Ž Ž
. Ž
. Hence, the log-likelihood for observation number t is y1r2 N ln 2p q ln G q
t X
Ž .
y1
.
8,9,10
2ln D q ´ D G D
´ .
t t
t t
t t
4. Empirical results from the treasury bond market
This section provides the empirical results of applying the multivariate model, which incorporates announcement effects to the U.S. Treasury market. First, we
present the results from estimating the mean equation and, subsequently, the results from estimating the covariance equation are given.
4.1. Conditional means Recall that the conditional means of the excess returns are assumed to be
Ž . described by a VAR 1 process where a level effect for announcement days is
Ž . added, cf. Eq. 4 . The point estimates of the addition to the conditional means on
announcement days, F
A
, range between 0.014 and 0.074 percentage points and
i
are, in general, increasing with the time to maturity of the bond. The announce- ment effects on the level of the conditional means are much smaller than those
Ž .
found by Jones et al. 1998 . The moderated results are ascribed to the more recent time period that we consider. In fact, the addition to the conditional mean on
announcement days is not significantly different from zero at the 10 level of significance for any of the maturities. Also, the joint test results in a p-value of
81.
11
Hence, this provides evidence that releases of macroeconomic news are not associated with risk premier in the sense of higher returns on announcement
Ž .
days, which is consistent with the findings of Li and Engle 1998 for the Treasury futures market. This also confirms our findings from the simple multivariate
model. Consequently, we reestimate the mean equation where we impose the restric-
tion that F
A
0. As the point estimates as well as the statistical significance of F
and F hardly change by imposing this restriction, we merely report the
1
results from the reduced mean equation, cf. Table 3. A few of the off-diagonal entries in the parameter matrix, F
are significantly different from zero indicating
1
8
Notice that when we consider the CCORR model with r
A
0 we obtain G s G and the
i j t
Ž .
log-likelihood function is simplified accordingly, cf. Bollerslev 1990 .
9
In the practical estimation, we simultaneously estimate the d ’s and the parameters of H , hence,
i t
we adjust the above log-likelihood function accordingly.
10
The estimation is conducted in GAUSS using the GAUSS module Constrained Maximum Likelihood. A combination of the Berndt–Hall–Hall–Hausman and the Newton–Raphson maximiza-
tion algorithm is employed. Starting values for the conditional variance are set to the unconditional variance. The likelihood function is conditional on the first observation.
11
All joint tests are conducted using the robust Wald test statistic.
C. Christiansen
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of Empirical
Finance 7
2000 479
– 507
495 Table 3
Conditional mean equation Ž
. Maturity year
2 3
5 7
10 30
Ž .
Ž .
Ž .
Ž .
Ž .
Ž .
F 0.006
0.002 0.008
0.003 0.010
0.005 0.013
0.006 0.015
0.007 0.022
0.011
0 i
Ž .
Ž .
Ž .
Ž .
Ž .
Ž .
F 0.024 0.071
0.412 0.102
0.484 0.154
0.471 0.202
0.420 0.250
0.753 0.365
1,2yr
Ž .
Ž .
Ž .
Ž .
Ž .
Ž .
F 0.064 0.048
y0.241 0.070
y0.025 0.108 y0.122 0.139
y0.074 0.174 y0.340 0.246
1,3yr
Ž .
Ž .
Ž .
Ž .
Ž .
Ž .
F 0.002 0.037
0.008 0.053 y0.239
0.083 0.046 0.110
y0.029 0.137 y0.248 0.202
1,5yr
Ž .
Ž .
Ž .
Ž .
Ž .
Ž .
F 0.036 0.029
0.079 0.043
0.172 0.067
y0.053 0.091 0.215
0.113 0.039 0.172
1,7yr
Ž .
Ž .
Ž .
Ž .
Ž .
Ž .
F y0.027 0.025
y0.014 0.037 y0.010 0.056
0.035 0.075 y0.164
0.093 0.300
0.145
1,10yr
Ž .
Ž .
Ž .
Ž .
Ž .
Ž .
