Are investors compensated for the additional counterparty risk in synthetic ETFs through lower tracking errors?

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Are investors compensated for the additional

counterparty risk in synthetic ETFs through

lower tracking errors?

Bart Slieker

Master Thesis,

Thesis Supervisor: Mark Dijkstra

University of Amsterdam,

MSc Business Economics, Finance track

May 2016

Abstract

This paper researches whether investors are compensated for the addi-tional counterparty risks incurred by investing in synthetic ETFs. It uses a sample of 820 exchange-traded funds and the credit default swap spread as a proxy for counterparty risk. Other papers have examined the tracking errors, and their relation to the replication method used, but this paper adds to the literature by taking the counterparty risk in consideration. This paper was not able to find conclusive evidence that investors in syn-tetic ETFs are compensated for counterparty risk through lower tracking errors.

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1 Statement of Originality

This document is written by Bart Slieker, who declares to take full responsibility for the contents of this document. I declare that the text and the work presented in this document is 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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List of Tables

1 Descriptive statistics . . . 19

2 Summarized results of the regressions on monthly tracking errors 21 3 Summarized results of the regressions on quarterly tracking errors 22 4 Summarized results of the regressions on annual tracking errors . 23 5 Summary of all tracking error periods with the sponsors . . . 24

6 Distribution of funds . . . 32

7 Monthly tracking errors with all control variables . . . 33

8 Quarterly tracking errors with all control variables . . . 34

9 Annual tracking errors with all control variables . . . 35

10 Monthly, quarterly, and annual tracking errors with the sponsors 36 11 Alternative tracking errors for all three time periods . . . 38

12 Alternative approximations for counterparty risk for all three time periods . . . 39

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2 Introduction

Exchange-traded funds were introduced by Nathan Most and Steven Bloom in 1993 when the SEC approved their Standard & Poor’s Depositary Receipts fund, or in short SPDR. After a period of struggling, the SPDR became a success and nowadays it has about $166 billion in assets under management (AuM) and trades on average $25 billion worth of shares a day (Balchunas, 2016). This is still a relative small portion of the total ETF market, which had grown to over $2.7 trillion in AuM by the end of 2014.

This first exchange-traded fund was simple. It bought the stocks listed on the S&P 500 and investors could trade this basket of stocks. An alternative method to replicate the return of the benchmark was created in 2001 in Eu-rope. These new funds used derivatives to replicate the returns and are called synthetic ETFs. This new replication method became recently under more reg-ulatory scrutiny as regreg-ulatory institutions began to express their concerns about the risks associated with exchange-traded funds, and more specifically, the risks associated with these synthetic ETFs. The IMF (2011) and the Financial Sta-bility Board (FSB, 2011) warned for the lack of transparency in exposure and the opacity of synthetic ETFs. Synthetic ETFs usually provide very little infor-mation about their counterparties. Both the IMF and the FSB argue that due to the counterparty risk, swap-based ETFs can become a source of contagion and systemic risk. In the financial world, investors want to be compensated for higher risks. So, are investors compensated for the additional counterparty risk through lower tracking errors?

This paper tries to address these concerns by researching whether investors in synthetic exchange-traded funds are compensated for the additional coun-terparty risk. A model which approximates councoun-terparty risk with the credit default swap rate is set up to test for differences in tracking errors between syn-thetic and physical exchange-traded funds. If synsyn-thetic etfs have lower tracking errors, this may be a form of compensation for the additional counterparty risk. The model will be used on a data set of 820 ETFs which are created by ten different sponsors.

The results stemming from the model remain inconclusive on whether in-vestors are compensated for the additional counterparty risk. It is shown in the

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results that when the credit default swap rate increases, the tracking errors de-crease, but the interaction variable between the credit default swap (CDS) rate and a dummy for synthetic replication is in none of the regressions significant. Even when the tracking errors are calculated in a different manner or when a different proxy for the counterparty risk is used, the interaction term remains insignificant.

The further outline of this paper is as follows. Section 2 provides the reader with a more thorough understanding of how ETFs are created. In section 3, this paper describes the related literature. Section 4 will describe the data set and the methodology. After this, section 5 will describe the results and in section 6 some robustness checks will be performed. Section 7 concludes with a summary where the main question will be answered, and in section 8 a discussion for for further research is included.

3 ETF construction

3.1 Replication methods

There are two main categories of replication for exchange-traded funds, phys-ical and synthetic replication. Within the synthetic ETF segment, there are two major ways of creation, the funded swap structure and the unfunded swap structure.

The creation of every exchange-traded fund starts with the ETF sponsor, who creates the fund, but there is a difference in how the ETF sponsor obtaines its exposure to the market. Figure 1 is a graphical representation of physical replication. In this case, the sponsor gives the authorized participants, who are usually also market makers, 50.000 creation units, or a multiple thereof. The sponsor receives the basket of securities needed to replicate the index in exchange for those creation units. These creation units are the denomination of the underlying asset and can be redeemed for a pre-specified number of shares. The authorized participant has to buy the securities for the sponsor in the secondary market, but the transaction between the authorized participant and

the sponsor takes place in the primary market. Investors can then in turn

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from the authorized participants or other investors. The value of the basket of securities held by the ETF sponsor is the basis in determining the net asset value (NAV) of the ETF (Ramaswamy, 2011).

Figure 1: Graphical representation of physical replication. In this structure, the sponsor holds the same assets as the benchmark.

Besides physical replication, ETF sponsors can choose between two synthetic replication methods. Synthetic exchange-traded funds are created in a similar fashion, but with one essential difference. The first process of synthetic repli-cation is referred to as the unfunded swap structure. This process is shown in Figure 2. Where in the physical replication method the authorized participant delivers the basket of the underlying securities, in a synthetic ETF, the autho-rized participant transfers cash to the sponsor. The sponsor then enters in a swap with a third party to receive the total return of the ETF index, given a notional amount. The cash received is also transferred to the swap counterparty and the sponsor receives a basket of securities as collateral, which may hold dif-ferent securities than the index the exchange-traded fund wishes to replicate. The swap counterparty is usually the parent bank’s asset management division (Ramaswamy, 2011).

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Figure 2: Graphical representation of the unfunded swap replication method

Figure 3 shows the funded swap structure. This is the second synthetic ETF structure. The difference with the unfunded swap structure is that instead of the sponsor, a custodian receives the collateral. Since the sponsor is not the beneficial owner of the collateral in case of a default of the counterparty, this structure can lead to delays in realizing the value of the collateral assets (Ramaswamy, 2011).

Figure 3: Graphical representation of the funded swap replication method

The difference in who holds the assets may create some differences in the risk profile, but this is outside the scope of this paper because it may not always be clear whether a synthetic ETF uses either an unfunded or a funded

swap structure1_{. Therefore, this paper makes a simplifying assumption that all}

synthetic ETFs are the same. In other words, this paper does not distinguish between the funded and unfunded swap structure.

1_{Deutsche Bank X-trackers, for example, allows its synthetic funds to switch between both}

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3.2 Benefits and drawbacks of the replication methods

Physical ETFs hold the constituent securities of the benchmark index. The main advantage of this replication method is transparency. Investors can see on a daily basis which securities they own through the fund, as well as the value of those securities.

Due to the way exchange-traded funds are created, all ETFs offer the oppor-tunity to redeem shares in that ETF. This can only be done in large amounts and by authorized participants and institutional investors, but in times of bull markets institutional investors may use this option as it is treated as a non-taxable transaction, and they can cash in profits without having to pay capital gain taxes. This redemption is usually done by delivering the portfolio of secu-rities that makes up the underlying index plus a cash amount. Physical ETFs have an advantage in this process since they own the assets and can sell these assets to cover the cash part when they receive a request for redemption. Syn-thetic ETFs can also sell assets to cover the cash part of a redemption request, but then they also have to renegotiate the swap because the difference between the net asset value and the swap cannot be larger than 10% under the UCITS regulation. Furthermore, they may not have the same portfolio of securities as the underlying index, so they may also have to buy the missing securities against unfavorable prices, which could adversely affect investors that maintain in the fund as they overpay for those securities. (Deville, 2008).

