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G7 Stock and Bond-market volatility
Scott B. Beyer, CFA*Gerald W. Buetow, Jr., CFA**
Robert R. Johnson, CFA***
ABSTRACT
This paper examines bond- and stock-market volatility of the G7 nations. Using weeklyreturns segmented annually, by five-year periods, and overall, from 1980-2003, wedocument the evolution of stock and bond returns, volatility of returns, and correlation ofreturns. Our findings challenge the notion that US bond-market volatility is increasing.Moreover, many G7 nations show a varying increase in stock- and bond-return volatility.We note correlations of returns and autocorrelations of market volatilities tend to beimperfectly related. This result suggests the international markets can play an importantrole in reducing portfolio risk, in some cases may offer superior return enhancement, andoffer an opportunity for increased risk-adjusted performance.
* Assistant Professor of Finance, College of Business, University of Wisconsin Oshkosh, (920) 424-7194, [email protected]
** President BFRC Services, LLC, (434) 923-3222, [email protected] and Director ofResearch, Atlantic Asset Management.
*** Executive Vice President, CFA Institute, (434) 951-5255, [email protected].
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1. Introduction
This paper studies the relationship between stock and bond volatility of the G7
nation markets. Stock and bond volatility is a popular topic in the current literature.
The assumed increase in volatility during the past 20 years, coupled with the advent of
numerous interest-rate derivative instruments, have together resulted in many financial
studies on stock versus bond-market volatility. Prior work establishes a relationship
between US stock and bond volatility, changes in relative risk between stocks and bonds,
and yield spreads in the market (Reilly, Wright, Chan (2000)). Other studies, as in
Johnson and Young (2002) and Young and Johnson (2004), analyze the stock- and bond-
risk relationship in select foreign markets. Reilly and Wright (2004) present summary
characteristics for the returns from a number of different asset classes.
This paper is singular with its simultaneous review of relative risk between stocks
and bonds from a global perspective. Past studies remark noteworthy differences in stock
and bond market behavior in select countries (e.g. Young and Johnson (2004), Johnson
and Young (2002), Engsted and Tanggaard (2001), Reilly, Wright, and Chan (2000)).
This study explores the extent to which these differences persist across the major markets
of the developed world. We analyze the weekly stock and bond returns, standard
deviation of returns, and correlation of returns for all G7 countries. Additionally, we
study the time-series behavior of the G7 market volatility of returns. This analysis allows
for a rigorous and synchronous review of volatility in several capital markets.
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2. Literature Review
Bond-Market Volatility
Although bond-market volatility studies are less prevalent than stock-market
studies, a rich literature reviewing bond market-return volatility exists. Past research
suggests bond-market volatility has greatly increased during the 1980s and 1990s.1
Increases in bond-market volatility can have a significant impact upon risk for market
participants. For instance, Longstaff and Schwert (1993) illustrate how changes in bond-
market volatility impacts bond investors, and Dialynas and Edington (1992) find that
these volatility changes can have a major impact on spreads and the value of bonds with
embedded bonds. Johnson and Young (2002) find that UK bond-market volatility surged
much sooner than the apparent surge in the US markets. However, Young and Johnson
(2004) show that Swiss bond-market volatility changed similarly to the US market. As
such, it has not yet been established whether bond-market volatility changes are
universal.
Stock-market volatility
An impressive extant literature exists on stock-market volatility. Central topics in
the stock-market volatility studies are: the trend in market volatility, the predictability of
market volatility, and the contribution to systematic risk attributed to volatility. Schwert
(1989, 1990) examines US stock volatility changes relative to macroeconomic variables
and documents a weak relationship.2 French, Stewart, and Stambaugh (1987) suggest
1 See for instance, Coleman, Fisher and Ibbotson (1993) or Reilly, Wright and Chan (2000).2 Morelli (2002) conducts a similar study on the UK market. However, this study suggests a tighterlinkage between macroeconomic variables and changes in stock-market volatility. Bohl and Henke (2003)review stock-market volatility in Poland and find, conditional upon trading volume, agreement with the
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that US stock-market volatility is increasing and find evidence that the expected market-
risk premium is linked to predictable volatility of stock returns. Wilson and Jones
(1987), and Jones and Wilson (1989), review changes in US stock-return volatility from
1871 to 1988 and conclude that stock-market volatility is not increasing. Li (1998),
however, suggests US market volatility is time varying, but underscores that the changing
reward to volatility ratio is more critical in explaining predictable variation in the risk
premia for stocks and bonds than the changing volatility of returns.
Other studies focus on systematic risk and the relationship between trading and
volatility. Campbell and Cochrane (1999) present a consumption-based model to explain
stock-market volatility over the long run. Suominen (2001) reviews the market volatility
issue with a microstructure approach and puts forward a model that suggests trading
volume can be useful in predicting equity-market volatility. Campbell, Lettau, Malkiel,
and Xu (2001) challenge the very nature of how many stocks it takes to properly
diversify an equity portfolio by investigating the increase in idiosyncratic risk. Grundy
and Kim (2002) analyze the affects of heterogeneous information flow and find that a
market with asymmetric information inflows is considerably more volatile than one with
all publicly announced signals. Hardouvelis and Theodossiou (2002) study the impact
margin requirements have on stock-market volatility and find that higher initial margins
are associated with lower subsequent volatility and lower conditional mean returns,
suggesting a reduction in systematic risk. Lee, Jiang, and Indro (2002) find that
sentiment has a role in explaining volatility and postulate that sentiment is a systematic
risk factor. The authors find evidence consistent with the notion that bullish sentiment
leads to lower implicit volatility.
Schwert (1989) study.