F y0.007 0.010
y0.017 0.015 y0.022 0.023
y0.011 0.030 0.014 0.037
y0.102 0.056
1,30yr
The VAR residuals are created as the residuals, y , from estimating the following equation by OLS: R sF qF R q y , where R is the vector of
t t
1 t I1
t t
excess returns at time t. White’s standard errors in parenthesis. Ž
. Indicates that the parameter is significantly different from zero two-sided test at a 10 level.
Ž .
Indicates that the parameter is significantly different from zero two-sided test at a 5 level. Ž
. Indicates that the parameter is significantly different from zero two-sided test at a 1 level.
Ž . Ž
. that the AR 1 specification in Jones et al. 1998 might not provide an adequate
Ž . description of the mean equation. Furthermore, a VAR 1 process is of high
enough order to eliminate autocorrelation in the means. Still, y
2
is significantly
t
autocorrelated. Thus, we continue by estimating the extended CCORR model for the VAR residuals.
4.2. Conditional coÕariance matrix A natural starting point for analyzing the implications on the covariance
structure of government bond returns of macroeconomic announcements is to examine the properties of the suggested covariance model without distinguishing
between announcement and non-announcement days. In so doing, we estimate an ordinary CCORR model, i.e. imposing the restriction that d s f
A
s f
y
s r
A
s 0
i i
i i j
for i, j s 1, . . . , 6 and i j. The results are shown in Table 4. Let us briefly comment on the results. For all maturities, the conditional variance processes are
very persistent, in that the sum of the GARCH parameters is large and close to unity, between 0.97 and 0.98. Still, robust Wald tests reject that any of the
Ž .
Ž processes evolve according to Integrated GARCH IGARCH specifications
p- .
values far below 1 . The Wald test is the preferable test statistic for IGARCH, Ž
. Ž
cf. Lumsdaine 1995 . Hence, the unconditional variance is given as s r 1 y f y
i i
. w . Moreover, due to the specification of the model, the conditional covariance
i
processes are also very persistent. All the ARCH and GARCH coefficients lie in the neighborhood of 0.03 and 0.94, respectively. The joint test that f and w are
i i
identical across maturities gives rise to a p-value of 29, which indicates that the persistence of the shocks to the volatility processes is maturity invariant. Yet, this
Ž finding does not apply for the AlevelB of the volatility processes, s
p-value
i
. below 1 .
In Table 5, we show the results from estimating the extended CCORR model Ž . Ž .
Ž . from Eqs. 3 , 5 and 7 . There are a number of compelling observations to be
made concerning the extended CCORR model and, consequently, we schedule our comments in the following order: firstly, the conditional variances, secondly the
conditional covariance structure and, finally, the correlation structure. The condi- tional variances are greater on announcement days by between 122 and 192.
The magnitude of the increase of the conditional volatility is somewhat larger than
Ž .
reported in Jones et al. 1998 . The level of the additional conditional variance on announcement days is decreasing as a function of the time to maturity of the bond.
Put differently, the reaction of short maturity bonds towards macroeconomic announcements seems to be stronger, in percentage terms, than the reaction of
long maturity bonds. This is what we would expect when the excess returns are mean reverting, because changes stemming from macroeconomic announcements
leave less time for recovering Aback to normalB before a short than a long maturity bond matures. What is more, we reject the preposition that the conditional
Ž variances increase by the same percentage on announcement days the p-value of
C. Christiansen
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of Empirical
Finance 7
2000 479
– 507
497 Table 4
Ordinary CCORR Model Ž
. Maturity year
2 3
5 7
10 30
Ž .
Ž .
Ž .
Ž .
Ž .
Ž .
s 0.000
0.000 0.001
0.000 0.002
0.000 0.003
0.001 0.005
0.001 0.009
0.002
i
Ž .
Ž .
Ž .
Ž .
Ž .
Ž .
f 0.036
0.005 0.035
0.005 0.033
0.004 0.039
0.004 0.034
0.004 0.027
0.004
i
Ž .
Ž .
Ž .
Ž .
Ž .
