An empirical examination of the benefits of international diversification

Int. Fin. Markets, Inst. and Money 15 (2005) 455–468

An empirical examination of the benefits ofinternational diversification

Jonathan Fletcher∗, Andrew Marshall1

Department of Accounting and Finance, University of Strathclyde, Curran Building,100 Cathedral Street, Glasgow G4 0LN, UK

Received 7 January 2004; accepted 3 November 2004Available online 8 March 2005

Abstract

We examine the benefits of international portfolio diversification for U.K. investors between January1985 and December 2000 using the approach of Wang [Wang, Z., 1998. Efficiency loss and constraintson portfolio holdings. Journal of Financial Economics 48, 359–375] and Li et al. [Li, K., Sarkar, A.,Wang, Z., 2003. Diversification benefits of emerging markets subject to portfolio constraints. Journalof Empirical Finance 10, 57–80]. We find significant increases in the Sharpe [Sharpe, W.F., 1966.Mutual fund performance. Journal of Business 39, 119–138] and certainty equivalent return (CER)performance in moving from a domestic strategy to an international strategy that includes either globalindustry or country equity portfolios, even in the presence of short selling restrictions. We also findsignificant diversification benefits using U.K. unit trusts with international equity objectives. However,U.K. international unit trusts do not capture all the diversification benefits provided by either globalindustry or country equity portfolios.© 2005 Elsevier B.V. All rights reserved.

JEL classification: G11; G15

Keywords: International diversification; Trusts; Mean-variance framework; Short selling; Performance

∗ Corresponding author. Tel.: +44 141 548 3892; fax: +44 141 552 3547.E-mail addresses: [email protected] (J. Fletcher), [email protected] (A. Marshall).

1 Tel.: +44 141 548 3894; fax: +44 141 552 3547.

1042-4431/$ – see front matter © 2005 Elsevier B.V. All rights reserved.doi:10.1016/j.intfin.2004.11.002

456 J. Fletcher, A. Marshall / Int. Fin. Markets, Inst. and Money 15 (2005) 455–468

1. Introduction

One of the major trends in financial markets during the past 20 years has been the growthof international investment opportunities available to investors. This trend is due to financialderegulation around the world and the lifting of investment restrictions faced by institutionalinvestors. International investment opportunities are attractive to investors because of thegreater opportunities for portfolio risk reduction than can be achieved by a domestic strategy(e.g.,Dimson et al., 2002).

Early studies byGrubel (1968)andLessard (1973)find small correlations across in-ternational equity markets.2 These correlations provide the basis for reducing the risk ofthe portfolio beyond that attainable by a domestic portfolio. However, a recent study byGoetzmann et al. (2002)find that correlation between equity markets have increased towardsthe end of the 20th century. In spite of the increased correlation in recent periodsDimsonet al. (2002)show there are still benefits in portfolio risk reduction through internationaldiversification.

A number of related studies question the benefits of international diversification from aU.S. perspective.Britten-Jones (1999)is unable to reject the mean-variance efficiency ofthe U.S. index relative to efficient frontier of developed equity markets.Errunza et al. (1999)find that the benefits of international diversification can be achieved through investing inmultinational companies, American depository receipts and country funds, which trade inthe USA.De Roon et al. (2001)find that the diversification benefits in emerging marketsdisappear when short sales constraints or transaction costs are imposed. On the other hand,Hentschel and Long (2004)find significant diversification benefits in developed equitymarkets.Li et al. (2003)andLi (2003)find significant benefits of diversification in emergingmarkets even when investors face short sales constraints.

We use the recent Bayesian approach developed byWang (1998)to evaluate the benefitsof international diversification from a U.K. perspective between January 1985 and Decem-ber 2000. We evaluate the diversification benefits using two measures. First, the increasein Sharpe (1966)performance in moving from a domestic mean-variance strategy to aninternational strategy as inCavaglia et al. (2002). Second, the increase in expected mean-variance utility (CER) in moving from the domestic strategy to the international strategysimilar toLi (2003)among others. This approach of evaluating diversification benefits hasthe attractive features that we can measure the magnitude of the diversification benefits andincorporates the impact of portfolio constraints.

