# International diversification through iShares and their rivals

## Jie Cao, Rao Fu and Yong Jin

#### Need to know

• The diversification benefits of iShares in comparison to closed-end country funds (CECFs) and American Depository Receipts (ADRs) is examined
• Mean-variance spanning and Sharpe ratio test results provide strong evidence that iShares can neither outperform nor replace CECFs and ADRs for international diversification
• A combination of these domestically traded securities could exhaust the gains from unattainable direct foreign investment

#### Abstract

ABSTRACT

This paper examines the diversification benefits of iShares in comparison with closed-end country funds and American depositary receipts between April 1996 and December 2013. iShares are country-specific exchange-traded funds that track specific Morgan Stanley Capital International country indexes, and thus are expected to provide diversification gains that are superior to their rivals. Our main findings are as follows. First, although all of these financial instruments are significantly exposed to the US market, they retain significant exposure to their home markets and provide important diversification benefits. Second, mean-variance spanning and Sharpe ratio test results provide strong evidence that iShares can neither outperform nor replace closed-end country funds and American depositary receipts for international diversification. Finally, a combination of these domestically traded securities could exhaust the gains from unattainable direct foreign investment.

#### Introduction

Studies on international diversification, such as those by Levy and Sarant (1970) and Solnik (1974), reveal that US investors can benefit from investing directly in foreign stock markets. Chang et al (1995) argue that, in reality, US investors may find it difficult to invest directly in certain foreign markets due to various barriers to international capital flows, such as capital market and exchange regulations and excessive transaction and information costs. These barriers have encouraged the innovation of many financial products to facilitate international investment, including international mutual funds, closed-end country funds (CECFs), American depositary receipts (ADRs) and iShares (formerly known as World Benchmark Shares (WEBS), which were introduced in April 1996 and have experienced rapid growth since then).

iShares have recently emerged as a popular alternative to their closed-end country fund and ADR rivals for international diversification. Unlike international mutual funds, which typically provide exposure to a basket of countries, iShares, CECFs and ADRs can be country-specific securities. In addition, all of them can be traded and sold short in the same way as common US stocks.

As unit investment trusts, iShares are listed on the American Stock Exchange (AMEX) as traded securities. iShares track specific Morgan Stanley Capital International (MSCI) country indexes and are expected to provide diversification benefits that are superior to those of CECFs and ADRs. In this paper, we investigate the diversification benefits of country-specific securities: iShares, CECFs and value-weighted ADR portfolios. iShares’ great potential for international diversification leads to two interesting issues. First, iShares may become dominant in the investment opportunity set and completely replace the role of other financial instruments for international diversification. This result can help to forecast the development and coexistence of iShares and their rivals. Second, iShares could make it more feasible to form optimal homemade portfolios that can exhaust the diversification gains from unattainable direct foreign investment.

Specifically, we aim to answer three questions. First, how effective are iShares and their rivals in providing international diversification benefits? To answer this, we examine the correlations and risk exposures of iShares and their net asset values (NAVs), CECFs and ADR portfolios and the diversification gains under portfolio optimization. Though iShares track MSCI country indexes and have a great potential for diversification gains, the tracking errors, transaction costs, various expense fees and the limits of international arbitrage make the returns on iShares deviate from the underlying indexes. For example, Zhong and Yang (2005) argue that the international diversification benefits of iShares are questionable because their returns are significantly influenced by, and sensitive to, the US market risk. The empirical results on other financial instruments are also mixed. For example, Bailey and Lim (1992) find that CECFs have no diversification gains, but Chang et al (1995) provide contradictory evidence. Therefore, one contribution of this paper is to revisit the international diversification benefits of all these financial instruments within the same sample period.

Second, have iShares made CECFs and ADRs redundant for international diversification? The rapid growth of iShares has generated competition to other financial instruments, which may become less attractive to US investors. In reality, US investors have an opportunity set that includes both iShares and their rivals: CECFs and ADRs. Even if iShares could offer the largest diversification benefits as a single investment method, other financial instruments can still play a role if they can provide supplemental diversification benefits. iShares track the foreign country indexes, so they may already cover all the diversification benefits generated by their rivals. However, ADR portfolios and CECFs generally hold different underlying assets from iShares; hence, combining iShares with their rivals may generate greater diversification gains than using iShares alone. We study this issue within the mean–variance spanning frameworks of Huberman and Kandel (1987), Ferson et al (1993) and Bekaert and Urias (1996).

Finally, can iShares, either alone or in combination with their rivals, achieve the same diversification gains as direct foreign investment? By including CECFs and ADRs in the homemade diversification portfolio, Errunza et al (1999) find that domestically traded securities can mimic foreign market indexes. Assuming that iShares are highly correlated with foreign market indexes, it will be more feasible to achieve the diversification gains as direct foreign investment by including iShares in the diversification portfolio. If that is the case, then investing in assets that trade only abroad would not be necessary in order to obtain the benefits of international diversification.

