Tracking ability of exchange-traded funds during times of financial turmoil : evidence from the 2008 financial crisis and 2010 sovereign debt crisis

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Tracking ability of exchange-traded funds during

times of financial turmoil:

Evidence from the 2008 financial crisis and 2010 sovereign debt

crisis

Abstract

This study examines the impact of the global financial crisis and the sovereign debt crisis on the tracking ability of 20 market index exchange-traded funds (ETFs). 12 ETFs track U.S. benchmark indices and 8 ETFs track MSCI European benchmark indices and covers the period 2006- March 2018. The findings show statistically significant effect of both the global financial crisis and European sovereign debt crisis. Furthermore, this study finds that the effects of both crisis periods are mainly determined by the net expense ratio. Dividends show also a positive and statistically significant effect on the tracking error, while trading volume show limited and neither significant effect during both crisis periods.

Name: Vincent Bervoets, 10561951 Thesis supervisor: Ryan van Lamoen Amsterdam Business School

MSc Finance, track: Quantitative Finance Master Thesis

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Statement of Originality

This document is written by Student Vincent Bervoets who declares to take full responsibility for the contents of this document.

I declare that the text and the work presented in this document are original and that no sources other than those mentioned in the text and its references have been used in creating it.

The Faculty of Economics and Business is responsible solely for the supervision of completion of the work, not for the contents

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1. Introduction

Over the last two decades, exchange-traded funds (ETFs) have become a popular investment vehicle in asset management. Nowadays, the numbers of Exchange traded funds in the world have grown from almost 300 in 2003 to nearly 5000 at the beginning of 2017, where from nearly 2000 are traded on U.S. exchanges. An ETF tracks a diversified basket of assets that trades on an exchange such as commodities, bonds, stocks of a specific industry or market index. According to an article of the Financial Times more than one trillion dollar in new money has flown into U.S. equity exchange-traded funds over the past five years (Flood, 2018). Compared to the conventional mutual funds, these ETFs have relative low transaction cost and are traded intraday on an exchange. The low costs and intraday trading and other advantages make this investment very attractive for investors. However, the volatility shock in February 2018 triggered investors to pull money from U.S. equity exchange-traded funds. Investors withdraw more than 23 billion dollar from these funds. This ends the expansion of money inflow into exchange-traded funds the last several years. Since, the global ETF market has reached five trillion dollars such liquidity shocks as in February 2018 raised a lot of questions on to what extent these shocks affect the ETF market prices.

The difference of a ETFs return and the return of the target market index is known as the tracking error of the fund, which is a measure of performance. The aim of an ETF is to replicate the risk and performance of its underlying index, and to try to keep the tracking error to a minimum level. The creation/redemption process of ETFs is important to keep the value of an ETF as close as possible to its underlying index. The so called authorized participants (APs) act as market makers, in order to provide more liquidity and keep the share price as close as possible to the underlying value. For example, if the demand for ETF shares is greater than the supply there will be deviation from its underlying price. The APs rebalance demand and supply by ordering new shares (creation units) from the ETF, in return for a basket of securities of its underlying index. However, the share price of an ETF becomes more vulnerable, because the ETF and benchmark index are more intertwined. It could be the case that APs fail to restore the supply and demand if they halt redemptions in times of a liquidity shocks or in times of extreme returns.

Given the expansive growth of these ETFs, a lot of research is done over the last few years. But not only academics concern about these investment products, also regulators and investors want to know how prices of ETFs evolve over time, especially during times of extreme returns. Since the expansive growth of money inflow into these exchange traded funds, regulators

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5 and investors want to know what might happen if this money flows out of these funds. It is therefore important to know how these tracking errors of ETFs evolve over time.

The existing literature about tracking error of ETFs is mainly focused on two different aspects. What are the determinants of tracking errors and/or the magnitude of tracking errors in specific countries or different kinds of ETFs? Osterhoff and Kaserer (2016) examine the determinants of tracking errors in German ETFs. Chu (2011) investigates the determinants and magnitude of ETFs on the Hong Kong exchanges. Blitz and Huij (2012) examine the tracking ability of emerging market ETFs. Further, Meinhardt et al. (2015) investigate the difference between synthetic and physical ETFs. They examine the drivers of synthetic and physical ETFs and study the differences in tracking ability, since the replication strategy differs between these ETFs. Rompotis (2009) investigate the performance of German exchange-traded funds. Moreover, Rompotis (2012) investigate the performance iShares fund company. However, the price dynamics of index ETFs over time and specifically during periods of financial turmoil is not elaborately examined yet in the existing literature. Therefore, the purpose for this research is to give new insights of the tracking error during times of extreme negative returns and focus on the 2008 financial crisis of and the 2010 sovereign debt crisis. The research question is therefore: What is the impact on tracking ability of index ETFs during times of extreme returns? This thesis deviate from the existing literature is mainly two ways. First, this study examines the differences of two main crisis periods last decade. Second, this thesis gives new insight in the specific tracking error determinants during times of these extreme negative market shocks.

In order to answer the research question this thesis performs a panel regression with fixed effects, which covers the period from January 2006 till 30 March 2018. The panel dataset contains of 20 exchange-traded funds traded on U.S. exchanges, where 12 ETFs tracking U.S. indices and 8 ETFs track European MSCI indices. Furthermore, the effect of tracking error determinants, such as expense ratio, turnover by volume, volatility and dividend are used to explain the ETFs tracking error.

The results of this study suggest that ETFs face difficulties in tracking their underlying benchmark in times of financial turmoil. The global financial crisis and European sovereign debt crisis show a negative and statistically significant effect on the tracking ability of market index exchange-traded funds. The results are in line with the findings of Drenovak et al. (2014). Moreover, the tracking error throughout the crisis periods is mainly determined by the expense ratio and also to a lesser extent by dividends. The impact of trading volume during the financial crisis is limited.

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6 The remainder of this thesis is structured as follows. Section two is the literature review, where this thesis focuses on the existing literature regarding determinants of exchange-traded funds tracking error and evidence concerning ETFs performance. Section three consists of two sub sections. First, subsection 1 describes the data followed by the subsection of the methodology. Further, the results and several robustness checks from the regression will be analyzed in section four. Finally, section 5 provides the overall conclusion of this research and suggestions for further research.

2. Literature review

This section provides an overview of the existing literature regarding tracking ability of exchange-traded funds. This section is divided into two parts. The first subsection provides evidence concerning the performance of exchange-traded funds in general. Thereafter, the key determinants of exchange-traded funds tracking error are discussed in subsection two.

2.1 Evidence from the performance of exchange-traded funds

Since the existence of open-end funds, also known as mutual funds or actively managed funds, there is a lot of research done about the performance of these funds. For example, to what extend can funds managers consistently outperform the markets? However, since the introduction of exchange-traded funds, they become a popular investment vehicle and seem to replace the comparable mutual funds. As mentioned in the introduction, ETFs have some advantages compared to the conventional mutual funds. ETFs are traded intraday and have lower operating expenses, which increase efficiency. Agapova (2011) examines and compare the performance of mutual and exchange-traded funds and to what extent the funds are substitutes of each other. According to Agapova (2011), ETFs show better performance because of the lower tracking error. Nevertheless, ETFs and mutual funds are not perfect substitutes instead they serve as an additional and alternative investment vehicle with different features. Furthermore, Aber et al. (2009) examine the performance and price movements of different iShares ETFs. Furthermore, they compared the tracking ability of ETFs and mutual index funds which track the same underlying index. The results show that conventional mutual funds perform on average better than their ETF competitor.

