International diversification with frontier markets

Transcription

1 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

2 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 Recently, frontier market mutual funds and exchange-traded funds (ETFs) have also been developed 1. 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 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, The Deutsche Bank launched the first frontier market ETF in Europe in early The Bank of New York Mellon created its frontier market ETF in June

3 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) 3

4 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. 4

5 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 minimumvariance 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 5

6 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. 6

7 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 7

8 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 data 2. 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. 8

9 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 1 st 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. ***Insert Table 2 about here*** 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 and for the frontier value-weighted and equal-weighted indices, respectively. The corresponding values are and 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 9

10 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 subsample 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. 10

11 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 subsample 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, 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 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 11

12 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. ***Insert Table 3 about here*** 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 subsample 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 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 12

13 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 timetrend 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 13

14 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. ***Insert Table 4 about here*** 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 14

15 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 15

16 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. ***Insert Table 5 about here*** In our study, we analyze the diversification benefits of broad frontier indices, as well as countryspecific 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 16

17 frontier market country. Tests based on the broad frontier indices cover the sample period from January 1989 through December 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. ***Insert Table 6 about here*** The spanning tests across our entire sample provide evidence that frontier market equities improve portfolio performance. The statistics of and 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 17

18 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. ***Insert Table 7 about here*** 18

19 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 and 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 19

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. ***Insert Table 8 about here*** 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 20

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.. 21

22 References Baele, Lieven, and Koen Inghelbrecht, 2009, Time-varying integration and international diversification strategies, Journal of Empirical Finance, 16, Bekaert, Geert, Robert J. Hodrick, and Xiaoyan Zhang, 2009, International stock return comovements, Journal of Finance, 64, Bekaert, Geert, Campbell R. Harvey, 1995, Time-varying world market integration, Journal of Finance, 50, Bekaert, Geert, Campbell R. Harvey, and Robin L. Lumsdaine, 2002, Dating the integration of world equity markets, Journal of Financial Economics, 65, Bekaert, Geert and Michael S. Urias, 1996, Diversification, integration and emerging market closed-end funds, Journal of Finance, 51, Carrieri, Francesca, Vihang Errunza and Ked Hogan, 2007, Characterizing world market integration through time, Journal of Financial and Quantitative Analysis, 42, Chen, Hsuan-Chi, and Keng-Yu Ho, 2009, Do IPO index portfolios improve the investment opportunities for mean-variance investors? Finance Research Letters, 6, Cheng, Ai-Ru, Mohammad R., Jahan-Parvar, and Philip Rothman, 2009, An empirical investigation of stock market behavior in the Middle East and North Africa, Journal of Empirical Finance, accepted manuscript. De Roon, Frans A., Theo E. Nijman and Bas J. M. Werker, 2001, Testing for mean-variance spanning with short sales constraints and transaction costs: The case of emerging markets, Journal of Finance, 56, Driessen, Joost, and Luc Laeven, 2007, International portfolio diversification benefits: Cross-country evidence from a local perspective, Journal of Banking and Finance, 31, Eun, Cheol S., Wei Huang, and Sandy Lai, 2008, International diversification with large- and small-cap stocks, Journal of Financial and Quantitative Analysis, 43, Huberman, Gur, and Shmuel Kandel, 1987, Mean-variance spanning, Journal of Finance, 42, Jayasuriya, Shamila A., and William Shambora, 2009, Oops, we should have diversified! Applied Financial Economics, 19, Odier, Patrick and Bruno Solnik, 1993, Lessons for international asset allocation, Financial Analysts Journal, 49, Pukthuanthong, Kuntara and Richard Roll, 2009, Global market integration: An alternative measure and its application, Journal of Financial Economics, 94,

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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/ / Bahrain 01/ / Botswana 01/ / Bulgaria 11/ / Croatia 01/ / Estonia 06/ / Ghana 01/ / Jamaica 01/ / Jordan 01/ / Kenya 02/ / Kuwait 01/ / Lebanon 04/ / Lithuania 01/ / Maurtius 01/ / Nigeria 07/ / Oman 11/ / Pakistan 01/ / Romania 10/ / Saudi Arabia 01/ / Slovenia 01/ / Sri Lanka 10/ / Trinidad and Tobago 01/ / Tunisia 01/ / Ukraine 02/ / United Arab Emirates 06/ /

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. Valueweighted frontier index Index PC1 Adjusted R 2 MSCI All Country MSCI Developed MSCI Emerging Panel A: MSCI Developed MSCI Emerging Value-weighted frontier index (0.560) (0.345) (0.220) (0.473) - Equal-weighted frontier index (0.009) (0.028) (0.023) (0.024) Panel B: Sub-sample 1 ( ) MSCI Developed MSCI Emerging Value-weighted frontier index (0.908) (0.804) (0.557) (0.364) - Equal-weighted frontier index (0.137) (0.259) (0.174) (0.536) Panel C: Sub-sample 2 ( ) MSCI Developed MSCI Emerging Value-weighted frontier index (0.512) (0.213) (0.199) (0.980) - Equal-weighted frontier index (0.013) (0.011) (0.019)