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Macroeconomic announcement effects on the
covariance structure of government bond returns
Charlotte Christiansen
)Department of Finance, The Aarhus School of Business, Fuglesangs Alle 4, DK-8210 Aarhus V, Denmark
Accepted 6 November 2000
Abstract
This paper concerns the effects of macroeconomic announcements on the covariance structure of US government bond returns for six different maturities; the study shows that the conditional variances, covariances, and correlation coefficients are significantly greater on announcement days. On non-announcement days, the correlation coefficients are rela-tively large and are greater the closer the bonds are with respect to the time to maturity. The maturity dependency is substantially dampened on announcement days and, hence, releases of macroeconomic news induce common movement in the government bond market that
strengthen the correlations.q2000 Elsevier Science B.V. All rights reserved.
JEL classification: G12; C32
Keywords: Constant conditional correlations model; Covariance; Government bonds; Macroeconomic announcements; Multivariate GARCH
1. Introduction
This paper assesses the impact of macroeconomic news releases on the U.S. government bond market. In particular, we study the effects that releases of the
Ž .
Employment Situation and the PPI Producer Price Index reports, published by the Bureau of Labor Statistics, have on the conditional covariance structure of excess bond returns for six different maturities.
)Tel.:q45-8948-6691; fax:q45-8615-1943.
Ž .
E-mail address: [email protected] C. Christiansen .
0927-5398r00r$ - see front matterq2000 Elsevier Science B.V. All rights reserved.
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( ) C. ChristiansenrJournal of Empirical Finance 7 2000 479–507 480
Contrary to stocks and corporate bonds, there is hardly any asset-specific or private information regarding Treasury bonds. Instead, changes in government bond returns depend on the arrival of public information, e.g. macroeconomic variables such as the inflation and the real interest rate, and the fiscal and monetary policy conducted. Accordingly, macroeconomic announcements affect the Treasury bond market. It is well known that the return volatility of financial assets, including bonds, are autocorrelated and highly persistent over time, for a
Ž .
review, cf. Bollerslev et al. 1992 . Hence, it has been suggested that the
announcements of macroeconomic news could explain the observed high degree of volatility persistence on the government bond market.
A number of empirical studies have been undertaken in the finance literature to examine the implications of macroeconomic announcements on the government bond market in a wide range of setups. Below is a brief and, by no means,
Ž .
exhaustive survey of this literature. Jones et al. 1998 study the effects of
announcements of employment and PPI figures on the conditional volatility of the excess returns of three different U.S. government bonds using daily data. The conditional variance is assumed to evolve according to a univariate Generalized
Ž .
Autoregressive Conditional Heteroscedasticity GARCH process, which is ex-tended to include level as well as persistence differences on announcement and non-announcement days. The results show that announcement shocks are not persistent and that the conditional variance is significantly higher on announce-ment days.
Ž . Ž .
In a framework similar to Jones et al. 1998 , Li and Engle 1998 study the
Ž
effects of macroeconomic announcements Consumer Price Index, PPI, and
Em-.
ployment situation reports on the volatility of the U.S. Treasury bond futures. Using a univariate GARCH framework, they find that announcement shocks are not persistent, that positive and negative announcement shocks are significantly different, and that persistence is stronger after bad news is released than after good
Ž .
news. Li and Engle 1998 do not discover significant increases in the returns on
Ž .
announcement days i.e. there is no risk premium for macroeconomic news . In a series of papers, Fleming and Remolona investigate macroeconomic
Ž
announcement effects on the Treasury market. Fleming and Remolona 1997,
.
1999a apply 1 year of intra daily data on the 5-year Treasury note and they find that the largest changes in price and trading volume stem from macroeconomic announcements. Moreover, the most influential announcements are the employ-ment and the PPI reports. The unexpected component of the announceemploy-ment is of importance for the reaction of the bond market. Immediately after macroeconomic announcements, the bond price changes sharply and the trading volume declines. Subsequently, there is a surge in trading activity and a high level of price volatility
Ž .
tends to persist. Using a longer sample, Fleming and Remolona 1999b estimate a homoscedastic affine model of yield changes using announcement surprises as
Ž .
Ž .
