Analysis of International ETF Tracking Error in Country-Specific Funds.
Keywords Exchange traded funds * Tracking error * Country-specific ETFs
Exchange-traded funds (ETFs), like mutual funds, invest in a pool of investment instruments. Unlike mutual funds, ETFs trade like individual shares on stock exchanges. ETFs have grown dramatically since their creation in 1990 (Davidson 2012). In 2016, the total number of ETFs worldwide was 4779 (Statista 2017). This study focuses on ETFs traded in the U.S. that have the stated objective of tracking a country-specific stock market index outside of the U.S. (e.g. ticker ASHR tracks the China Securities 300 Index in China). The goal of this study is to determine which fund or country-specific characteristics lead to accurate tracking of country-specific stock market indices.
Aggarwal (2004) finds it puzzling that investors in the U.S. tend to underweight international assets. However, Biais and Martinez (2004) point out there is a home bias due to better information closer to home and inefficiencies in international markets that produce different prices. For an investor in the U.S., investing in international ETFs should provide a low-cost method of reducing risk through diversification.
The majority of ETFs seek to track an index. Hougan (2015) contends that tracking difference is one of the most important statistics when evaluating ETF performance. Tracking difference is the difference between a fund's return and its benchmark return. Investors should expect "index fund returns will underperform the underlying index only to the extent of the management fees" (Frino and Gallagher 2001, p. 46). Several methods are used for calculating tracking error. Tracking error typically represents the average absolute value of the tracking difference or the standard deviation of the tracking differences.
Frino and Gallagher (2001) point out tracking error will always exist due to expenses, dividend payments, and the size and timing of index rebalancing. Pennathur et al. (2002), Mifire (2007) and Kanuri and McLeod (2015) question the diversification benefits of international ETFs due to U.S. price exposure and tracking error. Johnson (2009) studied tracking error between foreign ETFs and the underlying home index and foreign index returns relative to the U.S. index and whether the foreign exchange trades simultaneous with the U.S. markets were significant explanatory variables. Rompotis (2012) found German international ETFs are correlated with their underlying index, however, there is substantial tracking error.
Recent studies of ETF tracking error have focused on regional and global ETFs (Hassine and Roncalli 2013) and ETFs within a specific country. For example, Bas and Sarioglu (2015) focus on Turkish ETFs while Singh and Kaur (2017) focus on Indian ETFs. This unique study will look at all available country-specific ETFs. Additionally, this study will use the Heritage Foundation Economic Freedom Index (Miller and Kim 2017) as a possible explanatory variable for tracking error.
Data and Methodology
This study examines the tracking error of country-specific international ETFs relative to their benchmark. The ETF screener for the international equity category on Morningstar (2017) was used to identify country-specific ETFs. Screening for the China region (35), India equity (10), Japan stock (25), Latin America stock (12) and miscellaneous region (92) produced 174 ETFs. ETFs opened or closed in 2017, sector or size-specific (e.g. consumer sector, small-cap), diversified (e.g. blended funds of stocks and bonds), or invested in multiple countries were removed from the data set. This left 93 country-specific total market equity ETFs.
Table 1 summarizes the 93 country-specific ETFs from 47 different countries included in this study. For purposes of this study, Hong Kong and Taiwan are considered countries. Some countries have multiple ETFs (e.g. China has 10) whereas many countries have only one ETF (e.g. Vietnam). Multiple country-specific ETFs are included for several reasons. Each ETF tracking error will be examined with respect to five fund-specific characteristics and two country-specific characteristics. Thus, ETFs for the same country will have five fund-specific characteristics. Additionally, there are usually several unique country-specific benchmarks for a given country with multiple ETFs. For example, this study includes three country-specific ETFs for the total equity market in Brazil and each of those ETFs has a unique benchmark. Ticker EWZ uses the MSCI Brazil 25/50 Index, ticker DBBR uses the MSCI Brazil U.S. Dollar Hedged Index and ticker FBZ uses the NASDAQ AlphaDEX[R] Brazil Index. The use of unique benchmarks is common for the countries with multiple ETFs.
