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The EMU and Strategies of Asset Allocation
Paul Ehling∗
UNIL/FAME
Sofia B. Ramos†
UNIL/FAME and CEMAF/ISCTE
March 2002
Preliminary version‡
∗
HEC-University of Lausanne CH-1015 Switzerland. E-mail: paul.ehling@hec.unil.ch
†
HEC-University of Lausanne CH-1015 Switzerland. ISCTE, Av. Forcas Armadas 1649-026, Lisboa
Portugal. E-mails: sofia.correiabritoramos@etu.unil.ch, sofia.ramos@iscte.pt. The author acknowledges financial
support from Fundacao para a Ciencia e Tecnologia.
‡
We thank Jean-Pierre Danthine, Vihang Errunza, René Stulz, Ernst-Ludwig von Thadden, seminar
participants at the FAME Workshops, the 5th Conference of the Swiss Society for Financial Market Research (2002),
and the Euro Conference at NYU (2002) for helpful discussion and comments.
1
The EMU and Strategies of Asset Allocation
March 2002
Preliminary version
Abstract
We question, we argue, and through all of this, we confront two ways of doing
portfolio allocation: country versus industry diversification. Our strategy to rank the
portfolios is based on a new spanning test introduced by Kan and Zhou (2001). The
evidence provided in this paper supports the idea that industry portfolios are equivalent to
country portfolios in the Euro period, contrasting with previous periods that favour
country allocation. However, the results indicate that diversification benefits are not
exhausted when we opt for one of the approaches. Mixing both portfolio strategies offers
diversification gains. Moreover, part of the outperformance of country over industry
diversification disappears when we introduce restrictions on short selling. We group our
sample of European countries according to their ’status’ in relation to the EMU to
ascertain the importance of the monetary union on the two diversification approaches.
Unfortunately, from the results of this work, we cannot presently say whether the EMU
plays any causal role for the questions we raise.
JEL classification: G11, G15.
Keywords: Diversification gains, EMU, mean variance spanning.
2
1 Introduction
The gains from diversification and their implication for portfolio choice are one of
the major topics in financial economics. A closely related and thus an important question
is what factors drive the covariation in stock returns. From an international perspective,
this problem can be reformulated to the question of what role country and industry factors
play in explaining the variation in asset returns for a global portfolio. This issue has been
thoroughly addressed in a sequence of papers, Lessard (1976), Heston and Rouwenhorst
(1994), Griffin and Karolyi (1998)1, and the widespread consensus of these studies is that
country factor dominates industry factor2. A typical, though not tested, upshot from the
referred literature, see for instance the abstract of Heston and Rouwenhorst (1994), is that
country diversification is the superior strategy for risk reduction.
Therefore, in our paper, we address the question whether country allocation really
offers benefits over industry allocation. Our strategy is based on a new and very flexible
spanning test introduced by Kan and Zhou (2001), KZ hereafter. In principle, mean-
variance spanning tests are used to address the hypothesis that the efficient frontier of a
set of benchmark assets is the same as the efficient frontier of those benchmark assets and
some new assets3. We raise a slightly different question, namely whether a set of industry
portfolios can improve the minimum-variance frontier of country portfolios and vice-
versa. The so called step-down approach of KZ has the advantage4 that, in case spanning
is rejected, one knows exactly if the rejection originates from a difference in the means
between the test asset and the benchmark asset, that is, the slope of the tangency
portfolios starting from the origin is incongruent, or if the standard deviation of the
minimum variance portfolios are not the same.
An important ingredient to this story is the stylized idea that economic integration
would change the typical dominance of country factors over industry factors. Therefore,
we utilize a well-defined event of economic integration, namely the European Monetary
Union5, henceforth the EMU. Our second most important objective is resting exactly
upon this stylized assumption and, consequently, we shed more light on the impact of
EMU on diversification strategies in Europe. We isolate the EMU effect by considering
different kinds of samples: the EMU countries, European Community (EC) but non EMU
1
See Errunza and Padmanablan (1988), Grinold, Rudd and Stefek (1989), Drummen and Zimmermann (1992), Roll
(1992), Heston and Rouwenhorst (1995), Arshanapalli, Doukas and Lang (1997), Rouwenhorst (1999), Heckman, Narayanam and
Patel (1998) and Adjaouté and Danthine (2001a, b) for more on this.
2
There is, however, evidence that industry effects are getting more important (Roll (1992), Isakov and Sonney (2001) and
Carrieri, Errunza and Sarkissian (2002)).
3
Mean variance spanning tests, for instance, have been applied to the study of benefits of international diversification
mainly to the study of emerging markets as test assets (Bakaert and Urias (1996), and Errunza, Hogan, and Hung (1999)).
4
Gerard, Hillion and de Roon (2002) apply in a similar context, for a different time period and different data set, also a
spanning test. Our work differs from theirs in several aspects. First, the Jensen measure, that they use, implies that one believes in the
existence of a risk free rate that can be utilized in real life applications for portfolios. Second, it is well known that in practice the
minimum variance portfolio tends to perform well because it does not involve estimation of mean returns. Therefore, the minimum
variance portfolio, which plays a role in the tests we use, seems to be of interest. Clearly, the test of KZ is more general and as it will
be clear from section 2 also more flexible. Finally, the tests that are conducted in Gerard, Hillion an de Roon (2002) compare only
means, and, hence, it is questionable if their analysis should be labled as spanning test.
5
Note that the main impact of the Euro was the elimination of the foreign exchange rate risk within the Euro space, but its
effects extend to other areas like the elimination of constraints, for instance for pension funds, that could have enhanced the economic
segmentation of markets. Further, integration is well defined only from an asset pricing perspective, i.e. integration is when assets are
priced by global factors.
3
countries and others that are in a process of future entrance to the EC. We also cut the
data into three different periods: pre-convergence, convergence and Euro. Our claim is
that the four different groups, EMU countries, EC but non-EMU countries and EC
candidates, should reveal different levels of economic integration. That is, we wonder, in
general, whether country diversification is still the dominant portfolio allocation decision,
if ever, and, in particular, if the advent of the EMU has an impact on portfolio strategies
or not.
Our findings are the following: First, our results are aligned with the major
findings of the literature in the sense that country portfolios exhibit a higher mean
compared to industry portfolios over the whole sample. In particular, in the first two
subperiods we find that industries underperformed countries, i.e. overall industry
portfolios tend to be located below the security market line constructed out of country
indices. In the Euro period, industry strategies are as good as country motivated
portfolios, that is, they have the same mean. These results are robust across all tests we
undertake. Short sales restrictions are the exception. In this particular case part of the
outperformance of countries over industries is reduced. About the mimicking capabilities
of country and industry portfolios, our empirical results speak rather clearly, countries are
successful in explaining industry portfolios, but industry portfolios are not successful in
explaining country portfolios. However, we detect that countries are losing their ability of
mimicking industries and, hence, the tracking error is increasing with time.
Second, as to the role of EMU in strategies of asset allocation, somewhat
surprisingly and contrary to our expectations we cannot detect evidence of EMU
correspondence. Put differently, almost all results are identical across the groups of
countries. This means either the EMU is not responsible for the apparent shift in the mean
returns, at least not in a direct way6, or it affected all the countries in Europe regardless if
they joined the EMU or not.
Third, it deserves emphasis that our results indicate that neither country portfolios
span industry portfolios nor industry portfolios span country portfolios. Implying that
country motivated portfolios provided diversification benefits over industry portfolios, if
any, only in the case investment took place close to the tangency portfolios starting from
the origin. Hence, if this was or is not the case, investors should include both country
indices as well as in industry indices in their portfolio. Investing only in sectors or
countries does not exhaust the benefits of international diversification.
The paper proceeds as follows. In section 2, we briefly recall the nature of mean-
variance spanning and its application to our problem. Section 3 describes the data. In
section 4, we present our results. Concluding remarks are provided in Section 5.
6
Bolliger (2001) points out that most banks have reorganized their research departments according to industries. If this
reorganization led also to an immediate restructuring of the portfolios from country diversification to industry diversification, it is, in
principle, possible that we observe probably a unique and thus biased phenomena due to a massive flow of funds from country indices
to industry indices.
4
2 Methodology
2.1 Unconditional Me an Variance Spanning
The literature on mean variance spanning tests was initiated by Huberman and
Kandel (1987) who introduced regression-based tests for the spanning hypothesis. The
principle of mean-variance spanning is based on a set of K benchmark assets and a set of
N test assets. The K assets span a larger set of N+K assets if the minimum-variance
frontier of the K assets is identical to the minimum variance frontier of the N+K assets.