Balduzzi et al. 1997 investigate the impact of 27 different economic news announcements on the bond market using intra day data. In their paper, the surprise components of macroeconomic announcements are considered, where expectations of the variables are taken from surveys of money market managers. For price reactions of the 10-year Treasury note, the most important announcement
Ž .
is the Non-farm Payroll which is published in the Employment Situation report , and the second most important variable is the PPI figure. The paper shows that
trading volume and volatility are significantly higher following AimportantB
economic announcements.
Ž .
Ederington and Lee 1993 explore the impacts of 19 different announcements on the futures markets of Treasury bonds. Amongst others, the employment figure and PPI cause significant price changes. In addition, the paper concludes that the day-of-the-week effects are caused solely by the timing of macroeconomic news releases.
To the author’s knowledge, so far, no methodical studies have examined the effects of macroeconomic announcements on the covariance structure of govern-ment bond returns. Thus, the aim of this paper is to represent an improvegovern-ment of
Ž .
the univariate analysis of responses to risk i.e. releases of macroeconomic news ,
Ž .
which, according to Jones et al. 1998, p. 335 , is a potential limitation of the existing literature. In many fields of finance, is it paramount to apply a multivari-ate model of the distribution of asset returns. These areas include risk manage-ment, asset allocation, and asset pricing. A number of examples will further illustrate why it is interesting to study the implications of macroeconomic an-nouncements on the covariance structure of government bonds: A commercial bank’s capital requirement is determined by its Value-at-Risk, which again is calculated using the covariance matrix of the assets in its portfolio. Hence, macroeconomic announcement effects on the covariance structure of government bonds influence the capital requirements of a commercial bank holding govern-ment bonds. Consider another example, namely the portfolio choice of an investor: The investor’s optimal portfolio composition depends on the covariance of the assets in question. Thus, macroeconomic announcement effects on the covariance structure of government bonds might alter the optimal weights of the investor’s
Ž .
portfolio. Lastly, the value of a derivative contract e.g. a spread option with two
Žor more different government bonds as its underlying is altered by macroeco-.
nomic announcement effects on the covariance structure of bond returns.
A further reason why it is valuable to apply a multivariate framework in the
present analysis, is as follows.1 Even though we do not explicitly consider
zero-coupon bonds, our study of government bonds of different maturities is essentially also a study of the term structure of interest rates. Consequently, by applying a multivariate model, we are able to draw conclusions with respect to the
1
( ) C. ChristiansenrJournal of Empirical Finance 7 2000 479–507 482
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
Ž1991 , Chen and Scott 1993 , and Jeffrey 1998 . Moreover, this perspective. Ž . Ž .
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
ŽCCORR. model of Bollerslev Ž1990. 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
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.
Ž1998 . 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
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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
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
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
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%.5For 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
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Table 2
Simple multivariate model
Ž .
Maturity year 2 3 5 7 10 30
) ) )Ž . ) )Ž . )Ž . ) )Ž . )Ž . )Ž .
Q0 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 .
Q1 0.015 0.010 0.022 0.015 0.037 0.023 0.032 0.028 0.044 0.034 0.074 0.049
) ) )Ž .
dv 0.772 0.104
) ) )Ž .
dc 0.800 0.102
The table reports the results from estimating the following simple multivariate model for the excess returns R : R sQ qQ IAq´, whereQ , andQ are
t t 0 1 t t 0 1
parameter vectors and, IA 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.
Hi j, tsH0, i j1qdi j tI , wheredi jsdc if i/j anddv if isj, and H is a matrix of constants. Estimates of H are not reported. White’s standard errors in0 0
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.
) ) )
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
RtsQ0qQ1 tIAq´t,
Ž .
1where Q , and Q are parameter vectors and, IA is an announcement day
0 1 t
indicator function. ´t is the vector of normally distributed error terms, which have
mean zero and conditional covariance H :t
H sH
Ž
1qd IA.
,Ž .
2i j, t 0 , i j i j t
where di jsdc if i/j and dv if isj, and H0 is a matrix of constants. The
simple model implies that the conditional mean vector is greater by Q1 on
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 bydv dc .
The results from estimating the simple model are provided in Table 2.6 Neither
of the elements ofQ1 are significantly different from zero, which is supported by
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
Žcovariances are significantly greater on announcement days by 77% 80% .. Ž .
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, ´i tr hi i t, which are NIID 0,1 when the model is well specified. The
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 is0 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´ˆt. Secondly,
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Ž . Ž .
Ž.
Fig.