5
As with the bond-volatility studies, papers studying international stock-market
volatility are less common than studies of the US markets. Schwert (1998) looks at UK
stock-market volatility and remarks that although the pattern of UK stock volatility is
similar to US stock volatility, the UK stock volatility responded differently during both
the 1987 equity market crash and the oil embargos of the 1970s. Other research lends
support to the theory that international stock-market volatility patterns differ from those
of the US market. For instance, Clare and Thomas (1992) study the predictability of
market returns in Germany, Japan, UK, and US and find differences in their equity-
market volatility patterns. Bodart and Reding (1999) examine the behavior of stock and
bond returns vis-à-vis the volatility of exchange-rates and find an inverse relationship
between exchange-rate volatility and the correlation of international markets. Forbes and
Chinn (2003) suggest that the strongest linkage between any two markets, despite the
growth in global financial flows, still comes from direct trade. Thus, we may expect
some degree of variation in the volatility patterns of the world markets. Johnson and
Young (2002), Morelli (2002), Bohl (2003) and Young and Johnson (2004) all find
various distinctions in the volatility patterns of the world markets. Hence, the current
literature is unclear as to the stock-market volatility patterns across the various world
markets. Furthermore, the literature is ambiguous as to the interrelation between bond
and stock-market volatility and if the pattern of bond versus stock-market volatility is
globally universal.
This paper adds to the current literature base in several specific and important
ways. First, this study uniformly analyzes the volatility patterns of the bond and stock
markets of the G7 nations. Second, this study addresses the issue of bond versus stock-
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market volatility in each of the G7 countries. Third, this study looks at the changes in
correlation between bond and stock markets across the seven developed nations. Finally,
we look at the autoregressive properties of the capital-market volatilities of the G7
nations to ascertain the degree to which market volatility is predictable, or at least
exploitable in a portfolio context.
3. Data
The data used in this study is taken from Thompson Datastream.
The bond returns are derived from the benchmark ten-year bond in each country. As
described by Thompson :
Benchmark indices are based on single bonds. The bond chosen foreach series is the most representative bond available for the givenmaturity band at each point in time. Benchmarks are selectedaccording to the accepted conventions within each market.Generally, the benchmark is the latest issue within the givenmaturity band; consideration is also given to liquidity, issue sizeand coupon. Returns are chain-linked to previous day's value withcoupons re-invested into the index on the day they take place.
The equity returns are also from Datastream. Specifically, we use the Global Equity
Indices. Datastream Global Equity Indices are drawn from the Thompson Datastream
equities database. Equity-market indices are formulated with a representative sample of
stocks. Specifically, a minimum of 75 to 80% of the total market capitalization is
encapsulated within each of the equity-market indices in the database. The indices are
capital market weighted and are in general highly correlated with the more traditional
indices often cited in the press. For example, the Datastream Equity index for the United
States has a correlation with the S&P500 of over 99% for the period analyzed. The other
countries have similar characteristics. We use a single source for our data so that index
composition is consistent across countries. This eliminates any noise that might appear
7
when alternative sources are used. Also, by using the benchmark bond we sidestep the
problems often attributed with large-bond indices (i.e, getting market prices for illiquid
securities, dealing with spread changes, etc).
4. Methodology
To examine bond-market volatility we compute: the rolling standard deviation of
weekly returns for 52-week (one-year) calendar periods, the standard deviation for
discrete, nonoverlapping, 52-week calendar-year time periods, and the variance for
discrete, non-overlapping 260-week (five-year) calendar time periods. We use these
metrics to determine how bond-market volatility has changed over the past 25 years.
Furthermore, we run autoregressive conditional heteroskedasticity (ARCH) tests and
generalized autoregressive conditional heteroskedasticity (GARCH) models to
investigate the characteristics of the return volatility in each of the seven countries.
To examine bond-market volatility relative to stock-market volatility we compute
the following: the ratio of moving standard deviation of weekly rates of return for 52-
week calendar periods (bonds to stocks), the ratio of standard deviations for discrete,
non-overlapping 52-week calendar time periods for bonds to stocks, and the correlation
coefficient between the returns on long-term government bonds and total-market equity
returns for rolling weekly periods of three years are computed. These metrics permit
analysis of the changes in bond-market volatility in relation to the stock-market volatility
for the countries being reviewed. Furthermore, construction of the key metrics in this
manner allows for a comparison with previous research.
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5. Results
Bond-Market Volatility
Figures 1A – 1G depict the rolling 52-week total return, standard deviation of
returns, and price-implied yield to maturity for the G7 Benchmark 10-year Bond Indices.
The graphs illustrate the descriptive characteristics of the bond markets of the seven
nations. The bond volatilities, for instance, exhibit relative consistency in the direction of
the rolling volatility, with select areas where the volatilities diverge. Specifically, the
standard deviation of the bond returns increases across all markets during the end of 1987
and near the end of 1999. Perhaps the most remarkable spike in volatility occurs in the
early 1980s when volatility exceeds 16 percent in the US market and 14 percent in the
UK market. During the end of 1991 and again in late 2001 there is a degree of
divergence in the markets. This divergence in bond volatility is most prevalent during
the spring of 1997 and at the commencement of the Asian currency crisis. The price-
implied yield to maturity (YTM) has decreased in all major countries; recently, the YTM
has approached 4 percent in all of the major markets, except for Japan, which has a
negligible YTM. Bond-market returns are also fairly consistent among the seven nations.
Returns are the highest in the early 1980s with US returns reaching 40 percent and the
UK returns exceeding 60 percent. Annual bond returns experienced significant “peaks
and valleys” over the period. Each country seems to have a general level of returns
around which these extremes take place. Some might argue that annual bond returns
revert to a long run level. For our purposes here it is interesting to observe the bandwidth
of annual returns and the general decrease in that bandwidth over the period analyzed.
9
Two other characteristics are noteworthy in Figures 1A through 1H. First, is the
general decline in yields over the period for almost all of the countries. Second, is that the
level of volatility of bond returns is currently relatively low by historical standards. This
latter property is particularly evident in Italy. If both yields and volatility do revert over
time, then a possible implication of these results is for rising yields and volatility going
forward.
Stock-Market Volatility
Figures 2A through 2H display the 52-week moving return metrics for each of the
equity markets. Overall there are a greater number of peaks in the equity volatility than
the bond volatility. The seven markets all have volatility peaks during the 1987 crash,
while other periods tend to vary, market to market. This is consistent with the previous
research (Johnson and Young (2002), Morelli (2002), Bohl (2003) and Young and
Johnson (2004)) that has studied variance in the world market volatility patterns.