Furthermore, there is considerable research about the ETF performance in different countries. In line with the study of Frino and Gallagher (2002) with regard to the performance of Australian index funds, Gallagher and Segara (2006) investigate the performance of Australian ETFs. Next, Milonas and Rompotis (2006) study the performance of Swiss ETFs. Chu (2011)

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7 investigates the tracking ability of Hong Kong ETFs and which determinants drive tracking error of these funds. Rompotis (2012) study tracking ability and performance of ETFs traded on German exchanges.

Others study the performance and tracking ability of different types of ETFs. The literature mainly focuses on the biggest ETF market, namely market index ETFs, which track market indices worldwide, for example S&P500, AEX or DowJones. Other funds types are for instance: commodity ETFs, currency ETFs, sector or industry ETFs, Bond ETFs. Drenovak et al. (2014) investigate the tracking ability and performance of 31 European bond ETFs in the period from 2007 until 2010. In their study they find significant tracking errors, which are mainly attributed to the financial crisis. However, they used a sovereign debt crisis dummy variable, where the dummy equal one after 1 September 2008 and zero otherwise. Compared to this study they did not distinguish the different liquidity shocks of the financial crisis and debt crisis. Furthermore, similar to the study of Drenovak et al. (2014), Houweling (2011) investigate 129 U.S. fixed income ETFs, split into treasury, investment grade and high yield ETFs. Comparing both studies, the results of Drenovak et al. (2014) show higher tracking errors. Furthermore, Meinhardt et al. (2015) investigate the difference between physical and synthetic ETFs for fixed income and market index funds. Physical funds track an index such as the S&P500, which hold and replicate the assets of the underlying benchmark index. In contrast, synthetic funds replicate the performance based on derivatives. More precisely, compared to physical, the synthetic ETFs tracks the underlying without owning the securities. In their study they found similar performance measured by tracking error of physical and synthetic equity ETFs. However, according to the results synthetic ETF show better tracking ability compared to the physical fixed income ETF.

Overall, ETFs show significant tracking errors, which differ in their magnitude of different types of ETFs or even compared to the conventional mutual funds. The next subsection, describe the key determinants of the existing literature of the exchange-traded funds tracking error.

2.2 Determinants of the tracking error of exchange-traded funds

This sub section discusses and clusters several tracking error determinants and the impact on the tracking ability of exchange-trades funds. The existing literature suggests that the key determinant of ETFs tracking error is the operating expenses of an ETF also known as the expense ratio of an ETF. The higher the expenses are, the more difficult to replicate the return of the underlying index. Holding other factors constant, the expenses should therefore result in a

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8 larger tracking error of an ETF and therefore more underperformance of its underlying index (Charupat and Miu, 2013). The majority of research supports this view, where ETFs expense ratio has a (statistically significant) negative effect on the tracking ability of its underlying index: Elton et al. (2002), Rompotis (2009), Chu (2011), Blitz et al. (2012) and Osterhoff and Kaserer (2016). However, it is not necessarily consistent that the cheapest fund has the best performance. According to Blitz et al. (2012), one of the cheapest ETF in their sample with an expense ratio of only 0.35% per annum, is one of the worst performing ETFs. In contrast to the existing literature, Chu (2013) finds a negative and statistical significant effect of the expense ratio on ETFs tracking error. He argues that this is due to his sample composition of both psychical and synthetic exchange-traded funds. Furthermore, Rompotis (2012) found in his study of German ETFs a negative relationship between the expense ratio and ETF’s tracking error. Nevertheless, he found no evidence of the expense ratio, since the effect was not statistically significant

According to the existing literature the riskiness of an exchange-traded fund is another determinant of ETFs tracking error. The risk level in the market could influence the performance of tracking an underlying index. Higher market risk makes it more difficult to replicate the performance of the underlying index resulting in a higher tracking error (Chu, 2013). The ETFs riskiness also referred as the volatility of an ETF is calculated with different kind of measures. The most widely used method is the standard deviation of the daily return of an ETF. Rompotis (2012) investigate the performance and trading characteristics of 43 German exchange-traded funds in the period 2003 until 2005. He employs six different cross sectional regression analyses in order to examine the performance and trading characteristics. According to the tracking error model he found that risk is positive correlated with ETFs tracking error. Besides he found that risk is statistically significant. Rompotis (2012) defines risk as the standard deviation of the ETFs daily returns. Similar studies of Rompotis (2009) and Milonas and Rompotis (2006) also use the standard deviation of daily returns as risk measure. Rompotis (2009) investigates 73 iShares exchange-traded funds over the period October 2005- September 2006. He shows a positive and statistical significance relationship between ETFs risk and tracking error. Moreover, Milonas and Rompotis (2006) investigate Swiss exchange-traded funds in the period 2001-2005 and found also a positive and significant correlation between ETF risks and its tracking error. Shin and Soydemir (2010) employ a different volatility measure to explain ETFs tracking error. The volatility measure is the average daily ETF’s price change based on the highest, lowest and closing market price. They perform the same regressions for three different tracking error measures, where the volatility measure has a positive effect on the tracking error in all cases. However, the volatility is significant for only one tracking error measure.

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9 Furthermore, dividend payments may be problematic for exchange-traded funds to completely replicate the performance and risk of its underlying index. Chu (2013) argues that the delay in receiving the cash dividends and trading costs experienced by reinvesting cash dividends makes it more difficult for ETFs to track the underlying index. Elton et al. (2002) investigate the bugs for spiders, also known as Standard & Poor’s depositary receipt, an exchange-traded fund who tracks the S&P500. They argue that besides the expenses ratio, the dividend yield is the second import determinant in explaining the tracking error. In accordance of their expectations, they find that dividend yield has a positive effect on the ETF tracking errors. Moreover, Osterhoff and Kaserer (2016) investigate the determinants of German ETFs, and find that dividend yield, measured by the dividends divided by the net asset value, has a positive and statistically significant effect on ETFs tracking error.

Several academic papers mentioned the correlation of liquidity of ETFs and its tracking error. Previous literature mainly focus on two different methods, namely trading volume and the bid-ask spread. Chu (2013) used the logarithm of daily trading volume as liquidity measure and show that trading volume has not significant effect on tracking error. Moreover, the sign of trading volume is not consistent over the different tracking errors he used. In line with Chu (2013), Rompotis (2009) and Shin and Soydemir (2010) used logarithm trading volume as liquidity measure as well. Rompotis (2009) show a positive and statistically significant effect of trading volume on tracking error, but is close to zero. Shin and Soydemir (2010) investigate the tracking ability 26 exchange-traded funds in U.S., Europe and Asia and found a positive but not significant effect. The positive effect found by of Chu (2013) and Rompotis (2009) and Shin and Soydemir (2010) are unintuitive, because higher liquidity should reduce the tracking error due to lower trading costs. However, the effects of trading volume on tracking error are quite small. No consistent conclusion can be drawn with regard to the effect of trading volume of ETFs tracking error. On the other hand, Milonas and Rompotis (2006), Meinhardt et al. (2015) and Rompotis (2012) use the bid-ask spread as alternative liquidity measure. All of them find a positive effect of the spread on ETF tracking errors. In contrast to other studies, Osterhoff and Kaserer (2016) use a different liquidity measure in their study, which focus on the liquidity of the underlying index. The XLM variable is a weighted average of XETRA liquidity measure of all securities of an ETF portfolio. XLM measures the implicit trading cost, which are related to the round trip cost for a given order size. The higher XLM is, the higher the round trip costs are which corresponds to more illiquid securities. Osterhoff and Kaserer (2016) argue that relatively more illiquid securities should lead to higher tracking error, because of the higher round up trading costs. Consistent

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10 with their expectation, they find a positive statistically significant relationship between XLM and tracking error.