Ž .
w 0.933
0.011 0.936
0.010 0.939
0.009 0.942
0.007 0.938
0.007 0.952
0.006
i
Ž . Ž
. Ž
. Ž
. Ž
. Ž
. r
1.000 – 0.949
0.002 0.924
0.003 0.884
0.005 0.860
0.006 0.791
0.008
2yr, i
Ž . Ž
. Ž
. Ž
. Ž
. r
– 1.000 –
0.954 0.002
0.924 0.003
0.905 0.004
0.840 0.006
3yr, i
Ž . Ž
. Ž
. Ž
. r
– –
1.000 – 0.959
0.002 0.947
0.002 0.889
0.005
5yr, i
Ž . Ž
. Ž
. r
– –
– 1.000 –
0.975 0.001
0.930 0.003
7yr, i
Ž . Ž
. r
– –
– –
1.000 – 0.948
0.003
10yr, i
Ž . r
– –
– –
– 1.000 –
30yr, i
QML estimates of the ordinary CCORR model of the daily excess returns, R : R s m q ´ , where ´ is the vector of errors with mean 0 and conditional
t i t
i t i t
t 2
covariance matrix H . The diagonal elements of H : h s s q f ´
q w h . The off-diagonal elements of H : h
s r h
h , where i j.
t t
i i t i
i i ,ty1
i i i, ty1
t i j, t
i j i i , t
j j, t
Ž .
Bollerslev and Wooldridge 1992 robust standard errors in parenthesis.
C. Christiansen
r Journal
of Empirical
Finance 7
2000 479
– 507
498
Table 5 Extended CCORR model
Ž .
Maturity year 2
3 5
7 10
30 Ž
. Ž
. Ž
. Ž
. Ž
. Ž
. d
1.921 0.264
1.867 0.257
1.674 0.233
1.422 0.213
1.348 0.209
1.219 0.194
i
Ž .
Ž .
Ž .
Ž .
Ž .
Ž .
s 0.000
0.000 0.001
0.000 0.002
0.000 0.003
0.000 0.005
0.001 0.009
0.002
i
Ž .
Ž .
Ž .
Ž .
Ž .
Ž .
f 0.042
0.005 0.041
0.005 0.039
0.004 0.039
0.004 0.040
0.004 0.034
0.004
i A
Ž .
Ž .
Ž .
Ž .
Ž .
Ž .
f y0.033
0.015 y0.032
0.014 y0.055
0.013 y0.053
0.012 y0.056
0.012 y0.051
0.014
i y
Ž .
Ž .
Ž .
Ž .
Ž .
Ž .
f y0.003 0.016
y0.009 0.013 0.016 0.013
0.017 0.013 0.018 0.012
0.017 0.013
i
Ž .
Ž .
Ž .
Ž .
Ž .
Ž .
w 0.930
0.009 0.932
0.008 0.935
0.007 0.939
0.006 0.937
0.006 0.948
0.006
i
Ž . Ž
. Ž
. Ž
. Ž
. Ž
. r
1.000 – 0.939
0.003 0.912
0.004 0.871
0.005 0.847
0.006 0.776
0.009
2yr, i A
Ž .
Ž .
Ž .
Ž .
Ž .
r –
0.045 0.004
0.056 0.007
0.077 0.010
0.080 0.013
0.107 0.023
2yr, i
Ž . Ž
. Ž
. Ž
. Ž
. r
– 1.000 –
0.947 0.003
0.916 0.004
0.896 0.004
0.828 0.007
3yr, i A
Ž .
Ž .
Ž .
Ž .
r –
– 0.033
0.004 0.044
0.006 0.049
0.009 0.075
0.016
3yr, i
Ž . Ž
. Ž
. Ž
. r
– –
1.000 – 0.954
0.002 0.941
0.003 0.881
0.005
5yr, i A
Ž .
Ž .
Ž .
r –
– –
0.031 0.003
0.033 0.005
0.053 0.012
5yr, i
Ž . Ž
. Ž
. r
– –
– 1.000 –
0.971 0.001
0.924 0.003
7yr, i A
Ž .
Ž .
r –
– –
– 0.017
0.002 0.033
0.007
7yr, i
Ž . Ž
. r
– –
– –
1.000 – 0.945
0.003
10yr, i A
Ž .
r –
– –
– –
0.023 0.007
10yr, i A
A
QML estimates of the extended CCORR model of the daily excess returns, R : R s m q 1q d I ´ , where I is an announcement indicator function,
t i t
i t i t
i t t
Ž
A A y A
y
.
and ´ is the vector of errors with mean 0 and conditional covariance matrix H . The diagonal elements of H : h s s q f q f I
q f I I
´
i i
t t
t i i t
i ty1
i ty1 i, ty1
i, y
A A
Ž .