The main empirical results of this paper can be summarized as follows. First, iShares, CECFs and ADR portfolios all maintain statistically significant exposure to the US market factors. CECFs and ADR portfolios have higher US betas than their corresponding home market betas and thus behave more like common US stocks than iShares. However, iShares tend to have substantially higher US market betas and lower home market betas than their underlying assets. This could decrease the power of iShares to provide diversification benefits.

Second, despite their exposure to US market factors, iShares, CECFs and ADR portfolios still retain significant exposure to their home market factors and provide US investors with important diversification gains by forming optimal international portfolios. However, the results of Sharpe ratio changes do not support the hypothesis that iShares can provide higher diversification gains than CECFs and ADR portfolios.

Third, the results of our three mean–variance spanning tests provide strong evidence that iShares cannot completely replace CECFs or ADR portfolios. This result shows that CECFs and ADRs have not become redundant as international diversification tools after the emergence of iShares. It also tends to validate the coexistence of iShares, CECFs and ADRs in the future.

Fourth, a combination of iShares, CECFs and ADR portfolios could exhaust the gains from direct foreign investment. Although iShares fail to span the foreign market indexes in the mean–variance spanning framework, adding CECFs and ADR portfolios to the benchmark set increases the likelihood that foreign market index returns are spanned. The extra gains offered by direct foreign investment diminish as the benchmark set becomes augmented. This result suggests that US investors no longer need to trade abroad to achieve an internationally mean–variance-efficient portfolio.

The rest of the paper is organized as follows. Section 2 provides a brief overview of iShares, CECFs and ADRs and reviews the related literature. Section 3 describes our data and methodology. Section 4 reports and discusses the empirical results. Conclusions are presented in Section 5.

## 2 Background and literature review

### 2.1 iShares

WEBS were introduced in 1996 and renamed the iShares MSCI Index Fund by Barclays Global Investors in May 2000. iShares are listed on the American Stock Exchange as traded securities. Each iShare is constructed as an optimized portfolio that tracks the underlying MSCI index in a foreign country. They are denominated in US dollars, traded close to NAVs and can be bought, or sold short, and yield passive returns based on the index. Like open-end funds, iShares can be created or redeemed at will and thus experience much less premium and discount fluctuation than CECFs.

Khorana et al (1998) studied the performance and tracking ability of WEBS for the first six months after issuance. Using a single-index model, they documented the indexing efficiency of WEBS. Pennathur et al (2002) studied the performance and diversification gains of iShares and CECFs from 1996 to 1999. They found that iShares outperformed CECFs in weekly returns. The two-factor model shows that though iShares have some diversification benefits they still maintain substantial exposure to the US market. Zhong and Yang (2005) found that iShare returns are significantly influenced by and sensitive to US market risk and that the US market appears to be the key permanent driving factor. Thus, the international diversification benefits of iShares are questionable. On the other hand, Miffre (2007) showed that iShares enhance global asset allocation strategies. Investing in iShares generates efficient gains that cannot be achieved by country-specific open- and closed-end funds.

### 2.2 Closed-end country funds

Closed-end country funds are investment companies that are listed on a US exchange but actively invest in the securities of a particular foreign country. The funds trade at market prices that are determined in the US secondary market, while their NAVs are determined in the home countries. Closed-end funds normally sell at a premium or discount from their NAVs.

Bailey and Lim (1992) found that the CECFs’ returns tend to co-move with US market returns and suggested that CECFs do not provide as many international diversification benefits as direct investment in foreign equities. Chang et al (1995), using a sample of fifteen CECFs, documented that CECFs exhibit significant exposure to the US market factors and act more like US securities than their underlying foreign assets. However, CECFs retain significant exposures to home-country market factors and still provide substantial diversification benefits for US investors. Bekaert and Urias (1996) used the mean–variance spanning tests to examine US- and UK-traded country funds. They found diversification benefits for UK funds but not for US funds.

### 2.3 American depositary receipts

Previous studies support the diversification benefits of ADRs. Jiang (1998) studied the diversification gains and the dynamic pricing of ADRs and found that the ADR portfolios provided better diversification benefits than the broad foreign market index in the short term. Errunza et al (1999) employed country funds and ADRs to mimic foreign indexes and found that it is possible to achieve international diversification by only using ADRs.

## 3 Data and methodology

### 3.1 Data

The data set contains weekly returns for iShares and their NAVs, CECFs, ADR portfolios and MSCI indexes. The sample includes seventeen countries, for which seventeen corresponding iShares were originally introduced by Barclays in March 1996: Australia, Austria, Belgium, Canada, France, Germany, Hong Kong (China), Italy, Japan, Malaysia, Mexico, Netherlands, Singapore, Spain, Sweden, Switzerland and the UK. Based on the history of iShares, the sample covers the period between April 2, 1996 and December 31, 2013, resulting in 926 weekly observations. The sources for the foreign stock market indexes were the MSCI country indexes. The Standard & Poor’s 500 Composite Index (S&P 500) was used as a proxy for the US stock market.

