Analysis of the Tracking Error of Country Specific
German Exchange Traded Funds
Thesis MSc Finance Author: G. Falkenberg1 Supervisor: Dr. A. A. Tsvetkov University of Groningen 11-06-2019 Abstract
The aim of this study is to examine the relationship of the economic freedom index, market impact costs and turnover on the average daily tracking error from international exchange traded funds (ETFs). I use data for 92 country specific ETFs traded at Xetra from September 2013 to December 2018. The influence of the economic freedom index and market impact costs are not different from zero, whereas the turnover has a positive impact. Latter is too small to provide explanatory power and to be regarded significant. Further I find that physical ETFs have significantly lower tracking error than synthetic ETFs on average. This study extends the literature by evaluating the influence of economic freedom as well as ETF specific market impact costs on the tracking error of German ETF and corroborate the findings of recent literature
Keywords: exchange traded fund, tracking error, XLM, country-specific ETFs JEL classification: G10; G15; G19
Table of content
1. Introduction ... 4
2. Characteristics of exchange traded funds ... 5
3. Literature review ... 6
3.1. Determinants of tracking error ... 6
3.2. Economic freedom index ... 8
3.3. Possible research gaps ... 10
4. Methodology ... 12
4.1. Calculating tracking error ... 12
4.2. Specification of the regression ... 13
5. Description of the sample data ... 18
5.1. Descriptive statistics ... 21
5.2. Statistical tests ... 23
6. Empirical results ... 25
7. Interpretation of the results ... 29
8. Conclusion ... 32
9. List of references ... 33
List of tables
Table 1: Summary of the expected coefficients ... 10
Table 2: Geographical distribution of the etfs and underlying indices ... 19
Table 3: Descriptive statistics of tracking error per sample year in per cent ... 20
Table 4: Descriptive statistics of the tracking error per continent in per cent ... 20
Table 5: Descriptive statistics of the economic freedom index per continent ... 20
Table 6: Descripitve statistics for the indepent variables ... 22
Table 7: Pairwise correlation matrix of the dependent and independet variables ... 22
Table 8: Results of the complete regression ……….27
Table 9: Results of the regression distinguished by continents ………...…....28
1. Introduction
This study analysis the effect of market impact costs and market integration on the tracking error of international passive exchange traded funds (ETF). I use a sample of 92 ETFs traded on the German stock exchange Xetra over a period from September 2013 to December 2018. Xetra is an online exchange, linked to the Frankfurt stock exchange, with an average daily trading volume of 6 billion euros (May 2019). Understanding the determinants of tracking error is crucial for investors, managers and issuers as passive ETFs are evaluated based on the tracking error and are commonly used as investment and hedging instruments. The tracking error measures the quality of the index replication by the standard deviation of the differences in return between ETF and index. A higher tracking error means, that the return deviates from the index return more inconsistently which can accumulate to a significant loss in long-time performance and complicate hedging (Charupat and Miu, 2013). Researchers and issuers study the impact of different factors on the tracking error and find that the tracking error is mainly influenced by the total expense ratio and dividends. Further to this, numerous studies state hypotheses about the effects of liquidity, size, replication strategy and volatility on the tracking error. This study will control for these factors and investigate the effect of market integration and market impact costs on international ETFs with a fixed effect regression using Driscoll-Kraay standard errors. These factors are important as the ETF market grows rapidly, and ETFs replicate also indices from emerging markets. Those new markets can be restricted by governments through regulations which can complicate trading. This study measures this effect with the economic and investment freedom index provided from the heritage foundation. I find that the effect is neither economically nor statistically significant in my sample. Further I test for the effect of market impact costs on the tracking error, which is insignificant in my sample. My study corroborates findings of the literature on the impact of volatility and turnover and expands the literature by testing the effect of economic freedom for German ETFs.
2. Characteristics of exchange traded funds
As some concepts and terms are specific for ETFs and might cause confusion, the next paragraph briefly explains relevant specifications and provides general background information.
International ETFs are funds that track indices which are not domestic to the exchange they are traded on (Charupat and Miu, 2013). These funds are commonly used as investment and hedging instruments. In the last decades the number and volume of ETFs have increased significantly. Institutional as well as private investors have shown rising interest as ETFs can be traded easily over an exchange and provide access to a diversified portfolio. The possibility to mimic an index in a cheap and convenient matter with a liquid and exchange traded instrument, is one of the main advantages of ETFs.
3. Literature review
To evaluate the performance of passive ETFs the most common metrics are tracking difference and tracking error. In the literature, tracking error is defined as the standard deviation of the ETFs excess return over its benchmark over a specific period of time (Pope and Pradeep, 1994; Roll, 1992). The financial industry as well as the IOSCO and ESMA second this definition (IOSCO, 2013). The term tracking difference is defined as the absolute difference between the return of the ETF and the return of its benchmark (Johnson et al., 2013). This differentiation is crucial as it is often not clearly specified in the literature, which mostly uses the term tracking error, even though the measurements have contrasting interpretations. The tracking error measures the consistency and quality of index replication whereas the tracking difference captures the magnitude of the difference in absolute terms (Johnson et al., 2013). Important for both measures is the use of absolute difference, as otherwise positive and negative deviations might cancel each other out which results in an underestimation of the tracking error and difference (Frino and Gallagher, 2001). At this point it should be noted that a positive deviation from the benchmark (outperformance) is undesirable as well, as the goal of passive ETFs is to copy the benchmark as best as possible and not to outperform it (Hassine and Roncalli, 2013).
3.1. Determinants of tracking error
The most common explanatory variable is the total expense ratio (also management fee). Fees are charged by annualized rates based on the average net asset value of the ETF to compensate the costs of the issuer. The higher the expense ratio of an ETF, the more the ETF is expected to underperform the benchmark resulting in a larger tracking error, ceteri paribus (Charupat and Miu, 2013; Osterhoff and Kaserer, 2016). This positive coefficient is proven significant, statistically as well as economically, by the majority of the literature and is often described as the most important factor of tracking error (see for example Blitz, Huij, and Swinkels, 2012; Elton, Gruber, Comer, and Li, 2002; Frino and Gallagher, 2001; Osterhoff and Kaserer, 2016). Chu (2013) is one of the few that find a negative coefficient for the total expense ratio.
taxation by offering net indices, which reinvestment the dividends accounting for the worst possible dividend withholding tax rate. This allowed a more precise measurement of the impact of the dividend yield on the tracking error, which reduced the effect (Blitz et al., 2012). According to Frino and Gallagher (2001), dividends results in the fact that “prefect replication of the S&P500 is unachievable” and consequently in the existence of tracking difference and error. Following studies are able to support this finding of positive correlation between dividends and tracking error on the European as well as on Hong Kong’s market (Blitz et al., 2012; Chu, 2013). This effect is larger in periods with high dividend payments and may even lead to a seasonality in tracking error (Frino and Gallagher, 2001). Studies based on these results concluded that not only the dividend payments influence the tracking error but also that the withholding of dividend taxes explains a part of the tracking error (Blitz et al., 2012). The percentage of cash held by the ETF is also positively correlated to the tracking error, as the liquid asset is unable to track the index and leads to a “cash drag”. This effect may be larger in periods with large net cash flows (Frino and Gallagher, 2001; Osterhoff and Kaserer, 2016).
