The Dutch Exchange-Traded Fund : the effects of liquidity on Exchange-Traded Fund’s mispricing

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The Dutch Exchange-Traded Fund

The effects of liquidity on Exchange-Traded Fund’s mispricing

UNIVERSITEIT VAN AMSTERDAM

FACULTY OF ECONOMICS AND BUSINESS

BSc Economics and Business

Bachelor specialization Economics and Finance

Author:

M.M.A. Smeenk

Student number:

10409785

Thesis supervisor:

Dr. J. Lemmen

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PREFACE AND ACKNOWLEDGEMENTS

This paper is a thesis that is written as a part of finishing my Bachelor study in Economics and Business, specializing in Economics and Finance. I have done research regarding Exchange-Traded Funds because of the fact that the product is fairly new and has risen enormously in popularity. This paper provides both a general and a deeper understanding of Exchange-Traded funds and furthermore examines the effects of liquidity on Exchange-Traded Fund’s mispricing.

I would like to say special thanks to Dr. J. Lemmen for supervising me in the process of making this thesis, providing me with insights, reviewing my work and challenging me during the process.

ABSTRACT

Exchange-Traded Funds have grown tremendously since the introduction of the product in the financial markets. This has caught attention of many financial institutions, investors and academics. This study examines the effect of liquidity on Exchange-Traded fund’s mispricing. This paper provides profound information about the product, discussing its features, advantages and disadvantages. The effects of liquidity on mispricing for Exchange-Traded Funds were examined using daily data for the Think AEX UCITS Exchange-Traded Fund for the period from December 2009 - December 2014. A U-shaped relation was found between mispricing and liquidity for this Exchange-Traded Fund.

NON-PLAGIARISM STATEMENT

By submitting this thesis the author declares to have written this thesis completely by himself/herself, and not to have used sources or resources other than the ones mentioned. All sources used, quotes and citations that were literally taken from publications, or that were in close accordance with the meaning of those publications, are indicated as such.

COPYRIGHT STATEMENT

The author has copyright of this thesis, but also acknowledges the intellectual copyright of contributions made by the thesis supervisor, which may include important research ideas and data. Author and thesis supervisor will have made clear agreements about issues such as confidentiality.

Electronic versions of the thesis are in principle available for inclusion in any EUR thesis database and repository, such as the Master Thesis Repository of the Erasmus University Rotterdam

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LIST OF TABLES

Table 1: Assets of ETFs by type (March 2014-March 2015) 1 Table 2: Overview of literature review regarding pricing efficiency 5 Table 3: Overview of literature review regarding the pricing of assets and liquidity 7

Table 4: Data Summary 12

Table 5: Summary of results for panel A (December 2009 - December 2010) 15 Table 6: Summary of results for Panel B (December 2010 – December 2014) 16

LIST OF FIGURES

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1 1. Introduction

Exchange-Traded Funds (hereafter ETF) constitute a relatively new product on the financial markets. The first ETF was introduced in 1989 in the United States. This fund was designed to track the Standard and Poors 500 (better known as the S&P 500). So the first ETF was introduced in the United States, but the product was only much later introduced in the Dutch market. The market for ETFs has increased enormously in the last few years. Since their creation ETFs have become an increasingly popular

financial product. In the past decade alone more than 1.4 trillion U.S. Dollars in shares have been issued. They are particularly popular in the United States which has a 73% share of the total ETF market with 1411 funds that have 2 trillion U.S. Dollars in assets under their management. Globally the assets held by ETFs are worth 2.7 trillion U.S. Dollars of which 16% is held by European ETFs (Investment Company Institute, 2015).

Table 1: Assets of ETFs by type (March 2014-March 2015).

Numbers are in millions of dollars, where the domestic country resembles the United States. Source of Data: Investment Company Institute.

In 2010 more than $780 billion was invested in ETFs worldwide. By December 2013 they managed approximately $51 billion combined. Assets in the US rose from some $70 billion in 2000 to around $1.7 trillion by half 2014 (Madhavan, 2014). Worldwide ETFs in all asset classes invested now exceed $2.5 trillion.