Twenty-four CECFs were in existence in the sample period for thirteen of our seventeen countries.22Qualified closed-end country funds are identified from Yahoo Finance (http://finance.yahoo.com/) or the Closed-End Fund Forum. If a country had multiple funds listed, then we combined these funds to form a value-weighted portfolio. We excluded the UK since the only corresponding closed-end fund exited in 1999.

We selected the weekly prices for the seventeen MSCI indexes and the US S&P 500 index from DataStream. The corresponding weekly prices of iShares, CECFs and ADRs were taken from the Center for Research in Security Prices (CRSP). iShares’ NAVs were obtained from the iShares website (see http://www.iShares.com). Weekly returns were calculated by compounding daily returns with dividends. All prices and returns are US dollar denominated.

### 3.2 Portfolio optimization under modern portfolio theory

For investors facing $K$ risky assets, the investment opportunity set is described by the vector of expected returns on the $K$ assets, $\bar{r}$, and by $\varSigma$, the covariance matrix. Modern portfolio theory assumes that the investors’ preference can be represented by a utility function defined over the mean and variance of a portfolio’s return. The mean–variance efficient frontier constructed by $K$ risky assets consists of portfolios that have the smallest variance for every level of expected returns. For a given expected return, $\mu$, $x_{\mathrm{p}}(\mu)$ is a mean–variance frontier portfolio if

 $x_{\mathrm{p}}=\operatorname*{arg~{}min}_{x}\tfrac{1}{2}x^{\prime}\varSigma x% \quad\text{such that~{}}x^{\prime}l=1,~{}x^{\prime}\bar{r}=\mu.$ (3.1)

Vector $x_{\mathrm{p}}$ is the vector of weights of $K$ risky assets in the portfolio. If short sales are restricted, $x_{\mathrm{p}}\geq 0$ is imposed.

When a risk-free asset is available, the capital allocation line (CAL) is a straight line that intersects the risk-free rate and is tangential to the mean–variance efficient frontier constructed by the $K$ risky assets. Generally, the point of tangency is defined as the market portfolio. The Sharpe ratio of the market portfolio equals the slope of the CAL and is calculated as

 $\text{SHP}=\frac{r_{\mathrm{p}}-r_{\mathrm{f}}}{\sigma_{\mathrm{p}}},$ (3.2)

where $r_{\mathrm{p}}$ is the expected return of the market portfolio, $r_{\mathrm{f}}$ is the risk-free rate and $\sigma_{\mathrm{p}}$ is the standard deviation of the return of the market portfolio. The market portfolio has the largest Sharpe ratio of all the mean–variance frontier portfolios, and thus offers the best risk–return trade-off. In practice, given the $\bar{r}$ and $\varSigma$ of the $K$ assets, the market portfolio and its Sharpe ratio can easily be found with numerical optimization methods.

The change in the Sharpe ratios can be used to quantify the diversification gains. Adding $N$ diversification risky assets to the $K$ existing assets will create a new mean–variance efficient frontier and result in a new market portfolio. The difference between the Sharpe ratio of the new market portfolio and that of the old one gives the improvement: the larger the difference, the better the improvement.

### 3.3 Mean–variance spanning tests

In portfolio analysis, the question of whether one set of risky assets can improve the investment opportunity set of another set of risky assets has received considerable attention. Under the assumption that investors are only concerned with the mean and variance of assets, the question becomes whether an investor can extend their mean–variance efficient frontier by including additional assets in their portfolio. This addresses the diversification benefits and was first discussed by Huberman and Kandel (1987), who proposed a regression-based test of the hypothesis that the mean–variance frontier of a set of $K$ benchmark assets is the same as the mean–variance frontier of the $K$ benchmark assets plus $N$ additional test assets. Subsequent to Huberman and Kandel’s (1987) study, Ferson et al (1993) developed the regression-based mean–variance spanning test under nonnormality and conditional heteroscedasticity. Exploiting the duality between Hansen–Jagannathan bounds (Hansen and Jagannathan 1991) and the mean–variance frontier, De Santis (1993) and Bekaert and Urias (1996) designed equivalent mean–variance spanning tests under the stochastic discount factor approach.

In the literature, the first set of $K$ assets is called the benchmark set, and the set of $N$ additional assets is called the test assets. The Huberman–Kandel (HK) test involves estimating the following equation:

 $R_{B,t}=\alpha+\beta R_{A,t}+\varepsilon_{t},\quad t=1,2,\dots,T,$ (3.3)

where the $R_{B,t}$ are the returns on the $N$ test assets at time $t$, $R_{A,t}$ are the returns on the $K$ benchmark assets at time $t$, $\alpha$ is the $1\times N$ vector and $\beta$ is the $N\times K$ matrix. Huberman and Kandel show that $R_{B,t}$ is spanned by $R_{A,t}$ if and only if the following null hypothesis ($\mathrm{H}_{0}$) conditions hold:

 $\displaystyle\alpha$ $\displaystyle=0_{N},$ (3.4) $\displaystyle\beta 1_{K}$ $\displaystyle=1_{N},$ (3.5)

where $0_{N}$ is an $N$-vector of zeros and $1_{N}$ and $1_{K}$ are an $N$-vector and $K$-vector of ones, respectively. Assuming that $\alpha$ and $\beta$ are constant over time, Huberman and Kandel test these restrictions by using the likelihood ratio test based on ordinary least-squares (OLS) estimates of (3.3).