When measuring the effect of market liquidity on the tracking error, research focused on proxies such as trading volume and bid ask spreads. The results from recent studies are contradictory: Klein and Kundisch (2009) find a negative correlation between tracking error and trading volume for German ETFs and DAX certificates whereas Chu (2016), Delcoure and Zhong (2007), and Rompotis (2006) observe a counterintuitive positive correlation for their samples of Hong Kong traded and iShares ETFs. They explain this relationship with the hypothesis, that the higher turnover is caused by differences in investors beliefs. Those different options indicate mispricing which causes a higher tracking error (Blume et al., 1994). When measuring liquidity with bid-ask spreads the literature agrees on a statistical and economic positive correlation: a larger bid-ask spread correlates with a larger tracking error (Osterhoff and Kaserer, 2016)2. Osterhoff and Kaserer (2016) establish a new approach by using Xetra‘s liquidity measure XLM3 and therefore measuring the liquidity of an ETF based on the daily liquidity cost of the underlying stocks. They find a significant positive correlation, meaning that a larger liquidity cost of the underlying stocks leads to an increase in tracking error, although the impact is relatively small compared to the factors discussed above. The effect of the market impact costs on ETF level has not been studied yet.
The impact of volatility on the tracking error should be zero if perfect replication would be possible as the index and the ETF are aligned precisely. Due to the unfeasibility, of - even theoretical - perfect replication, the volatility of the index will increase the tracking error of the ETF causing a direct positive relationship (Chu, 2016; Frino and Gallagher, 2001; Qadan and Yagil, 2012). Qadan and Yagil (2012) conclude in their study about the impact of highly
volatile periods on the tracking error that in times of high volatility, the tracking ability of domestic ETFs is reduced - especially for ETFs in financial and real estate markets. Rompotis (2011) finds in his study on iShares ETFs that the risk of an ETF, measured by its volatility, significantly increases the tracking error.
Chu (2013) assumes that the size of an ETF is negatively correlated to the tracking error due to economies of scale: a larger fund is able to reduce transaction cost as well as further optimise mirroring the index. He finds a statistical significance for his sample of the Hong Kong market (Chu, 2013), which is supported by the findings of Cresson, Mike Cudd, and Lipscomb (2002) and Rowley and Kwon (2015). However, latter are hesitant to support the economic significance as the argumentation with economies of scale sounds dubious to them.
The choice of replication strategy can greatly influence performance of the ETF as it does not only influence the tracking properties but also the ability to attract customers (Abner, 2016). Full replicating ETFs hold the complete basket of the underlying index. This allows an accurate tracking but also exhibits high costs as even small stocks of the index have to be replicated, which effect on the index might not be worth the cost (Abner, 2016). Optimization strategies try to mimic the return of the index by investing into an optimised sample of the underlying securities and still maintain the risk and return characteristics. This strategy is often used if the index does not provide enough liquidity to be able to consistently trade the complete basket, which increases transaction costs (Frino and Gallagher, 2001). Swap based ETFs replicate the return of the index by lending its holdings to a counterparty (typically an investment bank) and then swapping the yield of the loan with the return of the index (Drenovak et al., 2014). This replication method is often referred to as synthetic replication. Synthetic ETFs are supposed to outperform physically replicating ETFs as they do not experience a cash drag and less trading costs (Johnson et al., 2013). However Drenovak et al. (2014) argue that this is only due to the different measurement methods and that physical ETFs are supposed to outperform synthetic ETFs regarding the tracking error and vice versa regarding the tracking difference. B. Johnson et al. (2013) and Mateus and Rahmani (2017) are unable to support Drenovak et al. (2014) finding as they find that synthetic ETFs have a lower tracking error than physical and no significant relationship between tracking error and replication method respectively.
3.2. Economic freedom index
production, distribution, or consumption of goods and services beyond the extent necessary for citizens to protect and maintain liberty itself” (Miller and Kim, 2013). The index measures the capability of companies and persons to make their own decisions and how much the government or other third parties interfere with the choice by regulations or constraints. (Miller and Kim, 2018). It ranges from the openness of markets to the effectiveness of laws and governments.
The index quantifies the economic freedom of a country on a scale from 1 to 100, in which 100 is the highest freedom value, based on following factors4:
• Property rights • Judicial effectiveness • Government integrity • Tax burden • Government spending • Fiscal health • Business freedom • Labour freedom • Monetary freedom • Trade freedom • Investment freedom • Financial freedom
Economic freedom is calculated as a combination of these factors and is not supposed to measure the economic growth of the economy but rather the rate at which economies are able to adjust to a changing world economy (Peterson, 2013). Even though, Miller and Kim (2018) argue, that there is a direct relationship between economic freedom and prosperity.
In my model the indices of economic and investment freedom are seen as a measurement for market integration (Johnson, 2009). Following Miller and Kim (2018), this is plausible as an economy that is more free is able to and will integrate in the global market. The straightforward quantitative approach of measuring market integration with the correlation between the return of the country index and the global index is not accurate as a different portfolio mix can lead to low correlation even though the markets are highly integrated (Pukthuanthong and Roll, 2009).
A higher market integration and freedom is supposed to result in easier and cheaper trading of financial instruments and should therefore increase the capability of traders to track the index. Especially the aspect of investment freedom should show this correlation as it assesses the free flow of capital which is necessary to invest in foreign markets. Hence a higher
economic freedom and investment freedom should result in a lower tracking difference. Saunders (2018) finds that there is a small negative statistically significant coefficient for international ETFs traded in the US.
W. F. Johnson (2009) regresses the Economic Freedom Index, among other variables, on ETF returns and cannot find statistically significant coefficients, even though he economically argues that a higher integration should lead to a higher return of the country index as well as the ETF. This is seconded by the Heritage foundation as their argumentation states that higher economic freedom leads to prosperity in the country (Miller and Kim 2018). The higher integration does not result in a higher return but in a lower tracking error, as foreign parties are able to invest into countries more easily and can therefore reduce costs associated with tracking the index (Saunders, 2018). As barriers - measured by economic and investment freedom - decrease, markets become more open for ETF issuers. A higher competition can further reduce tracking error as issuers are motivated to further optimise the tracking error to gain an advantage above the competition.
