• Geographical versus Industrial Diversification

Sponsored Links

Download the ebook

Geographical Versus
Industrial Diversification:
A Mean Variance
Spanning Approach
HEC-University of Lausanne and FAME
Sofia B. RAMOS
HEC-Universtiy of Lausanne, FAME and CEMAF/ISCTE
Research Paper N° 80
April 2003
FAME - International Center for Financial Asset Management and Engineering
The International Center for Financial Asset Management and Engineering (FAME) is a private
foundation created in 1996 at the initiative of 21 leading partners of the finance and technology
community together with three Universities of the Lake Geneva Region (Universities of
Geneva, University of Lausanne and the Graduate Institute of International Studies).
FAME is about research, doctoral training, and executive education with “interfacing”
activities such as the FAME lectures, the Research Day/Annual Meeting, and the Research
Paper Series.
The FAME Research Paper Series includes three types of contributions:
• First, it reports on the research carried out at FAME by students and research fellows.
• Second, it includes research work contributed by Swiss academics and practitioners
interested in a wider dissemination of their ideas, in practitioners' circles in particular.
• Finally, prominent international contributions of particular interest to our constituency are
included as well on a regular basis.
FAME will strive to promote the research work in finance carried out in the three partner
Universities. These papers are distributed with a ‘double’ identification: the FAME logo and
the logo of the corresponding partner institution. With this policy, we want to underline the
vital lifeline existing between FAME and the Universities, while simultaneously fostering a
wider recognition of the strength of the academic community supporting FAME and enriching
the Lemanic region.
Papers with strong practical implications are preceded by an Executive Summary, explaining in
non-technical terms the question asked, discussing its relevance and outlining the answer
provided. We hope the series will be followed attentively by all academics and practitioners
interested in the field covered by our name.
I am delighted to serve as coordinator of the FAME Research Paper Series. Please contact me if
you are interested in submitting a paper or with any suggestions concerning the series.
Prof. Martin Hoesli
University of Geneva, HEC
40 bd du Pont d'Arve
1211 Genève 4
Tel: +41 (022) 705 8122
[email protected]
40 bd du Pont d'Arve • P.O. Box 3 • CH-1211 Geneva 4 • tel +41 22 / 312 0961 • fax +41 22 / 312 1026
http://www.fame.ch • e-mail: [email protected]
Geographical versus Industrial
Diversification: A Mean Variance Spanning
Paul Ehling
HEC Lausanne and FAME, CH-1015, Switzerland
[email protected], [email protected]
Sofia B. Ramos
HEC Lausanne, FAME, CH-1015, Switzerland, and CEMAF/ISCTE,
Av. Forcas Armadas 1649-026, Lisbon, Portugal
[email protected], [email protected]
Initial version: February 2002
Current version: April 2003‡
‡ We would like to thank Jean-Pierre Danthine, Vihang Errunza, Christian Gourieroux, Albert Holly,
Raymond Kan, Michael Rockinger, Olivier Scaillet, René Stulz, Ernst-Ludwig von Thadden, seminar participants at
the FAME Workshops, the 5th Conference of the Swiss Society for Financial Market Research (2002), the Euro
Conference at NYU (2002), the University of Geneva seminar, the ECB workshop on Capital Markets and Financial
Integration in Europe (2002), the European Investment Review Conference (2002), the NFA Annual Meeting (2002),
the Macro Brown Bag Lunch at the Wharton School (2003), MFA Annual Meeting (2003) and CEMAF/ISCTE Lisbon
(2003) for helpful discussions and comments. Financial support from the National Center of Competence in Research,
“Financial Valuation and Risk Management” (Ehling) and the Fundacao para a Ciencia e Tecnologia (Ramos), is
gratefully acknowledged. The National Center of Competence in Research is managed by the Swiss National Science
Foundation on behalf of the Swiss federal authorities.
This paper addresses whether country allocation provides benefits over
industry allocation in a sample of European country and industry indexes.
