Do ETFs provide effective international diversification?

Research in International Business and Finance 25 (2011) 335–344

Contents lists available at ScienceDirect

Research in International Business and Finance j o ur na l ho me pa ge : w w w . e l s e v i e r . c o m / l o c a t e / r i b a f

Do ETFs provide effective international diversification? Mei-Yueh Huang a, Jun-Biao Lin b,∗ a b

Department of Industrial Management, Lunghwa University of Science and Technology, Taiwan Department of Money and Banking, National Kaohsiung First University of Science and Technology, Taiwan

a r t i c l e

i n f o

Article history: Received 31 March 2010 Received in revised form 21 March 2011 Accepted 25 March 2011 Available online 9 April 2011 JEL classification: C16 G11 G15 Keywords: Bootstrap Value at Risk Efficient frontier Exchange Traded Fund

a b s t r a c t Global investments have been a hot issue for years. Investors can diversify risks and obtain benefits from foreign markets by investing directly in the foreign security market or indirectly in Exchange-Trade Funds (ETFs). Because direct investments are not always feasible, we investigate whether indirect investments can replace direct investments. We create different regional optimal portfolios containing ETFs and ensure optimal asset portfolio allocation. In addition to mean-variance approach, the Sharpe index, we also adopt the Campbell et al. (2001) method to have the efficient frontier under control risks, the Value at Risk. We apply both normal and non-normal distributions for comparisons and find that different assumptions of return distributions affect the results of efficient frontier. The results show that international diversification is a reasonable strategy. In addition, when comparing ETFs and target market index portfolios, ETFs have higher Sharpe measures than target market indices especially in the emerging markets. However, there are no significant performance differences between direct and indirect methods even if we use different performance measures. We also find that the diversification benefits are the same before and after the Subprime crisis. We conclude that it is effective for investors to use indirect methods to create internationally diversified portfolios. © 2011 Elsevier B.V. All rights reserved.

1. Introduction Although Grubel (1968), Levy and Sarnat (1970), Solink (1974) and Lessard (1976) established the benefits of international diversification some time ago, it has only been in recent years that ∗ Corresponding author. Tel.: +886 7 6011000x3121. E-mail addresses: [email protected], [email protected] (J.-B. Lin). 0275-5319/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.ribaf.2011.03.003

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multinational investments have gradually begun to prevail. This is because investors can now obtain information more easily, most nations have removed investment barriers, and the diversification concept of multinational investment has become popular. There are several ways for investors to access other countries’ capital markets: direct investments in local markets, purchasing depositary receipts and investing in international mutual funds. The former one is usually known as direct investment and the last two are indirect. Investors who invest directly in foreign markets need to fully understand local market circumstances, including trading mechanisms, constraints and the market prospects. As it is generally difficult and time consuming for investors to obtain this information, investing in depositary receipts or international mutual funds is an easier option. Literatures have shown a lot about the benefits of indirect international portfolio diversification (Rowland and Tesar, 2004; Tsai and Swanson, 2009; Berrill, 2010; Berril and Kearney, 2010). However, although past empirical results seem promising for U.S. investors, recent studies argue that even if indirect international diversification may bring benefits, investors prefer investing in their home country to foreign opportunities. This is what we call “home bias puzzle”. Possible explanations for the home bias puzzle are provided by Amadi (2004) and Berril and Kearney (2010). A relatively new product, the Exchange Traded Fund (ETF) became available in the early 1990s, providing an alternative method of investing indirectly in international equities. ETFs are similar to mutual funds in that the market value is close to their net asset value (NAV). They are different from mutual funds in that ETFs are baskets of securities that trade on exchanges like individual stocks. They can hold stocks, bonds, commodities, gold and can include dozens, hundreds, or even thousands of companies under one umbrella unified by a particular investing theme. ETFs are designed to closely mirror indexes such as the S&P 500. As a stock, ETFs can be optioned, shorted, hedged, and bundled. ETFs are superior to active mutual funds for many reasons: they have lower fees on average, intraday liquidity, transparency and tax efficiency.1 The ETF has experienced a meteoric rise since inception. There are now over 1000 ETFs traded around the world,2 representing a value of over $800 million which is 994 times more than the value of ETFs in 1993. Deborah Fuhr, a world expert on ETFs has predicted that the global ETF market will grow to $2 trillion by the end of 2011 (Turner, 2008). In the literature, only a few studies concern ETFs. Pennathur et al. (2002) examine the performance and diversification of iShares3 and their rival closed-end funds. They find that iShares provide some diversification effect based on the single-index model. However, when the “true” diversifications are isolated, there is no difference between direct and indirect foreign investments. Poterba and Shoven (2002) compare returns of SPDR4 and Vanguard 500 Index Fund (VFINX).5 They argue that the tax returns before and after are similar for these two products. This implies that investors can reduce tax costs by holding ETFs. Doran et al. (2006) prove by using cash flow analysis that investors prefer ETFs to mutual funds. Since ETFs have become more and more popular with investors, this paper will examine whether these international investments provide a cost-effective benefit to them. Tsai and Swanson (2009) show that ETFs provide U.S. investors greater diversification benefits than do country funds. In this paper, one of our purposes is to investigate whether there is a significant difference between direct and indirect investments. Instead of using the single index model or multiple index models as in the previous studies to examine the diversification effect, in this paper, we adopt Chou’s (1997) concept to test the relative efficiency between two sets of securities. Our results show that international diversification provides higher returns and lower risks. Diversified portfolios that consist of S&P 500 and the different foreign markets have better performance than those invested only in the S&P 500, regardless of the occurrence

