master thesis: the efficiency of exchange-traded funds as

Master Thesis: The Efficiency of Exchange-Traded Funds as a market investment

Master Thesis:

The efficiency of Exchange-Traded Funds as a market

investment

Author: R.Bernabeu Verdu

ANR: 892508

Supervisor: Lieven Baele

Faculty: Tilburg School of Economics and Management

Department: Finance

Programme: Master in Finance


Abstract

Exchange-Traded Funds (ETFs) have become an important innovation in the financial markets

nowadays. They are low cost products designed to pursue passive replication strategies that

respond to investor’s demands of liquidity and efficiency. However, they suffer from tracking

errors and price mismatches even when they are designed to avoid them. I will show that, in

general, ETFs underperform their benchmarks by around 50 basis points every year and which

factors are responsible for this underperformance. For Leveraged or Inverse funds the results are

much worse as the underperformance is around 6% every year. Moreover, tracking errors will be

analyzed for both ETFs and LIETFs in order to find the reasons behind the underperformance of

the benchmarks. Finally, I will show that ETFs and LIETFs are very efficient in keeping the

fund’s market price close to the NAV.


Table of Contents

Abstract ........................................................................................................................................... 2

1-Introduction ................................................................................................................................. 4

2- ETF structure and competitive advantages. .............................................................................. 10

3-Current state of literature ........................................................................................................... 14

4-Research questions and methodology........................................................................................ 17

5-Sample description .................................................................................................................... 21

5.1-Data selection ...................................................................................................................... 21

5.2- Sample and descriptive statistics ....................................................................................... 24

5.2.1- ETFs ............................................................................................................................ 24

5.2.2-LIETF ........................................................................................................................... 26

6-Empirical results ........................................................................................................................ 28

6.1- ETFs ................................................................................................................................... 28

6.1.1-Capital Asset Pricing Model test .................................................................................. 28

6.1.2-ETF Tracking errors ..................................................................................................... 29

6.1.3-ETF Price efficiency ..................................................................................................... 33

6.2-LIETFs ................................................................................................................................ 34

6.2.1-Capital Asset Pricing Model test .................................................................................. 34

6.2.2-LIEFTs tracking errors ................................................................................................. 36

6.2.3-LIETFs price efficiency ............................................................................................... 38

7-Conclusions ............................................................................................................................... 39

References: .................................................................................................................................... 43

Appendix 1: Figures ...................................................................................................................... 46

Appendix 2: Tables ....................................................................................................................... 49

Appendix 3: List of variables and definitions ............................................................................... 58


1-Introduction

Since the development of Modern Portfolio theory by Markowitz (1952) investors have been

looking for efficient ways to diversity their portfolio in order to eliminate idiosyncratic risk and

obtain efficient portfolios that maximize return minimizing risk. The most direct way to do this is

replicating indices by buying all stocks or, at least, a representative sample of them. However,

this strategy is only available to large investors as retail investors would experience severe

transaction costs. Due to these problems, retail investors started demanding equity funds that

could buy stocks in large quantities resulting in lower transaction costs; causing the appearance

of the first passive mutual funds. These funds are intended to replicate indices charging fewer

fees to their customers than active funds, which look to outperform a market index. For this

purpose, passive funds hire fund managers that create portfolios of stocks (usually replicating an

index benchmark) offering the fund’s stock to retail investors with lower costs that it would be

for them to buy all the equity on their own.

On the other hand, there are active mutual funds that follow active strategies based on the

knowledge of professional managers, paying higher fees in exchange. In these funds, investors

give capital to the fund and it follows different strategies in order to obtain abnormal returns

compared with an index benchmark. Active funds usually pursue investment strategies that focus

in finding of α stocks (stocks that offer more (less) returns given their market risk (β)), these

stocks offer higher (lower) returns that companies with the same risk (following CAPM) and

therefore can be a productive investment if active funds are able to find them.