One crucial assumption of the HK test is that, conditional on $R_{A,t}$, the disturbances $\varepsilon_{t}$ are independent and identically distributed as multivariate normal with mean zero and variance $\varSigma$. However, if $\varepsilon_{t}$ is nonnormal and exhibits conditional heteroscedasticity, the likelihood ratio test will no longer be asymptotically $\smash{\chi_{2N}^{2}}$-distributed under the null hypothesis. In this case, a common alternative is the Gaussian mixture model (GMM) method of Hansen (1982), which depends on the moment conditions. Ferson et al (1993) present the GMM spanning tests under the regression approach. Assuming $R_{A,t}$ and $R_{B,t}$ are stationary with finite fourth moments, Ferson et al apply the GMM Wald test to test the linear restrictions of the null hypothesis.55Newey and West (1987) show that the GMM likelihood ratio test and the Lagrange multiplier test have the same form as the Wald test.

In addition to using the regression-based approach, Bekaert and Urias (1996) project a stochastic discount factor $m_{t}$ with mean $\alpha$ on the returns of the $N+K$ assets as

 $m_{t}=\alpha+[R_{t}-E(R_{t})]^{\prime}\beta(\alpha)+\varepsilon_{t},$ (3.6)

where $R_{t}=[R_{A,t},R_{B,t}]^{\prime}$, and $\alpha$ is a constant.

Recall the general conditional asset pricing restriction:

 $E[(1_{N+K}+R_{t})m_{t}]=1_{N+K}.$ (3.7)

Hence,

 $\beta(\alpha)=\varSigma_{R}^{-1}[(1-\alpha)1_{N+K}-\alpha\mu],$ (3.8)

where $\mu$ and $\varSigma_{R}$ are the mean returns and covariance matrix of $R_{t}$, respectively.

In order to test the Hansen–Jagannathan mean–variance spanning restrictions, Bekaert and Urias (1996) prespecify two values for $\alpha$, $\alpha_{1}$ and $\alpha_{2}$, and test the alternative hypothesis $(\mathrm{H}_{1})$:

 $C\beta(\alpha_{i})=0_{N},\quad i=1,2,$ (3.9)

where $C=[0_{N\times K},I_{N}]$.66The model follows the simplified, earlier version of Kan and Zhou (2012). In fact, the Bekaert–Urias (BU) test examines whether the $N$ test assets can help to explain the variance of the stochastic discount factor. Bekaert and Urias (1996) prove that $(\mathrm{H}_{1})$ is equivalent to $(\mathrm{H}_{0})$ for both unconditional and conditional mean–variance spanning tests. They test the restrictions of the null hypothesis with the GMM Wald test and make corrections for serial correlation.77This paper uses the $\mathrm{MV}_{3}$ statistic in Bekaert and Urias (1996).

## 4 Empirical tests

### 4.1 Descriptive statistics

#### 4.1.1 Mean and standard deviation

Table 2 presents the mean weekly returns and standard deviations for iShares and their underlying assets, CECFs, ADR portfolios and MSCI indexes between April 2, 1996 and December 31, 2013. Several observations can be made. Although iShares are designed to mimic MSCI indexes, the latter have a higher mean return than iShares for all seventeen countries. The difference between iShares and MSCI indexes, if it exists, may be decomposed into two parts: the difference between MSCI indexes and the iShares’ NAVs and the difference between iShares and iShares’ NAVs. The former is caused by tracking errors and transaction costs, and the latter is due to the trading premiums or discounts.88iShares invest not in every security in the target market indexes, but in a basket of securities closely representing the target market. Table 2 shows that the average weekly returns on MSCI indexes are 0.142% and very close to 0.141% for iShares, though there are significant differences for a few countries, eg, Austria. However, the average of weekly returns on iShares’ NAVs is 0.129%, which is lower than the 0.142% for MSCI indexes and 0.141% for iShares. We cannot exclude the possibility that the tracking errors between iShares’ NAVs and MSCI indexes could offset the trading premiums between iShares and their NAVs.

Although the creation and redemption features of iShares can help to reduce the trading premiums or discounts, the limits of international arbitrage make the returns of iShares more volatile than those of iShares’ NAVs (Zhong and Yang 2005). Note also that iShares’ NAVs have a similar standard deviation to MSCI indexes. However, the average standard deviation on iShares is 3.610%, which is slightly higher than the 3.551% for MSCI indexes and the 3.533% for iShares’ NAVs. Therefore, the evidence above suggests that iShares have different risk–return characteristics from MSCI indexes because of tracking errors, transaction costs and the limits of international arbitrage.