2
q w h , where I s1 if ´ - 0 and 0 else. The off-diagonal elements of H : h
s r 1q r I
h h
, where i j. Bollerslev and
ty 1 i
i i, ty1 i t
i t t
i j, t i j
i j t i i , t
j j, t
Ž .
Wooldridge 1992 robust standard errors in parenthesis. Indicates that the parameter is significantly different from zero at a 5 level.
Indicates that the parameter is significantly different from zero at a 1 level.
. H1 is well below 1, H1: d s PPP s d . Overall, this is in accordance with
1 6
Ž .
Fleming and Remolona 1999b who find that the reaction to macroeconomic announcements is strongest for the 2-year bond and, subsequently, declining for
Ž .
longer maturities. Counter intuitively, Christie-David and Chaudhry 1999 docu- ment that the effect of macroeconomic announcements on five different Treasury
futures is stronger the longer the time to maturity of the underlying contract. There is one important distinction to our analysis, however, namely that they compare
the level of the variances, whereas we compare the relative additions to the variances on announcement days.
Potential differences between positive and negative announcement shocks have our attention, i.e. H2: f
y
s PPP s f
y
s 0. In fact, we find no indications of
1 6
Ž differences in the persistency of positive and negative announcement shocks the
. p-value equals 44 . This is in stark contrast to the findings of Li and Engle
Ž .
Ž .
1998 concerning the futures market i.e. opposite the spot market for Treasury Ž
. Ž
. bonds, where negative positive announcement shocks increase decrease the
Ž .
subsequent volatility. Li and Engle 1998 explain the existence of the announce- ment leverage effect by the fact that investors take highly leveraged positions on
the futures market, which is not the case on the cash market. Thus, it is more likely to observe differences between positive and negative announcement shocks
on the futures market than on the cash market.
12
It is of interest whether the persistency of shocks is different on announcement days. The parameter estimates of f
A
are significantly negative, indicating that
i
announcement shocks are less persistent than other shocks. The fact that the persistency of announcement shocks do not tend to persist is taken as evidence
that announcement shocks do not cause the high degree of persistency observed in the government bond market. Furthermore, our findings suggest that the market
learns the implications of macroeconomic announcements quicker than other
Ž .
information. This reading is in accordance with Jones et al. 1998 and Li and Ž
. Engle 1998 . Still, we have merely considered two different types of macroeco-
nomic announcements and even though they are the most prominent announce- ments for the government bond market, other announcements are also influential.
Thus, it is not impossible, merely highly unlikely, that macroeconomic announce- ments cause the high degree of persistency observed in the government bond
market. The f
A
parameters are of about the same absolute size as the ARCH
i
parameters, which lead us to test the following simplifying preposition H3:
12
In order to look further into the differences between positive and negative announcement shocks, Ž .
and the differences between the cash and the futures markets, we estimate Eq. 5 as a univariate GARCH process for each of the series of VAR residuals. Still, we do not find any differences between
positive and negative announcement shocks. Hence, our result is not driven by us applying a multivariate model instead of a univariate model. Moreover, the conclusion is not altered, when we
Ž .
truncate our sample period to be roughly equivalent to the period studied in Li and Engle 1998 , namely 1989 to 1997.
f q f
A
s PPP s f q f
A
s 0. This hypothesis cannot be rejected, neither inde-
1 1
6 6
Ž .