Passively managed mutual funds have revolutionized the way retail investors behave, as they

have made it very easy and relatively cheap to get broad market exposure. However they had,


and still have, limitations in terms of liquidity and pricing efficiency. Mutual funds are structured

in two different ways: On the one hand, there are open-end funds that have important liquidity

problems as their shares do not trade in organized markets. The fund’s shares can only be bought

or sold back to the fund at the end of trading sessions for the Net Asset Value (NAV). The

advantage of this approach is that the difference between the price of the fund and the value of

the underlying assets is guaranteed to remain low as if they differ, arbitrageurs will intervene

buying or selling shares back to the fund until the difference is gone. However, the fact that the

shares can only be bought or sold at the end of the trading sessions is not optimal as it increases

transaction costs and reduces the ability of investors to liquid their investment. Moreover, they

also charge fees when buying or selling the fund’s shares decreasing even more liquidity and

increasing transaction costs. These additional fees are known as front-end loads1 if there are paid

when entering into a long position or back-end loads if they are charged when selling the long

position. This liquidity problem is an important concern for short term investors as they need to

realize multiple transactions and to be able to recover their money fast and with as low as

possible transaction costs. For long term investors, liquidity supposes less a challenge as they

plan to keep the money invested in the fund for a long period of time. However, the increasing

costs and higher probability of default of less liquid funds make them consider these restrictions

before making a final investment decision.

On the other hand, closed-end funds are funds that are exchanged between individuals in

organized markets, they are traded like shares and individuals can exchange them using brokers

and traders. The problem with these funds is that once the fund has issued shares they cannot be

redeem back, which means that shares can only be purchased or sold in the market and not back

1 12b-1 fees in United States


to the fund. As the price is not guaranteed to reflect the real value of the underlying assets, these

shares have the risk of important price deviations between their market price and the value of the

assets held by the fund. These deviations usually take form as a discounted price relative to the

fund’s NAV; signaling that investors value the fund’s shares less than the assets that back them.

The problem is that there is not a mechanism though which investors can use arbitrage and

eliminate deviations. The logic of this anomaly has become an important puzzle for finance

academics as prices should not differ that much from their fundamental value and it is subject to

important research (see e.g. Boudreaux (1973) or Pontiff (1996))

With the rise of new empirical research that showed that, in general, active funds underperform

their index benchmarks (e.g. Malkiel (1995)); and the acceptance that low cost passive strategies

can deliver superior results than traditional actively managed mutual funds, investors started

looking for low cost methods of replicating indices. They started demanding funds that could be

easily tradable and not prone to substantial discounts or premiums from the NAV.

As a consequence of these increasing demands, the first generation of Exchange-Traded Funds

(ETFs) known as Spiders were introduced in the year 1990 in Canada. Spiders were a hybrid

between open end funds and closed end funds. By construction there were very similar to passive

mutual funds in a sense that they were passively traded portfolios of securities but, in contrast to

open-end index mutual funds, Spiders were listed on exchanges like individual stocks and

therefore could be traded continuously throughout the trading session. Moreover they could be

redeemed back to the fund provider for the NAV. These products will later on be named

Exchange-Traded Funds and were created to avoid price deviations while allowing continuous

trading.


Because of the relative advantages of ETFs, their rapid expansion was inevitable. From Canada

they jumped to the rest of the world experiencing a very fast expansion starting in 2000 until

today. Next to ETFs a new variety of products were born with similar structures included in the

category of Exchanged Traded Products (ETPs).These products are Exchanged Traded Notes

(ETNs), Exchanged Traded Commodities (ETCs), alternative ETFs, currency ETFs, active ETFs,

inverse ETFs and leveraged ETFs. In the year 2000, there were 106 ETPs (92 ETFs) with asset

value of 79.4 billion U.S dollars (74.3 billion corresponding only to ETFs). By the end of 2012

there were 4748 ETPs (3297 ETFs) with asset value of 1.8 trillion dollars (1.6 trillion) an

average annual growth of 34% (see graph 1 and 2 in appendix 1). This exponential growth shows

how important these products have become in today’s financial markets.

If we take a look to the ETPs providers there are a total of 195 ETPs providers worldwide. ETFs

are the most important component with 89% of the total ETP market leaving the rest 11% for the

other types of funds. Furthermore, 84% of the value of the ETF’s assets is concentrated in only

10 providers that cope the market, leaving the other 16% for the other 185 providers (see figure 3

in appendix 1). By provider, ishares is the largest ETP provider with 39% market share followed

by State Street with 18% and Vanguard with 13%, all three supposing almost 70% of the market.