Whether this is the case or not can be tested by projecting the test assets on the
benchmark assets, that is,
Yt = α + ßX t + ε t , t = 1,...T ( 1)
where Y (N×1) are the returns on the N test assets at time t, 1×1) contains intercepts
DQG 1×K) the regression coefficients, X is an K-vector of returns on the benchmark
assets and, finally, (N×1) is the error term. The necessary and sufficient conditions for
mean variance spanning provided originally by Huberman and Kandel (1987) are, H0:
× 1Ι N and 1Ι N - × 1Ι K =0, where 1Ι Z denotes a Z-vector of ones. Kan and Zhou
(2001) propose to analyze in separate the two components of the spanning test
hypothesis. They show that the test is very sensitive to the restrictions on the betas,
although the restriction on the alphas has much more economical importance. Therefore
they propose two null hypothesis: H0 × 1Ι N and H0: 1Ι N - × 1Ι K =0 conditional on
× 1Ι N . The interpretation is the following H0 × 1Ι N tests if the tangency portfolio
has zero weight in the N test assets. Consider that X in equation 1 represents the SML,
hence, we check whether Y is above or below X. In other words we test the hypothesis of
X and Y exhibiting identical means. The second part of this step-down procedure, H0:
1Ι N - × 1Ι K =0, tests whether the global minimum variance portfolio has zero weights in
the test assets, i.e. is X sufficient to achieve all diversification benefits. In the remainder
we will denote the two parts of the test as Test 1 and Test 2, respectively. Note that for
mean variance spanning to hold both parts of the test have to be accepted. Another
important comment to be made here is that the overall significance level of the test is
p1 + p 2 − p1 p 2 , where p1 denotes the significance level of the first part of the step-down
procedure and p 2 is associated with the second part of the test. For more details on this,
in particular on the power of the tests, we refer the reader to KZ.
2.2 Country versus industry diversification
To confront portfolios based on country and industry diversification, we employ
the step-down tests of KZ introduced above. In our setting, assuming investors or
portfolio managers follow a strategy based on indices, we have two sets of benchmark
assets and two sets of test assets. This is because investors can construct their portfolio
either entirely out of country indices or industry indices. Define R C as the vector of raw
t
5
returns of m countries at time t and R It as the vector of raw returns of n industries at time
t. Consequently, two type of regressions are carried out in this paper
R C = α C + β C R It + ε tC ,
t t = 1,...T ( 2)
R It = α I + β I R C + ε tI ,
t t = 1,...T ( 3)
where α C , α I , β C , β I are the parameters to be estimated. Now, if α C =0× 1Ι and
β C × 1Ι =1 conditional on α C =0× 1Ι hold we can, indeed, conclude that investors should
base their strategies on industry portfolios only, since industries span countries. On the
other hand α I =0× 1Ι and β I × 1Ι =1 conditional on α I =0× 1Ι implies the opposite, that
is, country allocation is the superior portfolio diversification strategy, and, thus, mean
variance spanning is not rejected7. However, it is also possible that both null hypotheses
are rejected and, therefore, investors should form their portfolios out of country and
industry indices. Although the proposed procedure seems to be standard, one should bear
in mind some unavoidable weaknesses. First, even though the method of KZ reduces the
probability of a rejection of spanning due to the estimation problems DVVRFLDWHG ZLWK
this does not, in no way, improve the accuracy of the estimation. For instance, we
REVHUYH LQ RXU VDPSOH WKDW FRXQWULHV IDLO WR VSDQ WKHLU RZQ JURXS EHFDXVH LV UHMHFWHG
EXW ×1I=1 holds. Second, given that returns exhibit conditional heteroskedasticity our
OLS approach may lead to over rejections of the null hypothesis. KZ report, however,
that theoretically as well as empirically the results of an OLS regression are robust to
conditional heteroskedasticity. Further, for a comparison of performance between the
regression approach and the stochastic discount factor we refer the interested reader to
KZ.
3 Data
We use DataStream country and sector indices for the 11 EMU entrants8: Austria,
Belgium, Germany, Spain, Finland, France, Ireland, Italy, Greece, Netherlands and
Portugal. The following European countries are also considered Czech Republic,
Denmark, Hungary, Norway, Poland, Sweden, Switzerland and UK. Countries are
assigned to a group. Groups differentiate in relation to the level of monetary and
economical integration. The Group I is composed by the countries that belong
simultaneously to the EC and EMU, and consequently should present a higher level of
integration. Group II is composed by the countries that belong to the EC but not the
EMU. Group III contains the EC candidates and in Group IV are other European
countries.
7
A common approach is to use Sharpe ratios as measure of performance of portfolios (Gerard, Hillion and de Roon, 2001)
or evaluate changes in the Sharpe ratio for the test assets (Bekaert and Urias, 1996, Errunza, Hogan, Hung, 1999).
8
Note that Greece joined the Euro-zone in 2001 and Luxembourg is ignored.
6
Table 1: Composition of the groups
Groups Countries
Group I EC and EMU Austria, Belgium, Germany, Spain
Finland, France, Ireland, Italy
Netherlands, Portugal, Greece
Group II EC and non EMU UK, Denmark, Sweden
9
Group III EC candidates Hungary, Poland, Czech Republic
Group IV Others Switzerland, Norway.
The data provided by DataStream is weekly Euro denominated ranging from
January 1, 1988 till the end of December of 2001 (731 observations)10. The sample is also
cut in different subperiods not only to capture time patterns but one of the crucial
DVVXPSWLRQV RI WKH HVWLPDWLRQ SURFHGXUH LV WKDW DQG DUH FRQVWDQW RYHU WLPH ZKLFK Ls
more probable in short time periods.
Table 2: Description of the time periods
Sample Data Range Observations
Pre-convergence 01/01/1988-30/12/1994 365 observations
Convergence 11 06/01/1995-25/12/1998 208 observations
Euro 01/01/99-28/12/2001 157 observations
We focus our analysis on level three of DataStream12 sectors classification which
corresponds to 10 sectors: Cyclical Services (CS), Financials (FI), Information
Technology (IT), Noncyclical Services (NCS), Utilities (UT), Resources (RE), Basic
Industries (BI), General Industries (GI), Cyclical Goods (CG) and Non Cyclical Goods
(NCG). Based on these groups we recomputed the industry indices by building market
value weighted indices.
3.1 Descriptive statistics
In Table 3, we report the descriptive statistics of the country indices for the whole
period and the three subperiods. Since the whole sample includes a long period where
many important structural changes occurred in Europe, we direct our attention towards
the subperiods. Apparently, the mean return of the countries went through different
cycles over the time period under consideration. In particular, there seems to be a second
important reason, apart from the advent of the EMU, why cutting the time series into
three subperiods is a good strategy. During the convergence period for the Euro
candidates almost all stock markets in the world experienced a dramatic increase in value.
9
The new members scheduled for 2004 includes the countries in group III plus Slovenia, Slovakia and the three Baltic
republics, DataStream global indexes do not include the latter ones. Other candidates are Turkey, Bulgaria and Romania, but
DataStream global indices only account for Turkey.
10
The 11 EMU countries have the time series in Euros. All the other were in the national exchange rate. First they were
converted to £/british pound and then to Euros using the UK-Euro synthetic exchange rate. After 99, all countries have the exchange
rate against the Euro, which is what we used.
11
The convergence period goes from January 1995 to January 1999. The starting date of the convergence period is
associated with the signature of the Maastricht treaty and the end (December 31, 1998) with the fixing of the conversion rates.
12
DataStream offers several comparative advantages in relation to other data suppliers. First, DataStream provides a more
comprehensive industry desegregation that classifies indices into one of six levels. Level one has a broader grouping, while in the
other extreme, level six contains the maximum detailed classification. Note that some sectors do not exist in certain countries or the
history of the data is too short. Second, the definition of industries is consistent for all countries of the DataStream database, which
eliminates the potential bias induced by misclassification of firms. For more pros and cons of other data providers like MSCI compare
the discussion in Gerard, Hillion, and de Roon (2001).
7
For example, in the longest subperiod, pre-convergence, we observe only one country
with a return higher than 25%. Further, in the Euro period, which is somewhat short,
there is again only one country with an impressive return of about 25%. In contrast, the
convergence period exhibits for almost all countries returns in quite high double digits. In
the same vein the average mean in the pre-convergence period is 6.87% and in the Euro
period we observe an average mean return of 2.62% whereas in the convergence period
the mean is 23.13%. The patterns of the time series for the standard deviation of returns
are very similar to the one of the means. Again as for means and volatilities we observe a
uniform and drastic increase of correlation in the convergence period among countries
and between countries and industries. This increase is followed, as in the case of means
and standard deviations, by a less pronounced and less uniform drop in the Euro period13.
The up and down of correlations, however, takes place at very different levels.
Correlations between countries tend to be high and are never negative. On the other hand,
Table 3 also reports that 13 out of 19 correlations between countries and industries are
negative in the pre-convergence period. This value drops to 3 in the convergence period
and increases to 5 in the Euro period. Furthermore, correlations between countries and
industries are usually very close to zero and never above 0.2. That is, the average
correlation of countries, from all groups and over all periods, with industries is strikingly
low14. It deserves emphasis that this is the case even though the country and industry
returns are not pure. The low correlations suggest that adding industries to country
portfolios seems a promising strategy, as well as gives an indication about the result of
the spanning tests. In what concerns to correlation of industries, Table 4, nearly none of
the values in the very untypical convergence period exhibits differences to correlations in
other periods. In the Euro period we observe a decrease in the level of correlation, also
reported by Adjoute and Danthine (2001), but in contrast to the findings for countries,
industry correlations seem to be much more stable and larger on average.
13
The instability of correlation matrixes is a well-documented fact in the finance literature (Longin and Solnik, 1995,
Adjoute and Danthine, 2001), therefore, small changes in the correlations should not be emphasised. The most striking result is the
increase of correlation from countries of Group III that seems to be structural.
14
To our knowledge this has been reported first by Roll (1992).