Table 1: Summary of the expected coefficients
Variable Relationship Source
Total expense ratio positive Frino and Gallagher 2001; among others
Dividend yield positive Elton et al., 2002
Physical replication negative B. Johnson et al. 2013
Synthesised replication positive B. Johnson et al. 2013
Accumulating positive Frino and Gallagher 2001
Distributing negative Frino and Gallagher 2001
Volatility of the Index positive Frino and Gallagher 2001
XLM positive Osterhoff and Kaserer 2016
Turn Over positive/negative Chu 2013; Klein and Kundisch 2009
Log. Asset under
Management negative Chu 2013
Economic Freedom negative W. F. Johnson 2009; Saunders 2018
Investment Freedom negative W. F. Johnson 2009; Saunders 2018
Notes: This is a summary of the most common factors that determine the tracking error of ETFs consisting of the factor (left), the sign of the expected coefficient (middle) and a literature reference (right). Positive means an increase in the variable should lead an increase in the tracking error and vice versa.
3.3. Possible research gaps
In my study I intend to find results comparable to recent studies. I include the factors total expense ratio, treatment of dividends, volatility of the index, Xetras liquidity measure, Xetra turnover, the logarithm of assets under management, the economic freedom index as well as the investment freedom index.
To my knowledge the effect of market integration on tracking errors has not been tested for German ETFs yet. This factor can be important for investors that are trying to hedge with passives ETFs. If the quality of the replication of the benchmark is linked to the economic freedom of the country, investors are able to quickly assess the expected divergence of the ETF from its benchmark for the specific country (Saunders, 2018). Therefore investors would be able to forecast the additional risk for the specific country more reliable. Saunders (2018) regressed the economic freedom index on the tracking error of US ETFs. My study adapts and tests his result for German traded ETFs. As recent studies have shown, there are significant differences between European, Asian and US ETFs regarding tracking error and its determinants(Aber et al., 2009; Chu, 2013; Rompotis, 2012). Therefore, I assume, that the influence of market integration on the tracking error can differ across different exchanges too. I adept Saunders (2018) study by, using the XLM as a proxy for liquidity as extension to average trading volume and not include variables with dubious economic significance. Thus, this study extends the literature by examine the influence of economic freedom and ETF specific market impact costs on the tracking error of German ETF as well as corroborate the findings of recent literature.
From this follow my research questions:
RQ1: Which influence has the implicit liquidity cost, containing of bid-ask spread and market impact, of ETFs on their average daily tracking error?
RQ2: Is the tracking quality of country specific ETFs traded in Germany influenced by the market integration and restrictions of capital flows of the underlying country?
4. Methodology
The tracking error is defined in the literature as the standard deviation of the fund’s excess returns over the underlying index in a specific period. This is not to be confused with the tracking difference which measures the absolute excess return over a given period (Johnson et al., 2013). This study focuses on the replication quality of the ETF and not the actual performance difference between the ETF and the index. Therefore, I decide to use the tracking error and not the tracking difference.
4.1. Calculating tracking error
To calculate the tracking error one can either choose the change in net asset value (NAV) or the change in price over the chosen period. The literature suggests calculating the tracking error based on the NAV as it only reflects the manager performance of replicating the index and the price might be biased due to mispricing’s and unexploited arbitrage opportunities (Osterhoff and Kaserer, 2016). As this thesis is focused on the quality of the ETF to replicate the index and investor have to buy/sell ETFs at the market price and not the NAV, I choose to use the market price of the ETF instead (Mateus and Rahmani, 2017). The price of ETFs is efficient regarding their NAV which allows me to use the price instead of the NAV return without facing major biases (Tse and Martinez, 2007). Furthermore Ackert and Tian (2008) find a negative relationship between liquidity and mispricing. As liquidity is included in the regression, the relationship between liquidity and mispricing should counteract the bias and the effect of the mispricing will be nested in the liquidity coefficient.
I choose to base my study on monthly observation. The macroeconomic factors influencing the economic freedom index are rather consistent over time as they only change slowly which would make an analysis of daily or weekly data inefficient. Therefore, I use monthly observations to be able to investigate the change over time and still have a sufficient sample size for a time-series analysis. As the risk of overestimating the tracking error is as high in low frequency data as in high frequency data, this choice does not increase the exposure to this risk (Meinhardt, Mueller, and Schoene, 2015 as cited in Osterhoff and Kaserer, 2016)
As this study examines passive ETFs, the tracking error is calculated as the standard deviation of the ETF return over the index return. This is more appropriate as the aim of passive ETFs is to replicate the benchmark as close as possible opposed to active ETFs which focus on excess return. Therefore, I use the tracking error as a qualitative measurement (Drenovak et al., 2014; Mateus and Rahmani, 2017).
𝑟𝑖,𝑡 =
𝑆𝑖,𝑡
𝑆𝑖,𝑡−1− 1 Equation (1)
Where 𝑟𝑖,𝑡 is the return on the Index i – or the ETF e respectively - for the period t and
𝑆𝑖,𝑡is the price of the Index i / ETF e at the day t. Following this, I compute the daily excess return 𝑥𝑒,𝑡 of the ETFs over the indices following Equation (2)
𝑥𝑒,𝑡 = 𝑟𝑒,𝑡− 𝑟𝑖,𝑡 , Equation (2) where 𝑥𝑒,𝑡 is the deviation of the ETF e from his benchmark in period t and 𝑟𝑒/𝑖,𝑡 is the
daily return of the index i and the ETF e respectively.
The calculation of the tracking error follows Equation (3), 𝑇𝑟𝑎𝑐𝑘𝑒,𝑡 = √1
𝑛𝑡∗ ∑(𝑟𝑒,𝑡− 𝑟𝑖,𝑡)
2
Equation (3)
where 𝑇𝑟𝑎𝑐𝑘𝑒,𝑡 is the average daily tracking error for a specific ETF e in period t ,
(𝑟𝑒,𝑡− 𝑟𝑖,𝑡) is the deviation of the ETF e from his benchmark in period t calculated in Equation
(2). (Mateus and Rahmani, 2017; Pope and Pradeep, 1994; Roll, 1992).
The Variable Vola describes the volatility of the daily index return over a monthly period. It is calculated by square root of the average daily squared deviation from the monthly mean:
𝜎𝑖,𝑡 = √ 1
𝑛𝑡− 1∗ ∑(𝑟𝑖,𝑑− 𝑟̅̅̅̅)𝑖,𝑡
2
Equation (4)
Where 𝜎𝑖,𝑡 is the monthly volatility for a specific index i, 𝑟𝑖,𝑑 is the return in period d for index i, 𝑟̅̅̅̅ is the average return for the index i in month t and 𝑛𝑖,𝑡 𝑡 is the amount of trading days
for month t.