March 2015 February 2015 March 2014

Total Domestic Equity 1,268,914 1,280,319 1,048,751

Domestic (Broad-Based) 934,413 946,435 762,162 Domestic (Sector/Industry) 334,500 333,884 286,589 Global/International Equity 472,549 457,838 401,110 Hybrid 3,415 3,365 1,694 Bond 318,113 319,869 259,008 All 2,062,991 2,061,391 1,710,563

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2 This enormous growth has caught attention of financial institutions, investors and academics and

consequently the ETF market has been topic of interest in various papers. The reason for this enormous rise in popularity is mainly due to the ETF’s structure and the benefits arising from this structure. An ETF is an open-ended investment fund that pools stocks and/or bonds whose shares can be traded intraday on an exchange, just like a normal share of any publicly traded company. This pooling of assets has a diversifying effect and thus lowers firm-specific risk that is born by investors. Many ETFs attempt to follow a specific stock-index, i.e. they are trying to generate the same returns as the index. This is beneficial to many investors who would otherwise have to buy each stock individually leading to high transaction costs. Other costs such as fees tend to be a lot lower since ETFs are usually passively managed and they are more tax efficient than most other funds (Madhavan, 2014).

There is however a negative side to ETFs that has already been observed empirically, namely the fact that ETFs can be significantly mispriced on their exchange. This can be seen as a large cost which might remove the benefit an individual investor had when trading ETFs. Mispricing occurs when the trading price of the ETF deviates significantly from its Net Asset Value (hereafter NAV) or from the trading value of its underlying assets which may be a more current proxy of value, since NAV is only calculated at the end of the trading day. An ETF can therefore trade at a discount or at a premium relative to an objective intrinsic value and this may contradict the Efficient Market Hypothesis. In order to minimize such inefficient pricing ETFs have a creation and redemption mechanism. At the beginning of the day a portfolio is announced for which shares can be created or redeemed (Petajisto, 2013 and Charupat, 2013). If the fund trades at a premium, one can buy the portfolio of assets and create an ETF share at an authorized participant (hereafter AP) and sell it for a higher price. The other way around applies for a ETF trading at a discount. This process can be used to facilitate arbitrage in order to ensure that the price of the ETF is as close as possible to the NAV or the value of the fund’s underlying assets (Charupat and Miu, 2013). However the effectiveness of this form of arbitrage is limited due to transaction costs, bid-ask spreads and certain ETF requirements which could all hamper efficient pricing. There have been various studies made on the mispricing of ETFs by comparing their prices to the NAV. Petajisto (2013) shows that funds holding liquid domestic assets are usually priced efficiently, but that international or illiquid funds show large ETF price premiums relative to the NAV. Marshall et al. (2013) studied ETF arbitrage in the US at an intraday level by looking at two S&P 500 ETFs and found that few arbitrage opportunities arise in ETFs and that they are mainly due to decreasing liquidity resulting in increasing spreads.

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3 Ackert and Tian (2008) also looked into S&P 500 and country ETFs and found that they were priced inefficiently, consistent with significant limits to arbitrage. In particular country/international ETFs showed a large price premium due to time-zone differences. Part of the portfolio is closed on the home-market, but the portfolio as a whole can still trade.

ETFs resemble a claim on some underlying (group of) asset(s). They are designed to track the underlying asset(s), i.e. they are designed trying to generate the same returns. ETFs hold a portfolio composed of assets that closely tracks an index like the AEX, but does not fully replicate it (Madhavan, 2014). Many indexes are composed of thousands of assets, with both very big holdings and very small holdings. Some of these small holdings are so small that they may be quite expensive and sometimes are even

impossible to buy or sell (Madhavan, 2014). ETFs have characteristics of both open-end funds and closed-end funds. Like open-end funds ETFs can be created or redeemed for the NAV at the end of the day. ETFs issue and redeem shares only in a minimum value and with market-making firms only. These firms are better known as APs (Madhavan and Sobczyk, 2014 and Petajisto, 2013). A feature that is similar to a closed-end fund is that ETFs can be traded throughout the day for prices that can differ from their Net Asset Value. Most research has been done on US ETFs and country indexes (also known as international indexes, ETFs that have a claim on foreign assets) (Amihud, 2002, Marshall, 2013, Madhavan, 2014 and Ackert, 2008). Somehow there is a lack of research done on ETFs in the Dutch market tracking the AEX, more specifically the AEX ETF issued by www.thinketfs.com.

