international diversification with frontier markets annual... · market classifications. they focus...

International diversification with frontier markets

We provide an analysis of frontier market equities within an

international context. We aggregate individual frontier country indices

into a frontier market index for study. Our principal components

analysis indicates frontier markets exhibit very little integration with the

world market. Further, contrasting developed and emerging market

equities, we find no indication of increasing integration through time.

Given the lack of integration with the world market, mean-variance

spanning tests and mean-variance geometry indicate significant benefits

of frontier market diversification.

I. Introduction

We present an analysis of frontier markets with respect to world market integration and

international diversification. Finance theory has shown that the benefit of international diversification

decreases when the world markets become increasingly integrated. In other words, to study the

international diversification, it is important to understand the degree to which frontier markets are

integrated with the rest of the world markets. We implement the principal component approach of

Pukthuanthong and Roll (2009) to examine integration across frontier markets with the world

component. We then investigate the diversification benefits of frontier market investing, to an already

diversified international investor, by performing the mean-variance spanning tests of Huberman and

Kandel (1987). Our results indicate significant diversification benefits of frontier markets. The benefits

accrue not only to broad frontier market investments but also to most country-specific frontier market

investments.

Frontier markets are essentially "pre-emerging" markets that are expected to be reclassified as

emerging markets once capital and liquidity increase. The term “frontier market” is often used to

describe equity markets of smaller, less accessible, and yet still investable countries of the developing

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world. The term began used in 1990s when the Standard and Poor’s (S&P) started to track a frontier

market index, but gained wider awareness in 2007 when S&P launched the Select Frontier Index and the

Extended Frontier Index. To reflect the growing interest from international investors in these markets,

MSCI also launched its Frontier Markets Indices in late 2007. Recently, frontier market mutual funds and

exchange-traded funds (ETFs) have also been developed1. In general, S&P and MSCI as well as fund

managers have been emphasizing frontier markets’ strong growth potential and their low correlations

with emerging and developed markets, presenting great diversification opportunities.

Although frontier markets have attracted much attention, our understanding of these markets is

limited mainly due to the fact that they are relatively new to the investment community. While

numerous studies examine global relations across equity markets, very little research covering frontier

equity markets exists. The frontier market classification typically includes countries or markets that are

smaller than emerging markets. For example, the average market capitalization of countries defined as

frontier markets by MSCI was US$ 575 million, measured during the summer of 2009. The existing

research suggests that frontier market investment may offer benefits. Speidell and Krohne (2007) offer

an overview of frontier markets. They confirm that frontier markets typically exhibit low market

capitalizations. Further, they argue that frontier markets provide diversification benefits as they exhibit

low correlations with developed market equities. However, cross-market correlation may not be the

best indicator of diversification benefits (see e.g., Carrieri, Errunza and Hogan (2007) and

Pukthuanthong and Roll (2009)). Jayasuriya and Shambora (2009) study diversification benefits across

market classifications. They focus on optimal portfolios formed from developed markets, emerging

markets and a set of six frontier market countries, during a recent sample period. They find

1 On March 17, 2008, the Barclays Global Investors (BGI), one of the world’s largest asset managers, launched the

BGI Frontier Markets Fund which invests in 16 frontier markets and benchmarks to the MSCI Frontier Markets

Index. The Franklin Templeton Investments introduced its Templeton Frontier Markets Fund, the first actively

managed U.S.-registered frontier markets fund, on December 9, 2008. The Deutsche Bank launched the first

frontier market ETF in Europe in early 2008. The Bank of New York Mellon created its frontier market ETF in June

2008.

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improvement in terms of portfolio risk and return by increasing diversification across developing

markets and with respect to frontier markets, conclude that these assets may help minimize portfolio

risk. Finally, Cheng, Jahan-Parvar and Rothman (2009) use variations of the CAPM to study nine equity

markets within the Middle East North African region. Their sample includes both emerging and frontier

equity markets. They find that most markets within their sample exhibit low levels of integration, but

they also find that both global and local risks are priced.

The topics of international market integration and international diversification have generated a

large amount of research. However, existing research focuses on developed and emerging market asset

classes. In an early study, Solnik (1974) argues international diversification is quite beneficial, effectively

based on lower levels of cross-market correlations. Subsequently, Odier and Solnik (1993) argue that

despite increasing informational integration across markets, as well as correlation increases during

periods of high volatility, overall correlations remain low and consequently international diversification

remains beneficial. Recently, Rua and Nunes (2009) use wavelets to study cross-market correlations

within developed markets; their study presents an analysis of correlations through time, as well as

across time horizons.

From an asset-allocation perspective, cross-market correlations are clearly informational.

However, research suggests cross-market correlations may not be the best indicator of diversification

benefits, or of overall market integration. Recently Driessen and Laeven (2007) study diversification

benefits across developed and emerging markets with emphasis on diversification benefits for local

investors. Their analysis considers both first and second moments, and they find international

diversification to be most beneficial for emerging market investors. However, You and Daigler (2010)

find little evidence of international diversification benefits focusing on downside risk, and allowing for

conditional correlations. With respect to international integration, Carrieri, Errunza and Hogan (2007)

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argue against the validity of cross-market correlations as a measure of integration. Intuitively, they

discuss the case of Zimbabwe in which the large correlation with the worldwide price of copper and the

national market is not indicative of a highly integrated capital market. Pukthuanthong and Roll (2009)

also argue that cross-market correlations do not provide an adequate measure of integration. Varying

sensitivities to international factors across markets can lead to low correlations, despite high levels of

integration. Based on principal components, they detail levels of integration across countries and

provide evidence that integration tends to increase through time for the majority of countries within

their sample. However, they also document countries that become less integrated throughout their

sample.

Given the lack of research covering frontier equity markets, we provide an analysis of frontier

market integration, as well as frontier market diversification benefits. We conduct analyses across

frontier market countries, as well as across our broad frontier market indices, which include as many as

25 frontier market countries. The construction of our broad frontier market indices strengthens our

results by providing a lengthy sample period and minimizing country-specific noise. We apply the

Pukthuanthong and Roll (2009) measure of integration to broad indices across market classifications.

We find developed and emerging market indices exhibit significant exposure to the world market factor.

However, we find little evidence of integration between broad frontier market indices and the world

factor. Further, given the developed and emerging market indices, we find a significant increase in

integration through time, consistent with existing findings in the literature. However, there is no

evidence that frontier market integration is increasing through time. Our variance decomposition

further indicates that for most frontier market countries, the variance of the overall return is largely

attributable to idiosyncratic risk, rather than world or frontier market factors. This result suggests

country specific frontier market risk may be largely diversifiable.

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To assess the diversification benefits of frontier markets, we conduct mean-variance spanning

tests. As described by Huberman and Kandel (1987) mean-variance spanning tests determine if the

minimum-variance frontier of a large set of assets is spanned by the minimum-variance frontier of a

subset of the assets. If the subset of assets do not span the minimum-variance frontier formed by the

larger set of assets, then additional diversification would improve the risk-return characteristics of the

portfolio. The mean-variance approach directly measures diversification benefits by considering both

first and second moments. Existing research applies the mean-variance approach to test the

diversification benefits of specific test assets in many situations. For example, Bekaert and Urias (1996)

implement the methodology to test the diversification benefits of emerging markets, while Chen and Ho

(2009) analyze the benefits of IPO indices. Driessen and Laeven (2007) also utilize mean-variance

spanning tests in an international diversification context, while varying the benchmark assets across

geographical regions. We implement our analysis with a universe of developed, emerging and frontier

market assets. We then test if broad developed, and emerging market indices span the minimum-

variance frontier formed with the inclusion of broad frontier market indices, as well as country-specific

frontier market indices. We further test if the inclusion of a broad frontier market index is sufficient to

capture the diversification benefits offered by country-specific frontier indices.

Our results document strong diversification benefits from frontier market investment.