1
continued
( ) C. ChristiansenrJournal of Empirical Finance 7 2000 479–507 490
als appear to be significantly autocorrelated. Moreover, the Lagrange Multiplier
ŽLM 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
In the previous section, we have found evidence that any potential multivariate model of the announcement effects of the covariance structure of the government bond returns should allow for heteroscedasticity. Consequently, we suggest to apply a multivariate GARCH model. No specific multivariate GARCH specifica-tion is always preferred above all other specificaspecifica-tions and, apart from Kroner and
Ž .
Ng 1998 , there are hardly any comparative studies of multivariate GARCH models. Hence, it remains to decide which particular multivariate GARCH model to use, and to this end, we list our model choice criteria: Firstly, the total number of parameters must be kept at a minimum, which is even more important here because we introduce additional parameters to account for the announcements. Secondly, the model must guarantee that the conditional covariance matrix is positive definite. Thirdly, the model must be formulated such that we can make interesting conclusions as to the impacts of macroeconomic announcements on the covariance structure.
The limitation that the number of parameters should be fairly small restricts the
Ž .
available alternatives to the diagonal BEKK model, cf. Bollerslev et al. 1988 , the
Ž . Ž .
Constant Conditional Correlations model CCORR , cf. Bollerslev 1990 and the
Ž .
Factor-ARCH model, cf. Engle et al. 1990 . We assume that the reader is familiar with these models. It is not a straightforward problem which factors to apply in the factor ARCH-model, and there is no consensus as to how to define these. Hence,
we remove this specification from our shortlist.7
7
The main objection to the CCORR model is that large simultaneous shocks of opposite signs to two assets increase their conditional covariance. This objection is weakened by the fact that it is not likely that large positive and large negative shocks occur simultaneously for bonds of different maturities. The disadvantage of the diagonal BEKK model is that it still involves many parameters compared to
Ž Ž .
the CCORR model. In fact, in the simplest setup GARCH 1,1 and no
announce-.
ment effects , there are 108 parameters in the diagonal BEKK model, compared to 33 in the CCORR model. Both the CCORR model and the diagonal BEKK model,
Ž .
appropriately extended, meet the third criterion. Moreover, Jeffrey 1998
docu-Ž .
ments that the forward rate volatility and, thus, the interest rate volatility varies with the maturity, this feature is also accommodated by both specifications.
The above indicates that we might prefer the CCORR model extended to accommodate various differences between announcement and non-announcement days. In the CCORR model, the conditional variances evolve according to GARCH processes. The conditional correlations are assumed to be constant, which explains the phrase CCORR. Furthermore, the conditional covariances are propor-tional to the product of the corresponding volatilities.
The details of how the CCORR model is extended to accommodate announce-ment effects is presented in Section 3.2, but first the specification of the condi-tional mean equation is put forward in Section 3.1.
3.1. Conditional means
We consider the excess returns of N different government bonds, Ri t for is1,
. . . , N, and the conditional mean vector of R is denotedt mt:
A
(
Ri tsmi tq 1qdi tI ´i t,
Ž .
3where ´t is the vector of error terms and ItA is an indicator function for
Ž
announcement days we will return to a discussion of the parameterdi as well as
.
the distribution of ´t in the following section . When modeling mt we have to
ensure that the error terms are serially uncorrelated. Because our main interest lies in how the conditional covariance matrix evolves over time, we make the
simplifying assumption that Rt evolves according to a vector autoregressive
Ž Ž ..
process of order one VAR 1 where a level effect for announcement days is
included, that is:
m'F qF R qFAIA.
Ž .
4t 0 1 tI1 t
F andFA are N
=1 vectors, andF is an N=N matrix. The conditional mean
0 1
Ž . Ž .
specification is in line with Jones et al. 1998 who consider an AR 1 process
Ž .
combined with a level effect for announcement days, i.e. Eq. 4 where F1 is
( ) C. ChristiansenrJournal of Empirical Finance 7 2000 479–507 492
3.2. Conditional coÕariance matrix
In this section, we describe how the conditional covariance matrix evolves over
time. Firstly, the conditional variance of Ri t is assumed to be greater on
Ž . Ž .
announcement days by 1qdi , cf. Eq. 3 . The conditional covariance matrix of
the vector of error terms, ´t, is denoted H and is described by an appropriatelyt
Ž
extended version of the CCORR model. The diagonal elements of Ht i.e. the
. Ž .
conditional variances are assumed to evolve according to extended GARCH 1,1 processes:
h ssq
Ž
fqfAIA qfyIA Iy.