Strategy performance is compared using a mean-variance spanning test. We
find that, for investors with low risk aversion, industry allocation is as good
as investing in the complete set of assets. Moreover, in the most recent
subperiod coinciding with the inception of the Euro, country and industry
diversification are both effective. By contrast, investors with high risk
aversion should always mix country and industry portfolios. A striking aspect
of our analysis is that we do not find empirical evidence to support the
argument that country diversification is a superior approach.
Keywords: Diversification gains, EMU, mean-variance spanning, portfolio
allocation strategies.
JEL classification: G11, G15.
Executive summary
Stock returns are driven largely by country factors. This fact holds even
though recently industry effects become more important. A related stylized
puzzle is the much lower correlation within country indexes compared to
industry indexes. Not surprisingly, the banking industry adopted the country
allocation model as the traditional way for a simplified diversification.
In the present paper, we address the question whether country allocation
really offers benefits over industry allocation. Since neither the traditional
approach of analyzing the influence of country and industry factors in stock
returns nor the naïve comparison of average correlations allows testing for
differences in diversification gains, we adopt a different strategy. Namely,
we use a simple mean-variance model with constraints and a mean-variance
spanning test to address the hypothesis whether a set of industry portfolios
can improve the minimum-variance frontier of country portfolios and vice-
versa. The idea behind mean-variance spanning is intuitive and works as
follows. One simply tests the hypothesis whether the efficient frontier of a
set of restricted assets, for instance country indexes, is identical to the
efficient frontier of a complete set of assets, country and industry indexes.
Furthermore, in case spanning is rejected, we identify exactly which part of
the frontier causes the rejection. Either the slopes of the tangency portfolios
are (statistically) very different, or the minimum variance portfolios are
(statistically) not the same. In view of two-fund separation we can, then,
conclude about the location of the frontiers.
The study is based on data of the EMU entrants. To enlighten the influence
of industry effects in the most recent period but also to take into account a
possible influence stemming from the advent of the EMU we consider three
subperiods: Pre-Convergence, Convergence and Euro.
Based on the first part of the spanning test, which compares the
composition of tangency portfolios, we find that industry allocation cannot
be statistically distinguished from an investment in all indexes. The evidence
for countries is mixed, two subperiods favoring industry over country
allocation, e.g. adding industry portfolios to country portfolio significantly
improves the efficient frontier of the later one.
In contrast the country and industry efficient frontiers do not coincide
in the global minimum variance portfolio with the complete set of assets
(second part of the spanning test). In other words, mixing country and
industry indexes is relevant for investors with high risk aversion, while
investors preferring the tangency portfolio can pursue an industry motivated
It is of interest, however, to notice that in the most recent subperiod,
both country and industry tangency portfolios are statistically
indistinguishable from the tangency of the complete set of assets.
Overall the two components of the spanning test indicate that neither
country portfolios span industry portfolios nor industry portfolios span
country portfolios. This finding strongly confirms the superiority of a
diversification strategy that is based on country as well as industry motivated
Finally, our approach appears interesting for asset management since
i) the comparison between country and industry allocation considers
different levels of risk aversion and ii) quantifies the eventual contribution of
one or several assets, once included into the portfolio.
Diversification and its implication for portfolio choice is a major topic
in financial economics. A closely related and thus important matter is to
determine the factors driving the covariation in stock returns. From an
international perspective, this problem can be reformulated in terms of
ascertaining how country and industry factors determine variations in asset
returns for a global portfolio. This issue has been addressed in detail in a
sequence of papers (King (1966); Lessard (1974, 1976); Heston and
Rouwenhorst (1994); and Griffin and Karolyi (1998)) all of which indicate
that the country factor takes precedence over the industry factor1, typically
referring to country diversification as a superior strategy.