Dependent Variable: Tracking Error
Frino and Gallagher (2001) note several ways to measure tracking error. The average of the absolute value of the difference between ETF return and the benchmark return over some specified period is commonly used to measure tracking error. Absolute value is used in that under or over performance is a deviation from what an investor would expect and is an error. For this study, tracking error (Tracking Error) is defined as the absolute value of the median difference between the ETF net asset value return and the underlying benchmark return over a one-year period expressed in percentage terms.
Using the median rather than the average ensures there are half of the observations above and half of the observations below the tracking error value. The median tracking difference is taken from the previous 250 individual one-year observation periods. The data for median tracking difference were collected from ETF.com (2017).
Tracking Error = [absolute value of (250 trading day median : ETF 1 - year Return - Benchmark 1 - year Return)].
Tse and Martinez (2006) and Johnson (2009) used open hours of market overlap with the U.S. as an explanatory factor in their research. Overlap is the number of hours the country market is open during the hours of operation of the New York Stock Exchange. As overlap decreases, the chance of asymmetric information and mispricing increases. As overlap increases, the tracking error of the ETF is expected to decrease. The predicted coefficient estimate for the time overlap (.Hours-Overlap) expressed in hours is negative.
Bekaert and Harvey (1995) propose that countries become more or less integrated with one another over time. Similar to Johnson (2009), a measure of market integration is used as an explanatory variable in this study. As a market becomes highly integrated it is expected that tracking error would decrease. Peterson (2013) used The Heritage Foundation Economic Freedom Index (Miller and Kim 2017) for research comparing countiy-specific ETF returns with the Economic Freedom Index. Luo (2014) used the Economic Freedom Index to study volatilities in emerging markets. Morter (unpublished study) used subcomponents of the Economic Freedom Index to study ETF premiums and discounts. This tracking error study uses the 2017 index value for the Economic Freedom Index (Econ-Freedom). As economic freedom increases, the level of market integration increases. Countries that have a higher score on the Economic Freedom Index are expected to have lower tracking error. The predicted coefficient estimate for Econ-Freedom is negative.
Johnson (2009) found foreign index positive returns relative to the U.S. index were significant explanatory variables in the correlation coefficients between foreign ETF return and their underlying home index return. Johnson (2009) described this as a momentum effect. For purposes of this study, the relative return to the U.S. expressed as a percentage (Rel-Ret-to-USA) is calculated as the difference between the 1 -year ETF return and the 1 -year return on the Vanguard Total Stock Market ETF (ticker, symbol, VTI, return of 16.59% on August 5, 2017). The return data were collected from ETF.com (2017). The Vanguard Total Stock Market ETF was chosen since it is the largest ETF for the total U.S. equity market. As the relative return for the country-specific ETF increases, the tracking error is expected to decrease. The predicted coefficient estimate for Rel-Ret-to-USA is negative.
Fund-specific values for the number of holdings (UHoldings), assets under management expressed in billions of U.S. dollars (Fundsize), expense ratio expressed as a percentage (Expense-Ratio) and average daily dollar trading volume for the past 45 days as a percentage of assets under management (Liquidity) were collected from ETF.com (2017). As the number of holdings increases, it is harder to hold the optimal number of shares to mimic the benchmark (Aber et al. 2009). Thus, tracking error is expected to increase as the number of holdings increases, and the expected coefficient estimate for #Holdings should be positive. Tracking error is expected to decrease as the size of the fund increases (Chu 2011; Rowley and Kwon 2015). As the assets under management increase, more funds would be available to implement trading and tracking transactions, and tracking error should decrease. The expected coefficient estimate for Fundsize is negative. Since benchmarks do not include fees, tracking error is expected to increase as the expense ratio increases (Frino and Gallagher 2001). The expected coefficient estimate for Expense-Ratio is positive. Tracking error is expected to decrease as Liquidity increases (Osterhoff and Kaserer 2016). The more often ETF shares are traded, the more accurate the prices, returns and tracking error should be relative to the benchmark. The expected coefficient estimate for Liquidity is negative.
Table 2 summarizes the predicted relationship between the independent variables and tracking error. Table 3 lists the descriptive statistics (mean, median, minimum, maximum and standard deviation) for the tracking error and all of the independent variables.
Ordinary least squares regression with tracking error as the dependent variable was run on the independent variables.