1 Basically, an ETF does not require a fund manager to manage the portfolio. Therefore, the management fee is low. In addition, if the components of the index are relatively stable, it is obvious that costs from the frequent trade of individual stocks such as taxes and service charges are effectively reduced. 2 Reports from NYSE show that there were 797 ETFs listed in the US market space at the end of February 2009 and 698 ETFS in Europe at the end of 2008. See the following website for more details http://www.nyse.com/pdfs/Fact sheet ETFs.pdf. 3 iShares are a series of ETFs that track the MSCI foreign stock market indices. 4 SPDR is the first traded ETF in AMEX. 5 Vanguard 500 Index Fund is the earliest index mutual fund in the world.

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of the Subprime crisis. Our results are consistent with those reported by Levy and Sarnat (1970), Meric and Meric (1989), Harvey (1995), Solnik et al. (1996) and Goetzmann and Jorion (1999). International diversification is therefore, a reasonable strategy. In addition, our evidence also indicates that when direct or indirect investments are used to form portfolios, indirect investments have higher Sharpe measures than direct investments for all Sharpe measures. However, although the performances are different, our results show that there is no significant difference between direct and indirect investments for different markets. This implies that investors can obtain the same expected returns through ETFs instead of investing in market indices. The diversified benefits from ETFs and target market indices are the same. Since the Subprime crisis happens in our sample period, we also divide our sample period into two sub-periods to check whether the crisis affects the diversification effects. The first period is from June 2003 to May 2008; the other period is from June 2008 to March 2009. We find that the sub-period results are similar to the whole sample period; no significant difference is found between direct and indirect investments. The remainder of this paper is organized as follows. The data sources and a brief introduction to the statistical methods are in Section 2. In Section 3, we present and analyze the results. Section 4 contains concluding remarks. 2. Data and methodology The data include 19 iShare ETFs that are traded in NYSE Arca. These 19 ETFs cover European, American, Asian and African markets. The study period runs from 2 June 2003 to 31 March 2009. For ETF data, adjusted prices are collected from Yahoo! Finance. In addition to the sample of ETFs, we also obtain stock market returns from MSCI that correspond to the ETFs. The weekly returns are compounded to calculate the weekly portfolio returns used to form and test the benchmark portfolio. As well, the Standard & Poor’s 500 Index is collected as a standard of holding U.S. market assets. In order to compare the performance between direct and indirect investments, we use three performance measures. The first one is the Sharpe measure originally proposed by Sharpe (1966). The second measure is the modified Sharpe measure where the Value at Risk (VaR) is used instead of standard deviation that is used in the original Sharpe measure. Dembo (1997) points out that since VaR has been the character for risk evaluations, VaR should be used in substitution for standard deviation in the Sharpe measure to form the modified Sharpe measure. The main reason is that if the return distribution does not follow a normal distribution, based on the traditional Sharpe measure, there may be conflicts in investments. Later, Hodges (1998) also demonstrates the Sharpe ratio paradox, which indicates that the Sharpe measure is not valid in evaluations when returns are non-normality. Dowd (1999) provides the modified Sharpe measure where the VaR value is used instead of the standard deviation that is used in the original Sharpe measure. Hence in this paper, we will use Dowd’s measure, SDowd , as our second performance measure. The third performance measure is proposed by Campbell et al. (2001). They follow the concept of Mean-Value at Risk (Mean-VaR) efficient frontier. Similar to the Sharpe ratio, they use it to calculate the largest expected returns based on some certain VaR constraints. They find that under an incorrect assumption of realized return distributions, the circumstance of undervaluation of VaR becomes more and more significant with the increase in the confidence interval. However, in Campbell, Huisman and Koedijk’s paper, they use simple moving average6 (SMA) for VaR evaluations. Dowd (1998), Bali (2000), and Andrews (2003) find that SMA has two drawbacks. The first one is that SMA gives equal weight to all observations, which might ignore the effects of recent events. Another defect is the inappropriate assumption and constant variance, which would change with time in the real world. To overcome these two problems, we adopt the exponentially weighted moving average7 (EWMA) method. In order to test the differences between direct and indirect investments, the Gibbs sampling and Bootstrap methods are used when assets returns are under normal and non-normal distributions, respectively.