Finally, some papers use other but not widely used determinants of the tracking error. Some factors are fund size, exchange rate and premium/discount. First, Chu (2013) emphasizes the relevance of fund size, measured by total fund assets as factor of the tracking error. He suggests that the bigger the fund, the more efficient the fund can trade through lower trading costs, also known as economies of scale. Fund size should therefore be negative correlated with the tracking error. In accordance with his expectations, he found that fund size is negatively related to ETFs tracking error. Next, when exchange-traded funds are traded on U.S. exchanges, but track an index in foreign currency, the ETF is exposed to exchange rate risk. As mentioned above, Shin and Soydemir (2010) examine the performance and tracking ability of 26 U.S. traded ETFs, while several ETFs track foreign indices in foreign currency. They added therefore the factor exchange rate into the regression analysis as explanatory variable of tracking error. For all different tracking error measures they find a positive and statistically significant effect of exchange rate risk on tracking errors. Finally, Rompotis (2012) investigate the impact of absolute average premium on the tracking error. Premium/discount is the percentage deviation of the trading prices from its corresponding net asset value on a specific day. In his study he found a positive and statistically significant effect of absolute premium on ETFs tracking error.

As discussed in the literature review, the existing literature mainly focused on the performance and tracking ability among wide range of different exchange-traded funds. Since, the tracking error is a widely used method for the tracking ability, there is considerably literature done about what drivers are affecting the tracking error. With this in mind, serval studies investigate the performance and tracking ability of different company funds, such as iShares, Spider or in different countries, such as U.S., Germany, Hong Kong, Taiwan and Australia. The existing literature showed evidence of the existence of ETFs tracking error. However, given the relevant drivers for tracking errors, this study wants to give new insights on the tracking ability during times of financial instability. The following hypothesis will be tested with the research methods employed in section 3.2.

Hypothesis 1: Lower average frequency data results in overestimation of the tracking error

This thesis expects that lower average frequency results in overestimated tracking errors, since the averages are estimated on fewer observations.

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11 Hypothesis 2: Tracking errors of market index ETFs increase during crisis periods.

Since crisis periods are confronted with high volatility levels, the benchmark index should therefore more difficult to track. Furthermore, Drenovak et al. (2014) find in their study that European sovereign debt ETFs show significant tracking errors during 2007 and 2010, which are mainly attributed to the period of the financial crisis. This study expects therefore that the tracking errors of market index ETFs increase in periods of extreme returns.

Hypothesis 3: The structural relationship between the tracking error and their drivers change during the crisis periods?

This thesis believes that the impact of tracking error determinants change during times of financial turmoil. The determinants that have positive relationship with tracking error should have an even larger impact during the crisis periods. Furthermore, the variables which impact the tracking error in a negative manner should change into positive effect or a weakened effect during the crisis periods.

3. Dataset and methodology

First, section 3.1 describes the data; where the data is obtained and how the data is constructed in order to do the analyses. Second, section 3.2 defines the relevant research methods and econometric models and how these methods can be addressed to the research questions and hypothesis.

3.1 Data

The dataset consists of 20 exchange-traded funds (Table 1). All ETFs are traded on U.S. exchanges, where 12 ETFs track U.S. benchmark indices and 8 ETFs track MSCI indices in Europe. Furthermore, the symbol, Fund name, Assets under management (AUM) in thousand dollars, related benchmark index and expense ratio are reported in table 1. The ETFs are managed by several fund companies such as SPDR, also known as Spiders, iShares, Vanguard and PowerShares. The sample period start at 31-12-2005 until 30-03-2018. In this period several liquidity shocks in the United States as well as in Europe are investigated, such as the financial crisis and the sovereign debt crisis. Therefore both U.S. and Europe are collected for the dataset, but is thoroughly explained in the methodology.

Data of exchange-traded funds and benchmark indices are both collected from the database of Datastream and the annual net expense ratios are obtained from Morningstar. The dataset contains data for the sample period 1-2-2006 until 30-03-2018 except for the expense

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12 ratio, because the data of the annual net expense ratio is available since 2008. The data of exchange-traded funds consist of; daily closing prices in order to compute the daily returns of ETFs market prices as well as standard deviation. Furthermore, the intraday highest and lowest prices are collected to compute the daily market price volatility. Besides, another ETF trading characteristics are obtained such as daily dividend yield, daily market value in million dollars and daily turnover by volume in thousand dollars. Dividend yield is defined as the total dividend divided by the share price. The variable turnover by volume is measured by the total number of shares traded within a trading day, which is a measure of liquidity. The daily market value of an ETF is a measure for size and is measured by the market price times the number of shares outstanding, which is comparable to the asset under management reported in table 1. Daily closing prices are obtained of the specific benchmark indices to compute the daily returns as well. In order to match currency, some variables of European exchange-traded funds are obtained in U.S. dollars.

The difference between the biggest and smallest ETF is quite significant, since the market value range from nearly 246 billion to only 71 million dollar. However, SPDR S&P 500 ETF is the first exchange-traded fund ever and the biggest ETF worldwide. Furthermore, between the fund size and expense ratio is a clear relationship. Since the top ten ETF in this sample have the lowest expenses ranging from 0.04% to 0.24%. All the ETFs that track MSCI indices in Europe have an expense ratio of 0.49%, which is double or even quarter as much as exchange traded funds tracking U.S. indices. Tracking an index in various currencies is associated with higher expense ratios.

Table 1 List of exchange-traded funds

Table 1 below shows information about the ETFs in the database. The columns show respectively the symbol or ticker of the specific ETF, the name of the ETF, assets under management in dollars (AUM), the benchmark index of the specific ETF and the current annual net expense ratio.

Symbol Name AUM Benchmark index Expense _ratio

SPY SPDR S&P 500 ETF $245,899,892.21 S&P 500 0.09%

IVV iShares Core S&P 500 ETF $138,871,306.05 S&P 500 0.04%

VOO Vanguard S&P 500 ETF $85,524,557.27 S&P 500 0.04%

QQQ PowerShares QQQ $58,243,341.06 Nasdaq-100 0.20%

IJH iShares Core S&P Mid-Cap ETF $43,719,924.09 S&P Mid-Cap 0.07%

IWM iShares Russell 2000 ETF $40,595,716.81 Russell 2000 0.20%

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13 IA SPDR Dow Jones Industrial Average _ETF $20,724,569.77 Dow Jones 0.17% MDY SPDR S&P MidCap 400 ETF $19,308,577.17 S&P MidCap 0.24%

IWB iShares Russell 1000 ETF $18,967,608.39 Russell 1000 0.15%

IBB iShares Nasdaq Biotechnology ETF $8,495,314.73 Nasdaq Biotechnology 0.47%

IWV iShares Russell 3000 ETF $8,041,909.87 Russell 3000 0.20%

EWG iShares MSCI Germany ETF $4,065,952.46 MSCI Germany 0.49%

EWP iShares MSCI Spain ETF $1,031,426.44 MSCI spain 0.49%

EWL iShares MSCI Switzerland ETF $978,077.86 MSCI Switzerland 0.49%

EWQ iShares MSCI France ETF $780,710.56 MSCI France 0.49%

EWI iShares MSCI Italy ETF $728,254.32 MSCI Italy 0.49%

EWD iShares MSCI Sweden ETF $317,306.21 MSCI Sweden 0.49%

EWO iShares MSCI Austria ETF $269,805.60 MSCI Austria 0.49%

EWK iShares MSCI Belgium ETF $71,200.38 MSCI Belgium 0.49%

The data reported in table 1 is obtained from the ETF database (ETFdb).

