An enquiry into the Dutch exchange traded-fund landscape : tracking error and pricing efficiency

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An enquiry into the Dutch exchange

traded-fund landscape: Tracking error and pricing

efficiency

EMMET KING

February 2016

Abstract

This study examines the tracking errors and pricing efficiency of the ETFs that track the

main Dutch stock exchange, the AEX. By using several different methods, it finds that all 3

funds experience a small, yet statistically significant, tracking error. In addition, it finds

that the fund that is most efficient in terms of tracking error, commands a premium in

price, while the least efficient commands a discount. Only one of the funds is priced

efficiently over the time period considered.

Keywords: ETFs, Tracking Error, Pricing Efficiency

JEL Classification: G12, G14

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Statement of originality:

This document was written by Emmet King, who hereby take full responsibility for its contents. I declare that all text and work presented in this document are original and all sources that have been used are referenced.

The Faculty of Economics and Business is responsible only for the supervision in the creation of this document. The responsibility of the content falls solely on Emmet King.

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List of Tables and List of Figures:

Table 1 Directional influence of operational characteristics on the tracking error ... 9

Table 2 Summery statistics funds’ NAV ... 12

Table 3 Summery statistics funds’ discount/premium ... 13

Table 4 Operational characteristics ... 13

Table 5 Funds operational characteristics rank hypothesis ... 14

Table 6 Jarque-Bera results tracking error... 15

Table 7 Tracking error definition 1 (TE1) results... 15

Table 8 Tracking error regression results ... 16

Table 9 Tracking error regression results with robust standard errors ... 16

Table 10 Test results for regression coefficients ... 17

Table 11 Standard Errors of Regression ... 17

Table 12 Funds’ tracking error ranking results ... 18

Table 13 Jarque-Bera results pricing efficiency ... 18

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Chapter 1 Introduction

A passive investing strategy is becoming increasingly popular. Evidence of this is the growth of Exchange-Traded Funds (ETFs) over the last two decades. After being introduced in 1993, the market for this type of security has been growing strongly. In 2002 there were roughly 100 different ETFs, while in 2015, it’s over 2000 (Morningstar, 2015). At 2014’s end, the ETF markets accounted for more than $2 trillion in assets worldwide. (Madhavan, 2014)

ETFs display characteristics of both open-ended and closed-ended mutual funds. They are securities which are traded on a stock market that derive their value from a pre-defined portfolio of securities (Gallagher & Segara, 2006). Hence, as with closed-ended mutual funds, they can display departures in price from their Net Asset Value (NAV). Previous research has shown the existence of this, known as pricing inefficiency, in different ETF markets such as the US (Elton et al. , 2004), Europe (Blitz et al. , 2012), and Hong Kong (Kuok Kun Chu, 2001).

Whereas open-ended funds shares can be redeemed for their NAV, a specific amount of ETF shares can also be exchanged for either their NAV or the underlying portfolio of stocks it consists of, depending on the specific ETF. This raises the question why any significant deviations are not eliminated by the workings of the market.

Originally, ETFs were designed as being so called “Trackers”. Their purpose was to mimic the returns of a specific exchange. Now, a plethora of types of ETFs exist, which track the returns of specific sectors (e.g. tech, pharmaceutical, etc.), commodities, and different types of derivatives.

Tracking error is defined by Charupat and Miu (2012) as the differences between the funds’ NAV returns and the returns of the underlying indices that the funds tracks. It is a measure of how well a fund is performing its investment objective. The Dutch stock market, AEX, currently has 3 different ETFs tracking it. Although the funds are similar in composition, they differ in factors such as size, frequency of rebalancing, and frequency of dividend payout (funds’ prospectus, retrieved from

www.blackrock.com; www.Ithinketfs.nl; www.ssga.com, date consulted: 26/01/2016). The question then arises whether there are differences in their efficiency in mimicking the returns of the AEX, e.g. their tracking error.

There has been no previous research done into pricing efficiency and the presence of tracking error geared towards the Dutch market. This is of interest due to the similarity of composition, yet the differences in operational characteristics. Hence, the trackers of the main Dutch stock exchange, the AEX, lend themselves for analysis into the influence the differences in operational characteristics on tracking error. In addition, it is of interest to see if the efficiency of these tracker ETFs, e.g. the tracking error, is included in the pricing of a fund. In other words, will the fund with the lowest tracking error command a premium?

1.1. Objectives

The main objective of this study is to investigate the landscape of the different ETFs that track the AEX. This will be done by firstly comparing the tracking errors found by using several different methods of the three different ETFs. Secondly, we will look at the pricing efficiency of the ETFs tracking the AEX. This is done in order to investigate whether the price at which an ETF is bought and sold in the secondary market is consistent with the value of the underlying portfolio. In effect, we look at whether the AEX ETFs are sold at a discount or at a premium. Finally, by looking at the different fund prospectus, we will look at the factors in which the funds differ. This in order to see if the different funds’ rank in terms of tracking error are consistent with what the literature would predict based on

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differences in their operational characteristics. Also, we investigate whether the relative rank of a fund in terms of tracking error corresponds with their relative rank in pricing efficiency.