#### 4.1.2 Unconditional correlations

The return correlation between the US market index and a target foreign market index is a traditional measure of the benefits of international diversification: the lower the correlation, the greater the potential gains. Column 2 of Table 3 shows the correlations between MSCI indexes and the S&P 500 index. All seventeen MSCI indexes are positively correlated with the S&P 500 index, with an average correlation of 0.589. Malaysia has the lowest correlation (0.242), and Canada the highest (0.757), which indicates that Canada’s stock market is highly integrated with that of the United States. Generally, the correlations of most countries are greater than the corresponding results documented in previous research.1111See, for example, Errunza et al (1999, Table IV). Their sample is from 1976 to 1993. This suggests that the international financial markets have become more integrated over the past thirty years.

Table 3 also reports the correlations with the US S&P 500 index and with home country MSCI indexes for iShares and their NAVs, CECFs and ADR portfolios. In most cases, all these securities have lower correlations with the US market than with their home country market. Except for Mexico, all other iShares correlate more closely with the US market than their NAVs. However, all iShares’ NAVs correlate more closely with the home country market than iShares. This finding can also be attributed to the limits of international arbitrage.

The average correlations of iShares, CECFs and ADR portfolios with the US market are 0.659, 0.505 and 0.608, respectively. All these numbers are close to but still different from the 0.589 for MSCI indexes. This may suggest that these US traded securities can provide different diversification gains from direct investment in the foreign markets indexes.

The average correlations of iShares, CECFs and ADR portfolios with the home country market are 0.898, 0.673 and 0.685, respectively. iShares mimic MSCI indexes and thus have the highest correlations; most ADRs are large foreign companies that are included in the MSCI indexes, so ADR portfolios also exhibit high correlations. The high correlations of these domestically traded securities with home country markets question the need for costly direct foreign investment. Errunza et al (1999) state that correlations with respect to the US index overstate the gains from investing in securities that only trade abroad, because investors can use CECFs and ADRs to form homemade diversification portfolios.

### 4.2 Risk exposures from the two-factor market model

Some previous studies suggest that the returns of securities may be affected not so much by where the cashflows are generated as by where the securities are traded. Russell (1998) examines various US exchange-listed investment instruments and concludes that these securities behave more like their host exchange than their home exchange.

iShares, CECFs and ADRs are traded in the United States, but the cashflows from their underlying assets are generated in their home countries. Since iShares have much less premium and discount fluctuation than CECFs and ADRs, the latter may behave more like common US traded stocks than iShares. Moreover, iShares may behave more like US stocks than their NAVs, due to the limits of international arbitrage. If they do, we may question the effectiveness of iShares for international diversification.

To evaluate the US market risk exposure and the home-country market risk exposure for iShares and their NAVs, CECFs and ADR portfolios, we use a two-factor model that accounts for both US market risk and home country-specific risk:

 $R_{i,t}=\alpha_{i}+\beta_{\mathrm{US},i}R_{\mathrm{US},t}+\beta_{\mathrm{home}% ,i}R_{\mathrm{home},t}+\varepsilon_{i,t},$ (4.1)

where $R_{i,t}$ is the return on security $i$ at time $t$ and $R_{\mathrm{US},t}$ is the return on the US market index proxied by the S&P 500 index. Following Chang et al (1995), $R_{\mathrm{home},t}$ is derived as the residual from a regression of the respective MSCI index returns on the S&P 500 index return. $\varepsilon_{i,t}$ is the error item. $\beta_{\mathrm{US},i}$ and $\beta_{\mathrm{home},i}$ are parameters representing the sensitivities of security $i$ to the US market return and home country market return, respectively. $\alpha_{i}$ is the intercept.

If these securities facilitate effective diversification, we would expect their returns to exhibit significant exposure to home-country-specific market risk. Table 4 reports the estimation results for the entire sample period. It shows that all iShares, CECFs and ADR portfolios have significant home market betas at a 5% significance level. The average home market beta measure is 0.789 for iShares, compared with 0.633 for CECFs and 0.613 for ADR portfolios. However, all these securities also have significant US betas. The average US beta is 0.935 for iShares, compared with 0.792 for CECFs and 0.991 for ADR portfolios.

In most cases, CECFs tend to have a higher US beta than home country beta. Their average US beta (0.792) is larger than the average home country beta (0.633). This is also true for ADR portfolios, which have an average US beta of 0.991 versus an average home country beta of 0.613. It could suggest that CECFs and ADRs behave more like common US stocks.

Table 4 also shows that iShares have higher US beta values than iShares’ NAVs. The average US beta measure is 0.843 for iShares’ NAVs, compared with 0.935 for iShares. In addition, iShares have lower home country betas than iShares’ NAVs. The average home country beta value for iShares is 0.789, whereas the average home country beta value for iShares’ NAVs is 0.964. These results support the finding that iShares behave more like US stocks than their underlying assets do. These results are also consistent with the previous findings of Pennathur et al (2002) and Zhong and Yang (2005).