Ž pendently
p-value of 20 nor jointly with the previous hypothesis H2 n H3: .
p-value of 94 . Considering the results of the ordinary CCORR model, there is yet another
simplification worth pursuing. Again, the ARCH and GARCH coefficients are Ž
statistically identical across maturities H4: f s PPP s f n w s PPP s w ,
1 6
1 6
. results in a p-value of 53 . This also holds when considered in conjunction with
Ž .
the previous non-rejected hypotheses H2 n H3 n H4 implies a p-value of 83 . Thus, the persistency of shocks to the conditional variance processes is statistically
indistinguishable for the maturities that we consider. As in the ordinary CCORR model, the volatility processes are highly persistent, but still we reject the
Ž propositions of IGARCH processes the p-value of H5 is far below 1, H5:
. f q w s PPP s f q w s 1 . Also, the magnitude of the ARCH and the
1 1
6 6
GARCH parameters are not altered. As we would expect, given the summary statistics, cf. Table 1, the intercept term of the conditional volatility equation is
increasing with the time to maturity, i.e. the level of the unconditional volatility is greater the longer the time to maturity. Invariantly, the s ’s are statistically
i
Ž .
different p-value far below 1 .
The conditional covariance of the excess returns for a given pair of government bonds is larger the shorter the time to maturity of either of the bonds, ceteris
paribus. Equivalently, this also applies for the additional conditional covariance on macroeconomic announcement days. To the author’s knowledge, this is the first
time it is documented that the conditional variance of a long portfolio of government bonds is unambiguously and substantially greater on macroeconomic
announcement days, because the addition to the conditional variance is not offset by a decrease in the conditional covariances. Thus, the increase of the conditional
covariances and variances on macroeconomic announcement days are of economic importance, and will potentially influence investor behavior in areas such as risk
management, asset allocation, and asset pricing, cf. the Introduction. It is empha- sized, that this inference is merely feasible in the context of a multivariate model.
Let us look at the correlation structure of the government bond excess returns. As expected, even for non-event days the correlations are very strong, and the
correlations are stronger the closer the two bonds are with respect to their time to maturity; the point estimates range between 0.78 and 0.97. The correlations are
greater on announcement days by between 1.7 and 10.7. Excitingly, the relative additions to the correlations on announcement days are greater the further
A
Ž
A
apart the maturities and the r ’s are not identical across maturities H6: r s
i j 12
A
. PPP s r
implies a p-value far below 1 . Indeed, on announcement days the
56
correlations of the government bond excess returns are close to being perfect and Ž
. independent of maturity the correlations range between 0.86 to 0.99 . Yet, this
Ž Ž
A
. Ž
conclusion does not hold in a strict statistical sense H7: r 1 q r
PPP s r 1
12 12
56 A
. Ž
A
. Ž
A
. q r
s 1 and H8: r 1 q r
s PPP s r 1 q r
both result in p-values
56 12
12 56
56
. well below 1 . Nevertheless, on announcement days, the correlation is weaker
the further apart the maturities, but the decline is tremendously dampened com- pared to non-announcement days. According to the simple multivariate model, the
correlation coefficients are greater by 1.6 on announcement days, which indi- cates that the simple multivariate model vastly underestimates the strength of the
comovement of the government bond market.
To further illustrate that macroeconomic announcements induce a common movement in the government bond market, we compare the largest eigenvalues of
the correlation matrixes applicable for announcement and non-announcement days, respectively. This investigation resembles the principal components analysis con-
ducted on the term structure of interest rates, cf. e.g. Litterman and Scheinkman Ž
. 1991 . The sum of the eigenvalues is equal to the number of different maturities,
so we do not run into any scaling problems. Moreover, in the CCORR model, the unconditional and the conditional correlation matrix are identical. The proportion
of variation in the correlation matrix explained by the most important factor underlying the correlation structure is equal to the greatest eigenvalue divided by
the sum of the eigenvalues and, thus, the greater the largest eigenvalue, the more important is the most important common factor underlying the correlation struc-
ture. For non-announcement days, the most important factor explains 92 of the variation of the correlation structure, whereas the figure is 96 for announcement
days. This supports the interpretation that macroeconomic announcements induce a common movement in the correlation structure of government bond returns.
To sum up, we test the model down to the following specification, denoted the restricted CCORR model: f
y
s PPP s f
y
s 0 n f q f
A
s PPP s f q f
A
s
1 6
1 1
6 6
0 n f s PPP s f n w s PPP s w . For completeness, the results from esti-
1 6
1 6
mating the restricted CCORR model are provided in Table 6. We notice, that the parameters hardly change when going from the extended to the restricted CCORR
model, which lends support to the imposed restrictions. Besides, all of the above rejected hypotheses are also rejected in the restricted CCORR model.