4.2. Specification of the regression
A Hausman test evaluates the correlation between the random effect and the regressors. This is crucial as random effect models are biased if the individual effects and at least one of the regressors show significant correlation (Greene, 2003). The null-hypothesis states that the random effect model is unbiased – there is no significant correlation between the regressors and the individual effect. I rejected this hypothesis at all relevant significance levels and conclude that the random effect estimator is biased. This result supports my choice of a fixed effect model, as it shows that there are significant induvial effects, time or entity specific, which are correlated with the regressors.
The null hypothesis of the F test is that all individual effects are not different from zero. As the test results in a significant p-value at the 1% level, I reject the null hypothesis and conclude that there are significant fixed effects and that therefore the fixed effects estimator is appropriate (Greene, 2003).
Fixed effect models analyse the relationship between the dependent and independent variables within an entity (ETF). The regression controls for time-invariant effects, such as replication strategy, for each ETF by time-demeaning the data (Wooldridge, 2012). This allows me to study the net effect of the time-variant variables on the tracking error. The period of 64 months allows me further to study the dynamic effect over the last five years.
The Regression is computed with Driscoll-Kraay robust standard errors to account for the heteroskedasticity, autocorrelation and cross-sectional dependence (see Data for further details) to receive unbiased and efficient estimates.
The fixed effect estimation is based on Equation (5):
𝑦̃ 𝑖,𝑡 = (𝛼 + 𝑣𝑖) + 𝛽1𝑥̃1 𝑖,𝑡+ 𝛽2𝑥̃2 𝑖,𝑡… + 𝑢̃𝑖,𝑡 Equation (5) Where 𝑣𝑖 is the unknown intercept for each entity i, 𝛼 the constant, 𝑦𝑖,𝑡is the dependent variable for entity i and time t, 𝛽 is the coefficient for the indicated independent variable, 𝑥𝑖,𝑡 represents the independent variable , and 𝑢𝑖,𝑡 the error term. (Baltagi, 2005; Greene, 2003)
The notation 𝑥̃ follows from Equation (6) and describes the time de-meaning used in the fixed effects estimator, which is consistently used in the following equations:
𝑥̃𝑖,𝑡 = 𝑥𝑖,𝑡− 𝑥̅𝑖 Equation (6) where 𝑥̅ stands for the average of 𝑥𝑖 𝑖,𝑡. (Baltagi, 2005; Greene, 2003)
This leads to Equation (7) which is the complete panel-based regression model with fixed effects estimation:
𝑇𝑟𝑎𝑐𝑘̃𝑖,𝑡 = (𝛼 + 𝑣𝑖) + 𝛽1𝑉𝑜𝑙𝑎̃𝑖,𝑡+ 𝛽2𝑋𝑒𝑡𝑟𝑎𝑇𝑂̃ 𝑖,𝑡+ 𝛽3𝑋𝐿𝑀̃𝑖,𝑡 + 𝛽4𝐸𝑐𝑜𝐹𝑟𝑒𝑒̃ 𝑖,𝑡+𝛽5𝐼𝑛𝑣𝐹𝑟𝑒𝑒̃ 𝑖,𝑡+ 𝛽6𝐿𝑜𝑔𝐴𝑢𝑀̃ 𝑖,𝑡 + 𝛽7𝐷𝑖𝑣𝑌𝑖𝑒𝑙𝑑̃ 𝑖,𝑡+ 𝛽8𝑇𝐸𝑅𝑎𝑡𝑖𝑜̃ 𝑖,𝑡+ 𝑢̃𝑖,𝑡 ,
Equation (7)
where 𝑇𝑟𝑎𝑐𝑘𝑖,𝑡 is the average daily tracking error for the month t as calculated in Equation (3)
Vola describes the volatility of the daily index return over a monthly period. It is
calculated using Equation (4). I expect a significant positive coefficient. Tracking error is created by deviations between the return of the ETF and the underlying index. These deviations are due to differences in holdings as the ETF can never perfectly mirror the index at all times (Frino and Gallagher, 2001). The higher the volatility of the underlying index, the larger the influence of these small deviations, as the ETF cannot follow the index return precisely. Thus, resulting in a higher tracking error. This assumption was proven true in numerous studies, for example Frino and Gallagher (2001) and Qadan and Yagil (2012). Even though studies have already proven the significant influence of the volatility on the tracking error, it is still important to include it in the regression to not suffer from omitted variable bias.
XetraTO describes the monthly turnover of the ETF in 100.000€ on Xetra. The turnover
measures the average daily monetary value of all trades for a specific month on the exchange. It therefore allows to access the trading volume over a specific period and establish periods of high and low trading activity. Studies find positive as well as negative coefficients for trading volume (Delcoure and Zhong, 2007; Klein and Kundisch, 2009; Rompotis, 2006). I assume, that the relationship between turnover and tracking error is positive as turnover can be seen as a proxy for differences in investor beliefs which causes price deviations (Blume et al., 1994; Chu, 2016; Delcoure and Zhong, 2007). Therefore, I predict a positive sign for the coefficient of XetraTO.
XLM is the Xetra Liquidity Measure (XLM), which measures the market impact costs
with only the bid-ask spread. As a higher liquidity cost is supposed to lead to a higher tracking error I expect a positive significant coefficient.
EcoFree describes the value of the Economic Freedom Index in the specific month and
for the specific country. As the data is investigated by the heritage foundation over a period of a year, I decided not to edit the data by interpolating but rather assume that the index does not change over a period of one year. A higher economic freedom is supposed to represented a higher international market integration (Miller and Kim, 2018). I assume that the higher market integration reduces the tracking error of ETFs as replicating the index becomes easier which would result in a negative coefficient.
InvFree describes the value the of the Investment Freedom Index in the specific month
and for the specific country. It especially asses the free flow of capital with a focus of foreign capital by assessing the framework for investing, focusing on transparency and a broad spread of different equities. Any restrictions to the free flow of capital affect the score negative, disregarding if they are national or international. Restrictions on the flow of capital can affect the possibility and cost of managers to hold and trade the underlying assets of an ETF. Therefore, I assume that countries with high restrictions and obstacles should experience a higher tracking error as opposed to countries with a high investment freedom. Thus, the coefficient for InvFree should be negative. Both freedom indices are measured on a scale from 1 to 100 where 100 is highest possible value.
𝐿𝑜𝑔𝐴𝑢𝑀 describes the Assets under Management (AuM), which is the amount of money invested into the ETF and indicates the size of the fund. In my study AuM is measured in millions of Euros. As the spread between small and large funds ranges from 1,88 M€ to 36.685M€ (see Table 6), and I believe that the relationship between the assets under management and the tracking error is rather proportional than linear, I choose to use the natural logarithm of the fund size (Chu, 2013). The influence of the size of an ETF on its tracking error is not certain. Even though studies have found statistically significant negative coefficients, some researchers are hesitating to accept the economic theory which explains the relationship (Chu, 2013; Rowley and Kwon, 2015). The tracking error is supposed to decrease if the volume of the ETF increases, as the manager can make better use of the economies of scale and lower the relative transaction costs. In my opinion this theory make sense, especially if you take into consideration that the effect of the size of an ETF is only a small factor and does not have to explain a major part the tracking error. Therefore, I anticipate a negative significant coefficient for LogAuM.
