Time-Variation in the Benefits and Portfolio Allocation of...
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Time-Variation in the Benefits and Portfolio Allocation of International
Diversification with Investment Constraints
Wan-Jiun Paul Chiou*
Shippensburg University Shippensburg, PA 17257
Tel: 717-477-1139 Fax: 717-477-4067
Chiung-Min Eugene Tsai Central Bank of China, Taiwan
Taipei, Taiwan
This Version: August 28, 2006
* Corresponding author
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Time-Variation in the Benefits and Portfolio Allocation of International
Diversification with Investment Constraints
ABSTRACT
This paper investigates how the benefits and asset allocation of the constrained
internationally diversified portfolio alter over time. The time-varying economic sizes of
diversification benefits are persistently positive. The addition of upper bounds eludes a
portion of diversification benefits but substantially decreases the time-variation in gains
and asset weighting of global diversification. The expansion of coverage in the optimal
portfolio makes the asset allocations more realistic. The time trend characterized by the
filter of Hodrick and Prescott (1997) and regression suggest the diversification benefits
did not decrease even though the world capital market has become more integrated. The
emergence of profitable investments in the domestic market may substitute international
diversification benefits, while the volatility in exchange rate is compensated in global
diversification.
JEL Classifications: F36, G11, G15
Keywords: Diversification Benefits; Investment Constraints, International Portfolio.
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Time-Variation in the Benefits and Portfolio Allocation of International
Diversification with Investment Constraints
I. INTRODUCTION
The question of whether international diversification consistently benefits investors in a
more integrated global market is a critical issue to financial economists and professionals.
Previous studies have confirmed that the volatility of a domestic portfolio can be reduced
without sacrificing its expected return by investing in less-correlated overseas assets1.
Since the world economic system has increasingly integrated in the past decades, it is
critical to investigate the revolution of the potential benefits and the optimal strategy for
the global diversification portfolio. Furthermore, due to the lack of investibility of assets
in other countries, investors may not necessarily allocate funds internationally by
following the unrestricted efficient frontier suggested by Markowitz (1952).2 To
maximize the feasibility of asset allocation, various constraints such as short-selling and
over-weighting investment should be taken into account when the diversification benefits
are assessed. In this paper, (i) how the benefits and weighting of optimal international
diversifying strategies with various investment constraints alter over time is analyzed,
and (ii) what economic/financial variables affect the magnitude of diversification benefits
to local investors are explored.
Previous empirical evidence has confirmed the improvement of mean-variance
efficiency via international diversification from a single-period viewpoint, even with
1 For a more detailed discussion, see Cosset and Suret (1995); De Roon, Nijman, and Werker (2001); De Santis, and Gerard (1997); Fletcher and Marshall (2005); French and Poterba (1991); Harvey (1995); Li, Sarkar, and Wang (2003); Novomestky (1997); and Obstfeld (1994). 2 The investiblity of the stock market is the degrees that foreign investors can trade like the local investors in the domestic markets and liquidity of assets. See Bae, Chan, and Ng (2004).
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certain investment constraints. De Roon, Nijman, and Werker (2001), Harvey (1995), Li,
Sarkar, and Wang (2003), and Pástor and Stambaugh (2000) have shown that domestic
investors can enhance investment performance by including the assets from other markets
into the local portfolio when short-sales are not allowed. Errunza, Hogan, and Hung
(1999) find that U.S. investors can utilize domestically-traded American Depositary
Receipts (ADRs) to duplicate the benefits of international diversification. Cosset and
Suret (1995) find that including securities from high-political-risk countries still increase
mean-variance efficiency of portfolio. For portfolio managers, however, the dynamics of
the benefits and the optimal asset weighting are more critical in determining the long-
term diversification strategy. In addition, Green and Hollifield (1992) and Jagannathan
and Ma (2003) indicate that the extreme portfolio weights cast a suspicious shadow on
the practicability of the optimal asset allocation. We therefore construct the time-rolling
efficient frontiers with imposing excessive investment constraints. Differing from the
setting by Jagannathan and Ma (2003), this paper explicitly links the upper bounds of
portfolio weights with relative sizes of capitalization among international markets.
Subsequently, we investigate time variation in these global diversification benefits and
examine how other financial variables affect the economic size of diversifying gains.
This paper synthesizes the major concepts and/or modi operandi of De Roon,
Nijman, and Werker (2001); Driessen and Laeven (2005); Li, Sarkar, and Wang (2003);
Jagannathan and Ma (2003); and Wang (1998) and intends to maximize the practicability
in portfolio management. Our study differs from previous studies at least in two aspects.
First, the infeasibility of strategy caused by disproportional asset allocation among
international markets is considered. Previous empirical evidence suggests that the
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benefits of international diversification are not completely eroded by short-sale
constraints.3 However, no-short-selling optimal strategies do not cope with the
investment concentration in small markets. The disproportional portfolio weighting may
cause portfolio illiquidity and trigger excessive volatility in asset returns and correlation.
In this paper, the upper bound of portfolio weight is explicitly associated with the relative
size of market capitalization in each country. Including the short-sale and over-weighting
investments constraints allows global fund managers to generate more realistic allocation
strategies.
Second, this paper examines the dynamics in diversification gains and the
variation of portfolio weighting. In past decades, the correlations in the international
market increased, and the domestic expected returns in most countries declined (Bekaert
and Harvey, 2003; Bekaert, Harvey, and Ng, 2005). The former has a negative effect,
while the latter has a positive impact on the global diversification benefits to domestic
investors. Given the mixed influences discussed above, the long-term trend of
international diversification benefits is not clear a priori. Consequently, a thorough
empirical investigation is desired. The time-series analysis of potential gains helps to
determine whether international diversification still benefits domestic investors when the
world capital market is increasingly integrated. Moreover, the insight regarding the
factors that impact the extent of diversification benefits is useful in modifying the asset
allocation strategies.
For the empirical analysis, the monthly data on stock market index returns from
21 developed countries and 13 emerging markets for the period 1988 to 2005 are used.
The two measurements of diversification benefits for the local investors correspondingly 3 See De Roon, Nijman, and Werker (2001), Harvey (1995), and Li, Sarkar, and Wang (1998).
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reflect the motivations to include foreign securities in their portfolios. The first is the
increment of risk-adjusted premium by switching from a domestic portfolio to the
maximum Sharpe ratio (MSR) portfolio on the international efficient frontier4. The
second assessment of diversification benefits is the reduction in volatility by changing a
domestic portfolio as the global minimum-variance portfolio (MVP). The optimal
portfolio weighting and economic size of diversification benefits with various scenarios
of investing constraints, including only short-sale (SS) and short-sale plus over-weighting
(SS+OW), are investigated.
Our results are as follows. For all global portfolios with various investment
constraints, the diversification benefits are persistently positive. However, the economic
sizes of potential gains vary substantially, particularly for the strategies with less
restrictive constraints. For instance, the average and range of monthly Sharpe ratio
benefits for short-sale constrained portfolios are 0.1982 and from 0.4999 to 0.0059, while
the ones for short-sale-plus-three-time-over-weighting constrained portfolios are 0.0471
and from 0.1447 to 0.0028, respectively. The optimal asset allocations among countries
also alter drastically in the testing period. This implies that investors may need to modify
international asset allocation according to the market dynamics over time.
The cross-strategy comparisons suggest that including investment restrictions
prevents the generation of unrealistic optimal strategies. Our empirical findings indicate
that when portfolios are increasingly constrained, (i) the number of comprising assets in
the optimal international portfolio increases, (ii) the time-variation of weights for
components in the optimal portfolios decreases, and (iii) the temporal deviations of
4 Li, Sarkar, and Wang (2003) use the increase in expected return that is generated when the foreign assets are added in portfolio as an assessment of diversification benefits.
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diversification benefits reduce. Although restrictive investments cause a certain
proportion of loss in diversification benefits, those constraints may yield some
characteristics desired by asset management.
The time-series analyses conclude that the diversification benefits did not
significantly decrease over the testing period even though the world capital market has
become more integrated. This is also confirmed by the smoothing time-trend caught by
the filter of Hodrick and Prescott (1997). The diversification benefits generated by more
restrictive strategies, i.e., SS+OW(5) and SS+OW(3), were slowly growing. The finding
on the impact of economic/financial factors indicates that the emergence of profitable
investment in home market may substitute international diversification. On the other
hand, the volatility in currency exchange rate is compensated when international
diversification is implemented.
The rest of the paper is organized as follows. Section II presents the assessments
of global diversification benefits for domestic and passive international investors. In
Section III, the data and the time-variation of mean-variance efficiency and correlations
are described. Section IV discusses the empirical results of diversification benefits and
global portfolio weighting under investment constraints. Section V reports the findings on
the time-series analysis and the regression for the diversification benefits. Section VI
presents our conclusions and discusses possible future developments.
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II. METHODOLOGIES
The maximum increase in risk-adjusted performance and the greatest reduction in
volatility brought by the optimal international portfolios are used to estimate the benefits
of diversification for domestic investors. To enhance the feasibility of asset allocation,
the constraints such as short-sale (SS) and over-weighting (OW) investment are taken
into account. The time-series of diversification benefits with various weighting
restrictions are obtained by the time-rolling international efficient frontiers formed by the
monthly returns in 5 years.
Suppose a representative investor would like to minimize the volatility of her
portfolio, given the same return, by allocating funds among international markets. The
investment opportunities can be characterized as a vector of multivariate Gaussian
stochastic returns of N international assets:
R T = [ , ,..., ]r r rN1 2 . (1)
The expected returns in excess of the risk-free interest rate and the variance-covariance of
asset returns can be expressed as a vector μ and a positive definite
matrix V= [RR
T = [ , ,..., ]μ μ μ1 2 N
T – R R T] / N, respectively, where R is the vector of expected returns. Let
S be the set of all real vectors w that define the weight of each asset
such that
T = [ , ,..., ]w w wN1 2
w 1T = w w wN1 2 1+ + + =... , where 1 is an N-vector of ones.
Suppose the best predictors of expected returns, variances, and covariances among
assets are their past averages. This non-risk-loving investor thus follows the method of
Markowitz (1952) to form the global efficient frontier by using the monthly returns in 5
years. Combining the objective function and restrictions, the problem of the optimal
portfolio selection is then expressed as a Lagrangian:
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min ( ) ( ){ , , }w w Vw w w 1φ η φ μ ηΞ = + − + −12
1T Tp μ T , (2)
where μp denotes the expected return on the portfolio, and the shadow prices φ and η are
two positive constants. The quadratic programming solution for asset spanning, wp, can
be obtained by the first-order conditions of Equation (2). The negative portfolio weights,
i.e., short selling assets, are permitted in this setting. The subset Pk is defined as the array
of achievable portfolio weights with various investment constraints. If there are no
restrictions on asset allocation, then P0=S.
To make the optimal portfolio more realistic, we further add various investment
constraints. It is well-known that short-selling is not allowed for foreign investors in
many countries, particularly in less developed nations5. The restriction of non-negative
weights is incorporated in the system of Lagrangian in Equation (2). Since the incentives
of international diversification are not only to seek higher yields but also to reduce
volatility, an investor who desires to maximize risk-adjusted performance will select the
maximum Sharpe ratio (MSR) portfolio on the efficient frontier. The maximum Sharpe
ratio is:
MSR = max {( / ( ) }{ }w p p p p
pw Vw wT T Tμ) w ∈ P1 , (3)
where iP1 = ∈ ≤ ≤{ : , Nwp S 0 wi 1 =1 2, ,..., }
.