In this paper, we re-examine the performance of country and industry
allocation using a very flexible spanning approach introduced by Kan and
Zhou (2001) (henceforth referred to as KZ). In principle, mean-variance
spanning tests2 are used to tackle the hypothesis that the efficient frontier of
a set of restricted assets is the same as the efficient frontier of a complete set
of assets. Indirectly, spanning tests are also tests of performance of the
restricted set comparatively to the complete set of assets (See Jobson and
Korkie (1989).). Therefore, in this work, we investigate whether the
performance of a set of country portfolios (or industry portfolios) is
There is, however, evidence that industry effects are becoming increasingly important: Baca, Garbe, and
Weiss (2000), Cavaglia, Brightman and Aked, (2000), Isakov and Sonney (2003), Carrieri, Errunza and Sarkissian
(2002), Brooks and Del Negro (2002).
Mean-variance spanning tests have been applied to the study of benefits of international diversification,
mainly with emerging markets as test assets (Bakaert and Urias (1996), and Errunza, Hogan, and Hung (1999)). Gerard,
Hillion and de Roon (2002) also apply a spanning test in a context similar to ours, but using a different time period and
data set. Our framework differs from theirs in one important aspect: it considers an investor exclusively investing in
risky assets since our focus is on the direct comparison of the mean-variance frontiers of the indexes.
statistically equivalent to that of a complete set of assets. The step-down KZ
approach has the advantage that, in case of rejection, one can identify the
exact source of the rejection. Either the slopes of the tangency portfolios are
different (Test 1), or the minimum variance portfolios are not the same (Test
As a first step, we solve the optimization problem of an investor
restricted either to country or industry diversification. Each constrained
strategy yields an opportunity cost: the Lagrange multiplier. A major
strength of our approach is that we can establish a link between the step-
down procedure of KZ with the statistical significance of the Lagrange
multipliers. Moreover, since a negative sign of the Lagrange multiplier
directly implies a short position for the excluded index on the unconstrained
efficient frontier, one can even identify when the out-performance of a
strategy is due to short selling.
We focus on weekly country and sector index data of the EMU3
entrants during 1988-2002. The sample is divided into different subperiods:
Pre-Convergence, Convergence and Euro, in order to not only capture time
patterns but also to incorporate effects that may stem from actions
undertaken by the new monetary authority4.
Our findings are the following: Taken altogether, the tests indicate
that country portfolios do not span industry portfolios, nor do industry
portfolios span country portfolios. This finding points towards the
EMU stands for European Monetary Union.
In previous versions of this work we focused basically on all European countries with reasonable developed
stock markets, so that, we grouped non-EMU participating countries according to their status with respect to EMU or
EU. That analysis was carried out in Euro or synthetic Euro, while in the current version returns are calculated in US
dollar. Our results are qualitatively neither affected by the choice of currency nor by the chosen countries. The results
are available upon request.
superiority of a simultaneous diversification across geographically and
industrially motivated portfolios, over the traditional country model, as also
pointed out by research carried out using different methodologies (Adjaouté
and Danthine (2001b) and Carrieri, Errunza and Sarkissian (2002)).
The step-down approach of KZ provides additional insights. In
analyzing the two components of the spanning test, it becomes clear that the
country and industry efficient frontiers do not coincide in the global
minimum variance portfolio with the complete set of assets, while
intersection around the tangency portfolio5 is not rejected. Put simply,
mixing country and industry indexes is more relevant for investors with high
risk aversion, while investors preferring the tangency portfolio can pursue a
simplified allocation.
Based on the criteria of the first test, Test 1, which compares the slope
of the tangency portfolios, industry allocation cannot be statistically
distinguished from an investment in all indexes. The evidence for countries
is mixed, two subperiods favoring industry over country allocation, e.g.
adding industry portfolios to country portfolio significantly improves the
efficient frontier of the later one.
In the most recent subperiod, both allocations are statistically
indistinguishable from an investment in the complete set of assets, in
contrast to the beginning of the sample6.
This paper proceeds as follows: In Section II, we set up the mean-
variance model with the investment constraints and briefly recall the nature
of mean-variance spanning, pointing out the connection between these two
Henceforth, tangency portfolios will refer to portfolios whose tangent line starts from the origin.