These numbers show that the ETP market is very concentrated; having the main players an

important advantage compared with smaller less known families of funds.

The picture in the ETP market in the U.S in very similar to the global overview as it accounts for

71% of the global ETP market (1.3 trillion U.S dollars) using data from September 2012. There

are 49 ETF sponsors providing 1465 ETFs. The average growth of assets under management for

the last 13 years has been of 27% per year (see figure 4 in appendix 1) which is a little bit lower


than the global industry growth. ETFs are the most important component with 89% of the total

ETP market (see figure 4 in appendix 1). There are a total of 49 ETP providers, but as in the

global case their assets are very concentrated. The three most important providers account for

82.5% of the total assets under management, being ishares again the largest provider with 40%

of market share as shown by figure 5 in appendix 1.

The increased popularity and the rise of more complex products like Leveraged and Inverse

ETFs (LIETFs) augmented the possibilities for institutional asset allocation as well as for private

investing but at the cost of increasing complexity. In this context, LIETFs have acquired an

important role in the financial markets. These funds use synthetic replication in order to achieve

daily returns that are multiples (2, 3,-1,-2,-3 are the most usual) of the targeted benchmark. They

do not promise long term performance regarding the benchmark; instead the objective is to

provide a specific leverage on a daily basis. LIETFs must rebalance their assets continuously in

order to keep their promised multiple; this causes higher transaction costs that may explain their

higher fees and their relative underperformance (this will be discussed later). Another important

characteristic of LIETFs is their high trading volume, for example as of September 2009 they

supposed approximately 40% of the total trading volume for ETP in the U.S when their assets

are only a small fraction (around 5%) of the ETP market as stated by Charupat and Miu (2010).

These characteristics make them optimal for short term traders who wish to pursue speculative

trades in specific benchmarks as opposed to the more long term diversified approach of

conventional ETFs. LIETFs are also associated with gambling as they are perfect for investors

looking for high volatility liquid markets where it is possible to take very risky positions for the

sake of it.


The rest of the paper is organized as follows. The next section provides a more detailed

explanation of the structure and functioning of ETFs and the advantages of these funds. Section 3

provides a literature review consisting of related research. Section 4 will set the main research

questions and purposes of this paper. Section 5 will describe the data and methodology. Then,

section 6 will show the main empirical results. Finally, section 7 will present the main

conclusions of this paper.


2-ETF structure and competitive advantages

As a way to avoid price deviations ETFs have engineered a method called creation-redemption

process (view Figure 6 in the appendix) that guarantees that prices do not vary much from the

NAV. In order to do this, when an ETF provider wants to create new shares of its fund it turns to

an Authorized Participant (AP). An AP can be a market maker, a specialist or any other large

financial institution with buying power. The AP buys all the shares that compose the benchmark

index (or a representative sample) the ETF tries to replicate, and exchanges them with the ETF

provider for the ETF’s equally valued own shares at their NAV2. The exchange takes place in a

fair value basis as the block of underlying shares and the ETF shares are equally valued at the

NAV. Both participants benefit from the transaction because the ETF provider gets the stocks it

needs to track the index and the AP gets ETF shares to resell for profit. The process also works

in reverse, which means that AP can buy large blocks of the ETF shares and exchange them for

the underlying benchmark shares at the NAV. The process guarantees that the ETF market price

does not differs much from its NAV as if mismatch occurs, APs will intervene exchanging ETF

shares for underlying shares, or the other way around, using arbitrage until both, market price

and NAV, are equal. This system also saves money to the ETF provider as it does not incur in

transaction costs when the portfolio is constructed, it is the AP who buys the underlying stocks

(usually with low transaction costs as it is a big player in the market). This facts cause ETFs to

charge less fees than equivalent passive mutual funds.

Moreover, there are other characteristics that make ETFs more efficient and more attractive than

mutual funds.

2 This process is only done for large blocks of shares, usually 50,000 or more.


Cost Advantage: The majority of ETFs are passive investment products that usually try to

track the performance of a market index. This means that their turnover is low, as share

transactions only occur for rebalancing purposes. Furthermore, the passive approach

causes lower costs for ETFs as providers do not need to hire expensive managers and

perform complex market analysis. This cost efficiency is translated in lower expense

ratios that make them more attractive as investors usually consider fees as one of the

main determinants when choosing among similar funds.