We check the adequacy of the model specification in a number of ways. Firstly, we conduct diagnostic tests of the standardized residuals of the restricted CCORR
Ž .
model; in particular, we consider possible deviations from the NIID 0,1 case with Ž
respect to mean, standard deviation, excess kurtosis, skewness, autocorrelation up .
Ž .
to fifth order , autocorrelation of squared residuals up to fifth order , autocorrela- Ž
. tion of cross multiplied residuals up to fifth order , and remaining ARCH effects
Ž .
up to fifth order . At a 1 level of significance, the only serious problem that we discover is that the time series exhibit leptokurtosis, and a minor concern is that
the cross multiplied residuals of the 3- and 10-year bonds and the 5- and the Ž
. 10-year bonds are autocorrelated the p-values equal 0.6 and 0.9, respectively .
In passing, the diagnostic tests are qualitatively identical for the ordinary, the extended and the restricted CCORR specification. Secondly, potential parameters
instability as well as omitted variables are investigated. To this end, the following indicator functions are introduced: weekday indicator functions and another one
which divides the sample into two equally sized subperiods. Due to the number of
C. Christiansen
r Journal
of Empirical
Finance 7
2000 479
– 507
502
Table 6 Restricted CCORR model
Ž .
Maturity year 2
3 5
7 10
30 Ž
. Ž
. Ž
. Ž
. Ž
. Ž
. d
1.915 0.261
1.868 0.254
1.685 0.232
1.436 0.212
1.363 0.207
1.233 0.193
i
Ž .
Ž .
Ž .
Ž .
Ž .
Ž .
s 0.000
0.000 0.001
0.000 0.002
0.000 0.003
0.000 0.005
0.001 0.011
0.002
i
Ž .
f 0.038
0.005 Ž
. w
0.939 0.009
Ž . Ž
. Ž
. Ž
. Ž
. Ž
. r
1.000 – 0.939
0.003 0.912
0.004 0.871
0.006 0.847
0.006 0.776
0.009
2yr, i A
Ž .
Ž .
Ž .
Ž .
Ž .
r –
0.045 0.004
0.056 0.006
0.078 0.010
0.081 0.013
0.108 0.023
2yr, i
Ž . Ž
. Ž
. Ž
. Ž
. r
– 1.000 –
0.947 0.003
0.916 0.004
0.896 0.004
0.828 0.007
3yr, i A
Ž .
Ž .
Ž .
Ž .
r –
– 0.033
0.004 0.045
0.006 0.049
0.009 0.076
0.016
3yr, i
Ž . Ž
. Ž
. Ž
. r
– –
1.000 – 0.954
0.002 0.941
0.003 0.881
0.005
5yr, i A
Ž .
Ž .
Ž .
r –
– –
0.031 0.003
0.034 0.005
0.053 0.011
5yr, i
Ž . Ž
. Ž
. r
– –
– 1.000 –
0.971 0.002
0.924 0.003
7yr, i A
Ž .
Ž .
r –
– –
– 0.017
0.002 0.034
0.007
7yr, i
Ž . Ž
. r
– –
– –
1.000 – 0.945
0.003
10yr, i A
Ž .
r –
– –
– –
0.023 0.007
10yr, i A
A
QML estimates of the restricted CCORR model of the daily excess returns, R : R s m q 1q d I ´ , where I is an announcement indicator function, and
t i t
i t t
i t t
Ž
A
.
2
´ is the vector of errors with mean 0 and conditional covariance matrix H . The diagonal elements of H : h s s q f 1y I ´
q h . The
t t
t i i t
i ty1
i, ty1 i i, ty1
A A
Ž .
Ž .
off-diagonal elements of H : h s r
1q r I h
h , where i j. Bollerslev and Wooldridge 1992 robust standard errors in parenthesis.
t i j, t
i j i j t
i i , t j j, t
Indicates that the parameter is significantly different from zero at a 1 level.
parameters in the restricted CCORR model, it is impractical to make a formal test for the preposition that all the parameters are identical in the two subperiods as
well as on the different days of the week. As an alternative, we proceed by looking into the model applicability by regressing the standardized residuals on a number
of explanatory variables; the dummy variables listed above and the announcement
Ž .
indicator function lagged, contemporary and leaded . If the model is well
Ž .
specified, all the coefficients including the intercept are insignificantly different from zero. Individually, in merely one out of 36 cases is this violated, and robust
Wald tests of the joint significance of the explanatory variables imply p-values of 2.3, 0.2, 2.0, 6.9, 7.1, and 13.2, respectively, for each of the standard-
ized residual series. This is a borderline case, which indicates that there are weak signs of misspecification. Yet, the parameters seem to be time invariant and the
day of the week appears not to be an omitted variable. As a whole, the restricted CCORR model appears to be well specified.