8
Table 3: Descriptive Statistics for Countries
By columns: Annualized mean and standard deviation, average correlation with the sample countries, and average correlation with the 10 sectors.
Sample Whole Pre-Convergence Convergence Euro
Countries Mean Stdv. Corr(C) Corr(I) Mean Stdv. Corr(C) Corr(I) Mean Stdv. Corr(C) Corr(I) Mean Stdv. Corr(C) Corr(I)
AU 8.81% 18.15% 0.39 0.03 15.60% 21.54% 0.35 -0.36 3.28% 14.49% 0.48 0.11 0.37% 13.19% 0.29 0.01
BG 10.12% 14.69% 0.47 0.02 8.37% 12.54% 0.49 -0.09 25.12% 14.60% 0.52 0.08 -5.67% 18.64% 0.42 -0.03
GE 11.11% 17.70% 0.6 -0.03 10.47% 14.88% 0.47 -0.03 18.98% 16.94% 0.59 0.03 2.15% 23.73% 0.63 -0.09
SP 11.33% 18.29% 0.56 0.04 6.29% 16.53% 0.37 -0.08 29.86% 19.30% 0.57 0.06 -1.53% 20.45% 0.58 0.03
FI 18.49% 29.79% 0.42 0.01 6.52% 21.70% 0.41 -0.12 33.24% 26.18% 0.51 0.12 25.83% 45.74% 0.40 -0.06
FR 13.34% 17.86% 0.57 0.01 11.12% 15.97% 0.47 -0.09 20.18% 17.59% 0.56 0.00 9.45% 22.00% 0.60 0.02
IR 15.45% 17.93% 0.47 0.07 13.40% 17.31% 0.47 0.04 27.01% 16.93% 0.52 0.11 4.93% 20.42% 0.42 0.03
IT 9.14% 21.93% 0.49 0.04 5.13% 20.50% 0.20 -0.31 22.03% 22.46% 0.48 0.13 1.40% 24.34% 0.58 0.00
GR 23.44% 32.80% 0.32 0.03 25.24% 33.60% 0.09 -0.04 37.32% 29.10% 0.38 0.05 0.85% 35.44% 0.29 0.02
NL 13.05% 15.35% 0.58 0.06 10.79% 10.75% 0.47 0.06 24.93% 17.38% 0.60 0.09 2.57% 20.60% 0.58 0.03
PT 5.42% 16.65% 0.44 -0.02 -1.39% 14.02% 0.29 -0.28 23.25% 18.79% 0.49 0.05 -6.91% 17.35% 0.42 -0.07
UK 8.16% 15.73% 0.47 0.03 11.06% 14.60% 0.43 0.04 12.69% 15.13% 0.44 0.01 -4.57% 18.75% 0.51 0.03
DK 13.91% 16.15% 0.42 -0.02 13.52% 15.91% 0.30 -0.06 18.82% 14.49% 0.43 0.03 8.30% 18.67% 0.43 -0.06
SW 17.38% 23.39% 0.49 0.04 17.17% 23.82% 0.43 -0.04 23.89% 21.22% 0.52 0.05 9.26% 25.16% 0.48 0.03
HG 27.41% 29.85% 0.40 0.00 16.23% 23.96% 0.18 0.12 58.80% 34.49% 0.43 -0.05 -1.08% 28.88% 0.39 -0.02
PL 7.72% 39.83% 0.25 0.16 -67.70% 78.58% 0.11 0.02 28.34% 34.82% 0.31 0.20 1.07% 28.73% 0.32 0.13
CZ -1.34% 24.53% 0.27 0.06 -5.49% 37.44% 0.00 -0.16 -2.46% 20.24% 0.31 0.09 1.71% 23.80% 0.29 0.03
CH 13.54% 22.63% 0.48 0.02 19.54% 23.91% 0.44 -0.04 9.03% 20.89% 0.50 -0.03 5.56% 21.84% 0.49 0.05
NO 13.68% 16.04% 0.51 0.00 14.70% 13.63% 0.31 -0.08 25.14% 16.66% 0.53 -0.03 -3.87% 19.79% 0.51 0.02
Average 12.64% 6.87% 23.13% 2.62%
9
Table 4: Descriptive Statistics for Industries
By columns: Annualized mean and standard deviation, average correlation with the industries, and average correlation with the countries.
Sample Whole Pre-Convergence Convergence Euro
Industries Mean Stdv. Corr(I) Corr(C) Mean Stdv. Corr(I) Corr(C) Mean Stdv. Corr(I) Corr(C) Mean Stdv. Corr(I) Corr(C)
BI 5.64% 15.17% 0.70 0.08 5.08% 13.69% 0.78 -0.03 6.56% 14.22% 0.77 0.11 5.74% 19.24% 0.59 0.06
CG 4.68% 19.00% 0.67 0.08 4.93% 14.84% 0.68 -0.11 11.77% 19.70% 0.76 0.10 -5.37% 25.66% 0.62 0.07
CS 8.29% 15.68% 0.71 0.08 7.66% 13.85% 0.76 -0.03 16.80% 12.89% 0.77 0.13 -1.57% 21.88% 0.65 0.04
FI 9.48% 16.23% 0.71 0.04 5.68% 12.18% 0.76 -0.14 21.76% 18.09% 0.76 0.10 2.04% 21.14% 0.66 -0.02
GI 8.36% 16.16% 0.73 -0.04 7.88% 13.38% 0.76 -0.04 12.94% 15.55% 0.80 0.01 3.35% 21.96% 0.66 -0.12
IT 17.04% 28.87% 0.56 0.03 14.04% 16.83% 0.60 -0.07 33.84% 28.59% 0.66 0.08 1.67% 46.35% 0.50 -0.01
NCG 13.43% 13.66% 0.62 0.05 12.29% 11.99% 0.72 -0.07 22.64% 14.14% 0.75 0.06 3.80% 16.35% 0.44 0.05
NCS 10.56% 20.20% 0.70 -0.03 9.05% 14.79% 0.78 -0.16 26.56% 16.22% 0.79 0.03 -7.26% 32.26% 0.49 -0.07
RE 10.58% 18.86% 0.50 0.00 8.31% 14.62% 0.55 -0.05 13.65% 18.72% 0.64 -0.07 11.81% 26.47% 0.38 0.05
UT 9.39% 12.00% 0.55 0.01 10.42% 11.91% 0.64 -0.08 19.49% 11.10% 0.59 0.02 -6.48% 13.07% 0.46 0.00
Average 9.74% 8.53% 18.60% 0.77%
10
4 Empirical Results
4.1 Industry versus country allocation
In the first type of regressions, equation (2), the benchmark assets are the
industries from one of the groups, and the test assets are the corresponding country
indices. Table 5 contains alpha and its p-value country by country, Table 7 reports Test 1
for each of the groups, and the conditional test of all betas summing up to one, Test 2.
The overall picture shows an evolution over time for Test 1, it starts from
rejecting the null, till in the last period it does not reject, meaning that country indices do
have at least as high mean as industry portfolios, i.e. they pass the first part of the
spanning test. But due to the second part of the test, Test 2, spanning is always rejected.
For the whole sample we observe that the p-value for the first part of the spanning test is
too low for Group II and Group III to be justified with equal returns. This happens in the
pre-convergence period for Group I and again Group III. In the convergence period only
Group III fails the test and in the Euro period all groups pass the first part of the step-
down procedure. Note also that the intercept in the regressions tends to be positive
suggesting that if there is any difference between the means, country indices do have a
higher return. However, this finding is statistically insignificant and it seems to disappear
in the Euro period.
In the second round of regressions, equation (3), the benchmark assets are the set
of countries that compose the groups and the test assets are the industries common to that
group. If α I =0 it means we can base our strategies on countries, but a common fact to all
regressions, Table 6, is that many are negative. Given that for Group I the joint test tend
to reject that alphas are jointly equal to zero, Table 7, it means that industries
underperform compared to an investment in countries. For Group III we cannot
distinguish between the diversification approaches for the whole period and all
subperiods, that is, country portfolios yield exactly the same results in terms of returns as
industry portfolios. Group III appears to be very similar to Group I. The first part of the
spanning test, Test 1, is rejected for Group IV and its industries for the whole period and
the pre-convergence period, whereas in the convergence and Euro period the null
hypothesis is not rejected. Note that in the Euro period we cannot rank the portfolio
strategies in terms of their means. Lastly, as for the case with countries, spanning is
always rejected due to Test 2.
11
Table 5: Summary of results of regression (2)
C
By columns: is the intercept of the regression and p is the probability associated with the t-test.