We examine two main research questions. First, are there significant diversification ben-efits for U.K. investors in adding either global industry or country equity portfolios to adomestic mean-variance strategy? Second, are these diversification benefits provided byU.K. unit trusts3 with international equity objectives? We explore whether the results de-pend on the level of risk aversion and short selling is not allowed in the optimal portfolios.

Our study provides two main contributions. First, we extend the literature on internationalportfolio diversification by providing new evidence of diversification benefits from the U.K.

2 Correlations are even lower for emerging markets (Harvey, 1995). Emerging markets are also characterizedby high returns and volatility.

3 U.K. unit trusts are equivalent to open-end U.S. mutual funds.

J. Fletcher, A. Marshall / Int. Fin. Markets, Inst. and Money 15 (2005) 455–468 457

perspective rather than from the more traditional U.S. perspective. Second, we extend thegrowing literature on U.K. unit trusts (e.g.,Blake and Timmermann, 1998; Quigley andSinquefield, 2000; Fletcher and Forbes, 2002; Fletcher and Marshall, 2004among others)by exploring whether U.K. international trusts provide significant diversification benefits aspart of a mean-variance asset allocation strategy. This approach differs fromFletcher andMarshall (2004)who examine whether international trusts outperform domestic benchmarkstrategies.

We report three main findings in the paper. First, we find significant increases in theSharpe (1966)and CER performance in adding either the global industry or country equityportfolios to a domestic mean-variance strategy. Second, the level of risk aversion affectsthe size of the benefits. The increase in CER (Sharpe) performance is greater at the low(high) level of risk aversion. Third, we find significant increases in the Sharpe and CERperformance using U.K. international unit trusts. However, the size of the increase in per-formance using the international trusts is smaller than the global industry or country equityportfolios. Our findings suggest U.K. international unit trusts provide significant diversifi-cation benefits as part of a mean-variance asset allocation strategy but international trustsdo not capture all the diversification benefits.

The paper is organized as follows: Section2reports the method used in the paper; Section3 describes the data; Section4 presents the empirical results; finally Section5 concludes.

2. Method

Different approaches have been used in the academic literature to evaluate the benefits ofinternational diversification. The most common framework used is to examine the impacton the mean-variance efficient frontier as international assets are added to the investmentuniverse. When there are no portfolio constraints, there are various statistical tests to examinewhether a candidate portfolio lies on the ex ante mean-variance efficient frontier (e.g.,Gibbons et al., 1989; MacKinlay and Richardson, 1991)4 or whether two mean-variancefrontiers span each other (e.g.,Kan and Zhou, 2001for a review of the tests). However,these tests become more complex when investors face binding investment constraints suchas no short selling.De Roon et al. (2001)provide tests of mean-variance spanning wheninvestors face trading constraints but do not provide a measure of the size of diversificationbenefits.Basak et al. (2002)develop tests of mean-variance efficiency in the presence ofshort selling constraints. However, the test of Basak et al. is complex and only measuresthe reduction in variance.

A number of recent studies provide different measures of the size of diversificationbenefits (e.g.,Wang, 1998; Cavaglia et al., 2002; Li et al., 2003; Li, 2003among others).We use the increase inSharpe (1966)performance similar to Cavaglia et al. and the increasein CER performance similar to Li as our measures of diversification benefits. We adapt theBayesian approach ofWang (1998)to measure the size of diversification benefits and assessthe statistical significance of the benefits. The Bayesian approach of Wang has the advantage

4 A number of approaches are available to us to test mean-variance efficiency (e.g.,Shanken, 1996for a review)when investors face no investment constraints. A recent non-parametric test is proposed byWang (2002).


that it can be applied when investors face short selling constraints. We now describe ourapproach in more detail.

To evaluate the diversification benefits, we use the mean-variance framework. For a givenlevel of risk aversion (A), the goal of the investor is to select the portfolio ofN risky assetsto:

Max (E(rp) − 1

2Aσ2

p (1)

Subject toxi ≥ 0 (no short selling allowed)

N∑i=1

xi ≤ 1

whereA = 2 andA = 10.The termE(rp) is the expected excess return on the optimal portfoliop, σ2

p the variance, andxi is the optimal weight of risky asseti. The constraints in(1) donot allow short selling in theN risky assets or the risk-free asset. We consider risk aversionlevels of 2 (low) and 10 (high) in our analysis followingHanda and Tiwari (2003). We usea high-risk aversion of 10 to consider an extreme form of risk aversion.

