Time-Variation in the Benefits and Portfolio Allocation of ...conference/conference2006/...diversification benefits are persistently positive. The addition of upper bounds eludes a

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

[email protected]

Chiung-Min Eugene Tsai Central Bank of China, Taiwan

Taipei, Taiwan

This Version: August 28, 2006

* Corresponding author

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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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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.


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.


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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.


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.


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.


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.


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.


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.


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.


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


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


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



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



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



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


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



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


1H-P

δ US, 2

C. δUS,3

0.00

0.10

0.20

0.30

0.40

0.50

0.60


1H-Pδ US, 3

D. δUS,4

0.00

0.10

0.20

0.30

0.40

0.50

0.60


1H-Pδ US, 4

E. εUS, 1

0.00

0.05

0.10

0.15

0.20

0.25

0.30


1H-Pε US, 1

F. εUS, 2

0.00

0.05

0.10

0.15

0.20

0.25

0.30


1H-Pε US, 2

48

G. εUS, 3

0.00

0.05

0.10

0.15

0.20

0.25

0.30


1H-Pε US, 3

H. εUS, 4

0.00

0.05

0.10

0.15

0.20

0.25

0.30


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


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%


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%


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%


S. Europe

N. Europe

C\W Europe

Oceania

L. America

N. America

E. Asia


D. Short-sales and 3-time Over-Weighting Investment Constraints

0%

20%

40%

60%

80%

100%


S EuropeN EuropeC\W EuropeOceaniaL. AmericaN. AmericaE. Asia


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


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%


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%


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%


S Europe

S Europe

C\W Europe

Oceania

L. America

N. America

E. Asia


D. Short-sales and 3-time Over-Weighting Investment Constraints

0%

20%

40%

60%

80%

100%


S Europe

N Europe

C\WEuropeOceania

L. America

N. America

E. Asia


53

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