Transparency: ETFs are generally listed in market exchanges and trade like normal shares

which forces them to comply with the exchange transparency and transmission of

information rules. ETFs are obliged to publish their financial statements and prospectus

informing investors of all relevant changes in the fund’s policy. Moreover, they also have

to disclosure the components of the fund, their weights and the NAV of their shares daily,

which helps investors to be aware about what the fund is doing and how it is doing it.

Avoidance of principal-agent problem: The importance of the principal-agent problem is

well documented in many research papers like Grossman and Hart (1983) and Haubrich

(1994). This problem occurs when the manager of the fund, the agent, makes decisions

on behalf of the owners of the fund (investors), it is usual that the manager acts in his

own interest instead of acting in the interest of the investors. The problem is exacerbated

in active mutual funds when managers have a bonus or a stock-based compensation if

they are able to beat the market. This form of salary incentivizes them to pursue riskier

strategies that offer higher expected returns. In the ETF case, this issue is avoided as

managers are specifically instructed to replicate a market index and therefore assume the

same risk than the benchmark. However, recently there have appeared new types of ETFs


called active ETFs that try to outperform their benchmarks by pursuing active (alpha)

strategies. These products are usually cheaper than equivalent active mutual funds, but

suffer from the same problems when trying to outperform market benchmarks

(e.g.Malkiel (1995)).

Tax efficiency: The in and out capital flows of ETFs are also a source of improvement

compared to mutual funds. ETFs are structured in a manner that taxes are minimized for

the holder of the ETF and the ultimate tax bill (when the ETF is sold and investors pay

taxes for capital gains) is less than what the investor would have paid in a similarly

structured mutual fund. A mutual fund must constantly rebalance the fund by selling

securities to accommodate shareholder redemptions or to reallocate assets. The sale of

securities within the mutual fund portfolio creates capital gains for shareholders that are

subject to taxes. In contrast, ETFs administrate inflows and outflows by creating or

redeeming blocks of ETF shares that are exchanged for an equally valued amount of

benchmark stock, not creating any capital gains in the process. As a result, investors

usually are not exposed to capital gains on any individual security in the underlying

structure.

As ETP started to be more and more interesting for investors, investment banks started to enter

the market offering different new features, like new derivative structures, tailored for specific

investor’s demands and, as a consequence, the market started to be more and more complex. The

new and different types of replication methods used made ETFs more dissimilar to each other

and comparable investment products. Investors have now to differentiate between full

replication, optimized sampling and synthetic, swap-based, replication strategies:


Physical replication: This strategy consists in holding all, or substantially all, the stocks

with the same weights than the target benchmark. This method supposes higher

transaction costs as more stocks must be bought and rebalanced, but the risk of tracking

error is lower.

Sampling replication: The strategy consists in holding only a representative sample of the

benchmark that is supposed to give approximately the same returns than the benchmark.

This method supposes lower transactions costs as the fund needs to operate with less

stocks but increases the change of higher tracking errors.

Synthetic replication: This method tries to replicate an index benchmark using different

derivatives like swaps. They have the advantage of lower costs and more favorable tax

treatment (in some countries) than physical and sampling replication but may be prone to

higher errors and other risks as counterparty risk and lack of transparency.

In the equity market, physical and sampling ETFs are predominant in the U.S and synthetic

replication is only used for bond, commodity or leveraged/inversed replication (only 3% of the

ETFs used synthetic replication in the U.S as stated by Dickson et al. (2013)). In the U.S

legislation, swap-based replication has less favorable treatment than the rest of replication

methods because swap income has higher tax liability than capital gains incurred when trading

physical stocks3.

3 In Europe, however, synthetic replication is more common because of tax reasons. Physical or sampling based

ETFs must pay a tax called stamp duty (0.5% of the value of physical underlying securities in U.K) that swap-based

ETFs do not have to pay (Dickson et al., 2013).


3-Current state of literature

Due to their relative youth (the first ETF was created in 1990 in Canada, but they started to be

popular from 2002) research on these products is limited and focused mainly in U.S market.