Specifically, across the entire sample, the broad frontier market indices offer diversifcation benefits,

relative to developed and emerging market investment. These benefits tend to accrue based on shifting

the global minimum variance portfolio. The country specific tests indicate that country specific frontier

market investment further provides diversification benefits. These benefits tend to exist even after

including a broad frontier market index in the initial investment portfolio. Graphically, we extend these

results to show that frontier market diversification offers significant risk reduction potential. This result

is robust with and without short selling constraints and indicates that investors can achieve similar levels

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of expected return with lower risk by including frontier market equities. We also show that

diversification benefits of frontier market indices appear strongest during the latter part of our sample.

Finally, we show that frontier market diversification is beneficial in terms of risk reduction, when

alternative benchmarks are performing the worst as well as during periods in which benchmark

portfolios perform the strongest.

This paper makes several significant contributions. First, we provide empirical evidence on the

diversification benefit of a complete set of frontier markets. Existing studies focus mostly on a subset of

frontier markets (see, e.g., Cheng, Jahan-Parvar, and Rothman (2009) and Jayasuriya and Shambora

(2009)). Although Speidell and Krohne (2007) examine all potential frontier markets, their analysis is

limited to the correlation. Since the cross-market correlation may not be the best indicator of

diversification benefits, their results are far from conclusive. Second, we construct daily and monthly

equal-weighted and value-weighted frontier market indices. Existing indices start in 2007, but our

indices begin in 1989, allowing us to perform tests of the international diversification over a long period

of time. Third, we contribute to the market integration literature by extending the analysis to frontier

markets. We find little evidence of integration between broad frontier market indices and the world

markets. Furthermore, unlike other markets, there is no evidence that frontier market integration is

increasing through time. Lastly, our results are relevant to the recent findings in international

diversification. Bekaert, Hodrick, and Zhang (2009) find that country factors dominate industry factors in

international diversification and similarly, Baele and Inghelbrecht (2009) show that geographical

diversification continues to be superior to industry diversification. Our analysis of frontier markets

provides insights to the international diversification with respect to country factors and geographical

diversification. We leave the comparison between country factors and industry factors in the context of

frontier markets to future studies.

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The remainder of the paper is organized as follows. We outline how our data set is constructed

in the following section. Section III presents the principal component analysis and variance

decomposition analysis. Section IV provides the mean-variance spanning tests to analyze diversification

benefits of frontier markets. Section V concludes.

II. Data

Our study considers an analysis across market classifications; namely developed, emerging and

frontier. We obtain daily and monthly data from the MSCI world index, which is comprised of developed

market countries; we refer to this index as the developed market index. We also obtain data for the

MSCI all country world index, which includes developed and emerging markets, as well as the MSCI

emerging market index. In certain cases, we also consider returns to the US CRSP value-weighted market

portfolio. Finally, we consider returns to a broad selection of country-specific frontier market indices,

with a sample of 25 frontier market countries. Following Pukthuanthong and Roll (2009), we choose the

total return index for each country, when available. We also aggregate country-specific returns to

calculate broad frontier market indices. These indices allow an analysis across the frontier market

classification. Finally, throughout the study, all returns and values are denominated in US Dollars, based

on the Datastream exchange rate facility.

To create our frontier market sample, we obtain monthly and daily return data covering frontier

markets from datastream. The specific countries included, as well as dates of coverage, are detailed in

Table 1. Further, there are cases where we do not have reliable observations for every point within the

coverage period, therefore we also list the total number of valid monthly observations for each country

included in our sample. Given our sample of frontier market country index returns, we also obtain

country market capitilization data. We then construct equal-weighted and value-weighted frontier

market indices for both daily and monthly periodicities. To provide a lengthy sample for analysis, we

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begin our sample January 1989, and add countries to the index as the country-specific data becomes

available. Therefore, during the early years of our sample, our frontier indices contain relatively few

countries. However, as the sample progresses the coverage increases. Sub-sample analysis, as well as

analysis across countries confirm that our results are not driven by the early sample in which relatively

few countries enter the index. Pukthuanthong and Roll (2009) discuss data issues relating to stale prices.

Following their approach, we eliminate observations for a given country if the price index does not

change. Finally, given our focus on frontier markets from the perspective of a domestic investor, we

match frontier index returns only to dates of MSCI developed index returns. This further eliminates a

small number of stale prices from holidays.

Constructing the value weighted index is more difficult and requires certain degree of

estimation. First of all, market capitalization data is not readily available for every observation for every

country. Further, the periodicity of market capitalization is often longer than that of our return series.

For example, for daily returns, we have monthly market capitalization data, at best. In the cases in which

we did not have a fresh observation of market capitalization we use the most recent available

observation of market capitalization for which we had data2. In some instances we have no reliable

market capitalization data for a country, nor any reliable lagged observations. In these cases, to

construct the value-weighted index, we set the given country’s market capitalization equal to the

median level of all frontier market countries within the sample at that point in time.

***Insert Table 1 about here***

2 We use the most recent available market capitalization observation, rather than estimate market capitalization

based on subsequent returns and the previous observation, as this approach would miss any additions or deletions

from the index.

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III. Principal Component Analysis and Variance Decomposition

We examine the extent to which frontier markets are integrated within the global market.

Pukthuanthong and Roll (2009) consider the level of world integration across a broad sample of

developed, emerging and frontier country-specific indices. Specifically, they regress daily country index

returns on their global principal components. We adopt the similar approach using their principal

components and apply the methdology towards our broad frontier market indices. To consider

additionall market classifications, we also perform the similar analysis on the MSCI developed market

index, which represents developed markets, and the MSCI emerging market index. We present principal

component results in Table 2. We focus on the adjusted R-square, as this measure signifies the

proportion of an index’s return explained by global factors. We also consider the coefficient on the 1st

principal component as this component is comparable to a global market factor. As the principal

components are mutually orthogonal, interpretation of the remaining coefficient estimates is not

straightforward and consequently we do not report these remaining estimates. We report our prinicpal

component regression results in columns two and three of Table 2. To provide a comparison across the

principal component approach and the common correlation method, we also report cross-index

correlations, and associated p-values, within the final four columns of the table.


Results in Table 2 document a striking lack of world market integration across the frontier

indices, despite high levels of integration for the developed and emerging market indices. In Panel A, the

adjusted R-square from the principal component regressions are -0.0003 and 0.0045 for the frontier

value-weighted and equal-weighted indices, respectively. The corresponding values are 0.3974 and

0.5528 for the emerging market and developed market indices, respectively. The adjusted R-square

measures indicate that the principal components explain very little of the variation in frontier market

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returns, despite the evidence that they explain a large portion of emerging and developed market return

variation. Pukthuanthong and Roll (2009) argue that the first principal component equates to the global

market factor. Coefficients for the global market factor are large in magnitude and highly significant

based on the emerging and developed market indices. However, based on the full sample in Panel A, the

coefficient estimate for the value-weighted frontier index is insignificant. While the global market factor

parameter estimate is significant based on the equal-weighted frontier index, it is small in magnitude.

Comparable parameter estimates for the developed and emerging market indices are both over twenty

times larger in magnitude. In short, the developed and emerging market indices exhibit high levels of

world market integration based on principal component regressions and the global market factor, while

the evidence suggests frontier markets are not integrated.

Pukthuanthong and Roll (2009) argue that their principal component approach provides a better

analysis of world market integration, relative to the common correlation approach. Carrieri, Errunza and

Hogan (2007) also discuss the drawbacks towards cross-market correlations as a measure of integration.

The final four columns in Table 2 report cross-market correlations for the entire sample, and each sub-

sample considered. This allows a comparison of inferences drawn from the principal component

approach, relative to the correlation approach. We find comparable results and inference across the

principal component measure, as well as the correlation between the frontier market indices with the

world market. That is, cases in which the coefficient on the first principal component are significant tend

to correspond to cases in which the correlation with the world market are significant as well. However,

as explained by Pukthuanthong and Roll (2009), correlations do not provide a great measure of the level

of integration. Therefore, the magnitude of integration is likely best described by the prinicpal

component results.