´2 qwh ,Ž .
5 i i , t i i i ty1 i ty1 i , ty1 i , ty1 i i i , ty1where I-s1 if ´ -0 and 0 else. To ensure that the conditional variance is
i t i t
strictly positive, the following constraints are imposed:
s)0, f,fqfA,f
In Eq. 5 , we follow Li and Engle 1998 and allow positive and negative announcement shocks to have different implications on the future conditional
Ž .
volatility, in some sense including a leverage effect. The specification in Eq. 5 is,
Ž .
in fact, a version of the Glosten et al. 1993 GARCH model, where we have included announcement effects.
There is not a unique way of measuring volatility persistence; however, one simple and often used metric is the sum of the GARCH parameters. The
Ž .
specification in Eq. 5 permits differences in the persistence on announcement and non-announcement days in that the sum of the GARCH parameters is greater
A Ž A y. Ž .
on announcement days byfi fi qfi for positive negative announcement
shocks. When the market incorporates the information related to the
announce-Ž . A
ments faster slower than other kinds of information, the parameter fi is
Ž .
negative positive .
Ž .
The off-diagonal elements of Ht i.e. the conditional covariances are described
by:
A A
hi j, tsri j
Ž
1qri j tI.
(
hi i , thj j, t,Ž .
7where i/j. The conditional covariances are proportional to the product of the
applicable conditional volatilities. In accordance with the CCORR model, we assume that the conditional correlations are constant. We stress, that the assump-tion of constant condiassump-tional correlaassump-tions is nothing but a convenient working preposition. Moreover, the conditional correlations change deterministically by the
proportion rA on announcement days. The conditional covariance between bond i
i j
and j is also allowed to be different on announcement days, though, it is not quite
A A
(
equals 1qdi tI
(
1qdj tI hi j, t. If we disregard differences in hi j, t betweenannouncement days and non-event days, we see that the conditional covariance is
greater on announcement days by 1
(
qdi(
1qdj.Ž Ž ..
The specification that we apply for the diagonal elements of Ht Eq. 5 is
Ž .
similar to the univariate specification in Jones et al. 1998 . Their most general specification of the conditional variance of the bond excess return for a given
Ž .
maturity is aAregime switchingB model, which corresponds to Eq. 3 expanded
A Ž
(
by the multiplicative factor 1qc Ii ty1 i.e. the conditional variance
deterministi-. Ž .
cally changes regime the day following an announcement , wi in Eq. 5 is
allowed to differ on announcement days, and shocks are reduced to being
symmetric, i.e.fA
s0. For all maturities examined, they find that the conditional
i
variance does not follow the regime switching process and that the GARCH parameter for the lagged conditional variance is identical on announcement and non-announcement days. Their results lead us to analyze the GARCH specification
Ž .
in Eq. 5 .
3.3. Estimation practicalities
The multivariate model set up above is estimated using a two-stage estimation
Ž .
technique. In the first step, the conditional mean Eq. 4 , is estimated using
Ž .
Ordinary Least Squares OLS and applying White’s heteroscedasticity consistent standard errors. The differences between the returns and their conditional mean are
termed the VAR residuals: yt'Rtymt. The VAR residuals are now the basis
time series. The use of the residuals as observed data have been applied by Kroner
Ž .
and Ng 1998 amongst others in a similar setting.
In the last step, we estimate the second moment equation. The estimation is
Ž .
conducted using Quasi Maximum Likelihood QML with a Gaussian likelihood function and applying robust standard errors, cf. Bollerslev and Wooldridge
Ž1992 . The log-likelihood function can be stated in an appealingly simple manner.
( ) C. ChristiansenrJournal of Empirical Finance 7 2000 479–507 494
Ž Ž . Ž .