6 7

A simple moving average (SMA) is the unweighted mean of the previous n data points. An exponentially weighted moving average (EWMA) applies weighting factors which decrease exponentially.

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Instead of using the single index model or multiple index models to examine the diversification effect as in the most of the previous studies,8 in this paper, we adopt Chou’s (1997) concept to test the relative efficiency between two sets of securities. The following sections provide more details of our methodology. 2.1. The test for relative efficiency between two sets of securities In this section, we will briefly introduce the method proposed by Chou (1997) to test the relative efficiency between two sets of securities. In order to get the Sharpe measure, we use the Mean-Variance Portfolio Model to obtain efficient frontier. If a portfolio has the minimum variance among portfolios with the same expected rate of return, the portfolio is a frontier portfolio. In some empirical studies, all sets of returns should follow an IID multivariate normal distribution with constant mean and covariance matrix. That is, Ri ∼ G(u, ˙), and distribution G is the normal distribution. We define  = 12 /22 , where i ≡

i ˙ii−1 i is the maximum obtainable Sharpe measure for set i (i.e. Ingersoll, 1987).

The objective is to compare the relative potential performance of these two sets of assets. If we cannot reject the null hypothesis H0 :  = 1, the performance of these two portfolios will show no statistical differences. We use the Mean-Variance Portfolio Model to obtain efficient frontier followed by calculation of the Sharpe measure index. This approach is implemented via iterating the following steps: 1. Calculate  and ˙ of portfolios. 2. Let t = 1. By using the Mean-Variance Portfolio Model with different given expected returns, the largest Sharpe measure of the first portfolio set (12 ) will be obtained. 3. Again, using the different portfolio set, we will have another Sharpe measure (22 ). 4. Let (t) = 12 /22 . 5. Set t = t + 1, then go back to Step 2. After iterating the process, we have the distribution of .9 Then we can use this distribution to test the statistical hypothesis. We assume returns follow normal distributions and use Gibbs sampling to get the distribution of . However, in most cases, a non-normal distribution is a more appropriate assumption. Therefore, we also use stationary Bootstrap10 to have the distribution of . Again, once the distribution of  is obtained, we can test the statistical hypothesis. 2.2. Optimal portfolio sets with Value at Risk Based on Campbell et al. (2001), if we assume the initial investment is W0 and the lending or borrowing amount is B, then the budget constraint for the portfolio can be expressed as W0 + B =

n 

i Pi,0

(1)

i=1

where  i is the investment weight on ith risky asset, Pi,t is the price for asset i at time t. From Eq. (1), investors determine  i and B so that the maximum values of investment portfolios at the terminal date under some risk controls can be obtained. Choosing VaR* as the desired level, the downside risk can be expressed as Pr(W0 − WT,P ≥ VaR∗ ) ≤ 1 − ˛

8 9 10

See Bailey and Lim (1992), Johnson et al. (1993), Chang et al. (1995), Patro (2001), Pennathur et al. (2002). In this paper,  1 is the performance measure of the ETFs portfolio.  2 is the performance measure of index portfolio. In this paper, the bootstrap method means the stationary bootstrap method.