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Our broad frontier indices include data from each frontier market when data become available.

Consequently, coverage of the indices is thin during the early sample periods. We therefore include sub-

sample results to provide analyses across a lengthy sample, as well as more recent samples which

include many frontier equity markets. For example, our broad indices include 20 of the 25 frontier

market countries by January, 2000. Results in Panel C of Table 2, covering the eight years from January,

2000 through December, 2007, confirm the analysis based on the entire sample discussed above.

Specifically, considering both broad frontier market indices, we find small, or insignificant parameter

estimates for the world factor, and adjusted R-square measures very close to zero. These results

contrast the large and significant world market factor coefficients, and large adjusted R-square

measures for the world and emerging market indices. Finally, we present sub-sample results across

approximately five year periods in Panels D through G. The results confirm the discussion above.

Levels of world market integration are likely time-varying. For example, Carrieri, Errunza and

Hogan (2007) indicate world market integration tends to increase. However, they do document

reversals in levels of integration. Bekaert, Harvey and Lumsdaine (2002) estimate structural break

models to identify periods of segmentation and integration. They discuss that integration may be a

gradual process and often occurs after dates of official liberalization. To consider trends within the level

of frontier market integration, we follow Pukthuanthong and Roll (2009) who regress the R-square from

the principal component analysis on a simple time trend. Initially, we estimate the principal component

model based on subsequent six month sub-samples from January 1989 through December 2007. We

take the R-square measure from each six-month regression, and regress this on a time trend. We also

conduct a similar analysis based on bimonthly regressions and sub-periods. We report results in Table 3.

Results based on the entire sample and six-month regressions are shown in Panel A, while the remaining

panels detail results based on bimonthly regressions and the sample periods given. We again provide a

comparison of the principal component approach relative to the correlation approach. We report the

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principal component results in columns two and three. We report results based on correlations in the

final two columns. Results in these columns are based on regressing daily correlations formed from

either six month, or two month intervals and computed across the given index and the all country world

index, on a simple time trend, in the same fashion as the PC approach.


From Panel A in Table 3, we see that the time trend estimate is positive and highly significant for

the developed and emerging market indices, while the corresponding estimates are insignificant based

on the frontier market indices. Therefore, we document increasing world market integration based on

emerging and developed market indices, but no trend in frontier market integration. Interestingly, the

principal component approach is able to capture changing levels of integration that are not captured by

the simple correlation approach. For example, across the entire sample period, the principal component

approach indicates that the developed market is becoming increasingly integrated, while the

corresponding estimate based on correlations is insignificant. The results in this section further

compliment the earlier findings in that not only do frontier markets exhibit a low level of overall

integration, but the level of integration does not appear to increase. The bimonthly regression sub-

sample analyses presented in Panels B through H also document several interesting results. First, the

time trend is significant and positive based on the equal-weighted frontier index during the 1994

through 1998 sample period presented in Panel F. However, no other sub-sample provides significant

estimates for either frontier market index. Further, in unreported results based on monthly regressions,

the time trend coefficient for the value-weighted frontier market index is negative and marginally

significant during the years from 1989 through 1999. Overall, the time trend and sub-sample analyses

document that frontier markets are not increasingly integrated with the world equity market. Table 3

also documents sub-samples in which the MSCI Developed portfolio does not exhibit a positive trend in

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integration, consistent with the time-varying world market integration documented by Bekaert and

Harvey (1995). Specifically, the time-trend coefficient for our world portfolio is insignificant based on the

eight year sample from 2000 through 2007, presented in Panel D, as well as in the shorter sub-samples

from 1989 through 1993 and 2004 through 2007, presented in Panels E and H, respectively. Finally, in

most cases the principal component results are similar to the correlation results, with respect to frontier

markets. This is because both approaches fail to find a significant increase or decrease in world market

integration within our frontier market indices during most samples.

To further consider time-variation in levels of integration, we plot R-square measures from the

principal component analysis through time. In Figure 1, we plot R-square measures based on six-month

regressions, while Figure 2 documents results based on bimonthly regressions. The results are

comparable across figures and document several interesting findings. First, in Figure 1, the level of

integration for both frontier market indices remains essentially flat and approximately equal to zero.

This suggests a constant, and low-level of frontier market integration throughout the entire sample

period. Second, both figures document a dramatic time trend in terms of emerging market integration

approximately beginning during the early 1990s. Finally, the level of developed market integration

appears high and almost constant throughout the sample. This result helps explain the lack of a time-

trend for developed markets documented in the latter sub-samples presented in Table 3.

***Insert Figures 1 and 2***

The results presented above indicate broad frontier market indices exhibit a low level of world

market integration. Considering event-specific risk, Spiedell and Krohne (2007) argue that frontier

market volatility is not driven by the same factors that influence developed market volatility. Further, in

the context of Solnik (1974), if frontier market volatility is largely attributable to country-specific risk,

and not driven by global factors, then frontier market diversification will likely reduce portfolio risk. To

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further investigate the characteristics of frontier market returns, we perform a variance decomposition

of the country-specific frontier market returns. Eun, Lai and Huang (2008) implement the variance

decomposition in the context of international diversification across market capitilization, while Chen and

Ho (2009) perform a similar analysis on an IPO index. In our study, we regress country specific returns on

the MSCI developed index return as well as the value-weighted frontier market index return. That is, we

specify

��,� = � + ��,� + ��,� + ��,�, (1)

in which ��,� represents the return to individual frontier country i during period t, and �,� and �,�

represent the returns to the MSCI developed index and our value-weighted frontier index, respectively.

This specification assumes that country-specific frontier market returns are driven by a global factor and

a frontier-market factor. We then decompose the variance of the country-specific return into the

proportions attributable to the developed market, the frontier market, as well as the idiosyncratic

component. We define the overall variance of country i’s return as Var(��), while

�� ∗ ��(�)/��(��) and �

� ∗ ��(�)/��(��) (2)

determine the proportion of variance attributable to the developed market portfolio, and broad frontier

index, respectively. Finally, ��(��) determines the idiosyncratic, or country-specific component of

overall variance. We report results in Table 4.


From Table 4, it is clear that frontier market countries have little relation with the developed

market factor. Further, frontier market countries exhibit little relation with the broad frontier market

index. That is, for most contries, idiosyncratic volatility is the overwhelming proportion of the country’s

overall volatility. For example, the idiosyncratic volatility component contributes over 80% of the overall

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volatility for 18 of the 25 frontier markets, and over 90% for 13 of the frontier markets. The developed

market contributes over 25% of overall volatility only for Bulgaria, Croatia and LIthiuania. Finally, the

frontier market component contributes less than 10% of overall volatility for 22 of the 25 countries.

From the variance decomposition, it is apparent that frontier market volatility is largely country-specific,

with developed and frontier market factors contributing little to overalll volatility, for most frontier

market countries. This result further suggests frontier market diversification may lead to risk reduction

benefits.

IV. Diversification Benefits of Frontier Market Equities

We conduct mean-variance spanning tests to analyze diversification benefits of frontier market

equities. Our study is similar in purpose to the large body of literature analyzing potential diversification

benefits of international investing. However, we take a specific focus on diversification benefits of

frontier markets. To our knowledge, and contrasting the research covering developed and emerging

markets, very little research analyzing the benefits of frontier market investing exist. Mean-variance

spanning tests determine if the minimum-variance frontier formed with a subset of assets spans the

minimum-variance frontier formed with the entire set of assets (Huberman and Kandel (1987), Bekaert

and Urias (1996)). Following De Roon, Nijman and Werker (2001), as well as Chen and Ho (2009), we

specify the following model:

�� = � + �� + ��, (3)

in which �� represents the test asset return and �� represents the return of the K benchmark

portfolios. The spanning hypothesis may be tested based on the joint restriction that � = 0 and

� ≡ 1 − �1� = 0. Instances in which the spanning hypothesis is rejected indicate that the addition of

the test asset improves the mean variance performance of the overall portfolio, relative to the

performance of the portfolio formed from the benchmark assets. Chen and Ho (2009) further discuss

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step-down tests to determine the source of rejection of the null hypothesis of spanning. Testing the

hypothesis that � = 0 is equivelant to testing whether the tangency portfolios from the set of K

benchmark portfolios is the same as the tangency portfolio formed from the K benchmark portfolios

combined with the test asset. Imposing the restriction that � = 0 and testing the hypothesis that � = 0

indicates whether the global minimum variance portfolios differ across the set of K benchmark

portfolios relative to the K benchmark portfolios combined with the test asset.