A drawback of physical ETFs is that the fund manager has to adjust the composition of his portfolio on a regular basis, as the underlying index may re-balance, or add and delete constituent securities. Transaction costs can make this expensive, especially for broad indices, composed of hundreds of stocks, or illiquid indices. Some ETFs try to solve this problem by using a technique called sampling. This means that some securities with a low weighing in the index are left out. This technique has the potential risk that the ETF’s returns deviate from the benchmark when a security with a low weight in the benchmark, and thus is not included in the ETF’s holdings, shows abnormal high or low returns (Maurer and Williams, 2015).

Another problem with re-balancing physical ETFs is that it creates an arbi-trage opportunity, since exchanges announce changes in the composition prior

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to implementation. Even though ETF managers may be prepared for this, tim-ing may be a constraint for them. An arbitrageur may short sell the stocks most likely to be deleted and buy the stocks that are the most likely to be included before the ETF managers can sell or buy them. Thus, the arbitrageur’s profit comes at the expense of the ETF investors. (Chen, Noronha and Singal, 2006). Synthetic replication does not have the problem of having to re-balance their portfolios periodically or having to use techniques like sampling because the swap counterparty has to pay the ETF sponsor the total return of the index. In other words, the re-balancing in not the problem of the ETF anymore, but rather of the swap counterparty. This may, however, be reflected in swap spreads.

These synthetic replication methods are also not without their drawbacks. Investors in a synthetic ETF may not know which assets are used in the total return swap because ETF sponsors do not always disclose this. In the case of illiquid securities, where synthetic ETFs are often used, this can lead to a liq-uidity mismatch between short-term liabilities and long-term funding (Aggarwal and Schofield, 2012).

Transaction costs may seem like a problem that only physical ETFs en-counter, but synthetic ETFs are also exposed to the swap spread, which is the spread between the index return and the return the ETF receives. These spreads are often not disclosed and are thus hard to assess for investors (Maurer and Williams, 2015).

3.3 Counterparty risk in ETFs

Currently, European exchange-traded funds are regulated under the Undertak-ings for Collective Investment in Transferable Securities (UCITS) Directive. Under this directive, measures are taken to minimize the risks involved with investing in ETFs. The most basic requirement is the disclosure of replication method, and when a fund uses a synthetic replication method, more stringent rules on how to use the derivatives apply.

Under UCITS, counterparty risk is defined as the difference between the net asset value of the ETF and the value of the substitute basket. This difference is not allowed to exceed a threshold of 10% of the net asset value at any given time when the counterparty is a certified credit institution, such as a European

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branch of a bank. It is also allowed to engage in swaps with other financial intermediaries, such as hedge funds, but then the threshold level is set at 5% (Directive 2009/65/EC of the European Parliament and of the Council, 2009). To comply with the regulations of UCITS, this counterparty risk is actively managed on a daily basis by resetting swaps. Furthermore, most funds have stricter rules in place to ensure that they will not come near the threshold levels as they face severe penalties for breaking this threshold.

While the value of the securities held by the sponsor may not be less than 90% of the fund’s net asset value, it is not always clear what kind of securities the sponsor has as collateral. The UCITS Directive does not pose any restrictions on the collateral other than that the collateral must be of high quality and be liquid (Directive 2009/65/EC of the European Parliament and of the Council, 2009). This is another source of counterparty risk.

Swaps are usually automatically terminated if a counterparty’s credit rating falls below a certain standard or when the counterparty defaults. In this case, the ETF sponsor may be able to initiate a new swap with a new counterparty. When that fails, however, the sponsor has to liquidate the collateral in order to either purchase the underlying securities or close the fund. This forced liquida-tion may expose investors to potential losses in both cases. If an ETF sponsor has used only one counterparty for the swap, or the counterparty is the coun-terparty in multiple swaps, this risk may be even higher (Foucher and Gray, 2014).

4 Related literature

This paper focuses on passively managed exchange-traded funds. They are

created to replicate the return of a benchmark as closely as possible. In contrast to actively managed funds, absolute returns are not as important since they are not the primary objective of these funds. Therefore, tracking errors, which are the differences between the benchmark return and the ETF return, are used to evaluate the quality of the ETF. The closer the tracking error is to zero, the better the exchange-traded fund replicates the index and the better the ETF is (Johnson, Bioy, Kellett, & Davidson, 2013).

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Shin and Soydemir (2010) focus their research about exchange-traded funds

on tracking errors, which the authors estimated using three methods. The

first method they used is taking the average absolute differences between the returns of the exchange-traded fund and its benchmark. The second method to estimate tracking errors was to use the standard errors from a regression

model using daily returns of both the ETF and its benchmark. The third

method they applied to estimate tracking errors was by taking the standard deviation of differences between the exchange-traded fund and its benchmark. They showed that in their sample of 26 ETFs tracking errors are negative and significant, implying that ETFs underperform compared to their benchmarks. One of the reasons of this underperformance is currency conversion according to the authors. Some exchange-traded funds trade in an other currency than the currency of the underlying securities. This happens, for example, when an in Euros denominated ETF replicates the S&P 500, an in dollars denominated index. When a conversion from the local currency to the trading currency takes place, a depreciation of the trading currency leads to an increase of the fund’s net asset value, increasing the difference with the underlying benchmark. This effect is statistically significant at the 5% level.

Blitz and Huij (2012) argue that exchange-traded funds that track global emerging markets show higher tracking errors than developed market ETFs. They used a sample of seven exchange-traded funds with combined assets under management of $67 billion. The authors show that the average tracking errors of 1% - 1.5% for the emerging markets ETFs are higher than the tracking errors of 0.5% - 0.8% for funds that track equity indexes for developed markets. As an explanation for this, the authors argue that the distribution in returns is higher in emerging markets than in developed markets. They combine this with the fact that five out of the seven funds use some form of physical replication, such as sampling, which means that a fund only takes a sample of the whole index. This is done to keep transaction costs down. As a result, when a security that is not in their portfolio performs unexpectedly good or bad, the fund misses this return and the tracking error increases. The funds that use this technique show on average worse tracking errors than the funds that use full replication and synthetic replication.

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Maurer and Williams (2015) used the Sortino ratio2_{, the Omega ratio}3_{, and}

the Modified Sharpe ratio4_{besides tracking errors to compare the risk and return}

characteristics of synthetic and physical equity ETFs. It is argued that synthetic ETFs present greater risk than physical ETFs due to counterparty risk and that investors may be compensated for that risk in three manners. The first manner is a lower total expense ratio (TER), the second is improved liquidity, and the third is a lower tracking error. The total expense ratio shows how much the costs of the exchange-traded fund are, expressed as a percentage of the the average value of the fund’s assets over a year. To control for different management styles, the authors limited their sample set to just three ETF sponsors, which are BlackRock, Lyxor, and Deutsche Bank, as they expected that differences in companies also have an influence on decisions made and thus the returns of ETFs (e.g. whether or not paying out dividends or domiciliation, which has an influence on taxation). Using an ANOVA model, they found that differences in return between the three fund sponsors used were not statistically different at the 5% level. Furthermore, they found that ETFs that trade in the same currency as their underlying index show a lower tracking error than ETFs that trade in a different currency. Their main finding on tracking errors, however, was that physical ETFs replicate a benchmark with, in aggregate, a similar efficiency as their synthetic counterparts. On top of that, the synthetic ETFs in their sample were not cheaper in terms of the total expense ratio. Lastly, they used bid-ask spreads as a proxy for liquidity and found that bid-ask spreads were tighter for physical ETFs. Combining these facts, they remained inconclusive

2_{The Sortino ratio is like the Sharpe ratio, but it only uses downside risk. It is defined as}

Sortino =rN AV − rindex σdownside

(1) .