What is more, our findings appear to be robust to model choice. A previous draft of this paper applied the factor-ARCH model where the first and the second
principal components were assumed to capture the variation of the unknown systematic risk factors. The factor-ARCH model was extended to allow for
macroeconomic announcement effects in a fashion closely resembling the exten- tion of the CCORR model presented here. In contrast to the CCORR model, the
principal components factor-ARCH model is not well founded, neither statistically nor economically, which is the reason why we have abandoned its use. Still, these
two multivariate heteroscedastic models give rise to quantitatively identical results concerning the impact of macroeconomic announcements on the covariance
structure of government bond returns, which corroborates that the empirical findings are invariant to the exact model specification.
Let us briefly outline our findings regarding the conditional covariance struc- ture of the government bond returns.
v
The conditional variance is greater on macroeconomic announcement days, and the addition is of economic importance and is a decreasing function of the
time to maturity of the bond. The conditional variance is highly persistent and there are neither any statistical differences between positive and negative an-
nouncement shocks nor are there persistency differences across different maturi- ties. Announcement shocks appear not to be persist and the information related to
announcements are incorporated faster by the market than other kinds of informa- tion.
v
The conditional covariance of government bonds is positive, and substantially greater on macroeconomic announcement days. The addition to the conditional
covariance of government bonds with different maturities is decreasing with the time to maturity of either of the bonds.
v
The government bond excess returns are strongly correlated, and the correla- tion is greater the closer the bonds are with respect to the time to maturity. In
contrast, the increase in the correlation on announcement days is greater the
further apart the bonds are with respect to the time to maturity. This implies that the government bond market is closer to being perfectly correlated on announce-
ment days than on other days, and that the correlation coefficients are less maturity dependent on announcement days.
Referring back to the Introduction, although we do not explicitly consider returns of zero-coupon bonds, this is also a study of the impact of macroeconomic
announcements on the term structure of interest rates. Accordingly, let us compare our findings to those of the literature of the term structure of interest rates. By
Ž .
Ž .
applying a one-factor path dependent Heath et al. 1992 model, Jeffrey 1998 finds that the forward rate volatility depends nonlinearly on the time to maturity as
well as the level of the term structure of interest rates. We are able to confirm his findings in that the processes for the conditional volatility are not statistically
identical for the various maturities even though the persistency appears to be maturity invariant. In particular, this also holds for the addition to the conditional
variance induced by macroeconomic announcements. Also, by nature, any GARCH type model implies that the level of the conditional variance depends on the
current state of the term structure via the squared residuals. Litterman and
Ž .
Ž .
Scheinkman 1991 and Chen and Scott 1993 document that the term structure of interest rates can be described by at least two factors. We find that macroeconomic
announcement effects are not identical across all maturities, neither with respect to the conditional variance nor with respect to the conditional covariance, and
correlation. Still, macroeconomic announcements induce a common movement in the government bond market, which is in accordance with a model for the term
structure of interest rates that includes fewer factors than different maturities and,
Ž .
Ž .
thus, the findings of Litterman and Scheinkman 1991 and Chen and Scott 1993 , with the reservation that we have merely analyzed the arrival of a subset of the
public information available to government bond investors. Fleming and Re- Ž
. molona 1999b study the impact of macroeconomic announcements on the term
structure by applying a two-factor homoscedastic affine yield model. They focus Ž
. their attention on the impacts on the first moment i.e. the mean and find that the
announcement effects are strongest for medium term bonds. In contrast, our major concern is the impacts on the covariance structure and, in addition, we find that
there are hardly any reactions in the mean with respect to macroeconomic announcements.
5. Conclusion