We perform the empirical analysis to follow also for the 10 countries with the worldwide largest market
capitalization by the end of the year 2002. These are: Germany, France, Italy, the Netherlands, UK, Switzerland, USA,
Canada, Japan, and Australia. The results of this analysis are again qualitatively similar and available upon request.
methods as well as their application to our research question. Section III
describes the data. Section IV presents our results. Concluding remarks are
provided in Section V.
Consider an economy with several countries, each with several risky
assets that belong to different industries. Countries are indexed by j , and
industries by i . Stock shares are perfectly divisible, in positive supply and
normalized to one. The currency is identical across countries, eliminating the
exchange rate as a source of risk. Moreover, there are no taxes, transaction
costs, dividends, or capital controls and borrowing and short selling are
allowed without restrictions.
~ ~
Country indexes are denoted by c j and industry indexes by d i . The
vector of expected returns of the indexes follows a normal distribution with
mean γ and a covariance matrix
 Φ j Φ ji 
Φ ' Φ  ,

 ji i 
where Φ j and Φ i are the covariance matrices of country and industry
indexes respectively, Φ ji is the covariance matrix of both country and
industry indexes, and Φ ji ’ denotes, as usual, the transpose of Φ ji . All the
(sub-) matrices are positive definite.
In this one period model, investors make their investment choice at
date zero and receive returns on their investment at the terminal date. All
individuals have the same negative exponential utility function U = −e − ρW ,
where W is the wealth at the end of the period and ρ ( ρ > 0 ) denotes the
coefficient of absolute risk aversion. Investors maximize expected utility and
cj 
the net return for each investor is defined as R = w'  ~  , where w is the
d 
 i
vector of investment weights in the indexes.
We formulate country and industry allocation as an optimization
problem involving a restriction (3) on strategies, which represents the
exclusion of industry or country indexes from portfolios. Typically, the
decision to follow a constrained strategy is related with some sort of
imperfection in capital markets, but we do not further elaborate on the
specific source of the friction. Given the form of the utility function,
preferences are in fact mean-variance, as expressed in the following
( 1)
~ 1
max E R − ρ var R
w 2
( 2) s.t. w '1 = 1
( 3) wl = 0 for l = j ∨ i ,
where 1 denotes a vector of ones. The optimal portfolio for constrained
investors is (for details, see Ramos (2002)),
( 4) w *l = (ρΦ )
[(γ − µ 1) − λ ], l = j ∨ i ,
z l
where λ l is the Lagrange multiplier associated with the exclusion of industry
or country indexes, and µ z equals the expected return on the zero covariance
portfolio7 of w j * . Note that µ z can be interpreted as the intercept of a ray
tangent to the portfolio. We interpret the Lagrange multiplier λ l as the
shadow cost of excluding an asset from the opportunity set. It also describes,
A portfolio z is said to be zero covariance with respect to a portfolio p if there is no correlation between them.
indirectly, how the optimal value of the utility function changes when there
is a slight relaxation of the respective constraint. To facilitate later
discussion, it is worth mentioning that the loss (gain) caused by excluding an
index can be ranked, so as to enable identifying the country (industry) index
which contribution is potentially of more use to an investor whose portfolio
is industry- (country-) motivated. Note, however, that the value of the
contribution is always relative since it depends on the set of excluded assets
and on the specific efficient portfolio, which determines µ z .
For a given sample of indexes, testing the hypothesis λ = 0 is of
considerable interest, since it conveys the potential contribution of the
excluded indexes. Consider an ordinary linear regression, with X and Y
containing index returns, α as intercepts, β the matrix of the regression
coefficients, ε the error term and T as the size of the time series sample,
( 5) Yt = α + ßX t + ε t , t = 1,...T .