DivYield measures the dividend yield of the ETF in per cent, calculated as the dividend
cash to be held by the ETF, I assume that months with higher dividend yields have a higher tracking error due to the cash-drag. This is significant in numerous studies such as Blitz et al. (2012) and Elton et al. (2002). Therefore, I include the variable to control for the positive effect of dividend yields on the tracking error.
TERatio is the annualized total expense ratio in percent. It includes all fees the issuers
charges ETFs during a financial year. Not included are transaction costs investors face when buying/selling an ETF. As the fees are paid by the ETF, it reduces the ETFs performance and requires cash to be held by the ETF. Both effects increase the tracking error. Thus, I anticipate a positive coefficient for TERatio. However, as I use a fixed effect regression which demeans independent variables, the coefficient might not be as significant as in studies using pooled OLS estimators as the in between variance in rather small (see Table 6).
5. Description of the sample data
Xetra is the largest German online-based stock exchange. One can currently trade over 1300 ETFs on it, most of them being passive5. For this study I selected 92 passive equity ETFs.
The selection is based on following criteria:
• the ETF must be listed before September 2013 and still be in existence in December 2018
• the ETF must track a foreign country specific equity index
• the index is not allowed to only invest in a specific submarket of the country • the ETF must be traded on Xetra
The date selection results in a time frame of 64 monthly periods. An index is country specific (international) if it only consists of equities of one country. I further neglect indices which only track one aspect of the market (growth, small cap, industrials), as specific sub-indices can have their own correlation which is not part of this study. The ETFs are not chosen randomly as the population of ETFs is not large enough to provide a sufficiently large sample by randomized choice. I am able to include 30 countries from 6 continents in my studies which are represented by 44 different indices as can be seen in Table 2.
Table 2 shows the variety of countries included in the study as well as the number of ETFs for each country. It can be clearly seen that ETFs from strong economic countries are over represented in comparison to ETFs that track indices of emerging market countries. This can be explained, as for prominent countries, such as the US and the United Kingdom, the majority of the ETF issuer offer an own ETF, whereas countries that are less popular only are offered by a few issuers. This could be due to barriers of establishing high quality ETFs or due to not sufficient demand. A complete overview over the sample is presented in Appendix A
Sources for the data are Thomson Reuters EIKON as well as the homepage of Xetra accessible via “https://www.xetra.com”. From the website I collected the master data of the ETFs (Replication strategy, benchmark and issuer for example) as well as the measure for the liquidity of the ETF (XLM and Turn Over). From EIKON is downloaded the time-series of prices for the ETFs and indices, on which the calculation of tracking error and volatility is based, as well as the dividend yield and total expense ratio. If the data from Xetra had missing or unclear values I used the websites and documents published by the issuer of the ETF to ensure the quality of the data. I assessed the timeseries of the economic freedom index over the website of the heritage foundation (https://www.heritage.org/index) on which the data of the index is published yearly. The data for assets under management and XLM had a few missing values (85 for AuM and 165 for XLM): I decided to interpolate the missing values from the values before and afterwards. This is plausible as both variables do not show extremes within volatility and the assumption that the assets under management and the liquidity costs move
linear between two time periods is acceptable. The data was formatted in Microsoft Excel and afterwards imported in Stata which was used for the regression and analysis of the data.
Table 2: Geographical distribution of the ETFs and underlying indices
Continent Country Number of
ETFs Replicated Indices
Africa 1
South Africa 1 MSCI South Africa
Asia 35
Bangladesh 1 MSCI Bangladesh Investable Market
China 4 FTSE China 50, MSCI China
Hong Kong 1 Hang Seng
India 2 MSCI India, Nifty 50
Indonesia 2 MSCI Indonesia
Japan 12 MSCI Japan, Nikkei 225, TOPIX
Malaysia 3 MSCI Malaysia
Pakistan 1 MSCI Pakistan Investable Market Philippines 1 MSCI Philippines Investable Market
Singapore 1 MSCI Singapore Investable Market
South Korea 2 MSCI Korea
Taiwan 3 MSCI Taiwan
Thailand 1 MSCI Thailand
Vietnam 1 FTSE Vietnam
Europe 28
Austria 3 ATX
France 2 CAC 40
Greece 1 MSCI Greece IMI + Coca-Cola 20-35
Italy 2 FTSE MIB
Portugal 1 PSI 20
Russia 1 MSCI Russia
Spain 1 MSCI Spain
Switzerland 4 Dow Jones Switzerland, Titans 30, SLI, SPI
Turkey 2 MSCI Turkey
United Kingdom 11 FTSE 100, FTSE 250, FTSE All-Share, MSCI United Kingdom
North America 22
Canada 5 MSCI Canada, S&P/TSX 60
United States 17 MSCI USA, S&P 500
Oceania 2
Australia 2 S&P/ASX 200
South America 4
Brazil 3 MSCI Brazil
Mexico 1 MSCI Mexico
Total 92 44
Table 3: Descriptive statistics of tracking error per sample year in per cent
Year Obs. Mean Median Min. Max. SD Skew. Kurtosis
2013 323 0.1582 0.1100 0.0006 2.3560 0.2397 6.3857 51.2074 2014 978 0.1570 0.0884 0.0005 2.7761 0.2020 5.5289 60.5090 2015 1,003 0.3121 0.1982 0.0008 4.7479 0.3937 4.6065 36.3003 2016 1,062 0.2317 0.1400 0.0007 1.7052 0.2561 2.2528 9.4407 2017 1,092 0.0934 0.0772 0.0003 0.8245 0.0781 2.9136 17.5146 2018 1,091 0.1804 0.1071 0.0001 1.3613 0.2054 2.2838 8.9852 Overall 5,549 0.1915 0.1133 0.0001 4.7479 0.2563 5.0703 51.5393
Notes: This table contains the descriptive statistics for the average daily tracking error in per cent per sample year. The last row describes the tracking error over the complete sample period. It shows the mean, median, minimum, maximum, standard deviation, skewness and kurtosis as well as the number of observations for each year. The tracking error is calculated according to Equation (3).