Table 2 reports the descriptive statistics of the dependent and independent variables for the sample period 1-2-2006 until 30-03-2018. First, the tracking error (TE) variable is the absolute daily return differences of the ETF and its underlying index. The tracking error is in absolute values, so the minimum value is therefore zero. The maximum tracking error is remarkable, where the return difference is almost 18 percent based on daily frequency. The average daily tracking error for this sample period is 0.363 percent. The descriptive statistics of the variables size and volume are not reported in the natural logarithms, just to explore the real numbers of these variables. Size is the daily market capitalization of the ETFs in million dollars. The average daily market value of the ETF sample is almost 16 billion dollar. The minimum and maximum daily market capitalizations are respectively, around the 5 million and 300 billion dollar. The difference in market value among the ETFs is quite extensive and is also reflected in the standard deviation, which is almost 33 billon dollar. Since, the data consist of the biggest ETFs worldwide which are primarily track U.S. indices. On the other hand, the data consist also of ETFs tracking European MSCI indices of relatively small countries such as, Belgium, Austria and Sweden. Daily turnover and daily fund size variables are highly correlated with each other. This is reasonable since the relatively big funds are also more traded throughout the day. The average daily trading volume is more than 16 million trades. The variable annual expense ratio shows the data from 2008, which can be seen in the number of observation. The average annual expense ratio is almost 0.32 percent, with the minimum and maximum of respectively 0.04 and 0.92 percent. As can been seen in table 1, especially the ETFs who track the MSCI indices in Europe have considerable higher expense ratios. The volatility of ETF trading prices has a mean

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14 of 1.35 percent. The minimum and maximum values are respectively, 0.40 and 3.56 percent. Finally, the daily dividend has an average value of 2.24 percent. The minimum dividend is zero, which is reasonable since dividends can’t be negative, while the maximum value is 24.51 percent. Table 2 Descriptive statistics

This table 2 reports descriptive statistics of number of observation, mean, standard deviation, minimum and maximum value of the subsequent variables: Daily market capitalization (Size), daily dividend yield (Dividend), daily turnover by volume (Volume), annual net expense ratio (ER), standard deviation of the returns on annual frequency and the daily tracking error in absolute values (TE).

Variables Obs. Mean SD Min Max

Size 62,669 15,734 32,981 5.070 306,801 Dividend 62,669 2.238 1.907 0 24.51 Volume 60,428 16,047 46,758 1.200 871,547 ER 52,957 0.318 0.184 0.040 0.920 Volatility 62,848 1.354 0.644 0.402 3.563 TE 62,668 0.363 0.691 0 17.95

Table 3 Correlation matrix

Table 3 reports the correlation matrix and consists the correlation coefficients of the following variables: The average daily tracking error (TE), the annual net expense ratio (ER), the natural logarithm of the average market capitalization (LnSize), the average dividend yield (Dividend), the standard deviation of ETFs return (Volatility) and the natural logarithm of the average trading volume (LnVolume)

TE ER LnSize Dividend Volatility LnVolume

TE 1.000 ER 0.761 1.000 LnSize -0.658 -0.836 1.000 Dividend 0.526 0.491 -0.552 1.000 Volatility 0.711 0.391 -0.403 0.414 1.000 LnVolume -0.362 -0.563 0.802 -0.436 -0.111 1.000 3.2 Methodology

As mentioned above, the tracking error of an exchange-traded fund is defined as the deviation in returns of the exchange-traded fund from its underlying index. Therefore, the returns are calculated first for the ETFs and its corresponding benchmark index. The daily returns, Rfund (1) and Rindex (2) are calculated by the differences of the natural logarithm of the

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15 daily closing prices of ETF i and its corresponding index (see formulas (1) and (2) below). The existing literature mainly uses the standard method of calculating daily returns, such as Rompotis (2012). However, the stylized fact about daily returns is that the distribution is skewed and consists of fatter tails. For this reason this research uses the natural logarithm of the daily closing prices, in order to compute the daily returns. This method is also used by Singh and Kaur (2016). Furthermore, several papers use the net asset value instead of trading price in order to compute the returns of exchange-traded funds. Osterhoff and Kaserer (2016) argue that the net asset value is not biased by the arbitrage opportunity, when trading prices are traded at discount or premium. However, this study makes use of the ETFs daily trading closing prices, since this is also the realized return by investors and is also widely used by other papers (Milonas and Rompotis, 2006; Rompotis, 2012; Meinhardt et al., 2015; and Chu, 2011).

𝑅𝑓𝑢𝑛𝑑_𝑖𝑡 = 𝐿𝑜𝑔(𝑆ℎ𝑎𝑟𝑒 𝑝𝑟𝑖𝑐𝑒_𝑖𝑡) − 𝐿𝑜𝑔(𝑆ℎ𝑎𝑟𝑒 𝑝𝑟𝑖𝑐𝑒_𝑖𝑡−1) (1)

𝑅𝑖𝑛𝑑𝑒𝑥_𝑖𝑡 = 𝐿𝑜𝑔(𝐼𝑛𝑑𝑒𝑥_𝑖𝑡) − 𝐿𝑜𝑔(𝐼𝑛𝑑𝑒𝑥_𝑖𝑡−1) (2)

Subsequently, the daily tracking error is the key variable in this thesis. There are several methods which can be used to calculate the tracking error. Roll (1992) and Pope and Yadav (1994) suggested several tracking error methods as measure for fund performance. The literature adopts primarily three different methods, where the return difference in absolute value is the well-known method of the tracking error (e.g. Frino and Gallagher, 2001; Milonas and Rompotis, 2006; Shin and Soydemir, 2010; Chu, 2011). The key tracking error computation in this study is also based on the the difference in ETF’s return and the return of its underlying index in absolute terms. Furthermore, several papers use several tracking error methods in their study (e.g. Shin and Soydemir, 2010; Milonas and Rompotis, 2006; Chu, 2011). The other methods for tracking error is measured by the standard deviation in return differences and is calculated with formula (4) below and the regression analysis (5). However, the standard deviation of the return differences has two shortcomings (Chu, 2011). First, the standard deviations of return differences could result in zero if the exchange-traded funds regularly under- or outperforms by the same amount. Furthermore, this method assumes serial uncorrelated return differences. This assumption may not be valid, since daily returns are almost affected by serial autocorrelation. The third method for the tracking error is based on the regression analyses, where the returns of an ETF are regressed on the returns of its corresponding benchmark index. This method is similar to the well-known CAPM, also known as the capital asset pricing model. The alpha in the regression model measures the excess return achieved by the exchange-traded fund(s) above the

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16 underlying index. Since ETFs are passively managed investment vehicles, the alpha should not be significant different from zero. Further, the beta of the regression model corresponds to the systematic risk of the exchange-trade fund(s). Since ETFs aim to replicate the performance and risk of its benchmark index, the beta coefficient is not expected to be different from unity. The 𝑅2 of the regression analysis is expected to be close to one as well and is used as fourth method for the tracking error by Chu (2011) and Chu (2013). Furthermore, the error term of the regression model, also known as the standard residual, is the performance that is unexplained by the analysis. Besides, Drenovak et al. (2014) investigate the performance of sovereign debt exchange-traded funds during the European sovereign debt crisis. They adopt an additional and different cointegration method in which they differ from other studies. The main tracking error measure for this study is based on the most primarily used method in the existing literature, namely the return differences, see equation 3. The other two measures are considered to check the robustness of the findings.