Ramos (2003) shows that the aforementioned Lagrange multipliers λ are
related to the regression parameters α and β as follows:
( 6)
(r r
λ = α + µz 1 − β 1 . )
Huberman and Kandel (1987), HK hereafter, propose Equation (5) to
test mean-variance spanning. 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. Note that in this approach, the debate extends beyond merely country
and industry portfolios. The spanning test compares the performance of the
K benchmark assets (country or industry allocation) with the entire
r r r
spectrum of assets (N + K ) using the hypothesis H 0 : α = 0 × 1 and 1 − β 1 = 0 .
In our setting, investors can construct their portfolio either entirely
from country indexes or industry indexes, leading to two sets of benchmark
assets and two sets of test assets. Define c jt as the vector of raw returns of
j countries at time t and d it as the vector of raw returns of i industries at
time t . Then, adjusting regression (5) to our version of spanning test results
(7) c jt = α j + β j d it + ε jt , t = 1,...T
(8) d it = α i + β i c jt + ε it , t = 1,...T
where α j , α i , β j , β i are the parameters to be estimated.
The HK test is very sensitive to the restrictions on the betas, while the
restriction on the alphas has much more economical weight. Therefore, KZ
propose to analyze separately the two components of the spanning test. That
said, they decompose the null into two null hypotheses, H 0I : α = 0 × 1 and
r r r
H 0II : 1 − β 1 = 0 , conditional on α = 0 × 1 , which are denoted by Test 1 and
Test 2, respectively. Recall that for mean-variance spanning to hold, both
parts of the test have to be accepted. Also important to notice is that the
overall significance level of the test is 1 − p1p 2 , where p1 denotes the p-value
for the first part of the step-down procedure, and p 2 is associated with the
second part of the test. Refer to KZ for more details on this, specifically, on
the power of the tests.
Test 1 focuses on the difference in the slopes of the tangency
portfolios between the restricted and complete set of indexes. Roughly
speaking, it expresses the risk-return trade-off relation. On the other hand,
the second part of this step-down procedure, Test 2, investigates whether the
global minimum variance portfolio has zero weight in the test assets, i.e.,
whether the assets contained in X are sufficient to achieve all diversification
benefits. Again, this approach has the advantage that, in case spanning is
rejected, one can identify the exact source of it. Moreover, it prevents the
beta term from commanding the overall decision8.
In dealing with portfolios based on country and industry
diversification, we apply the step-down tests of KZ, introduced above, to
equations (7) and (8). Therefore, if H 0I is not rejected for α j = 0 × 1 (if H 0I is
not rejected for α i = 0 × 1 ), investors preferring the tangency portfolio can
base their strategies on industry (country) portfolios. If H 0I and H 0II are not
rejected, industry (country) diversification is an optimal strategy for any
investor since industries (countries) span countries (industries). If H 0I for
both regressions is not rejected, we can conclude that both are statistically
equivalent around the tangency portfolio.
Notice that for each portfolio on the mean-variance frontier, there is a
corresponding Lagrange multiplier. Hence, we could test for an infinite
amount of points, which is somewhat impracticable. We thus restrict our
attention to a particular point on the mean-variance frontier, which will
prove to provide several advantages.
Proposition 1: Suppose an investor whose optimal portfolio choice
implies µ z =0, i.e. the tangent of the portfolio that passes through the origin,
Recall that the p-values for Test 1 and Test 2 can be chosen independently. Hence, it is possible and
reasonable to put less wait, by decreasing the p-value, on Test 2.
i) The hypothesis H 0I : α = 0 × 1 is equivalent to the hypothesis
H0 :λ = 0 .
ii) The weight of the excluded asset in the optimal portfolio equals
* α
xl = ,
ρσ εε
where σ2εε is the variance of the error terms in the univariate regression.
The proposition illustrates a key result since it relates our analytical
framework with mean-variance spanning. More concretely, it establishes a
link between the step-down procedure and the test for the Lagrange
multiplier, and shows the circumstances whereby Test 1 is also a test of the
statistical significance of the Lagrange multiplier. Moreover, we can relate
the sign of the intercept with the sign of the optimal weight of the excluded
asset on the unrestricted efficient frontier.