### 4.3 Diversification gains from optimal asset allocation

In reality, it is very costly or impossible for US investors to directly invest in certain foreign stock markets. Even in the markets open to foreign investors, the number of securities eligible for investment is often limited. Therefore, it is difficult to invest in a portfolio equivalent to the market index of foreign countries.

iShares, CECFs and ADRs provide US investors with the opportunity to obtain international diversification gains without trading abroad. Section 4.2 shows that all these securities have statistically significant risk exposures to home country markets. In this subsection, we examine the diversification gains via iShares, CECFs and ADR portfolios through portfolio optimization (the methodology is described in Section 3.2). Since iShares track the MSCI indexes and behave less like US stocks than CECFs and ADR portfolios, we may expect iShares to provide better gains than CECFs and ADRs. However, the fact that iShares behave more like US stocks than their underlying assets do potentially limits the power of iShares for international diversification.

First, for each country we solve for the optimal tangent portfolio composed of the US market index and the corresponding iShare. Second, we solve for the optimal tangent portfolio composed of the US market index and all seventeen iShares in the sample. Then the diversification gains are measured by the change in the Sharpe ratios, which is calculated as the Sharpe ratio of the optimal tangent portfolio minus the Sharpe ratio of the US market. We repeat the steps above for CECFs and ADR portfolios. For comparison, we redo the second step for iShares for the thirteen countries in which CECFs exist and for the eleven countries in which ADR portfolios exist.

In solving for the optimal tangent portfolio, the weekly risk-free rate is set to zero and short sales are allowed.1212iShares, CECFs and ADRs all are exchange-traded securities and can be sold short. Table 5 presents the change in Sharpe ratios for iShares, CECFs and ADR portfolios, for the entire sample period and for two subperiods: April 1996 to December 2004, and January 2005 to December 2013.

Over the entire sample period, Mexico provides the highest gain for iShares (0.0144) and for ADR portfolios (0.0315); Canada provides the highest gain (0.0141) for CECFs. Diversifying the US market index by adding seventeen iShares increases the weekly excess return per unit of risk to 0.0571. Thirteen CECFs and eleven ADR portfolios also help increase the weekly excess return per unit of risk to 0.0627 and 0.1020, respectively. These results indicate that iShares, CECFs and ADRs do provide diversification gains.

It is surprising that among the thirteen countries with CECFs, iShares underperform CECFs for eight of these countries (except Japan, Mexico, Singapore, Spain and Switzerland). Among the eleven countries with ADRs, ADR portfolios outperform iShares for ten countries (except Italy). The gain by iShares from the thirteen countries with CECFs is 0.0466, which is smaller than the gain by CECFs of 0.0627. Also, the gain by iShares from the eleven countries with ADRs is 0.0478, much smaller than the counterpart of 0.1020.

The results above also hold for two subperiods. The diversification gains are much higher (lower) in the second subperiod than the first period for iShares and CECFs (ADR portfolios). CECFs are more likely to outperform iShares in the second subperiod than in the first. However, ADR portfolios are more likely to outperform iShares in the first subperiod than the second.

Though they are difficult to interpret, these results are consistent with the previous findings of Jiang (1998) that ADR portfolios provide better diversification gains than foreign market indexes. This may suggest that ADR portfolios and actively managed CECFs concentrate on better-than-average firms from their respective markets, while iShares contain more extensively value-weighted assets. The inferior results for iShares could suggest that value-weighting within a country does not guarantee the mean–variance efficiency of a portfolio composed of value-weighted iShares.

### 4.4 Mean–variance spanning tests

#### 4.4.1 iShares versus CECFs

The rapid growth of iShares has generated competition with other financial instruments, which thus may become less attractive to investors. However, as shown in the previous section, iShares do not always outperform CECFs and ADRs, as anticipated. Alternatively, we could ask whether iShares are able to completely replace CECFs and ADRs in terms of diversification. In reality, US investors have an opportunity set including both iShares and their rivals: CECFs and ADRs. Even if iShares could offer the best diversification benefits as a single investment tool, CECFs and ADRs could still play a role if they provide supplemental diversification benefits over iShares.

In this subsection, we apply three spanning tests (described in Section 3.3) to investigate whether there are additional diversification gains in adding CECFs to the existing opportunity set, which consists of the S&P 500 index and iShares. In other words, we test whether adding CECFs can significantly extend the mean–variance efficient frontier constructed by the S&P 500 index and iShares. For comparison, only the thirteen countries for which CECFs exist are included in this test.

Figure 1 plots the shift in the mean–variance efficient frontier after adding thirteen CECFs to the benchmark set composed of the S&P 500 index and thirteen iShares. Although all assets, including the thirteen CECFs, lie within the original frontier formed by the S&P 500 index and thirteen iShares, US investors still can expand the efficient frontier by adding these CECFs to their portfolios. The optimal tangent portfolio moves up from T1 to T2 and the corresponding Sharpe ratio also increases.