To measure the diversification benefits, we consider two mean-variance strategies. First,the investor allocates their wealth between the U.K. market index and the domestic risk-free asset. We refer to this strategy as the domestic strategy. Second, the investor allocatestheir wealth between the U.K. market index, (N − 1) international assets, and the domesticrisk-free asset. We refer to this strategy as the international strategy.

We measure the diversification benefits in two ways for a given level of risk aversion.First, the increase inSharpe (1966)performance in moving from the domestic strategy tothe international strategy as:

DSharpe= E(ri )

σi− E(rd)

σd(2)

where i = international and d = domestic.Second, we use the certainty equivalent return (CER) in moving from the domestic

strategy to the international strategy as:

CER=[E(ri ) − 1

2Aσ2

i

]−

[E(rd) − 1

2Aσ2

d

](3)

Since the mean-variance frontier shifts leftwards when we add more assets to the investmentuniverse, the DSharpe and CER measures have a minimum value of zero. One complica-tion that arises with the DSharpe measure is when the domestic strategy holds 100% inthe risk-free asset. In this situation, the Sharpe performance of the domestic strategy isundefined. We convert the Sharpe performance of the domestic strategy in this situation tozero.

In the Bayesian approach ofWang (1998), we assume a non-informative prior aboutthe expected excess return vector and covariance matrix. We definee andV as the sampleestimates of the expected excess returns and covariance matrix of theN risky assets drawnfrom a multivariate normal distribution andT is the number of observations. The assumption


of a non-informative prior implies that the posterior probability density function is givenby:

p(u, �|R) = p(u|�, e, T ) · p(�|V, T ) (4)

wherep(u|�, e, T) is the conditional distribution of a multivariate normal (e, (1/T) �)distribution andp(�|V, T) is the marginal posterior distribution that has an inverse Wishart(TV, T − 1) distribution (e.g.,Zellner, 1971).

Wang (1998)proposes a Monte Carlo method to estimate the approximate posterior dis-tribution of the diversification benefit measures. We use his four-step approach to estimatethe approximate posterior distribution of the DSharpe and CER measures. First, we drawa random sample of the covariance matrix (�) from an inverse Wishart (TV, T − 1) distri-bution. Second, given the covariance matrix (�) from step one, we draw a random sampleof expected excess returns (u) from the multivariate normal (e, (1/T) �) distribution. Third,given the expected excess returns and covariance matrix from steps one and two, we solvethe portfolio problem in(1) for domestic and international strategies at the two levels ofrisk aversion. The DSharpe and CER measures from Eqs.(2) and (3)are then calculated.Fourth, we repeat steps 1 to 3 10,000 times as in Wang and inLi et al. (2003)to obtain anapproximate posterior distribution of the DSharpe and CER measures.

We use the approximate posterior distributions of the DSharpe and CER measures toestimate the size of the diversification benefits and assess the statistical significance. Theaverage values from the posterior distribution provide the average diversification benefitsin terms of the DSharpe and CER measures. The standard errors are given by the standarddeviations from the posterior distributions. If the international strategy provides significantdiversification benefits, we expect the average DSharpe and CER measures to be morethan two standard errors from zero. The 1 and 5 percentiles from the posterior distribu-tion provide the size of the diversification benefits at the posterior probabilities of 0.99and 0.95.

When we run steps one to four, we also obtain the approximate posterior distribution ofthe optimal portfolio weights in the international strategy. We use the posterior distributionto assess the statistical significance of the average weights in the risky assets. The pos-terior distribution has the attractive feature since, althoughBritten-Jones (1999)providesthe distribution theory of the optimal portfolio weights when there are no constraints, thedistribution theory for the constrained case is unknown (e.g.,Li et al., 2003).