1.2. Organization

This paper is organized as follows. The next chapter provides literature study. First we will delve into some background information on ETFs, after which we will discuss the concepts of tracking error and pricing efficiency, and what previous research has stated about these. Chapter 3 will discuss the methodology how to we will calculate the pricing efficiency and tracking error of the different ETF trackers. Chapter 4 will contain information about the data we will use, where we retrieved it from, and what manipulation were needed. In chapter 5 we will present the results of our research. Finally in chapter 6 we will present our conclusions, the limitations of our study, and suggestions for further research.

Chapter 2 Literature Review

2.1. Background information

ETFs are similar to mutual funds. However, they command certain advantages over mutual funds, which are outlined by Poterba and Shoven (2002) and Miffre (2007). They include intraday trading as opposed to open-ended funds only being able to trade after NAV is determined after trading closes.

In relative terms, ETFs are more tax efficient than mutual funds. Partially due to the fact when an investor redeems shares, instead of incurring capital gains as is the case in mutual funds, the ETF can redeem the shares “in-kind” (more on this below). By redeeming in this manner, no sales are made, and hence no capital gain is incurred.

ETFs are also more transparent in terms of costs and holdings. After trading closes at days’ end, the fund publishes its holdings together with the NAV of the fund. In addition, the costs charged for running an ETF, called the expense ratio, are much lower than that of a conventional mutual fund. Also, contrary to mutual funds, ETFs generally do not have other costs associated with them. Mutual funds often charge both a front-end and back-end load. These are percentage charges on the total amount of assets invested into the fund. For example, a front-end load of 2% would mean that of say €1000, - paid to the fund, only €980, - would be actually invested. A back-end load of 3% for example would mean that if one would want to redraw funds of say €1000, - out of a mutual fund, the investor would end up only receiving €970, -. An ETF does not have such costs associated with it.

The creation/redemption process of ETFs is a hybrid of the two types of mutual funds. Institutional traders (also called Authorized Participants, APs) can purchase (or sell) blocks of ETF shares, called creation units, from (or to) the ETF issuer at NAV, much like an open-ended mutual fund. Commonly, this is done “in-kind” meaning that the AP deposits (or redraws) a portfolio of shares in which the fund holds its positions for a block of shares (or the underlying pre-defined portfolio) plus a cash fee. This is the primary market of ETFs. However, they are also traded continuously throughout the day on a stock exchange, this is the secondary market. This is contrary to open-ended mutual funds, which can only be traded after NAV is determined after days’ close. Hence, as touched upon in the introduction, there is a possibility for the price at which an ETF is traded to depart from the value of the underlying portfolio.

The primary market allows the ETF issuer to create a balance between the supply and the demand for the ETF. This is done by allowing the amount of shares available to increase when there is

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a higher demand. The secondary market ensures liquidity for investors. There, a single ETF share can be traded, as opposed to complete creation blocks which can amount from 50,000 up to 100,00 ETF shares (Gallagher & Segara, 2006).

Due to having both a primary and a secondary market, an ETF share derives its value from two different sources. The first being the NAV of the pre-defined portfolio of underlying securities which make up the ETF. The second being the price at which it is traded on the stock market. The possibility of being able to create/redeem ETFs should create bounds for the price of the ETF relative to the NAV, ensuring a degree of pricing efficiency. For example: If the price of an ETF is much lower than the value of the underlying shares in the portfolio, an AP would buy a number ETF shares in the secondary market (enough to create a creation block), and redeem it for the underlying shares at the ETF issuer in the primary market. In practice, the ETF issuer can minimize this from happening by regulating the amount of ETF shares available.

2.2 Pricing efficiency

Despite the above mentioned mechanisms, previous research has shown a statistically significant lack of pricing efficiency. Pricing efficiency can be seen as a measure of how close the market price of an ETF share is to the funds’ NAV. Generally, it is researched by looking at whether the price that an ETF is trading at, on average, commands a premium or a discount, relative to its NAV (Charupat & Miu, 2013).

Petajisto (2013) finds that the prices of ETFs can deviate from their NAV significantly. He states that, on average, prices can fluctuate within a band of 260 basis points despite the above mentioned arbitrage mechanisms. Ackert and Tian (2000), however, find that ETFs that track specific indices experience more pricing efficiency. They find that trackers of the S&P 500, on average, do not trade at a significant discount or premium. They do, however, report higher deviations for the MidCap 400 trackers, which they attribute to the higher costs of arbitrage.

2.3 Tracking error

Tracking error is defined by Charupat and Miu (2012) as the difference between the funds’ NAV returns and the returns of the underlying indices that the funds track. Due to the objective of these ETFs being to replicate the returns of the AEX, it can be seen as a measure of its performance in achieving its investment objectives.