Prior to presenting spanning results, we present simple cross-market correlations from the

country-specific frontier indices with the benchmark indices described above. Correlations are often

used as a measure of potential diversification benefits, however, correlations focus only on second

moments, while the spanning tests consider both first and second moments of the distribution. The

correlations, presented in Table 5, indicate significant variation in correlations across the frontier market

countries. For example, Bulgaria, Croatia and Lithuania are all highly correlated with the US, developed

and emerging market indices, with correlations approximately equal to 0.5 or higher. However, Ghana,

Jamaica and Nigeria, for example, all exhibit insignificant correlation with the relevant benchmark

portfolios.


In our study, we analyze the diversification benefits of broad frontier indices, as well as country-

specific frontier indices, relative to a broad diversified portfolio across market classifications. Therefore,

the vector of benchmark portfolio returns, which we define as ��, consists of the Fama-French US

market portfolio, the MSCI developed index, and the MSCI emerging market index. In analyses of

country-specific frontier indices, we also provide additional results in which we add the broad value

weighted frontier index to the grouping of benchmark portfolios described above. Our initial spanning

analysis tests the spanning restrictions for both of the broad frontier market indices, as well as for each

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frontier market country. Tests based on the broad frontier indices cover the sample period from January

1989 through December 2008. Tests based on country-specific frontier indices cover the entire sample

for which we have data for the given country. Country-specific sample periods are defined in Table 1.

We present the spanning results in Table 6.


The spanning tests across our entire sample provide evidence that frontier market equities

improve portfolio performance. The statistics of 18.65 and 41.23 strongly reject the null hypothesis of

spanning for both the broad value-weighted and equal-weighted frontier indices, respectively. Further,

the step-down tests indicate that both rejections can be attributed to different global minimum variance

portfolios. Further, for the country-specific indices, we find many test assets improve portfolio

performance. Specifically, we reject spanning for 15 of the country-specific frontier indices at the 5%

level. Interestingly, for the country-specific rejections, we continue to reject spanning after augmenting

the set of benchmark portfolios with the value-weighted frontier index. That is, even after adding a

broad investment in frontier markets, inclusion of specific frontier market countries continues to

provide benefits. Further, we observe that the rejections are due to both the tangency portfolio

hypothesis in some cases, and the global minimum variance portfolio in others. We find that the

spanning approach provides a more accurate representation of potential diversification benefits,

relative to the common correlation approach. From Table 5, Bulgaria, Croatia and Lithuania are all highly

correlated with our benchmark portfolios. However, spanning tests indicate that each of the markets

would provide further diversification benefits.

Given the evidence that broad frontier market diversification improves portfolio performance

presented above, we now graphically document the potential performance gains. Specifically, we plot

the mean-variance frontier formed from the three benchmark asset portfolios. We then plot the

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potential mean-variance frontiers formed by augmenting the three benchmark asset portfolios with

either the value-weighted or equal-weighted frontier index. We present results allowing short-sales in

Figure 3 and results with no short-sale restriction in Figure 4.

***Insert Figures 3 and 4***

Figures 3 and 4 confirm the mean-variance spanning results. Specifically, we see large portfolio

improvements accrue by including frontier indices. The graphs suggest a 2%-4% reduction in risk, while

maintaining a given level of expected return based through the equal-weighted frontier index, as well as

a 1%-2% reduction based on the value-weighted index. Interestingly, it seems that the equal-weighted

index offers incremental portfolio improvement beyond the value-weighted index. This indicates that

smaller markets may have offered superior performance during our sample, or may have a lower

relation with global factors.

To further assess the benefits of frontier market investment, we conduct spanning analyses

across sub-periods, as well as across quartiles of benchmark performance. First, we split the 20 year

sample into four subsequent five year periods and conduct the spanning tests across each sample for

the broad frontier indices. We also define a measure of benchmark portfolio performance. Specifically,

we construct an equal-weighted index comprised of the three benchmark asset portfolios. We then

assign each monthly observation to a performance quartile. Finally, we conduct spanning tests across

each quartile. This analysis indicates if frontier market investing provides benefits during periods of

benchmark downturns, risk reduction, or benefits during periods of strong benchmark performance as

well. We report the sub-period analysis and performance quartile results in Table 7.


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The sub-period analysis indicates frontier market investment provides the strongest benefits

during the latter sample periods. For both broad indices, we fail to reject spanning during the initial

sample period, while we strongly reject spanning during the 1999 through 2003 and 2004 through 2008

samples. During the 1994 through 1998 sample, the statistic of 5.24 marginally rejects spanning for the

value-weighted index, while the statistic of 9.68 strongly rejects based on the equal–weighted index.

The step-down tests indicate a similar pattern across indices. Namely, we reject spanning based on

differing global minimum variance portfolios during the 1994 through 1998, and 2004 through 2008

samples, while the 1999 through 2003 rejections are based on the tangency portfolio.

The results based on levels of benchmark performance are interesting. As expected, we strongly

reject spanning during periods of the worst benchmark performance. Statistics of 12.35 and 23.39 reject

spanning for the value-weighted and equal-weighted indices, respectively, given the quartile of the

lowest benchmark returns. Further, the inclusion of the frontier indices would improve both the

tangency portfolio and the global minimum variance portfolio in these cases. We fail to reject spanning

for both portfolios conditional on the second benchmark performance quartile. The statistic of 4.87

marginally rejects spanning based on the value-weighted index and the highest benchmark portfolio

quartile. However, spanning is strongly rejected given either the third or fourth quartile of benchmark

performance based on the equal-weighted frontier index. The final rejections indicate that frontier

market diversification not only offers benefits during periods of poor benchmark returns, but also during

periods of strong benchmark performance.

Our results document striking diversification benefits of frontier markets. However, Bekaert and

Urias (1996) argue that analyzing non-investable indices may overstate diversification benefits.

Therefore, we present an analysis of frontier market diversification based on exchange traded funds.

Due to the limited available history, we focus on presenting measures of portfolio risk and return across

20

varying levels of international diversification. We focus on exchange traded funds representing the ex-

USA Developed Market, the S&P500, the MSCI Emerging markets index and the frontier market index,

and denote these ETFs based on their ticker symbols as VEU, SPY, EEM and FRNMX, respectively. We

present risk and return characteristics for each ETF across the entire sample for which the frontier

market ETF is available, approximately January 2009 through November 2009, as well as across the

sample from January 08, 2009 through March 9, 2009 which represents a period of extreme market

decline in which the S&P 500 fell approximately 25%. We also construct portfolios across the developed

and emerging market ETFs and then analyze the benefits of frontier markets by shifting portfolio

weights towards the frontier market index. We conduct comparisons across an equal weighted strategy

in which funds are either allocated with 1/3 weighting in the EEM, SPY and VEU, or are allocated with

1/4 portfolio weighting to each of the four ETFs. In this way the second equal weighting scheme includes

the frontier market. Finally, we conduct comparisons across portfolio weighting strategies that are tilted

towards the domestic market, with a majority of weights in the SPY and VEU. We present results in

Table 7.