𝑇𝑟𝑎𝑐𝑘𝑖𝑛𝑔 𝑒𝑟𝑟𝑜𝑟𝑖 = ∑ 1 𝑛ǀ𝑅𝑓𝑢𝑛𝑑𝑖𝑡− 𝑅𝑖𝑛𝑑𝑒𝑥𝑖𝑡ǀ 𝑡=1 𝑛 (3) 𝑇𝑟𝑎𝑐𝑘𝑖𝑛𝑔 𝑒𝑟𝑟𝑜𝑟 𝑆𝐷𝑖 = √ ∑𝑁 (𝑇𝐸_𝑖− 𝑇𝐸̅̅̅̅)2 𝑖=1 𝑁 − 1 (4) 𝑅𝑒𝑡𝑢𝑟𝑛𝑖 = 𝛼 + 𝛽 ∗ 𝑅𝑒𝑡𝑢𝑟𝑛𝑗+ 𝜀𝑖 (5)

The tracking error method from formula (3) is the daily tracking error. The frequency method differs among the different papers. Osterhoff and Kaserer (2016) deviate from the existing literature and use daily frequency method, while Shin and Soydemir (2010) and most of the literature use average daily tracking error over a given period of time. Osterhoff and Kaserer (2016) use daily returns, since they consider ETF investment as short-term investments. Therefore they want to focus and investigate the daily liquidity changes on the daily tracking ability. However, Pope and Yadad (1994) pointed out that high-frequency data may overestimate the tracking error. In Contrast, Meinhardt et al. (2015) show that low-frequency data result in high and significant tracking error as well. Nevertheless, the difference in average frequency methods within the same dataset has not been showed. This thesis tries to give new insight in the different average frequency methods within the same dataset, and show which data frequency fits

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17 the data best. Regression of the methods, absolute daily tracking error and absolute average tracking error are used to determine how the frequency fits the dataset and what the impact is on ETF’s tracking error. All the regression analyses in this study are panel regressions. Panel regression both allow for cross-section and time-series analysis. Since this study contains 20 different exchange-traded funds over a longer period of time, the panel regressions is the appropriate method to use. Furthermore, firm and year fixed effect are included into the regression analysis (6), (7) and (8). Company fixed effects control for specific ETF characteristics within the ETF and year fixed effects control for specific year events. First, the average annual regression equation (6) is used to determine the impact of average daily tracking error at annual frequency. Moreover, clustered standard errors, adjusted at exchange-traded fund levels are applied to all regression analysis in this thesis.

ǀ𝑇𝑟𝑎𝑐𝑘𝑖𝑛𝑔 𝑒𝑟𝑟𝑜𝑟_𝑖𝑡ǀ

= 𝛼_𝑖+ β₁𝐸𝑅_𝑖𝑡+ β₂𝐿𝑛(𝑆𝑖𝑧𝑒)_𝑖𝑡+ β₃𝑉𝑜𝑙𝑎𝑡𝑖𝑙𝑖𝑡𝑦_𝑖𝑡+ β₄𝐷𝑖𝑣𝑖𝑑𝑒𝑛𝑑_𝑖𝑡

+ β₅𝐿𝑛(𝑉𝑜𝑙𝑢𝑚𝑒)_𝑖𝑡+ ε_𝑖𝑡 (6) Equation (6) is the baseline panel regression and the tracking error of ETF i at time t is explained by the following explaining variables. The ER is the annual expense ratio of ETF i at time t. According to the literature the expenses for operating an exchange-traded fund are the key factor of the existence of the ETFs tracking error. The composition of the underlying index changes continuously. Therefore, an ETF has to make transaction in order to synchronize the value of its underlying index. Investors in ETFs have to pay these transaction costs, which are at the cost of realized returns, which disturb the tracking ability of the benchmark index. In line with the existing literature this study also expects a positive relationship between the expense ratio and the tracking error. Next, the variable size is the natural logarithm of the average daily market capitalization of ETF i at time t. The natural logarithm provides better distributions of the dataset and result is convenient interpretations of the coefficient. This variable is not extensively used by the literature. However, we include this variable since the total fund size range from 245 billion to only 71 million. This study expects a negative relationship between size and the tracking error, since bigger funds can be managed more efficient through trading at lower transaction cost (economies of scale). The variable volatility or risk of ETF i at time t is the standard deviation of the daily returns for a given time period. ETFs with relative high volatility face problems in replicating the performance and risk of the benchmark index. This study expects therefore that the volatility have a positive impact on the tracking error. Furthermore, the variable volume is computed by the natural logarithm of the average daily turnover by volume. Turnover by volume

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18 serves as a proxy for liquidity of an exchange-traded fund. The higher the turnover by volume, the more liquid an ETF is, since the security can be quicker and easier traded in the market. More liquid securities face smaller time gap to adapt unbalances of ETF prices from its underlying index. Therefore, the variable ln(Volume) is expected to have a positive effect on the tracking ability and hence result in lower tracking errors. Finally, the variable dividend is measured by the average daily dividend yield. The delay in dividend payments and the trading costs of reinvesting the dividend payments into ETFs, impede the ability of exchange-traded funds to track underlying indices. In accordance with the literature, this study expects that dividends have a positive impact on the ETFs tracking error. Furthermore, the expected relationship of the dependent and independent variables are confirmed by the correlation coefficients in the correlation matrix.

The following regression equation (7) is used to analyze the monthly and quarterly average absolute daily tracking error. The expense ratio is dropped from equation (6) since it is the only variable on annual frequency. Besides, the variable size is also dropped from the regression due to the high correlation between both expense ratio and trading volume (see table 3). The dependent variables are based on monthly and quarterly averages.

= α𝑖 + β1𝑉𝑜𝑙𝑎𝑡𝑖𝑙𝑖𝑡𝑦𝑖𝑡+ β2𝐷𝑖𝑣𝑖𝑑𝑒𝑛𝑑𝑖𝑡+ β3𝐿𝑛(𝑉𝑜𝑙𝑢𝑚𝑒)𝑖𝑡

+ ε_𝑖𝑡 (7)

Regression equation (8) yields the regression based on the daily frequency. In order to test the H1: Lower frequency data results in overestimation of the tracking error, the regression of (6), (7) and (8) are used. Regression (8) differs especially in one way from the above regressions. In equation (6) and (7), the volatility is measured by the standard deviation of the daily returns, which cannot be calculated among one daily return. Therefore, the daily ETF market price variability is calculated with the following formula:

𝐷𝑉𝑜𝑙𝑎𝑡𝑖𝑙𝑖𝑡𝑦_𝑖𝑡 = 𝑃𝑡,ℎ𝑖𝑔ℎ− 𝑃𝑡,𝑙𝑜𝑤 𝑃_{𝑡,𝑐𝑙𝑜𝑠𝑒} Where,

𝑃_{𝑡,ℎ𝑖𝑔ℎ} = The highest trading price in day t 𝑃_{𝑡,𝑙𝑜𝑤} = The lowest trading price in day t 𝑃𝑡,𝑐𝑙𝑜𝑠𝑒 = The closing price in day t