ETFs can be composed of any combination of assets, including derivatives (Madhavan, 2014). ETFs that include derivatives are called synthetic ETFs, because they do not hold all physical assets that generate the returns (Madhaven, 2014). Consequently ETFs that hold all physical assets are called physical ETFs. According to Fassas (2014), this differences in the making up of the ETF might be influencing the price error as well.

The goal of this paper is to examine the effects of liquidity of both the ETF and the underlying (group of) asset(s) on the price error. Somehow there is a lack of research on ETFs in the Dutch market, so this paper tries to examine the effects of liquidity using data from a Dutch ETF.

In a liquid market without any limits on arbitrage, any mispricing should not be observed (Ackert, 2008). Mispricing would be bigger when products are less liquid (Petajisto, 2013 and Ackert, 2008).

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4 Noteworthy Ackert and Tian (2008) find a non-linear relationship between mispricing and liquidity for international or country ETFs, this includes ETFs that have foreign assets in the underlying portfolio. A negative relationship is expected between mispricing and the liquidity (Amihud, 2002). And since the Dutch ETFs include little to almost no foreign weight in their portfolio a negative relationship between mispricing and liquidity will be expected for the Dutch ETF.

This paper shows that mispricing for the Dutch ETF is indeed very small as was hypothesized due to former research and thus it might be unprofitable to exploit this arbitrage opportunity. The results however do indicate a significant relationship between the price error and the liquidity of the fund. At first a negative relation between price error and liquidity was found, being highly significant which was expected according to efficient market theory and prior research. The interesting thing is that the additional evidence suggests a non-linear relationship between price error and liquidity.

This paper is organized as follows, in section 2 a literature review will be done regarding mispricing and liquidity effects, in section 3 the methodology will be explained and defined, in section 4 the data will be discussed, in section 5 the results will be summarized and discussed and in section 6 a summary and some suggestions for further research will conclude this paper.

2. Literature Review

The literature review below is split up into two parts. In the first part the review regarding the pricing of ETFs is summarized; in the second part the effects of liquidity on the pricing of ETFs/assets are reviewed. The tables provide a quick summary regarding all the research that was read and used for this paper. Then a general tendency in research results will be deduced and consequently the hypotheses will be stated.

2.1 Literature Review (Pricing Efficiency ETFs)

The table below shows a literature review of research done on the pricing efficiency of ETFs.

The table shows the author(s), the country or region of the sample, the time period of the sample and the results.

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5 Table 2: Overview of literature review regarding pricing efficiency.

Author(s) Region/Country Time Period Liquidity Measure Results Engle and Sarkar

(2006). US indices including major ones and international indices. Up to 2000. - Average price deviation is smaller for domestic ETFs than for international ETFs (0.35 percent vs. 0.01 percent) and the price deviation is more persistent for international ETFs. Delcoure and Zhong (2007). MSCI country-specific indices. Up to 2002. - ETFs trade at economically significant premiums (10 to 50 percent of the time), however not persistent. Ackert and Tian

(2008).

International ETFs and US ETFs.

2002-2005. - Emerging-market

ETFs have larger median deviations than developed-market ETFs (0.20 average vs. 0.41 average). Petajisto (2013). US and International ETFs . 01/2007-12/2010. - Average premium of 14 bp. Fluctuating between a 260 bp. band.

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6 Marshall, Nguyen

and Visaltanachoti (2013).

US SPDR Trust ETF and iShare ETF (Tracking S&P 500).

2001-2010. Bid-Ask spread. Average daily mispricing is -0.1%.

Ackert and Tian (2000).

US S&P500 ETFs. 01/1993-12/1997 - No significant mispricing was observed Elton, Gruber,

Comer and Li (2002)

US S&P500 ETFs 1993-1998 - No significant

mispricing, but a non-persisting tracking error of 1.8bp was observed

In most research no large significant, persisting mispricing was observed for developed market ETFs. In emerging market ETFs and international ETFs the mispricing was still small but larger than domestic developed market ETFs. Research found that international ETFs have larger price deviations because of time zone differences, since international ETFs have an international portfolio composition. Because of these holdings in foreign stocks stale prices can occur. A part of the portfolio underlying the fund can still trade even if the home market for a particular asset is already closed. Note that all research regarding mispricing makes use of an implicit assumption fundamental to ETFs, the feature that ETFs exhibit a creation-redemption mechanism. This mechanism ensures an arbitrage opportunity when prices get too far out of line. Each day a portfolio of assets is announced for which shares can be created and redeemed for a particular fund. Keep in mind that fund shares can only be created or redeemed by APs. If the NAV of the portfolio deviates from the price of the ETF, investors can take advantage and exploit this arbitrage opportunity. This process will continue until the price is back to the non-arbitrage value. Because of this mechanism it was already expected that mispricing should be small and non-persisting for ETFs. Thus if prices would deviate from their NAVs, it is just a matter of hours before this deviation is cleared since arbitrageurs will quickly exploit this opportunity. Consequently, the hypothesis in this paper states that mispricing for the Dutch AEX ETF should be fairly small.