Sample Whole Pre-Convergence Convergence Euro
C C C C
Countries p p P p
AU 0.06% 0.39 0.22% 0.07 -0.07% 0.54 -0.01% 0.94
BG 0.04% 0.44 0.03% 0.62 0.13% 0.17 -0.05% 0.65
GE 0.05% 0.12 0.11% 0.00 0.08% 0.18 0.04% 0.60
SP -0.01% 0.89 -0.14% 0.04 0.01% 0.89 0.04% 0.74
FI 0.13% 0.19 0.11% 0.45 0.11% 0.49 0.29% 0.12
FR 0.00% 0.97 -0.02% 0.72 -0.01% 0.84 0.16% 0.02
IR 0.16% 0.03 0.13% 0.24 0.26% 0.03 0.05% 0.79
IT 0.04% 0.56 0.04% 0.63 -0.01% 0.92 0.10% 0.34
GR 0.35% 0.03 0.50% 0.04 0.43% 0.11 -0.04% 0.91
NL 0.05% 0.14 0.05% 0.10 0.06% 0.33 -0.01% 0.89
PT 0.02% 0.76 -0.04% 0.71 0.15% 0.26 -0.03% 0.80
UK 0.04% 0.52 0.14% 0.10 0.07% 0.52 -0.13% 0.40
DK 0.16% 0.03 0.18% 0.11 0.15% 0.19 0.17% 0.29
SW 0.15% 0.06 0.10% 0.39 0.08% 0.50 0.24% 0.10
HG 0.62% 0.00 0.23% 0.74 1.04% 0.00 0.05% 0.84
PL 0.27% 0.07 1.60% 0.00 0.56% 0.00 0.07% 0.73
CZ -0.05% 0.65 -0.13% 0.75 -0.04% 0.75 0.16% 0.39
CH 0.09% 0.13 0.09% 0.33 0.19% 0.05 -0.03% 0.83
NO 0.01% 0.69 0.00% 0.97 0.09% 0.17 -0.07% 0.37
12
Table 6: Summary of results of regression (3)
I
is the intercept of the regression and p is the probability associated with the t-test.
Sample Whole Pre-Convergence Convergence Euro
I I I I
Group I p p P p
BI -0.08% 0.07 -0.07% 0.08 -0.13% 0.04 0.07% 0.58
CG -0.15% 0.01 -0.08% 0.19 -0.27% 0.00 -0.11% 0.50
CS -0.05% 0.20 -0.02% 0.53 0.03% 0.62 -0.12% 0.28
FI -0.06% 0.07 -0.08% 0.01 -0.12% 0.04 -0.01% 0.91
GI -0.07% 0.04 -0.07% 0.03 -0.09% 0.05 -0.01% 0.91
IT -0.06% 0.46 0.05% 0.59 0.04% 0.81 -0.34% 0.03
NCG 0.09% 0.06 0.06% 0.13 0.06% 0.28 0.07% 0.62
NCS 0.02% 0.78 0.12% 0.03 0.14% 0.07 -0.25% 0.13
RE -0.01% 0.83 -0.06% 0.30 -0.04% 0.71 0.08% 0.66
UT 0.08% 0.05 0.12% 0.01 0.15% 0.03 -0.10% 0.39
Group II
BI -0.07% 0.38 -0.12% 0.22 -0.27% 0.01 0.23% 0.27
CG -0.13% 0.16 -0.14% 0.22 -0.19% 0.19 -0.08% 0.78
CS -0.02% 0.81 -0.02% 0.81 0.02% 0.83 -0.07% 0.69
FI 0.04% 0.58 -0.04% 0.69 0.06% 0.65 0.16% 0.42
GI -0.04% 0.57 -0.05% 0.62 -0.10% 0.37 0.00% 1.00
IT -0.02% 0.90 0.20% 0.19 0.09% 0.64 -0.48% 0.10
NCG 0.11% 0.17 0.01% 0.89 0.14% 0.27 0.13% 0.54
NCS -0.01% 0.90 -0.02% 0.88 0.20% 0.22 -0.23% 0.49
RE 0.07% 0.49 0.00% 1.00 -0.01% 0.96 0.23% 0.44
UT 0.13% 0.19 0.11% 0.43 0.17% 0.30 -0.03% 0.88
Group III
BI -0.42% 0.00 -0.22% 0.61 -0.79% 0.00 -0.03% 0.89
CG -0.38% 0.09 -1.53% 0.05 -0.76% 0.05 0.17% 0.46
CS -0.37% 0.02 -1.76% 0.00 -0.45% 0.09 -0.10% 0.60
FI -0.25% 0.05 -1.34% 0.00 -0.48% 0.00 0.36% 0.08
GI -0.37% 0.10 -1.86% 0.02 -0.30% 0.29 -0.24% 0.55
IT -0.27% 0.42 0.06% 0.96 -0.31% 0.55 -0.25% 0.56
NCG -0.40% 0.00 -1.08% 0.03 -0.71% 0.00 0.05% 0.81
NCS -0.13% 0.59 0.61% 0.77 -0.19% 0.45 -0.22% 0.30
RE -0.34% 0.09 -1.37% 0.23 -0.69% 0.01 -0.01% 0.96
UT -0.19% 0.19 0.16% 0.74 -0.35% 0.10 -0.07% 0.73
Group IV
BI -0.04% 0.50 -0.03% 0.71 -0.17% 0.20 0.03% 0.80
CG 0.13% 0.32 0.27% 0.18 -0.17% 0.43 0.35% 0.18
CS -0.10% 0.26 -0.16% 0.13 -0.02% 0.91 -0.04% 0.86
FI -0.04% 0.46 -0.08% 0.24 -0.06% 0.65 0.09% 0.49
GI -0.12% 0.10 -0.06% 0.48 -0.17% 0.13 -0.10% 0.66
IT -0.21% 0.01 -0.40% 0.00 -0.08% 0.42 0.00% 0.98
NCG 0.13% 0.00 0.15% 0.01 0.05% 0.52 0.09% 0.41
NCS -0.02% 0.89 -0.03% 0.86 -0.05% 0.83 -0.09% 0.80
RE 0.03% 0.68 0.08% 0.44 -0.22% 0.09 0.17% 0.40
UT 0.07% 0.28 0.07% 0.43 0.02% 0.89 -0.01% 0.97
13
Table 7: Summary of results of regression (2) and (3)
By columns: R2is the adjusted R2. Test 1 is a joint test whether all are equal to zero. Test 2 is a joint test for the sum of
the coefficients of the regressors. The probability of accepting the null hypothesis is p.
Regression (2) Regression (3)
Group I Av. R2 Test 1 p Test 2 p Av. R2 Test 1 p Test 2 p
Whole 0.58 17.68 0.09 218.36 0.00 0.76 27.04 0.00 340.65 0.00
Pre-Convergence 0.52 26.34 0.01 148.70 0.00 0.83 32.22 0.00 112.96 0.00
Convergence 0.67 14.34 0.21 107.90 0.00 0.81 32.50 0.00 260.13 0.00
Euro 0.67 10.06 0.53 158.40 0.00 0.73 9.96 0.44 55.10 0.00
Group II
Whole 0.41 8.87 0.03 592.22 0.00 0.32 7.52 0.68 360.57 0.00
Pre-Convergence 0.35 5.92 0.12 273.81 0.00 0.35 5.80 0.83 145.96 0.00
Convergence 0.51 2.62 0.45 130.08 0.00 0.41 13.21 0.21 118.49 0.00
Euro 0.54 4.63 0.20 174.01 0.00 0.32 6.35 0.78 205.73 0.00
Group III
Whole 0.55 21.01 0.00 82.61 0.00 0.40 39.41 0.00 159.33 0.00
Pre-Convergence 0.58 9.25 0.03 10.99 0.01 0.34 39.72 0.00 27.83 0.00
Convergence 0.63 40.56 0.00 107.43 0.00 0.46 65.98 0.00 34.82 0.00
Euro 0.56 0.91 0.82 40.58 0.00 0.41 5.92 0.82 282.48 0.00
Group IV
Whole 0.79 2.50 0.29 43.41 0.00 0.40 22.41 0.01 1147.01 0.00
Pre-Convergence 0.79 0.95 0.62 20.24 0.00 0.40 23.16 0.01 356.01 0.00
Convergence 0.82 5.61 0.06 26.30 0.00 0.43 8.79 0.55 654.04 0.00
Euro 0.80 0.85 0.65 8.32 0.02 0.42 4.05 0.94 403.74 0.00
Overall, the empirical evidence supports that country portfolios have been the
better way to invest in the past. Even though in the euro period, the traditional advantage
of country portfolios over industry portfolios seems to disappear. But all these findings
depend heavily on the assumption that investors hold a portfolio close to the tangency
portfolio passing through the origin. In the same vein, if investors have been or are
interested in holding the minimum-variance portfolio, there is statistical and economical
evidence that investing in country and industry portfolios is the best strategy. In terms of
diversification gains the second part of the test, Test 2, tells us in all cases we consider
that benefits are not exhausted when we opt for one of the strategies. Moreover, we
cannot detect evidence for any kind differences in the groups of countries. In other words
the pattern of evolution for the tests is almost identical across groups. Unfortunately, this
implies that from the results of our work, we cannot presently say whether the EMU
plays any causal role for portfolio diversification.
Given that we do not find convincing evidence about EMU being responsible for
our results and, therefore, one may regard the groups as arbitrary, we merge all the
countries. In Table 8, we report the test for countries as well as industries. In this case, we
find that the first part of the test, Test 1, is always rejected in the first three subperiods.
As indicated by our previous findings, the very last period yields quite similar returns for
both portfolio strategies around the tangency portfolio, i.e. we cannot reject the null. The
second part of the spanning test is, as before, always rejected.
To address concerns some part of our findings might be driven by the influence of
country factors in industry indices and industry factors in country indices, which can be
relevant for countries with large weights in some industries and vice-versa, we
recomputed all DataStream indices, excluding the presence of country factors in industry
indices and of industry factors in country factors. In other words, when country x is
regressed on a set of industries, these industry indices will not include any industry
belonging to country x. The tables containing these test statistics can be found in the
appendix. In summery, there are not many differences compared to our previous results.