Table 6 reports the $p$-values associated with HK, Ferson–Foerster–Keim (FFK) and BU test statistics on each of the thirteen CECFs as well as a joint test on all thirteen CECFs.1313In the joint test, the benchmark set includes the S&P 500 index and thirteen iShares; the test set includes thirteen CECFs. The value is explained as the degree to which we can reject the mean–variance spanning test. The HK test (Huberman and Kandel 1987) is the likelihood ratio test under OLS regression. The FFK test (Ferson et al 1993) is the regression-based GMM Wald test under conditional heteroscedasticity. The BU test (Bekaert and Urias 1996) is the GMM Wald test under the stochastic discount factor approach (see Section 3.3 for details).

All three tests are performed over the whole sample period as well as two subperiods. Table 6 also reports the associated change in Sharpe ratios ($\Delta\text{SHP}$), which can be used to demonstrate the economic significance. The results from the whole period show that the HK test rejects spanning at the 5% confidence level for all countries except Germany, Hong Kong and Malaysia. The joint test also rejects spanning, and the change in Sharpe ratios is 0.0414.

If returns exhibit conditional heteroscedasticity, the HK test, which relies on the normality assumption, may not be appropriate. For robustness of the results, we also applied two GMM Wald tests: FFK and BU. The results of these two tests are similar to those of the HK test for the entire period. Generally, the $p$-values of the FFK and BU tests are slightly higher than those of the HK test, which indicates the HK test may incur an over-rejection problem under the assumption of nonnormality.

The results for the two subperiods are similar. In both subperiods, the three joint tests all reject spanning for all CECFs. In the first subperiod the HK (FFK/BU) test rejects spanning for ten (nine/nine) out of the thirteen countries. In the second subperiod there are only ten countries with CECFs because those of Australia, France and Italy ceased to exist after 2004. In the second subperiod, the HK (FFK/BU) test rejects spanning for six (five/five) out of the ten countries. The economic significance is similar in both subperiods, with a change in Sharpe ratios of 0.0454 and 0.0401, respectively.

#### 4.4.2 iShares versus ADR portfolios

We apply the same spanning tests to investigate whether there are extra diversification gains when adding ADR portfolios to the existing opportunity set consisting of the S&P 500 index and iShares. For comparison, only the eleven countries for which ADR portfolios are available are included in this test.

Figure 2 plots the shift in the mean–variance efficient frontier after adding eleven ADR portfolios to the benchmark set composed of the S&P 500 index and the eleven iShares. The US investors can also expand the efficient frontier by adding ADR portfolios to the benchmark set. The optimal tangent portfolio moves up from T1 to T2 and the corresponding Sharpe ratio is also increased.

Table 7 reports the $p$-values associated with the HK, FFK and BU test statistics on each of the eleven ADR portfolios as well as a joint test on all ADR portfolios. All three tests are performed over the whole sample period and two subperiods. The results from the whole period show that the HK, FFK and BU tests consistently reject spanning at the 5% confidence level for all countries except France, Hong Kong, Mexico, Spain and Switzerland. The joint test also rejects spanning. The change in Sharpe ratio is 0.0794 for the joint test, which indicates that adding ADR portfolios generates significant extra diversification gains.

The results of the two subperiods do not vary much. In both subperiods, the three joint tests all reject spanning for all ADR portfolios. The HK (FFK/BU) test rejects spanning for seven (seven/six) of the eleven countries in the first subperiod and rejects spanning for eight (six/six) of the eleven countries in the second period. Further, the economic significance is stronger in the first subperiod than in the second subperiod, with changes in Sharpe ratios of 0.1421 and 0.0548, respectively.

#### 4.4.3 Domestically traded securities versus direct foreign investment

Sections 4.4.1 and 4.4.2 conclude that iShares cannot totally replace CECFs and ADR portfolios. Therefore, both CECFs and ADRs can maintain their roles as international diversification tools, even with competition from iShares. In this subsection, we examine the combination of these domestically traded securities as a substitute for costly direct foreign investment. Errunza et al (1999) found that domestically traded securities can mimic foreign market indexes by using CECFs and ADRs. Since Table 3 shows that iShares are highly correlated with foreign market indexes, it will be more likely to achieve the diversification gains as direct foreign investment with the help of iShares.1414In Table 3, the average correlation of iShares with MSCI indexes is 0.898. Moreover, combining iShares with CECFs and ADRs should increase this likelihood because the latter provide extra gains over iShares.

We construct three benchmark sets composed of domestically traded securities. Set 1 consists of the S&P 500 index and the corresponding iShares for all seventeen countries in the sample. Set 2 includes the S&P 500 index and the corresponding iShares and CECFs for all thirteen countries with CECFs. Set 3 includes the S&P 500 index and the corresponding iShares, CECFs and ADR portfolios for all nine countries for which both CECFs and ADRs are available. Further, we apply the mean–variance spanning tests to examine whether there are extra diversification gains by adding MSCI indexes to three sequentially augmented benchmark sets.