3. Data

We evaluate the diversification benefits between January 1985 and December 2000 usingthree sets of international assets. We use global industry portfolios, country equity portfolios,and investment sector portfolios of unit trusts. We choose 1985 as our starting point becausethe number of international funds began to rise sharply in the middle of the 1980s. We donot examine the role of emerging markets because our sample of international trusts doesnot include emerging market trusts. All returns used in our study are in U.K. £ sterling. Weuse the Datastream U.K. equity index as the domestic market index. We calculate excess


returns using the return on the one-month U.K. Treasury Bill as the risk-free asset (collectedfrom Datastream).

3.1. International assets

Our first set of assets is the monthly excess returns on ten global industry portfolios.We use the value weighted global industry portfolios constructed by Thomson FinancialDatastream. We use the level three industry sectors of resources, basic industries, generalindustrials, cyclical consumer goods, noncyclical consumer goods, cyclical services, non-cyclical services, utilities, information technology, and financials. We collect the returns ofthe industry portfolios from Thomson Financial Datastream.

Our second set of international assets is the monthly excess returns of 16 developedcountry equity markets. We use the Datastream indexes for Australia, Belgium, Canada,Denmark, France, Germany, Hong Kong, Ireland, Italy, Japan, Netherlands, Norway, Sin-gapore, Sweden, Switzerland, and U.S. We exclude Spain due to insufficient return data.We collect the returns from Thomson Financial Datastream. Industry and country equityportfolios are used in recent studies byDahlquist and Sallstrom (2002)andHentschel andLong (2004).

Tables 1 and 2provide summary statistics of the global industry portfolios (Table 1)and country equity portfolios (Table 2). The tables include the mean, standard deviation,minimum, and maximum monthly excess returns. We do not report the correlations toconserve space.

Table 1shows that the average excess returns range between 0.134% (cyclical consumergoods) and 0.775% (information technology) across the industry portfolios. The informationtechnology sector has the highest standard deviation across the ten industries. The non-cyclical consumer goods sector has the lowest standard deviation and the second highestaverage return. The unreported correlations across the industry portfolios range between0.457 and 0.934. Most of the correlations lie between 0.6 and 0.8.

Table 1Summary statistics of global industry portfolios

Industry Mean Standard deviation Minimum Maximum

Resources 0.409 5.145 −26.107 14.474Basic industries 0.142 5.202 −21.903 15.615General industrials 0.390 5.286 −26.183 14.113Cyclical consumer goods 0.134 5.355 −24.089 14.347Noncyclical consumer goods 0.714 4.588 −22.524 11.459Cyclical services 0.371 4.914 −22.281 13.058Noncyclical services 0.414 5.454 −13.244 21.451Utilities 0.342 4.652 −11.003 27.760Information technology 0.775 7.232 −27.069 20.251Financials 0.489 5.685 −21.239 19.815

The table includes summary statistics of the Datastream global industry excess returns (U.K. £) between January1985 and December 2000. The statistics includes the mean, standard deviation, minimum, and maximum ofmonthly excess returns (%).


Table 2Summary statistics of country equity portfolios

Country Mean Standard deviation Minimum Maximum

Australia 0.472 7.171 −47.260 18.732Belgium 0.635 5.402 −25.086 20.466Canada 0.302 5.904 −27.747 15.921Denmark 0.672 5.076 −14.336 17.386France 0.932 5.894 −23.230 18.914Germany 0.562 5.721 −21.903 18.855Hong Kong 1.102 9.391 −49.270 29.915Ireland 1.106 6.335 −30.081 22.795Italy 0.688 7.805 −16.899 28.382Japan 0.098 6.999 −17.312 21.199Netherlands 0.786 4.527 −21.990 12.604Norway 0.760 7.453 −30.216 20.484Singapore 0.279 8.333 −41.375 26.237Sweden 0.944 7.087 −24.626 22.324Switzerland 0.891 5.179 −23.657 17.598U.K. 0.620 4.725 −26.470 13.962U.S. 0.655 5.675 −26.017 14.495

The table includes summary statistics of the Datastream country equity excess returns (U.K. £) and the U.K.Financial Times All Share index (FTA) between January 1985 and December 2000. This comprises the mean,standard deviation, minimum, and maximum of monthly excess returns (%).