Many of the current research finds that ETF prices are very close to NAV in United States

(Ackert and Tian (2008), Elton et.al.(2002) but country ETFs are not (Engle and Sakar (2006)),

meaning that although ETF are designed to be efficiently priced, evidence signals persistent

premiums or discounts especially for ETF that are not based in U.S. Engle and Sarkar (2006)

started examining the end-of-day and intra-day data, measuring the premiums’ magnitude as well

as their persistence. They focused on the influences of the creation-redemption process on

domestic and international funds. They arrive to the conclusion that international funds face

higher premiums than their domestic counterparts as market discrepancies cannot be capitalized

efficiently. For international funds the creation-redemption process involved in the arbitrage

mechanism for institutional investors is more complicated and costly while the ability of hedging

risk is also tremendously reduced.

Based on this, research papers have focused on trying to find the logic behind tracking errors and

price deviations. Some important factors have been detected, Elton et.al. (2002) finds that the

most important sources of mispricing are management fees and dividends received but not yet

paid out, this cash flows are not put in interest bearing accounts which causes underperformance.

On the other hand Gastineau (2004) finds that the expense ratio alone explains much of the

difference in pricing. Ackert and Tian (2008) find that mispricing of country funds is related to

momentum, illiquidity and size effects concluding that the relationship between fund premiums

and market illiquidity shapes as an inverted U, they arrive to this conclusion after finding that the


premium is positively related to liquidity but negatively related to squared liquidity . Blitz, Huij

and Swinkels (2010) find that taxes are determinant for the mispricing, especially dividend taxes.

Another important factor researchers have found significant is liquidity. Blitz and Huij (2012)

conclude that when there is a high spread of cross-sectional returns, the tracking errors tend to be

higher than when this spread is low because of bad liquidity (especially in Emerging Markets).

Another important topic is the method of replication each ETF uses, as stated before, physical,

sampling or synthetic replication. Although research is even scarcer in this topic, there are some

papers that focus in the performance differences between synthetic and physical replication.

William (2014) concludes that physical ETFs replicate the performance of benchmarks similarly

to synthetic ETFs meaning that synthetic holders are not compensated for the additional

(counterparty) risk they bear. Elia (2012), on the other hand, states that ETFs that follow a

synthetic replication strategy instead of holding the Benchmark’s securities enjoy a lower

tracking error and higher tax efficiency, even though they underperform both the benchmarks

and the traditional counterparts. However, none of these papers focuses on the differences

between physical and sampling replication (which is one of the points of this paper) that are the

predominant replication methods in the U.S, market that accounts for 70% of the total ETF

market by assets under management.

Research has also covered the differences between ETF and conventional passive mutual funds,

trying to assess which of both products is more efficient. Agapova (2011) finds that conventional

index funds and ETFs are substitutes, but not perfect substitutes. ETFs have not replaced the

conventional index funds, but they are a new investment vehicle that has added new features

previously unavailable in conventional mutual funds, helping completing the market. Harper,


Madura and Schnusenberg (2006) obtained evidence that ETFs have higher mean return and

higher Sharpe ratio than foreign closed-end funds, while closed-end country funds show negative

alphas. This indicates that passive investment strategies using ETFs could be superior to active

investment strategies using closed-end mutual funds.

Regarding LIETFs, there is not much research available as they started to become popular very

recently (2007-2008). The main objective of the scarce research has been to find out the reasons

of tracking errors and mispricing. Charupat and Miu (2010) analyze leveraged ETFs and find

that they are usually held by very short term investors causing occasional large premiums and

discounts from NAV. Moreover, the behaviour of premiums is different between bull and bear

ETFs. Lu,Wang and Zhang (2009) analyze the long term performance of leveraged ETFs in

order to check if they achieve the promised multiples in the long run (they usually promise to

achieve this performance in the short run but not for longer periods of time). Their results

confirm that leveraged ETFs track reasonably well over one month or less but get significant

deviations for longer periods of time. They arrive to the conclusion that leveraged ETFs are not

long term substitutes for long or short positions in the index benchmarks. Finally, Avellaneda

and Zhang (2010) study the underperformance of leveraged ETF and arrive to the formula that

links the return of leveraged funds with the corresponding multiple of the unleveraged fund

return and its variance.