Given that returns may exhibit conditional heteroscedasticity, an
unadjusted OLS approach to our research question may lead to over-
rejection of the null hypothesis. Therefore, all reported p-values are based on
external bootstrap simulations, which explicitly avoid over-rejections due to
We use DataStream country and sector indexes for the eleven EMU
entrants10: Austria, Belgium, Finland, France, Germany, Greece, Ireland,
KZ report that the spanning test is robust against heteroscedasticity. Indeed, we do not observe any over-
rejection compared to the standard OLS results.
Note that Greece joined the Euro-zone in 2001 and Luxembourg is not taken into account.
Italy, the Netherlands, Portugal, and Spain. The data provided by
DataStream is weekly US dollar denominated ranging from 1 January 1988
through the end of December 2002 (783 return observations). The sample is
divided into different subperiods (see Table 1) in order to not only capture
time patterns but also to incorporate effects that may stem from actions
undertaken by the new monetary authority. The subperiods are labeled Pre-
Convergence, Convergence, and Euro. Note that the starting date of the
Convergence period is associated with the signing of the Maastricht treaty,
while the end of the period (31 December 1998) is associated with the fixing
of the conversion rates. However, one can argue that markets already
anticipated the future accession of countries. Thus, in one of our robustness
tests, we extended the beginning of the Euro period by one year. Since this
change did not affect test results, we held the official dates of the EMU.
Description of the subperiods
Sample Data Range Observations
Pre-Convergence 01/01/1988-30/12/1994 365 observations
Convergence 06/01/1995-25/12/1998 208 observations
Euro 01/01/1999-27/12/2002 210 observations
The data provided by DataStream is weekly Euro denominated ranging from January 1, 1988 till the end of December of 2002 (783
return observations). 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.
We focus our analysis on level three of DataStream sector
classification, which corresponds to 10 sectors: Basic Industries (BI),
Cyclical Goods (CG), Cyclical Services (CS), Financials (FI), General
Industries (GI), Information Technology (IT), Noncyclical Consumer Goods
(NCG), Noncyclical Consumer Services (NCS), Resources (RE) and
Utilities (UT). Based on this industry classification, we compute industry
indexes by building market-value weighted indexes for each of the groups
we consider.
In Table 2, we report the descriptive statistics of the country indexes
for the whole period and the three subperiods. Since the whole sample
includes a rather long period during which many important structural
changes occurred in Europe, we direct our attention towards the subperiods.
The descriptive statistics of the country returns apparently went through
different cycles over the time period under consideration. The subperiods
show different means: For instance, during the Convergence period for the
Euro candidates, almost all stock markets experienced a dramatic increase in
value, yielding rather high double digit returns. In contrast, in Pre-
Convergence, none of the countries experienced a return higher than 20%,
and in the Euro period, there are no countries with positive index returns.
The average mean in the Pre-Convergence period is 7.08%, and, in the Euro
period, we observe an average mean return of -9.75% whereas, in the
Convergence period, the mean is 20.45%.
Again as for means, correlations also show a time variation11. For
example, in the Convergence period, there is an increase of correlation
among countries and between countries and industries. A less pronounced
and less uniform drop follows this increase in the Euro period. The surges
and drops in correlations, however, occur at different levels. Correlations
between countries tend to be lower than correlations between countries and
industries. This relationship, however, becomes less pronounced over time.
The instability of correlation matrices is a well-documented fact in the finance literature (Longin and
Solnik (1995), Adjoute and Danthine, (2001a,b)). Therefore, small changes in correlation should not be emphasized.
With regard to industries (see Table 3), we find that the correlation
within industries is higher than the correlation of an industry with countries.
In the Euro period, the level of correlation drops, as also reported by Adjoute
and Danthine (2001b), but in contrast to the findings for countries, industry
correlations seem to be more stable and greater, on average.
[Tables 2 and 3]
The empirical results presented here refer to the regressions (7), (8),
and Test 1 and Test 2.