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7 2.2 Literature Review (Liquidity)

The table below shows a literature review of research done on the effects of liquidity on pricing efficiency. The table shows the author(s), the country or region of the sample, the time period of the sample the liquidity measure that was used and the results.

Table 3: Overview of literature review regarding the pricing of assets and liquidity.

Author(s) Region/Country Time Period Liquidity Measure Results Amihud (2002) US NYSE stocks 1964-1997 Amihud’s

Illiquidity Measure Illiquidity has a highly significant and positive effect on expected returns. Unexpected illiquidity has a significant and negative effect on returns. (Effects are stronger for small stocks) Acharya and Pedersen (2005) US stocks (listed on NYSE and AMEX) 07/1962-12/1999 Amihud’s Illiquidity Measure The required return of a security is increasing in the covariance of its illiquidity and the market’s

illiquidity Madura and Ngo

(2008) 01/1997-09/2004 A liquidity proxy calculated as the ratio of the trading volume to the number of shares outstanding Portfolios with more pronounced increases in the liquidity proxy realize significantly higher returns for four quarters

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8 Ackert and Tian

(2008) US ETFs and International ETFs 2002-2005 Square root transformation of Amihud’s Illiquidity

Measure and the non-transformed Illiquidity Measure A negative but insignificant relation between premium and illiquidity. When the transformed measure is added, the squared measure is, often significant, positively related to the price error. This suggests a U-shaped

relationship Petajisto (2013) US and

International ETFs

01/2007-12/2010 Intraday spread An increasing spread as the trading volume of the fund decreases ($1B at or below 10bp vs. $1M at or above 100bp) Madhavan and Sobczyk (2014)

US domiciled ETFs 2005-2014 Presumed liquidity scaling for asset classes

Price staleness decreases as liquidity increases

Although several measures of liquidity can and have been used in former research, there is a general tendency in the results. Meaning that it seems to be the case that all the measures should lead to the same general result. The general result constitutes a negative relation between the price error and the liquidity of the asset, with the exception of Ackert (2008). Ackert (2008) found a U-shaped relation since they added a squared transformation of a liquidity measure. There is no general result whether this price error is a discount or a premium. A problem that was often emphasized for the existence of mispricing was staleness in prices. Staleness in asset prices can occur when an asset is thinly traded. This means the price is not up-to-date due to a lack of trading, i.e. the price is old and does not incorporate all available information.

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9 It is then expected in this paper that liquidity should have a negative effect on the price error of the asset, which is in line with the Efficient Market Hypothesis.

Summarizing the hypotheses mathematically;

𝐻0 : 𝑝𝑟𝑖𝑐𝑒 𝑒𝑟𝑟𝑜𝑟 = 0 𝐻1: 𝑝𝑟𝑖𝑐𝑒 𝑒𝑟𝑟𝑜𝑟 ≠ 0 and 𝐻0: 𝐶𝑜𝑟𝑟(𝑝𝑟𝑖𝑐𝑒 𝑒𝑟𝑟𝑜𝑟, 𝑙𝑖𝑞𝑢𝑖𝑑𝑖𝑡𝑦) = 0 𝐻1: 𝐶𝑜𝑟𝑟(𝑝𝑟𝑖𝑐𝑒 𝑒𝑟𝑟𝑜𝑟, 𝑙𝑖𝑞𝑢𝑖𝑑𝑖𝑡𝑦) < 0 3. Methodology

Since this paper makes use of some formulas and ambiguous variables, these are explained thoroughly such that any misunderstanding is omitted. All formulas are displayed mathematically below, where each formula is further expounded.