3_{The Omega ratio provides an alternative view on volatility. It is defined as}

Ω(r) = Rb r(1 − F (x))dx Rr aF (x)dx (2)

, where r is the maximum loss an investor is willing to take, (a,b) is the time period and F is the cumulative distribution of the returns.

4_{In the modified Sharpe ratio, volatility is replaced by a value-at-risk measure.}

M odif iedSharpe = µ − rf rf− M V aRp

(3)

,where µ is the portfolio return , rf is the risk free rate and MVaRpis the portfolio value at

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whether synthetic ETFs compensate investors for the higher risks.

In an empirical study of 35 ETFs listed on the Swiss Stock Exchange, Naumenko and Chystiakova (2015) find that synthetic exchange-traded funds turn out to be less accurate in replicating the benchmark return than physical exchange-traded funds. They calculated tracking errors in the same ways as Shin and Soydemir (2010), but instead of only using the standard deviation of the return differences, they also used the standard deviation of the absolute return differences. Then, they ran a regression model with the total expense ratio, the logarithm of trading volume, the number of securities, and a dummy for synthetic replication on all these tracking errors. They found out that both physical as well as synthetic ETFs suffer from high tracking errors, which were significant at the 1% level. Synthetic ETFs had worse tracking errors than their physical counterparts in all regressions. This increase in tracking errors was as high as 0.136%.

Cooper and Mello (1991) researched the default risks of swaps. They argue that there are two kinds of risks involved with a swap. The first is called the rate risk, meaning that during the swap lifetime exchange rates and interest rates vary, and thus the present value of the remaining cash flows to be paid in the swap can vary. This risk can easily be hedged by taking an offsetting position.

The second type of risk they identify is the default risk, which is another name for counterparty risk, as this is the risk that the counterparty will default on its obligations. Therefore, this is much harder to hedge and it will be a significant determinant of the risk of that swap. The cost of a default by the counterparty depends on four things: the value of the swap at the moment of default, the event that triggers the default, the relation between the swap value and the event that triggers the default, and the rule for sharing claims in a default. Furthermore, in cases where a financial institution is the counterparty in multiple swaps, this may lead to more defaults triggered by the first default if a swap payoff depends on another swap payoff.

Duffie and Huang (1996) provide a model to assess the influence of the credit quality of both parties in a swap. They used the spread of the short term interest rate of the swap counterparties over the short term default-free interest rate. A

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reduced form model in which the default characteristics are estimated is used to derive the influence of the credit quality. The authors found that swap spreads are inelastic with regard to the credit quality of the swap counterparty. In other words, higher counterparty risk is not priced in the swap.

The hypothesis of this paper is that investors are compensated for a higher counterparty risk through a lower tracking error. Since synthetic ETFs are usually used for harder to replicate benchmarks, and their tracking errors do not differ significantly from the tracking errors of physical ETFs, it is expected that investors are compensated for the higher risk in the form of a better tracking error.

5 Data and methodology

5.1 Model

To test the influence of counterparty risk on the performance of ETFs, this paper uses the tracking error of the funds as dependent variable and regresses it against the credit default swap rate of the counterparty. The CDS rate gives an investor an indication how risky a company is, since a credit default swap is an insurance against a default of the counterparty, and the spread paid is the price of that insurance. When the CDS rate is high, investors perceive the company as more likely to default on its obligations and thus more risky. Since there is no way to directly measure the counterparty risk in a swap transaction, the credit default swap spread is used as a proxy to estimate the counterparty risk.

T Ei,t = β1CDSi,t+ β2SRi+ β3(CDSi,t∗ SRi) + Controls + Ui,t (4)

In this equation, TEi,tis the tracking error of exchange-traded fund i on time

t, CDSi,t is the average credit default swap rate of the counterparty over the

same time period as the tracking error, SRi is a dummy which is equal to one if

the ETF uses synthetic replication, and the third variable is an interaction term between the dummy and the credit default swap rate. The interaction term tests whether the CDS rate has a more significant influence when the index is

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replicated using a swap. Physical ETFs are, up to a certain level, also exposed to counterparty risk since some of them lend out their securities. Synthetic exchange-traded funds, on the other hand rely completely on counterparties for their returns. The interaction term is included to test whether there is a significant relation between synthetic ETFs and the counterparty risk, rather than a general relation between exhange-traded funds and counterparty risk that also includes physical ETFs. Therefore, this is the main variable of this research.

The tracking errors that are used in the regression model are calculated using the method of Shin and Soydemir (2010). Their method defines the tracking error as:

T E1=

Pn

t=1|ERi,t−BRi,t|

n (5)

where T E1is the tracking error, ERi,tis the total return of the exchange-traded

fund, BRi,t is the total return of the underlying index and n is the number of

trading days. Blitz and Huij (2012) argue that bid-ask effects, stale prices and differences in trading hours can increase short term return deviations, and thus overestimate the tracking error when it is calculated on a daily basis. The bid-ask effects may be observed when a very liquid stock is included in an illiquid ETF or vice versa. In those instances, a benchmark’s return may deviate from the ETF’s return due to differences in liquidity. Stale prices are old prices which not necessarily reflect all information anymore. Illiquid assets may have stale prices, but the price of a liquid ETF on that asset may have all information incorporated. Due to these differences in trading volumes, prices of ETFs and their underlying assets may drift apart from each other. Differences in trading hours may also create temporary discrepancies in values of ETFs and their underlying as new information is directly incorporated in the price where the exchange is open, but not where the exchange is closed.

Therefore, they calculate tracking errors based on a monthly and annual

basis. This paper follows their reasoning by calculating the tracking errors

per month, quarter, and year. When holding the exchange-traded fund for a longer time period, these small daily trading discrepancies between the index and the ETF will average out, but the investor will be more exposed to the

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counterparty risk as a longer time period will also increase the uncertainty about the counterparty’s ability to pay the swap returns. Using different holding periods will give a better insight in the relation between the holding period and the counterparty risk.

To ensure that this model only tests the influence of the perceived counter-party risk, several control variables are introduced. The first control variable is a dummy for the asset class, which is called fixed income dummy. This dummy equals zero if the ETF tracks an equity benchmark and one if it tracks a fixed income benchmark. Meinhardt, Mueller, and Schoene (2015) found that syn-thetic ETFs on the Frankfurt stock exchange have similar tracking errors as physical ETFs when they track equity indices, but lower tracking errors when they track fixed income indices. The total expense ratio also has a significant negative influence on tracking errors according to Elton, Gruber, and Busse (2004). Therefore, the total expense ratio is also included as a control variable. When an index has more constituents, physical ETF sponsors may use sam-pling. This technique can lead to larger tracking errors in case a security that is not included realizes abnormal returns. To adjust for this, the number of index constituents is also included as a control variable. Since this value can be an integer between 1 and 1,000 the logarithm of the value is used in the regressions. Following the reasoning by Blitz and Huij (2015), the payout policy of dividends or interest may also have an effect on the tracking error, so a variable which shows the exchange-traded fund’s dividend yield, is included. The last control variable is how many assets under management the ETF has. The logarithm of this value is used because the smallest fund is just over $250,000 while the largest funds are over a billion dollars. For larger ETFs, the larger transaction sizes may reduce the relative costs and therefore achieve a better tracking error. Since the sample is made up of time series of multiple ETFs, the results may be biased due to correlation within these groups of ETF data. Therefore, it is not possible to use the assumption that the data is distributed independently and identically. This will be solved by using standard errors that are clustered per ISIN code5_.

5_{ISIN stands for International Securities Identification Number. It is a unique code that}

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5.2 Data and sample selection

A dataset is created using all available exchange-traded funds from the top 10

fund sponsors in november 20146(Morningstar, 2014). Together, these sponsors

make up about 90% of the total European ETF market.