Results in Panel A indicate that the available sample is not one of strong frontier market

performance, relative to the other ETFs. Specifically, the FRNMX reports a holding period return of 14%,

compared to 64% for the EEM and 37% for the VEU. However, the frontier market ETF did not exhibit as

drastic declines during the extreme down market, falling only 19%, compared to over 25% for the

developed market ETFs. Comparisons across weighting strategies that include or exclude frontier

markets are presented in Panel B. There is some evidence that frontier markets provide diversification

benefits during the extreme down market sample. Annualized standard deviations for the portfolios that

21

include frontier markets are equal to 36% and 39%. These values compare to statistics of 45% and 43%

for the portfolios that exclude the frontier market ETF.

V. Conclusions

Our study considers returns to frontier market countries, as well as to broad frontier market

indices. The results relate to the large bodies of literature concerning levels of world market integration

as well as diversification benefits of international investing. These two large topics are likely related, as

levels of integration likely impact benefits of diversification. However, we take a specific focus on

frontier markets, which previously have received relatively little attention. We find evidence that

frontier markets exhibit very low levels of world market integration, and that levels are not increasing.

Further, we find frontier market volatility is largely idiosyncratic. Finally, our mean-variance analysis

suggests significant portfolio improvement from frontier market allocation.

.

22

References

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its application, Journal of Financial Economics, 94, 214-232.

23

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Banking and Finance, 34, 163-173.

24

Table 1. Country-specific frontier index summary statistics and sample period

We present summary statistics regarding the country-specific frontier indexes within our sample.

First and Last refer to the dates a given country enters and exits the sample, while n documents the

number of monthly return observations. We define �� as the monthly return for country i.

Country First Last n

�� (��)∗ 10^3

��(��)∗ 10^3 �# (��) ��$(��)

Argentina 08/1993 12/2008 185 -1.021 15.072 -0.478 0.409

Bahrain 01/2000 02/2008 98 9.046 1.331 -0.077 0.106

Botswana 01/1996 01/2008 145 17.443 3.668 -0.144 0.373

Bulgaria 11/2000 12/2008 98 16.621 13.804 -0.549 0.291

Croatia 01/1997 12/2008 144 6.290 10.473 -0.483 0.317

Estonia 06/1996 12/2008 151 7.751 12.755 -0.507 0.284

Ghana 01/1996 01/2008 145 -4.238 2.943 -0.171 0.219

Jamaica 01/1996 01/2008 143 9.713 7.168 -0.237 0.370

Jordan 01/1989 12/2008 240 6.892 2.874 -0.196 0.155

Kenya 02/1990 12/2008 227 0.861 6.871 -0.280 0.492

Kuwait 01/1995 12/2008 168 9.273 2.537 -0.205 0.155

Lebanon 04/2000 01/2008 25 38.220 55.543 -0.288 0.375

Lithuania 01/2000 12/2008 108 9.753 7.294 -0.415 0.174

Maurtius 01/1996 01/2008 141 10.416 2.669 -0.208 0.214

Nigeria 07/1995 02/2008 152 19.970 4.705 -0.196 0.251

Oman 11/1996 12/2008 146 7.653 4.740 -0.252 0.277

Pakistan 01/1989 12/2008 240 3.463 9.774 -0.507 0.345

Romania 10/1997 12/2008 135 -1.314 14.975 -0.512 0.341

Saudi Arabia 01/1998 01/2008 121 15.018 5.414 -0.227 0.171

Slovenia 01/1994 12/2008 180 5.677 5.687 -0.273 0.244

Sri Lanka 10/1990 12/2008 219 1.228 5.465 -0.239 0.202

Trinidad and

Tobago

01/1996 02/2008 145 12.995 1.848 -0.090 0.151

Tunisia 01/1998 12/2008 132 7.141 1.456 -0.162 0.142

Ukraine 02/1998 02/2008 121 15.176 18.846 -0.542 0.861

United Arab

Emirates

06/2005 02/2008 33 -3.410 16.095 -0.291 0.271

25

Table 2. The degree of global market integration

We present the coefficients of the first principal component and their t-statistics and adjusted R-

squared of the principal component regression. We regress dollar-denominated index returns on ten

global factors, which are estimated by out-of-sample based on the covariance matrix in the previous

calendar year computed with the returns from 17 major countries, the “pre-1974 cohort” present on

DataStream in 1973 and remaining present every year thereafter. The first principal component

captures the global factor as described in Pukthuanthong and Roll (2009). Coefficients are multiplied by

10^3 in order to show detail. The final four columns report cross-index correlations of daily returns for

each sub-sample.

Index PC1

Adjusted

R2

MSCI All

Country

MSCI

Developed

MSCI

Emerging

Value-

weighted

frontier

index

Panel A: 1989 - 2007

MSCI Developed 1.7620

(0.000) 0.5528

0.9860

(0.000) - - -

MSCI Emerging 1.9950

(0.000) 0.3974

0.5484

(0.000)

0.5110

(0.000) - -

Value-weighted frontier

index

0.0315

(0.560) -0.0003

0.0135

(0.345)

0.0175

(0.220)

-0.0103

(0.473) -

Equal-weighted frontier

index

0.0758

(0.009) 0.0045

0.0313

(0.028)

0.0324

(0.023)

0.0323

(0.024)

0.6253

(0.000)

Panel B: Sub-sample 1 (1989-1999)


(0.000) 0.5578

0.9764

(0.000) - - -


(0.000) 0.2993

0.5017

(0.000)

0.4716

(0.000) - -


index

0.0089

(0.908) -0.0013

0.0047

(0.804)

0.0110

(0.557)

-0.0171

(0.364) -


index

0.0768

(0.137) 0.0072

0.0212

(0.259)

0.0256

(0.174)

0.0116

(0.536)

0.7184

(0.000)

Panel C: Sub-sample 2 (2000-2007)


(0.000) 0.6983

0.9956

(0.000) - - -


(0.000) 0.5664

0.6047

(0.000)

0.5585

(0.000) - -


index

0.0518

(0.512) 0.0004

0.0274

(0.213)

0.0282

(0.199)

0.0006

(0.980) -


index

0.0816

(0.013) 0.0000

0.0559

(0.011)

0.0516

(0.019)

0.0760

(0.001)

0.4067

(0.000)

26

Panel D: Sub-sample 1 (1989-1993)


(0.000) 0.6332

0.9570

(0.000) - - -


(0.000) 0.1994

0.3896

(0.000)

0.3787

(0.000) - -


index

0.0674

(0.553) 0.0036

0.0178

(0.524)

0.0295

(0.291)

-0.0283

(0.311) -


index

0.1220

(0.203) 0.0136

0.0130

(0.640)

0.0205

(0.464)

-0.0274

(0.327)

0.8421

(0.000)

Panel E: Sub-sample 2 (1994-1998)


(0.000) 0.7099

0.9964

(0.000) - - -


(0.000) 0.4243

0.6226

(0.000)

0.5684

(0.000) - -


index

0.0017

(0.990) -0.0068

-0.0115

(0.679)

-0.0084

(0.762)

-0.0204

(0.464) -


index

0.0470

(0.485) 0.0014

0.0358

(0.199)

0.0366

(0.189)

0.0514

(0.065)

0.6231

(0.000)

Panel F: Sub-sample 3 (1999-2003)


(0.000) 0.6594

0.9979

(0.000) - - -


(0.000) 0.4353

0.5426

(0.000)

0.5094

(0.000) - -


index

0.1740

(0.048) 0.0040

0.0556

(0.046)

0.0526

(0.058)

0.0616

(0.027) -


index

0.0601

(0.152) -0.0023

0.0445

(0.110)

0.0408

(0.143)

0.0932

(0.001)

0.3948

(0.000)

Panel G: Sub-sample 4 (2004-2007)


(0.000) 0.7317

0.9902

(0.000) - - -


(0.000) 0.7182

0.7411

(0.000)

0.6769

(0.000) - -


index

-0.1410

(0.316) 0.0101

-0.0279

(0.369)

-0.0223

(0.474)

-0.0640

(0.039) -


index

0.0821

(0.063) 0.0090

0.0680

(0.028)

0.0634

(0.041)

0.0464

(0.135)

0.4141

(0.000)

27

Table 3. World market integration through time

We present regression of adjusted R-square from principal component model on time. First, we regress

daily dollar-dominated index returns on ten global factors, which have been estimated by out-of-sample

components based on the covariance matrix in the previous calendar year computed with the returns

from 17 major countries i.e., the “pre-1974” described in Pukthuanthong and Roll (2009). We fit the

result monthly R-squares for each index to a simple linear time trend for all illustrated years. The time

trend slope coefficients and p-values are given underneath the ‘PC’ heading. Comparable results from

regressing simple daily return correlations for the given index with the MSCI all country world index, on

a time trend are presented underneath the ‘Correlation’ heading. In Panel A we present results for the

entire sample based on six-month regressions. In the remaining panels we present results based on

bimonthly regressions for the given sample period. Comparably, results in Panel A are based on six-

month correlation estimates, while the remaining correlation anslyses are based on bimonthly

correlations of daily returns.