3.1 Tracking Error versus Mispricing

The concepts tracking error and mispricing are often used interchangeably while they are essentially very different. Firstly pricing efficiency or mispricing will be calculated in the same way as has been done in former research (Madhavan, 2014 and Ackert, 2008). Mispricing is defined as the difference between the price of the Exchange-Traded Fund and the Net Asset Value of the fund. Resulting in a premium or discount in the price of the Exchange-Traded Fund

Thus the price of the Exchange-Traded Fund at time t minus the Net Asset Value of the fund at time t gives the premium or discount at time t. It might be interesting to see if the same results hold for relative mispricing, defining the relative premiums or discounts as a percentage of the fund’s Net Asset Value.

𝑅𝑒𝑙𝑎𝑡𝑖𝑣𝑒 𝑃𝑟𝑒𝑚𝑖𝑢𝑚 𝑜𝑟 𝐷𝑖𝑠𝑐𝑜𝑢𝑛𝑡𝑡 =

𝑃𝑟𝑖𝑐𝑒 𝐸𝑇𝐹𝑡− 𝑁𝐴𝑉𝑡 𝑁𝐴𝑉𝑡

∗ 100% (2)

So dividing the absolute price error at time t by the Net Asset Value of the fund at time t gives the relative tracking error at time t.

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10 Secondly the tracking error is defined as the difference between the return of the fund and the return of the index it is supposed to track. So the tracking error is defined as follows

𝑇𝑟𝑎𝑐𝑘𝑖𝑛𝑔 𝐸𝑟𝑟𝑜𝑟𝑡 = 𝑅𝐸𝑇𝐹,𝑡− 𝑅𝐽,𝑡 (3)

This actually resembles the tracking efficiency of the fund relative to the index. The tracking error at time t is equal to the difference of the return of the Exchange-Traded Fund at time t and the return of index J at time t. Stating specifically, this paper only uses the relative price error as defined above. 3.2 Liquidity Measure

Regarding the measure for liquidity a lot of measures are available to calculate a product’s liquidity. Examples are the bid-ask spread, transaction-by-transaction market impact and the probability of information-based trading. Although these measures are very accurate, they are quite complex and require lots of microstructure data. These are not available for many stock markets and if they are available they do not cover long time periods (Amihud, 2002, Acharya, 2005). For these reasons this paper uses Amihud’s illiquidity measure (2002), the same measure Acharya (2005) and Ackert (2008) used. The measure is calculated from daily data that are readily available for most markets (Amihud, 2002). Although the measure is rougher and less accurate than the measures named above, this

measure can be calculated for longer time periods (Amihud, 2002). The illiquidity measure is defined as;

Where Ri is the absolute return for stock I and VOLi is the daily volume for that stock. The intuition is

that a stock has a high value of ILLIQ if the stock moves a lot in response to small changes in volume. Although this measure is rough, it closely relates with the Amivest measure of illiquidity (Amihud, 2002 and Acharya, 2005). The Amivest measure has been used quite often in papers using the finer

microstructure data (Acharya, 2005). The ILLIQ measure shows correct relations with other, finer measures (Amihud, 2002). Therefore it is used in this research, since it is easy to calculate and should still lead to general results.

𝐼𝐿𝐿𝐼𝑄𝑖 = |𝑅𝑖| 𝑉𝑂𝐿𝑖

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11 3.3 Research Method

This paper tries to study the effect of liquidity on mispricing using the following time series regression stated mathematically below;

Where;

PEi,t = the price error for ETF i at time t.

Xi,t = the illiquidity measure for ETF i at time t.

Xj,t = the illiquidity measure for index j at time t.

α = the constant ε = the error term

Using Amihud’s Illiquidity measure after Ackert (2008), Acharya (2005) and Amihud (2002). But adding the squared illiquidity measure as well for both the ETF and index after Ackert (2002), to account for a potential non-linear relationship between mispricing and liquidity. This paper has, in addition to most other research, added the liquidity measure for the underlying index as well following Ackert (2008). Since the ETF is supposed to track the index, it can be argued that mispricing could be influenced by the liquidity of the index itself. Moreover, by adding the underlying index an indicator for market liquidity is incorporated as well. Since the ETF trades on the Dutch market tracking the AEX, the liquidity of the AEX could be a proxy for the liquidity in the Dutch market.