Similar to the Schwert (1988) study, we find that equity volatility is roughly 2.5
times that of bond-market volatility. Of course high- and low-volatility periods exist for
each asset class. Bond-market volatilities are higher in the earlier time frame, 1980 to
1988, while equity-market volatility is greatest the during the 1987 crash and again, more
recently, since 2001. The patterns of the G7 nation volatilities are fairly consistent and
seem to move together without any clearly identifiable lead-lag relationship.
The equity figures also illustrate the dividend yield (DY) and the price to earnings
(PE) ratio for each country index. In every country, note how stable the DY has been over
period – though it has experienced a slight decline. The PE ratio has also behaved
10
similarly across each G7 market. Specifically, it has experienced a recent decline off
historical highs but remains at historically high levels.
Bond-Market Volatility versus Stock-Market Volatility
Figures 3A through 3G graph the correlation between the stock- and bond-market
returns for the G7 nations. Also shown on the graph is the ratio of equity-index standard
deviation of returns to that of the debt-index standard deviation of returns. While most of
the markets exhibit an increase in the ratio of equity risk to debt risk, the correlation
between the returns has been trending downward over the period. The Japanese market is
the exception to this general result as it shows both decreasing stock risk to bond risk
ratio and higher correlation between bond and stock returns.
We observe the opposite trend found in Johnson and Young (2002) and Reilly,
Wright, and Chan (2000) as the ratio of stock-market volatility to bond-market volatility
illustrates a positive trend.3 However, we also note, the most recent data shows the stock
risk to bond risk ratio seems to be reverting to its 2000 levels and thus the trend of the
ratio for the most recent years is again negative.
In almost every instance the correlation between bonds and equities is at
historically low levels. If correlation possesses a reversion aspect than this might suggest
a reduction in diversification benefits going forward. Evidence of this is implicated by the
up-tick in correlation over the past year or so in all markets except Japan.
Interestingly, the ratio of stock- to bond-return volatility is markedly different for
the seven markets. Review of Table 1 shows the overall equity-return and bond-return
correlations and risk ratios for each of the nations under analysis. The US, UK and
3 Both of these papers graph the ratio of bond volatility to stock volatility, but remark a positive trend.
11
Canadian markets each have risk ratios of approximately 2.0. Germany and France have
about the same value of 3.25, while Italy and Japan have slightly lower ratios,
approaching 3.1. Perhaps even more interesting is the fact that the risk ratios and
correlations are so different across countries. These differences in overall correlations
could be critical in a diversification context.
In order to study how the returns varying over time, Table 2 summaries the
discrete 260-Week (five-year) variances of the bond and stock indices and shows the
ratio of stock-market volatility of returns to bond-market volatility of returns. All of the
results in Table 2 are expressed in weekly terms. Using an F-test statistic we confirm the
significance of the ratio. Thus, stock-market volatility of returns are, statistically,
consistently greater than bond-market volatility of returns for each of the seven countries.
This is consistent with the descriptive results above and supports the evidence found by
previous researchers (Reilly, Wright, and Chan (2000) and Johnson and Young (2002)).
Perhaps most intriguing of the results from Table 2 is the variation in skewness
and kurtosis over time. Note, the bond and equity 3rd and 4th moments are stochastic in
nature and distinctive across countries. These differences can be very important for both
valuation of the underlying securities, in this case the stock and bond indexes , as well as
any derivatives written on the underlying assets. It may be possible, however, for
investment managers to capture some of these effects by modeling the changing nature of
the underlying volatility.
The results in Table 2 confirm a very important property that was observed in the
Figures and that is that the distributional characteristics between bond and equity returns
are not stable through time. This fact has tremendous asset allocation implications.
12
Clearly, since every distributional moment changes significantly through time using an
asset allocation approach that is heavily influenced by historical results is at best
problematic. Moreover, attempting to allocate across assets and countries based on a
point estimate is probably not a very useful exercise. The dynamic nature of the moments
must be incorporated into the asset allocation process. Below we attempt to do that for
bond and equity return volatility.
Time-Series Properties of Market Volatilities
In this section we investigate the time series characteristics of the return
volatilities. We first test for ARCH characteristics using the Portmanteau Q-statistic
suggested in McLeod and Li (1983) and a Lagrange Multiplier (LM) test suggested by
Engle (1982).4 While these tests enable us to quantify whether non-linear disturbances
exist in the data they do not specify exactly how to model them. In other words, we are
able to conclude whether ARCH characteristics exist but unable to know exactly how to
properly capture them using a GARCH framework (Bollerslev (1986)). However, for
each GARCH formulation we can test for mis-specification using the normality test of
Jarque and Bera (1980). In this analysis we only provide basic GARCH results to
illustrate that the characteristics of the volatilities can be captured by such modeling.5
The magnitude of the volatility of the weekly returns is certainly an indicator of
the volatility of the annual returns. If serial correlation exists, then one could use
volatility data to forecast future volatility. Given the importance market volatility has
upon the formation of returns expectations and potential wealth, forecasting volatility is
4 The LM test is asymptotically equal to the test used by Breusch and Pagan (1979).5 In this study we do not try to find the optimal GARCH permutation, rather we leave that for a futurestudy.
13
likely to be of great interest to market participants.6 One common approach to establish
autocorrelations is to run an Ordinary Least Squares (OLS) regression of a one-period
lagged variable (i.e., volatility) upon itself. To establish additional critical lags the
process can be repeated for n-periods.7
The first step in evaluating the time series properties of the return volatilities is to
test for the presence of ARCH characteristics. As explained above we use the Q-statistic
and the LM statistic for both equity and bond returns. The results appear in Tables 3 and
4. In every country it appears that the return volatilities exhibit ARCH characteristics at
every order of lag magnitude. Again, these results suggest a GARCH framework for
best capturing the dynamics of the return volatility. However, the exact GARCH model
is not indicated by the test results so we keep our GARCH results relatively simple and
present only our GARCH (1,1) results. GARCH modeling is a common framework often
used in the finance literature. Specifically, our GARCH(1,1) can be modeled as:
),0(~ 21
221
2
tt
ttt
N ση
γηβσασ
+
− ++=
In this model we assume the variance is a function of some constant , a fraction, β, of
variance from the previous period, and γ of an error term.