One should not have a problem to construct the portfolio that yields the highest risk-
adjusted-premium on the international efficient frontier by allocating capital according to
the weights of the MSR portfolio (MSRP).
5 See De Roon, Nijman, and Werker (2001), Harvey (1995), Li, Sarkar, and Wang (2003), and Pástor and Stambaugh (2000).
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Furthermore, the over-weighting (OW) investment constraints are taken into
consideration. Specifically, the investor considers the relative magnitude of market
capitalization in each country when determining global asset allocation. The subset of
portfolio weights PJ with constraints SS+OW(U) can be described as:
:{ SPJ ∈= pw ,1)(0 ≤≤≤ ii CapUww i N=1 2, ,..., } , U>1, (4)
where w(Cap)i is the proportion of the market value of each country i in the world, and U
is any real number greater than 1.6 Differing from Jagannathan and Ma (2003), in this
paper, the upper bound is explicitly determined by the share of market value in the world.
Therefore, the MSR on the constrained international efficient frontiers is
MSRJ = })/(){(max T21
TT}{ JP∈ppppw wVwwμw
p. (5)
There are three reasons that international investors need to consider the
unattainability of short-sale and excessive investments. First, when making decisions
regarding the fund allocations in international assets, investors not only consider the
profitability but also take into account marketability of investment targets. The
centralization of funds in the minor markets is counter to the goal of diversification and
may cause the illiquidity of portfolio. Second, the excessive foreign capital in- and out-
flows in small markets may trigger volatility in asset values. This may generate dramatic
changes of mean-variance efficiencies and correlations among international financial
markets. Finally, in many countries, foreign investors are prohibited to short-sell and to
hold more than a certain proportion of company shares.7 It is particularly true in most
developing countries. A large percentage of foreign capital allocation on the investing 6 In this paper, we report the changes of benefits of diversification with over-weighting investment constraints by setting L equal to 3, 5, and 10. 7 The limit of foreign ownership is often imposed in so-called “strategic” industries, such as banking, energy, utility, and media. See Bae, Chan, and Ng (2004).
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vehicles in those small markets may be impractical from legal and institutional aspects.
Accordingly, the strategies that consider boundaries of weights are more realistic.
Differing from studies by De Roon, Nijman, and Werker (2001), Li, Sarkar, and
Wang (2003), and Wang (1998) that utilize the change of raw return to measure benefits,
we use the increase in risk-adjusted premiums. For the U.S. investor, the increment of
unit-risk return brought by international diversification is
USUS SRMSRδ JJ, −= , (6)
where SR is the Sharpe ratio for the U.S. domestic portfolio and J denotes the various
investment constraints.
The other measurement for the benefits of diversification is the greatest reduction
in volatility as a result of international diversification. Elton and Gruber (1995) suggest
that investors may seek to minimize the variance of a portfolio because of the lack of
predictability of expected returns. In this case, one may want to invest in the minimum-
variance portfolio (MVP). The weighting of the MVP can be characterized as:
:{w MVP pw= ∈Tpp
Tpw wVww
p[min }{ ]}JP , (8) , J
where PJ can be various domains of portfolio weights on the efficient frontiers.
Following the methodologies suggested by Li, Sarkar, and Wang (2003), the maximum
decline in volatility by diversifying internationally with various investment constraints is
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J MVP,T
J MVP,J, ]V /[1ε USUS Vww−= . (9)
In this study, the global efficient frontiers and the Sharpe ratio are estimated by
using monthly returns in five years. The time-series of δUS,J and εUS,J for domestic
investor with various investment constraints can be generated by rolling over the asset
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returns in the next periods. The weightings for the MSRP and the MVP in each period are
also calculated.
III. DATA
We use U.S. Dollar-denominated monthly returns of the Morgan Stanley Capital
International (MSCI) indices for 21 developed countries and 13 developing countries.
The U.S. 90-day T-Bill yield, the proxy of risk-free interest rate, S&P 500 Information
Technology index, U.S. Dollar Trade Weighted Index, U.S. Consumer Price Indices, and
Barron's Confidence Index are collected from Global Financial Data. The market
capitalizations are obtained from the World Federation of Exchanges. The sample period
is from January 1988 to December 2005.
Table 1 lists the countries, their average growth rates for market values from 1992
to 2005, and the proportions of world market capitalization as of the end of 1992, 1999,
and 2005. The value-weighted average growth rate of market capitalization for all
countries during the sample period is 10.6%. For our sample, the countries of the largest
growth in market value were Finland, Turkey, Greece, Norway, Brazil, and Spain. On the
other hand, Mexico, Japan, and Malaysia, and Thailand are of the lowest growth rates.
The variation within each group of countries at different developmental stages and in
various areas is considerable. Over the sample period, the stock markets in developed
countries consistently represent more than 90% of world equity market value.
[INSERT Table 1 ABOUT HERE]
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The countries are grouped into seven geographical regions: Central/Western
Europe, Northern Europe, Southern Europe, East Asia, North America, Latin America,
and Oceania. Market capitalization is weighted heavily on three major continents: North
America, Europe, and East Asia. The relative sizes of equity markets among countries
fluctuated over the period. As of the end of 2005, the seven largest markets by country
are the U.S., Japan, U.K., France, Canada, Germany, and Hong Kong. Overall, they
account for about four-fifths of equity market values in the world. Among them, the U.S.
market continuously is of the largest capitalization during the sample period, though the
proportion of market value varied over time. On the other hand, the capitalization of the
emerging markets is relatively small. As of the end of 2005, Brazil, Korea, and Taiwan
are the only developing countries with a world capitalization share greater than one
percent.
Table 2 reports summary statistics of the annualized return and monthly Sharpe ratio
for each market. For our sample, the raw return of stock markets in developing countries,
in general, is higher than the stock markets in developed countries. However, the cross-
region difference of equity returns among emerging markets is considerable. The stock
prices in Latin America outperformed the ones in other countries, while the countries in
East Asia performed worse than the rest of the world. Due to its economic recession,
Japan is the only country of a zero return during the sample period. In addition, the
Sharpe ratios in developed countries, on average, are higher than the ones in the emerging
markets. The countries of the maximum mean-variance efficient domestic portfolio are
the U.S., Switzerland, the Netherlands, and Finland. It is consistent with the previous
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findings that the mean-variance efficiency of equity prices in emerging markets is lower
due to the higher volatility. The mean of time-series of Sharpe ratios for three developed
countries (Austria, Japan, and New Zealand) and eight developing countries (Argentina,
Indonesia, Korea, Philippines, Portugal, Thailand, Turkey, and Taiwan) are negative.
[INSERT Table 2 ABOUT HERE]
Table 2 also indicates the time-variation of risk-adjusted performance in each
stock market. The averages of the standard deviation of Sharpe ratio for the developed
countries and emerging markets are 0.118 and 0.114, respectively. Compared to the
means of Sharpe ratio, the range of the unit-risk return of each market during the sample
period is considerable. Among each group of countries categorized by developmental
stages or regions, the periods for the highest and lowest Sharpe ratios disperse
significantly. For the developed countries, the maximum domestic Sharpe ratio most
likely occurred in three years: 1994, 1998, and 2005. For most emerging markets, the
greatest Sharpe ratios came about before 1998. For all countries, the years with the large
number of minimum Sharpe ratios are 1998, 2002, and 2003. The local investors in most
emerging markets generated the worst risk-adjusted performance in 1998 and the ones in
developed countries get the lowest in 2002 and 2003. This is because the emerging
markets lost a great deal of value in the financial crises while the evaporation of high-
tech bubbles after 2000 and economic recession caused by terrorist attack against the
U.S. in 2001 had a great impact on the equity markets’ performance in the developed
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countries. Overall, the risk-adjusted performances of stock prices demonstrate different
movements among markets.
The non-synchronism of mean-variance efficiency across countries imply the
potential gains to domestic investors by diversifying their portfolios globally. For
instance, in Table 2, there are 10 markets of the best risk-adjusted performance and 6
markets of the worst in 1998. Similarly, 4 countries had the highest Sharpe ratio and 3
countries had the lowest in 2000. This suggests that the cross-market performances differ
drastically within the same year, and local investors may avoid loss in their home markets
by allocating their funds optimally in other countries.
Table 3 shows the means of the unconditional correlation coefficients of each
country with all other markets and with countries grouped by regions in two sub-periods.
The developed countries, in general, demonstrate higher correlations with the other
markets than the emerging markets. Most countries also have the highest coefficients of
correlation with the other countries of the same region and with the ones in North
America. The magnitudes of correlations increase over time, however, the phenomena
that the emerging markets are less correlated with other countries can be constantly
observed in the two sample period. The fact that most markets are less correlated with the
countries from other regions indicates possible diversification benefits from inter-
continent investments. In addition, the stock markets in the rest of the world tend to have
considerable price co-movements with the markets in North America, particularly the
United States.
[INSERT Table 3 ABOUT HERE]
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The cross-temporal comparison of correlation also provides the evidence of the
enhancement of integration of the international financial market. The means of
correlation of each market with all other countries in the second period is persistently
greater than the ones in the first period. In the first period, some markets are negatively
correlated or almost uncorrelated with certain areas. The enhancement of correlation is
particularly considerable for the emerging markets with the countries that are in the
different regions. All means of correlation coefficient in the second period are increasing
and positive. This supports the enhancement of integration of the international financial
market over the past two decades.
The above findings regarding the dynamics of international market returns
highlight the need of over-time analysis on the strategies and benefits of international
diversification. The non-synchronous movement of risk-adjusted returns among
international markets suggests that the local investors have a chance to improve the
mean-variance efficiency of their portfolios by investing in foreign assets. Since the
return vector and variance-covariance matrix show noticeable time-variation, it is
appropriate for investors to keep rebalancing the weighting for the optimal portfolios.
Although, intuitively, the enhancement of global capital market integration causes the
shrinkage of diversification benefits, it remains unclear whether international
diversification is still desired by domestic investors. Furthermore, most previous studies
incorporate only a small number of emerging markets to determine the benefits and
strategies of diversification for investors in developed countries. They also did not
consider the impact of over-weighting investment constraints. This study portrays how
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diversification benefits and strategies change over time while taking into account the
more feasible strategies of a wider coverage of international equity markets.
IV. EMPIRICAL RESULTS
In this section, the empirical results regarding the time-variation in the international
diversification benefits are reported. In the first sub-section, we examine the revolution of
the maximum increase in the risk-adjusted performance and the maximum decrease in the
standard deviation by investing the global efficient portfolio for the U.S. investor during
the testing period. The change of distribution of weighting in different countries
classified by developmental stages and regions is presented in the second sub-section. We
particularly compare the diversification benefits and portfolio weighting across strategies
to highlight the impact of investment constraints on asset management.
4.1. Time-Varying Benefits of International Diversification
Figure 1 exhibits the efficient frontiers of the global portfolio at the end of each
year from 1993 to 2005. Because of the chronological deviation of mean-variance
efficiency and correlations among markets, the shape and size of efficient frontiers vary
drastically. The movement of efficient frontiers also does not follow specific direction.
The efficient frontier gradually shifted to the northwest from 1993 to 1994 then
progressing in an adverse path from 1994 to 1997. The position of optimal portfolios did
not change significantly during 1998 to 2001. For our sample, the possible investment
sets in 2002 and 2003 were the smallest and moved toward the northwest in 2004 and
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2005. The above revolution of mean-variance efficient portfolio is affected by the
business cycle of the world economy. Since the returns and risks are time-varying, the
key issue to note is that the intertemporal comparison of diversification benefits should
be based upon relative values, such like δ and ε.