The initial sample created contained 1,846 ETFs. Some exchange-traded funds, however, are the same ETF, but in a different currency. In this case, the ETFs get a different ISIN code. Lyxor, for example, has two ETFs with different ISIN codes that both track the MSCI World Healthcare index. These funds have the same tickercode, are replicated in the same way and have the same securities in their portfolio, but one is listed in London in British Pounds and the other in Milan in Euros. To control for this, Bloomberg tickers without country codes are checked for duplicates. This leaves 1,321 unique ETFs, with a combined AuM of $ 892 billion.

After deletion of the duplicate funds, all funds that are not domiciled in Europe and all funds for which the data is incomplete are deleted. This leaves a sample set of 1,247 exchange-traded funds. Then, all funds with a multi-asset focus, leveraged ETFs, or with a focus on specialty products, such as the VIX volatility index or a hedge fund index for example, are also deleted. These funds are left out because they are not always comparable with a benchmark, which can be the case for multi-asset ETFs or a specialty products ETF that tracks a hedge fund index. This leaves a total of 820 ETFs with a combined AuM of $ 296 billion.

Descriptive statistics of the sample are displayed in Table 1. On average, the ETFs in this data set have assets under management of $ 361 million. BlackRock’s iShares has the largest market share with over $ 163 billion in assets under management spread over 157 different exchange-traded funds. X-trackers has with 194 different ETFs the most funds. These funds have a combined assets under management of almost $ 47 billion. For ETF Securities, there are only two ETFs in the sample set with a combined AuM of just over $ 48 million. ETF Securities is one of the largest European sponsors with over $ 13 billion in AuM, but they focus mostly on commodity and currency ETFs, which are

6_{The sponsors included in this sample are iShares (BlackRock), db X-trackers (Deutsche}

Bank), Lyxor, UBS ETFs, Source ETFs, Amundi ETF, ETF Securities, Vanguard, SPDR ETFs (SSGA), and Deka ETFs.

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not considered in this paper. The smallest exchange-traded fund in the sample comes from UBS and has only $ 270 thousand in assets under management.

Table 1: Descriptive statistics

Mean Median Largest Smallest Standard Deviation Number of ETFs Assets under Management iShares 1,039.57 190.37 52,671.24 1.67 4,444.38 157 163,212.57 X-Trackers 240.43 58.89 4,269.15 0.48 543.55 194 46,651.83 Lyxor 189.35 61.22 3,297.85 0.50 386.24 126 23,857.71 Vanguard 703.11 151.47 8,468.28 3.91 1,929.65 19 13,359.09 Source ETF 174.26 44.71 2,543.25 0.68 422.68 70 12,198.40 UBS 130.82 26.38 1,495.63 0.27 248.06 85 10,989.22 SPDR 126.26 41.99 1,410.46 2.62 223.35 83 10,479.4 Amundi 197.65 57.74 1,500.35 9.19 328.83 42 8,301.22 Deka 169.61 43.37 1,730.19 3.60 314.09 43 7,293.23 ETF Securities 24.26 24.26 29.37 19.15 7.22 2 48.53 Total 361.45 66.32 52,671.24 0.27 2,022.56 820 296,391.21

This table shows the descriptive statistics of the ETF sponsors used in the sample. All values, except the number of funds are in millions of dollars.

An overview of the distribution of the funds is provided in Table 2 in the appendix. Both Vanguard and State Street have ETFs domiciled in Europe even though they are American investment companies. Their American background may be a reason that both companies do not offer synthetic ETFs. Amundi, on the other hand, an European ETF provider, and it solely uses synthetic replication. In this data set, there are 329 synthetic exchange-traded funds and 491 physical ETFs. When looking at the underlying index, there are 597 ETFs that track an equity index and 223 exchange-traded funds that track a fixed income index.

For all these 820 funds and their benchmarks, adjusted closing prices, which are closing prices that are adjusted for dividend payments, are obtained for a period of up to three years. Returns are then calculated based on these adjusted closing prices. For the benchmark indices, however, it is assumed for simplicity that all the benchmarks provide the total return.

Data on swap counterparties has to be sought per ETF in either the prospec-tus or the factsheet. DB X-trackers, Lyxor and UBS always use the same coun-terparty in their swaps. Amundi uses multiple counterparties, which were BNP Paribas, Crédit Agricole, and Société Générale for the ETFs in the sample set. According to the initial sample set, BlackRock’s iShares, Vanguard, UBS, ETF

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Securities, and SSGA do not use synthetic replication or do not have synthetic ETFs that are eligible in the data set, so there are no counterparties for these sponsors needed. These sponsors are the party that has to deliver the assets in case of a default, so their credit default swap (CDS) rates are included for physical ETFs. Daily 5-year implied CDS rates over a period of three years are obtained using the Bloomberg terminal. These daily rates are then used to calculate the average CDS rate per month, quarter and year, depending on the time horizon of the tracking errors.

6 Results

The results displayed in table 2 show that in regressions 1, 2, and 4 monthly tracking errors decrease significantly when the credit default swap rate increases

by one basis point7_{, implicating that investors are compensated for the}

counter-party risk in both synthetic and physical ETFs by getting a better match with the underlying benchmark. The dummy for synthetic exchange-traded funds is negative, but it is in none of the regressions significant, implying that there is no significant difference in tracking errors between synthetic and physical exchange-traded funds. When including the interaction term between the CDS spread and the dummy for synthetic ETFs, the credit default swap spread is only significant in regression 4. The interaction term itself is in none of the regressions significant, and regressions 3 - 9 show positive values for the in-teraction term. This means that monthly tracking errors are higher when the CDS spread of the counterparty of a synthetic exchange-traded fund increases. Regression 9 shows the results from a monthly time fixed effects model and it has to be noted here that while in all other regressions an increase in the CDS spread has a lower tracking error as a result, this model shows an increase in the tracking error. This may implicate that the other models face some omitted variable bias.

Table 7 in the appendix shows the full results with all control variables included for the regressions on the monthly tracking errors. A dummy variable for ETFs that track fixed income indices is in all the regressions negative and

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significant at the 5% or better. From that, it can be concluded that the fixed income ETFs in this sample set have lower tracking errors than the equity ETFs. The control variable for the total expense ratio is not significant in regression 5, but it is in all the other regressions. There, it has a positive value in all of the regressions and it is significant at the 1% level. This is in line with the expectations that the costs of the exchange-traded fund increase the difference between the index returns and the fund’s returns. The logarithm of the number of index constituents and the assets under management have an influence of

almost zero on the tracking error. When a fund pays out a dividend, this

increases the tracking error. This is significant at the 1% level. The small value for the logarithm of the assets under management looks like a logical result, since fund sizes are usually in millions of dollars, while the credit default swap rate is quoted in basis points.

Table 2: Summarized results of the regressions on monthly tracking errors

(1) (2) (3) (4) (5) (6) (7) (8) (9) CDS -0.247* -0.130** -0.220 -0.235* -0.196 -0.117 -0.125 -0.133 0.059

(0.147) (0.062) (0.134) (0.132) (0.134) (0.107) (0.108) (0.103) (0.201) Synthetic Replication Dummy -0.00153 -0.00289 -0.00141 -0.00151 -0.000156 -0.000324 -0.000468

(0.002) (0.002) (0.002) (0.002) (0.001) (0.001) (0.001) (CDS * Synthetic) 0.157 0.0318 0.0316 0.0262 0.0387 0.0484 0.08683

(0.140) (0.126) (0.124) (0.119) (0.121) (0.114) (0.218) Controls no no no yes yes yes yes yes no Time Fixed Effects no no no no no no no no yes Clustered SEs yes yes yes yes yes yes yes yes yes N 22256 22256 22256 22256 22256 22256 22256 22256 22256 F 2.842 2.414 2.045 39.43 54.62 63.71 56.99 54.95 9.49

This table shows the summarized results of the regressions on the monthly tracking errors. The results shown are denoted in percentage points. The full table with the values of the control variables included can be found in Table 7 in the appendix. *p ≤ 0.10, **p ≤ 0.05, ***p ≤ 0.01.