Table 2shows that the average excess returns on the country equity portfolios rangebetween 0.098% (Japan) and 1.106% (Ireland). The countries with the highest standarddeviation tend to be from the Far East (Hong Kong, Singapore). Comparing the countryportfolios with the industry portfolios, we find that the country equity portfolios are morevolatile than the industry portfolios. The unreported correlations between the equity port-folios range between 0.274 and 0.844. Most of the correlations lie between 0.3 and 0.6. Thecorrelations are lower than the industry correlations.

3.2. Sample of unit trusts

Our third set of assets is six value weighted portfolios of U.K. unit trusts with inter-national equity objectives. We form our sectors by identifying all U.K. trusts with inter-national equity objectives at the start of 1985 from the 1985 Unit Trust Yearbook (pub-lished by the Financial Times Business Information). We include trusts that have equityobjectives of International, North America, Europe, Australia, Japan, and Far Eastern. Wetrack the history of each trust through to the end of 2000. We treat name changes andtransfers of the trusts as a continuation of the original trusts. We treat trusts that weretaken over or wound up during the sample period as a termination. Where a trust changesits’ investment objective to a non-international equity objective or changes to an open-ended investment company, we treat this as a termination. We collect monthly returnson the trusts up until their termination or change in objective. We have 282 trusts in oursample.


Table 3Summary statistics of international unit trust investment sectors

Panel A Mean Standard deviation Minimum Maximum

International 0.334 4.833 −29.710 15.021North American 0.416 5.530 −32.383 15.900Europe 0.663 4.993 −27.882 16.129Australia 0.165 7.449 −49.915 18.833Japan 0.032 7.089 −20.211 19.718Far East 0.179 6.469 −34.207 19.760

Panel B correlations International North American Europe Australia Japan

North American 0.845Europe 0.851 0.655Australia 0.582 0.513 0.479Japan 0.644 0.375 0.477 0.317Far East 0.828 0.653 0.656 0.613 0.687

The table includes summary statistics for equal weighted portfolios of trusts sorted by investment sector betweenJanuary 1985 and December 2000. The summary statistics are the mean, standard deviation, minimum, andmaximum of monthly excess returns (U.K. £) (%). The six investment sectors are International, North American,Europe, Australia, Japan, and Far East.

We calculate the monthly returns of each trust from monthly offer prices and dividendspaid by the trust in the month that the dividend is declared ex-dividend. We collect the offerprices from the Finstat managed fund database provided by the Financial Times Informa-tion Service and Money Management. We use the dividend information from the Finstatdatabase and the annual Extel U.K. Dividend and Fixed Interest Record. We collect the in-vestment objective and size of the trusts at the start of each year from the annual Unit TrustYearbooks.

We form the six value weighted investment sector portfolios of trusts as follows. At thestart of 1985, we allocate all trusts on the basis of their investment objective at the start ofthe year. The size of each trust at the start of the year is used as the initial weights in theportfolios. We calculate the monthly buy and hold excess returns on each portfolio duringthe next twelve months. Where a trust dies during the year, we reallocate the weights acrossthe other trusts in the portfolio accordingly. We repeat this approach at the start of eachyear until 2000. Our approach to forming the value-weighted portfolio should minimize theimpact of survivorship bias (e.g.,Carhart et al., 2002).

Table 3reports summary statistics of the excess returns of the six investment sectorportfolios of trusts. Panel A reports the mean, standard deviation, minimum, and maximummonthly excess returns and panel B reports the correlations. We find a wide spread in averageexcess returns and standard deviations across the six sectors. The three Asia Pacific sectorshave the lowest average excess return and highest standard deviation. Europe providesthe highest average excess return and the international sector provides the lowest standarddeviation. The pattern in means and standard deviation mirrors the numbers inTable 2.The correlations in panel B range between 0.317 and 0.851. The highest correlations arebetween the International, North America, Europe, and Far East sectors. The Japan andAustralia sectors have the lowest correlations.