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19 ǀ𝑇𝑟𝑎𝑐𝑘𝑖𝑛𝑔 𝑒𝑟𝑟𝑜𝑟_𝑖𝑡ǀ

= α_i+ β₁𝐷𝑉𝑜𝑙𝑎𝑡𝑖𝑙𝑖𝑡𝑦_𝑖𝑡+ β₂𝐷𝑖𝑣𝑖𝑑𝑒𝑛𝑑 𝑦𝑖𝑒𝑙𝑑_𝑖𝑡+ β₃𝐿𝑛(𝑉𝑜𝑙𝑢𝑚𝑒)_𝑖𝑡 + ε_𝑖𝑡 (8) Furthermore, this thesis elaborates the tracking error in periods of extreme negative returns and how the drivers of the tracking error change during these periods. This study expects tracking error to increase during times of extreme returns. Several dummies are considered which corresponds to periods of extreme negative returns and added to the regression equation (7) which is based on annual frequency. After the bankruptcy of the Lehman Brothers, the financial markets are confronted with great uncertainty and period of high volatility. Therefore the dummy FC is added, which is equal to one for financial crisis and refers to the period 2008-2009 and zero otherwise, see regression (9). Second, after the financial crisis another major crisis arises and had a significant effect on the financial markets. This crisis, the European sovereign debt crisis affected the financial market worldwide and had his origin in Europe in the aftermath of the financial crisis. The SDC dummy is equal to one for the period 2010-2011 and zero otherwise. Both crisis dummies are added, which yield in regression (11). Regression equations (9) and (11) are used to test hypothesis 2: Tracking errors of market index ETFs increase during crisis periods.

Next, this study investigates the effects of the tracking error drivers during the crisis periods. This study predicts tracking error drivers to have a reinforce effect of variables with expected positive relationship with tracking error during the financial crisis and the sovereign debt crisis. The variables with a structural predictable negative relationship are likely to have a weakened effect during the financial crisis and the sovereign debt crisis. Regression equations (10) and (12) add the interaction variables with respectively the financial crisis dummy and both crisis dummies. Regression equations (10) and (12) are used to test Hypothesis 3: The structural relationship between the tracking error and their drivers change during the crisis periods. The variable volatility is dropped from the regressions (9), (10), (11) and (12) since this thesis wants to investigate the impact during crisis periods. Crisis periods are inherent to periods of high volatility, which could influence the crisis effects.

= α_𝑖 + β₁𝐸𝑅_𝑖𝑡 + β₂𝐷𝑖𝑣𝑖𝑑𝑒𝑛𝑑 𝑦𝑖𝑒𝑙𝑑_𝑖𝑡+ β₃𝐿𝑛(𝑉𝑜𝑙𝑢𝑚𝑒)_𝑖𝑡

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20 ǀ𝑇𝑟𝑎𝑐𝑘𝑖𝑛𝑔 𝑒𝑟𝑟𝑜𝑟_𝑖𝑡ǀ = α𝑖 + β1𝐸𝑅𝑖𝑡+ β2𝐷𝑖𝑣𝑖𝑑𝑒𝑛𝑑 𝑦𝑖𝑒𝑙𝑑𝑖𝑡+ β3𝐿𝑛(𝑉𝑜𝑙𝑢𝑚𝑒)𝑖𝑡+ β4𝐹𝐶𝑡 + β₅(𝐸𝑅_𝑖𝑡∗ 𝐹𝐶_𝑡) + β₆(𝐷𝑖𝑣𝑖𝑑𝑒𝑛𝑑 𝑦𝑖𝑒𝑙𝑑_𝑖𝑡∗ 𝐹𝐶_𝑡) + β₇(𝐿𝑛(𝑉𝑜𝑙𝑢𝑚𝑒)_𝑖𝑡 ∗ 𝐹𝐶_𝑡) +Ɛ_𝑖𝑡 (10) ǀ𝑇𝑟𝑎𝑐𝑘𝑖𝑛𝑔 𝑒𝑟𝑟𝑜𝑟𝑖𝑡ǀ = α𝑖+ β1𝐸𝑅𝑖𝑡+ β2𝐷𝑖𝑣𝑖𝑑𝑒𝑛𝑑 𝑦𝑖𝑒𝑙𝑑𝑖𝑡+ β3𝐿𝑛(𝑉𝑜𝑙𝑢𝑚𝑒)𝑖𝑡+ β4𝐹𝐶𝑡 + β₅(𝐸𝑅_𝑖𝑡∗ 𝐹𝐶_𝑡) + β₆(𝐷𝑖𝑣𝑖𝑑𝑒𝑛𝑑 𝑦𝑖𝑒𝑙𝑑_𝑖𝑡∗ 𝐹𝐶_𝑡) + β₇(𝐿𝑛(𝑉𝑜𝑙𝑢𝑚𝑒)_𝑖𝑡 ∗ 𝐹𝐶𝑡) +Ɛ𝑖𝑡 (11) ǀ𝑇𝑟𝑎𝑐𝑘𝑖𝑛𝑔 𝑒𝑟𝑟𝑜𝑟𝑖𝑡ǀ = α_𝑖 + β₁𝐸𝑅_𝑖𝑡+ β₂𝐷𝑖𝑣𝑖𝑑𝑒𝑛𝑑 𝑦𝑖𝑒𝑙𝑑_𝑖𝑡+ β₃𝐿𝑛(𝑉𝑜𝑙𝑢𝑚𝑒)_𝑖𝑡 + β₄𝐹𝐶_𝑡+ β₅𝑆𝐷𝐶_𝑡+𝛽₆(𝐸𝑅_𝑖𝑡 ∗ 𝐹𝐶_𝑡) + β₇(𝐷𝑖𝑣𝑖𝑑𝑒𝑛𝑑 𝑦𝑖𝑒𝑙𝑑_𝑖𝑡∗ 𝐹𝐶_𝑡) + 𝛽₈(𝐿𝑛(𝑉𝑜𝑙𝑢𝑚𝑒)_𝑖𝑡∗ 𝐹𝐶_𝑡) + β₉(𝐸𝑅𝑖𝑡 ∗ 𝑆𝐷𝐶𝑡) + β10(𝐷𝑖𝑣𝑖𝑑𝑒𝑛𝑑 𝑦𝑖𝑒𝑙𝑑𝑖𝑡∗ 𝑆𝐷𝐶𝑡) + 𝛽₁₁(𝐿𝑛(𝑉𝑜𝑙𝑢𝑚𝑒)_𝑖𝑡∗ 𝑆𝐷𝐶_𝑡) +Ɛ_𝑖𝑡 (12)

4. Regression results

The first part of this section provides the results of the different tracking error frequencies. Next, part two of this section provides the results of the financial crisis and sovereign debt crisis on the ETFs tracking error. The last part of the results consists of several robustness checks in order to test the robustness of the results.