[INSERT FIGURE 1 ABOUT HERE]
Figure 2 shows the impact of trading constraints on the mean-variance efficiency
of the global portfolios. Each Sharpe ratio curve is formed by the returns during 1988:01
to 2005:12 with various investment restrictions. The Sharpe ratio curve with short-sale
constraints is the most mean-variance efficient one. When the over-weighting (OW)
constraints are added, the benefits of international diversification decrease. The Sharpe
ratio curves move southeast when the weighting constraints become increasingly
restrictive (from 10, to 5, to 3). The U.S. portfolio lies on the southeast in the graph. This
suggests to the U.S. investor that the global diversification with any level of investment
restrictions are preferable to holding merely a domestic portfolio.
[INSERT FIGURE 2 ABOUT HERE]
Panel A of Table 4 presents the potential benefits of international diversification
to the U.S. domestic investor. Table 2 shows that the U.S. portfolio alone has an average
monthly Sharpe ratio of 0.121 and an annual standard deviation of 14.1% during the
testing period. For the local investor, the short-selling-constrained efficient frontier
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results in a mean Sharpe ratio of 0.1982 and a median increase in Sharpe ration of
0.1617. On average, the greatest potential reduction in volatility brought by international
diversification is 22.61% of the U.S. domestic portfolio risk. When the over-weighting
(OW) investment constraints are added and increasingly restrictive, the maximum
increases in risk-adjusted return and the maximum decrease in the standard deviation
gradually diminish but do not completely eradicate. For the most restricted case, i.e.,
SS+OW(2), the mean for δ is 0.0471 and the mean for ε is 14.88% over the sample
period. The fact that the minimums of two measures of diversification benefits under
various scenarios are positive suggests international diversification is desired even though
the investment constraints are included. The values of the first quartile for each indicator
suggest that the international diversification benefits to the U.S. investor are not trivial
over the majority of the testing period. Compared to the mean and median of δ with
various constraints, the large standard deviations suggest substantial time-variation of
increase in mean-variance efficiency brought by international diversification.
[INSERT TABLE 4 ABOUT HERE]
Figure 3 graphically demonstrates the time-series of the potential diversification
benefits to the U.S. investor. To observe the long-term trend of diversifying gains, each
measure of potential benefits is smoothed by the filter purposed by Hodrick and Prescott
(1997). The time-series of diversification benefits with various investment constraints
fluctuate over time. It is the same for the H-P smoothing trends. The benefits under
various trading constraints move in the same direction but are not proportional in size.
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Specifically, the diversification benefits with the most restrictive constraints, i.e., δ US, 4
and ε US, 4, are the least volatile over the testing period than those of less constrained asset
allocation. When the Sharpe ratio benefits of no-short-selling portfolio are high, the
divergences of diversification benefits among the optimal strategy under various
constraints expand. This suggests that the effectiveness of the less restrictive diversifying
strategies seems to be more sensitive to the change of market returns. Meanwhile, the
more constrained asset allocations help investors eliminate portfolio uncertainty since a
certain portion of weighting shifts to other second-best alternatives, which generally are
larger markets of high mean-variance efficiency and correlations with other countries.
[INSERT FIGURE 3 ABOUT HERE]
Panel B of Table 4 numerically illustrates the time-varying characteristics of
diversification benefits. For the U.S. investor, the improvement of mean-variance
efficiency is greatest from 1993 to 1994 and from the end of 2004 to the end of 2005. The
values of δ under different constraints significantly diminish in late 1998 and are
constantly small before 2003. In 2004 and 2005, the Sharpe ratio benefits are of about
equal size from 1993 to 1994. One possible explanation is that the emergence of
profitable investing targets at home, particularly high-tech and internet companies,
between the late 1990s and the early 2000s provide the U.S. investor alternatives other
than international diversification. The evaporation of bubbles and the economic recession
worsened by the terrorist attack in 2001 make investing in overseas assets increasingly
appealing to the U.S. domestic investor after 2002.
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The time-series of reduction in portfolio risk brought by global diversification is
dissimilar to the one of mean-variance efficiency benefits. The values of ε with various
investment restrictions are low during 1994 to 1996 while the values of δ generated from
corresponding strategies are high. Even when the most restrictive constrains (SS+OW(2))
are added, the U.S. domestic investor may constantly reduce 13% to 18% of portfolio risk
by diversifying globally after 1997. In Panel C of Table 4, the coefficients of correlation
between the two indicators of diversification benefits under the same investment
constraints are negative. This implies a trade-off relation between δ and ε in the long-
term, particularly when more restrictive weighting constraints are imposed.
The optimal global diversifying strategies indeed generate benefits to the local
investor, even though the short-sale and over-weighting constraints are increasingly
restrictive. In the long term, international diversification benefits are time-varying and do
not significantly fall. The time-series and the H-P time trends indicate a possible linkage
between the availability of superior investments in the domestic market and the Sharpe
ratio benefits brought by international diversification. The negative correlation between
the increase in mean-variance efficiency and the decrease in portfolio risk suggests they
are trade-offs in international diversification.
4.2. Variation of Weighting
Table 5 shows the weights of each group of countries for the MSR portfolios
under various investment constraints. The mean, standard deviation, maximum of weight,
and proportion of non-zero-weight months during the testing period are reported. The
average weight and number of selected markets in each year demonstrate the change of
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constituents in the optimal portfolios. Panel A shows the weighting distribution when
only short-sale is prohibited. Comparing with the mean in each group, the high standard
deviation suggests a considerable time-variation of weights. When the over-weighting
investment restrictions are added and more constrained, as exhibited in Panel B, C, and
D, the variation in shares on the optimal global asset allocation for each group of
countries decreases. In addition, the maximum values of weights for developed countries,
emerging markets, and each region gradually decline when OW constraints are more
restrictive. The import of upper-bounds in portfolio weighting drive the capital
distribution more proportional to the size of market and result in less substantial
alteration in asset allocation.
[INSERT TABLE 5 ABOUT HERE]
The comparison of the components of the optimal portfolio with various
constraints indicates that less restrictive strategies may be infeasible. We first investigate
the asset allocation in countries of different developmental stages. Shown in Panel A of
Table 5, the no-short-selling portfolio weighting in emerging markets not only fluctuates
drastically but is also disproportionate to the distribution of the world capital market
value. On average, the investors who wish to maximize portfolio mean-variance
efficiency should place 31.41% of wealth in emerging markets, which represent merely
7.4% of total market value of all countries at the end of 2005.8 As the over-weighting
investment constraints are included and more restrictive, which are exhibited in Panel B,
8 The weight of capitalization for emerging markets is between 4.19% (2000) and 9.39% (1994) during the sample period.
22
C, and D, the average weight on the assets in developing countries decreases, while the
probability that securities in other second-best markets are selected in the MSR portfolios
increase. Similar findings are graphically demonstrated in Figure 4. The short-sale
constrained strategies heavily distribute funds in emerging markets to maximize the
Sharpe ratio during 1993–1996 and 2003–2004 and allocate almost nothing in 1998 and
2001. On the other hand, the weighting of the portfolios with upper bounds are less
volatile and have no overwhelming distribution on emerging markets.
[INSERT FIGURE 5 ABOUT HERE]
We then examine asset allocation in different regions. Panel A of Table 5 shows
that overwhelming investments can also be found in small-cap regional portfolios, such
as Latin America, Northern Europe, Southern Europe, and Oceania when only short-
selling is considered. On the other hand, the weights for areas of large market value, such
as North America and Central/Western Europe are zero for a number of periods. The
more restrictive OW constraints decrease portfolio weight to other second-best mean-
variance-efficient markets of larger capitalization. As shown in Panel B, C, and D of
Table 5, the weighting of the more constrained MSR portfolios are not as unbalanced as
the one in short-sale-forbidden portfolios. For the case of SS+OW(3), the weights are
proportional to the relative magnitude of international market capitalization, and assets in
each area are more frequently included in the MSR portfolio. Furthermore, in most
regions, the time-variation of weight for each area is lower than the other three less
23
restrictive scenarios9. Figure 6.A graphically presents the asset allocation of the MSR
portfolio without upper bounds. The weightings of all regions vary significantly and the
overwhelming component for the MSR portfolio in small markets is common over the
sample period. The execution of such strategies may cause illiquidity of a portfolio and
trigger excessive price volatility when excessive funds flow in and out of those small
markets. This eventually changes the relationship of mean-variance efficiency and
correlation among markets. In Figure 6.B, C, and D, as the OW constraints become more
limited, the major components of the MSR portfolios concentrate assets in North
America, Central/Western Europe, and East Asia. Their weighting distributions also
change less drastically over the sample period than the ones of less constrained portfolios.
The number of market indices selected in the basket also authenticates the
essentialness of more restricted portfolio strategies. The time-series average for no-short-
selling asset allocation is 4.2 national indices in the testing period. That implies, overall,
that more than 80% international portfolios are redundant. The inclusion of over-
weighting constraints effectively expands the coverage of the optimal portfolio to 9.6
(SS+OW(10)), 11.8 (SS+OW(5)), and 13.3 (SS+OW(3)). Although a certain portion of
Sharpe ratio benefits are lost due to the “compulsorily” diversifying international
diversifications, the inclusion of upper-bounds also increases the invariance of weighting
and benefits, as well as expand the assets chosen in the optimal portfolios.
[INSERT TABLE 6 ABOUT HERE]
9 The only exception is North America since the average of weight increases as the investment constraints are increasingly restrictive.
24
A similar conclusion can also be found in the weighting of the MVP. As reported
in Panel A of Table 6, when there are no constraints on the upper bounds, the average
optimal weight on the emerging markets is disproportional, although the weighting
imbalance of the MVP is less than the one of the MSRP with corresponding investment
restrictions. In addition, the regional components of the MVP differ from the ones of the
MSRP. Geographically, the weights of the MVP on the securities in Latin America and
Northern Europe are less than the ones of the MSR portfolio, while the weighting on the
assets in Central/Western Europe and North America is heavier. Even though the
weightings on East Asian indices are similar, the MVP allocates more funds in developed
countries but the MSRP place great weighting on emerging markets in this area. This
phenomenon occurs because the goal to hold the MVP is to generate the least risky
investment and the allocations direct to the assets in the countries where the security
prices are less volatile. The numbers of countries selected in the MVP are more than the
one in the MSRP under the same investment constraints. On average, 2.79 emerging
markets and 5.76 developed countries are included in the short-sales constrained MVP
within one month. In Table 7, similar to the transformation of the MSRP, the time-
variation in benefits and weighting decreases and the coverage of selected portfolios
expands as the OW investing constraints become more restrictive. The weights for the
emerging markets and the regions of small market values also become less heavy.
[INSERT FIGURE 7 ABOUT HERE]
25
Figure 7 shows diverse patterns of time-variation of the components of the MVP
with various investment constraints. The weighting of emerging markets is relatively
small during 1997 to 2000 and 2003, and their time-series patterns differ from the ones of
the MSRP. In addition, the weighting for developed countries in the MVP is higher than
the ones in the MSR during the sample period due to the fact that stock prices in those
countries are persistently less risky than those in emerging markets. In Figure 8, the
weighting of North American assets seems to decline over time in all circumstances. On
the other hand, securities in Central/Western Europe and East Asia progressively
contribute to the lessening of portfolio volatility.