Pope and Yadav (1994) list 3 different ways of measuring the tracking error. The first one being the average of the absolute difference in returns between the ETFs NAV returns and the benchmark index returns:

𝑇𝐸1=ē𝑖,𝑡=

∑𝑡=1 𝑛 ⃓ 𝑒𝑖,𝑡 ⃓

𝑛 Where 𝑒𝑖,𝑡 = 𝑅𝐸𝑇𝐹𝑖,𝑡− 𝑅𝐴𝐸𝑋,𝑡 and n is the number of periods.

In the situation of tracking error of tracker ETFs, the benchmark index would be the returns of the index the ETF is tracking.

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The second definition of tracking error given is the standard deviation of the return differences between the ETFs NAV and the benchmark index:

𝑇𝐸2= √ 1 𝑛 − 1 ∑ 𝑡=1 𝑛 (𝑒𝑖,𝑡−ē𝑖,𝑡)2

Where ē_𝑖,𝑡 is the average of the absolute difference in returns between the ETFs NAV returns and the benchmark index returns, 𝑒𝑖,𝑡 = 𝑅𝐸𝑇𝐹𝑖,𝑡− 𝑅𝐴𝐸𝑋,𝑡, and n the number of periods.

Kuak-Kun Chu (2011) argues that this second definition would not be appropriate with the use of daily data. This is due to the daily returns most probably being serially correlated. In addition, he points out that if the ETF consistently under- or overperforms the index it is tracking by the same amount, such as the expense ratio charged daily, this definition would yield a tracking error of zero.

The final definition of tracking error given by Pope and Yadav (1994) is given by the standard error of the regression (SER) in the estimation of the Capital Asset Pricing Model (CAPM):

𝑅𝐸𝑇𝐹𝑖,𝑡 = 𝛼 + 𝛽 ∗ 𝑅𝐴𝐸𝑋,𝑡+ 𝑒𝑡 𝑇𝐸3= 𝑆𝐸𝑅 = √ 𝑆𝑆𝐸 𝑛 − 2= √ ∑ _𝑡=1𝑛 (𝑅𝐸𝑇𝐹𝑖,𝑡− 𝑅ˆ𝐸𝑇𝐹𝑖,𝑡)2 𝑛 − 2

Where 𝑆𝑆𝐸 is the sum of squared errors, 𝑅𝐸𝑇𝐹𝑖,𝑡 is the return on the ETF for a given date, 𝑅ˆ𝐸𝑇𝐹𝑖,𝑡 the

predicted return on the ETF for a given date, and n the number of periods.

They do, however, point out a problem with this measure. If the beta in the regression is not equal to 1, the resulting tracking error would be different from the previous two definitions. In the case where we are investigating the tracking error of tracker ETFs, a beta that is significantly different from 1 could imply that the ETF is not meeting its investment objective of replicating the returns of the index it is tracking.

Cresson et al. (2002) expand the third definition of tracking error given by Pope and Yadav (1994) by also examining the resulting R2_{of the regression.}

𝑅2₌𝑆𝑆𝑅

𝑆𝑆𝑇

Where SSR is the sum of squared errors, and SST the total sum of squares.

They argue that it can be seen as a measure of fit of the returns of the tracking and the benchmark. A higher measure of fit, or equivalently, a high R2_{, would mean that the returns are similar,} and the tracker is therefore mimicking the returns of the index to a higher degree.

Charaput and Miu (2013) outline several factors that influence the tracking error, and therefore the performance, of an ETF. Firstly, the management fees or expense ratio, which are the costs of managing the ETF by the funds’ issuers. Typically, they are charged on daily bases using

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annualized rates. An ETF with a higher expense ratio, ceteris paribus, will experience a higher tracking error. Secondly, Charaput and Miu (2013) point toward the transaction costs of the fund buying and selling the assets under management. Hence, funds that rebalance their portfolio more often, will incur transaction costs more frequently. The more frequently transaction costs are incurred, the higher transaction costs will be for the fund. Higher transaction costs will then evidently lead to a higher tracking error.

Finally, Charaput and Miu (2013) mention dividends and cash holdings of the fund. Dividends from the securities held in the fund can accumulate before they are distributed to the shareholders of the ETF. A delay in the reinvestment of dividends received can result in a higher tracking error. Hence, funds that payout dividend more frequently should experience a lower tracking error relative to those who payout less frequently.

In addition, Grinblatt and Titman (1989) argue that fund size has a negative relation with tracking error. While they argue that this could be due to lower transaction costs incurred due to the economies of scales of larger funds, they also admit that this could be due to sampling error.