In the first type of regressions (equation (7)), the benchmark assets are
the industry indexes, and the test assets are the country indexes. Table 4
contains sorted alphas and their p-values, country by country. Recall that we
interpret the intercepts as the shadow costs of excluding an asset from the
opportunity set12 which, then, translates into the associated variation in
utility. We find the following countries in two out of three subperiods with
negative sign for alpha: Belgium, France, Italy, and Portugal. Hence, these
countries represent potential candidates for a short position. Notice,
however, that the Lagrange multiplier is in none of the cases statistically
different from zero. We observe that Germany in the Pre-Convergence
Notice that the Lagrange multiplier can be interpreted as described above if and only if one of the assets is
added to the benchmark assets. Any additional asset can change the weight as well as the sign of the first test asset in
the optimal portfolio. Another restrictive assumption is that the zero covariance portfolio is hold constant.
subperiod, at a 95% confidence level, and France in the Euro subperiod, at a
90% confidence level, qualify as candidate to improve (statistically) the
efficient set based on industry portfolios.
[Tables 4 and 5]
In the second round of regressions, equation (8), the benchmark assets
are the EMU countries, and the test assets are the 10 industry indexes. Table
5 reports the following results for industries. Noncyclical Consumer Goods
and Utilities exhibit (positive) alphas significantly different from zero in the
whole period and the Pre-Convergence subperiod. Noncyclical Services
shows in the Pre-Convergence and the Convergence subperiod Lagrange
multiplier, which are both positive and statistically different from zero. We
also observe two Lagrange multipliers with significantly negative sings.
These are the Cyclical Consumer Goods in the Convergence subperiod and
the Information Technology in the Euro subperiod.
There are some common features to all the regressions in Tables 4-5.
Countries tend to have positive intercepts while industries show more
negative ones. This can be interpreted as “underperformance” of industry
indexes in relation to their mimicking portfolios, and also indicates that
these indexes would appear in an unconstrained optimal portfolio with a
negative sign. To verify this, we compute the composition of the optimal
unconstrained tangency portfolio and, indeed, industries with a negative
intercept have a negative weight in the portfolio. Further, only industry
indexes appear with significantly negative Lagrange multiplier.
The results of Test 1 are reported in Table 6, as well as the conditional
test of all betas summing up to one, Test 2. Taken together, the mean-
variance spanning hypothesis is always rejected due to the second part of the
spanning test, Test 2. Thus efficient frontiers do not coincide in the global
minimum variance portfolio and none of the allocation strategies is
sufficient to attain all the diversification benefits. Consequently, investors
should mix both country and industry portfolios in order to maximize utility.
Given that Test 1 generally has much more economical importance,
the following comparison between countries and industries is based on this
test only. Adding country indexes to industries leads never to statistically
significant diversification gains, while adding industries improves country
allocation in the Pre-Convergence and Convergence period at a 95%
confidence level.
[Table 6]
To some extent, the surprisingly good performance of industries can
be considered puzzling. However, Gerard, Hillion and de Roon (2002)13 find
similar results with MSCI data14 for G-7 countries. Using the DataStream
database, they conclude that country diversification was equivalent to
industry diversification.
In examining the differences across time periods, we find that in the
beginning of the sample, constrained strategies do not always yield similar
Notice that they do not reject mean-variance spanning, as we do. We believe that this difference of results
is due to the inclusion of the risk free rate and therefore they do not evaluate the global minimum variance portfolio.
The MSCI data was removed from the latest version of the paper.
performance, whereas in the most recent period, following a country or
industry allocation produces statistically indifferent results.
To address concerns about the influence of country factors in industry
indexes and industry factors in country indexes, which can be relevant for
countries having substantial weight in some industries and vice-versa, we re-
compute all DataStream indexes. In other words, when country x is
regressed on a set of industries, these industry indexes do not include any
industry that belongs to country x. In summary, Test 2 (not reported) is
always rejected, while regression (7) contains some changes. That is, Test 1
is rejected for the whole sample as well as for the Converg

Use: 0.0985