4.1 Results of tracking error frequency

Table 4 reports six different regressions analyses, where different intervals are used to compute the average tracking error. First, the regression of five determinants is regressed on the annual average tracking error. The effect of the expense ratio is unintuitive since the effect is negative, which is contrary to the literature where mainly positive effects are found. Besides, the effect is significant which is comparable with the result found by Chu (2013). Chu (2013) argues that a possible reason is due to the sample composition. The variables dividend, volatility and trading volume are statistically significant with significant levels of respectively 5, 1 and 1 percent. The effect of dividends on ETFs tracking error is positive, which is in line with the existing literature. An increase of 100 basis points in the dividend yield, raise the tracking error on average by 3.1 basis points ceteris paribus. Furthermore, trading volume has also the expected negative effect, since more liquid assets have lower time gap regarding price adjustments of ETFs trading price. An increase of 100 basis points in trading volume increase, reduce the tracking error by 19.9 basis points ceteris paribus. Funds riskiness is clearly the most important determinant in

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21 explaining the tracking error in this sample. If the volatility of an ETF increases by 100 basis points, the tracking error rises with 25.3 basis points ceteris paribus. Moreover, the variables size is positive, which was not expected beforehand and contrary to the results found by Chu (2013). He argues that bigger exchange-traded funds can benefit more from economies of scale regarding lower transaction cost. However, table 3 reports the correlation coefficients of the dependent and independent variables. The variable size is both highly correlated with the expense ratio and trading volume variable with correlation coefficient of respectively -0.836 and 0.802. Since the results in regression equation may be biased due to multicollinearity, the variable size is dropped from the regression equation and not used for further analyses. The results of regression equation (2) are comparable to the results found in regression (1). Both the magnitude and significant level of all the variables are comparable, except for the effect of trading volume. The effect of trading volume is almost twice as low compared to regression (1) and was probably biased due to multicollinearity. In order to compare the results of quarterly, monthly and daily tracking error, the expense ratio is also dropped from the model see regression (3). Besides, there is no evidence for an effect of the expense ratio on tracking error.

The results of regression (3), (4) and (5) which are respectively the annual, quarterly and monthly tracking error are quite similar to each other. However, trading volume seems consistent in all cases. By an increase of 100 basis points and holding other things constant, the annual, quarterly and monthly trading volume reduces the tracking error between 7.3 and 7.8 basis points. The effect of dividends seems to overestimate the quarterly and monthly tracking error, since both have larger effect by the same magnitude compared to the annual tracking error in (3). The inverse effect can be applied to the volatility, where the effect in annual tracking error is superior compared to comparable effects of quarterly and monthly average tracking error. The daily tracking error has different results compared to the other, because of the different volatility measure and also daily data. The daily volatility measure indicates an overestimation of the volatility in the annual, quarterly and monthly tracking error. While, the dividend are likely to be overestimated, since the effect of the other tracking error frequencies are smaller. Besides, the daily natural logarithm of trading volume is relatively small and also not statistically significant. The results of the different (average) frequencies are mixed, and therefore no overall conclusion can be drawn. Nevertheless, all the effects and their magnitude considered, the annual average tracking error seems to be the best fit of this sample and is therefore used for further analyses. Besides, the effect of expense ratio can be investigated in times of financial turmoil.

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22

Table 4 Impact of different average frequency methods on the tracking error

Table 4 below shows the output of panel data regressions of the tracking error determinants with different frequencies with firm fixed and year fixed effects. The dependent variables are respectively, annual average tracking error (column 1), annual average tracking error (column 2), annual average tracking error (column 3), quarterly average tracking error (column 4), monthly average tracking error (column 5), and daily tracking error (column 6). The sample covers the period 2006- march 2018. Clustered standard errors, adjusted at exchange-trade fund level, are reported in parentheses. ***, **, * indicates respectively the significance levels of 1 %, 5% and 10%

Dependent variable: Tracking error

(1) (2) (3) (4) (5) (6)

Independent variables Annual TE Annual TE Annual TE Quarterly TE Monthly TE Daily TE

ER -0.247** -0.267 (0.115) (0.181) Ln(Size) 0.177*** (0.019) Dividend 0.031** 0.042* 0.051*** (0.012) (0.021) (0.017) Volatility 0.253*** 0.316*** 0.315*** (0.060) (0.077) (0.074) LnVolume -0.199*** -0.108*** -0.078*** (0.015) (0.031) (0.019) Volatility quarter 0.244*** (0.050) Dividend quarter 0.071*** (0.014) LnVolume quarter -0.073*** (0.021) Volatility month 0.268*** (0.046) Dividend month 0.066*** (0.014) LnVolume month -0.076*** (0.018) DVolatility 0.087** (0.035) DividendYield 0.105*** (0.015) Ln Volume -0.006 (0.013) Constant 0.292 0.738* 0.465** 0.475*** 0.485*** 0.100 (0.213) (0.419) (0.163) (0.149) (0.129) (0.101) Observations 52,937 52,937 62,828 62,699 62,655 60,427 R-squared 0.861 0.779 0.759 0.714 0.647 0.194

Firm FE Yes Yes Yes Yes Yes Yes

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23 4.2 Results of the financial crisis and sovereign debt crisis

Table 5 reports four different regressions analyses. The first and the third regression are based on the baseline regression added with respectively the global financial crisis dummy (FC) and sovereign debt crisis (SDC) dummy. The first and third regressions are to determine whether the financial crisis and sovereign debt crisis have a positive effect on the tracking error. After that, this thesis tested whether the tracking error determinants have a significant effect during periods of extreme market shocks.

As can be seen in table 5 regression 1, the financial crisis has a positive and statistically significant effect on the tracking error with significance level of 1 percent. The effect of financial crisis is notable, since the effect is quite extensive. In period of the global financial crisis, the tracking error increases on average by 35.2 basis points holding other variables constant. Furthermore, the impact of the variables expense ratio, dividend and volume is referred to the period of no financial crisis. The expense ratio outside the period of financial crisis has a positive effect, but is not statistically significant. This is not completely in line with the existing literature, since they found the expense ratio as the key factor of ETF’s tracking error. Possible explanation is due to the stable expense ratio over time. The cash inflow of ETFs has grown over time, and therefore the size of ETFs as well. The expense ratio is stable over time or even decreasing over time, since ETFs can trade over time more efficient. Next, Dividends have a positive and significant impact on the tracking error with significance level of 5 percent. Nevertheless, the effect of dividends is relatively small. An increase of 100 basis points of the dividend yield, increase the tracking error on average by 5.4 basis points holding other variables constant. The effect of dividends in regression equation 1 is in line with the literature and also with the expected relationship of dividends and tracking error. The natural logarithm of trading volume has a negative and significant effect on the tracking error. This effect was expected, because trading volume is highly correlated with fund size, which leads to lower trading cost. However, the findings of liquidity variable in the existing literature are not consistent. Besides, the effect of trading volume is again relativity small. An increase of 100 basis points in trading volume, decrease the tracking error on average by only 7.9 basis points ceteris paribus.

Regression (1) in table 5 displays that the financial crisis has an additional effect on the tracking error. But to investigate the effect of the individual drivers during the financial crisis, interaction variables with the financial crisis dummy are added to regression equation (1), see regression (2). The reference effect of the expense ratio outside the financial crisis is positive, but again not statistically significant. However, the magnitude is more than three times bigger compared to the results found in regression equation 1 reported in table 5. Besides, the expense

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24 ratio has an additional statistically significant effect during the period of the financial crisis. An increase of 100 basis points in the expense ratio, increase the tracking error by 113.1 basis points through the financial crisis holding other variables constant. Therefore, the effect of the expense ratio turns into an even larger positive effect during the financial crisis. This effect is reasonable, since the financial markets are confronted with high levels of volatility. This lead to more trades, which increases the transaction cost and limit therefore the tracking ability of an exchange-traded fund. Furthermore, the initial effect outside the crisis period of dividend is again positive, but compared to the results from regression equation 1 is table 5 extremely small. Nevertheless, during the liquidity shock in 2008, dividends have an increased, but not statistically significant effect on the tracking error. The liquidity variable measured by turnover by volume, has also a positive effect on the tracking error during the global financial crisis. In normal economic circumstances was a negative effect expected, since more liquid ETFs can track their benchmark index better and more efficient. This effect is found in regression (1), where the trading volume variable has on average a negative and statistically significant effect on the tracking error. However, the effect of trading volume turns during the financial crisis into a positive effect but is not statistically significant. So there is not enough evidence that the tracking ability increases for liquid ETFs. More liquid ETFs face therefore also difficulties in tracking their benchmark index in periods of extreme liquidity shocks, such as the global financial crisis.