[INSERT FIGURE 8 ABOUT HERE]
Our empirical results suggests that adding more restrictive investment constraints
decreases diversification benefits but generates some desired attributes in managing asset
allocation. First, the coverage of both the MSR portfolio and the MVP expands when the
upper bounds are more restrictive. For the most constrained case, overall, the MSR
portfolio includes 13.25 countries and the MVP 15.62 countries per month, respectively.
Furthermore, the time-variation for the weights in the optimal portfolios decreases. This
is due to the fact that optimalization with less restrictive constraints is likely to generate
the corner solutions, which are sensitive to the relative sizes of mean-variance efficiency
among markets. Therefore, it is not astonishing that the more restrictive diversification
benefits are less time-varying since the second best markets with large capitalization are
included. The consideration of OW investing limitations not only makes the optimal
26
investment strategy more feasible but also generates some desired traits in portfolio
management.
V. EXPLAINING THE TIME-VARIATION IN DIVERSIFICATION BENEFITS
In this section, we explore time-series analysis and factors that impact the
potential gains from overseas investments. Bekaert and Harvey (1995); Bekaert, Harvey,
and Ng (2005); De Jong and De Roon (2005); and Errunza, Losq, and Padmanabhan
(1992) have documented that the international capital markets, particularly in developing
countries, become gradually more integrated. It is natural to question whether global
diversification benefits shrink due to the decrease in the level of market segmentation.
Moreover, local investors may wonder what economic variables drive the variation of
diversification benefits in the long run. Driessen and Laeven (2005) report the factors that
may explain cross-nation difference of diversification benefits. However, a time-series
analysis of potential gains may be more useful in formatting long-term optimal portfolio
strategies. We use a regression framework that includes the time-series of other variables
to investigate the above issues. To shorten our analysis, we focus on the Sharpe ratio
benefits. This is also because the change of risk-adjusted performance reflects the time
variations of both expected return and volatility on efficient frontiers.
We collect the following time-series data. First, we collect data on the returns of
high-technology and internet-related industries. It is expected that the benefits of
international diversification are small for the periods of profitable investing opportunities
available in the domestic market. Once there are newly developing industries with
27
optimistic prospectives recognized by the public at home, the local investor may seek to
diversify their portfolios by allocating funds in these emerging investment targets. The
risk-return of S&P 500 Information Technology index is used as a proxy for the domestic
alternative investment.10 Furthermore, to examine the influence of exchange rate
exposure on diversification benefits, the time-series of the U.S. Dollar Trade Weighted
Index is obtained. The volatility in foreign exchange rate is computed as the ratio of the
difference between the highest and the lowest indices and the average of the beginning
and ending indices in each month. To compensate the uncertainty in currency translation,
it is expected that the relationship between exchange risk and diversification benefits is
positive. Third, stock market capitalization is also collected and used as a proxy for the
degree of stock market integration. Bekaert and Harvey (1995) show that countries of
larger local markets are more integrated into world capital markets than countries of
smaller markets. It is expected that the increase in the ratio of local market capitalization
to the world market value will reduce diversification benefits. To observe
macroeconomic impact, the time-series of the inflation rate (measured by the monthly
change of the Consumer Price Indices in the U.S.) and the leading business indicator
(calculated by the change rate of Barron's Confidence Index) are also collected11. The
former is factored into the equation to account for the instability and growth in economy
while the latter is intended to characterize investors’ prospects for economic growth.
10 The S&P 500 Information Technology index is a more appropriate proxy for the stock price of the high-technology and internet-related companies than the other available competitors, e.g., the NASDAQ indices. It covers domestically listed companies that primarily develop software, services, hardware and equipment in various technology fields, such as Internet, application, systems, databases management, and consulting. 11. Barron's Confidence Index is calculated by dividing the average yield on high-grade bonds by the average yield on intermediate-grade bonds. A rising ratio indicates investors are demanding a lower premium in yield for increased risk and so are optimistic to economy.
28
Both factors are supposed to move in the opposite directions of the global diversification
benefits.
Panel A of Table 7 reports the partial autocorrelation coefficients of selected
periods for each measure of diversification benefits. Since efficient frontiers in month t
and month t-1 are formed by 59 overlapping returns, it is not surprising that each
assessment of diversifying gains is positively correlated with its one-period lag at 1%
significant level12. The autocorrelations drastically diminish after the first period. For the
lags greater than one period, neither the economic sizes nor the statistical significance of
autocorrelations are trivial. To determine the stationarity of each time-series, Phillips-
Perron and Dickey-Fuller tests are implemented. The statistics shown in Panel A suggest
that the unit-root hypothesis should be rejected for each time-series of the Sharpe ratio
benefits.
The regression results are reported in Panel B of Table 7. The independent
variables are used to explain the maximum increase in Sharpe ratio (δJ) under various
investment constraints. The one-period lag of dependent variable is accommodated to
control the autoregressive property of diversifying gains. A constant was added but not
reported. A significant autocorrelation can be found in each measure of benefits. The
Sharpe ratio benefits for the portfolios with tighter weighting restrictions, SS+OW(5) and
SS+OW(3), were slightly increasing over time while the diversification benefits of less
constrained portfolios do not show a significant time-trend. This suggests that the
integration of the world financial market does not make global diversification less
attractive to U.S. investors. In contrast, the potential economic advantages brought by
12 Σιμιλαρ πηενομενα αλσο χαν βε φουνδ ιν τηε τιμε−σεριεσ οφ εJ. The result is available upon request.
29
overseas investment to domestic investors grew when more feasible strategy, i.e.,
portfolios with upper-bound constraints, were implemented.
We are interested in the impact of other factors on the economic size of global
diversification benefits. For all scenarios with various allocation constraints, the
emergence of more profitable investments in the local market can replace enhancement of
mean-variance efficiency brought by global diversification at 1% statistical significance
level. As the weighting becomes more restrictive, the substitute effect of domestic
alternatives decreases. The negative relation between Sharpe ratio measure and domestic
alternative portfolio performance suggests that the home bias is less sizeable when local
investments are less mean-variance efficient. On the other hand, the volatility in foreign
exchange rate is positively correlated with diversification benefits. The coefficients for
exchange rate risk decrease as investment constraints become increasingly restrictive
while the statistical significance enhances. The Durbin-Watson statistics indicate that the
autocorrelation in error terms for these regressions are insignificant.
We also explored other time-series as descriptive variables, such as U.S. equity
market capitalization to the world market value (proxy for the international integration),
inflation rate (proxy for macroeconomic uncertainty and growth), and by the change in
Barron's Confidence Index (proxy for the leading business indicator). However, those
factors are not statistically significant, and including them in models does not alter the
results (not reported). In sum, it is found that the availability of profitable investment
opportunities in the local market and the volatility in exchange rate have the most
explanatory power on the international diversification benefits.
30
VI. CONCLUSIONS
The time-variation of the global diversification benefits to the U.S. local investor
have been examined. . The main findings of the analyses of the diversification gains
under various short-sales and over-weighting investment constraints are as follows. First,
the diversification benefits of optimal portfolio, even the most constrained, are time-
varying but persistently positive. The optimal asset weighting among countries alters
during the testing period as well. This suggests that it is appropriate for investor to revise
international asset allocation according to the market dynamics. Second, the inclusion of
restrictive investment constraints makes the optimal strategy more realistic. Although
more limiting investment restrictions sacrifice part of diversification benefits, some
appealing innovations for asset management transpire: a reduction in the temporal
deviation of diversification benefits, an expansion in the range of comprising assets, and
a decrease in time-variation of components in the optimal portfolio. Third, the Hodrick-
Prescott filter and time-series analysis suggest that the diversification benefits did not
significantly decrease over the testing period even though the world capital market has
become more integrated. Instead, the diversification gains generated by more restrictive
strategies gradually grew. Fourth, the availability of profitable investing opportunity in
the domestic market replaces a part of the gain brought by overseas investments. The
volatility in currency exchange rate is compensated when international diversification is
implemented.
We add to the current literature on international portfolio management by offering
time-series analysis of diversification benefits with more realistic assumptions. Previous
studies have confirmed diversification benefits by using simulation (Li, Sarkar, and
31
Wang 2003; Wang 1998), by adding weighting constraints (De Roon, Nijman, and
Werker 2001; Jagannathan and Ma 2003), and by investigating its time-variation
(Driessen and Laeven, 2005; Huang and Zhong, 2006), this paper intends to combine
their major concepts and/or modi operandi, and maximizes the feasibility of international
portfolio management. Furthermore, we investigate the impact of economic/financial
variables on global diversification benefits and show the substitution effect of local
investments and premium for the exposure of foreign exchange rate.
There are two caveats to our analysis in this paper. First, we consider the long-
term optimal asset allocation without using a conditional model to forecast returns and
volatilities. Bekaert and Harvey (1995) and Bekaert, Harvey, and Ng (2005) document
the time-variation of the integration of the international financial market. Chan, Karceski,
and Lakonishok (1999) develop a dynamic model to estimate variance-covariance matrix
to form an efficient frontier. Huang and Zhong (2006) apply the Dynamic Conditional
Correlation (DCC) in modeling efficient frontiers. Wang (2005) empirically investigates
the shrinkage approach that incorporates prior information and beliefs to avert model
uncertainty. Chang, Errunza, Hogan, and Hung (2005) and Hodrick, Ng, and Sengmueller
(1999) examine the pricing of systematic and hedging risks for market portfolios and
exchange rate in international asset pricing. Harvey (1995) also suggests the
predictability of equity returns, particularly in emerging markets. However, the purpose
of this paper is to investigate the time-varying international diversification benefits and
their changes caused by various investment constraints over the long term. Future
research into the forecasting of diversification benefits may apply dynamic asset pricing
theory or take into account portfolio hedging.
32
Second, this paper evaluates diversification benefits from the perspective of the
U.S. investor but not those of domestic investors in different countries. Driessen and
Laeven (2005) compare the cross-country disparity of international diversification
benefits from a static viewpoint but not from a dynamic perspective. A cross-market
comparison on the inter-temporal analysis of the gains brought by an international
optimal portfolio will allow us to widely explore the international deviation in the long
run and the impact of economic/financial factors on diversification benefits in different
countries.