When running these regressions for tracking errors that are calculated on

a quarterly basis, similar results can be seen as in table 2 and 7. Table 3

shows a summary of these results. The full results can be found in Table 8

in the appendix. It can be seen that the credit default swap spread has a

negative influence on the tracking errors in regressions 1, 2, 3, and 4, which is significant at the 10% level or better. Synthetic replication yields a negative but insignificant result in all regressions. The interaction term shows again positive and insignificant values.

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tracking errors, which are at least significant at the 5% level. The total expense ratio is significant at the 1% level in regressions 6 - 8, and it has a positive value, which is in line with the results for monthly tracking errors. Index constituents show an insignificant but negative result in all regressions in which they are used. Increasing the dividend yield also increases the tracking errors. This result is significant at the 5% level. In regression 8, it can be seen that the assets under management have a slightly negative, but insignificant influence on tracking errors. A notable difference with the results from the monthly regressions is that the influence of the CDS spread is negative in regression 9, which is the time fixed effects model.

Table 3: Summarized results of the regressions on quarterly tracking errors

(1) (2) (3) (4) (5) (6) (7) (8) (9) CDS -0.281* -0.176** -0.309* -0.318* -0.282 -0.177 -0.185 -0.190 -0.1449

(0.00155) (0.00261) (0.00227) (0.00222) (0.002) (0.002) (0.002) (CDS * Synthetic) 0.236 0.113 0.113 0.0753 0.087 0.0942 0.2633

(0.179) (0.162) (0.161) (0.151) (0.154) (0.147) (0.234) Controls no no no yes yes yes yes yes no Time Fixed Effects no no no no no no no no yes Clustered SEs yes yes yes yes yes yes yes yes yes N 7866 7866 7866 7866 7866 7866 7866 7866 7866 F 3.121 2.535 3.324 34.70 44.91 61.24 54.65 55.72 11.52

This table shows the summarized results of the same regressions on the quarterly tracking errors. All results are denoted in percentage points. The full table with the values of the control variables included can be found in Table 8 in the appendix. *p ≤ 0.10, **p ≤ 0.05, ***p ≤ 0.01.

Table 4 shows a summary of the regressions when the tracking errors are calculated on an annual basis. The full results can be found in Table 9 in the appendix. In these regressions, the credit default swap spread is negative and significant in regressions 1 - 5. Also, the interaction term is in all regressions positive and not significant, which is in line with the results from the monthly and quarterly tracking errors.

The dummy variable that indicates whether an ETF tracks a fixed income index is only significant in regression 4 and 5. The total expense ratio is signif-icant at the 1% level in all regressions except for 5, where it is not signifsignif-icant at all. The number of index constituents shows again slightly negative, but insignificant results. The same goes for the assets under management. On an annual basis, paying out dividends decreases the tracking error. The regressions

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show that tracking errors decrease with approximately 0.08 percentage points when the dividend yield increases by one percentage point. These results are significant at the 5% level. Also, in regression 9, an increasing credit default swap spread decreases the tracking error. From this, it can be concluded that there are some short term variables missing in the model that have a significant influence on short term tracking errors, but these decrease in significance when looking at the longer term.

Table 4: Summarized results of the regressions on annual tracking errors

(1) (2) (3) (4) (5) (6) (7) (8) (9) CDS -0.372* -0.356** -0.580* -0.589* -0.550* -0.302 -0.311 -0.318 -0.028

(0.00118) (0.00392) (0.00357) (0.00351) (0.0025) (0.003) (0.002) (CDS * Synthetic) 0.397 0.297 0.303 0.102 0.116 0.129 0.3821

(0.328) (0.305) (0.303) (0.228) (0.231) (0.222) (0.396) Controls no no no yes yes yes yes yes no Time Fixed Effects no no no no no no no no yes Clustered SEs yes yes yes yes yes yes yes yes yes

In this table, the tracking errors are calculated on an annual basis. The same regression models are used in this table as in Table 2 and Table 3. The full results are shown in Table 9 in the appendix. All results are in percentage points. *p ≤ 0.10, **p ≤ 0.05, ***p ≤ 0.01.

Choices made by a sponsor may also affect the tracking errors of ETFs. One can think of choices for domiciliation which affects the taxation of those funds for instance. Therefore, a summary of the regressions with the sponsors as control variables are shown in table 5 and the full results are shown in Table 10 in the appendix.

The credit default swap spread has a 10% significance and is negative in all regressions. Synthetic replication yields a negative, but insignificant result in all three regressions. The interaction term shows positive results, but these are not significant. These results are in line with the other regressions.

Tracking a fixed income index decreases tracking errors but this is only significant for monthly and quarterly tracking errors. The total expense ratio is significant at the 1% level and it increases the tracking errors with at least 87 basis points for each percentage increase of the costs. Higher dividend yields decrease the tracking errors. This effect is significant in all three regressions.

When looking at the sponsor specific influence, it can be seen that especially Source ETF and Deutsche Bank have a significant influence on the tracking

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errors. Source ETF has higher tracking errors in all three regressions which are significant at the 1% level. Deutsche Bank also has a significance of 1% in all regressions, but their influence is negative when looking at monthly tracking errors and positive when looking at quarterly and annual tracking errors. A fund that is created by Lyxor has slightly higher tracking errors, but this is only significant for the annual tracking errors. State Street’s SPDRs have slightly lower monthly and quarterly tracking errors, but these are not significant. The annual tracking errors are significant at the 5% level, but these have a positive influence. When a fund is created by Amundi, it also faces higher tracking

errors, which are significant for quarterly and annual tracking errors. ETF

Securities decreases the tracking errors in all time periods, but these results are insignificant. If an investor chooses a fund sponsored by UBS, he will face higher tracking errors, but these are only significant at the 5% level for the monthly tracking errors.

From these results, it can be concluded that the choice to invest in an ETF from a certain sponsor does have an influence on the tracking errors, but this does not affect the compensation the investor gets when the counterparty gets more risky.

Table 5: Summary of all tracking error periods with the sponsors

Monthly Tracking Errors Quarterly Tracking Errors Annual Tracking Errors

CDS -0.1873* -0.2629* -0.5613* (0.105) (0.149) (0.292) Synthetic replication -0.00096 -0.0015 -0.00298 (0.00112) (0.0015) (0.0031) (CDS * Synthetic replication) 0.0504 0.1139 0.2975 (0.0007) (0.151) (0.288)

Controls yes yes yes

Time Fixed Effects no no no

Clustered SEs yes yes yes

N 21721 7698 2644

F 106.13 66.94 63.27

This table shows the summarized results of the regressions where the sponsors are included as control variables. The full results of this table can be found in Table 10 in the appendix. Results in this table are denoted in percentage points. *p ≤ 0.10, **p ≤ 0.05, ***p ≤ 0.01.

In some of the regression models the influence of the credit default swap rate is significant. This significance means that for both investors in synthetic as physical exchange-traded funds higher counterparty risks are compensated

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with a lower tracking error. One possible explanation for this is that under UCITS regulation the value of the swaps is not allowed to differ more than 10% from the fund’s net asset value at any given moment or they will face the risk of heavy penalties or even losing their license. ETF sponsors therefore actively manage this risk and keep more stringent threshold levels for themselves and thus the counterparty risk may be lower than the legal threshold resulting in a small influence on the total risk.