PC Correlation

Index Time Adjusted R2 Time Adjusted R2

Panel A: 1989 - 2007

MSCI Developed 2.03*10-3

(0.003) 0.2069

6.94*10-4

(0.178) 0.0235

MSCI Emerging 1.90*10-2

(0.000) 0.7053

1.16*10-2

(0.000) 0.399

Value-weighted frontier index -3.60*10-4

(0.375) 0.0003

3.83*10-4

(0.800) -0.026

Equal-weighted frontier index -6.64*10-5

(0.886) -0.0272

2.43*10-3

(0.111) 0.043

Panel B: 1989 – 2007


(0.012) 0.0568

5.90*10-5

(0.535) -0.0055


(0.000) 0.4866

3.92*10-3

(0.000) 0.2926


(0.858) -0.0086

7.76*10-5

(0.857) -0.0086


(0.553) -0.0055

5.42*10-4

(0.255) 0.0027

Panel C: Sub-sample 1 (1989-1999)


(0.010) 0.0599

3.81*10-4

(0.118) 0.0228


(0.005) 0.1142

5.53*10-3

(0.001) 0.1591


(0.516) -0.0071

1.82*10-4

(0.866) -0.0152

Equal-weighted frontier index 5.96*10-4

(0.612) -0.0110

9.29*10-4

(0.395) -0.0041

28

Table 3 (cont’d).

Panel D: Sub-sample 2 (2000-2007)

MSCI Developed -3.69*10-4

(0.660) -0.0174

-3.56*10-4

(0.202) 0.0142


(0.000) 0.3717

5.17*10-3

(0.001) 0.2165


(0.339) -0.0018

-1.71*10-3

(0.203) 0.0140


(0.918) -0.0215

2.08*10-3

(0.236) 0.0093

Panel E: Sub-sample 1 (1989 – 1993)


(0.154) 0.0544

1.25*10-3

(0.290) 0.0057

MSCI Emerging -1.07*10-3

(0.854) -0.0345

1.17*10-3

(0.843) -0.0342


(0.852) -0.0337

4.36*10-3

(0.240) 0.0151


(0.661) -0.0274

4.27*10-3

(0.233) 0.0165

Panel F: Sub-sample 2 (1994-1998)


(0.003) 0.0844

4.51*10-4

(0.006) 0.2117


(0.004) 0.2392

8.81*10-3

(0.034) 0.1204

Value-weighted frontier index 6.34*10-4

(0.847) -0.0341

3.12*10-3

(0.373) -0.0062


(0.021) 0.0720

7.03*10-3

(0.043) 0.1082

Panel G: Sub-sample 3 (1999-2003)


(0.011) 0.1203

-1.25*10-4

(0.086) 0.0693


(0.002) 0.2605

-1.38*10-3

(0.673) -0.0290

Value-weighted frontier index 3.06*10-4

(0.934) -0.0353

2.48*10-3

(0.396) -0.0089


(0.818) -0.0340

4.76*10-4

(0.893) -0.0350

Panel H: Sub-sample 4 (2004-2007)


(0.644) -0.0436

-4.32*10-5

(0.969) -0.0454


(0.000) 0.4180

8.86*10-3

(0.014) 0.2108


(0.973) -0.0454

-3.35*10-3

(0.338) -0.0018


(0.500) -0.0129

8.70*10-3

(0.100) 0.0782

29

Table 4. Frontier market variance decomposition

Table presents results from the variance decomposition using the MSCI developed index and our value

weighted frontier market index as the two factors. With the Chen and Ho (2009) paper as a reference,

the developed index is comparable to their use of the CRSP market index and the frontier market index

is comparable to their use of each size and book/market portfolio. First and last refer to the data

availability for each country. Variance is the overall variance for the country’s return. The final three

columns present the percentage of the overall variance accounted for by the developed market, frontier

market and idiosyncratic component, respectively.

Country Variance

Developed market

proportion

Frontier market

proportion

Idiosyncratic

proportion

Argentina 0.0151 0.2285 0.0400 0.7315

Bahrain 0.0013 0.0828 0.0621 0.8551

Botswana 0.0037 0.0211 0.0183 0.9606

Bulgaria 0.0138 0.2845 0.0986 0.6169

Croatia 0.0105 0.2906 0.0993 0.6100

Estonia 0.0128 0.0998 0.0567 0.8435

Ghana 0.0029 0.0098 0.0167 0.9734

Jamaica 0.0072 0.0008 0.0038 0.9954

Jordan 0.0029 0.0497 0.0886 0.8617

Kenya 0.0069 0.0497 0.0333 0.9170

Kuwait 0.0025 0.0454 0.0617 0.8930

Lebanon 0.0555 0.0489 0.0275 0.9236

Lithuania 0.0073 0.3140 0.0881 0.5979

Maurtius 0.0027 0.0009 0.0400 0.9591

Nigeria 0.0047 0.0024 0.0022 0.9954

Oman 0.0047 0.0518 0.0458 0.9024

Pakistan 0.0098 0.0091 0.0573 0.9336

Romania 0.0150 0.0963 0.1498 0.7539

Saudi Arabia 0.0054 0.0079 0.2320 0.7600

Slovenia 0.0057 0.0865 0.4730 0.4405

Sri Lanka 0.0055 0.0440 0.0796 0.8764

Trinidad and

Tobago

0.0018 0.0001 0.0051 0.9948

Tunisia 0.0015 0.0342 0.0265 0.9393

Ukraine 0.0188 0.0390 0.0192 0.9418

United Arab

Emirates

0.0161 0.0028 0.0919 0.9052

30

Table 5. Frontier market correlation

Entries within the table represent correlations across frontier market country and index returns, with

the Fama and French US market portfolio, the MSCI Developed market portfolio, the MSCI Emerging

market portfolio and our Value-weighted frontier market index.

US Developed Emerging Frontier

Value-weighted

Frontier Index

0.2590

(0.000)

0.3085

(0.000)

0.3325

(0.000) -

Equal-weighted

Frontier Index

0.3757

(0.000)

0.4245

(0.000)

0.5024

(0.000)

0.7245

(0.000)

Argentina 0.449

(0.000)

0.4780

(0.000)

0.5664

(0.000)

0.3668

(0.000)

Bahrain 0.2357

(0.020)

0.2877

(0.004)

0.3769

(0.000)

0.3003

(0.003)

Botswana 0.1247

(0.135)

0.1453

(0.081)

0.1790

(0.031)

0.1587

(0.057)

Bulgaria 0.4657

(0.000)

0.5333

(0.000)

0.5700

(0.000)

0.5260

(0.000)

Croatia 0.5320

(0.000)

0.5391

(0.000)

0.6017

(0.000)

0.4984

(0.000)

Estonia 0.2776

(0.001)

0.3159

(0.000)

0.3919

(0.000)

0.3409

(0.000)

Ghana -0.1210

(0.147)

-0.0991

(0.236)

-0.0589

(0.481)

0.1099

(0.188)

Jamaica -0.0089

(0.917)