Table 4Diversification benefits of global industry portfolios

Panel A Mean Median Standard deviation 1% 5%

DSharpeLow 0.211 0.216 0.058 0.074 0.110High 0.337 0.342 0.062 0.182 0.225

CERLow 1.276 1.234 0.395 0.561 0.716High 0.620 0.611 0.138 0.340 0.411

Panel B weights Low mean Standard deviation High mean Standard deviation

U.K. 0.099 0.121 0.081 0.040Resources 0.087 0.119 0.080 0.043Basic industries 0.065 0.085 0.083 0.031General industrials 0.087 0.074 0.101 0.023Cyclical consumer goods 0.067 0.084 0.092 0.030Noncyclical consumer goods 0.103 0.113 0.083 0.035Cyclical services 0.088 0.073 0.095 0.019Noncyclical services 0.096 0.123 0.094 0.045Utilities 0.066 0.105 0.055 0.043Information technology 0.146 0.158 0.140 0.059Financials 0.095 0.111 0.094 0.039

The approximate posterior distribution of the increase in theSharpe (1966)(DSharpe) and CER (monthly %)performance between the international and domestic strategy is estimated between January 1985 and December2000 using the approach ofWang (1998). The domestic strategy is where the investor allocates their wealth betweenthe U.K. market index and domestic risk-free asset. The international strategy is where the investor allocates theirwealth between the global industry portfolios, U.K. market index, and domestic risk-free asset. Low (high) is therisk aversion level of 2 (10). Panel A reports summary statistics of the posterior distribution of the DSharpe andCER measures. The summary statistics are the mean, median, standard deviation, 1 and 5 percentiles. Panel Breports the mean and standard deviations from the posterior distribution of the optimal weights in the internationalstrategy.

4. Empirical results

We begin our analysis by estimating the diversification benefits using the global industryportfolios as the international assets.Table 4reports the results. Panel A of the table presentssummary statistics from the posterior distributions of the DSharpe and CER measures forthe two levels of risk aversion (low and high). The summary statistics include the mean,median, standard deviation, 1 and 5 percentiles from the posterior distributions. Panel Breports the mean and standard deviations from the posterior distributions of the optimalweights from the international strategy for the two levels of risk aversion.

Table 4shows that there are significant diversification benefits using the global industryportfolios. There is a significant increase in theSharpe (1966)and CER performance forboth levels of risk aversion. The mean DSharpe and CER performance measures are bothmore than two standard errors from zero. The increase in the Sharpe and CER performanceremains large at the posterior probabilities of 0.95 and 0.99. There is a difference in the sizeof the diversification benefits of the DSharpe and CER measures between the two levels ofrisk aversion. The DSharpe (CER) performance is greater for the high (low) level of risk


aversion. The smaller CER performance at the higher level of risk aversion is similar toLi (2003). The smaller CER performance at the high level of risk aversion stems in partfrom the impact of risk aversion in the tradeoff between mean and variance in the CERmeasure.

The weights in panel B ofTable 4show that there is a positive average weight in eachrisky asset for the international strategy. The highest average weight is in the informationtechnology portfolio and the smallest average weight is in the utilities portfolio. However,the high standard errors reflect the uncertainty in the portfolio weights. None of the averageweights at the low level of risk aversion are more than two standard errors from zero. At thehigh level of risk aversion, the standard deviations of the optimal weights are reduced. Thisreduction of the standard deviations leads to all of the average weights being more than twostandard errors from zero except for the utilities and resources sectors.

Table 4suggests that there are significant diversification benefits for a U.K. investor evenin the presence of short selling constraints. We next explore the diversification benefits ofusing the country equity index portfolios as the set of international assets.Table 5reportsthe results that are the same asTable 4. Table 5show that there is a significant increase intheSharpe (1966)and CER performance using the country equity portfolios. The averageDSharpe and CER performance is more than two standard errors from zero for the two levelsof risk aversion. As with the global industry portfolios, the DSharpe (CER) performance isgreater for the high (low) level of risk aversion. There continues to be substantial increasesin Sharpe and CER performance at the posterior probabilities of 0.99 and 0.95.

The average weights in panel B ofTable 5show some variation across the country equityportfolios at the two levels of risk aversion. The average weight is highest in Hong Kongand Ireland and smallest in Japan. There is a lot of uncertainty in the average weights asreflected in the high standard deviations. As with the global industry portfolios, the degreeof uncertainty reduces at the high level of risk aversion. However, none of the averageweights in the risky assets in panel B ofTable 5are more than two standard errors fromzero.