33
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35
Table 1. Countries and Weights of Market Capitalization The average growth rate of market values from 1992 to 2005 and the weight of each country to the total market value of all countries as of the end of year 1992, 1999, and 2005 are reported. Panel A: Developed Countries
Country Symbol Growth Rate 1992 1999 2005 Area Australia AUS 14.81% 1.27% 1.24% 2.08% Oceania Austria AUT 15.14% 0.19% 0.10% 0.33% C/W Europe Belgium BEL 12.72% 0.61% 0.53% 0.78% C/W Europe Canada CAN 14.96% 2.31% 2.28% 3.83% N. America Switzerland CHE 13.09% 1.81% 2.00% 2.41% C/W Europe Germany DEU 10.16% 3.31% 4.14% 3.15% C/W Europe Denmark DNK 14.28% 0.31% 0.28% 0.48% C/W Europe Spain ESP 19.11% 0.94% 1.25% 2.48% C/W Europe Finland FIN 24.37% 0.12% 1.01% 0.54% N. Europe France FRA 13.13% 3.12% 4.34% 4.20% C/W Europe U.K. GBR 9.60% 8.86% 8.25% 7.89% C/W Europe Hong Kong HKG 14.97% 1.64% 1.76% 2.72% E. Asia Ireland IRL 16.12% 0.16% 0.20% 0.29% C/W Europe Italy ITA 15.04% 1.23% 2.10% 2.06% C/W Europe Japan JPN 5.36% 22.14% 12.89% 11.80% E. Asia Netherlands NLD 10.24% 1.28% 2.00% 1.23% C/W Europe Norway NOR 20.00% 0.17% 0.18% 0.49% N. Europe New Zealand NZL 8.14% 0.14% 0.08% 0.10% Oceania Singapore SGP 13.62% 0.47% 0.57% 0.66% E. Asia Sweden SWE 14.39% 0.73% 1.08% 1.14% N. Europe U.S.A. USA 10.75% 43.01% 48.33% 43.88% N. America
Panel B: Emerging Markets
Country Symbol Growth Rate 1992 1999 2005 Area Argentina ARG 7.48% 0.18% 0.16% 0.12% L. America Brazil BRA 19.78% 0.43% 0.66% 1.23% L. America Chile CHL 12.48% 0.28% 0.20% 0.35% L. America Greece GRC 22.19% 0.10% 0.57% 0.37% S. Europe Indonesia IDN 15.84% 0.11% 0.18% 0.21% E. Asia Korea, S. KOR 15.72% 1.03% 0.88% 1.85% E. Asia Malaysia MAL 5.37% 0.87% 0.40% 0.47% E. Asia Mexico MEX 4.28% 1.32% 0.44% 0.62% L. America Philippines PHL 7.62% 0.15% 0.12% 0.10% E. Asia Portugal PRT 16.08% 0.09% 0.20% 0.17% C/W Europe Thailand THL 6.11% 0.55% 0.17% 0.32% E. Asia Turkey TUR 24.10% 0.09% 0.33% 0.42% S. Europe Taiwan TWN 12.74% 0.96% 1.09% 1.23% E. Asia
36
37
Table 2. Return and Sharpe Ratio in Each Market The mean of return for each market from 1988:01 to 2005:12 is annualized. The mean, median, standard deviation, maximum, and minimum of monthly Sharpe ratio using previous 60 monthly returns for each market are reported. Panel A: Developed Countries
Sharpe Ratio Country
Mean Return Mean Median St. Dev Max Time Min Time
AUS 0.074 0.005 0.001 0.069 0.201 Dec-05 -0.122 Oct-01 AUT 0.087 -0.033 -0.091 0.134 0.392 Dec-05 -0.172 Jun-00 BEL 0.081 0.041 0.020 0.127 0.376 Aug-98 -0.196 Apr-03 CAN 0.083 0.021 0.024 0.093 0.219 Sep-00 -0.169 Aug-94 CHE 0.107 0.116 0.117 0.151 0.411 Mar-98 -0.197 Apr-03 DEU 0.076 0.041 0.046 0.111 0.309 Jul-98 -0.199 Apr-03 DNK 0.119 0.066 0.060 0.093 0.312 Apr-98 -0.142 Apr-03 ESP 0.072 0.034 0.005 0.116 0.295 Aug-98 -0.145 Aug-93 FIN 0.093 0.084 0.081 0.162 0.375 Jan-93 -0.261 Apr-00 FRA 0.092 0.054 0.057 0.091 0.254 Jan-00 -0.139 Apr-03 GBR 0.061 0.029 0.025 0.133 0.291 Mar-98 -0.293 Apr-03 HKG 0.088 0.037 -0.002 0.115 0.251 Sep-94 -0.145 Oct-02 IRL 0.076 0.039 0.002 0.140 0.372 May-98 -0.200 Mar-03 ITA 0.050 0.001 -0.010 0.083 0.179 Apr-98 -0.163 Apr-03 JPN 0.000 -0.096 -0.089 0.060 0.048 Jul-97 -0.240 Sep-98 NLD 0.082 0.089 0.122 0.158 0.360 Jun-98 -0.213 Apr-03 NOR 0.093 0.005 -0.015 0.090 0.241 Jan-98 -0.183 Oct-02 NZL 0.016 -0.027 -0.034 0.136 0.254 Nov-05 -0.249 Dec-00 SGP 0.066 0.007 -0.023 0.107 0.223 Feb-96 -0.190 Sep-98 SWE 0.114 0.070 0.013 0.128 0.341 Mar-00 -0.139 Oct-02 USA 0.091 0.121 0.114 0.171 0.393 Jan-00 -0.147 Apr-05 Panel B: Emerging Markets
Sharpe Ratio Country
Mean Return Mean Median St. Dev Max Mo-Yr Min Mo-Yr
ARG 0.162 -0.004 -0.019 0.101 0.165 Mar-94 -0.235 Jun-02 BRA 0.153 0.029 0.024 0.089 0.230 Jul-97 -0.181 Oct-02 CHL 0.137 0.052 0.046 0.173 0.368 Nov-94 -0.217 Oct-02 GRC 0.100 0.007 0.009 0.105 0.229 Oct-99 -0.180 Jul-95 IDN 0.054 -0.055 -0.064 0.108 0.149 Dec-05 -0.279 Oct-98 KOR 0.062 -0.029 -0.042 0.079 0.206 Dec-05 -0.239 Jan-98 MAL 0.043 0.002 0.013 0.126 0.233 Jan-94 -0.272 Nov-98 MEX 0.204 0.073 0.045 0.133 0.437 Feb-94 -0.131 Feb-99 PHL 0.029 -0.043 -0.104 0.171 0.266 Oct-95 -0.269 Nov-01 PRT 0.017 -0.013 -0.041 0.127 0.283 May-98 -0.242 May-03 THL 0.032 -0.036 -0.002 0.141 0.213 Jan-94 -0.273 Sep-98 TUR 0.088 -0.001 -0.004 0.064 0.143 Jan-94 -0.136 Feb-95 TWN 0.049 -0.042 -0.040 0.065 0.122 Sep-97 -0.174 Oct-02
Table 3. Coefficients of Correlation Among Markets The averages of unconditional coefficients of correlation of each country with other countries of different regions during two periods, 1988:01 – 1996:12 and 1997:01 – 2005:12 are reported. Panel A: Developed Countries
World Average Latin America North America East Asia Central/West Europe North Europe South Europe Oceania
88 - 96 97 - 05 88 - 96 97 - 05 88 - 96 97 - 05 88 - 96 97 - 05 88 - 96 97 - 05 88 - 96 97 - 05 88 - 96 97 - 05 88 - 96 97 - 05
AUS 0.28 0.55 0.14 0.58 0.43 0.66 0.25 0.53 0.29 0.54 0.43 0.57 0.04 0.40 0.66 0.70 AUT 0.31 0.43 0.07 0.39 0.17 0.41 0.30 0.31 0.42 0.56 0.34 0.39 0.34 0.34 0.22 0.52 BEL 0.32 0.45 0.06 0.32 0.41 0.48 0.26 0.23 0.51 0.68 0.35 0.47 0.16 0.37 0.15 0.42 CAN 0.31 0.56 0.13 0.61 0.65 0.79 0.34 0.47 0.33 0.58 0.39 0.67 0.02 0.45 0.42 0.63 CHE 0.32 0.51 0.02 0.40 0.39 0.58 0.25 0.33 0.50 0.69 0.38 0.55 0.17 0.40 0.27 0.52 DEU 0.35 0.57 -0.01 0.52 0.33 0.71 0.26 0.36 0.58 0.73 0.42 0.69 0.19 0.52 0.22 0.54 DNK 0.30 0.50 0.01 0.47 0.27 0.65 0.20 0.31 0.49 0.65 0.45 0.59 0.15 0.38 0.19 0.46 ESP 0.39 0.57 0.22 0.56 0.40 0.66 0.29 0.38 0.51 0.71 0.55 0.63 0.18 0.51 0.42 0.58 FIN 0.28 0.40 0.12 0.37 0.33 0.60 0.27 0.25 0.32 0.46 0.55 0.55 0.03 0.43 0.38 0.41 FRA 0.33 0.59 0.10 0.50 0.40 0.72 0.24 0.35 0.53 0.76 0.35 0.73 0.17 0.53 0.23 0.55 GBR 0.38 0.56 0.06 0.51 0.51 0.70 0.29 0.38 0.54 0.70 0.54 0.63 0.10 0.48 0.45 0.57 HKG 0.33 0.47 0.17 0.55 0.49 0.57 0.41 0.54 0.34 0.40 0.35 0.43 0.10 0.26 0.30 0.55 IRL 0.37 0.48 0.09 0.43 0.40 0.58 0.33 0.32 0.51 0.61 0.50 0.51 0.22 0.43 0.34 0.53 ITA 0.28 0.49 0.05 0.46 0.29 0.56 0.25 0.26 0.38 0.66 0.40 0.59 0.15 0.49 0.19 0.46 JPN 0.27 0.38 0.06 0.34 0.26 0.50 0.21 0.40 0.40 0.36 0.38 0.40 0.06 0.24 0.26 0.52 NLD 0.40 0.58 0.02 0.49 0.51 0.68 0.30 0.38 0.61 0.76 0.51 0.65 0.16 0.47 0.39 0.55 NOR 0.34 0.54 0.14 0.58 0.41 0.66 0.24 0.39 0.46 0.63 0.55 0.54 0.10 0.49 0.38 0.61 NZL 0.25 0.48 0.06 0.44 0.28 0.51 0.22 0.48 0.27 0.48 0.39 0.47 0.12 0.39 0.66 0.70 SGP 0.40 0.47 0.15 0.55 0.48 0.57 0.52 0.57 0.44 0.37 0.45 0.42 0.17 0.31 0.37 0.60 SWE 0.38 0.55 0.13 0.52 0.44 0.71 0.31 0.39 0.50 0.66 0.57 0.65 0.19 0.53 0.47 0.55 USA 0.32 0.56 0.19 0.57 0.65 0.79 0.29 0.45 0.39 0.62 0.40 0.65 0.00 0.46 0.29 0.54
39
40
Panel B: Emerging Markets World Average Latin America North America East Asia Central/West Europe North Europe South Europe Oceania
88 - 96 97 - 05 88 - 96 97 - 05 88 - 96 97 - 05 88 - 96 97 - 05 88 - 96 97 - 05 88 - 96 97 - 05 88 - 96 97 - 05 88 - 96 97 - 05