A second possible explanation is that physical ETFs lend out shares to in-vestors that want to take short positions. They can do this because they often have the same securities for a longer time period and by lending out their hold-ings, they can increase their return and lower their tracking error (Aggarwal and Schofield, 2014). When lending out securities, the borrower immediately sells those shares on the market and he promises to pay the ETF a fee for the lend-ing, any dividends that the ETF receives when holding the security, and that he will repay the shares at some point. If the borrower defaults, the ETF may face problems retreiving the shares he lent out. This way, physical exchange-traded funds are also exposed to counterparty risk and it may have a more significant influence than expected upfront.

7 Robustness checks

Shin and Soydemir (2010) and Maurer and Williams (2015) both use an ad-ditional way to calculate the tracking error. This second method to estimate tracking errors defines them as the standard deviation of differences between the ETF return and the benchmark return. This can be calculated as follows:

T E2=

s

Pn

t=1(N Di,t− N Di)2

n − 1 (6)

In this equation N Di,t is the difference between the return of ETF i with its

benchmark on day t, and n is the number of trading days. Values close to zero implicate that the fund closely replicates its benchmark. New monthly, quarterly and annual tracking errors are calculated with this formula.

The regressions are rerun with the fixed income dummy, the total expense ratio and the dividend yield as control variables. The control variables for the

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number of index constituents and the assets under management are left out as they were insignificant in all previous regressions. Even though the time fixed effects model did not return any significant results, it is rerun with the new tracking errors to ensure there will be no omitted variable bias.

Table 11 in the appendix shows the results of both the standard OLS re-gression with the control variables and the time fixed effects rere-gression for all three time horizons. Comparing these results with the results from the first method of calculating tracking errors, it can be noted that the time fixed effects model again does not provide any significant results. Another thing that has to be noted is that the credit default swap spread is not significant in any of the regressions with the alternative method of calculating the tracking errors, whereas it was significant in a portion of the regressions with the primary track-ing error calculations. The influence on tracktrack-ing errors, however, is negative in all but one of the new regressions, as was the case with original regressions. The fixed income dummy was included because it yielded significant results in the original regressions, but was not significant in any of the robustness checks. The total expense ratio did yield significant results, where the influence on the monthly and quarterly tracking errors were in line with the original regressions. The influence on the annual tracking errors is approxiamtely 60% higher than in the original regressions. Increasing the dividend yield slightly decreases the tracking errors in all three regressions. These results are significant for monthly and quarterly tracking errors and are in line with the results of the primary regressions.

When defining counterparty risk as the risk that the counterparty will default on its obligations, rather than the official UCITS definition, it is possible to get another approximation of counterparty risk. This paper uses one such model to estimate the default probabilities for a 3-month and a 3-year time period. These probabilities are calculated with the Bloomberg Issuer Default Risk Model. This

model, which is based on the Black & Scholes formula for option pricing8_{, is}

an equity market based view of the default risk, where the default probability is estimated on the probability that the value of a company’s assets will fall

8_{One can view a company as a call option on it’s liabilities. If one applies this to the Black}

& Scholes formula, one can calculate the distance to default for that company, which is the number of standard deviations the company is away from a default. This distance to default can then in turn be used to calculate the probability of a default.

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below the value of its liabilities. Due to the volatile nature of public debt and equity markets, this model tends to overestimate the short term risk, and thus the 3-year probability is also used to minimize the influence of this volatility.

Table 12 in the appendix shows both OLS regressions and time fixed effects regressions. In the results of the OLS regressions, it can be seen that when the default probability increases on both the short term, as well as the long term, the tracking errors increase, implying that investors are not compensated, but penalized, when counterparty risk increases. The effect of an increase in the short term default probability is approximately 15 times the effect when the long term default probability increases. These results are all significant. Synthetic replication yields in all regressions insignificant values and in all but one negative values. The time fixed effects models shows mixed results where the default probability has both positive and negative values and all results are insignificant.

The fixed income dummy gave significant results in the original regressions, but with the alternative proxy the influence of the dividend yield was insignifi-cant. The dividend yield and the total expense ratio, however, do show results that are in line with the original regressions.

Comparing the results of both the original and the alternative method of calculating the tracking errors, it can be concluded that the results are similar and that the interaction term between the proxy for counterparty risk is insignif-icant in all cases. This also applies to the alternative proxies for counterparty risk. These results were also in line with the primary regressions, albeit that some results were a lot more extreme, and therefore it may be concluded that the primary regressions give a indication of the relation between counterparty risk and the tracking errors.

8 Conclusion

This paper tried to determine whether investors in synthetic ETFs are compen-sated for the additional counterparty risk incurred by the swap transaction. Af-ter an explanation of the creation and a brief discussion of the related liAf-terature, this paper did an empirical study on the perceived riskiness of a counterparty

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on the tracking errors of exchange-traded funds.

A dataset of 820 different exchange-traded funds from 10 different ETF sponsors was created to test this relation. Since counterparty risk cannot be determined directly, the credit default swap spread of the counterparty and the fund sponsor was used as a proxy of counterparty risk. In this model several control variables were added to ensure only the influence of counterparty risk was tested.

The results from the regression models show that investors in exchange-traded funds may be compensated for higher risks through lower tracking errors, but that this goes for both physical and synthetic ETFs. When only looking at synthetic exchange-traded funds, tracking errors are affected insignificantly by a higher CDS spread. Furthermore, where a negative relation was expected, most of the interaction terms were positive, implying that tracking errors of synthetic exchange-traded funds increase when the counterparty becomes more risky. Therefore, the hypothesis of this paper cannot be rejected and it must be concluded that investors are not compensated for the additional risk incurred through lower tracking errors.

9 Discussion

The main variable, the credit default swap spread, was an approximation for the actual counterparty risk. This approximation, however, was imperfect. The reason for this is that the credit default swap spread is determined based on the default risk of the whole institution, rather than just the part that is involved in the swap with the ETF. This may understate the actual risks of the counterparty as the whole financial institution is likely to be more diversified than just the trading desk involved with the swap and thus better able to mitigate the risks. When a sponsor uses synthetic replication, it also uses the same counterparty for multiple swaps. X-trackers and Lyxor, for example, always use the same counterparty, their parent bank, for their swaps. Foucher and Gray (2014) argue that the main motivation for an ETF counterparty to enter in a swap arises from synergies with its normal banking activities. This may lead to unobserved synergies for the counterparty and thus a lower counterparty risk.

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This paper only looks at compensation for the additional risks through a lower tracking error. The results show that investors do not get any compensa-tion through lower tracking errors, but it may very well be that they are com-pensated in other forms. One can think of an improved liquidity for instance as compensation.

For simplicity, it is assumed in this paper that all benchmarks are total return benchmarks. This may have overstated the influence of dividend payments by the exchange-traded funds. Deutsche Bank, for example, has two ETFs on the Eurostoxx 50 net return index. One that retains the dividends and one that pays them out. The index retains the dividend in its calculation and the ETF that retains the dividends has a lower average tracking error. To control for this, one could check whether the ETF and the index have the same dividend policy, which is retain or pay-out, and include a dummy variable which equals one in the case they have the same dividend policy.

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10 References

Aggarwal, R., & Schofield, L. (2014). The Growth of Global ETFs and Reg-ulatory Challenges. Advances in Financial Economics (Advances in Financial Economics, Volume 16) Emerald Group Publishing Limited, 16, 77-102.

Balchunas, E. (2016, March 7). The ETF Files. How the U.S. Government inadvertently launched a 3 trillion industry. Bloomberg. Retrieved April 10, 2016, from http://www.bloomberg.com

Blitz, D., & Huij, J. (2012). Evaluating the performance of global emerging markets equity exchange-traded funds. Emerging Markets Review, 13(2), 149-158.

Chen, H., Noronha, G., & Singal, V. (2006). Index changes and losses to index fund investors. Financial Analysts Journal, 62(4), 31-47.

Cooper, I. A., & Mello, A. S. (1991). The default risk of swaps. The Journal of Finance, 46(2), 597-620.