The net expense ratio has an additional and statistically significant effect during the financial crisis period. Nevertheless, only the impact of the expense ratio during the financial crisis is extensive. In contrast, the effect of dividends and trading volume are comparable and both positive. Nevertheless, both variables have not a significant effect during times of extreme market returns. The overall conclusion is therefore that during the financial crisis the tracking error increases significantly, which is generally determined by the expense ratio.

Since this thesis shows evidence of an additional effect on ETFs tracking error throughout the financial crisis, this thesis wants to investigate another key liquidity shock and its effect on the tracking error. The second large crisis that had an impact on the financial markets worldwide was the sovereign debt crisis. In order to investigate the impact of the sovereign debt crisis on the tracking error, the dummy of sovereign debt crisis is added to regression (1), where the sovereign debt crisis referred to the period 2010-2011. According to table 5 regression equation (3), the sovereign debt crisis has a positive and statistically significant impact on the tracking error. During the sovereign debt crisis the tracking error increased on average by 15.4 basis points holding other things constant. The reference period, where no crisis period applies, consists of the period where both the financial crisis and sovereign debt crisis are not applicable.

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25 This initial effect of regression equation (3) is comparable with the results found in regression equation (1), except for the expense ratio. The expense ratio is negative, but not statistically significant. The negative relationship is contrary to the literature, since a positive relationship between tracking error and expense ratio was expected in all cases. However, Rompotis (2012) found also a negative effect of the expense ratio on ETFs tracking error, but was neither statistically significant. The effects of dividend and trading volume are also comparable, where the magnitude, sign and significance level are similar. The effect of financial crisis is even bigger after controlled for the sovereign debt crisis. After controlling for the sovereign debt crisis, the financial crisis has on average an additional effect of 38.9 basis points, which is comparable but slightly larger than the results found in regression (1). Both crisis periods has an extra impact on the tracking error. Furthermore, this thesis wants to investigate the impact of the tracking error drivers throughout the crisis periods. Therefore, the financial crisis and sovereign debt crisis interactions with tracking error determinants are added to the regression.

Table 5 regression equation (4) reports the results with interactions of both financial crisis and sovereign debt crisis. The interaction variables with financial crisis are similar to those found in regression (2). The expense ratio is again significant with 1 percent level during the financial crisis. An increase of 100 percent in the expense ratio, increase the tracking error on average by 135.1 basis points ceteris paribus. The tracking error is again primarily determined by the expense ratio during the financial crisis. However, the effect of dividends throughout the financial crisis is almost identical compared to regression (2), but is now statistically significant. The effect is relatively small, but an increase of 100 basis points in dividends during the financial crisis, increases the tracking error on average by 5.2 basis points holding other things constant. The tracking error determinants in the reference period, so outside the crisis period are not statistically significant. Furthermore, the effects of the SDC interactions are comparable to the FC interactions, but with different magnitude levels. The expense ratio has also a positive and significant impact on the tracking error during the sovereign debt crisis. If the expense ratio increases with 100 basis points throughout the sovereign debt crisis, the tracking error increases on average with 58 basis points ceteris paribus. Moreover, dividend has also a positive and significant effect on the tracking error. Ceteris paribus, the tracking error increases by 4.2 basis points if dividend increases by 100 basis points throughout the European debt crisis. In contrast to the results of the financial crisis interactions, has trading volume a negative relationship with the tracking error during the sovereign debt crisis.

The effects of the financial crisis and sovereign debt crisis are mixed. The results from both the global financial crisis and sovereign debt crisis show an additional and significant effect

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26 on the tracking error. The tracking error throughout the financial crisis is mainly influenced by the expense ratio in a positive manner. Furthermore, trading volume turns into a positive effect as well during the financial crisis, but is not statistically significant. The sovereign debt crisis shows an additional effect on the tracking error as well. However, the size of the effect compared to the financial crisis is almost three times smaller. Besides, the interaction variables SDC and FC with expense ratio are both positive and statistically significant, where the FC effect is again substantial larger. Finally, the results of trading volume are mixed. Trading volume has a positive impact during the financial crisis, while the sovereign debt crisis has a negative effect on the tracking error, but are neither statistically significant. The direction of the effect is therefore dependent on the magnitude of the crisis. The market shock of the financial crisis is substantial large, that trading volume turns into a positive manner. This thesis concludes therefore that both crisis periods had a significant effect on the tracking error, but the size of the effect is dependent on the magnitude of the crisis. Furthermore, the determinants of tracking error are mainly determined by the crisis periods and primarily by the expense ratio, since none of the variables show a significant effect throughout the periods of financial stability. Therefore, this study shows significant effects of the two biggest market shocks in the last decade.

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Table 5 Effects of the global financial crisis and the European sovereign

debt crisis on the Exchange-Traded funds’ tracking error

Table 5 below shows the output of panel data regressions of the effects of the financial crisis and sovereign debt crisis on the tracking error with firm fixed effects. The dependent variable is the average absolute tracking error (TE1) and applies to all four columns. The following independent variables apply to all four regressions as well: annual net expense ratio (ER), average dividend yield (Dividend) and the natural logarithm of the average turnover by volume (Ln Volume). The next dependent variables are added to each column: financial crisis dummy (FC) with one for 2008-2009 and zero otherwise (column 1), FC dummy and FC interaction variables with respectively, ER, Dividend and Ln (Volume) (column 2), sovereign debt crisis dummy (SDC) with one for period 2010-2011 and zero otherwise and FC dummy (column 3) and FC and SCD dummies and their interaction variables with respectively, ER, Dividend and Ln (Volume). The sample covers the period 2008- march 2018. Clustered standard errors, adjusted at company level, are reported in parentheses. ***, **, * indicates respectively the significance levels of 1 %, 5% and 10%.

Dependent variable: Tracking error (TE1)

(1) (2) (3) (4)

Independent variables FC FC interaction FC & SDC FC & SDC interaction

ER 0.091 0.343 -0.276 -0.037 (0.482) (0.308) (0.261) (0.170) Dividend 0.054** 0.0008 0.060** 0.002 (0.021) (0.019) (0.023) (0.016) LnVolume -0.079** -0.011 -0.074** 0.017 (0.030) (0.020) (0.034) (0.017) FC 0.352*** -0.270** 0.389*** -0.255* (0.063) (0.110) (0.069) (0.143) SDC 0.154*** -0.060 (0.038) (0.073) ER*FC 1.131*** 1.351*** (0.223) (0.263) Dividend*FC 0.050 0.052* (0.030) (0.029) LnVolume*FC 0.014 0.007 (0.010) (0.012) ER*SDC 0.580*** (0.099) Dividend*SDC 0.042** (0.019) LnVolume*SDC -0.009 (0.007) Constant 0.730** 0.267 0.761** 0.130 (0.292) (0.170) (0.297) (0.156) Observations 52,937 52,937 52,937 52,937 R-squared 0.567 0.690 0.630 0.811

Firm FE Yes Yes Yes Yes

Year FE No No No No

4.3 Robustness checks

This subsection analyzes and discusses several robustness checks, where different methods are employed or variables are added to the regressions. The first robustness check consists of a different method for the tracking error variable (TE2). As discussed in section 3.2,

Tracking ability of exchange-traded funds during times of financial turmoil : evidence from the 2008 financial crisis and 2010 sovereign debt crisis