14
Therefore, we do not elaborate further on the influence of country factors in industry
returns and industry factors in country returns.
Table 8: Results of the tests for regression (2) and (3) without groups
The values are the result of chi-squared tests. p is the probability of accepting the null hypothesis.
Regression (2) Regression (3)
Whole Chi-square value p Chi-square value p
Test 1 136.64 0.00 23.7 0.01
Test 2 3967.15 0.00 8480.14 0.00
Pre-Convergence
Test 1 60 0.00 9.85 0.45
Test 2 1725.89 0.00 2908.00 0.00
Convergence
Test 1 124.32 0.00 47.33 0.00
Test 2 696.71 0.00 3828.14 0.00
Euro
Test 1 5.68 1.00 2.47 0.99
Test 2 792.58 0.00 3399.17 0.00
4.2 Testing for diversification gains
Another relevant question, when we analyze the process of integration of markets,
is whether the enlargement of the economic space will represent a shift in the mean-
variance frontier to the left. Under this setting there are only two groups of countries. The
benchmark assets are the EMU countries, the test assets are the market portfolios from all
the other countries in our sample. One way of testing the relevance of the assets is to
mimic the countries outside the EMU with Group I, that is,
R C = α GI + β GI R GI + ε tGI
t t ( 4)
where GI denotes Group I and R C contains the returns of all countries outside the EMU.
t
Our findings, see Table 9, suggest that for an investor located in one of the countries
participating in the EMU it is very questionable to invest into one or each of the potential
future candidates, as long as the portfolio of the investors is located close enough to the
tangency portfolio starting from the origin. Due to the second part of the test, Test 2,
overall spanning is always rejected. These findings are very similar to KZ. They report
identical results for an US investor considering an investment into a set of developed
countries.
15
Table 9: Summary of results of regression (4)
By columns: the intercept of the regression and p is the probability related with the t-test.
Sample Whole Pre-Convergence Convergence Euro
Countries Intercept p Intercept p Intercept p Intercept p
UK 0.01% 0.84 0.09% 0.31 0.00% 0.98 -0.13% 0.34
DK 0.14% 0.04 0.16% 0.13 0.12% 0.30 0.12% 0.46
SW 0.13% 0.18 0.17% 0.28 0.05% 0.72 0.12% 0.54
HG 0.36% 0.03 0.29% 0.24 0.65% 0.03 -0.07% 0.80
PL 0.00% 1.00 -1.26% 0.45 0.21% 0.50 -0.02% 0.95
CZ -0.13% 0.43 -0.11% 0.87 -0.23% 0.22 0.00% 0.99
CH 0.07% 0.44 0.20% 0.18 -0.19% 0.24 0.06% 0.75
NO 0.09% 0.10 0.15% 0.05 0.13% 0.20 -0.12% 0.42
Table 10: Summary of results of regression (4)
Test 1 is a joint test whether all C are equal to zero. Test 2 is a joint test for the sum of the coefficients of the regressors.
Av. Ad. R2 Test 1 P Test 2 p
Whole 0.28 14.64 0.07 496.67 0.00
Pre-Convergence 0.17 12.26 0.14 115.29 0.00
Convergence 0.34 11.19 0.19 208.56 0.00
Euro 0.37 2.63 0.96 239.17 0.00
4.3 Short sales constraints
Previous work on similar ground indicates that results can change to the opposite
when short sales restrictions are introduced15. Thus both regressions, equation (2) and
equation (3), are re-estimated with short sales restrictions.
Under this setting the number of αC significantly different from zero is reduced,
therefore, we conclude that the outperformance of countries over industries in terms of
their means was very much depending on the fact that short selling was allowed. In the
convergence period only one αC is significantly different from zero (for a confidence
interval of 95%), and none in the Euro period. In regression (3) the number of negative αI
decreases and there are even some positive and significantly different from zero. Again
the results confirm the idea that once the possibility of short selling is eliminated the
outperformance of countries over industries, in terms of their returns, is reduced. In the
Euro period the number of αI significantly different from zero decreases sharply, and the
low values of the chi-square tests indicate that we cannot reject the null.
A striking result is that the sum of the beta coefficients is very close to zero for
the majority of the countries, the only exceptions are UK and Switzerland. Inversely, in
regression (3) the sum of the factor loadings is clearly bigger than one.
15
Roon, Nijman and Werker (2001) introduce short-sales restrictions and transaction costs in mean variance spanning tests.
Their benchmark assets were the MSCI indexes for Europe, US and Japan, while the test assets were from emerging markets. The
diversification benefits that exist from adding the emerging markets to an international portfolio disappeared when they introduce
short-sales restrictions.
16
4.4 Style Analysis
Until now our discussion has focused on the mean variance spanning properties of
strategies of asset allocation. A complementary approach can be added by studying the
mimicking properties of portfolios. Style analysis, see Sharpe (1992), is used to answer
the question whether a set of portfolios can replicate another portfolio. The
implementation requires positive loadings of the factors, ( β i ≥ 0, ∀i ), and, additionally,
∑
the loadings have to sum up to one, ( β i = 1), so that, a mimicking portfolio, the one
that yields the lowest tracking error variance, can be built.
In our paper we raise the question whether the return of a country portfolio can be
replicated by industry portfolios and vice-versa. The intercepts will give the expected
excess return of the test portfolio relative to the mimicking portfolio.
Our empirical results speak rather clearly, countries are successful in explaining
industry portfolios, but industry portfolios are not successful in explaining country
portfolios. The explanation is easy to understand if we recall the results of the previous
subsection when we imposed short-sales constraints only. The sum of betas was
extremely low, summing up in most cases to values close to zero. Therefore, forcing
them to add up to one, yields not only negative R2 but implies a model which is far away
from being optimal. Based on this reasoning it is very difficult if not impossible to
interpret the tests statistics in an appropriate way.
Nonetheless countries can explain the returns of industries. In this case the
intercepts become positive and significantly different from zero, except in the Euro
period where they are no longer different from zero. Another important result is that the
average R2 tends to decrease over time, it is higher in the pre-convergence period than in
the Euro period, hence it seems that countries are losing their ability of mimicking
industries and, hence, the tracking error is increasing.
The contrast of the results is rather puzzling and demands explanations. Other
authors found similar patterns but here they are more drastic. Since our paper concerns
about spanning and the influences of the Euro on asset allocation strategies the apparent
differences in the mimicking properties of portfolios are beyond the scope of the paper
und, thus, will be addressed in future research.
17
Table 11: Summary of results of regression (2) with short selling constraints
For each sample period we report the intercept of regression (2), the probability of the hypothesis αC =0, Σβi is the sum of the coefficients of the regression and R2is the adjusted coefficient of determination
of the regression.
Whole Pre-Convergence Convergence Euro
Countries DC p 6Ei R2 DC p 6Ei R2 DC p 6Ei R2 DC p 6Ei R2
AU 0.00% 0.30 0.01 0.31 0.00% 0.31 0.02 0.45 0.00% 0.15 0.01 0.47 0.00% 0.44 0.00 0.30
BG 0.00% 0.24 0.04 0.58 0.00% 0.33 0.04 0.52 0.00% 0.20 0.04 0.67 0.00% 0.13 0.03 0.70
GE 0.00% 0.33 0.29 0.86 0.01% 0.32 0.34 0.87 0.01% 0.27 0.27 0.88 0.00% 0.41 0.25 0.92
SP 0.00% 0.18 0.10 0.72 -0.01% 0.01 0.10 0.69 0.00% 0.44 0.11 0.84 0.00% 0.37 0.08 0.79
FI 0.00% 0.13 0.04 0.57 0.00% 0.41 0.01 0.14 0.00% 0.41 0.02 0.67 0.00% 0.41 0.05 0.79
FR -0.01% 0.07 0.27 0.85 -0.01% 0.10 0.27 0.82 -0.01% 0.19 0.25 0.86 0.02% 0.11 0.28 0.94
IR 0.00% 0.07 0.01 0.40 0.00% 0.22 0.01 0.28 0.00% 0.05 0.01 0.52 0.00% 0.42 0.01 0.51
IT -0.01% 0.08 0.13 0.67 -0.01% 0.10 0.13 0.57 -0.02% 0.16 0.12 0.66 0.00% 0.46 0.16 0.87
GR 0.00% 0.41 0.01 0.18 0.00% 0.49 0.00 0.11 0.00% 0.30 0.01 0.33 0.00% 0.36 0.01 0.19
NL 0.01% 0.13 0.15 0.82 0.01% 0.10 0.13 0.82 0.01% 0.23 0.19 0.85 -0.01% 0.26 0.15 0.92
PT 0.00% 0.33 0.01 0.35 0.00% 0.19 0.00 0.14 0.00% 0.45 0.02 0.55 0.00% 0.27 0.01 0.50
UK -0.01% 0.06 0.93 0.99 0.00% 0.26 0.95 1.00 -0.01% 0.26 0.89 0.99 -0.02% 0.19 0.91 0.99
DK 0.00% 0.07 0.01 0.28 0.00% 0.12 0.01 0.13 0.00% 0.12 0.02 0.43 0.00% 0.40 0.02 0.43
SW 0.00% 0.22 0.07 0.77 0.00% 0.20 0.05 0.71 -0.01% 0.21 0.09 0.89 0.01% 0.17 0.07 0.83
HG 0.08% 0.01 0.38 0.55 0.12% 0.01 0.44 0.56 0.05% 0.14 0.33 0.81 -0.01% 0.41 0.31 0.72
PL -0.07% 0.03 0.40 0.71 -0.15% 0.00 0.34 0.65 -0.03% 0.24 0.33 0.89 0.01% 0.44 0.56 0.91
CZ 0.02% 0.28 0.39 0.63 0.00% 0.49 0.56 0.65 0.01% 0.42 0.38 0.83 0.04% 0.12 0.24 0.68
CH 0.06% 0.07 0.90 0.82 0.06% 0.14 1.02 0.87 0.06% 0.21 0.79 0.78 0.04% 0.33 0.81 0.79
NO 0.00% 0.48 0.11 0.78 -0.01% 0.21 0.13 0.77 0.01% 0.17 0.10 0.83 -0.01% 0.10 0.09 0.93
18
Table 12: Results of the regression (3) with short selling constraints: whole sample
For each sample period we report the intercept of regression (3), the probability of the hypothesis αC =0, Σβi is the sum of the coefficients of the regression and R2is the adjusted coefficient of determination
of the regression.