Hence, the log-likelihood for observation number t isy1r2 N ln 2p qln Gt q
< < XŽ .y1 .8,9,10
2ln Dtq´t DtGtDt ´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, FA
, 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 FA
'0. As the point estimates as well as the statistical significance of
F0 and F1 hardly change by imposing this restriction, we merely report the
results from the reduced mean equation, cf. Table 3. A few of the off-diagonal
entries in the parameter matrix,F1 are significantly different from zero indicating
8
Notice that when we consider the CCORR model with rA'0 we obtain GsG and the
i j t
Ž .
log-likelihood function is simplified accordingly, cf. Bollerslev 1990 . 9
In the practical estimation, we simultaneously estimate thedi’s and the parameters of H , hence,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 condimaximiza-tional variance are set to the uncondimaximiza-tional variance. The likelihood function is conditional on the first observation.
11
()
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Table 3
Conditional mean equation
Ž .
Maturity year 2 3 5 7 10 30
) ) )Ž . ) ) )Ž . ) )Ž . ) )Ž . ) )Ž . ) )Ž .
F0 i 0.006 0.002 0.008 0.003 0.010 0.005 0.013 0.006 0.015 0.007 0.022 0.011
) ) ) ) ) ) ) ) ) ) )
Ž . Ž . Ž . Ž . Ž . Ž .
F1,2yr 0.024 0.071 0.412 0.102 0.484 0.154 0.471 0.202 0.420 0.250 0.753 0.365
) ) )
Ž . Ž . Ž . Ž . Ž . Ž .
F1,3yr 0.064 0.048 y0.241 0.070 y0.025 0.108 y0.122 0.139 y0.074 0.174 y0.340 0.246
) ) )
Ž . Ž . Ž . Ž . Ž . Ž .
F1,5yr 0.002 0.037 0.008 0.053 y0.239 0.083 0.046 0.110 y0.029 0.137 y0.248 0.202
) ) ) )
Ž . Ž . Ž . Ž . Ž . Ž .
F1,7yr 0.036 0.029 0.079 0.043 0.172 0.067 y0.053 0.091 0.215 0.113 0.039 0.172
) ) )
Ž . Ž . Ž . Ž . Ž . Ž .
F1,10yr y0.027 0.025 y0.014 0.037 y0.010 0.056 0.035 0.075 y0.164 0.093 0.300 0.145
)
Ž . Ž . Ž . Ž . Ž . Ž .
F1,30yr y0.007 0.010 y0.017 0.015 y0.022 0.023 y0.011 0.030 0.014 0.037 y0.102 0.056 The VAR residuals are created as the residuals, y , from estimating the following equation by OLS: Rt tsF0qF1RtI1qy , where R is the vector oft 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 .
( ) C. ChristiansenrJournal of Empirical Finance 7 2000 479–507 496
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, yt2 is significantly
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 dsfAsfysrAs0
i i i i j
for i, js1, . . . , 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 sir1yfiy
.
wi . Moreover, due to the specification of the model, the conditional covariance
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 fi and wi are
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, si p-value
.
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 recoveringAback to normalBbefore a short than a long maturity
bond matures. What is more, we reject the preposition that the conditional
Ž
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Table 4
Ordinary CCORR Model
Ž .
Maturity year 2 3 5 7 10 30
) ) )Ž . ) ) )Ž . ) ) )Ž . ) ) )Ž . ) ) )Ž . ) ) )Ž .
si 0.000 0.000 0.001 0.000 0.002 0.000 0.003 0.001 0.005 0.001 0.009 0.002
) ) )Ž . ) ) )Ž . ) ) )Ž . ) ) )Ž . ) ) )Ž . ) ) )Ž .
fi 0.036 0.005 0.035 0.005 0.033 0.004 0.039 0.004 0.034 0.004 0.027 0.004
) ) )Ž . ) ) )Ž . ) ) )Ž . ) ) )Ž . ) ) )Ž . ) ) )Ž .
wi 0.933 0.011 0.936 0.010 0.939 0.009 0.942 0.007 0.938 0.007 0.952 0.006
) ) ) ) ) ) ) ) ) ) ) ) ) ) )
Ž . Ž . Ž . Ž . Ž . Ž .
r2yr, i 1.000 – 0.949 0.002 0.924 0.003 0.884 0.005 0.860 0.006 0.791 0.008
) ) ) ) ) ) ) ) ) ) ) )
Ž . Ž . Ž . Ž . Ž .
r3yr, i – 1.000 – 0.954 0.002 0.924 0.003 0.905 0.004 0.840 0.006
) ) ) ) ) ) ) ) )
Ž . Ž . Ž . Ž .
r5yr, i – – 1.000 – 0.959 0.002 0.947 0.002 0.889 0.005
) ) ) ) ) )
Ž . Ž . Ž .