Table 4: Descriptive statistics of the tracking error per continent in per cent
Continent Obs. Mean Median Min. Max. SD Skew. Kurtosis
Africa 64 0.2599 0.2177 0.0446 0.9610 0.1773 1.5669 5.8737 Asia 2,202 0.2535 0.1658 0.0217 3.1761 0.2558 3.4047 22.0070 Europe 1,638 0.0914 0.0405 0.0001 4.7479 0.2518 10.5206 146.8864 North America 1,298 0.1757 0.1076 0.0252 1.0275 0.1896 2.4248 8.9545 Oceania 124 0.1888 0.1212 0.0289 1.5587 0.1981 3.5873 21.0565 South America 223 0.3883 0.2805 0.0424 2.7761 0.3615 3.4599 19.8602
Notes: This table contains the descriptive statistics for the average daily tracking error in per cent per continent. It shows number of observations, the mean, median minimum, maximum, standard deviation, skewness and kurtosis for each continent. The tracking error is calculated according to Equation (3).
Table 5: Descriptive statistics of the economic freedom index per continent
Continent Obs. Mean Min. Max. SD
Africa 64 62.42 61.80 63.00 0.3875 Asia 2,202 67.49 50.80 90.20 9.7536 Europe 1,638 71.69 50.60 81.70 7.6078 North America 1,298 76.37 75.10 80.20 1.4572 Oceania 124 81.18 80.30 82.60 0.6417 South America 223 57.76 51.40 67.00 5.3237 Overall 5,549 70.66 50.60 90.20 8.8512
5.1. Descriptive statistics
The descriptive statistics for the average daily tracking error can be seen in Table 3. The mean and median are 0.1915% and 0.1133% per month over the complete sample period. The tracking error is leptokurtic in all sample periods and therefore exhibits heavier tails than expected in normal distribution. The positive skewness in all periods shows that the tails are heavier on the right side of the distribution. This indicates that there are more positive (a higher tracking error) extreme values than extremes which a lower than the median. This is also shown in the median which is lower than the mean in all periods. Common literature finds higher values for the average daily tracking error as Chu (2013) reports a minimum of 0.36% and Mateus and Rahmani (2017) an average of 0.58% and a minimum of 0,21%. In 2014 the mean tracking error and its standard deviation are substantially higher than in the rest of the sample periods. Opposing this is the year 2017, which exhibits lower mean tracking error and standard deviation.
Table 4 shows the mean tracking error per continent over the whole sample period. The values of Africa, Oceania and South America should be handled with caution as the number of observations is relatively small since there are only a few ETFs which track indices of these continents. The average tracking error in Europe is considerably smaller compared to Asia and North America, even though Europe has the highest maximal average daily tracking error compared to the other two continents. This is also shown in the extreme kurtosis for Europe, which is sign for many outliers.
This geographical difference can hardly be explained by the economic freedom index as Japan, the US and Canada are all exhibiting high economic freedom values. If you compare Table 4 with Table 5 this becomes obvious: North Americas average tracking error is higher even though the Economic Freedom index is higher and would therefore expect a lower average tracking error. An explanation could be the difference in trading hours as the Xetra stock exchange is not open during the whole trading day in Asia and North America due to time differences. In their studies, W. F. Johnson (2009) and Tse and Martinez (2007) find a statistically significant correlation between the overlapping trading hours and tracking error of ETFs. Notable is the significantly higher minimum tracking error of North American ETFs, especially compared to Asian ETFs, which is close to the minimum of European ETFs.
The average economic freedom index per continent is shown in Table 5. This only includes countries which are represented in this study6. Comparable to Table 4, the means of the continents Africa, Oceania and South Africa must be interpreted carefully as the number of ETFs is very small. Under this remark the average of Oceania is not representative for the whole continent as Australia is the only country in the sample and thus it can hardly give information for the whole continent.
Table 6: Descripitve statistics for the indepent variables
Variable Mean SD Between Within Min. Max.
XetraTO (0.1 M€) 6.92 12.59 11.58 7.99 0.00 202.48 XLM (0.1 M€) 33.35 29.65 23.27 18.14 2.64 297.78 LogAuM (Log M€) 4.82 1.63 1.61 0.47 0.63 10.51 AuM (M€) 440.83 1278.97 1231.28 845.36 1.88 36685.05 EcoFree 70.66 8.85 8.81 1.28 50.60 90.20 InvFree 69.53 17.86 17.68 3.56 15.00 90.00 Vola (%) 0.9453 0.5097 0.3076 0.4093 0.1303 6.0262 TERatio (%) 0.4092 0.2077 0.2061 0.0344 0.0500 0.85 DivYield (%) 0.1162 0.5460 0.1623 0.5208 0.00 6.8232
Notes: this tables shows the mean, median, standard deviation (SD), within standard deviation, between standard deviation, minimum and maximum for the independent variables Xetra turnover (XetraTO), liquidity cost (XLM), logarithmic asset under management (LogAuM), Assets under Management (AUM), economic freedom index (EcoFree), investment freedom index (InvFree), volatility of the index (Vola), total expense ratio (TERatio) and Dividends (DivYield). The unit of each variable is specified in parenthesis under the name. EcoFree and InvFree are indices valued from 1 to 100 in absolute numbers.
Table 7: Pairwise correlation matrix of the dependent and independet variables
Variable Track XetraTO XLM LogAuM EcoFree InvFree Vola DivYield TERatio
Track 1.00 XetraTO 0.04* 1.00 XLM 0.16* -0.25* 1.00 LogAuM -0.08* 0.51* -0.47* 1.00 EcoFree -0.15* 0.05* -0.16* 0.14* 1.00 InvFree -0.21* 0.05* -0.16* 0.14* 0.78* 1.00 Vola 0.40* -0.03 0.17* -0.11* -0.33* -0.2* 1.00 TERatio 0.17* -0.03 0.1* -0.15* -0.54* -0.64* 0.25* 1.00 DivYield 0.04* -0.04* 0.00 -0.03 0.05* 0.06* 0.03* -0.04* 1.00
Notes: this table shows the pairwise correlation coefficients of the tracking error (Track) Xetra turnover (XetraTO), liquidity cost (XLM), logarithmic asset under management (LogAuM), economic freedom index (EcoFree), investment freedom index (InvFree), volatility of the index (Vola), Dividends (DivYield) and total expense ratio (TERatio). * indicates a statistically significant value different from zero based on a two-tailed test at the 1% level.
within standard deviation. While the economic freedom index varies highly between countries it changes only slowly over time. Both liquidity measures exhibit a high kurtosis and positive skewness whereas the other variables are close to the standard distribution.
Table 7 shows the pairwise correlation between the tested variables. As expected the variables EcoFree and InvFree exhibit a high significant correlation (0.7825). This is due the calculation of the economic freedom index (EcoFree) as the index of investment freedom (InvFree) is a substantial part of it. This high correlation between may cause multicollinearity, for which I test using the variance inflation factor in the following chapter.
5.2. Statistical tests
When conducting a panel regression several assumptions must be tested before being able to ensure an unbiased and efficient estimator. Therefore, I tested the data for serial autocorrelation, heteroskedasticity, cross-sectional independence, stationarity as well as the applicability of fixed effects in comparison to pooled OLS and random effects.
