impact on the term structure of interest rates of macroeconomic announcements. Conveniently, the literature of the empirical properties of the term structure of
interest rates provides a basis for comparison, cf. e.g. Litterman and Scheinkman Ž
. Ž
. Ž
. 1991 , Chen and Scott 1993 , and Jeffrey 1998 . Moreover, this perspective
Ž .
links our work to Fleming and Remolona 1999b . Above, it is established that there is a strong relation between releases of
employment and PPI figures and the government bond market. These macroeco- Ž
. nomic announcements are released periodically monthly on pre-announced dates
and, hence, they are not clustered in time. Furthermore, the contents of the reports are instantaneously available to all market participants. Consequently, in the
following, we investigate the effect of these announcements in a heteroscedastic multivariate model of the excess returns of six government bonds with different
maturities. More specifically, by extending the Constant Conditional Correlations Ž
. Ž
. CCORR
model of Bollerslev 1990
to include announcement effects, we document that the conditional variances, covariances, and correlations of bond
excess returns are significantly larger on macroeconomic announcement days. The excess returns of the government bond market are strongly correlated and the
correlation is stronger the closer the bonds are with respect to the time to maturity. The maturity dependency is substantially dampened on announcement days, which
implies that releases of macroeconomic news induce common movements in the government bond market. The rise on macroeconomic announcement days in the
conditional covariance of two government bonds is of economic importance and is an decreasing function of the time to maturity of either of the bonds. Similarly, the
addition to the conditional variance on macroeconomic announcement days is substantial and is a decreasing function of the time to maturity of the bond. It
appears that announcement shocks do not persist at all and that the information related to announcements are incorporated faster by the market than other kinds of
information. The conditional variance is highly persistent and there are not any statistical differences between positive and negative announcement shocks. Like-
wise, the persistency of the conditional volatility seems to be identical across bonds of different maturities.
The outline of this paper is as follows. In Section 2, the data as well as some preliminary results are presented. Subsequently, the multivariate model of the
bond excess returns is set up in Section 3, which is followed by the empirical results in Section 4. Finally, concluding remarks are found in Section 5.
2. The data
2.1. Bond returns and announcement days The return series being examined are the daily excess returns of 2-, 3-, 5-, 7-,
10-, and 30-year U.S. Treasury bonds. The excess return is defined as the return of
holding the bond in excess of the risk-free spot rate, which by assumption is equal to the 3-month Treasury bill rate. Ideally, we would apply an overnight risk-free
interest rate, but unfortunately, we would then have to use interest rates from the money market, i.e. LIBOR rates, whereby we incur other kinds of problems. As a
result, we stick to the 3-month Treasury rate. The data cover the period January 1, 1983 to December 31, 1998, providing a total of 3999 observations. Hence, the
analysis covers the period after the so called Monetary Experiment of the U.S. Federal Reserve. From October 1979 to late 1982, the Federal Reserve targeted the
quantity of reserves and, in particular, the stock of M1 money. In contrast, following the Monetary Experiment, the Federal Reserve returned to targeting the
Ž .
level of interest rates. Previous studies, e.g. Jeffrey 1998 , have provided evi- dence of a structural break in the term structure of interest rates related to the
change in monetary policy. The returns from holding the bonds are calculated from the Federal Reserve’s
Adaily constant maturity interest rateB series, in the same manner as Jones et al. Ž
. 1998 . The constant maturity yields are interpolated by the U.S. Treasury from
the daily yield curve, which is based on the closing bid yields of actively traded Treasury securities in the secondary market.
2
The macroeconomic announcements included in the present study are the Employment Situation Report and the PPI Report published by the Bureau of
Labor Statistics. There are 188 announcements of Employment Reports and PPI statistics, which implies a total of 376 different announcement days. The PPI and
the employment reports are released monthly, and always at 8:30 AM EST.
The two types of macroeconomic announcements considered in this paper are Ž
. chosen for a couple of reasons. Firstly, in a recent study, Balduzzi et al. 1997
investigate the impacts of 27 different types of economic announcements on the price changes of Treasury bond prices. Their study shows that the most important
types of macroeconomic announcements for changes in, e.g. the 10-year bond price are the Employment Situation Report and the PPI Report. Secondly, these
types of macroeconomic news are released periodically on pre-announced dates and are, thus, serially uncorrelated. Finally, the empirical analysis is comparable to
Ž .
3
Jones et al. 1998 . 2.2. Preliminary analysis
Before we turn to the estimation of a multivariate model, we take a quick look at the sample moments of the data. Table 1 includes summary statistics for the
2
The daily excess returns of the 5-, 10-, and 30-year bonds of the period 1983 to 1995 have been downloaded from Owen Lamont’s home page at the University of Chicago. The remaining returns have
been downloaded from the home page of the Federal Reserve Bank of Chicago.
3
Ž .
Ž .