r7yr, i – – – 1.000 – 0.975 0.001 0.930 0.003
) ) )
Ž . Ž .
r10yr, i – – – – 1.000 – 0.948 0.003
Ž .
r30yr, i – – – – – 1.000 –
QML estimates of the ordinary CCORR model of the daily excess returns, R : Rt i tsmi tq´i t, where´t is the vector of errors with mean 0 and conditional 2
covariance matrix H . The diagonal elements of H : ht t i i tssiqf ´i i ,ty1qwihi i, ty1. The off-diagonal elements of H : ht i j, tsri j
'
hi i , thj j, t, where i/j.Ž .
()
di 1.921 0.264 1.867 0.257 1.674 0.233 1.422 0.213 1.348 0.209 1.219 0.194
) ) )Ž . ) ) )Ž . ) ) )Ž . ) ) )Ž . ) ) )Ž . ) ) )Ž .
si 0.000 0.000 0.001 0.000 0.002 0.000 0.003 0.000 0.005 0.001 0.009 0.002
) ) )Ž . ) ) )Ž . ) ) )Ž . ) ) )Ž . ) ) )Ž . ) ) )Ž .
fi 0.042 0.005 0.041 0.005 0.039 0.004 0.039 0.004 0.040 0.004 0.034 0.004
A ) )Ž . ) )Ž . ) ) )Ž . ) ) )Ž . ) ) )Ž . ) ) )Ž .
fi y0.033 0.015 y0.032 0.014 y0.055 0.013 y0.053 0.012 y0.056 0.012 y0.051 0.014
y Ž . Ž . Ž . Ž . Ž . Ž .
fi y0.003 0.016 y0.009 0.013 0.016 0.013 0.017 0.013 0.018 0.012 0.017 0.013
) ) )Ž . ) ) )Ž . ) ) )Ž . ) ) )Ž . ) ) )Ž . ) ) )Ž .
wi 0.930 0.009 0.932 0.008 0.935 0.007 0.939 0.006 0.937 0.006 0.948 0.006
) ) ) ) ) ) ) ) ) ) ) ) ) ) )
Ž . Ž . Ž . Ž . Ž . Ž .
r2yr, i 1.000 – 0.939 0.003 0.912 0.004 0.871 0.005 0.847 0.006 0.776 0.009
A ) ) )Ž . ) ) )Ž . ) ) )Ž . ) ) )Ž . ) ) )Ž .
r2yr, i – 0.045 0.004 0.056 0.007 0.077 0.010 0.080 0.013 0.107 0.023
) ) ) ) ) ) ) ) ) ) ) )
Wooldridge 1992 robust standard errors in parenthesis.
) )
Indicates that the parameter is significantly different from zero at a 5% level.
) ) )
.
H1 is well below 1%, H1: d1sPPPsd6 . Overall, this is in accordance with
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 announcedocu-ments 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: fysPPPsfys0. 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
Ž1998 concerning the futures market i.e. opposite the spot market for Treasury. Ž .
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 fA 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 announceannounce-ments 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 fA
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 .
( ) C. ChristiansenrJournal of Empirical Finance 7 2000 479–507 500
f qfA
sPPPsf qfA
s0. This hypothesis cannot be rejected, neither
inde-1 1 6 6
Ž . Ž
pendently p-value of 20% nor jointly with the previous hypothesis H2nH3:
.
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: f1sPPPsf6nw1sPPPsw6,
.
results in a p-value of 53% . This also holds when considered in conjunction with
Ž .
the previous non-rejected hypotheses H2nH3nH4 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:
.
f1qw1sPPPsf6qw6s1 . Also, the magnitude of the ARCH and the
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 si’s are statistically
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 ri j’s are not identical across maturities H6: r12s
A .
PPPsr56 implies a p-value far below 1% . Indeed, on announcement days the
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: r12 1qr12 PPPsr561
A. Ž A. Ž A.
qr56 s1 and H8: r12 1qr12 sPPPsr561qr56 both result in p-values
.
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
Ž1991 . 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: fy
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
Žup 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 .