Group I DI p 6Ei R2 Group II DI p 6Ei R2 Group III DI p 6Ei R2 Group IV DI p 6Ei R2
BI -0.06% 0.07 21.91 0.78 BI -0.08% 0.09 1.93 0.62 BI -0.05% 0.31 2.43 0.43 BI -0.06% 0.15 5.36 0.57
CS 0.01% 0.39 12.31 0.82 CS -0.03% 0.20 4.21 0.85 CS -0.15% 0.05 1.88 0.37 CS -0.14% 0.03 5.36 0.56
GI -0.01% 0.32 8.35 0.90 GI -0.04% 0.25 4.42 0.66 GI 0.19% 0.07 2.81 0.60 GI -0.13% 0.03 6.44 0.56
FI -0.03% 0.13 18.77 0.88 FI 0.03% 0.28 5.21 0.81 FI -0.15% 0.09 3.14 0.55 FI -0.03% 0.30 7.11 0.58
IT 0.07% 0.16 20.62 0.78 IT 0.16% 0.05 14.56 0.72 IT 0.05% 0.39 2.45 0.22 IT -0.22% 0.00 3.77 0.20
NCG 0.08% 0.02 15.83 0.65 NCG 0.08% 0.08 1.10 0.60 NCG 0.10% 0.10 2.76 0.64 NCG 0.13% 0.00 6.98 0.67
NCS 0.08% 0.07 18.47 0.76 NCS -0.04% 0.32 2.40 0.59 NCS 0.00% 0.49 2.26 0.30 NCS -0.02% 0.43 3.36 0.08
UT 0.07% 0.03 14.22 0.63 UT 0.07% 0.19 0.85 0.41 UT -0.03% 0.34 1.81 0.52 UT 0.04% 0.25 1.15 0.13
RE -0.01% 0.42 5.94 0.57 RE 0.04% 0.31 0.97 0.43 RE 0.01% 0.46 2.23 0.32 RE -0.05% 0.25 1.55 0.70
CG -0.12% 0.01 19.67 0.78 CG -0.09% 0.09 7.86 0.70 CG -0.15% 0.09 2.34 0.54 CG 0.11% 0.04 7.82 0.83
Table 12 (cont): Results of the regression (3) with short selling constraints: pre-convergence period
For each sample period the table reports αI , the intercept of regression (3), and the probability of the hypothesis αI =0. Σβi is the sum of the coefficients of the regression. The reported R2is adjusted.
Group I DI p 6Ei R2 Group II DI p 6Ei R2 Group III DI p 6Ei R2 Group IV DI p 6Ei R2
BI -0.05% 0.06 22.31 0.90 BI -0.09% 0.03 3.58 0.84 BI 0.08% 0.34 2.30 0.22 BI -0.04% 0.27 4.61 0.60
CS 0.02% 0.30 19.74 0.85 CS -0.01% 0.36 3.71 0.90 CS -0.17% 0.05 1.83 0.49 CS -0.19% 0.02 4.62 0.60
GI -0.01% 0.43 8.17 0.93 GI -0.02% 0.32 4.88 0.83 GI 0.39% 0.01 2.83 0.58 GI -0.06% 0.21 5.37 0.58
FI -0.03% 0.15 12.09 0.93 FI -0.01% 0.43 5.21 0.86 FI -0.45% 0.01 3.59 0.39 FI -0.06% 0.18 5.01 0.57
IT 0.07% 0.18 11.81 0.67 IT 0.32% 0.01 17.19 0.54 IT 0.14% 0.21 1.32 0.17 IT -0.40% 0.00 4.00 0.18
NCG 0.06% 0.04 7.45 0.85 NCG 0.04% 0.24 3.69 0.77 NCG 0.23% 0.01 2.67 0.59 NCG 0.18% 0.00 6.09 0.69
NCS 0.13% 0.00 15.51 0.78 NCS -0.02% 0.40 1.13 0.74 NCS 0.02% 0.47 0.16 0.00 NCS -0.03% 0.44 2.14 0.06
UT 0.11% 0.00 13.40 0.77 UT 0.10% 0.17 1.06 0.53 UT 0.09% 0.12 1.24 0.49 UT 0.05% 0.28 1.90 0.30
RE -0.04% 0.23 7.12 0.75 RE 0.01% 0.47 1.50 0.51 RE -0.01% 0.48 0.92 0.06 RE -0.02% 0.42 1.26 0.76
CG -0.04% 0.18 19.13 0.82 CG -0.07% 0.18 9.79 0.73 CG -0.27% 0.09 1.70 - 0.16 CG 0.29% 0.00 6.93 0.87
19
Table 12 (cont): Results of the regression (3) with short selling constraints: Convergence period
For each sample period we present αI , the intercept of regression (3) and the probability of the hypothesis αI =0. Σβi is the sum of the coefficients of the regression. R2is the coefficient of determination of
the regression.
Group I DI p 6Ei R2 Group II DI p 6Ei R2 Group III DI p 6Ei R2 Group IV DI p 6Ei R2
BI -0.12% 0.03 19.94 0.84 BI -0.28% 0.00 3.69 0.62 BI -0.31% 0.01 2.82 0.80 BI -0.12% 0.16 6.34 0.55
CS 0.06% 0.13 12.92 0.83 CS -0.03% 0.32 5.20 0.83 CS -0.16% 0.26 2.00 0.33 CS -0.01% 0.46 5.41 0.61
GI -0.08% 0.04 12.91 0.92 GI -0.08% 0.20 4.41 0.66 GI 0.24% 0.14 3.32 0.68 GI -0.12% 0.12 6.12 0.69
FI -0.06% 0.13 25.50 0.91 FI 0.00% 0.48 3.27 0.85 FI 0.02% 0.41 3.28 0.90 FI 0.06% 0.33 8.62 0.57
IT 0.06% 0.34 29.22 0.75 IT 0.25% 0.05 12.94 0.78 IT -0.07% 0.44 2.18 0.14 IT -0.06% 0.24 3.32 0.32
NCG 0.09% 0.04 5.91 0.89 NCG 0.08% 0.18 3.42 0.73 NCG -0.05% 0.36 3.33 0.82 NCG 0.13% 0.06 8.18 0.74
NCS 0.19% 0.01 8.67 0.82 NCS 0.13% 0.14 1.15 0.61 NCS 0.08% 0.34 2.90 0.63 NCS 0.03% 0.45 5.40 0.13
UT 0.15% 0.02 9.23 0.67 UT 0.07% 0.31 0.80 0.37 UT -0.16% 0.13 2.36 0.70 UT 0.02% 0.42 0.92 0.03
RE -0.11% 0.17 5.11 0.64 RE -0.07% 0.30 1.75 0.55 RE 0.01% 0.48 3.10 0.59 RE -0.34% 0.01 4.27 0.70
CG -0.23% 0.01 18.76 0.80 CG -0.10% 0.21 8.23 0.66 CG -0.23% 0.12 3.04 0.81 CG -0.20% 0.05 6.37 0.73
Table 12 (cont): Results of the regression (3) with short selling constraints: Euro period
For each sample period the reports αI , the intercept of regression (3) and the probability of the hypothesis αI =0. Σβi is the sum of the coefficients of the regression. R2is the coefficient of determination of
the regression.