-0.0288

(0.733)

-0.0072

(0.932)

0.0552

(0.513)

Jordan 0.2123

(0.001)

0.2229

(0.001)

0.2004

(0.002)

0.3519

(0.000)

Kenya 0.1692

(0.011)

0.2229

(0.001)

0.1991

(0.003)

0.2432

(0.000)

Kuwait 0.2016

(0.009)

0.2130

(0.006)

.2363

(0.002)

0.3082

(0.000)

Lebanon 0.2436

(0.241)

0.2210

(0.288)

0.3213

(0.117)

0.1886

(0.367)

Lithuania 0.4916

(0.000)

0.5603

(0.000)

0.6089

(0.000)

0.5170

(0.000)

Maurtius -0.0131

(0.877)

0.0296

(0.727)

0.1147

(0.176)

0.2022

(0.016)

Nigeria 0.0532

(0.515)

0.0492

(0.548)

0.1320

(0.105)

0.0544

(0.506)

Oman 0.2133

(0.010)

0.2277

(0.006)

0.2674

(0.001)

0.2844

(0.001)

Pakistan 0.1134

(0.080)

0.0954

(0.141)

0.2396

(0.000)

0.2571

(0.000)

Romania 0.2686

(0.002)

0.3104

(0.000)

0.5053

(0.000)

0.4780

(0.000)

31

Table 5 (cont’d).

Saudi Arabia 0.0845

(0.357)

0.0891

(0.331)

0.1686

(0.065)

0.4898

(0.000)

Slovenia 0.2330

(0.002)

0.2726

(0.000)

0.2726

(0.000)

0.7478

(0.000)

Sri Lanka 0.2030

(0.003)

0.2098

(0.002)

0.3715

(0.000)

0.3340

(0.000)

Trinidad and

Tobago

0.0098

(0.907)

-0.0108

(0.897)

-0.0914

(0.274)

-0.0721

(0.389)

Tunisia 0.1394

(0.111)

0.1850

(0.034)

0.1108

(0.206)

0.2244

(0.010)

Ukraine 0.1600

(0.080)

0.1974

(0.030)

0.3117

(0.001)

0.1744

(0.056)

United Arab

Emirates

0.0406

(0.823)

0.0534

(0.768)

0.0098

(0.957)

0.3078

(0.081)

32

Table 6. Mean-variance spanning tests

We present results from mean-variance spanning tests for our sample of broad frontier market

indices and country-specific frontier market indices. We use OLS to estimate the following model

�� = � + �� + ��,

Where �� represents the test asset return and �� represents the return of the K benchmark

portfolios. We define K to include the Fama-French US market portfolio, the MSCI developed market

index and the MSCI emerging market index in the second through fourth columns. In the fifth through

seventh columns, we expand K to also include our Value-weighted Frontier market index. Entries in

the table correspond to Wald-statistics and associated p-values for each test. Spanning tests the joint

restrictions that � = 0 and � ≡ 1 − �1� = 0. In the event we reject Spanning at the 10% level, we

present step-down tests to determine the source of rejection. Tangency tests the hypothesis � = 0

and indicates whether the two tangency portfolios are statistically different. GMV tests the

hypothesis � ≡ 1 − �1� = 0, conditional on � = 0, and indicates whether the global minimum

variance portfolios differ. The sample is monthly from January 1989 through December 2008.

% = &�'(, �)*+ , �*,*-.′ % = 0�'(, �)*+ , �*,*-,�-12�3′ Test Asset Spanning Tangency GMV Spanning Tangency GMV

Value-weighted

Frontier Index

18.65

(0.000)

0.81

(0.367)

17.85

(0.000)

- - -

Equal-weighted

Frontier Index

41.23

(0.000)

1.67

(0.196)

39.44

(0.000)

- - -

Argentina 34.08

(0.000)

0.16

(0.692)

34.08

(0.000)

39.41

(0.000)

0.37

(0.541)

39.17

(0.000)

Bahrain 9.43

(0.009)

4.69

(0.030)

4.56

(0.033)

13.33

(0.001)

2.86

(0.091)

10.27

(0.001)

Botswana 13.68

(0.001)

10.99

(0.001)

2.51

(0.113)

15.35

(0.001)

9.75

(0.002)

5.28

(0.022)

Bulgaria 20.58

(0.000)

3.59

(0.058)

16.54

(0.000)

30.35

(0.000)

2.26

(0.133)

27.72

(0.000)

Croatia 34.52

(0.000)

0.28

(0.597)

34.41

(0.000)

55.83

(0.000)

0.07

(0.797)

56.14

(0.000)

Estonia 8.99

(0.011)

1.18

(0.277)

7.80

(0.005)

14.55

(0.001)

0.86

(0.354)

13.70

(0.000)

Ghana 1.64

(0.440)

- - 0.56

(0.758)

- -

Jamaica 1.56

(0.459)

- - 1.16

(0.561)

- -

Jordan 14.82

(0.001)

2.61

(0.106)

12.13

(0.001)

31.10

(0.000)

1.97

(0.160)

29.01

(0.000)

Kenya 7.85

(0.020)

0.06

(0.814)

7.83

(0.005)

13.64

(0.001)

0.00

(0.984)

13.70

(0.000)

Kuwait 10.33

(0.006)

5.07

(0.024)

5.13

(0.024)

16.80

(0.000)

4.42

(0.036)

12.12

(0.001)

Lebanon 0.50

(0.777)

- - 0.59

(0.743)

- -

Lithuania 29.14

(0.000)

3.81

(0.051)

24.67

(0.000)

39.82

(0.000)

2.86

(0.091)

36.32

(0.000)

33

Table 6 (cont’d).

% = &�'(, �)*+ , �*,*-.′ % = 0�'(, �)*+ , �*,*-,�-12�3′ Test Asset Spanning Tangency GMV Spanning Tangency GMV

Maurtius 7.49

(0.024)

7.43

(0.006)

0.05

(0.816)

8.38

(0.015)

6.11

(0.013)

2.18

(0.140)

Nigeria 11.52

(0.003)

11.37

(0.001)

0.15

(0.702)

11.34

(0.004)

10.80

(0.001)

0.50

(0.480)

Oman 5.70

(0.058)

1.74

(0.187)

3.94

(0.047)

9.81

(0.007)

1.37

(0.241)

8.41

(0.004)

Pakistan 0.83

(0.661)

- - 4.88

(0.087)

0.00

(0.979)

4.90

(0.027)

Romania 2.08

(0.354)

- - 10.67

(0.005)

0.13

(0.721)

10.61

(0.001)

Saudi Arabia 4.43

(0.109)

- - 16.32

(0.000)

1.31

(0.253)

14.97

(0.000)

Slovenia 15.28

(0.001)

1.88

(0.170)

13.33

(0.000)

105.84

(0.000)

1.10

(0.294)

104.68

(0.000)

Sri Lanka 3.83

(0.148)

- - 10.60

(0.005)

0.05

(0.820)

10.60

(0.001)

Trinidad and

Tobago

11.59

(0.003)

11.29

(0.001)

0.28

(0.598)

11.70

(0.003)

11.54

(0.001)

0.15

(0.699)

Tunisia 11.47

(0.003)

6.39

(0.012)

4.89

(0.027)

14.32

(0.001)

5.60

(0.018)

8.41

(0.004)

Ukraine 2.77

(0.250)

- - 3.57

(0.167)

- -

United Arab

Emirates

0.20

(0.903)

- - 1.31

(0.520)

- -

34

Table 7. Mean-variance spanning across sub-samples and levels of benchmark performance.

We present results from mean-variance spanning tests for our sample of broad frontier market indices.

We use OLS to estimate the following model

�� = � + �� + ��,

Where �� represents the test asset return and �� represents the return of the K benchmark portfolios.