ARG 0.06 0.36 0.18 0.57 0.16 0.42 0.05 0.33 0.02 0.31 0.02 0.36 0.14 0.36 0.17 0.37 BRA 0.10 0.52 0.12 0.67 0.08 0.63 0.08 0.42 0.08 0.56 0.22 0.53 0.16 0.41 0.13 0.54 CHL 0.08 0.51 0.14 0.66 0.14 0.61 0.14 0.50 0.04 0.46 0.08 0.52 0.01 0.48 -0.03 0.56 GRC 0.19 0.39 0.09 0.38 0.06 0.40 0.11 0.23 0.29 0.50 0.18 0.45 0.35 0.33 0.15 0.38 IDN 0.14 0.34 0.05 0.36 0.20 0.35 0.20 0.48 0.11 0.26 0.14 0.25 0.13 0.19 0.20 0.42 KOR 0.15 0.38 0.06 0.33 0.19 0.42 0.22 0.45 0.13 0.32 0.23 0.39 -0.07 0.27 0.16 0.53 MAL 0.33 0.34 0.10 0.38 0.41 0.36 0.46 0.49 0.33 0.26 0.37 0.26 0.16 0.20 0.30 0.36 MEX 0.16 0.52 0.22 0.65 0.25 0.69 0.21 0.48 0.12 0.48 0.20 0.55 0.00 0.45 0.14 0.57 PHL 0.27 0.37 0.15 0.41 0.34 0.43 0.39 0.51 0.24 0.29 0.20 0.26 0.16 0.20 0.29 0.48 PRT 0.28 0.46 0.09 0.36 0.20 0.50 0.18 0.26 0.40 0.64 0.32 0.57 0.41 0.40 0.28 0.42 THL 0.28 0.41 0.17 0.42 0.36 0.46 0.41 0.57 0.26 0.31 0.21 0.31 0.21 0.18 0.20 0.62 TUR 0.09 0.38 0.06 0.48 -0.05 0.52 0.11 0.25 0.11 0.38 0.03 0.51 0.35 0.33 0.01 0.41 TWN 0.15 0.40 0.14 0.54 0.12 0.49 0.25 0.47 0.13 0.32 0.14 0.36 0.05 0.28 0.06 0.45
Table 4. International Diversification Benefits to U.S. Investors The mean, median, standard deviation, maximum, minimum, and the first quartile of each assessment of constrained diversification benefits to US domestic investor are reported. The averages of each year are presented. Panel A. Summary Statistics
δUS, 1 δUS, 2 δUS, 3 δUS, 4 εUS, 1 εUS, 2 εUS, 3 εUS, 4
Mean 0.1982 0.0997 0.0677 0.0471 22.61% 19.42% 17.42% 14.88% Median 0.1617 0.0995 0.0707 0.0474 24.02% 20.80% 18.52% 15.79% St. Dev. 0.1406 0.0632 0.0451 0.0330 4.52% 4.21% 3.90% 3.35% Max 0.4999 0.2555 0.1893 0.1447 28.26% 25.52% 23.03% 19.71% Min 0.0059 0.0059 0.0045 0.0028 11.80% 10.94% 9.52% 8.09% 1st Quartile 0.0792 0.0404 0.0254 0.0174 20.16% 15.43% 14.32% 12.43% Panel B. Average of Each Year Year δUS, 1 δUS, 2 δUS, 3 δUS, 4 εUS, 1 εUS, 2 εUS, 3 εUS, 4
1993 0.4037 0.1303 0.0788 0.0491 27.04% 19.00% 15.21% 11.70% 1994 0.4067 0.1776 0.1120 0.0731 16.39% 13.39% 10.98% 8.88% 1995 0.2208 0.0942 0.0639 0.0441 13.32% 12.19% 10.85% 9.33% 1996 0.1576 0.1108 0.0773 0.0552 18.50% 16.76% 15.58% 13.97% 1997 0.1242 0.1098 0.0760 0.0532 22.26% 19.01% 17.74% 15.64% 1998 0.1044 0.0774 0.0564 0.0423 20.22% 14.56% 13.89% 12.91% 1999 0.0174 0.0119 0.0087 0.0065 24.08% 21.04% 19.17% 15.98% 2000 0.0577 0.0345 0.0237 0.0179 24.29% 23.04% 20.93% 17.81% 2001 0.0685 0.0200 0.0132 0.0096 26.38% 24.14% 21.87% 18.47% 2002 0.0945 0.0381 0.0215 0.0124 23.75% 22.61% 19.64% 16.18% 2003 0.2244 0.1182 0.0700 0.0434 25.35% 23.72% 21.57% 18.12% 2004 0.2615 0.1654 0.1207 0.0879 26.74% 22.10% 19.81% 17.34% 2005 0.4347 0.2084 0.1580 0.1181 25.64% 20.88% 19.21% 17.11%
Panel C. Coefficient of Correlation
ρ(δUS, 1, εUS, 1) ρ(δUS, 2, εUS, 2) ρ(δUS, 3, εUS, 3) ρ(δUS, 4, εUS, 4)-0.020 -0.264 -0.254 -0.133
41
Table 5. MSR Portfolio Weights The summaries of the MSR portfolio weights and number of selected countries with various investment constraints for emerging markets (EM), indices of Latin America (LA), North America (NA), East Asia (EA), Central/West Europe (C/W EU), North Europe (N EU), South Europe (S EU), and Oceania (OC), are reported. Non-Zero is the percentage of months during sample period that the weight is greater than zero. The mean of weights for each year is also reported. Panel A. Short-sales Constraints
Weight Number EM DC LA NA EA C/W EU N EU S EU OC EM DC
Mean 0.3141 0.6859 0.1755 0.1703 0.1282 0.3350 0.1773 0.0114 0.0024 1.75 2.47 St. Dev. 0.3668 0.3668 0.2769 0.2290 0.2586 0.3062 0.3006 0.0280 0.0124 Maximum 1.0000 1.0000 0.8774 0.8518 1.0000 1.0000 1.0000 0.1441 0.0803 6.00 7.00 Non-Zero 67.31% 95.51% 48.72% 48.08% 50.64% 78.21% 51.92% 23.72% 5.13%
1993 0.8286 0.1714 0.6799 0.0000 0.1078 0.1693 0.0000 0.0431 0.0000 5.42 1.83 1994 0.8570 0.1430 0.7789 0.0000 0.0472 0.1388 0.0000 0.0351 0.0000 3.83 1.58 1995 0.5585 0.4415 0.4867 0.0577 0.0773 0.3777 0.0007 0.0000 0.0000 2.42 2.25 1996 0.2691 0.7309 0.1332 0.2181 0.1359 0.4832 0.0293 0.0000 0.0001 3.08 2.83 1997 0.0738 0.9262 0.0388 0.3905 0.0345 0.4271 0.1085 0.0005 0.0000 2.42 4.00 1998 0.0050 0.9950 0.0044 0.2652 0.0000 0.6808 0.0491 0.0006 0.0000 0.33 5.17 1999 0.0516 0.9484 0.0000 0.6697 0.0000 0.1913 0.0874 0.0516 0.0000 0.67 4.25 2000 0.0167 0.9833 0.0000 0.4770 0.0000 0.0855 0.4207 0.0167 0.0000 0.42 3.42 2001 0.0000 1.0000 0.0000 0.0839 0.0000 0.2439 0.6722 0.0000 0.0000 0.00 2.42 2002 0.0915 0.9085 0.0222 0.0000 0.0693 0.0026 0.9059 0.0000 0.0000 0.33 1.08 2003 0.9622 0.0378 0.0296 0.0071 0.9326 0.0000 0.0306 0.0000 0.0000 1.75 0.42 2004 0.3341 0.6659 0.1073 0.0452 0.2268 0.6172 0.0006 0.0000 0.0029 1.58 1.50 2005 0.0347 0.9653 0.0000 0.0000 0.0346 0.9370 0.0000 0.0000 0.0283 0.50 1.42
Panel B. SS+OW(10) Constraints
Weight Number EM DC LA NA EA C/W EU N EU S EU OC EM DC
Mean 0.1208 0.8792 0.0505 0.4323 0.1322 0.2833 0.0506 0.0086 0.0425 3.92 5.63 St. Dev. 0.1000 0.1000 0.0418 0.2328 0.1336 0.1824 0.0426 0.0141 0.0754 Max 0.3314 1.0000 0.1322 0.9369 0.4450 0.9166 0.1446 0.0456 0.1827 10.00 11.00 Non-Zero 86.54% 100.00% 69.23% 92.95% 64.10% 92.31% 74.36% 33.33% 28.85%
1993 0.1841 0.8159 0.0793 0.3588 0.3003 0.2269 0.0000 0.0348 0.0000 8.50 4.92 1994 0.2050 0.7950 0.0955 0.2530 0.3228 0.3015 0.0000 0.0273 0.0000 8.00 5.00 1995 0.0992 0.9008 0.0789 0.4184 0.2138 0.2881 0.0008 0.0000 0.0000 5.17 4.67 1996 0.1096 0.8904 0.0600 0.4663 0.1319 0.3139 0.0229 0.0000 0.0051 4.42 6.08 1997 0.0817 0.9183 0.0442 0.5162 0.0360 0.3251 0.0770 0.0015 0.0000 2.75 5.83 1998 0.0121 0.9879 0.0062 0.5201 0.0000 0.3995 0.0705 0.0037 0.0000 1.00 7.75 1999 0.0179 0.9821 0.0000 0.7691 0.0000 0.1227 0.0920 0.0163 0.0000 0.75 4.92 2000 0.0144 0.9856 0.0000 0.6706 0.0000 0.1864 0.1286 0.0144 0.0000 0.67 4.67 2001 0.0091 0.9910 0.0079 0.6847 0.0000 0.2364 0.0699 0.0012 0.0000 0.25 3.67 2002 0.0748 0.9252 0.0276 0.3081 0.0472 0.5394 0.0631 0.0000 0.0146 1.17 2.67 2003 0.2282 0.7718 0.0505 0.2630 0.3074 0.1424 0.0646 0.0026 0.1695 4.83 5.67 2004 0.2916 0.7084 0.1185 0.2593 0.2043 0.1888 0.0378 0.0104 0.1811 6.83 8.00 2005 0.2422 0.7578 0.0876 0.1318 0.1546 0.4123 0.0310 0.0000 0.1827 6.58 9.33
42
Panel C. SS+OW(5) Constraints Weight Number EM DC LA NA EA C/W EU N EU S EU OC EM DC
Mean 0.0782 0.9218 0.0328 0.5409 0.0985 0.2666 0.0328 0.0057 0.0227 4.60 7.28 St. Dev. 0.0579 0.0579 0.0246 0.2387 0.1113 0.1727 0.0279 0.0082 0.0386 Max 0.2251 1.0000 0.0675 0.9684 0.6717 0.7051 0.0878 0.0228 0.0914 10.00 14.00 Non-Zero 91.03% 100.00% 73.08% 100.00% 65.38% 94.87% 74.36% 37.82% 36.54%
1993 0.1138 0.8861 0.0454 0.5655 0.1680 0.2006 0.0000 0.0205 0.0000 9.42 6.33 1994 0.1166 0.8834 0.0555 0.5292 0.1735 0.2250 0.0000 0.0159 0.0009 8.75 6.75 1995 0.0844 0.9156 0.0545 0.6341 0.1564 0.1518 0.0029 0.0000 0.0004 6.42 5.17 1996 0.0775 0.9225 0.0398 0.6328 0.1414 0.1686 0.0129 0.0000 0.0045 5.00 7.08 1997 0.0627 0.9373 0.0312 0.6575 0.0323 0.2231 0.0516 0.0021 0.0023 3.25 8.33 1998 0.0182 0.9818 0.0086 0.6100 0.0000 0.3166 0.0602 0.0046 0.0000 1.83 9.50 1999 0.0096 0.9904 0.0000 0.7992 0.0000 0.1403 0.0517 0.0088 0.0000 0.75 5.50 2000 0.0096 0.9904 0.0000 0.6911 0.0000 0.2317 0.0678 0.0094 0.0000 0.75 5.33 2001 0.0064 0.9936 0.0039 0.7584 0.0000 0.2021 0.0343 0.0013 0.0000 0.50 4.25 2002 0.0567 0.9433 0.0217 0.5408 0.0350 0.3566 0.0316 0.0000 0.0144 1.67 4.42 2003 0.1318 0.8682 0.0365 0.3545 0.2800 0.1942 0.0435 0.0019 0.0893 5.42 8.00 2004 0.1707 0.8293 0.0638 0.1297 0.1526 0.5022 0.0539 0.0065 0.0914 8.00 11.17 2005 0.1586 0.8414 0.0654 0.1297 0.1409 0.5535 0.0155 0.0038 0.0914 8.00 12.75
Panel D. SS+OW(3) Constraints
Weight Number EM DC LA NA EA C/W EU N EU S EU OC EM DC
Mean 0.0525 0.9475 0.0208 0.6157 0.0853 0.2371 0.0228 0.0042 0.0142 5.01 8.24 St. Dev. 0.0378 0.0378 0.0155 0.2611 0.1079 0.1815 0.0178 0.0053 0.0233 Max 0.1351 1.0000 0.0403 0.9811 0.4514 0.7048 0.0527 0.0137 0.0548 13.00 16.00 Non-Zero 92.95% 100.00% 73.08% 100.00% 65.38% 94.87% 76.92% 44.87% 41.03%