Table 8 reports the $p$-values associated with the HK, FFK and BU test statistics on each MSCI index as well as a joint test on all MSCI indexes for the three benchmark sets. All three spanning tests are performed over the entire sample period and two subperiods. Table 8(a) shows the results for the entire period. For the first set of benchmark assets, the HK test rejects spanning at the 5% confidence level for all seventeen countries except for Austria, Canada and Mexico. The FFK and BU tests provide consistent results, while the $p$-values are much higher for Germany, Italy and Spain. All three joint tests reject spanning. The change in Sharpe ratio is as low as 0.0217 for the joint test. These findings indicate that though iShares cannot mean–variance span MSCI indexes, the extra gains are relatively small.

As expected, the $p$-values increase as we move sequentially from set 1 to set 3. Take set 2, for example: the HK test fails to reject spanning for three more countries: Australia, France and Italy. Although most of the joint tests still reject spanning, both the FFK and BU joint tests fail to reject spanning at the 5% confidence level for set 3. The results indicate that adding CECFs and ADR portfolios to the benchmark set increases the likelihood that foreign market index returns are mean–variance spanned by US-traded assets.

Figures 3 and 4 illustrate the result above. Figure 3 plots the shift in the efficient frontier after adding seventeen MSCI indexes to the benchmark set composed of the S&P 500 index and seventeen iShares. Figure 4 plots the shift in the efficient frontier after adding nine MSCI indexes to the benchmark set composed of the S&P 500 index and all iShares, CECFs and ADR portfolios for nine countries. The shift in the efficient frontiers is far greater in Figure 3 than in Figure 4. Consistent with the result of the mean–variance spanning test, the two efficient frontiers almost overlap in Figure 4. Based on these results, we conclude that, although iShares alone fail to replace the foreign market indexes, a combination of iShares, CECFs and ADR portfolios could exhaust the gains from unattainable direct foreign investment. Therefore, investing in assets that only trade abroad would not be necessary in order to obtain the benefits of international diversification.

For a robustness check, parts (b) and (c) of Table 8 report the results for the two subperiods. Similarly to the results of part (a), tests for set 1 reject spanning for most countries, and the $p$-values increase on moving sequentially from set 1 to set 3 for both 1996–2004 and 2005–13.

## 5 Conclusion

iShares have become one of the most popular international diversification instruments in the United States. In this paper, we investigate the diversification benefits of iShares and their rivals (CECFs and American depositary receipts) between April 1996 and December 2004. Three important issues relating to these securities and international investment are addressed.

First, do iShares and their rivals provide effective diversification gains? We find that iShares, CECFs and ADR portfolios all exhibit significant exposure to the US market factors. Because of the open-ended nature of iShares, CECFs and ADRs behave more like US stocks than iShares. However, the limits of international arbitrage make iShares behave more like US stocks than their NAVs. Despite their exposure to the US market factors, iShares, CECFs and ADR portfolios all maintain significant exposure to their home country market factors. Based on correlations and portfolio optimization, we confirm that all these securities provide important diversification gains. However, the results do not support the hypothesis that iShares can exceed CECFs and ADRs.

Second, can iShares replace CECFs and ADRs for international diversification? The results of three mean–variance spanning tests provide strong evidence that iShares are not able to totally replace CECFs and ADR portfolios. Therefore, both CECFs and ADRs can maintain their roles as international diversification tools, even with the competition from iShares. This result also tends to forecast the coexistence of iShares, CECFs and ADRs in the future.

Third, can these domestically traded securities achieve the same diversification gains as costly direct foreign investment? The results of mean–variance spanning tests show that, although they are highly correlated with the foreign market indexes, iShares fail to substitute for them. However, a combination of iShares, CECFs and ADR portfolios could exhaust the gains from direct foreign investment. Therefore, the necessity of investing in assets that only trade abroad is questionable.

One unsolved issue needs further study. It is not clear why iShares provide lower diversification gains than CECFs and ADRs. One possible reason is that ADR portfolios and actively managed CECFs concentrate on better-than-average firms from their respective markets, while iShares contain more extensively value-weighted assets. Another reason could be that, as they belong to the same fund family, iShares may have higher correlations with each other than the relatively independent CECFs and ADRs.

## Declaration of interest

The authors report no conflicts of interest. The authors alone are responsible for the content and writing of the paper.

## Acknowledgments

We thank Farid Aït-Sahalia (the journal’s editor-in-chief), Shuming Liu, Raymond Kan, Tao Shu, Dragon Tang, the anonymous referee and seminar participants at University of Texas at Austin for helpful discussions and useful suggestions. We have benefited from the comments of participants at the Financial Management Association Annual Meeting 2006. We are grateful for research assistance from Yvonne Chou. The work described in this paper was partly supported by a grant from the Research Grant Council of the Hong Kong Special Administrative Region, China (Project CUHK 14501115). All remaining errors are our own.

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