement of married couples .(published in Journal of Applied Econometrics, 2004, pp. 687-704)

166. S. Rasmus, S. Asmussen and M. Wiktorsson (February 2004), Pricing of some exotic options

with NIG-Lévy input.( Computational Science - ICCS2004 (M. Bubak, G.D. van Albada, P.M.A. Sloot, J.J. Dongarra, eds.)) Springer-Verlag

167. M.Ø. Nielsen (February 2004), Efficient inference in multivariate fractionally integrated time

series models.(Econometrics Journal, 7, 63-97) 168. R. Poulsen (February 2004), Exotic options: Proofs without formulas. 169. S. Gryglewicz (March 2004), Stock repurchase as an alternative to dividend payout: Empirical

evidence from the Warsaw stock exchange. 170. K. Bechmann and J. Raaballe (March 2004), The differences between stock splits and stock

dividends – evidence from Denmark. 171. H. Schmidli (March 2004), On Cramér-Lundberg approximations for ruin probabilities under

optimal excess of loss reinsurance.

172. H. Schmidli (March 2004), On optimal investment and subexponential claims. 173. T. Engsted and C. Tanggaard (March 2004), Speculative bubbles in stock prices? Tests based

on the price-dividend ratio. 174. M. Svenstrup and S. Willemann (April 2004), Reforming housing finance – Perspectives from

Denmark. 175. T. Busch (May 2004), A robust LR test for the GARCH model. 176. J. Bartholdy and P. Peare (May 2004), Estimation of expected return: CAPM vs Fama and

French. 177. C. Sponholtz (May 2004), The information content of earnings announcements in Denmark. 178. O.E. Barndorff-Nielsen and R. Stelzer (June 2004), Absolute moments of generalized

hyperbolic distributions and approximate scaling of normal inverse Gaussian Lévy-Processes.

179. A.-S. Reng Rasmussen (June 2004), Estimating the consumption-capital asset pricing model

without consumption data: Evidence from Denmark. 180. C. Christiansen (July 2004), Decomposing European bond and equity volatility. 181. G. Peskir and N. Uys (August 2004), On Asian options of American type. 182. M. Ørregaard Nielsen (September 2004), Noncontemporaneous cointegration and the

importance of timing. 183. P. Raahauge (September 2004), Upper bounds on numerical approximation errors. 184. P. Raahauge (September 2004), Higher-order finite element solutions of option prices. 185. M.C. Jones, J.Perch Nielsen and C. Tanggard (September 2004), Local linear density

estimation for filtered survival data, with bias correction. 186. B.M. Bibby, M. Jacobsen and M. Sørensen (December 2004), Estimating functions for

discretely sampled diffusion-type models. 187. C. Tanggaard (December 2004), Errors in trade classification: Consequences and remedies. 188. M.Ø. Nielsen (December 2004), Semiparametric estimation in time series regression with long

range dependence. 189. C. Strunk Hansen and B.E. Tuypens (December 2004), Proxying for expected returns with

price earnings ratios. 190. C. Strunk Hansen and B.E. Tuypens (December 2004), Long-run regressions: Theory and

application to US asset markets.

191. K.N. Daniels and M. Shin Jensen (December 2004), The effect of credit ratings on credit default swap spreads and credit spreads

192. T. Busch (December 2004), Testing the Martingale restriction for option implied densities. 193. W. Schmid and D. Tzotchev (December 2004), Sequential monitoring of the statistical

properties of the univariate affine diffusion with application to interest rates. 194. O.E. Barndorff-Nielsen and N. Shephard (December 2004), Power variation and time change. 195. O.E. Barndorff-Nielsen and N. Shephard (December 2004), Impact of jumps on returns and

realised variances: econometric analysis of time-deformed Lévy-processes. 196. O.E. Barndorff-Nielsen, P. Reinhard Hansen, A. Lunde, and N. Shephard (December 2004),

Regular and modified kernel-based estimators of integrated variance: the case with independent noise.

197. O. Di Miscia (December 2004), Nonparametric estimation of diffusion process: a closer look. 198. O. Di Miscia (December 2004), Estimation of continuous-time interest rate models: a

nonparametric approach. 199. O. Di Miscia (December 2004), Term structure of interest models: concept and estimation

problem in a continuous-time setting. 200. B.J. Christensen and P. Raahauge (December 2004), Latent Utility Shocks in a Structural

Empirical Asset Pricing Model (with Peter Raahauge) 201. M. Shin Jensen and M. Svenstrup (January 2005), Optimal allocation of simulation paths in

the primal-dual algorithm. 202. B.J. Christensen and M.Ø. Nielsen (February 2005), The implied-realized volatility relation

with jumps in underlying asset prices. 203. M.Ø. Nielsen (February 2005), Multivariate Lagrange multiplier tests for fractional

integration. 204. T. Engsted and C. Tanggaard (Mach 2005), The comovement of US and German bond markets.

ISSN 1398-6163

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