Deville, L. (2008). Exchange traded funds: History, trading, and research. In Handbook of Financial Engineering (pp. 67-98). Springer US.

Duffie, D., & Huang, M. (1996). Swap rates and credit quality. The Journal of Finance, 51(3), 921-949.

Elton, E. J., Gruber, M. J., & Busse, J. A. (2004). Are investors rational? Choices among index funds. the Journal of Finance, 59(1), 261-288.

Financial Stability Board (2011, April). Potential financial stability issues aris-ing from recent trends in Exchange-Traded Funds (ETFs). Financial Stability Board note. Retrieved April 12, 2016, from http://www.fsb.org

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vulnerabilities and Risks. Financial System Review, 37-46.

IMF (2011). Global Financial Stability Report: Durable Financial Stability: Getting There from Here. Retrieved April 12, 2016, from http://www.imf.org

Johnson, B., Bioy, H., Kellett, A., & Davidson, L. (2013). On the Right Track: Measuring Tracking Efficiency in ETFs. Hg. v. Morningstart ETF Research.

Maurer, F., & Williams, S. O. (2015). Physically Versus Synthetically Repli-cated Trackers: Is There A Difference In Terms Of Risk?. Journal of Applied Business Research, 31(1), 131.

Meinhardt, C., Mueller, S., & Schoene, S. (2014). Physical and Synthetic

Exchange-Traded Funds: The Good, the Bad, or the Ugly?. The Journal of Investing, 24(2), 35-44.

Naumenko, K., & Chystiakova, O. (2015). An Empirical Study on the Differ-ences between Synthetic and Physical ETFs. International Journal of Economics and Finance, 7(3), p24.

Ramaswamy, S. (2011). Market Structures and Systemic Risks of Exchange-Traded Funds.

Shin, S., & Soydemir, G. (2010). Exchange-traded funds, persistence in track-ing errors and information dissemination. Journal of Multinational Financial Management, 20(4), 214-234.

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Appendices

Table 6: Distribution of funds

Synthetic ETFs Physical ETFs ETFs based on equity indices ETFs based on fixed income indices Number

of ETFs

Assets under Management (in millions)

Number of ETFs

Assets under Management (in millions) iShares 0 0 157 163,212.2 112 120,985.3 45 42,226.9 X-Trackers 122 21,818.4 72 24,823.4 125 35,494.2 69 11,157.6 Lyxor 105 15,465.1 21 8,392.6 107 19,258.2 19 4,599.5 Vanguard 0 0 19 13,359.1 16 13,386.7 3 172.4 Source ETF 59 8,539.2 11 3,659.2 63 8,682.9 7 3,515.5 UBS 0 0 84 10,989.2 72 10,385.6 12 603.6 SPDR 0 0 83 10,479.4 50 5,598.2 33 4,881.2 Amundi 42 8,302.1 0 0 24 4,828.6 18 3,473.5 Deka 1 14.0 42 7,279.1 26 4,890.5 17 2,402.6 ETF Securities 0 0 2 48.5 2 48.5 0 0 Total 329 54,148.8 491 242,242.7 597 223,358.7 223 73,032.8

Overview over the distribution of funds provided by the biggest ETF sponsors, where in the first panel the number of funds are denoted in the first column and the second column shows the combined assets under management of those funds in millions. The first two columns provide an overview of how many exchange-traded funds are synthetic and how many are physical. The equity column shows how many ETFs track an equity index and fixed income shows how many track a fixed income index. ETFs which are denominated in different currencies, and for which not all data available is, are already deleted in this table.

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Table 7: Monthly tracking errors with all control variables

(1) (2) (3) (4) (5) (6) (7) (8) (9) CDS -0.247* -0.130** -0.220 -0.235* -0.196 -0.117 -0.125 -0.133 0.059

(0.002) (0.002) (0.002) (0.002) (0.001) (0.001) (0.001)

(CDS * Synthetic) 0.157 0.0318 0.0316 0.0262 0.0387 0.0484 0.08683 (0.140) (0.126) (0.124) (0.119) (0.121) (0.114) (0.218) Fixed Income Dummy -0.00481*** -0.00401** -0.00213** -0.00197** -0.00195**

(0.00124) (0.00200) (0.001) (0.001) (0.001) Total Expense Ratio 0.411 0.799*** 0.826*** 0.815***

(0.425) (0.180) (0.188) (0.187) Index Constituents -0.000112 -0.000103 -0.0000738 (0.000) (0.000) (0.000) Dividend Yield 0.000576*** 0.000571*** (0.000) (0.000) log AuM -0.0000915 (0.000) Constant 0.00752*** 0.00722*** 0.00787*** 0.00918*** 0.00722* 0.00370** 0.00366** 0.00531*** -0.08051*** (0.00212) (0.00183) (0.00218) (0.00245) (0.00406) (0.002) (0.002) (0.002) (0.025)

Time Fixed Effects no no no no no no no no yes

Clustered SEs yes yes yes yes yes yes yes yes yes

N 22256 22256 22256 22256 22256 22256 22256 22256 22256

F 2.842 2.414 2.045 39.43 54.62 63.71 56.99 54.95 9.49

This table shows the influence of the CDS rate on the monthly tracking error in different regressions. Column 1 shows the influence of only the CDS rate. In column 2, a dummy for synthetic replication is added, and in column 3 an interaction term between both is introduced. Columns 4 - 8 include several control variables. Column 9 shows a time fixed effects regression. After the inclusion of the synthetic replication dummy, the CDS rate variable is not significant. The interaction term is in none of the regressions significant, but it is positive, which implies that investors are not compensated for the additional risk from investing in synthetic ETFs. All results are in percentage points. *p ≤ 0.10, **p ≤ 0.05, ***p ≤ 0.01.

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Table 8: Quarterly tracking errors with all control variables

(1) (2) (3) (4) (5) (6) (7) (8) (9)

CDS -0.281* -0.176** -0.309* -0.318* -0.282 -0.177 -0.185 -0.190 -0.1449

(0.00155) (0.00261) (0.00227) (0.00222) (0.002) (0.002) (0.002)

(CDS * Synthetic) 0.236 0.113 0.113 0.0753 0.087 0.0942 0.2633

(0.179) (0.162) (0.161) (0.151) (0.154) (0.147) (0.234)

Fixed Income Dummy -0.00486*** -0.00406** -0.00222*** -0.00205*** -0.00203***

(0.001) (0.002) (0.001) (0.001) (0.001)

Total Expense Ratio 0.417 0.803*** 0.832*** 0.824***

(0.438) (0.210) (0.219) (0.222) Index Constituents -0.000167 -0.000158 -0.000134 (0.000) (0.000) (0.000) Dividend Yield 0.000598** 0.000594** (0.000) (0.000) log AuM -0.000074 (0.000) Constant 0.00787*** 0.00759*** 0.00857*** 0.00984*** 0.00788* 0.00446** 0.00441** 0.00572*** -0.072** (0.002) (0.002) (0.003) (0.003) (0.004) (0.002) (0.002) (0.002) (0.028)

N 7866 7866 7866 7866 7866 7866 7866 7866 7866

F 3.121 2.535 3.324 34.70 44.91 61.24 54.65 55.72 11.52

This table shows the same regressions as Table 2, but with quarterly calculated tracking errors instead of monthly tracking errors. This table shows similar results as with monthly tracking errors. The results in this table are denoted in percentage points. *p ≤ 0.10, **p ≤ 0.05, ***p ≤ 0.01.