()
di 1.915 0.261 1.868 0.254 1.685 0.232 1.436 0.212 1.363 0.207 1.233 0.193
) ) )Ž . ) ) )Ž . ) ) )Ž . ) ) )Ž . ) ) )Ž . ) ) )Ž .
si 0.000 0.000 0.001 0.000 0.002 0.000 0.003 0.000 0.005 0.001 0.011 0.002
) ) )Ž .
r2yr, i 1.000 – 0.939 0.003 0.912 0.004 0.871 0.006 0.847 0.006 0.776 0.009
A ) ) )Ž . ) ) )Ž . ) ) )Ž . ) ) )Ž . ) ) )Ž .
r2yr, i – 0.045 0.004 0.056 0.006 0.078 0.010 0.081 0.013 0.108 0.023
) ) ) ) ) ) ) ) ) ) ) )
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.
vThe 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
( ) C. ChristiansenrJournal of Empirical Finance 7 2000 479–507 504
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
We have argued that it is both interesting and highly relevant from a financial economics point of view to examine the implications of macroeconomic an-nouncements on the covariance structure of government bond returns. In the previous literature examining the effects of macroeconomic news on the bond market, the analysis is conducted using univariate frameworks, cf. e.g. Ederington
Ž . Ž . Ž .
and Lee 1993 , Balduzzi et al. 1997 , Jones et al. 1998 and Li and Engle
Ž1998 . The main contribution of the present paper has been to extend this analysis.
to a multivariate framework and, to this end, we have applied an extended version
Ž . Ž .
of the constant conditional correlations CCORR model, cf. Bollerslev 1990 . The main findings of the empirical work can be summarized as follows: The conditional variances, conditional covariances, and correlations are greater on announcement days than on non-announcement days. The correlation coefficients are relatively large and are greater the closer the bonds are with respect to the time to maturity. In contrast, the greater the relative addition to the correlation is, the further apart the bonds are with respect to the time to maturity, indicating that the government bond market is closer to being perfectly correlated on announcement days than on other days. In other words, the correlation coefficients are less maturity dependent on announcement days. Hence, releases of macroeconomic news induce common movements in the bond market, which strengthen the correlations. The addition to the conditional covariance of government bonds with different maturities is increasing with the time to maturity of either of the bonds. The addition to the conditional variance on macroeconomic announcement days is a decreasing function of the time to maturity of the bond. The conditional volatility is highly persistent and there are not any statistical differences between positive and negative announcement shocks. Likewise, the persistency of the conditional volatility seems to be identical across bonds of different maturities. 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. On the whole, the restricted CCORR model seems to provide an adequate description of the data at hand.
( ) C. ChristiansenrJournal of Empirical Finance 7 2000 479–507 506
It is conceivable that the impact of macroeconomic news releases on bond returns depends on the general state of the economy, i.e. whether we are in a recession or an expansion. In principle, this could be investigated using the U.S. business cycle data prepared by the National Bureau of Economic Research
ŽNBER . However, in the 16 years we consider 1983 to 1998 . there are only 8. Ž .
Ž .
months of recession from July 1990 to March 1991 , providing a total of 16 announcements during recession. Hence, we would incur serious small sample problems if we were to investigate this hypothesis, which has deterred us from looking further into this issue.
Above, we have conducted several specification tests, which support the estimated model. Yet, we would like to know how well the model actually predicts future variances and covariances. One way to assess this would be to regress predicted values on subsequently realized values. However, for second moments, we cannot observe the realized values. Instead, we would have to use sample
Ž
moments calculated using one observation squared returns and cross multiplied
. Ž .
returns . Andersen and Bollerslev 1998 show that daily data in a GARCH framework always result in very low R-squares when conducting the above
Ž .
regression even when the model is correctly specified . They find that high frequency data resolve this problem because this allows us to calculate daily sample moments using several observations. As we do not have access to high frequency data, the issue of predictability is left for future research.
Acknowledgements
The paper was completed whilst the author was visiting the University of California, San Diego, in Spring 2000. The hospitality of the Economics Depart-ment is gratefully acknowledged. Helpful comDepart-ments and suggestions from an anonymous referee, Allan B. Andersen, Robert Engle, Tom Engsted, Svend Jakobsen, Raman Uppal, and seminar participants at the CEPR Capital Markets Conference, the French Finance Association’s 1999 meeting, and the European Finance Association 1999 Doctoral Tutorial are appreciated. In particular, useful hints and suggestions from Jesper Lund helped improving the paper. Naturally, the author is responsible for any errors.
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