The study in Jones et al. 1998 is limited to three different maturities, 5, 10, and 30 year and the Ž
. data cover an earlier time period October 1979 to December 1995 .
Table 1 Summary statistics: treasury bond excess returns
Ž .
Panel A: Full sample 3999 observations Ž
. Maturity year
Mean Std. Dev.
Minimum Maximum
2 0.007
0.128 y0.655
1.527 3
0.009 0.188
y1.060 2.058
5 0.012
0.290 y1.730
3.010 7
0.016 0.373
y2.260 3.914
10 0.018
0.459 y2.780
4.690 30
0.025 0.674
y3.890 7.250
Ž .
Covariance year 2
3 5
7 10
30 Correlation year
2 0.016
0.023 0.034
0.042 0.051
0.068 3
0.947 0.035
0.052 0.065
0.078 0.106
5 0.922
0.954 0.084
0.104 0.126
0.173 7
0.884 0.924
0.958 0.139
0.167 0.233
10 0.860
0.904 0.946
0.974 0.211
0.292 30
0.786 0.835
0.884 0.926
0.945 0.455
Ž .
Panel B: Announcement days 376 observations Ž
. Maturity year
Mean Std. Dev.
Minimum Maximum
2 0.021
0.198 y0.655
0.585 3
0.029 0.289
y0.949 0.910
5 0.046
0.435 y1.446
1.310 7
0.045 0.535
y1.788 1.869
10 0.057
0.652 y2.479
2.430 30
0.091 0.926
y3.082 3.040
Ž .
Covariance year 2
3 5
7 10
30 Correlation year
2 0.039
0.056 0.083
0.099 0.117
0.155 3
0.980 0.083
0.123 0.148
0.177 0.236
5 0.961
0.978 0.189
0.228 0.275
0.370 7
0.935 0.957
0.982 0.287
0.345 0.470
10 0.910
0.940 0.970
0.988 0.426
0.581 30
0.849 0.884
0.919 0.949
0.961 0.857
Ž .
Panel C: Non-announcement days 3623 observations Ž
. Maturity year
Mean Std. Dev.
Minimum Maximum
2 0.006
0.118 y0.655
1.527 3
0.007 0.174
y1.060 2.058
5 0.009
0.270 y1.730
3.010 7
0.013 0.352
y2.260 3.914
10 0.014
0.434 y2.780
4.690 30
0.018 0.642
y3.890 7.250
Ž .
Table 1 continued Ž
. Panel C: Non-announcement days 3623 observations
Ž .
Covariance year 2
3 5
7 10
30 Correlation year
2 0.014
0.019 0.029
0.036 0.044
0.059 3
0.937 0.030
0.045 0.056
0.068 0.092
5 0.911
0.947 0.073
0.090 0.110
0.152 7
0.871 0.916
0.952 0.124
0.148 0.208
10 0.848
0.896 0.940
0.971 0.188
0.262 30
0.772 0.824
0.877 0.921
0.941 0.413
Ž .
Summary statistics for treasury bond excess returns in , i.e. scaled by 100 for the period January 1, 1983 to December 31, 1998. Announcement days denote days in the sample period when the Bureau of
Labor Statistics published Employment Situation reports or PPI statistics. Numbers in italic are the correlation coefficients.
bond excess returns. Apart from considering the full sample, the observations have been grouped into announcement and non-announcement days.
4
It is evident, that the average excess returns are larger on announcement days for all maturities. The sample mean of the excess returns for the different
maturities on announcement days are between 0.021 and 0.091 whereas on non-announcement days the averages range between 0.006 and 0.018.
5
For all the breakdowns of the data, the average excess returns increase with time to
maturity. As the variances and covariances on announcement days are greater than those
on non-announcement days, we conduct a joint test for the null hypotheses that the means and the covariance matrixes are identical in the two subsamples, cf. Kai-Tai
Ž .
2
Ž .
and Yao-Ting 1990, Section 5.3 . The resulting x 21 test statistic is highly
significant; however, because it is a joint test, subhypothesis might be acceptable. Hence, we test the null hypothesis that the covariance matrices are identical but
without making any assumptions on the means. Notwithstanding, the test statistic leads to rejection of the hypothesis. Thus, we conclude that the covariance matrix
applicable for announcement days is significantly different from the one applicable for non-announcement days. It is remarked, that the underlying assumptions, e.g.
homoscedasticity, for these test statistics are probably not fulfilled.
4
Ž .
Following Jones et al. 1998 , no distinction is made between the employment and PPI announce- ments and the empirical estimation in Section 4 is also based on this assumption. Furthermore, Li and
Ž .
Engle 1998 found that there are no report specific effects for the conditional volatility on Treasury bond futures.
5
It is extremely difficult to test whether the mean vectors in two subsamples are identical without Ž
. assuming identical covariance matrixes, cf. Kai-Tai and Yao-Ting 1990, Section 5.2 .