Tracking Error = a + [[beta].sub.1] (Hours-Overlap) + [[beta].sub.2] (Econ-Freedom)+ [[beta].sub.3] (Rel-Ret-to--USA) + [[beta].sub.4] (#Holdings) + [[beta].sub.5] (Fundsize) + [[beta].sub.6] (Expense--Ratio) + [[beta].sub.7] (Liquidity) + [epsilon].
Table 4 reports the correlation coefficient and value between Tracking Error and each of the independent variables. Each of the independent variable correlation coefficients have the predicted sign for the relationship with Tracking Error. Econ-Freedom, Rel-Ret-to-USA, and Expense-Ratio are the three independent variables that have a statistically significant
correlation with Tracking Error in a univariate sense. The correlation coefficient is not statistically significant for Hours-Overlap, Fundsize, #Holdings and Liquidity. Ordinary least squares regression was conducted to see if these relationships hold in a multivariate sense.
Before considering the regression results, the possible effects of multicollinearity between the independent variables was considered. Table 4 reports the correlation coefficient and p-value between each pair of independent variables. The correlation coefficients can be used to determine if multicollinearity will be a problem in a multivariate regression. Allison (2012) indicates that multicollinearity starts to become a problem when correlation coefficients exceed 0.6 and variance inflation factors (VIF) exceed 2.5. The highest level of correlation between the independent variables is between Econ-Freedom and Expense-Ratio (-0.30). This is well below the level of correlation typically associated with multicollinearity issues. Additionally, Table 5 reports the VIFs for the independent variables are all below 1.30. Thus, the regression results can be interpreted under the assumption that multicollinearity is not a cause for concern.
Table 5 reports the results for the ordinary least squares regression with Tracking Error as the dependent variable. The overall model fit is better than similar studies (e.g. Johnson 2009) with an R2 of 0.37 and an adjusted [R.sup.2] of 0.31. The coefficient estimates for all seven of the independent variables had the predicted sign. Consistent with the findings from the correlation coefficients, Econ-Freedom, Rel-Ret-to-USA, and Expense-Ratio were the three independent variables that had a statistically significant effect on Tracking Error. Similarly, Hours-Overlap, Fundsize, #Holdings and Liquidity were not statistically significant in either the univariate or multivariate analyses.
Based on the coefficient estimates in Table 5, Tracking Error will decrease due to an increase in Econ-Freedom, an increase in Rel-Ret-to-USA and a decrease in the Expense-Ratio. If Econ-Freedom increases by one unit, then Tracking Error will fall by 0.04%. If Econ-Freedom increases by one standard deviation (9.33), then tracking error will fall by 0.37%. This result is consistent with market integration theory (Bekaert and Harvey 1995). As the index value increases, indicating more economic freedom and more economic integration, tracking error decreases. The use of Econ Freedom as an explanatory variable for tracking error is unique to this study and represents a new finding.
If Rel-Ret-to-USA increases by one unit then Tracking Error will fall by 0.04%. If Rel-Ret-to-USA increases by one standard deviation (13.81%), then tracking error will fall by 0.55%. This result is consistent with Johnson's (2009) momentum effect. As the country-specific ETF return increases relative to the total USA equity market, tracking error decreases.
Consistent with Frino and Gallagher (2001), as the expense ratio decreases, tracking error decreases. It would be intuitively pleasing if the estimated coefficient estimate for Expense-Ratio was one, indicating a one-for-one change in Tracking Error due to a change in expenses. In Table 5, if Expense-Ratio decreases by one unit then Tracking Error falls by 3.12%. If Expense-Ratio decreases by one standard deviation (0.15%) then tracking error falls by 0.47%. These results indicate higher expenses have an amplified effect on tracking error. The significance of Expense-Ratio is consistent with other recent studies. Rowley and Kwon (2015) and Chu (2011) also found that expense ratios have a significant positive relationship with tracking error.
The results for Hours-Overlap, Liquidity, and Fundsize have the predicted signs consistent with previous research, but were not statistically significant. Johnson's (2009) study of 20 ETFs found that the market trading hours overlap had a significant negative effect on tracking error. Osterhoff and Kaserer (2016) found that liquidity of individual stocks in the underlying portfolio had an impact on tracking error for German ETFs. Liquidity for this study was specific to the ETF liquidity rather than the individual stocks underlying the ETF. Chu (2011) for Hong Kong ETFs and Rowley and Kwon (2015) for U.S. ETFs found tracking error to be significantly negatively related to fund size.