The results of the GARCH procedure are given in Table 5. Upon review of Table
5, we see that the GARCH model seems to fit the volatility data for the bond- and stock-
market volatilities. Note, in agreement with our ARCH tests presented earlier, in every
case the coefficients to our model are statistically significant at the one percent level.
However, the normality test in every case suggests that the residuals exhibit some non-
6 For example, see Ang and Bekaert (2004).7 Additionally, one can look at the autocorrelation functions (ACF) and partial autocorrelation functions(PACF). A rich literature exists that explains how to establish which lags are likely to be the most critical.
14
normal characteristics. This implies that our GARCH (1,1) model is not capturing all of
the kurtosis in the residuals.8 In some cases, like the UK, the sum of coefficients are very
close to unity implying that we may have a nonstationary distribution.9
Studying the bond- and stock-volatility via the GARCH technique permits more
robust analysis by which to establish the interaction of bond- and stock-market volatility.
Overall our results are contrary to Young and Johnson (2004), but consistent with the
findings in Reilly, Wright, and Chan (2000). Given that the other G7 nations are likely to
be more similar to the US rather than the Swiss market studied in Young and Johnson
(2004), one might expect the GARCH results to be closer to the Reilly, Wright, and Chan
(2000) study, for the remaining countries.
While we have some specification problems in our approach, they still imply that
a statistically significant relationship exists between future volatility and historical
volatility and innovations. Research by Ang and Bekaert (2004) showed that an inverse
relationship exists between return and volatility. Therefore, being able to understand any
predictable patterns in volatilities using our GARCH framework may enable us to better
allocate resources across assets and countries.
6. Conclusions
This paper presents perhaps the first synchronous review of the bond-market and
stock-market volatilities of the G7 nations. Our findings support some of the recent
literature in the field (Reilly, Wright, Chan (2000) and Johnson and Young (2002)), but
also uncovers critical differences in the key volatility-based metrics of the seven markets.
8 This is a common occurrence as noted in Campbell, Lo and Mackinlay (1997) and Bollerslev (1987).Again, it is not our goal in this paper is not to find the best fit,12 The specifics on dealing with this problem is illustrated in Nelson (1990).
15
One such noteworthy difference within the capital markets studied is the shape
and trend of the capital-market volatilities of the G7 nations. Although we find that, for
the most part, the movement in volatilities of the the capital markets of these nations
tends to exhibit a similar shape, distinct periods of divergence can and do exist.
Furthermore, the bond-market and stock-market return correlation and volatility
ratios are strikingly different from market to market. A GARCH decomposition of the
volatility indicates the volatility of the markets tends to be correlated, or predictable.
Given the relationships established within this study, and the important role volatility
plays in market valuations and diversification, the results of this paper are likely to be of
interest to investors and investment managers. Particularly relevant are investment
strategies that can be employed to capitalize on volatility changes. Given the inverse
relationship between return and volatility documented by Ang and Bekaert (2004) are
findings our particularly interesting.
Prior research and conventional market wisdom both suggest that market
volatility has been increasing. Although we note a modest upward trend, the capital
market volatilities of recent years are generally decreasing. Hence, our results are
important because they challenge popular beliefs about the upward trend of market
volatility. Moreover, the current levels of correlation between bond and equity returns
are extremely low by historical standards and have been showing signs of increasing. On
a final note, and perhaps most importantly, a study of the volatility patterns and serial
correlation suggests the potential to earn abnormal profits by adjusting your portfolio
holding according to predictable shifts in volatility. This area warrants further research.
16
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Figure 1A Moving 52-Week US Ten-Year Government Bond Index Returns,Standard Deviation of Returns, and Implied Yield-to Maturity.
-20%
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0%
10%
20%
30%
40%
50%
60%
70%
12/31/1980
12/31/1982
12/31/1984
12/31/1986
12/31/1988
12/31/1990
12/31/1992
12/31/1994
12/31/1996
12/31/1998
12/31/2000
12/31/2002
Ret
urns
0.00%
2.00%
4.00%
6.00%
8.00%
10.00%
12.00%
14.00%
16.00%
18.00%
St. D
ev &
YTM
Returns Std. Dev. YTM
Figure 1B Moving 52-Week UK Ten-Year Government Bond Index Returns,Standard Deviation of Returns, and Implied Yield-to Maturity.
21
-15%-10%-5%0%5%
10%15%20%25%30%35%
1/1/1986
1/1/1988
1/1/1990
1/1/1992
1/1/1994
1/1/1996
1/1/1998
1/1/2000
1/1/2002
1/1/2004
Ret
urns
0.00%
2.00%
4.00%
6.00%
8.00%
10.00%
12.00%
14.00%
St. D
ev &
YTM
Returns Std. Dev. YTM
Figure 1C Moving 52-Week Canadian Ten-Year Government Bond Index Returns,Standard Deviation of Returns, and Implied Yield-to Maturity.
-15%-10%-5%0%5%
10%15%20%25%30%35%40%
2/5/1986
2/5/1988
2/5/1990
2/5/1992
2/5/1994
2/5/1996
2/5/1998
2/5/2000
2/5/2002
Ret
urns
0.00%
2.00%
4.00%
6.00%
8.00%
10.00%
12.00%
St. D
ev &
YTM
Returns Std. Dev. YTM
Figure 1D Moving 52-Week French Ten-Year Government Bond Index Returns,Standard Deviation of Returns, and Implied Yield-to Maturity.
22
-15%
-10%
-5%
0%
5%
10%
15%
20%
25%
30%
12/31/1980
12/31/1982
12/31/1984
12/31/1986
12/31/1988
12/31/1990
12/31/1992
12/31/1994
12/31/1996
12/31/1998
12/31/2000
12/31/2002
Ret
urns
0.00%
2.00%
4.00%
6.00%
8.00%
10.00%
12.00%
St. D
ev &
YTM
Returns Std. Dev. YTM
Figure 1E Moving 52-Week German Ten-Year Government Bond Index Returns,Standard Deviation of Returns, and Implied Yield-to Maturity.