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Table 9: Annual tracking errors with all control variables

(1) (2) (3) (4) (5) (6) (7) (8) (9)

CDS -0.372* -0.356** -0.580* -0.589* -0.550* -0.302 -0.311 -0.318 -0.028

(0.00118) (0.00392) (0.00357) (0.00351) (0.0025) (0.003) (0.002)

(CDS * Synthetic) 0.397 0.297 0.303 0.102 0.116 0.129 0.3821

(0.328) (0.305) (0.303) (0.228) (0.231) (0.222) (0.396)

Fixed Income Dummy -0.00450*** -0.00337* -0.00191 -0.00169 -0.00162

(0.00137) (0.00198) (0.00132) (0.00139) (0.00146)

Total Expense Ratio 0.605 0.907*** 0.943*** 0.930***

(0.426) (0.299) (0.314) (0.311) Index Constituents -0.000209 -0.000198 -0.000136 (0.0003) (0.00029) (0.00034) Dividend Yield -0.000779** -0.000769** (0.000367) (0.000358) log AuM -0.000195 (0.000242) Constant 0.00907*** 0.00901*** 0.0107*** 0.0119*** 0.00917* 0.00555* 0.00549* 0.0089*** -3.3184** (0.00256) (0.00237) (0.00368) (0.00392) (0.00484) (0.00288) (0.00287) (0.00287) (1.596)

N 2689 2689 2689 2689 2689 2689 2689 2689 2689

F 3,593 3,315 4,024 54.15 61.37 69.36 60.08 59.39 69.00

This table shows the results when the tracking errors are calculated on a annual basis. The results shown are denoted in percentage points. *p ≤ 0.10, **p ≤ 0.05, ***p ≤ 0.01.

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Table 10: Monthly, quarterly, and annual tracking errors with the sponsors

Monthly Tracking Errors Quarterly Tracking Errors Annual Tracking Errors

CDS -0.1873* -0.2629* -0.5613* (0.105) (0.149) (0.292) Synthetic replication -0.00096 -0.0015 -0.00298 (0.00112) (0.0015) (0.0031) (CDS * Synthetic replication) 0.0504 0.1139 0.2975 (0.0007) (0.151) (0.288)

Fixed income dummy -0.0084** -0.0018*** -0.00148

(0.0007) (0.0007) (0.0013)

Total expense ratio 0.8727*** 0.8813*** 1.0124***

(0.173) (0.198) (0.297) Dividend yield -0.00049** -0.00052** -0.00069* (0.00023) (0.00027) (0.00037) Lyxor 0.00048 0.00057 0.0014** (0.0005) (0.00048) (0.0006) Deutsche Bank -0.0019*** 0.0020*** 0.0032*** (0.00046) (0.00044) (0.00064) SSGA -0.00019 -0.00001 0.0013** (0.00035) (0.0003) (0.0006) Amundi 0.00089 0.00102* 0.0017* (0.00055) (0.00053) (0.0009) ETF Securities -0.0008 -0.00133 -0.0015 (0.0012) (0.0015) (0.002) UBS 0.0013** 0.00113 0.00118 (0.0006) (0.0007) (0.0009) Source 0.002*** 0.00239*** 0.00397*** (0.0005) (0.00052) (0.0007) Constant 0.0028*** 0.0034*** 0.00503** (0.001) (0.0013) (0.0023)

Time fixed Effects No No No

Clustered SEs Yes Yes Yes

N 21721 7698 2644

F 106.13 66.94 63.27

In this table, the results from regressions with the sponsors, fixed income dummy, total expense ratio, and the dividend yield as control variables are shown. Results are denominated in percentage points. *p ≤ 0.10, **p ≤ 0.05, ***p ≤ 0.01.

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Table 11: Alternative tracking errors for all three time periods

Monthly Tracking Errors

Quarterly Tracking Errors

Annual Tracking Errors

(1)

(2)

(3)

(4)

(5)

(6)

CDS

-0.0774

-0.01078

-0.1497

-0.2152

-0.336

0.3397

(0.086)

(0.085)

(0.137)

(0.161)

(0.301)

(0.932)

Synthetic Replication Dummy

0.00038

-0.00008

0.0011

(0.0012)

(0.0015)

(0.0044)

(CDS * Synthetic)

0.0056

0.3365

0.0727

0.499 0.0909

0.679 (0.093)

(0.2199)

(0.1448)

(0.338)

(0.573)

Fixed Income Dummy

-0.00031

-0.00009

0.00256

(0.0018)

(0.0021)

(0.00496)

Total Expense Ratio

0.778***

0.8432**

1.379*

(0.287)

(0.354)

(0.788)

Dividend Yield

-0.00064**

-0.00076*

-0.00149

(0.00036)

(0.00045)

(0.00102)

Constant

0.00185

-0.0701**

0.00247

-0.08*

0.0022

-6.046

(0.00159)

(0.0341)

(0.00193)

(0.045)

(0.0043)

(5.031)

Time Fixed Effects

No

Yes

No

Yes

No

Yes

Clustered SEs

Yes

N

21695

7694

2644

F

34.20

17.92

26.36

16.67

18.72

23.92

This table shows a linear regression model with the fixed income dummy, the total expense ratio and the dividend yield as control variables (columns 1, 3, and 5) and a time fixed effect model (columns 2, 4, and 6). The dependent variable is the tracking error calculated using the second method. *p ≤ 0.10, **p ≤ 0.05, ***p ≤ 0.01.

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Table 12: Alternative approximations for counterparty risk for all three time periods

Short term default probability Long term default probability

Monthly Quarterly Annual Monthly Quarterly Annual Monthly Quarterly Annual Monthly Quarterly Annual (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) Default Probability 1.791*** 1.489** 1.308** 0.1139 -0.0524 -0.2182 0.112*** 0.117** 0.1189* -0.015 0.0379 -0.049

(0.581) (0.599) (0.599) (0.461) (0.535) (0.736) (0.038) (0.0512) (0.062) (0.198) (0.0736) (0.092) Synthetic Replication Dummy -0.0011 0.0015 -0.228 -0.00149 -0.0019 -0.0025

(0.001) (0.0013) (0.0017) (0.001) (0.0013) (0.0017)

(Synthetic * Default Prob) 0.0454 0.8031 1.615 2.461 3.1412 3.092 0.4564 0.913 1.443 2.778 2.616 3.525 (1.824) (2.35) (2.68) (2.997) (3.594) (4.155) (1.6648) (2.025) (2.304) (3.13) (2.796) (4.068) Fixed Income Dummy -0.00116 -0.0115 -0.0005 -0.00114 -0.0011 -0.00049

(0.0009) (0.0009) (0.0017) (0.00096) (0.00096) (0.0017) Dividend Yield -0.0006** -0.00064** -0.00082** -0.00059** -0.00062** -0.00079**

(0.00024) (0.00027) (0.0004) (0.00024) (0.00026) (0.00039) Total Expense Ratio 1.0253*** 1.056*** 1.241*** 1.035*** 1.074*** 1.258*** (0.231) (0.2704) 0.396) (0.233) (0.274) (0.403)

Constant 0.00096 -0.000936 0.00041 -0.0616*** -0.0625** -2.4299** 0.00035 -0.0002 -0.00036 -0.621*** -0.6122** -2.507** (0.0009) (0.00087) (0.0014) (0.0212) (0.0282) (1.083) (0.001) (0.0011) (0.0018) (0.021) (0.0286) (1.1996) Time Fixed Effects No No No Yes Yes Yes No No No Yes Yes Yes Clustered SEs Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes N 19014 6734 2273 19014 6734 2273 19014 6734 2273 19014 6734 2273 F 63.92 62.57 56.16 16.27 9.02 13.08 70.62 70.80 73.27 6.16 4.89 23.79

This table shows the regression models with alternative measures for the counterparty risk. The first part uses the probalility of default within 3 months (columns 1 - 6) and the second part uses the default probability within 3 years (columns 7 - 12). Columns 1, 4, 7, and 10 use monthly tracking errors. Columns 2, 5, 8, and 11 use quarterly tracking errors and columns 3, 6, 9, and 12 use annual tracking errors. *p ≤ 0.10, **p ≤ 0.05, ***p ≤ 0.01.

Are investors compensated for the additional counterparty risk in synthetic ETFs through lower tracking errors?