Ninety-three country-specific exchange-traded funds (ETFs) from 47 different countries were examined in this study. In accordance with market integration theory (Bekaert and Harvey 1995), the Heritage Foundation Economic Freedom Index was a significant explanatory variable for tracking error. As the index value increases, indicating more economic freedom and more economic integration, tracking error decreases. In agreement with the Johnson's (2009) momentum effect, the ETF return relative to the USA equity market return is a significant explanatory variable for tracking error. As the country-specific ETF return increases relative to the total USA equity market, tracking error decreases. Finally, consistent with Frino and Gallagher (2001), the ETF expense ratio is a significant explanatory variable for tracking error. As the expense ratio increases, tracking error increases.
These findings should be of interest to investors seeking to invest internationally. The realized return from investing in a specific country can be noticeably different from its benchmark. For example, if the country's Econ-Freedom index is one standard deviation below average, the Rel-Ret-to-USA is one standard deviation below average and the Expense-Ratio is one standard deviation above average, the actual ETF return is predicted to be 1.39% below the benchmark return. Rel-Ret-to-USA cannot be known prior to investing. However, a given country's Econ-Freedom index and Expense-Ratio are relatively easy to find. Investors seeking returns from international investments should carefully examine their country of interest Economic Freedom Index and fund-specific expense ratio in order to anticipate any divergence from their exchange-traded fund return and the return of the benchmark index.
Limitations of the study include the specific time-period studied. The time-period was a specific one-year period of analysis. Tracking error may vary over time. Longer (e.g. five-year) and shorter (e.g. three-month) time-periods may produce different results. Another limitation is the definition of tracking error. The use of the median rather than the mean is unique to this study and may affect comparison with previous empirical research.
Future research could examine the robustness of the findings of this paper. Some suggestions could be the use of different proxies for tracking error, examining different time-periods (i.e. three-month tracking error, five-year tracking error, etc.) and controlling for regional differences between groups of countries. Furthermore, examining additional explanatory variables such as proxies for market size (e.g. gross domestic product) and market volatility (e.g. standard deviation of benchmark returns) may be worth consideration.
Acknowledgements The author would like to thank the participants of the international financial markets session at the Eighty-Fourth International Atlantic Economic Conference, held October 5-8,2017 in Montreal. Canada for their useful comments and suggestions.
Published online: 2 May 2018
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Kent T. Saunders 
[mail] Kent T. Saunders
 Anderson University, Anderson, SC. USA