As stated, the investment objective of trackers is to replicate the returns of the indices they are trying to mimic. An ETF has a choice in the way it attempts to replicate the returns. This involves a trade-off between tracking error and the performance, e.g. how well the ETF replicates the indices returns (Charupat & Miu, 2013). To minimize its tracking error, a funds’ portfolio would have to be a weighted-average of the market capitalization of all securities contained in the index it is tracking. However, this exact-replication strategy has some disadvantages associated with it. Some securities may have to be held in small proportions, making it administratively inconvenient. Changes in the composition of the underlying index call for rebalancing of the funds’ portfolio to reflect the new weighted-averages (Beasley, Meade, & Change, 2003). Consequently, more rebalancing leads to the fund incurring more transaction costs. In light of this, many ETFs choose to implement an imperfect replication strategy in order to lower transaction costs, but thereby incurring a higher tracking error. The way this imperfect replication strategy is created is beyond the scope of this research, but what’s important is that the fund uses only a few of the securities listed on the index it is mimicking in order to replicate its returns.

Below, the direction of the effect on the tracking error of each operational characteristic is summarized:

Table 1 Directional influence of operational characteristics on the tracking error

Operational characteristic Direction of influence on tracking error

Expense ratio Positive

Size of fund Negative

Frequency of rebalancing Positive Frequency of dividend payment Positive

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Chapter 3 Methodology

3.1 Methodology: Tracking error

In order to determine the tracking error of each ETF, we will use two of the tracking error definitions by Pope and Yadav (1994). Namely, the absolute difference in daily returns between the ETFs’ NAV and the benchmark index. Or, in our case, the absolute difference in daily returns between a ETFs’ NAV and the AEXs daily returns:

𝑇𝐸1=

∑𝑡=1 𝑛 ⃓ 𝑒𝑖,𝑡 ⃓

𝑛

Secondly, we use the Standard Error of Regression (SER) in the Capital Asset Pricing Model (CAPM). The dependent variable in the regression will be the daily returns of the AEX. The independent variable will be the daily returns of the NAV of the ETF.

𝑅𝐸𝑇𝐹𝑖,𝑡 = 𝛼 + 𝛽 ∗ 𝑅𝐴𝐸𝑋,𝑡+ 𝑒𝑡

The β in this regression should be equal to 1, because the ETF is mimicking the AEX. If this is statistically significantly different from 1, then the ETF is failing in its investment objective. Secondly, the α should be equal to zero if there is no tracking error. Hence, we can express our null hypotheses as follows:

𝐻0: 𝛽 = 1 𝑣𝑠 𝐻1: 𝛽 ≠ 1

𝐻0: 𝛼 = 0 𝑣𝑠 𝐻1: 𝛼 ≠ 0

However, as described in the literary study, there are several factors which can influence the performance of an ETF. These factors can have a negative effect on the tracking error, therefore causing the alpha to be nonzero and most probably negative. The SER is a representation of the average deviation from the regression line. The smaller the SER for a specific ETF is, the better it mimics the returns of the index it is tracking:

𝑆𝐸𝑅 = √𝑆𝑆𝐸 𝑛 − 2= √

∑ _𝑡=1𝑛 (𝑅𝐸𝑇𝐹𝑖,𝑡− 𝑅ˆ𝐸𝑇𝐹𝑖,𝑡)2

𝑛 − 2

Finally, following Cresson et al. (2002), we will also compare the resulting R2 _{of the regressions of the} different ETFs as a measure of tracking error.

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3.2 Methodology: Pricing Efficiency

The concepts tracking error and mispricing are often used interchangeably while they are essentially very different. Pricing efficiency or mispricing will be calculated in the same way as has been done in former research by Jares and Laving (2004):

To determine whether an ETF share is being priced efficiently, e.g. if the price at which the share is being traded at reflects its true underlying value, we compare its NAV with the price of the ETF at which it is being traded on in the market. The NAV reflects the ETFs per share value that is derived from the underlying pre-defined portfolio. Due to the NAV only being published daily after trading closes, we use the daily close price of the ETF share to compare it with. If, for example, the value of the portfolio of shares an ETF is made up of is higher than the actual closing price of the ETF share, we say the share is trading at a discount. While if the value is lower than the closing price of the share, it is trading at a premium. In order to determine the discounts/premium.

% 𝑑𝑖𝑠𝑐𝑜𝑢𝑛𝑡 = (𝑁𝐴𝑉𝑡− 𝐸𝑇𝐹𝑡) 𝑁𝐴𝑉𝑡

x 100%

Where NAV is the Net Asset Value for each fund, and ETF is the quoted daily price for each fund. A negative value of % discount will indicate that the ETF share is trading at a premium relative to its NAV. Next, we will calculate the descriptive statistics for each individual fund. These will include the mean, minimum, maximum, and standard deviation.

Next, in order to be able to apply a statistical test to see whether there is a significant pricing deviation, we will need to determine whether the data is normally distributed. To do so, we use the Jarque-Bera test. If the skewess is equal to 0, and kurtoses to 3, then we can assume the data as being normally distributed. After that, we can run a student t-test to determine whether the mean is significantly different from 0. In other words, we test whether there is a significant discount (mean >0) or premium (mean<0). This is done by testing the following hypotheses:

𝐻0: 𝜇𝑖 = 0 𝑣𝑠 𝐻1: 𝜇𝑖 ≠ 0

Where 𝜇𝑖 is the average premium/discount for an ETF.