4. Data

The data were collected from Datastream, Euronext and the fund’s issuer. The data regarding the prices and returns were all retrieved from Datastream for both the index and the ETF. The NAVs for the ETF were retrieved from www.thinketfs.com, which issues the fund. The trading volume numbers for both the ETF and the index were retrieved from Euronext, which supplies all data for Datastream. For this paper daily data were collected because the fund started in December 2009. Monthly data would mean a fairly small sample which would result in little statistical power. The time-series runs from December 2009 till the end of 2014. Since different sources were used, time series from the three sources were different. The prices that were retrieved from Datastream are closing prices in euros.

𝑃𝐸𝑖,𝑡= 𝛼 + 𝛽1∗ 𝑋𝑖,𝑡+ 𝛽2∗ 𝑋𝑗,𝑡+ 𝛽3∗ (𝑋𝑖,𝑡) 2

+ 𝛽4∗ (𝑋𝑗,𝑡) 2

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12 The returns from Datastream are expressed as a percentage from the very start of the fund, this is why the numbers are so high for daily data. And the volume numbers retrieved from Euronext are the euro nominated trading values for that specific day.

Before the data were used, all days for which one of the factors was missing were deleted from the sample. Only days that had complete information for prices, NAVs, returns and volume numbers were included. Because a ratio was used to calculate the liquidity, the denominator cannot be zero. As the fund started in 2009 it was not traded much in the beginning, as could be expected for a new asset. All days for which the trading volume was zero were regarded as incomplete days. After deleting all days that had incomplete information, 1238 days are left to use in this paper which should provide enough statistical power. The table below provides some descriptive statistical information on the data sample. For each dataset the table reports the mean, the median, the 25th_{and 75}th_{percentile values and the}

standard deviation. Table 4: Data Summary.

Returns are expressed as percentages from the start of the fund. 4.1 Price Error

The graph below displays the price error over time. It can be easily seen that the average pricing error is small but not zero, as was expected by arbitrage theory given that transaction costs are not equal to zero. Furthermore from the table can be deducted that the mispricing is a discount for more than 50% of the time. The price error has a fairly large range, ranging from 1.3999% discount to a 2.2144% premium but note that most values are close to zero. By looking at the graph below and ignoring the first year from the start of the fund, it can be seen that the price error is apparent but not persistent.

Name Mean Median Percentile

Standard Deviation (%) 25% 75% 1 ETF Price (€) 35.33 34.75 32.89 37.96 3.67 2 ETF NAV (€) 353.22 347.40 328.43 379.56 36.70 3 ETF Return (%) 117.07 112.90 105.20 130.92 16.17 4 ETF Volume (€) 726910.30 411380.30 127143.60 839986.13 1239911.31 5 AEX Price (€) 351.00 344.87 326.78 378.12 37.11 6 AEX Return (%) 953.45 917.13 848.39 1071.76 137.56 7 AEX Volume (€) 1402947294.07 1311062315.97 1107580970.14 1590234779.74 517468989.18 8 Price Error (%) 0.0115 -0.0045 -0.0357 0.0290 0.1749

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13 The price error is often quite close to zero but, when a profitable arbitrage opportunity occurs (a peak in the graph) it is cleared the next day. One other observation from the graph is that the fund’s positive price errors, the premiums, are higher than the negative price errors, the discounts.

Figure 1: Time graph of the price error.

By looking at the graph, the high volatility in the first year can immediately be seen. Since the fund started in December 2009 it can be argued that the fund needed some start-up time.

This distortion is cleared by running two regressions, using the same independent and dependent variables. The first regression includes all data, the second regression excludes the first year to account for (some of) the start-up time.

4.2 Data computations

The data are not immediately ready to be used. The returns are calculated for each day and turned into absolute numbers since the illiquidity measure has to be a positive number. The same transformation concerning the absoluteness of the data is done for the price error, because this paper tries to determine the effect of liquidity on mispricing without making any conclusions about this mispricing being a premium or a discount. Therefore only absolute price errors are used in the regression.