Tables 4 and 5show that there are significant diversification benefits for a U.K. investorusing either the global industry or country equity portfolios as the international assets. Themagnitude of the diversification benefits inTable 5is greater thanTable 4suggesting thatthe diversification benefits are greater for the country equity portfolios. This finding differsfrom Cavaglia et al. (2000). Cavaglia et al. find that global industry portfolios providegreater diversification benefits than country equity portfolios especially in the more recentperiod. However, the difference in findings betweenTables 4 and 5might be due to thelarger number of assets used in the country equity portfolios.

We next explore whether international unit trusts provide the same diversification benefitsas the global industry or country equity portfolios.Table 6examines the benefits of usingthe six investment sector portfolios of trusts in the international strategy.

Table 6shows that there are significant diversification benefits using the investment sectorportfolios of trusts. The average DSharpe and CER performance is more than two standarderrors form zero for both levels of risk aversion. The performance is greater for the high(low) level of risk aversion for the DSharpe (CER) measure. At the posterior probabilitiesof 0.95 and 0.99, there are also reasonable diversification benefits. However, the magnitudeof the benefits is not as large as the global industry or country equity portfolios.


Table 5Diversification benefits of country equity portfolios


DSharpeLow 0.288 0.296 0.060 0.130 0.178High 0.502 0.512 0.059 0.340 0.391

CERLow 1.637 1.602 0.360 0.919 1.098High 1.060 1.047 0.143 0.774 0.847


U.K. 0.057 0.090 0.051 0.035Australia 0.027 0.079 0.040 0.047Belgium 0.060 0.098 0.058 0.042Canada 0.036 0.071 0.044 0.036Denmark 0.053 0.100 0.047 0.041France 0.080 0.117 0.069 0.044Germany 0.057 0.097 0.060 0.043Hong Kong 0.114 0.166 0.111 0.071Ireland 0.110 0.147 0.088 0.056Italy 0.045 0.107 0.064 0.062Japan 0.008 0.043 0.017 0.034Netherlands 0.062 0.081 0.053 0.028Norway 0.061 0.118 0.069 0.058Singapore 0.019 0.064 0.042 0.049Sweden 0.084 0.137 0.082 0.057Switzerland 0.077 0.111 0.061 0.040U.S. 0.051 0.085 0.046 0.036

The approximate posterior distribution of the increase in theSharpe (1966)(DSharpe) and CER (monthly %)performance between the international and domestic strategy is estimated between January 1985 and December2000 using the approach ofWang (1998). The domestic strategy is where the investor allocates their wealth betweenthe U.K. market index and domestic risk-free asset. The international strategy is where the investor allocates theirwealth between the country equity portfolios, U.K. market index, and domestic risk-free asset. Low (high) is therisk aversion level of 2 (10). Panel A reports summary statistics of the posterior distribution of the DSharpe andCER measures. The summary statistics are the mean, median, standard deviation, 1 and 5 percentiles. Panel Breports the mean and standard deviations from the posterior distribution of the optimal weights in the internationalstrategy.

The weights in panel B ofTable 6show that the highest average weight is in the Europe(Far East) sector for the low (high) risk aversion level and the lowest average weight is in theJapan sector. The average weight on the International sector is more than two standard errorsfrom zero at the low level of risk aversion. At the high level of risk aversion, the averageweight on the U.K. index, International, North America, Europe, and Far East sectors areall more than two standard errors from zero.

Tables 4–6show that all three sets of international assets provide significant diversifi-cation benefits for a U.K. investor even in the presence of short selling constraints. Thisfinding supports the continuing usefulness of international diversification strategies evenin developed equity markets (e.g.,Dimson et al., 2002; Hentschel and Long, 2004). Ourfindings about the international unit trusts suggest a more positive role than observed in


Table 6Diversification benefits of international unit trusts


DSharpeLow 0.159 0.161 0.058 0.038 0.063High 0.220 0.221 0.070 0.065 0.105

CERLow 0.819 0.765 0.349 0.244 0.358High 0.339 0.330 0.139 0.073 0.129


U.K. 0.166 0.146 0.122 0.044International 0.154 0.074 0.136 0.029North American 0.159 0.149 0.139 0.050Europe 0.174 0.148 0.131 0.045Australia 0.128 0.174 0.143 0.072Japan 0.082 0.136 0.108 0.068Far East 0.137 0.138 0.152 0.047