If this null hypothesis is rejected, it would be of further interest to test whether there is a statistically significant discount or premium. Hence, we will follow up by conducting a second test involving a one-tailed test on the μ’s. The second hypothesis can be stated one of the below, depending on whether we find a negative or positive μ:

𝐻0: 𝜇𝑖 = 0 𝑣𝑠 𝐻1: 𝜇𝑖 ≻ 0

𝐻0: 𝜇𝑖 = 0 𝑣𝑠 𝐻1: 𝜇𝑖 ≺ 0

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Chapter 4 Data

As stated in the introduction, there are currently 3 different ETFs that track the AEX. Namely: iThink AEX UCITS ETF (ticker: TDT.AS), SPDR AEX UCITS ETF (ticker: AEXT.AS), and iShares AEX UCITS ETF (ticker: IAEX.AS). Of these 3, iThink is relatively the youngest, being created on 14/12/2009. In order to have a statistically representative view, we will investigate a time period of 6 years. Starting from the date of creation of the last ETF, 14/12/2009, until 14/12/2015. Due to the funds’ NAV being published on a daily basis, this is the shortest time interval we can use.

In order to calculate the tracking errors of the funds, we first retrieve data for the AEX index from DataStream (date consulted: 22/12/2015). Next, we consult the different fund issuer websites in order to retrieve their daily NAVs (www.blackrock.com; www.Ithinketfs.nl; www.ssga.com date consulted: 26/01/2016). There, we find a .CSV file with NAV published for each individual ETF. However, some days an NAV is quoted, but the AEX is not, and other days the AEX is quoted but the NAV is not. Therefore, we need to remove the data points for which we don’t have both the ETFs’ NAV and the AEX price. These differ among the three funds, hence, we end up with 3 different AEX returns. In order to calculate their tracking errors, we require daily mutations instead of nominal price amounts. Therefore, we transform the data into percentage change per day, or daily return. The following table shows the summary statistics for each fund:

Table 2 Summery statistics funds’ NAV

(1) (2) (3) (4) (5) VARIABLES Amount of observations Mean Standard deviation Minimum observation Maximum observation

R_NAV_AEXT

1,459

0.000292

0.0117

-0.0524

0.0730

R_NAV_TDT

1,531

0.000252

0.0113

-0.0519

0.0728

R_NAV_IAEX

1,509

0.000254

0.0115

-0.0524

0.0737

Where, R_NAV_AEXT is the daily return on the NAV of the SPDR ETF (ticker: AEXT.AS), where R_NAV_TDT is the daily return on the NAV of the iThink ETF (Ticker: TDT.AS), and where R_NAV_IAEX is the daily return on the NAV of the iShares ETF (Ticker: IAEX.AS).

For the pricing efficiency of the funds, we retrieve their daily prices from DataStream (date consulted: 22/12/2015). Here, we look at the nominal prices. However, as was the case with the data for tracking error, there are mismatches of dates between quoted prices and published NAV. Again, we remove data points for which we don’t have both the ETFs’ price quotation and the ETFs’ NAV. We then can calculate the discount or premium and the descriptive statistics needed. The following table shows the summary statistics of the discount/premium for each fund:

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Table 3 Summery statistics funds’ discount/premium

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VARIABLES Amount of observations Mean Standard deviation Minimum observation Maximum observation

Discount_SPDR

1,523

0.000127

0.000920

-0.00883

0.0106

Discount_iThink

1,539

-0.000114

0.00185

-0.0221

0.0157

Discount_iShares

1,552

-6.51e-06

0.00112

-0.0164

0.0107

Where Discount_SPDR is the discount caclulated for the ETF SPDR(ticker:AEXT.AS), where Discount_iThink is the discount calculated for the ETF iThink (ticker:TDT.AS ), and where discount iShares is the discount calculated for the ETF iShares (ticker: IAEX.AS).

In order to compare the results, we again consult the different ETF issuer websites in order to retrieve the prospectus and investor information. Using these, we look at the size of the different funds (assets under management), the expense ratio they charge, the frequency at which they rebalance their portfolio, and the frequency at which they distribute dividends. These will be presented together with the tracking errors found and pricing efficiency in order to see if the hypothesized results are consistent with the effect of these factors described in the literary study. A table is presented below summarizing these operational characteristics:

Table 4 Operational characteristics

Fund Ticker: Size (€mln) Expense ratio (%) Rebalancing frequency (yearly) Dividend frequency (yearly) Ithink AEX UCITS

ETF TDT.AS 135.81 0.3 4 4 SPDR AEX UCITS ETF AEXT.AS 47.77 0.3 4 1 iShares AEX

UCITS ETF IAEX.AS

398.58 0.3 1 4

Where, size is assets under management in millions, and the expense ratio is the daily costs of running the fund.