(2)

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Table 1 The table shows the summary statistics of ETFs that were traded in AMEX. Adjusted prices were collected from Yahoo! Finance. The study period ran from 2 June 2003 to 31 March 2009. We also found that both ETFs and market index returns showed leptokurtic and fat tail. These results can also be found at the Jarque–Bera tests which reject the hypothesis that our sample returns have normal distributions. Observations

Returns (%)

Panel A: European and American markets U.S.A. 1468 −0.0067 Germany 1468 0.0206 England 1468 −0.0043 Switzerland 1468 0.0181 Italy 1468 −0.0117 France 1468 0.0076 Sweden 1468 0.0175 Netherlands 1468 0.0051 Austria 1468 0.0143 Belgium 1468 −0.0097 Canada 1468 0.0281 Panel B: Asia markets Japan 1468 0.0118 Taiwan 1468 0.0042 Singapore 1468 0.0328 1468 0.0283 Hong Kong Malaysia 1468 0.0281 Panel C: Other markets South Africa 1468 0.0500 Australia 1468 0.0295 Mexico 1468 0.0510 ***

Std.

Max.

Min.

Skewness

Kurtosis

Jarque–Bera

0.0138 0.0178 0.0170 0.0145 0.0169 0.0170 0.0217 0.0172 0.0197 0.0170 0.0166

0.1355 0.1807 0.1578 0.1112 0.1425 0.1228 0.1249 0.1343 0.1513 0.0926 0.1169

−0.1036 −0.1197 −0.1281 −0.0866 −0.1121 −0.1157 −0.1470 −0.1394 −0.1355 −0.1459 −0.1164

0.0755 0.4008 −0.1903 −0.4031 −0.1656 −0.0679 −0.3134 −0.5408 −0.7647 −1.0499 −0.6657

20.23 17.52 18.74 11.73 14.13 13.80 11.88 14.17 14.83 13.31 11.44

18153.13*** 12928.24*** 15154.61*** 4698.40*** 7584.41*** 7137.05*** 4849.07*** 7703.54*** 8710.43*** 6772.03*** 4464.89***

0.0168 0.0214 0.0199 0.0203 0.0157

0.1470 0.1325 0.1653 0.1570 0.0864

−0.1097 −0.1176 −0.1173 −0.1313 −0.1239

0.2978 0.0798 0.1572 0.2092 −0.4428

11.97 7.81 10.73 12.19 9.14

4944.01*** 1418.83*** 3657.05*** 5171.28*** 2355.19***

0.0256 0.0206 0.0207

0.2062 0.1889 0.1944

−0.2240 −0.1324 −0.1165

−0.3533 −0.0845 0.3334

14.84 14.63 12.76

8607.20*** 8281.64*** 5856.99***

Significant level of 1%.

where ˛ is the significance level and P is the terminal value of the portfolio. Under the above assumption, Campbell et al. showed that the maximum portfolio values at the terminal date, P , will be P :

Max S(P) =

rP − rf ϕ(˛, P)

(3)

where S(P) can be viewed as a performance measure, which is similar to the Sharpe measure. ϕ(˛, P) is the relative VaR which can be shown in Eq. (4). ϕ(˛, P) = W0 rf + VaR(˛, P)

(4)

We take the maximum portfolio values, P , as the performance measure, SCHK , That is11 SCHK =

rP − rf ϕ(˛, P)

(5)

Based on this framework, Campbell et al. show that the borrowing or lending amount, B, can be determined as B=

W0 (VaR∗ − VaR(˛, P  )) VaR∗ − VaR(˛, P  ) =  ϕ(˛, P  ) rf + VaR(˛, P )

(6)

3. Empirical results A description of some summary statistics on our data is shown in Tables 1 and 2. Tables 1 and 2 show that ETFs have higher average returns than corresponding market index returns regardless of which markets. Among these markets, Mexico has the largest return difference between ETFs and corresponding market index returns (0.0214%). However, volatilities in ETFs are larger than

11

For more details, please refer to Campbell et al. (2001).