-20.00%
-10.00%
0.00%
10.00%
20.00%
30.00%
40.00%
50.00%
60.00%
4/1/1992
4/1/1993
4/1/1994
4/1/1995
4/1/1996
4/1/1997
4/1/1998
4/1/1999
4/1/2000
4/1/2001
4/1/2002
4/1/2003
Ret
urns
0.00%
2.00%
4.00%
6.00%
8.00%
10.00%
12.00%
14.00%
16.00%
St. D
ev &
YTM
Returns Std. Dev. YTM
Figure 1F Moving 52-Week Italian Ten-Year Government Bond Index Returns,Standard Deviation of Returns, and Implied Yield-to Maturity.
23
-15%
-10%
-5%
0%
5%
10%
15%
20%
25%
30%
1/2/1985
1/2/1987
1/2/1989
1/2/1991
1/2/1993
1/2/1995
1/2/1997
1/2/1999
1/2/2001
1/2/2003
Ret
urns
0.00%
2.00%
4.00%
6.00%
8.00%
10.00%
12.00%
14.00%
St. D
ev &
YTM
Returns Std. Dev. YTM
Figure 1G Moving 52-Week Japanese Ten-Year Government Bond Index Returns,Standard Deviation of Returns, and Implied Yield-to Maturity.
0%
2%
4%
6%
8%
10%
12%
14%
16%
18%
12/30/1980
5/14/1982
9/26/1983
2/7/1985
6/22/1986
11/4/1987
3/18/1989
7/31/1990
12/13/1991
4/26/1993
9/8/1994
1/21/1996
6/4/1997
10/17/1998
2/29/2000
7/13/2001
11/25/2002
4/8/2004
USStdev UKStdev CanStdev FrStdevGermStdev ItStdev JapStdev
Figure 1H Moving 52-Week Ten-Year Government Bond Index Standard Deviationof Returns for All G7 Nations.
24
-40%
-20%
0%
20%
40%
60%
80%
12/31/80
12/31/82
12/31/84
12/31/86
12/31/88
12/31/90
12/31/92
12/31/94
12/31/96
12/31/98
12/31/00
12/31/02
0
5
10
15
20
25
30
35
P/E
Rat
io
Returns Std. Dev. DY PE
Figure 2A Moving 52-Week US Equity Market Index Returns, Standard Deviationof Returns, Price/Earnings Ratio, and Default Yield.
-60%
-40%
-20%
0%
20%
40%
60%
80%
12/31/80
12/31/82
12/31/84
12/31/86
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12/31/00
12/31/02
0
5
10
15
20
25
30
P/E
Rat
io
Returns Std. Dev. DY PE
Figure 2B Moving 52-Week UK Equity Market Index Returns, Standard Deviationof Returns, Price/Earnings Ratio, and Default Yield.
25
-40%
-20%
0%
20%
40%
60%
80%
100%
12/31/1980
12/31/1982
12/31/1984
12/31/1986
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12/31/1990
12/31/1992
12/31/1994
12/31/1996
12/31/1998
12/31/2000
12/31/2002
0
5
10
15
20
25
30
P/E
Rat
io
Returns Std. Dev. DY PE
Figure 2C Moving 52-Week Canadian Equity Market Index Returns, StandardDeviation of Returns, Price/Earnings Ratio, and Default Yield.
-60%
-40%
-20%
0%
20%
40%
60%
80%
100%
120%
12/31/80
12/31/82
12/31/84
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12/31/92
12/31/94
12/31/96
12/31/98
12/31/00
12/31/02
0
5
10
15
20
25
P/E
Rat
io
Returns Std. Dev. DY PE
Figure 2D Moving 52-Week French Equity Market Index Returns, StandardDeviation of Returns, Price/Earnings Ratio, and Default Yield.
26
-60%
-40%
-20%
0%
20%
40%
60%
80%
100%
12/31/80
12/31/82
12/31/84
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12/31/98
12/31/00
12/31/02
0
5
10
15
20
25
P/E
Rat
io
Returns Std. Dev. DY PE
Figure 2E Moving 52-Week German Equity Market Index Returns, StandardDeviation of Returns, Price/Earnings Ratio, and Default Yield.
-100%
-50%
0%
50%
100%
150%
200%
250%
300%
12/31/80
12/31/82
12/31/84
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12/31/00
12/31/02
0
5
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20
25
30
P/E
Rat
io
Returns Std. Dev. DY PE
Figure 2F Moving 52-Week Italian Equity Market Index Returns, StandardDeviation of Returns, Price/Earnings Ratio, and Default Yield.
27
-60%
-40%
-20%
0%
20%
40%
60%
80%
100%
12/31/80
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12/31/02
0
10
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40
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70
80
90
P/E
Rat
io
Returns Std. Dev. DY PE
Figure 2G Moving 52-Week Japanese Equity Market Index Returns, StandardDeviation of Returns, Price/Earnings Ratio, and Default Yield.