Group I DI p 6Ei R2 Group II DI p 6Ei R2 Group III DI p 6Ei R2 Group IV DI p 6Ei R2
BI 0.12% 0.18 51.92 0.70 BI 0.22% 0.12 3.19 0.39 BI -0.05% 0.38 2.01 0.62 BI 0.00% 0.49 6.61 0.60
CS -0.05% 0.31 19.35 0.86 CS -0.04% 0.35 5.52 0.81 CS -0.11% 0.27 1.98 0.37 CS -0.09% 0.32 7.49 0.54
GI 0.08% 0.21 12.30 0.88 GI 0.01% 0.48 8.26 0.54 GI -0.29% 0.20 2.65 0.59 GI -0.15% 0.23 10.00 0.57
FI 0.05% 0.27 41.11 0.89 FI 0.10% 0.22 5.20 0.74 FI 0.35% 0.00 2.07 0.80 FI 0.05% 0.33 12.66 0.82
IT -0.02% 0.45 16.42 0.88 IT -0.25% 0.15 15.89 0.83 IT -0.31% 0.18 2.85 0.62 IT -0.03% 0.43 3.32 0.23
NCG 0.17% 0.11 31.17 0.47 NCG 0.06% 0.38 0.70 0.33 NCG 0.06% 0.36 2.05 0.65 NCG 0.04% 0.38 8.28 0.61
NCS -0.12% 0.26 37.26 0.77 NCS -0.22% 0.22 4.00 0.52 NCS -0.26% 0.04 4.40 0.89 NCS -0.11% 0.37 4.86 0.10
UT -0.09% 0.21 25.21 0.53 UT -0.04% 0.42 0.54 0.23 UT -0.09% 0.31 2.11 0.37 UT -0.02% 0.46 0.15 0.03
RE 0.18% 0.20 21.22 0.48 RE 0.22% 0.21 1.99 0.31 RE -0.02% 0.47 2.43 0.68 RE 0.13% 0.25 1.25 0.61
CG -0.05% 0.36 59.03 0.75 CG -0.10% 0.31 10.36 0.65 CG 0.18% 0.17 1.77 0.52 CG 0.32% 0.03 14.02 0.75
20
Table 13: Results of the tests for regression (2) and (3) with no short sales
constraint.
The values are the result of chi-squared tests.
Regression (2) Regression (3)
Group I Group II Group III Group IV Group I Group II Group III Group IV
Whole
Test 1 10.94 5.23 9.13 2.29 20.29 11.01 10.30 28.25
Test 2 8216549.19 965829.56 6082.98 87780.08 391.87 209.27 1’830.34 3’139.13
PreConvergence
Test 1 12.77 2.50 16.48 1.78 24.89 11.14 22.42 37.39
Test 2 8196783.22 562999.48 1070.71 38107.31 159.37 195.45 520.69 1’724.85
Convergence
Test 1 7.48 2.41 1.76 1.57 29.92 17.22 11.26 14.34
Test 2 3080752.04 276760.21 7906.35 23251.69 122.77 54.98 2’209.34 964.85
Euro
Test 1 3.98 1.72 1.43 1.89 5.62 4.92 13.42 5.10
Test 2 5944466.23 161239.50 2427.97 59284.25 65.52 55.89 510.93 885.89
5 Conclusions
This paper addresses two main issues: First, we confront two ways of doing
portfolio allocation: country versus industry diversification. Second, we group our sample
of European countries according to their ’status’ in relation to the EMU to ascertain the
importance of the monetary union on the diversification approaches.
We show that country motivated portfolios, indeed, do have a higher mean
compared to industry portfolios. That is, the slope of the tangency portfolios starting from
the origin to the minimum-variance frontier for country portfolios is larger than for
industries. However, in the Euro subperiod both diversification approaches yield identical
returns. Further, our results indicate, Test 2, that greater diversification gains can be
reached by cross-country and cross-industry investment. Moreover, part of the
outperformance of country over industry diversification disappears when we introduce
restrictions on short selling. About the mimicking capabilities of country and industry
portfolios, our empirical results speak rather clearly, countries are successful in
explaining industry portfolios, but industry portfolios are not successful in explaining
country portfolios. Finally, we cannot presently say whether the EMU plays any causal
role for diversification strategies.
21
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23
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7 Appendix
Table 14: Summary of the results of regression (2) with the industry indices
without country factors
Countries are presented in the first column. For each sample period is presented αC , the intercept of regression (2) and the
probability of the hypothesis α =0. The sample periods are described in table. (a) for those regressions there were not sufficient
C
observations to obtain sound results, so opt for not present the results.
Whole Pre-Convergence Convergence Euro
Countries DC p DC p DC p DC p
AU 0.07% 0.37 0.21% 0.09 -0.07% 0.54 -0.01% 0.94
BG 0.06% 0.23 0.07% 0.32 0.21% 0.03 -0.07% 0.54
GE 0.03% 0.56 0.08% 0.31 0.05% 0.59 0.05% 0.66
SP 0.04% 0.50 -0.04% 0.72 0.18% 0.12 0.00% 0.98
FI 0.20% 0.09 0.12% 0.43 0.22% 0.27 0.31% 0.32
FR 0.06% 0.24 0.07% 0.39 0.02% 0.87 0.24% 0.01
IR 0.17% 0.03 0.12% 0.30 0.28% 0.02 0.07% 0.70
IT 0.00% 0.96 -0.04% 0.76 0.00% 1.00 0.05% 0.73
GR 0.37% 0.02 0.47% 0.05 0.48% 0.07 -0.03% 0.93
NL 0.09% 0.04 0.09% 0.11 0.13% 0.14 0.00% 0.98
PT 0.03% 0.70 -0.04% 0.70 0.18% 0.19 -0.05% 0.72
UK 0.09% 0.23 0.00 0.14 0.09% 0.46 -0.24% 0.39
DK 0.17% 0.03 0.00 0.08 0.17% 0.15 0.16% 0.35
SW 0.21% 0.04 0.00 0.15 0.05% 0.78 0.23% 0.23
HG 0.27% 0.59 (a) (a) (a) (a) 0.27% 0.59
PL 0.32% 0.16 (a) (a) (a) (a) 0.06% 0.84
CZ -0.01% 0.98 (a) (a) (a) (a) 0.11% 0.64
CH 0.01% 0.83 0.00 0.92 0.10% 0.13 -0.06% 0.47
NO 0.01% 0.79 0.00 0.66 0.09% 0.15 -0.09% 0.29
24
Table 15: Summary of the results of regression (3) with the country indices
without industry factors
Industries for the different groups are presented in the first column. For each sample period is presented αI the intercept of
regression 3 and the probability of the hypothesis αI =0.
PERIOD Whole Pre-Convergence Convergence Euro
Group I DI p DI p DI p DI p
BI -0.04% 0.41 -0.03% 0.48 -0.11% 0.13 0.18% 0.18
CG -0.10% 0.10 -0.04% 0.60 -0.24% 0.01 -0.01% 0.94
CS 0.00% 0.92 0.01% 0.73 0.07% 0.25 -0.02% 0.88
FI 0.01% 0.86 -0.04% 0.33 -0.05% 0.56 0.05% 0.66
GI -0.01% 0.79 -0.04% 0.34 -0.06% 0.28 0.11% 0.30
IT 0.13% 0.25 0.08% 0.39 0.22% 0.26 0.07% 0.82
NCG 0.14% 0.00 0.10% 0.02 0.11% 0.06 0.18% 0.23
NCS 0.10% 0.18 0.17% 0.01 0.22% 0.01 -0.20% 0.40
RE 0.06% 0.49 0.01% 0.95 -0.03% 0.82 0.19% 0.45
UT 0.12% 0.01 0.16% 0.00 0.24% 0.00 -0.12% 0.34
Group II
BI -0.07% 0.27 -0.10% 0.10 -0.29% 0.00 0.25% 0.19
CG -0.08% 0.32 -0.07% 0.44 -0.11% 0.40 -0.07% 0.79
CS -0.01% 0.78 0.00% 0.97 0.00% 0.96 -0.01% 0.92
FI 0.06% 0.29 0.00% 0.95 0.04% 0.71 0.17% 0.33
GI -0.02% 0.73 -0.01% 0.81 -0.08% 0.47 0.04% 0.82
IT 0.17% 0.21 0.38% 0.02 0.28% 0.17 -0.32% 0.44
NCG 0.12% 0.07 0.06% 0.41 0.13% 0.21 0.09% 0.67
NCS 0.02% 0.86 0.01% 0.91 0.17% 0.18 -0.18% 0.59
RE 0.07% 0.42 0.04% 0.73 -0.03% 0.82 0.26% 0.38
UT 0.10% 0.19 0.14% 0.21 0.10% 0.48 -0.02% 0.91
Group III
BI -0.18% 0.11 0.08% 0.89 -0.38% 0.01 -0.05% 0.77
CG -0.10% 0.62 -0.18% 0.76 -0.27% 0.45 0.20% 0.32