We find that the funds all charge an identical expense ratio. As stated in the literature study, expense ratios have a negative effect on the tracking error. However, due to all funds experiencing the same negative effect, these will not influence the relative ranking of the tracking error of the different funds. Hence, these will not be explored further in this study.

Using the above operational characteristics, combined with the table summarizing the directional effect of said characteristics, we can formulate a hypothesis of the ranking for each characteristic, and therefore a ranking for tracking error.

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Table 5 Funds operational characteristics rank hypothesis

Fund Size Rebalancing

frequency

Dividend frequency

Sum ranks Final rank Ithink (ticker:TDT.AS) 2 2 1 5 2 SPDR (ticker:AEXT.AS) 3 2 2 7 3 Ishares (ticker: IAEXT.AS) 1 1 1 3 1

Shows the rank of each fund for all operational characteristic under consideration, the sum of this ranks, and the final rank.

Hence, we would hypothesize that IAEX experiences the lowest tracking error, followed by TDT, while AEXT experiences the highest one.

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Chapter 5 Results

5.1 Tracking error results

After having calculated the first definition of tracking error (TE1) in excel, and having calculated the daily returns on each fund and its corresponding AEX price quotations, we need to check the distribution of the data.

In order to determine whether the data follows a normal distribution, we perform a Jarque-Bera test. The idea behind this test is that if the data has a skewness equal to zero, and kurtoises equal to 3, it can be said to be normally distributed. The Jarque-Bera test calculates the probability of this being the case. The corresponding hypothesis is:

𝐻0: (𝑛𝑜𝑟𝑚𝑎𝑙𝑖𝑡𝑦) 𝑡𝑟𝑢𝑒 𝑣𝑠 𝐻1: (𝑛𝑜𝑟𝑚𝑎𝑙𝑖𝑡𝑦) 𝑢𝑛𝑡𝑟𝑢𝑒

Below we present the results of the Jarque-Bera test:

Table 6 Jarque-Bera results tracking error

(1) (2) VARIABLES Jarque-Bera statistic P-value R_NAV_AEXT 13.113 0.001 R_AEX1 2.18 0.336 R_NAV_TDT R_AEX2 1.843 8.804 0.398 0.012 R_NAV_IAEX R_AEX3 6.243 2.839 0.044 0.242

Jarque-Bera statistic for the NAV returns for each fund and the corresponding return on the AEX, and the corresponding P-values of their test statistic.

We fail to reject the null hypothesis for all variables except the returns on the NAV of the SPDR ETF (ticker: AEXT.AS). However, due to the large number of observations (more than 1450) in combination with the Central Limit Theorem, we nonetheless will assume the data as being approximately normally distributed and continue by conducting parametric rather than non-parametric tests.

The values of the first definition (TE1) of tracking error by Pope and Yadav (1994), the absolute difference in daily returns between a ETFs and the AEXs daily returns, are as follows:

Table 7 Tracking error definition 1 (TE1) results

Fund: SPDR (ticker:AEXT.AS) iThink (ticker:TDT.AS) iShares (ticker: IAEX.AS)

TE1: 0.00127 0.00115 0.00128

Where TE1 is the average absolute difference in daily returns between a ETFs’ NAV and the AEXs daily returns.

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We find that the iThink ETF (ticker: TDT.AS) has the lowest tracking error when using this definition. The difference between the other ETFs, iShares (ticker: IAEX.AS) and SPDR (ticker: AEXT.AS), is small.

Next, we look at the results from our regression of the daily returns on the NAV of the ETF on the daily returns on the AEX. In order to see if the data suffers from heteroskedasticity, we run the regression twice, once with normal, and once with robust standard errors.

Table 8 Tracking error regression results

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VARIABLES R_NAV_AEXT R_NAV_AEXT R_NAV_IAEX

R_AEX1 1.043*** (0.00566) R_AEX2 1.032*** (0.00420) R_AEX3 1.041*** (0.00496)

Constant 7.19e-05 2.56e-05 8.44e-05

(6.23e-05) (4.55e-05) (5.38e-05)

Observations 1,459 1,531 1,509

R-squared 0.959 0.975 0.967

Standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1

Where R_NAV_ are the daily returns on the NAV of the funds, and R_AEX are the daily returns on the corresponding price quotations from the AEX. The test examines whether the coefficients are unequal to zero.

Table 9 Tracking error regression results with robust standard errors

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VARIABLES R_NAV_AEXT R_NAV_TDT R_NAV_IAEX

R_AEX1 1.043*** (0.00582) R_AEX2 1.032*** (0.00515) R_AEX3 1.041*** (0.00622)

Constant 7.19e-05 2.56e-05 8.44e-05

(6.26e-05) (4.55e-05) (5.39e-05)

Observations 1,459 1,531 1,509

R-squared 0.959 0.975 0.967

Robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1

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Where R_NAV_ are the daily returns on the NAV of the funds, and R_AEX are the daily returns on the corresponding price quotations from the AEX. The test examines whether the coefficiencts are unequal to zero, using robust standard errors.