Autocorrelation is a common issue when studying the tracking error of ETFs, as it leads to a bias in the standard errors as well as reducing the efficiency of the regression (Wooldridge, 2002). To test for autocorrelation, I conducted the Wooldridge test as suggested in Drukker (2003). The null-hypothesis of no serial correlation is rejected at all relevant significance levels. Therefore, I conclude that the data is biased by significant (at least first-order) autocorrelation.
To test if the data shows heteroskedasticity, I conducted the modified Wald test for group wise heteroskedasticity as suggested by Greene (2003) and Baum (2001). I reject the null-hypothesis of homoscedastic standard errors at all relevant significance levels and conclude, that the standard errors are heteroskedastic.
Panel data is likely to have substantial cross-sectional dependence in the error terms. The dependence can be caused be common shocks and / or unobserved components which influence the error term (De Hoyos and Sarafidis, 2006). Suggested tests include the Friedman test statistic, Frees statistic as well as cross section dependence test of Pesaran (Frees, 1995; Friedman, 1937; Pesaran, 2004). As in my study N (the number of ETFs) is larger than T (number of time periods), all three tests should yield suitable results which lead to the same conclusion. As the panel is unbalanced I choose to use Pesaran’s test for cross section dependence which also yields robust results in the presence of unit roots and structural breaks. (De Hoyos and Sarafidis, 2006; Pesaran, 2004). The null-hypothesis of Pesaran’s test is that the errors are cross-sectional independent. This hypothesis is rejected at all relevant significance levels. Therefore, I conclude that the data shows cross-sectional dependence. This result must be expected as the chosen sample consists of ETFs with similar patterns, especially as the sample was not chosen randomly (Hoechle, 2007).
test proposed by Pesaran (2007) as well as Baltagi (2005). This eliminates the cross-sectional dependence, hence is able to create unbiased results as well as handle unbalanced panels (Im et al., 2003; Pesaran, 2007). I reject the null-hypothesis that all series are non-stationary at all relevant significance levels and conclude that the data can be regarded as stationary7.
As the correlation matrix shows high and moderate dependency between the independent variables (see Table 7), I tested for multicollinearity using the variance inflation factor (VIF) whose results are presented in Appendix B. As none of the VIFs are above five- the highest value being 3.19 for EcoFree, multicollinearity is not regarded a significant problem in my study (Studenmund, 2014)
As the data shows autocorrelation, heteroskedasticity as well as cross-sectional dependence I use Driscoll and Kraay standard errors. These are superior over the commonly used White Standard errors, as the latter are biased if the data shows cross-sectional dependence which invalids statistical inference based on those (Petersen, 2009). The often used Newey-West standard errors suffer the same bias, as they are able to account for heteroskedasticity and autocorrelation, but are biased by cross-sectional dependence (Hoechle, 2007). Driscoll and Kraay standard errors are consistent if the time dimension (T) is sufficiently large relative to the cross-sectional dimension (N). Sufficiently large means in this context that time serial correlation can be reduced to a modest level by including lagged variables or applying an appropriate transformation. The standard errors are consistent as well, if N is larger than T, given that T is sufficiently large (Driscoll and Kraay, 1998). Choosing the correct standard errors is crucial, especially as Petersen (2009) concluded that financial literature uses a wide array of different standard errors in panel models but often does not adjust for possible dependence in the residuals.
6. Empirical results
The results from my fixed effect panel regression are presented in Table 8 and Table 9. Table 9 shows the regression result over the complete sample period and size. Before regressing the average daily tracking error on all factors together, tracking error is regressed on each of the independent individually to better determine the influence of explanatory variables on the tracking error. Table 9 shows the regression results over the whole sample period by continents, where continents with less than 200 observations are dropped. The full table, including the omitted continents, can be seen in Appendix E. The explanatory power is with an R² of 15.2% lower to comparable studies in literature. This is especially true for European ETF with an R² of 7.95% compared to 22.9% and 21.9% in North America and Asia.
Table 8 reports statistically significant coefficients for both liquidity measures (XLM and XetraTO). XetraTO is significant at the 1% level and has a positive sign. This meets my expectations as the theory would predict that a lager turnover is a sign for differences in investor beliefs, which causes a higher tracking. This is in line with studies such as (Chu, 2016; Delcoure and Zhong, 2007; Rompotis, 2006). The magnitude of this effect is only marginal, as the coefficient is approximately 0.0029 basis points. XetraTO is also significant at the 1% level regressed separately with a coefficient of 0.0034 basis points, which increases the robustness of this coefficient. The explanatory power of XetraTO is small as the R² of the regression is only 1.41%. The regression by continents (Table 9) shows that the Xetra turnover is also significant at all continents. The coefficient for Asia is with 0.0043 basis points larger than for the complete sample whereas the coefficient for European countries is with 0.0010 noticeable smaller. The American coefficient is close the overall sample.
XLM reports a statistically significant coefficient at the 10% level with a positive value
of 0.0007 basis points. The sign is in line with my expectations as an increase in liquidity costs should result in an increase in tracking error. Evaluated on its own, XLM exhibits a slightly larger coefficient of 0.0009 basis points which is insignificant. XLM has no significant coefficient for specific continents. The signs follow my expectations, but the magnitude is very small, hence I conclude that there is no economic significant relationship
LogAuM shows negative coefficient which is statistically insignificant. The sign is in
line with Chu (2013) and my expectations, as with an increase in size the ETF is able to reduce relative tracking error. Chu (2013) reports a statistically significant coefficient, which my sample cannot confirm. As I use the logarithmic value of the asset under management this coefficient is negligible small as the even under statistical significance the tracking error would decrease by relative 0.0043%. Regressed separately, the coefficient is also not significant and with an R² below 0.01% the economic significance is hardly arguable.
explanatory power of EcoFree is therefore not present in my sample. This is inconsistent with the study of Saunders (2018), who finds a significant negative coefficient. Across continents, Table 9 shows a positive significant coefficient at the 5% level for North American ETFs which further contradicts the theory. This is likely to be caused by the small amount of countries in North America, especially as most of the ETFs are tracking the United States.
InvFree exhibits a positive coefficient which is statistically insignificant. This is not in
line with the theory, as I expect a negative relation between tracking error and investment freedom. Regressed on its own, the explanatory power is negligible small. Across continent the sign is not consistent. For Europe the effect is larger compared to other continents with a coefficient of – 0.0095 basis points, but statistically insignificant and still too small to be able to justify an economic relationship.
The volatility of the index is significant at the 1% level and has a positive coefficient of 20.08 basis points. This is in line with the literature as well as my expectations (Frino and Gallagher, 2001). The volatility of the underlying index explains most of the deviation of the tracking error as the R² of the separate regression is with 13.1% very close to the R² of the complete regression of 13.6%. The impact of the volatility is also significant across all continents. Notable is the significantly smaller coefficient for European ETFs with 11.23 basis points as opposed to 26.01 basis points and 23.44 basis points in Asia and North America. As a higher volatility increases the impact of even small deviations from the index, these results make sense, even though the coefficient is higher than expected.