-2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 14-12-09 14-02-10 14-04-10 14-06 -10 14-08-10 14-10-10 14-12-10 14-02-11 14-04-11 14-06-11 14-08-11 14-10-11 14-12-11 14-02-12 14-04 -12 14-06-12 14-08-12 14-10-12 14-12-12 14-02-13 14-04-13 14-06-13 14-08-13 14-10-13 14-12-13 14-02-14 14-04-14 14-06-14 14-08-14 14-10-14 14-12-14

Price Error (%)

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14 5. Results

The results for the robust regression are shown in the tables below for the AEX ETF with the t-statistics in parentheses below the estimates. The robust version is used since it is most likely that

heteroskedasticity and autocorrelation are apparent. Because the regression is done on two data groups the results are split up into two panels, panel A and panel B. Panel A represents the data including the first year from the start of the fund, so this includes all data (December 2009 – December 2014). Panel B represents the data excluding the first year from the start of the fund (December 2010 – December 2014), so this accounts for some start-up time and particular days that lead to extreme results (Flash Crash 6th_{of May 2010). The dependent variable (PE) is the funds absolute price error defined as the}

difference between the price of the fund and the NAV divided by the NAV. The independent variables include the illiquidity measure for the ETF (ILLIQETF), the illiquidity measure for the AEX (ILLIQAEX), the squared illiquidity measure for the ETF (ILLIQETF2), the squared illiquidity measure for the AEX

(ILLIQAEX) and a constant (_cons) is added. The asterisks *,**,*** indicate significance at a 10%, 5% and 1% level respectively.

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15 Table 5: Summary of results for panel A (December 2009 - December 2010).

PE is the funds absolute price error defined as the difference between the price of the fund and the NAV divided by the NAV, which is the dependent variable. The independent variables include ILLIQETF the illiquidity measure for the ETF, ILLIQAEX the illiquidity measure for the AEX, ILLIQETF2 the squared illiquidity measure for the ETF, ILLIQAEX2 the squared illiquidity measure for the AEX and a constant (_cons) is added. The numbers between parentheses are the t-statistics and *,**,*** indicate significance at a 10%, 5% and 1% level respectively.

In Panel A the illiquidity effect of the ETF is positive and highly significant in all regressions, this is a confirmation of what was found by previous research. There seems to be a negative relation between mispricing and liquidity. However since mispricing for this particular Dutch ETF is very small (average of 0.01%) it might not be profitable to exploit these arbitrage opportunities because of the existence of transaction costs (bid-ask spreads and commission fees) (Ackert, 2008 and Elton, 2010). When adding the squared terms in the regression, a negative and highly significant relation is found between squared illiquidity of the ETF and the price error. This shows that the relationship between liquidity and the price error might be U-shaped. The illiquidity measure for the index is also positive but insignificant.

Panel A: 12/2009-12/2014 (1) (2) (3) (4) ILLIQETF 16.638 (41.98)*** 16.616 (42.00)*** 89.647 (27.67)*** 89.647 (27.67)*** ILLIQAEX 304849.30 (1.61) 190609.20 (0.90) 190609.20 (0.90) ILLIQETF2 -1302.971 (-24.99)*** -1302.971 (-24.99)*** ILLIQAEX2 0 (omitted) _cons 0.034 (40.22)*** 0.033 (24.56)*** 0.032 (24.18)*** 0.032 (24.18)*** R2 _0.0099 _0.0110 _0.0208 _0.0208 F statistic 1762.17 882.54 345.59 345.59 n 1236 1236 1236 1236

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16 The squared illiquidity measure for the index is omitted because of collinearity, all other coefficients fully explain that variable so this effect is captured by the remaining variables. Also note that the coefficient results for the illiquidity measures of the index are much higher than the coefficient estimates for the illiquidity measures of the ETF. This is because of the higher trading volume for the index which results in a very small illiquidity measure.

The table below shows the results for the second regression, excluding the first year of data from the regression.

Table 6: Summary of results for Panel B (December 2010 – December 2014).

Again, PE is the funds absolute price error defined as the difference between the price of the fund and the NAV divided by the NAV, which is the dependent variable. The independent variables include ILLIQETF the illiquidity measure for the ETF, ILLIQAEX the illiquidity measure for the AEX, ILLIQETF2 the squared illiquidity measure for the ETF, ILLIQAEX2 the squared illiquidity measure for the AEX and a constant (_cons) is added. The numbers between parentheses are the t-statistics and *,**,*** indicate significance at a 10%, 5% and 1% level respectively.