We find that the robust standard errors are slightly different from the non-robust standard errors. Hence, we conclude that the data is heteroskedastic, and therefore we will continue using the results from the regression with the robust standard errors to correct for this.

The results of testing the hypotheses of the β’s being equal to 1, and the α’s being equal to zero, using robust standard errors, are as follows.

Table 10 Test results for regression coefficients

Fund β t-statistic 1 α t-statistic 2

SPDR (ticker:AEXT.AS) 1.043 (0.0058) 7.388*** 0.000072 (0.000063) 1.149 iThink (ticker:TDT.AS) 1.032 (0.0052) 6.185*** 0.000026 (0.000046) 0.563 iShares (ticker: IAEX.AS) 1.041

(0.0062)

6.546*** 0.000084

(0.000054)

1.566 Where t-statistic 1 tests if β equals 1, and t-static 2 tests if α equals 0.

Contrary to what was expected, we find high t-statistics for the tests on β, meaning that we reject the hypothesis of β being equal to 1. In addition, we find low t-statistics for the tests on α, meaning that there is not enough statistical evidence to infer that α is statistically different to zero.

The higher than 1 β’s can be interpreted as the daily returns on the ETFs’ NAV actually “exaggerating” the daily returns of the AEX itself. If the AEX makes a positive return on a given day, the ETF will, on average, make a more positive return. Conversely, if the AEX makes a negative return on a given day, the ETF will, on average, make a more negative return.

The remaining measures for tracking error are the SER and the R2_{. These are summarized in} the following table:

Table 11 Standard Errors of Regression

Fund Root-MSE SER R2

SPDR (ticker:AEXT.AS) 0.00238 5.6644E-06 0.959 Ithink (ticker:TDT.AS) 0.00178 3.1684E-06 0.975 Ishares (ticker: IAEX.AS) 0.00209 4.3681E-06 0.967

Where Root-MSE is the root Mean-Squares Error, SER is the Standard Error of the Regression of the daily returns on the NAV of the ETF on the daily returns on the AEX, and R2_{the ratio of explained to} total variation of said regression.

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Recall that the SER is a representation of the average deviation from the regression line. The smaller the SER for a specific ETF is, the better it mimics the returns of the index it is tracking, and therefore the lower the tracking error of that ETF is. We see that TDT experiences the lowest tracking error over the period considered, next the IAEX, and finally the AEXT. In addition, we see that the R2_, which can be seen as a measure of fit of the returns of the tracking and the benchmark, is consistent with the SER in its ranking. Recall that a higher R2_{indicates a better fit, and hence a lower tracking} error. The ranking here would be TDT highest, next IAEX, and finally AEXT.

Summarizing the ranking of all the measures of tracking errors over the period considered of the different funds gives us the following table:

Table 12 Funds’ tracking error ranking results

Fund TE1 β SER R2 Sum ranks Final rank

TDT 1 1 1 1 4 1

AEXT 2 3 3 3 11 3

IAEX 3 2 2 2 9 2

We see that the iThink ETF (ticker: TDT.AS) ranks best on all measures of tracking error. Hence, we can infer that the iThink ETF experiences the lowest tracking error over the time period considered. The SPDR ETF (ticker: AEXT.AS) ranks lowest in all measures except the first. Hence, we see a discrepancy in the rankings of the first measure of tracking error (TE1) compared to the other measures. As pointed out by Pope and Yadav (1994), if the regression β is not equal to 1, the measures of TE1 and TE2 will be different from those of the SER and R2_.

5.2 Pricing efficiency results:

Again, we start by determining whether the data follows a normal distribution. Using the Jarque-Bera test, we test the following hypothesis:

𝐻0: (𝑛𝑜𝑟𝑚𝑎𝑙𝑖𝑡𝑦) 𝑡𝑟𝑢𝑒 𝑣𝑠 𝐻1: (𝑛𝑜𝑟𝑚𝑎𝑙𝑖𝑡𝑦) 𝑢𝑛𝑡𝑟𝑢𝑒

The results are as follows:

Table 13 Jarque-Bera results pricing efficiency

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VARIABLES

Jarque-Bera

statistic

P-value

Discount_SPDR

81210.02

0 Discount_iThink

Discount_iShares

116817.8

491123

0

Jarque-Bera statistic for the discount calculated for each fund and the corresponding P-values of their test statistic.

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We reject the null hypothesis for all three discounts, meaning that normality is not satisfied. However, due to the large number of observations (more than 1450) in combination with the Central Limit Theorem, we nonetheless will assume the data as being approximately normally distributed and continue by conducting parametric rather than non-parametric tests.

Next, we conduct a student t-test on the discount/premium means, μ, in order to determine if they are significantly different from 0. To do so, we first test the hypothesis of μ being equal to zero.