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Table 2 The table presents the summary statistics of index returns from MSCI. The study period ran from 2 June 2003 to 31 March 2009. We also found that both ETFs and market index returns showed leptokurtic and fat tail. These results can also be found at the Jarque–Bera tests which reject the hypothesis that our sample returns have normal distributions. Observations

Returns (%)

Panel A: European and American markets U.S.A. 1468 −0.0128 Germany 1468 0.0133 England 1468 −0.0136 Switzerland 1468 0.0097 Italy 1468 −0.0215 France 1468 0.0047 Sweden 1468 0.0051 Netherlands 1468 −0.0073 Austria 1468 0.0030 Belgium 1468 −0.0236 Canada 1468 0.0189 Panel B: Asia markets 1468 0.0033 Japan Taiwan 1468 0.0001 Singapore 1468 0.0247 Hong Kong 1468 0.0189 Malaysia 1468 0.0200 Panel C: other markets 1468 0.0411 South Africa Australia 1468 0.0150 0.0296 Mexico 1468 ***

Std.

Max.

Min.

Skewness

Kurtosis

Jarque–Bera

0.0138 0.0158 0.0154 0.0129 0.0156 0.0158 0.0194 0.0155 0.0196 0.0160 0.0167

0.1096 0.1159 0.1216 0.0973 0.1247 0.1184 0.1405 0.1053 0.1335 0.1066 0.1028

−0.0947 −0.0964 −0.1043 −0.0749 −0.1089 −0.1157 −0.1053 −0.1151 −0.1344 −0.1546 −0.1425

−0.2656 0.0944 −0.0897 0.1653 0.1032 0.0935 0.2034 −0.1303 −0.3041 −1.1670 −0.9569

16.06 13.28 16.40 11.44 16.35 15.21 10.89 14.56 13.93 16.62 15.36

10461.68*** 6469.711*** 10996.66*** 4365.64*** 10913.19*** 9128.168*** 3817.223*** 8189.338*** 7333.246*** 11688.62*** 9568.143***

0.0157 0.0159 0.0149 0.0150 0.0106

0.1147 0.0783 0.0856 0.1045 0.0555

−0.0951 −0.0717 −0.0981 −0.1257 −0.1128

−0.1813 −0.3358 −0.3934 −0.2262 −0.9116

8.06 5.76 8.87 11.93 14.61

1573.923*** 494.0065*** 2146.422*** 4891.468*** 8457.176***

0.0208 0.0182 0.0188

0.1235 0.0881 0.1516

−0.1357 −0.1597 −0.1090

−0.4260 −1.1964 −0.0384

8.41 14.46 10.95

1833.098*** 8391.726*** 3864.602***

Significant level of 1%.

in market indices as well. This implies that higher returns come with higher risks. Generally speaking, there are higher returns for ETFs in Asian markets. Three of the Asian markets (Singapore, Hong Kong and Malaysia) are among the top 5 for ETF returns. If we compare the differences of returns between ETFs and market indices, we find that Asian markets have the largest differences of returns. For example, the return of ETFs in Taiwan market is 0.0042%, which is 42 times that of the Taiwan market index. We also find that both ETF and market index returns show leptokurtic and fat tail. These results can also be found at the Jarque–Bera tests which reject the hypothesis that our sample returns have normal distributions. In this section we examine the diversification effect of ETFs. Since ETFs provide investors with an alternative to form their portfolios, we first consider whether investors who invest in ETFs to form portfolios could have achieved better performance than those who invest only in the S&P 500. Second, as the Subprime crisis has a huge influence on the U.S. economy, we also divide our whole sample period into two sub-periods for further analysis. The first period is from June 2003 to May 2008; the second one is from June 2008 to March 2009. Third, from Table 1, we see that ETFs do not follow normal distributions. Therefore, in order to have a complete comparison, both normal and non-normal distribution assumptions are used for comparison. The results in Table 3 show that when the Campbell et al.’s measure (SCHK )12 is used for performance evaluation, diversified portfolios have better performance when ETFs show normal distributions.13 This indicates that investing in ETFs will result in higher returns and lower risk than investing in S&P 500 alone, regardless of which sample period was considered. We find that different markets present different diversification effects. When all the existing ETFs are contained in the portfolio (global markets), we get the highest diversification effect. The second highest is in the European and American market. We also find that the performance of S&P 500 and ETF portfolios change greatly when the

12 For the performance measure of S&P 500, we used the Bootstrap method to construct the distribution of returns of S&P 500. Once we have the distribution, we can then get the VaR based on the 95% confidence interval. Finally, by using the VaR, the Sharpe measure under Campbell et al. (2001) can be obtained. 13 We also used other two performance measures and obtained similar results.