1993 0.0720 0.9280 0.0314 0.6856 0.0986 0.1731 0.0000 0.0113 0.0000 9.75 6.83 1994 0.0741 0.9259 0.0358 0.6563 0.1045 0.1858 0.0000 0.0108 0.0068 8.92 7.50 1995 0.0674 0.9326 0.0362 0.7579 0.1082 0.0915 0.0057 0.0000 0.0005 7.00 5.58 1996 0.0580 0.9420 0.0244 0.7320 0.1064 0.1206 0.0136 0.0000 0.0030 5.50 7.92 1997 0.0448 0.9552 0.0191 0.7284 0.0292 0.1776 0.0405 0.0028 0.0025 3.75 9.58 1998 0.0138 0.9862 0.0070 0.6771 0.0000 0.2706 0.0416 0.0038 0.0000 1.92 10.58 1999 0.0058 0.9942 0.0000 0.8285 0.0000 0.1351 0.0312 0.0053 0.0000 0.75 5.42 2000 0.0078 0.9922 0.0000 0.7498 0.0000 0.2000 0.0434 0.0068 0.0000 1.17 5.67 2001 0.0049 0.9951 0.0024 0.7780 0.0000 0.1954 0.0228 0.0015 0.0000 0.67 4.92 2002 0.0340 0.9660 0.0130 0.7245 0.0210 0.2139 0.0189 0.0000 0.0086 1.67 4.42 2003 0.0835 0.9165 0.0233 0.5269 0.2044 0.1624 0.0281 0.0012 0.0536 5.58 8.83 2004 0.1097 0.8903 0.0383 0.0778 0.2853 0.4991 0.0400 0.0047 0.0548 8.75 14.58 2005 0.1064 0.8936 0.0394 0.0815 0.1509 0.6570 0.0103 0.0061 0.0548 9.75 15.25
43
Table 6. MVP Weights The summaries of the MVP weights and number of selected countries with various investment constraints for emerging markets (EM), indices of Latin America (LA), North America (NA), East Asia (EA), Central/West Europe (C/W EU), North Europe (N EU), South Europe (S EU), and Oceania (OC), are reported. Non-Zero is the percentage of months during sample period that the weight is greater than zero. The mean of weights for each year is also reported. Panel A. Short-sales Constraints
Weight Number EM DC LA NA EA C/W EU N EU S EU OC EM DC
Mean 0.1423 0.8577 0.0351 0.2340 0.1365 0.5626 0.0000 0.0075 0.0242 2.79 5.76 St. Dev. 0.0928 0.0928 0.0593 0.2379 0.1390 0.2364 0.0000 0.0144 0.0344 Max 0.3310 1.0000 0.2311 0.7088 0.5558 0.8920 0.0000 0.0527 0.1345 7.00 9.00 Non-Zero 98.08% 100.00% 66.03% 67.95% 100.00% 100.00% 0.00% 28.21% 53.85%
1993 0.3085 0.6915 0.2109 0.3328 0.0612 0.2706 0.0000 0.0363 0.0881 6.50 5.67 1994 0.1834 0.8166 0.1029 0.5827 0.0441 0.2242 0.0000 0.0370 0.0091 4.42 5.50 1995 0.1137 0.8863 0.0374 0.6434 0.0562 0.2338 0.0000 0.0202 0.0091 3.00 6.42 1996 0.1133 0.8867 0.0158 0.5416 0.0976 0.3409 0.0000 0.0041 0.0000 2.67 7.50 1997 0.0916 0.9084 0.0071 0.3815 0.0887 0.5226 0.0000 0.0000 0.0000 2.00 7.50 1998 0.0144 0.9856 0.0027 0.2964 0.0444 0.6557 0.0000 0.0002 0.0006 1.25 6.58 1999 0.0207 0.9793 0.0000 0.1581 0.0381 0.8024 0.0000 0.0000 0.0014 1.00 5.08 2000 0.1147 0.8853 0.0049 0.0715 0.0620 0.8365 0.0000 0.0000 0.0252 2.08 6.00 2001 0.1474 0.8526 0.0372 0.0000 0.1191 0.8340 0.0000 0.0000 0.0098 3.00 4.92 2002 0.1036 0.8964 0.0060 0.0000 0.1143 0.8558 0.0000 0.0000 0.0238 2.42 4.33 2003 0.1108 0.8892 0.0125 0.0086 0.1760 0.7224 0.0000 0.0000 0.0805 2.75 4.75 2004 0.2339 0.7661 0.0179 0.0213 0.3725 0.5386 0.0000 0.0000 0.0497 3.00 5.58 2005 0.1423 0.8577 0.0351 0.2340 0.1365 0.5626 0.0000 0.0075 0.0242 2.17 5.00
Panel B. SS+OW(10) Constraints
Weight Number EM DC LA NA EA C/W EU N EU S EU OC EM DC
Mean 0.0761 0.9239 0.0132 0.3055 0.1167 0.5159 0.0013 0.0103 0.0371 3.46 7.74 St. Dev. 0.0481 0.0481 0.0128 0.2827 0.0931 0.2712 0.0061 0.0153 0.0422 Max 0.1860 1.0000 0.0535 0.7742 0.3857 0.9011 0.0310 0.0456 0.1675 9.00 11.00 Non-Zero 93.59% 100.00% 72.44% 75.00% 99.36% 100.00% 5.77% 50.00% 64.10%
1993 0.1748 0.8252 0.0423 0.6033 0.0831 0.1302 0.0004 0.0425 0.0982 8.33 8.58 1994 0.1156 0.8844 0.0230 0.7284 0.0549 0.1128 0.0000 0.0396 0.0413 5.42 7.83 1995 0.1015 0.8985 0.0176 0.7267 0.0646 0.1475 0.0000 0.0208 0.0228 3.83 8.17 1996 0.1237 0.8763 0.0213 0.5847 0.1002 0.2840 0.0000 0.0099 0.0000 3.67 8.67 1997 0.1073 0.8927 0.0212 0.4644 0.1019 0.4106 0.0000 0.0018 0.0000 2.75 8.67 1998 0.0213 0.9787 0.0084 0.4135 0.0638 0.4954 0.0168 0.0022 0.0000 1.58 9.67 1999 0.0057 0.9943 0.0000 0.2475 0.0265 0.7248 0.0000 0.0012 0.0000 0.92 7.17 2000 0.0449 0.9551 0.0019 0.1021 0.0392 0.8238 0.0003 0.0124 0.0203 2.83 7.25 2001 0.0600 0.9400 0.0168 0.0044 0.1004 0.8459 0.0000 0.0032 0.0293 3.33 8.58 2002 0.0273 0.9727 0.0017 0.0000 0.0965 0.8568 0.0000 0.0001 0.0449 2.33 6.58 2003 0.0583 0.9417 0.0059 0.0000 0.1703 0.7132 0.0000 0.0000 0.1106 3.25 5.75 2004 0.0773 0.9227 0.0075 0.0262 0.2680 0.5993 0.0000 0.0000 0.0990 3.67 6.67 2005 0.0719 0.9281 0.0039 0.0703 0.3473 0.5625 0.0000 0.0000 0.0160 3.08 7.08
44
Panel C. SS+OW(5) Constraints Weight Number EM DC LA NA EA C/W EU N EU S EU OC EM DC
Mean 0.0562 0.9438 0.0077 0.3633 0.1257 0.4414 0.0017 0.0085 0.0515 4.09 9.37 St. Dev. 0.0360 0.0360 0.0074 0.2486 0.0923 0.2059 0.0050 0.0086 0.0406 Max 0.1387 1.0000 0.0324 0.7644 0.3678 0.7110 0.0278 0.0228 0.0914 9.00 12.00 Non-Zero 94.23% 100.00% 72.44% 100.00% 100.00% 100.00% 14.10% 63.46% 70.51%
1993 0.1300 0.8700 0.0216 0.6163 0.0982 0.1373 0.0124 0.0228 0.0914 8.67 10.75 1994 0.0936 0.9064 0.0114 0.7246 0.0585 0.0964 0.0010 0.0228 0.0853 6.42 9.08 1995 0.0784 0.9216 0.0113 0.7277 0.0586 0.1369 0.0000 0.0128 0.0527 4.25 9.17 1996 0.0870 0.9130 0.0125 0.6234 0.0776 0.2771 0.0000 0.0095 0.0000 4.42 8.92 1997 0.0760 0.9240 0.0184 0.5093 0.0810 0.3847 0.0002 0.0064 0.0000 4.08 9.08 1998 0.0213 0.9787 0.0074 0.4289 0.0684 0.4829 0.0091 0.0032 0.0000 1.75 10.25 1999 0.0048 0.9952 0.0000 0.3447 0.0552 0.5903 0.0000 0.0019 0.0079 1.00 9.92 2000 0.0287 0.9713 0.0009 0.2245 0.0437 0.6480 0.0000 0.0110 0.0719 2.83 9.67 2001 0.0445 0.9555 0.0048 0.1321 0.1201 0.6520 0.0000 0.0092 0.0817 3.42 10.17 2002 0.0216 0.9784 0.0009 0.1602 0.1394 0.6192 0.0000 0.0025 0.0777 2.50 9.75 2003 0.0511 0.9489 0.0047 0.0625 0.2312 0.6064 0.0000 0.0071 0.0881 4.83 9.67 2004 0.0526 0.9474 0.0038 0.0579 0.2727 0.5734 0.0000 0.0014 0.0909 5.33 8.00 2005 0.0407 0.9592 0.0026 0.1112 0.3301 0.5336 0.0000 0.0000 0.0224 3.67 7.42
Panel D. SS+OW(3) Constraints
Weight Number EM DC LA NA EA C/W EU N EU S EU OC EM DC
Mean 0.0416 0.9584 0.0056 0.4609 0.1401 0.3471 0.0020 0.0077 0.0366 4.76 10.86 St. Dev. 0.0260 0.0260 0.0053 0.1993 0.1006 0.1470 0.0052 0.0045 0.0237 Max 0.0994 1.0000 0.0241 0.7905 0.3802 0.5994 0.0189 0.0137 0.0548 9.00 14.00 Non-Zero 99.36% 100.00% 77.56% 100.00% 100.00% 100.00% 15.38% 83.33% 75.64%
1993 0.0872 0.9128 0.0145 0.6739 0.0860 0.1435 0.0174 0.0129 0.0518 8.67 12.58 1994 0.0652 0.9348 0.0068 0.7713 0.0491 0.1045 0.0016 0.0137 0.0530 7.17 10.50 1995 0.0551 0.9449 0.0070 0.7495 0.0509 0.1444 0.0000 0.0077 0.0405 4.92 9.83 1996 0.0695 0.9305 0.0069 0.6824 0.0783 0.2229 0.0000 0.0092 0.0002 6.17 9.25 1997 0.0647 0.9353 0.0139 0.5633 0.0840 0.3292 0.0004 0.0091 0.0000 5.58 9.83 1998 0.0205 0.9795 0.0045 0.4750 0.0827 0.4269 0.0058 0.0051 0.0000 2.50 10.58 1999 0.0051 0.9949 0.0000 0.4199 0.0773 0.4699 0.0000 0.0021 0.0308 1.50 12.00 2000 0.0218 0.9782 0.0007 0.3296 0.0681 0.5412 0.0000 0.0086 0.0519 3.00 11.25 2001 0.0324 0.9676 0.0060 0.2592 0.1489 0.5258 0.0003 0.0080 0.0519 3.58 12.17 2002 0.0167 0.9833 0.0005 0.3183 0.1838 0.4387 0.0000 0.0062 0.0526 3.00 11.17 2003 0.0369 0.9631 0.0037 0.2434 0.2740 0.4153 0.0000 0.0090 0.0546 5.25 11.00 2004 0.0395 0.9605 0.0064 0.2306 0.2921 0.4077 0.0000 0.0085 0.0548 6.08 11.42 2005 0.0265 0.9735 0.0022 0.2751 0.3465 0.3418 0.0000 0.0000 0.0344 4.50 9.58
45