We define K to include the Fama-French US market portfolio, the MSCI developed index and the MSCI

emerging market index. Entries in the table correspond to Wald-statistics and associated p-values for

each test. Spanning tests the joint restrictions that � = 0 and � ≡ 1 − �1� = 0. In the event we reject

Spanning at the 10% level, we present step-down tests to determine the source of rejection. Tangency

tests the hypothesis � = 0 and indicates whether the two tangency portfolios are statistically different.

GMV tests the hypothesis � ≡ 1 − �1� = 0, conditional on � = 0, and indicates whether the global

minimum variance portfolios differ. The sample is monthly from January 1989 through December 2008.

We split the overall sample into four equal test-periods identified in the initial column The test assets

are defined as the Value-weighted, and Equal-weighted, Frontier indices in Panels A and B Respectively.

In Panels C and D, we construct an equal-weighted index of our three benchmark portfolios, and sort

observations based on quartiles of the index’s performance.

Sample period Spanning Tangency GMV

Panel A: Value-weighted Frontier Index and sub-sample analysis

01:1989-12:1993 2.07

(0.356)

1.16

(0.282)

0.90

(0.342)

01:1994-12:1998 5.24

(0.073)

0.06

(0.810)

5.27

(0.022)

01:1999-12:2003 7.54

(0.023)

5.74

(0.017)

1.66

(0.197)

01:2004-12:2008 15.13

(0.001)

0.61

(0.434)

14.62

(0.000)

Panel B: Equal-weighted Frontier Index and sub-sample analysis

01:1989-12:1993 1.67

(0.434)

0.37

(0.544)

1.32

(0.251)

01:1994-12:1998 7.38

(0.025)

0.46

(0.496)

6.99

(0.008)

01:1999-12:2003 9.68

(0.008)

5.84

(0.016)

3.54

(0.060)

01:2004-12:2008 56.90

(0.000)

2.54

(0.111)

52.93

(0.000)

35

Table 7 (cont’d).

Benchmark

Performance Spanning Tangency GMV

Panel A: Value-weighted Frontier Index

1st

Quartile 12.35

(0.002)

6.91

(0.009)

4.93

(0.026)

2nd

Quartile 3.61

(0.164)

3.20

(0.074)

0.40

(0.529)

3rd

Quartile 2.97

(0.226)

1.02

(0.313)

1.95

(0.162)

4th Quartile 4.87

(0.088)

0.07

(0.798)

4.88

(0.027)

Panel B: Equal-weighted Frontier Index

1st

Quartile 23.39

(0.000)

12.84

(0.000)

8.84

(0.003)

2nd

Quartile 3.03

(0.219)

1.36

(0.244)

1.67

(0.197)

3rd

Quartile 9.93

(0.007)

1.22

(0.269)

8.67

(0.003)

4th Quartile 18.96

(0.000)

1.68

(0.195)

17.07

(0.000)

36

Table 8. Diversification benefits based on ETFs.

We present international portfolio return and standard deviation statistics. Portfolios are formed with Exchange traded funds in which EEM

represents the MSCI Emerging markets index ETF, FRNMX represents the frontier market ETF, SPY represents the S&P500 ETF, and VEU

represents the FTSE All-World ex US ETF. ETF characteristics are reported in Panel A for the given samples. In Panel B, portfolio characteristics

are reported for various weighting schemes across the ETFs considered. Specifically, Equal- No represents an equal weighting scheme across the

EEM, SPY and VEU ETFs, Equal- Yes represents the inclusion of the frontier market ETF in which equal weights are assigned to all four ETFs,

Developed- No represents an allocation shifted towards developed markets with 50% in the SPY, 30% in VEU and the remaining 20% in EEM and

finally, Developed- Yes represents an allocation shifted towards developed markets that also includes frontier markets with an allocation of 17%,

9%, 47% and 27% across EEM, FRNMX, SPY and VEU, respectively. Statistics are presented in decimal form.

01/08/2009 – 11/24/2009 01/08/2009 – 03/09/2009

Panel A: ETF risk-return statistics

Annualized Holding

Period Return σ

Annualized Holding

Period Return σ

EEM 0.6364 0.4037 -0.1864 0.5570

FRNMX 0.1425 0.2566 -0.1870 0.4414

SPY 0.2407 0.2765 -0.2518 0.3704

VEU 0.3678 0.3476 -0.2740 0.4759

Panel B: Risk-return statistics across portfolio weights

Equal- No 0.4104 0.3352 -0.2374 0.4586

Equal- Yes 0.3536 0.2734 -0.2205 0.3647

Developed- No 0.3545 0.3161 -0.2452 0.4308

Developed- Yes 0.3353 0.2919 -0.2390 0.3922

37

Fig 1: Indicators of global market integration by index returns from January 1989 to December 2007. Our measure of market integration is the adjusted R-square from a regression of country index returns on global factors. Plotted here are 6-month adjusted R-squares estimated for each index. We regress daily dollar-denominated index returns on 10 global factors, which are estimated by out-of-sample principal components based on the covariance matrix in the previous calendar year computed with the returns from 17 major countries, the “pre-1974 cohort” present on DataStream in 1973 and remaining present every year thereafter. FIV is value-weighted frontier index; FIE is equal-weighted frontier index; ERET is MSCI emerging market index; and WRET is MSCI developed market index

-0.2

0

0.2

0.4

0.6

0.8

1

FIV FIE ERET WRET

38

Fig 2: Indicators of global market integration by index returns from January 1989 to December 2007. Our measure of market integration is the adjusted R-square from a regression of country index returns on global factors. Plotted here are bimonthly adjusted R-squares estimated for each index. We regress daily dollar-denominated index returns on 10 global factors, which are estimated by out-of-sample principal components based on the covariance matrix in the previous calendar year computed with the returns from 17 major countries, the “pre-1974 cohort” present on DataStream in 1973 and remaining present every year thereafter. FIV is value-weighted frontier index; FIE is equal-weighted frontier index; ERET is MSCI emerging market index; and WRET is MSCI developed market index

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Tim

e

Au

g-8

9

Ap

r-9

0

De

c-9

0

Au

g-9

1

Ap

r-9

2

De

c-9

2

Au

g-9

3

Ap

r-9

4

De

c-9

4

Au

g-9

5

Ap

r-9

6

De

c-9

6

Au

g-9

7

Ap

r-9

8

De

c-9

8

Au

g-9

9

Ap

r-0

0

De

c-0

0

Au

g-0

1

Ap

r-0

2

De

c-0

2

Au

g-0

3

Ap

r-0

4

De

c-0

4

Au

g-0

5

Ap

r-0

6

De

c-0

6

Au

g-0

7

FIV FIE ERET WRET

39

Fig 3: Short sale is allowed. Portfolio 1 includes the U.S. market, the MSCI Developed Index, and the MSCI Emerging Market Index. Portfolio 2 includes the U.S. market, the MSCI Developed Index, the MSCI Emerging Market Index, and the Value Weighted Frontier Market Index. Portfolio 3 includes the U.S. market, the MSCI Developed Index, the MSCI Emerging Market Index, and the Equally Weighted Frontier Market Index.

Fig 4: Short sale is prohibited. Portfolio 1 includes the U.S. market, the MSCI Developed Index, and the MSCI Emerging Market Index. Portfolio 2 includes the U.S. market, the MSCI Developed Index, the MSCI Emerging Market Index, and the Value Weighted Frontier Market Index. Portfolio 3 includes the U.S. market, the MSCI Developed Index, the MSCI Emerging Market Index, and the Equally Weighted Frontier Market Index.

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.11 0.12 0.13 0.14 0.15 0.16 0.17

Ex

pe

cte

d R

etu

rn

Standard Deviation

Mean-Variance Frontier

Portfolio 1

Portfolio 2

Portfolio 3

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

0.11 0.115 0.12 0.125 0.13 0.135 0.14 0.145 0.15 0.155

Ex

pe

cte

d R

etu

rn

Standard Deviation

Mean-Variance Frontier

Portfolio 1

Portfolio 2

Portfolio 3

international diversification with frontier markets annual... · market classifications. they focus...

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