0%
5%
10%
15%
20%
25%
30%
35%
40%
45%
50%
5/25/79
2/18/82
11/14/84
8/11/87
5/7/901/31/93
10/28/95
7/24/98
4/19/01
1/14/04
US Stdev UK Stdev Can Stdev Fr StdevGermStdev ItStdev JpStdev
Figure 2H
28
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
12/31/80
12/31/82
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12/31/94
12/31/96
12/31/98
12/31/00
12/31/02
Cor
rela
tion
0.00.51.01.52.02.53.03.54.04.55.0
Equ
ity R
isk/
Bon
d R
isk
Correlation Ratio
Figure 3A Correlation of US Bond and US Stock Market Returns and Ratio of USStock to US Bond Market Volatility
-1-0.8-0.6-0.4-0.2
00.20.40.60.8
12/31/80
12/31/82
12/31/84
12/31/86
12/31/88
12/31/90
12/31/92
12/31/94
12/31/96
12/31/98
12/31/00
12/31/02
Cor
rela
tion
0.0
1.0
2.0
3.0
4.0
5.0
6.0
Equ
ity R
isk/
Bon
d R
isk
Correlation Ratio
Figure 3B Correlation of UK Bond and UK Stock Market Returns and Ratio of UKStock to UK Bond Market Volatility
29
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1/1/861/1/88
1/1/901/1/92
1/1/941/1/96
1/1/981/1/00
1/1/021/1/04
Cor
rela
tion
0.0
1.0
2.0
3.0
4.0
5.0
6.0
Equ
ity R
isk/
Bon
d R
isk
Correlation Ratio
Figure 3C Correlation of Canadian Bond and Canadian Stock Market Returns andRatio of Canadian Stock to Canadian Bond Market Volatility
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
2/5/862/5/88
2/5/902/5/92
2/5/942/5/96
2/5/982/5/00
2/5/02
Cor
rela
tion
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
Equ
ity R
isk/
Bon
d R
isk
Correlation Ratio
Figure 3D Correlation of French Bond and French Stock Market Returns and Ratioof French Stock to French Bond Market Volatility
30
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
12/31/80
12/31/82
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Cor
rela
tion
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
Equ
ity R
isk/
Bon
d R
isk
Correlation Ratio
Figure 3E Correlation of German Bond and German Stock Market Returns and Ratioof German Stock to German Bond Market Volatility
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
4/1/924/1/93
4/1/944/1/95
4/1/964/1/97
4/1/984/1/99
4/1/004/1/01
4/1/024/1/03
Cor
rela
tion
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
9.0
10.0
Equ
ity R
isk/
Bon
d R
isk
Correlation Ratio
Figure 3F Correlation of Italian Bond and Italian Stock Market Returns and Ratio ofItalian Stock to Italian Bond Market Volatility
31
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1/2/851/2/87
1/2/891/2/91
1/2/931/2/95
1/2/971/2/99
1/2/011/2/03
Cor
rela
tion
0.0
2.0
4.0
6.0
8.0
10.0
12.0
14.0
Equ
ity R
isk/
Bon
d R
isk
Correlation Ratio
Figure 3G Correlation of Japanese Bond and Japanese Stock Market Returns andRatio of Japanese Stock to Japanese Bond Market Volatility
Table 1: Correlation of Returns for the G7 Nation Bond and Equity IndexesThis table shows the correlation of returns between the Bond Indexes and theEquity Indexes of the G7 nation markets from 1980 to 2003 (the entire samplestudied within the paper). Listed in parentheses are the t-stat for the correlationcoefficient and the F-Stat for the ratio of volatilities, respectively.
Country CorrelationRatio of Stock-Return Volatility to
Bond-Return Volatility
US 17.88% 1.88UK 22.86% 1.87
Canada 9.25% 2.02France 20.98% 3.22
Germany 11.54% 3.27Italy 24.21% 3.17Japan 0.18% 3.10
32
Table 2: Bond and Equity Return Summary Statistics for the 5-year periods (1980-2003)Table 2 contains the summary statistics for both bond and equity returns over 5-year returnperiods for each of the G7 nations. The first Column lists the Country (The United States(US), the United Kingdom (UK), Canada (CAN), France (FR), Germany (GER), Italy (IT), andJapan (JAP)) and the period (1 = 1980-1984, 2 = 1985-1989, 3 = 1990-1994, 4 = 1995-1999, 5= 2000-2003) in which the return occurs. The following columns list the Correlation of thebond and equity returns (ρ), the ratio of the equity-return volatility to bond-return volatility(RRV), Returns (Ret), Standard Deviation of returns (Std), Skewness of returns (Sk), and theKurtosis of the returns (K) for both the Bond Indexes (B) and the Equity Indexes (E)respectively.
NationPeriod
ρ RRV BRet ERet BStd EStd BSk BSk BK EK
US/1 0.38565 122% 0.220% 0.308% 1.708% 2.085% 0.753 0.361 2.155 0.867US/2 0.23326 195% 0.240% 0.368% 1.164% 2.270% 0.284 -1.607 2.172 8.359US/3 0.49053 195% 0.127% 0.210% 0.912% 1.779% -0.126 -0.186 0.224 1.571US/4 0.20349 239% 0.140% 0.522% 0.870% 2.076% -0.328 -0.639 0.362 1.759US/5 -0.34395 276% 0.158% ( 0.069%) 1.072% 2.955% -0.466 0.322 0.500 0.980UK/1 0.37634 128% 0.332% 0.494% 1.720% 2.194% -0.458 0.009 3.828 0.428UK/2 0.15766 215% 0.237% 0.382% 1.053% 2.268% 0.340 -2.545 3.708 16.010UK/3 0.55986 166% 0.216% 0.229% 1.198% 1.985% 0.190 0.782 1.456 3.408UK/4 0.23868 214% 0.207% 0.381% 0.886% 1.894% -0.276 -0.173 0.432 0.390UK/5 -0.42338 360% 0.116% ( 0.079%) 0.754% 2.715% -0.479 0.490 1.614 4.323CAN/1 . . 0.232% . 2.272% . 0.447 . 1.824CAN/2 0.02650 192% 0.218% 0.252% 1.089% 2.087% 0.806 -1.705 6.464 9.962CAN/3 0.34714 140% 0.164% 0.131% 1.116% 1.564% -0.102 -0.127 -0.050 0.765CAN/4 0.16184 204% 0.202% 0.409% 0.926% 1.892% -0.354 -0.629 0.777 1.904CAN/5 -0.17819 280% 0.161% 0.071% 0.821% 2.302% -0.180 -0.211 0.744 0.937FR/1 . . 0.336% . 2.520% . -0.527 . 3.871FR/2 0.42652 312% 0.223% 0.515% 0.972% 3.028% 0.115 -1.015 1.157 6.241FR/3 0.58360 262% 0.180% 0.113% 0.905% 2.368% -0.619 -0.328 1.968 0.528FR/4 0.21839 304% 0.180% 0.520% 0.768% 2.338% -0.344 -0.317 1.003 0.923FR/5 -0.39330 455% 0.144% ( 0.075%) 0.804% 3.656% -0.232 0.326 0.853 2.454GER/1 0.41654 164% 0.165% 0.241% 0.855% 1.403% 0.508 -0.038 4.767 0.109GER/2 0.12362 362% 0.119% 0.347% 0.707% 2.558% 0.396 -1.191 1.371 4.888GER/3 0.50300 272% 0.136% 0.097% 0.800% 2.178% -0.665 -0.604 1.976 1.513GER/4 0.18998 329% 0.157% 0.440% 0.716% 2.359% -0.661 -0.546 0.463 1.472GER/5 -0.41211 517% 0.131% ( 0.144%) 0.715% 3.696% -0.293 -0.017 0.481 1.584IT/1 . . 0.610% . 3.916% . -0.098 . 2.352IT/2 . . 0.543% . 3.124% . -0.166 . 1.415IT/3 0.45917 236% 0.243% 0.071% 1.336% 3.157% -0.594 0.089 2.710 0.177IT/4 0.38100 298% 0.287% 0.471% 1.037% 3.091% 0.124 -0.021 2.872 1.076IT/5 -0.40792 455% 0.142% ( 0.090%) 0.687% 3.128% -0.578 -0.372 1.493 1.038JAP/1 0.22792 242% 0.232% 0.327% 0.637% 1.542% 0.639 0.047 3.912 2.129JAP/2 0.19762 233% 0.103% 0.475% 1.041% 2.423% -0.529 -0.529 4.323 2.297JAP/3 0.08805 407% 0.126% ( 0.161%) 0.724% 2.946% -0.976 0.203 3.325 2.800JAP/4 -0.16460 314% 0.150% 0.134% 0.812% 2.549% -0.457 0.538 2.386 1.315JAP/5 -0.23330 455% 0.054% ( 0.183%) 0.683% 3.110% -1.936 0.058 9.748 0.169
33
Table 3: ARCH Results for the G7 Nation Bond-Index ReturnsThis table displays key parameters and metrics from the ARCH test of the G7 nation bond-index returns. Panel A.and panel B each display ARCH metrics for The United States (US),the United Kingdom (UK), Canada (CAN), France (FR), Germany (GER), Italy (IT), andJapan (JAP).