The approximate posterior distribution of the increase in theSharpe (1966)(DSharpe) and CER (monthly %)performance between the international and domestic strategy is estimated between January 1985 and December2000 using the approach ofWang (1998). The domestic strategy is where the investor allocates their wealthbetween the U.K. market index and domestic risk-free asset. The international strategy is where the investorallocates their wealth between six value-weighted portfolios of international unit trusts, U.K. market index, anddomestic risk-free asset. Low (high) is the risk aversion level of 2 (10). Panel A reports summary statistics of theposterior distribution of the DSharpe and CER measures. The summary statistics are the mean, median, standarddeviation, 1 and 5 percentiles. Panel B reports the mean and standard deviations from the posterior distribution ofthe optimal weights in the international strategy.

Fletcher and Marshall (2004). Fletcher and Marshall find that U.K. international unit trustsdo not outperform domestic benchmark strategies. Our findings suggest that internationalunit trusts provide significant diversification benefits as part of a mean-variance asset allo-cation strategy.

When we compare the DSharpe and CER measures inTable 6to Tables 4 and 5, theinternational trusts do not capture all the diversification benefits provided by global industryor country equity portfolios. This finding differs fromErrunza et al. (1999), although we donot use the same type of investment strategies as Errunza et al. We explore this issue in moredetail by comparing the performance of two mean-variance strategies. In the first strategy,we allow the investor to select their optimal portfolio for a given level of risk aversion fromthe U.K. market index, the six investment sector portfolios of trusts, and the domestic risk-free asset. In the second strategy, we allow the investor to allocate their wealth across theU.K. market index, six investment sector portfolios of trusts, and global industry (countryequity) portfolios, and the domestic risk-free asset. We estimate the DSharpe and CERmeasures between the two strategies using the approach described earlier. If the investmentsector portfolios of trusts do not capture the diversification benefits provided by the globalindustry or country equity portfolios, we expect the average DSharpe and CER measuresto be more than two standard errors from zero.


For the global industry portfolios, the average DSharpe (CER) performance is 0.115(0.928) at the low level of risk aversion and 0.247 (0.613) at the high level of risk aversion.With the exception of the average CER measure at the low level of risk aversion, all of theaverage DSharpe and CER performance is more than two standard errors from zero. Forthe country equity portfolios, the average DSharpe (CER) performance is 0.171 (1.281) atthe low level of risk aversion and 0.375 (0.993) at the high level of risk aversion. All of theaverage DSharpe and CER performance is more than two standard errors from zero. Thisfinding confirms the results inTables 4–6that the investment sectors portfolios of trusts donot capture all the diversification benefits.

5. Conclusions

We examine the diversification benefits for a U.K. investor between January 1985 andDecember 2000 using three different sets of international assets. There are three mainfindings in the paper. First, there are significant increases in theSharpe (1966)and CERperformance in adding either global industry or country equity portfolios to a domestic assetallocation strategy. This finding suggests that there are significant diversification benefits fora U.K. investor in developed equity markets even in the presence of short selling constraintsand supportsDimson et al. (2002)andHentschel and Long (2004).

Second, the level of risk aversion affects the size of the benefits. The increase in CER(Sharpe, 1966) performance is greater at the low (high) level of risk aversion. The pattern inCER performance is similar toLi (2003). Third, we find significant diversification benefitsusing U.K. international unit trusts as the international assets. However, international unittrusts do not capture all the benefits provided by either the global industry or country equityportfolios. This finding suggests a more positive role for international trusts compared toFletcher and Marshall (2004)who finds that U.K. trusts do not provide superior performancewhen compared to domestic benchmark strategies. One issue we do not consider in our studyis the diversification benefits provided by emerging market unit trusts. We leave this issueto future research.

Acknowledgements

We acknowledge the financial support of INQUIRE UK. This article represents theviews of the authors and not of INQUIRE. Helpful research assistance was provided bySally Cooper and Louise McCann. Helpful comments were received from an anonymousreviewer.

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An empirical examination of the benefits of international diversification

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