The total expense ratio (TERatio) is statistically insignificant. This contradicts most studies in the literature, where the total expense ratio represents one of the major significant explanatory variables. Economically, this variable is significant with a coefficient of 0.1365 basis points. The explanatory power worsens if you inspect the continents individually: the coefficient is negative for Europe and North America which strictly contradicts recent studies and theories. The size of the coefficient is comparable to Chu (2013) who finds a positive coefficient of 0.353 basis points.
7. Interpretation of the results
The constant, which represents the average fixed effect for the entities in a fixed effect model, is not significant at the overall sample and negative which means that there are unobserved time fixes effects which reduce the tracking of these funds. Appendix D shows the regression divided into replication strategies. As the constants of synthetic and physical ETFs are both significant at 10 and 5 per cent level respectively, I conclude that physical replicating ETFs have on average a significantly lower tracking error compared to synthetic ETFs. This finding is in line with the theory and findings of Drenovak et al. (2014). Between different dividend policies I cannot find a statistically significant difference. However, the fixed effect of distributing ETFs is substantially lower then accumulating ETFs. As distributing ETFs track price dividends, they are not affected by the tracking error increasing effect of dividend withholding taxes and time differences in reinvesting the dividends, this effect is expected and with a difference of 0.85 basis points of economic significance. Common literature seconds this finding as Osterhoff and Kaserer (2016) find a significant negative coefficient for distributing ETFs. Analysing the constant across continents, I find that there are significant unobserved fixed effects for North American and European ETFs.
XetraTO seems statistically robust. The coefficient is statistically significant across
different replication methods, dividend policies and continents (see Appendix C and Appendix D). The effect seems larger for distributing ETFs that are on a different continent as the stock exchange. Latter relationship could be due to the time differences in opening hours of the stock exchanges of the underlying index and the ETF which can cause an increased influence of different beliefs. However, as the coefficients are only marginal (beneath 0.005 basis points in all regression) the economic significance is questionable. The tracking error will only increase by approximately 0.036 basis points if the turnover increases by one standard deviation. Therefore, I conclude that even though there is a statistical correlation between tracking error and turnover, the effect is too small to be of economic significance
XLM is only statistically significant and at the 10% level for physical and distributing
ETFs. The sign fits the stated hypothesis that an increase in market impact costs increases the tracking error. Nonetheless, as the coefficient is below 0.001 basis points and does not show any significant explanatory power on its own, I conclude that there is no significant relationship between the liquidity cost of the ETF on its tracking error in my sample. Regarding the first research question, I conclude that even though there is a statistically significant positive relationship between implicit liquidity cost and tracking error for European ETFs, the influence is only marginally and should not be considered as economic significant. More important than the liquidity cost of the ETF are the liquidity costs of the underlying stocks as Osterhoff and Kaserer (2016) show.
index offers the most explanatory power in my sample and is statistically as well as economically significant, as an increase in the volatility of the index by one standard deviation would increase the tracking error on average by approximately 10.2 basis points. this means that a higher volatility of the underlying index, decreases the replication quality of the ETF significantly.
DivYield is neither in the overall sample, nor at a continent level statistically significant.
This is against my expectations and recent literature, which find a significant coefficient. The coefficient is larger than other variables, which shows the economic significance of the variable as an increase in the dividend yield by one standard deviation could lead to an increase of daily tracking error 0.8316 basis points. Further unexpected is that the coefficient is also insignificant if regressed on distributing ETFs alone. Regarding the replication strategy the influence of the dividend yield seems larger for synthetic ETFs, however there is no statistical significance.
The statistical insignificance of TERatio can be explained, as the TERatio is constant for most ETFs and has only a small within standard deviation. The demeaning performed by the fixed effect estimator removes the effect for most entities and reduces therefore the explanatory power of the variable. Further, a higher total expense ratio leads to constant underperformance which affects the tracking difference but is not expected to have a major influence on the tracking error.
The coefficients of EcoFree and InvFree are both statistically insignificant across nearly all sub samples. Notable is the significant negative EcoFree coefficient for synthetic replicating ETFs with -0.0114 basis points. The positive significant coefficient for North America is caused by the composition of the sub sample as most of the ETFs track an US index. The coefficient does not seem robust, as the sign switches between subsamples for which the theory offers no explanation and which are likely caused by the coefficient being close to zero. As the coefficient is only marginal, neither statistically significant nor robust, I conclude that the impact of economic freedom, measured by the economic freedom index or the investment freedom index, is not significant in my sample. Therefore, I conclude that in my sample for German ETFs the market integration of countries underlying international ETFs has no economic significant relationship with the tracking error of the ETFs. This answers the second research question as the restrictions of capital flow are measured by InvFree and the market integration by EcoFree. Both variables are neither economically nor statistically significant, which denies the second research question.
8. Conclusion
In this study I try to find further explanatory factors for the tracking error of international ETF traded at Xetra. To well-known factors such as dividend yield and total expense ratio, measurements for economic freedom, investment restrictions and market impact cost were added.
As shown above I find a significant relationship for the dividend yield and volatility of the underlying index. The turnover of the ETF is statistically significant at the 1% level for my sample. This effect is robust over different sub-samples such as continents, dividend policies and replication strategy. this effect can be explained as a higher tracking error enables more arbitrage opportunities and hence to a higher turnover. Thus, I conclude that there is a positive relationship between average daily tracking error and monthly turnover. As the coefficient is only marginal, I doubt the economic significance of this finding. I am also able to verify that physical outperform synthetic ETFs regarding their tracking error.
Against my hypothesis, I am unable to find a statistically significant relationship between both tracking error and the economic freedom index as well as investment freedom index. As the economic impact is only marginal I conclude, that there is no significant relationship between the tracking error and neither market integration nor restrictions to cashflows. I am also unable to confirm the hypothesis that market impact costs of ETFs significantly influence the average daily tracking error.
This study is limited, in aspect of the calculation of the tracking error, as I use the price return as basis of my calculation and not the NAV return, which tends to provide more robust results. This was caused to the limited availability of daily NAV data, which use would cause a significant reduction of sample size and period. Using a fixed estimator introduces some limitations as well. Apart from the standard OLS assumptions, the demeaning removes time invariant effects. While this enables the measurements of the influence of the country specific economic freedom index on the tracking error of ETFs, it removes the explanatory power of the total expense ratio. This may lead to an omitted variable bias which might affect the reliability of this study negatively. This would explain why I receive some unexpected sings for variables that are proven significant by a numerous of researchers, especially the negative coefficient for total expense ratio for European ETFs.
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