Panel A: Portmanteau Q-Statistic ResultsThis panel of the table displays the Q-Statistic for 12 lags (Order) of the weekly bond-indexreturns. Below the Q-statistic is the p-valve for each country and each lag, respectively.
Order US. UK CAN FR GER IT JAP1 96.857 2.656 0.197 15.523 5.559 17.954 12.144
<.0001 0.040 0.334 <.0001 <.0001 <.0001 <.00012 113.855 5.786 1.113 34.673 15.653 26.747 37.460
<.0001 0.001 0.014 <.0001 <.0001 <.0001 <.00013 119.484 8.296 3.402 43.907 39.084 30.094 42.384
<.0001 0.001 0.015 <.0001 <.0001 <.0001 <.00014 129.404 18.835 12.454 55.355 56.550 30.507 90.972
<.0001 0.103 0.657 <.0001 0.018 <.0001 0.0015 137.385 22.165 14.106 103.121 83.541 31.965 117.221
<.0001 0.055 0.573 <.0001 0.000 <.0001 <.00016 141.889 22.231 17.140 113.588 85.586 35.736 134.288
<.0001 0.001 0.009 <.0001 <.0001 <.0001 <.00017 155.507 22.618 19.659 122.041 90.269 40.985 151.509
<.0001 0.002 0.006 <.0001 <.0001 <.0001 <.00018 158.851 46.441 22.709 130.684 106.076 44.246 170.218
<.0001 <.0001 0.004 <.0001 <.0001 <.0001 <.00019 164.765 47.169 22.994 140.504 113.373 61.373 197.987
<.0001 <.0001 0.006 <.0001 <.0001 <.0001 <.000110 173.440 47.466 23.364 165.596 119.578 62.161 201.077
<.0001 <.0001 0.010 <.0001 <.0001 <.0001 <.000111 195.258 47.469 24.561 169.229 120.063 75.792 205.415
<.0001 <.0001 0.011 <.0001 <.0001 <.0001 <.000112 207.377 50.004 27.854 174.643 122.140 93.361 206.495
<.0001 <.0001 0.006 <.0001 <.0001 <.0001 <.0001
34
Panel B: Lagrange Multiplier (LM) Statistic ResultsThis panel of the table lists the LM Statistic for 12 lags of the weekly bond Index returns.Below the LM statistic is the p-valve for each country and each lag, respectively.
Order US. UK CAN FR GER IT JAP1 96.704 2.661 0.202 15.545 5.574 17.932 12.138
<.0001 0.055 0.341 <.0001 <.0001 <.0001 <.00012 98.817 5.544 1.115 30.891 14.717 23.253 34.043
<.0001 0.002 0.017 <.0001 <.0001 <.0001 <.00013 99.628 7.604 3.349 35.344 34.690 24.324 35.667
<.0001 0.002 0.020 <.0001 <.0001 0.000 <.00014 104.504 16.859 12.023 40.872 46.523 24.325 71.940
<.0001 0.103 0.653 <.0001 0.018 <.0001 0.0015 106.187 18.927 13.335 74.702 63.671 25.090 85.372
<.0001 0.063 0.573 <.0001 0.001 <.0001 <.00016 106.671 18.991 15.579 76.357 63.676 27.509 88.590
<.0001 0.004 0.016 <.0001 <.0001 0.000 <.00017 113.810 19.025 17.120 76.966 63.966 30.121 93.827
<.0001 0.008 0.017 <.0001 <.0001 <.0001 <.00018 113.855 38.556 18.763 78.465 69.356 30.863 97.346
<.0001 <.0001 0.016 <.0001 <.0001 0.000 <.00019 115.810 38.580 18.775 80.134 71.011 41.760 104.195
<.0001 <.0001 0.027 <.0001 <.0001 <.0001 <.000110 118.440 38.583 18.783 87.253 72.078 42.085 105.123
<.0001 <.0001 0.043 <.0001 <.0001 <.0001 <.000111 127.133 38.784 19.125 87.336 72.663 50.339 105.523
<.0001 <.0001 0.059 <.0001 <.0001 <.0001 <.000112 127.966 39.286 20.879 87.442 72.708 58.482 107.031
<.0001 <.0001 0.052 <.0001 <.0001 <.0001 <.0001
35
Table 4: ARCH Results for the G7 Nation Equity-Index ReturnsThis table displays key parameters and metrics from the ARCH test of the G7 nation equity-index returns. Panel A and panel B each display ARCH metrics for The United States (US),the United Kingdom (UK), Canada (CAN), France (FR), Germany (GER), Italy (IT), andJapan (JAP).