Table 7. Time-Series Analysis of International Diversification Benefits In Panel A, the partial autocorrelation coefficients of selected periods of each of the maximum increase in Sharpe ratio under various investment constraints to the U.S. domestic investors (δJ), and Phillips-Perron, and Dickey-Fuller statistics are reported. In Panel B, the results of time-series regression are reported. The independent variables are the risk-return of domestic high-technology and internet related companies (proxies by the S&P 500 Information Technology index, SRHT) and the volatility of the exchange rate (accessed by using the U.S. Dollar Trade Weighted Index, VolFX.) A constant was added but not reported. The results of other economic variables that do not have explanatory power are also not reported. To observe the trend of global diversification benefits, time variable is included. The lagged variable is included to control the autoregressive property of diversifying gains. The adjusted R-square and Durbin-Watson of each regression are reported. * indicates significance at 10% level; ** indicates significance at 5% level; *** indicates significance at 1% level, respectively. Panel A. Partial Autocorrelations and Unit-Root Tests
Measure δUS,1 δUS, 2 δUS, 3 δUS, 4
1 0.9659 *** 0.9586 *** 0.9544 *** 0.9454 ***
2 -0.0914 -0.1258 -0.1169 -0.0965
3 0.0696 0.1142 0.1189 0.0992
4 -0.0548 -0.0232 0.0123 0.0355
5 0.0355 0.0031 0.0198 0.0533
6 0.0352 0.0814 -0.0015 -0.0584
9 -0.0061 0.0369 0.0578 0.0819
12 0.0003 -0.0345 0.0255 0.0690
15 0.1202 0.0929 0.0718 0.0428
18 -0.0301 0.0417 0.0564 0.0552
21 -0.0821 -0.0860 -0.0293 -0.0404
24 -0.1063 -0.0214 -0.0450 -0.0383
Phillips-Perron Statistics -0.798 -0.618 -0.619 -0.641
Dickey-Fuller Statistics -0.626 -0.719 -0.511 -0.381
Panel B. Regression Results Dependent Variable δUS, 1 δUS, 2 δUS, 3 δUS, 4
Independent Variables
Time 0.0003 0.0003 0.0003 * 0.0002 **
Lag (-1) 0.9414 *** 0.9190 *** 0.9199 *** 0.9100 ***
SRHT -0.0469 *** -0.0260 *** -0.0168 *** -0.0124 ***
VolFX 9.4832 * 8.8439 ** 7.3644 ** 6.4101 *** 2R 0.9718 0.9502 0.9479 0.9370
Durbin-Watson 1.8138 1.8435 1.8619 1.9420
46
Figure 1. Unconstrained Efficient Frontiers: 1993 – 2006 The unconstrained efficient frontiers at the beginning of each year from 1993 to 2005 are presented. The efficient frontiers are constructed by the previous 60 monthly returns.
-0.01
0.00
0.01
0.02
0.03
0.04
0.05
0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18
9394
95
96
98
03
04
0001
99
9702
05
Monthly Expected Return
Monthly St. Dev. Figure 2. Sharpe Ratio on Constrained Efficient Frontiers This graph demonstrates the curves of annualized risk-adjusted premium on global efficient frontiers of under various investment constraints as well as the U.S. domestic portfolio during 1988:01 – 2005:12. The investment constraints include short-sale (SS) and over-weighting (OW) investment. The number in parentheses denotes the upper limit of times of proportion of domestic market value to world capitalization.
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40
Short-sales (SS)SS + OW(10)SS + OW(5)SS + OW(3)US
St. Dev.
Sharpe Ratio
US
47
Figure 3. Time-Variation International Diversification Benefits for the U.S. Investors The international diversification benefits for the U.S. investor are assessed by the increase in Sharpe ratio by investing the MSR portfolio and the decrease in volatility by investing the MVP. The optimal portfolios are constructed by using data of previous 60 months with considering various investment constraints. The long-term trend smoothed by the filter purposed by Hodrick and Prescott (1997) for each time-series (H-P(.)) is illustrated.
A. δUS,1
0.00
0.10
0.20
0.30
0.40
0.50
0.60
Jan-93 Jan-95 Jan-97 Jan-99 Jan-01 Jan-03 Jan-05
1H-Pδ US, 1
B. δUS,2
0.00
0.10
0.20
0.30
0.40
0.50
0.60
Jan-93 Jan-95 Jan-97 Jan-99 Jan-01 Jan-03 Jan-05
1H-P
δ US, 2
C. δUS,3
0.00
0.10
0.20
0.30
0.40
0.50
0.60
Jan-93 Jan-95 Jan-97 Jan-99 Jan-01 Jan-03 Jan-05
1H-Pδ US, 3
D. δUS,4
0.00
0.10
0.20
0.30
0.40
0.50
0.60
Jan-93 Jan-95 Jan-97 Jan-99 Jan-01 Jan-03 Jan-05
1H-Pδ US, 4
E. εUS, 1
0.00
0.05
0.10
0.15
0.20
0.25
0.30
Jan-93 Jan-95 Jan-97 Jan-99 Jan-01 Jan-03 Jan-05
1H-Pε US, 1
F. εUS, 2
0.00
0.05
0.10
0.15
0.20
0.25
0.30
Jan-93 Jan-95 Jan-97 Jan-99 Jan-01 Jan-03 Jan-05
1H-Pε US, 2
48
G. εUS, 3
0.00
0.05
0.10
0.15
0.20
0.25
0.30
Jan-93 Jan-95 Jan-97 Jan-99 Jan-01 Jan-03 Jan-05
1H-Pε US, 3
H. εUS, 4
0.00
0.05
0.10
0.15
0.20
0.25
0.30
Jan-93 Jan-95 Jan-97 Jan-99 Jan-01 Jan-03 Jan-05
1H-Pε US, 4
49
Figure 4. Weight of Emerging Markets for the MSR Portfolio The sum of emerging markets weights for the MSR portfolios with various investment constraints during 1993:01- 2005:12 are presented. The efficient frontiers are formed by the previous 60 monthly returns.
0.00
0.20
0.40
0.60
0.80
1.00
Jan-93 Jan-95 Jan-97 Jan-99 Jan-01 Jan-03 Jan-05
SSSS+OW(10)SS+OW(5)SS+OW(3)
%The Weights of Emerging Markets
50
Figure 5. Regional Distribution of Weight of MSR Portfolio A. Short-sales Constraints
0%
20%
40%
60%
80%
100%
Jan-93 Jan-95 Jan-97 Jan-99 Jan-01 Jan-03 Jan-05
S. Europe
N Europe
C/W Europe
Oceania
L. America
N. America
E. Asia
Regional Distribution of Weight of MSR Portfolio with Short-sales Constraints
B. Short-sales and 10-time Over-Weighting Investment Constraints
0%
20%
40%
60%
80%
100%
Jan-93 Jan-95 Jan-97 Jan-99 Jan-01 Jan-03 Jan-05
S Europe
N. Europe
C\W Europe
Oceania
L. America
N. America
E. Asia
Regional Distribution of Weight of MSR Portfolio with Short-sales and 10-time Over-Weighting Investment Constraints
C. Short-sales and 5-time Over-Weighting Investment Constraints
0%
20%
40%
60%
80%
100%
Jan-93 Jan-95 Jan-97 Jan-99 Jan-01 Jan-03 Jan-05
S. Europe
N. Europe
C\W Europe
Oceania
L. America
N. America
E. Asia
Regional Distribution of Weight of MSR Portfolio with Short-sales and 5-time Over-Weighting Investment Constraints
D. Short-sales and 3-time Over-Weighting Investment Constraints
0%
20%
40%
60%
80%
100%
Jan-93 Jan-95 Jan-97 Jan-99 Jan-01 Jan-03 Jan-05
S EuropeN EuropeC\W EuropeOceaniaL. AmericaN. AmericaE. Asia
Regional Distribution of Weight of MSR Portfolio with Short-sales and 3-time Over-Weighting Investment Constraints
51
Figure 6. Weight of Emerging Markets for the Minimum-Variance Portfolio The sum of emerging markets weights for the MVP with various investment constraints during 1993:01- 2005:12 are presented. The efficient frontiers are formed by the previous 60 monthly returns.
0.00
0.20
0.40
0.60
0.80
1.00
Jan-93 Jan-95 Jan-97 Jan-99 Jan-01 Jan-03 Jan-05
SSSS+OW(10)SS+OW(5)SS+OW(3)
% The Weights of Emerging Markets
52
Figure 7. Regional Distribution of Weight of MVP A. Short-sales Constraints
0%
20%
40%
60%
80%
100%
Jan-93 Jan-95 Jan-97 Jan-99 Jan-01 Jan-03 Jan-05
S EuropeN EuropeC\W EuropeOceaniaL. AmericaN. AmericaE. Asia
Regional Distribution of Weight of MVP with Short-sales
B. Short-sales and 10-time Over-Weighting Investment Constraints
0%
20%
40%
60%
80%
100%
Jan-93 Jan-95 Jan-97 Jan-99 Jan-01 Jan-03 Jan-05
S Europe
N Europe
C\W Europe
Oceania
L. America
N. America
E. Asia
Regional Distribution of Weight of MVP with Short-sales and 10-time Over-Weighting Investment Constraints
C. Short-sales and 5-time Over-Weighting Investment Constraints
0%
20%
40%
60%
80%
100%
Jan-93 Jan-95 Jan-97 Jan-99 Jan-01 Jan-03 Jan-05
S Europe
S Europe
C\W Europe
Oceania
L. America
N. America
E. Asia
Regional Distribution of Weight of MVP with Short-sales and 5-time Over-Weighting Investment Constraints
D. Short-sales and 3-time Over-Weighting Investment Constraints
0%
20%
40%
60%
80%
100%
Jan-93 Jan-95 Jan-97 Jan-99 Jan-01 Jan-03 Jan-05
S Europe
N Europe
C\WEuropeOceania
L. America
N. America
E. Asia
Regional Distribution of Weight of MVP with Short-sales and 3-time Over-Weighting Investment Constraints
53