CS -0.24% 0.12 -1.42% 0.01 -0.19% 0.44 -0.09% 0.62
FI 0.01% 0.95 -0.88% 0.14 -0.05% 0.77 0.43% 0.01
GI -0.03% 0.9 -0.59% 0.49 0.18% 0.48 -0.34% 0.36
IT -0.06% 0.86 -0.31% 0.82 -0.01% 0.99 -0.35% 0.35
NCG -0.01% 0.94 -0.36% 0.56 -0.04% 0.82 0.06% 0.73
NCS 0.09% 0.7 0.10% 0.96 0.17% 0.46 -0.36% 0.17
RE 0.00% 0.99 -1.65% 0.18 -0.03% 0.91 -0.01% 0.96
UT -0.09% 0.51 0.86% 0.1 -0.17% 0.36 -0.07% 0.75
Group IV
BI -0.05% 0.37 -0.06% 0.42 -0.11% 0.38 0.01% 0.95
CG 0.12% 0.36 0.25% 0.21 -0.13% 0.53 0.29% 0.24
CS -0.12% 0.11 -0.21% 0.03 0.02% 0.91 -0.08% 0.71
FI -0.06% 0.38 -0.12% 0.08 0.06% 0.70 0.03% 0.84
GI -0.13% 0.06 -0.09% 0.24 -0.11% 0.28 -0.16% 0.50
IT -0.22% 0.01 -0.43% 0.00 -0.06% 0.54 -0.02% 0.91
NCG 0.23% 0.00 0.27% 0.00 0.27% 0.02 0.04% 0.80
NCS -0.04% 0.78 -0.05% 0.81 -0.05% 0.85 -0.12% 0.72
RE 0.09% 0.42 0.21% 0.22 -0.26% 0.14 0.26% 0.28
UT 0.06% 0.40 0.05% 0.55 -0.11% 0.13 0.18% 0.18
25
Table 16: Summary of the tests for regression (2) with the industry indices
without country factors
Test 1 is a joint test for the hypothesis that all αC =0. Test 2 is a joint test for the hypothesis that repressors of each equation
add up to one. Both tests follow a chi-square distribution. The probability of the test is presented in the right. (a) for those regressions
there were not sufficient observations to obtain sound results, so opt for not present the results. The Preconvergence period:
01/01/1988-30/12/1994; Convergence Period: 1/1/1995-30/12/1998; Euro period: 1/1/1999-30/12/2001
Regression(2) Regression (3)
Whole Test 1 p Test 2 p Test 1 p Test 2 p
Group I 22.05 0.02 245.36 0.00 21.41 0.02 378.82 0.00
Group II 10.52 0.01 592.30 0.00 10.83 0.37 267.12 0.00
Group III 2.29 0.51 52.24 0.00 5.85 0.83 282.36 0.00
Group IV 0.11 0.95 67.49 0.00 32.44 0.00 969.16 0.00
Pre-Convergence
Group I 14.08 0.23 173.27 0.00 26.62 0.00 130.92 0.00
Group II 7.33 0.06 373.05 0.00 11.23 0.34 51.65 0.00
Group III 14.67 0.14 37.59 0.00
Group IV 0.20 0.90 30.47 0.00 38.08 0.00 225.58 0.00
Convergence
Group I 21.71 0.03 66.09 0.00 31.89 0.00 240.81 0.00
Group II 2.73 0.44 101.49 0.00 16.84 0.08 135.21 0.00
Group III 10.99 0.36 48.76 0.00
Group IV 4.31 0.12 25.57 0.00 10.86 0.37 680.51 0.00
Euro
Group I 8.39 0.68 172.13 0.00 6.81 0.74 61.85 0.00
Group II 3.10 0.38 93.82 0.00 4.65 0.91 167.41 0.00
Group III 0.54 0.91 25.57 0.00 11.52 0.32 439.99 0.00
Group IV 1.64 0.44 19.15 0.00 3.38 0.97 345.47 0.00
26
Table 17: Results of the style analysis of regression (3):
Countries are presented in the first column. For each sample period is presented αI , the intercept of regression (3) and the
probability of the hypothesis α =0. R2 is the coefficient of determination of the regression.
I
Group I Group II Group III Group IV
DI p R2 DI p R2 DI p R2 DI p R2
BI 0.08% 0.11 0.41 -0.07% 0.11 0.62 -0.04% 0.38 0.30 0.04% 0.30 0.37
CS 0.13% 0.02 0.40 0.00% 0.46 0.83 -0.14% 0.08 0.30 -0.04% 0.31 0.44
GI 0.13% 0.03 0.43 -0.02% 0.37 0.62 0.10% 0.27 0.39 -0.01% 0.45 0.33
FI 0.11% 0.05 0.40 0.07% 0.06 0.78 -0.13% 0.18 0.33 0.10% 0.12 0.28
IT 0.28% 0.02 0.20 0.26% 0.06 0.25 0.04% 0.41 0.15 -0.16% 0.03 0.13
NCG 0.20% 0.00 0.37 0.08% 0.08 0.60 0.12% 0.12 0.40 0.27% 0.00 0.26
NCS 0.20% 0.01 0.28 0.01% 0.46 0.56 0.02% 0.45 0.21 0.03% 0.42 0.06
UT 0.13% 0.01 0.31 0.07% 0.20 0.41 -0.02% 0.38 0.43 0.05% 0.24 0.13
RE 0.16% 0.03 0.21 0.04% 0.31 0.43 0.03% 0.42 0.24 0.01% 0.44 0.67
CG 0.03% 0.30 0.61 -0.05% 0.19 0.77 -0.14% 0.14 0.44 0.26% 0.00 0.78
Pre-Convergence
BI 0.07% 0.19 0.47 -0.06% 0.12 0.82 0.06% 0.38 0.15 0.06% 0.26 0.39
CS 0.12% 0.04 0.45 0.01% 0.38 0.89 -0.15% 0.09 0.41 -0.09% 0.18 0.46
GI 0.11% 0.07 0.49 0.00% 0.49 0.78 0.18% 0.19 0.37 0.06% 0.28 0.31
FI 0.04% 0.25 0.52 0.02% 0.34 0.84 -0.49% 0.02 0.19 0.04% 0.31 0.29
IT 0.20% 0.04 0.28 0.40% 0.02 0.15 0.13% 0.22 0.17 -0.32% 0.01 0.10
NCG 0.17% 0.00 0.47 0.05% 0.18 0.76 0.20% 0.05 0.37 0.32% 0.00 0.27
NCS 0.20% 0.01 0.35 0.00% 0.50 0.73 -0.02% 0.47 -0.06 0.00% 0.49 0.05
UT 0.14% 0.01 0.35 0.11% 0.15 0.53 0.08% 0.14 0.48 0.07% 0.19 0.28
RE 0.14% 0.05 0.26 0.01% 0.46 0.50 0.00% 0.49 0.06 0.06% 0.29 0.73
CG 0.04% 0.31 0.57 -0.03% 0.32 0.85 -0.28% 0.09 -0.24 0.45% 0.00 0.84
Convergence
BI 0.10% 0.21 0.43 -0.26% 0.00 0.56 -0.29% 0.07 0.48 0.09% 0.28 0.35
CS 0.29% 0.00 0.46 0.00% 0.48 0.81 -0.15% 0.27 0.25 0.16% 0.14 0.50
GI 0.17% 0.09 0.43 -0.05% 0.33 0.52 0.21% 0.25 0.37 0.09% 0.25 0.49
FI 0.32% 0.02 0.37 0.14% 0.08 0.77 0.03% 0.45 0.50 0.37% 0.03 0.28
IT 0.56% 0.02 0.21 0.42% 0.06 0.30 -0.06% 0.45 0.10 0.03% 0.38 0.21
NCG 0.34% 0.00 0.43 0.11% 0.09 0.73 0.00% 0.49 0.44 0.41% 0.00 0.28
NCS 0.47% 0.00 0.34 0.17% 0.07 0.60 0.10% 0.34 0.36 0.21% 0.21 0.06
UT 0.37% 0.00 0.32 0.07% 0.31 0.37 -0.18% 0.17 0.48 0.02% 0.43 0.03
RE 0.20% 0.12 0.26 -0.03% 0.41 0.54 0.08% 0.40 0.35 -0.19% 0.10 0.64
CG 0.13% 0.13 0.68 -0.03% 0.36 0.79 -0.11% 0.29 0.79 0.01% 0.48 0.61
Euro
BI 0.07% 0.35 0.32 0.22% 0.11 0.39 -0.05% 0.39 0.57 -0.06% 0.36 0.43
CS -0.08% 0.35 0.37 -0.03% 0.41 0.75 -0.10% 0.29 0.30 -0.16% 0.24 0.43
GI 0.09% 0.34 0.38 0.02% 0.46 0.51 -0.24% 0.28 0.43 -0.25% 0.16 0.39
FI -0.04% 0.42 0.36 0.12% 0.20 0.71 0.34% 0.02 0.71 -0.07% 0.36 0.39
IT 0.10% 0.42 0.18 -0.18% 0.36 0.31 -0.26% 0.27 0.43 -0.06% 0.37 0.20
NCG 0.08% 0.31 0.21 0.06% 0.38 0.33 0.04% 0.40 0.54 -0.03% 0.44 0.24
NCS -0.16% 0.32 0.25 -0.19% 0.26 0.43 -0.24% 0.20 0.57 -0.15% 0.32 0.07
UT -0.20% 0.08 0.29 -0.04% 0.41 0.23 -0.07% 0.35 0.27 -0.01% 0.48 0.01
RE 0.16% 0.28 0.16 0.22% 0.20 0.31 -0.04% 0.44 0.55 0.17% 0.20 0.58
CG -0.11% 0.28 0.59 -0.08% 0.33 0.68 0.17% 0.19 0.49 0.19% 0.11 0.80
27
Table 18: Results of the tests of the style analysis.
The values are the result of chi-squared tests. The Preconvergence period: 01/01/1988-30/12/1994; Convergence Period:
1/1/1995-30/12/1998; Euro period: 1/1/1999-30/12/2001.
Regression (2) Regression (3)
Group I Group II Group III Group IV Group I Group II Group III Group IV
Whole
Test 1 129.24 18.38 3.47 6.69 43.58 10.41 6.04 33.81
Pre-Convergence
Test 1 81.64 9.98 6.63 6.47 30.32 8.10 13.33 44.74
Convergence
Test 1 137.46 4.54 2.32 0.93 56.00 16.68 4.48 17.12
Euro
Test 1 1.25 1.64 0.27 0.16 3.67 3.76 7.45 4.26
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