Panel A: Portmanteau Q Statistic ResultsThis panel of the table displays the Q Statistic for 12 lags of the weekly bond-index returns.Below the Q statistic is the p-valve for each country and each lag, respectively.
Order US. UK CAN FR GER IT JAP1 96.8567 170.9438 129.7465 88.9104 99.7588 52.1452 35.9909
<.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.00012 113.8546 173.3183 141.9671 132.6919 133.6755 77.4038 79.9258
<.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.00013 119.4836 173.5453 149.9876 207.1919 180.916 133.374 98.2018
<.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.00014 129.4038 177.5717 154.2514 233.232 227.1436 162.1519 113.9927
<.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.00015 137.3854 180.2276 155.3101 243.4234 238.8076 179.5098 140.1085
<.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.00016 141.8889 188.8687 156.4834 251.8374 254.4596 203.3373 143.8158
<.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.00017 155.5065 193.5697 159.5733 273.3122 271.6029 211.9495 147.8479
<.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.00018 158.8514 198.2842 167.2036 283.464 292.6922 215.4693 147.9965
<.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.00019 164.7652 203.1561 172.1963 289.5971 299.7956 257.3388 152.1134
<.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.000110 173.4399 203.8067 172.9383 295.807 305.0638 268.3458 158.6544
<.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.000111 195.2576 204.9766 180.6959 302.7458 311.9397 281.0168 162.8191
<.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.000112 207.3765 205.3757 183.2381 306.8939 327.4778 296.3853 165.2654
<.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001
36
Panel B: Lagrange Multiplier (LM) Statistic ResultsThis panel of the table lists the LM Statistic for 12 lags of the weekly bond Index returns.Below the LM statistic is the p-valve for each country and each lag, respectively.
Order US. UK CAN FR GER IT JAP1 96.7036 170.6287 129.4803 88.7856 99.5883 52.1242 35.9771
<.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.00012 98.8167 182.9997 129.5078 106.9583 109.4429 65.3471 68.4211
<.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.00013 99.6277 184.8285 132.9545 145.1474 131.2255 100.978 74.3351
<.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.00014 104.5037 187.3461 133.3628 146.3518 144.2851 107.9429 78.5331
<.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.00015 106.1869 187.3953 133.3652 146.3531 144.332 110.2637 89.6512
<.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.00016 106.6711 193.7086 133.7238 146.3647 146.8309 114.9357 89.765
<.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.00017 113.8103 193.7267 135.0414 153.8459 148.5971 114.9392 89.7745
<.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.00018 113.8552 195.7909 138.2853 154.4674 152.8402 115.1015 90.6641
<.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.00019 115.8101 196.7214 138.7214 154.6126 152.8558 136.5223 92.0599
<.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.000110 118.44 197.1581 138.8659 154.6217 152.8568 136.7153 94.913
<.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.000111 127.1328 198.3223 144.5551 155.1908 153.1534 139.1094 95.8679
<.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.000112 127.9659 198.6353 144.6624 155.3002 157.2184 139.8777 95.9731
<.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001
37
Table 5: GARCH (1,1) Model Results for the G7 Nation Bond- and Equity-IndexReturnsThis table displays the key parameters and metrics from the GARCH (1,1) equation,where volatility is modeled as 2 2 2
1t t tσ α βσ γη−= + + and 21~ (0, )t tNη σ+ . The first 4
columns list the coefficients from the GARCH Model. Given in the parentheses beloweach of the GARCH coefficients is the relevant t-stat (All valves are significant at the 1%level). The last 3 columns contain evaluation metrics from the GARCH estimates,specifically, the unconditional variance (UCV), Log Likelihood ratio (LL), and theAkaike information criterion (AIC).
Panel A:Bond-indexResults
Country Intercept γ β UCV LL AIC US
(n=1256)0.001737
(6.08)5.4004E-6
(3.47)0.1066(6.97)
0.8556(38.93)
0.0001428 3882.881 -7757.76
UK(n=1256)
0.001957(6.82)
1.0612E-6(3.55)
0.0396(6.83)
0.9534(160.71)
0.0001511 3862.941 -7717.88
Canada(n=994)
0.001955(6.48)
4.9709E-6(2.74)
0.0654(3.48)
0.8862(27.70)
0.00010273 3189.201 -6370.40
France(n=989)
0.001991(8.07)
2.8949E-6(3.13)
0.0741(5.48)
0.8862(41.61)
0.0000728 3342.056 -6676.11
Germany(n=1256)
0.001716(8.92)
2.2699E-6(3.94)
0.1057(7.44)
0.8586(46.73)
0.00006362 4411.160 -8814.32
Italy(n=669)
0.001984(6.13)
9.9233E-7(3.00)
0.0615(6.63)
0.9277(95.48)
0.0000914 2171.942 -4335.88
Japan(n=1047)
0.001226(5.75)
3.3906E--6(6.20)
0.1202(7.93)
0.8320(47.37)
0.00007089 3635.059 -7262.11
38
Panel B: Equity-Index Results
Country Intercept γ β UCV LL AIC US
(n=1256)0.003301
(5.86)0.0000157
(3.81)0.1053(7.15)
0.8666(44.98)
0.00056049 3074.113 -6140.22
UK(n=1256)
0.003598(6.36)
0.0000393(3.94)
0.1161(6.97)
0.8045(28.76)
0.00049569 3076.625 -6145.25
Canada(n=1256)
0.002614(5.13)
0.0000185(3.87)
0.1154(7.21)
0.8427(38.67)
0.00044113 3190.307 -6372.61
France(n=1256)
0.004035(5.72)
0.0000542(4.89)
0.1583(8.83)
0.7719(28.48)
0.00077628 2829.931 -5651.86
Germany(n=1256)
0.002819(4.99)
0.0000118(4.04)
0.1104(8.86)
0.8730(62.44)
0.00071215 3016.323 -6024.64
Italy(n=1256)
0.002955(3.44)
0.0000642(3.63)
0.1184(6.41)
0.8230(28.48)
0.00109358 2574.085 -5140.17
Japan(n=1256)
0.002380(4.00)
0.0000104(3.30)
0.1086(7.50)
0.8815(61.39)
0.00105154 2930.929 -5853.85