Table 1 Country-specific ETFs sorted by number and country Country ETFs Country ETFs China 10 Switzerland 2 Japan 10 Taiwan * 2 Germany 6 Argentina 1 United Kingdom 6 Austria 1 South Korea 4 Belgium 1 Brazil 3 Chile 1 Canada 3 Denmark 1 Australia 2 Egypt 1 Colombia 2 Finland 1 Hong Kong * 2 France 1 India 2 Greece 1 Indonesia 2 Ireland 1 Israel 2 Italy 1 Mexico 2 Malaysia 1 Norway 2 Netherlands 1 Poland 2 New Zealand 1 Country ETFs Nigeria 1 Peru 1 Philippines 1 Portugal 1 Qatar 1 Russia 1 Saudi Arabia 1 Singapore 1 South Africa 1 Spain 1 Sweden 1 Thailand 1 Turkey 1 United Arab Emirates 1 Vietnam 1 * For purposes of this study, Hong Kong and Taiwan are considered countries. Source: Own calculations using Morningstar (2017) and ETF.com (2017) Table 2 Independent variables and the predicted relationship with Tracking Error Independent Predicted Source Variable Relationship Hours-Overlap Negative (-) Johnson (2009) Econ-Freedom Negative (-) Bekaert and Harvey (1995) Rel-Ret-to-USA Negative (-) Johnson (2009) #Holdings Positive (+) Aber et al. (2009) Fundsize Negative (-) Chu (2011) Expense-Ratio Positive (+) Frino and Gallagher (2001) Liquidity Negative (-) Osterhoff and Kaserer (2016) Table 3 Descriptive statistics (rounded to two decimals) Variable Mean Median Minimum Tracking Eiror (%) 0.88 0.56 0.01 Hours-Overlap (hours) 1.53 0.00 0.00 Econ-Freedom (index #) 68.72 69.60 50.40 Rel-Ret-to-USA* (%) 4.21 2.46 -46.01 #Holdings (#) 106.37 55.00 20.00 Fundsize (Billions USS) 0.92 0.13 0.0015 Expense-Ratio (%) 0.58 0.60 0.30 Liquidity (%) 1.95 1.39 0.03 Variable Maximum Std. Dev. Tracking Eiror (%) 12.79 1.45 Hours-Overlap (hours) 6.50 2.18 Econ-Freedom (index #) 89.80 9.33 Rel-Ret-to-USA* (%) 43.63 13.81 #Holdings (#) 946.00 135.03 Fundsize (Billions USS) 16.70 2.21 Expense-Ratio (%) 1.10 0.15 Liquidity (%) 10.09 1.90 * the 1-year return on the Vanguard Total Stock Market ETF. which is the largest ETF for the total USA equity market, was 16.59% as of August 5. 2017 from ETF.com (2017). Source: Own calculations using data from Miller and Kim (2017) and ETF.com (2017) Table 4 Correlation matrix with p-value in parentheses (rounded to two decimals) Tracking Hours- Econ- Rel-Ret- Error Overlap Freedom to-USA Tracking 1.00 Error Hours- -0.12 1.00 Overlap (0.25) Econ- -0.32 -0.01 1.00 Freedom (0.00) ** (0.89) Rel-Ret- -0.36 -0.07 -0.10 1.00 to-USA (0.00) ** (0.50) (0.36) #Holdings 0.05 -0.29 -0.19 0.08 (0.66) (0.01) ** (0.07) (0.44) Fundsize -0.07 -0.05 -0.04 0.06 (0.53) (0.61) (0.71) (0.57) Expense- 0.46 -0.08 -0.30 -0.17 Ratio (0.00) ** (0.47) (0.00) ** (0.10) Liquidity 0.01 0.19 -0.27 0.01 (0.94) (0.07) (0.01) ** (0.94) Expense- #Holdings Fundsize Ratio Liquidity Tracking Error Hours- Overlap Econ- Freedom Rel-Ret- to-USA #Holdings 1.00 Fundsize 0.20 1.00 (0.06) Expense- -0.15 -0.10 1.00 Ratio (0.16) (0.36) Liquidity -0.12 0.19 0.00 1.00 (0.24) (0.07) (0.99) * and ** denote statistical significance at the 5% and 1% level of significance respectively. Source: Own calculations using data from Miller and Kim (2017) and ETF.com (2017) Table 5 OLS Regression results on Tracking Error (rounded to two decimals); N=93 Variable Coefficient Std. Error Intercept 2.11 1.50 Hours-Overlap -0.07 0.06 Econ-Freedom -0.04 0.02 Rel-Ret-to-USA -0.04 0.01 #Holdings 0.00 0.00 Fundsize -0.02 0.06 Expense-Ratio 3.12 0.95 Liquidity -0.02 0.07 [R.sup.2] 0.37 Adjusted [R.sup.2] 0.31 Variable t Stat P-value VIF Intercept 1.41 0.16 Hours-Overlap -1.15 0.25 1.15 Econ-Freedom -2.60 0.01 * 1.35 Rel-Ret-to-USA -3.75 0.00 ** 1.07 #Holdings 0.45 0.65 1.30 Fundsize -0.37 0.71 1.10 Expense-Ratio 3.30 0.00 ** 1.26 Liquidity -0.31 0.76 1.22 [R.sup.2] Adjusted [R.sup.2] * and ** denote statistical significance at the 5% and 1% level of significance respectively. Source: Own calculations using data from Miller and Kim (2017) and ETF.com (2017)
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|Title Annotation:||exchange-traded funds|
|Author:||Saunders, Kent T.|
|Publication:||Atlantic Economic Journal|
|Date:||Jun 1, 2018|
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