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Table 3 This table shows the optimal portfolio performance comparing with different portfolio ETFs and S&P 500. Both normal and nonnormal distributions are considered in this table. The optimal portfolio is calculated based on SCHK . The confidence interval is 95% for Value at Risk in the performance measure SCHK . We divide the whole sample period into two sub-period (June 2003–May 2008; June 2008–March 2009) in order to examine the influence of Subprime crisis. The D.P. (difference percentage) shows the difference under different distributions assumptions.

Panel A: 200306–200903 Global markets European and American markets Asia markets Emerging markets S&P 500 Panel B: 200306–200805 Global markets European and American markets Asia markets Emerging markets S&P 500 Panel C: 200806–200903 Global markets European and American markets Asia markets Emerging markets S&P 500

Normality

Non-normality

D.P. (%)

0.0341 0.0239 0.0129 0.0164 −0.0360

0.0376 0.0267 0.0143 0.0187

−9.30851 −10.4869 −9.79021 −12.2995

0.0582 0.0509 0.0295 0.0388 0.0118

0.0607 0.0539 0.0355 0.0494

−4.11862 −5.56586 −16.9014 −21.4575

0.0360 0.0301 0.0161 0.0178 −0.0346

0.0378 0.0341 0.0164 0.0208

−4.7619 −11.7302 −1.82927 −14.4231

Subprime crisis happens. When the sample periods occur during the Subprime crisis, the second subperiod, investors even have negative average returns in S&P 500 and much lower than in the first sub-period but still positive average returns in ETF portfolios. The results are similar when we use the Bootstrap method to form our portfolios which are under non-normal distributions. This implies that even in different return distribution assumptions, these results still lead to the same conclusion that diversified portfolios are better for U.S. investors. This is consistent with Levy and Sarnat (1970), Meric and Meric (1989), Harvey (1995), Solnik et al. (1996), Goetzmann and Jorion (1999) who show that international diversification is a sensible strategy. We also find that different distribution assumptions will influence the diversification effect. In Table 3, it shows that under the wrong assumption, a normal distribution will undervalue the international diversification effect. The differences of diversified effects are even up to 21.45% (emerging markets in Panel B). Table 3 also shows that diversified portfolios are beneficial to U.S. investors. Therefore, we want to examine further whether differences exist between direct and indirect investments in foreign countries. Table 4 shows the results of three definitions of Sharpe ratios under the Gibbs sampling method and the Bootstrap method. The results in Table 4 suggest that the average values of  are greater than 1 for all markets, which means that Sharpe ratios of ETF are larger than market indices. Among these markets, emerging markets have the largest . These results indicate that portfolios based on ETFs will have better performance than market indices. We also find that the Gibbs sampling method with normal distribution assumptions has higher values of average  than the Bootstrap method that assumes non-normal distributions. This phenomenon is shown in all the three performance measures we use. As mentioned earlier, a non-normal distribution assumption is more appropriate. The above results imply that the Gibbs sampling method may overvalue the differences between ETFs and target market indices. Since the average values of  are greater than 1, this means that Sharpe ratios of ETFs are larger than market indices. However, we find that these differences were insignificant at the 5% level for all four portfolios because we cannot reject the hypothesis that  = 1. This indicates that there is no significant difference between the direct and indirect investments. Investors can create their portfolios by investing in ETFs instead of in market indices. Again, we also find that these results are the same even though we assume different distributions of returns.