Panel B: 12-2010/12-2014 (1) (2) (3) (4) ILLIQETF 118.611 (0.97) 95.251 (0.77) 249.736 (0.87) 249.736 (0.87) ILLIQAEX 281964.30 (1.56) 258233.60 (1.39) 258233.60 (1.39) ILLIQETF2 -2478233 (-0.57) -2478233 (-0.57) ILLIQAEX2 0 (omitted) _cons 0.032 (35.09)*** 0.030 (23.10)*** 0.030 (22.40)*** 0.030 (22.40)*** R2 _0.0007 _0.0022 _0.0025 _0.0025 F-statistic 0.94 1.71 1.28 1.28 n 1014 1014 1014 1014

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17 When the first year of the fund was excluded from the data all of the coefficient estimates became insignificant. The normal illiquidity measure for the ETF became insignificant for all cases, whereas it first was highly significant in all of the cases. The relationship between illiquidity and the price error still remained the same, all estimates still have a positive effect. The squared illiquidity measure becomes insignificant as well, but the sign of the coefficient remains positive. So the results suggest an

insignificant, inversely U-shaped relation. Whenthe first year of the dataset was excluded from the sample, the results for the illiquidity measure of the AEX were still insignificant. There was, however, no change in the sign of the estimated coefficients for the illiquidity measure of the AEX. And consequently the squared illiquidity measure for the AEX was omitted due to collinearity.

In summary, a significant relation was found between the price error and the liquidity, which constitutes a negative relationship. This is in line with the results of prior research and the hypothesis (Amihud, 2002, Petajisto, 2013 and Marshall, 2008). A significant result was also found for the squared term for the ETF, however all estimates became insignificant when the first year was omitted from the

regression.

A significant relationship between the price error and the squared liquidity measure was found and the results suggest that there might be a U-shaped relationship. This is in line with prior research from Ackert and Tian (2008) that the relation might be non-linear. However these results became insignificant in the second regression. This means it is impossible to draw a conclusion whether this relationship is linear or non-linear. The price error was also found to be really small, which was again in line with prior research (Ackert, 2000, Elton, 2002, Delcoure, 2007 and Petajisto, 2013) and expectations according to Efficient Market Theory.

6. Conclusion and concluding remarks

This paper reports the results of a research trying to examine the effects of liquidity on ETF mispricing, using the Dutch AEX ETF. According to efficient market theory and earlier research, there should be no price error if there are no limits on arbitrage. The financial markets are unfortunately not efficient and thus transaction costs are apparent. But because of the creation and redemption mechanism in the ETF market, arbitrage opportunities can be exploited very easily if these price errors turn profitable. This means that the price error should be fairly small because of this mechanism.

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18 This expectation was also confirmed for the Dutch ETF used in this research. The average price error was only 1 basis point, fluctuating between about a 140 basis point discount and a 220 basis point premium. Although the range is quite big, these numbers include extremes. Furthermore these extremes mostly occurred in the first year of the start of the fund, which could be assigned to the start-up time of the fund. The majority of the price errors however was close to zero. The results reported in this paper show a highly significant negative relationship between the price error and the liquidity of the ETF. This is in line with results of prior research and the Efficient Market Theory. After Ackert (2008) squared terms were added to the regression to account for a possible non-linear relationship between price and liquidity. Interestingly these estimated coefficients are significant, indicating that the relation may be non-linear. These estimated results are ambiguous meaning that in the first regression the results were significant and in the second regression the results were insignificant. An explanation for the ambiguous results might be the fairly simple liquidity measure that was used in this research. Another explanation could be the selection of the fund. Most research was done an US ETFs, the Dutch ETFs are quite new and don’t have many years of data available. This is why daily data was used, to have big enough of a sample. Keep in mind that the sample was cleared of all days for which data was missing before using it. Incomplete days were deleted from the sample because these days could not be used in the regression due to missing numbers or non-allowable calculations (dividing by zero).

Further research might examine the effects of liquidity including finer liquidity measures using somewhat finer, microstructure data. Another suggestion for further research might be to investigate this possible non-linear relation between price error and liquidity as what was found by Ackert (2008) as well. Further research might also examine the effects of portfolio composition on mispricing, as these effects might be apparent (Fassas, 2014). Maybe later on in the future, when the Dutch ETFs are more established and have more years of data available, research can be done using monthly data. In this way the deletion of data should not be needed and the sample would remain complete.

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19

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20 Petajisto, A. (2013) ‘Inefficiencies in the Pricing of Exchange-Traded Funds’ (Working Paper No.

The Dutch Exchange-Traded Fund : the effects of liquidity on Exchange-Traded Fund’s mispricing