Table 14 Pricing efficiency t-test results

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VARIABLES Mean Standard

Error T-statistic P-value (2-sided) P-value (1-sided)

Discount_SPDR

0.000127 0.000024 5.3883 0.0000 0.0000

Discount_iThink

-0.000112 0.000048 -2.4193 0.0157 0.0078

Discount_iShares

-0.000003 0.000029 -0.2289 0.8190

-Test results for each fund testing if the average discount/premium (𝜇) is equal to zero (2-sided) and if there is an average discount or premium (1-sided)

For the ETF SPDR (ticker: AEXT.AS) we find a t-value of 5.3883 and a corresponding P-value of zero. This means that we must reject the null hypothesis that 𝜇𝑆𝑃𝐷𝑅 is equal to 0. Hence, we continue our

analysis by testing whether there is a statistical significant average discount. We test our second hypothesis with the alternative hypothesis of 𝜇𝑆𝑃𝐷𝑅 being larger than 0. We see that the one sided

P-value is 0, meaning that we can infer with enough statistical evidence that the SPDR ETF is trading at a slight, yet statistically significant, discount on average over the time period investigated for all significance levels.

The mean t-test for the iThink (ticker: TDT.AS) ETF resulted in a t-value of -2.4193, and a corresponding P-value of 0.0157. This implies that there again is enough statistical evidence to reject the null hypothesis of 𝜇𝑖𝑇ℎ𝑖𝑛𝑘 being equal to zero. Again, we test our second hypothesis, with the

alternative hypothesis this time being that 𝜇𝑖𝑇ℎ𝑖𝑛𝑘 is smaller than 0. In this case, we see that the

one-sided P-value is equal to 0.0078, meaning that we can infer with enough statistical evidence that the iThink ETF is trading at a slight, yet statistically significant, premium (negative discount) on average over the time period investigated for all significance levels.

Lastly, the mean t-test for the iShares (ticker: IAEX.AS) ETF results a t value of -0.2289 and a corresponding P-value of 0.8190. Here, there is not enough statistical evidence to reject to null hypothesis of 𝜇𝑖𝑆ℎ𝑎𝑟𝑒𝑠 being equal to zero. Hence, We can infer that over the time period investigated,

the iShares ETF was not traded at an average premium nor a discount, and hence can be seen as being priced efficiently at all significance levels.

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Chapter 6 Summary and conclusion

This paper has attempted to explore the landscape of the ETFs tracking the AEX, the main Dutch stock exchange. This is done by looking at the operational characteristics of the different ETFs, their tracking error, and their pricing efficiency. From previous literature, it outlines the operational characteristics that have an influence on tracking error. Using this, we predict which of the funds would be most efficient, e.g. the fund that suffers from the smallest tracking error. It continues by using different methods of measuring the tracking error, and ranks their relative position. However, due to their β’s in a regression of the ETFs NAV return on the index itself not being equal to 1, these are not fully consistent with each other. In addition, these larger than 1 β’s can be interpreted as the ETFs returns “exaggerating” the returns of the index they are tracking.

Furthermore, we find that the rankings of the tracking errors of the different funds do not correspond with the ranks that would be predicted by the operational characteristics. Regarding pricing efficiency, we find that of the three ETFs, over the time period investigated, only one is actually priced efficiently, namely the iShares ETF (ticker: IAEX.AS). In terms of relative tracking error, this fund is ranked second. The SPDR ETF (ticker: AEXT.AS) trades at a slight, yet statistically significant, discount over the time period investigated. In terms of relative tracking error, the SPDR ETF ranks last. Finally, the iThink ETF (tracker: TDT.AS) trades at a slight, yet statistically significant, premium over the time period investigated. In term of relative tracking error, the iThink ETF ranks first.

Interestingly, we see that the ETF with the lowest tracking error commands a premium in price, while the ETF with the highest tracking error commands a discount. It would be of interest to conduct further research on this over different time periods and/or in other markets to see if this is a reoccurring theme.

Limitations

We find that the data on the NAV return of the SPDR ETF, and on the discounts calculated for all the ETFs are not normally distributed. Hence, we assume an approximate normal distribution based on the large amount of observations and Central Limit Theorem.

In ranking the relative influence of different operational characteristics on the tracking error of ETFs, we also simply assume equal weights. It is highly probably that some characteristics way stronger than others. This would be of interest to conduct further research on.

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Appendix 1: Discounts graphed

-. 0 1 -. 0 0 5 0 .0 0 5 .0 1 SPD R D isco u n t 7/1/2009 1/1/2011 7/1/2012 1/1/2014 7/1/2015 SPDR Dates -. 0 2 -. 0 1 0 .0 1 .0 2 iT h in k D isco u n t 7/1/2009 1/1/2011 7/1/2012 1/1/2014 7/1/2015 iThink Dates -. 0 1 5 -. 0 1 -. 0 0 5 0 .0 0 5 .0 1 iSh a re s D isco u n t 7/1/2009 1/1/2011 7/1/2012 1/1/2014 7/1/2015 iShares Dates

An enquiry into the Dutch exchange traded-fund landscape : tracking error and pricing efficiency