C. Christiansen
r Journal
of Empirical
Finance 7
2000 479
– 507
486
Table 2 Simple multivariate model
Ž .
Maturity year 2
3 5
7 10
30 Ž
. Ž
. Ž
. Ž
. Ž
. Ž
. Q
0.006 0.002
0.015 0.003
0.009 0.004
0.013 0.006
0.014 0.007
0.018 0.011
Ž .
Ž .
Ž .
Ž .
Ž .
Ž .
Q 0.015 0.010
0.022 0.015 0.037 0.023
0.032 0.028 0.044 0.034
0.074 0.049
1
Ž .
d 0.772
0.104
v
Ž .
d 0.800
0.102
c
The table reports the results from estimating the following simple multivariate model for the excess returns R : R sQ qQ I
A
q ´ , where Q , and Q are
t t
1 t t
1
parameter vectors and, I
A
is an announcement day indicator function. ´ is the vector of error terms which have mean zero and conditional variance H ;
t t
t
Ž
A
. H
s H 1q d I
, where d s d if i j and d if is j, and H is a matrix of constants. Estimates of H are not reported. White’s standard errors in
i j, t 0, i j
i j t i j
c v
parenthesis. Indicates that the parameter is significantly different from zero at a 10 level.
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.
As we would expect, the correlation coefficients of the excess returns are remarkably high. For the full sample, the correlation coefficients range between
0.79 and 0.97. On announcement days, all correlation coefficients are larger than for the full sample; the opposite is the case for non-announcement days.
As a first assessment of the macroeconomic announcement effects on the covariance structure of government bond returns, we suggest a simple multivariate
model. Let R denote the vector of excess returns at time t:
t
R s Q q Q I
A
q ´ , 1
Ž .
t 1 t
t
where Q , and Q are parameter vectors and, I
A
is an announcement day
1 t
indicator function. ´ is the vector of normally distributed error terms, which have
t
mean zero and conditional covariance H :
t
H s H
1 q d I
A
, 2
Ž .
Ž .
i j, t 0 , i j
i j t
where d s d if i j and d
if i s j, and H is a matrix of constants. The
i j c
v
simple model implies that the conditional mean vector is greater by Q on
1
announcement days, i.e. the means do not necessarily shift in a parallel manner on Ž
. announcement days. In contrast, we assume that all the variances covariances
Ž .
increase by the same percentage on announcement days, namely by d d .
v c
The results from estimating the simple model are provided in Table 2.
6
Neither of the elements of Q
are significantly different from zero, which is supported by
1
Ž .
the joint test the p-value equals 6.4 . Surprisingly, there is no indication that investors are compensated by higher excess returns on announcement days for the
additional uncertainty related to releases of macroeconomic news. What is more interesting, from our perspective, is the fact that the variances
Ž .
Ž .
covariances are significantly greater on announcement days by 77 80 . Consequently, the correlations are 1.6 greater on announcement days than on
ordinary days. In order to validate the simple multivariate model, we analyze the standardized
Ž .
residuals, ´ r h , which are NIID 0,1 when the model is well specified. The
i t i i t
squared standardized residuals as well as the cross multiplied standardized residu-
6
The estimation is conducted in GAUSS using the GAUSS module Constrained Maximum Likelihood and a combination of the Berndt–Hall–Hall–Hausman and the Newton–Raphson maxi-
mization algorithm. The model is estimated by applying a Gaussian likelihood function where H is concentrated out and is replaced by the covariance matrix applicable for non-announcement days. A
Ž . two-step procedure is applied: Firstly, we run the regression in 1 and hereby calculate ´ . Secondly,
ˆ
t
Ž . we apply ´ to estimate Eq. 2 . No ex ante restrictions are imposed to ensure positive definiteness, it is
ˆ
t
merely checked ex post.
C. Christiansen
r Journal
of Empirical
Finance 7
2000 479
– 507
488
Ž .
Ž .
Fig. 1. Daily excess returns of 3- and 10-year bond. Panel A: Daily excess returns in of the 3-year bond. Panel B: Daily excess returns in of the 10-year bond. The unit of measurement on the x-axes is trading days elapsed since January 1, 1983.
Ž. Fig.
1 continued
.
als appear to be significantly autocorrelated. Moreover, the Lagrange Multiplier Ž
. LM test documents that ARCH is present in the standardized residuals. Overall,
our findings imply that the simple multivariate model does not address the issue of heteroscedasticity adequately, which points towards a heteroscedastic model, e.g. a
multivariate GARCH model. Another benefit of employing the more involved multivariate GARCH specification is that it will enable us to look further into the
persistency of the announcement shocks.
For illustrative purposes, the properties of the daily excess returns of the 3- and 10-year bonds are shown graphically in Fig. 1. The graphs also suggest that a
model including heteroscedasticity is required to describe the evolution of the bond excess returns as there are signs of volatility clustering. Setting up the
multivariate GARCH model is the subject of the following section.
3. The multivariate model