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Table 4 The table shows the comparisons between Bootstrap and Gibbs sampling methods. Both these two methods are used to examine whether differences exist between direct and indirect investments in foreign countries. If the mean values are greater than 1 which means that ETFs have larger performance measures than market indices. C.I. represents 95% confidence interval. SP is the traditional Sharpe ratio. SDowd is the Sharpe ratio proposed by Dowd (1999). SCHK is the Sharpe ratio proposed by Campbell et al. (2001). Global markets

European and American markets

Asia markets

Emerging markets

1.1249 (0.339, 1.466)

1.0712 (0.349, 1.423)

1.1419 (0.473, 1.516)

1.3593 (0.660, 2.585)

1.4170 (0.562, 2.187)

1.4527 (0.831, 2.310)

1.0369 (0.365, 1.420)

1.0130 (0.293, 1.507)

1.1460 (0.408, 1.451)

1.5293 (0.620, 2.546)

1.467 (0.662, 2.287)

1.4723 (0.768, 2.322)

1.0511 (0.388, 1.921)

1.0851 (0.378, 1.969)

1.0605 (0.393, 1.515)

1.3858 (0.761, 2.228)

1.6014 (0.915, 3.146)

1.3135 (0.632, 2.110)

SP Bootstrap Mean 1.0373 C.I. (0.342, 1.707) Gibbs sampling Mean 1.3508 C.I. (0.580, 2.283) SDowd Bootstrap Mean 1.0322 C.I. (0.350, 1.718) Gibbs sampling Mean 1.4608 (0.562, 2.303) C.I. SCHK Bootstrap Mean 1.1901 (0.341, 1.607) C.I. Gibbs sampling Mean 1.4127 C.I. (0.713, 2.758)

Fig. 1. Mean-ϕ efficient frontier of the global market at the confidence level of 1%.

Campbell et al. compare optimal portfolios by using SMA and historical simulations under normal and non-normal distributions of asset returns. They find that the efficient frontier based on normal distributions will be higher than that based on non-normal distributions. However, as we mention, there are defects in SMA. We also use EWMA and Bootstrap method to obtain our efficient frontiers for diversified portfolios. Figs. 1 and 2 show the results of efficient frontier in two market portfolios. We find that normal distribution return assumptions form higher efficient frontiers than non-normal distributions. This might imply that normal distribution assumptions will underestimate the VaR in SMA. This result is consistent with Campbell et al. (2001). However, when using EWMA and Bootstrap method, we find that normal distributions have an overestimation of VaR which is contrary to that reported in Campbell et al. (2001). Campbell et al. (2001) also mention that an inappropriate distri-

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Fig. 2. Mean-ϕ efficient frontier of the Europe and America markets at the confidence level of 1%.

bution assumption will result in too high an allocation into risky assets. However, our EWMA results suggest that investors will put too low an allocation into risky assets which form a too conservative investment strategy. These results all imply that an appropriate distribution assumption might be an important issue in calculating VaR. 4. Conclusions Our findings demonstrate that diversified portfolios that consist of investments in both the S&P 500 and foreign markets have better performance than those that invest in the S&P 500 only, regardless of the occurrence of the Subprime crisis. When direct or indirect investments are used to form portfolios, we find that indirect investments have higher Sharpe measures than direct investments, especially in the emerging markets. This means that ETFs may offer more diversified benefits than target market indices under different assumptions of return distributions. However, although the performances are different, they are not statistically significant. This implies that direct investments and indirect investments will provide the same performance returns to investors. Based on this, investors who invest in foreign markets in ETFs, will have no performance difference from those who invest in a more direct way. Furthermore, we find that the diversification benefits are the same before and after the Subprime crisis. This implies that even if a market crisis happens, investors can still have better performance through an international diversified portfolio. In addition, the results indicate that there is no performance difference between ETFs and direct investments. Taking this into account, future research could attempt analyze why there is no performance difference between ETFs and direct investments. In addition, more indirect investment products might be used for a further analysis. Acknowledgement We acknowledge and thank Judy Acreman-Isakovic and Colm Kearney for helpful comments and suggestions. References Amadi, A., 2004. Equity home bias: a disappearing phenomenon. Unpublished Working Paper. Andrews, D.W.K., 2003. Testing when a parameter is on the boundary of the maintained hypothesis. Econometrica 69 (3), 683–734. Bailey, W., Lim, J., 1992. Evaluating the diversification benefits of the new country funds. J. Portfolio Manage. 18 (3), 74–80. Bali, T.G., 2000. Testing the empirical performance of stochastic volatility models of the short-term interest rate. J. Financ. Quant. Anal. 35 (2), 215.

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