4-Research questions and methodology

One of the aims of this paper is to assess the efficiency of ETFs as substitute for investment in a

particular market index as a whole. For this purpose, the first step is to use the Capital Asset

Pricing Model (CAPM) to find out if the returns of ETFs and LIETF achieve perfect replication

or if they underperform somehow their respective index benchmarks. This method to test the

performance of funds against the market has already been used in other papers like Rompotis

(2009) and Chong et al. (2011). The formulas are shown below:

Equation 1: ( )

Equation 2: ( )

Being

and the monthly returns of the fund’s NAV.

α is the abnormal return of the asset .

is the sensitivity of the of the ETF or LIETF excess return to the excess return of the market.

the monthly return of the risk free rate defined as the 3-months U.S T-Bill.

the leveraged fund’s promised multiple.

In the ETF case, if ETFs are perfect trackers, I expect to obtain a beta of 1 as ETFs track

benchmark indices and their sensitivity should be approximately equal to the market.

Theoretically α should be insignificantly different from 0 as ETFs are not constructed to obtain


any extra return than the market, neither positive nor negative. However, given the fact that ETFs

charge an expense ratio for their services, the value of α is expected to be negative and close to

the average monthly expense ratio of 0.033% or 0.4% in yearly terms.

For the case of LIETFs it is first necessary to multiply the benchmark return by the fund’s

promised multiple to obtain the equivalent promised return of the respective fund. I do not expect

a beta of exactly 1 but relatively near, as these funds are not created to track indices in the long

run precisely and are prone to subtantial tracking errors. Regarding α, it is expected to be

negative and even lower than the average expense ratio. LIETFs tend to underperform their

benchmarks, this is due to the fact that they are designed to track benchmarks during short

periods of time and therefore they are more prone to underperformance in longer periods as

explained by Lu, Wang and Zhang (2009).

After this analysis, the two dimensions of efficiency in funds, pricing efficiency and tracking

efficiency, will be studied. Pricing efficiency indicates how closely the price of an ETF or a

LIETF follows its NAV and analyzes the reasons for premiums or discounts. Pricing efficiency

is measured using the formula bellow:

( )

Being

the market price of the fund at the end of the month.

the Net Asset Value of the fund’s assets at the end of the month.


ETFs are designed to be price efficient and, following the creation-redemption process, all

possible premiums or discounts should disappear almost immediately due to the action of AP

looking for arbitrage returns. When an AP observes a price discount it can buy enough ETFs

shares to create a block and then exchange it for a block of the underlying stock that composes

the index. As the NAV is higher than the market price, the market value of the shares is higher

than the ETF price; the AP can sell the underlying shares in the market obtaining profit in the

process. The opposite process can also happen when the price of the fund trades at a premium.

The AP will buy a blocks of shares of the underlying stocks and trade it for a block of the ETF

shares. As the ETF shares are valued higher than the underlying stocks the AP will obtain returns

with no additional risk. The same argument applies for LIETFs but using derivatives and other

products as underlying assets.

In reality, this process is not as straightforward as it seems as premium and discounts are likely

to appear and persist. These deviations are, however, smaller than for closed-end mutual funds.

One of the points of this paper is to find out the amounts and importance of the deviations and

the reasons behind them so investors can have better criteria when choosing among possible

funds that replicate an index.

The other dimension this paper aims to analyze is tracking efficiency, defined as the degree to

which the NAV return of a fund follows the return of its benchmark index. Tracking errors

measure how closely an ETF tracks its index benchmark (or a multiple times the index in the

case of LIETFs).

√( )


: the NAV monthly returns.

: the index benchmark monthly returns.

the leveraged fund’s promised multiple. For common ETFs this number is 1.

In theory it should not be any significant difference as ETFs and LIETFs are created to replicate

an index but this is not always the case and tracking errors are a good method to measure how

much returns differ from the benchmarks. The analysis of tracking errors is essential in order to

find out if buying an ETF (LIETF) is the same than buying an equivalent part of an index

(multiple of the index) in terms of risk and return. The objective is to determine which factors

and variables are responsible for the difference between the fund’s and the benchmark’s

performance.


5-Sample description

5.1-Data selection

In this section I will comment the construction of the dataset and its main characteristics using

descriptive statistics. For the realization of this paper it has been needed to construct two

datasets, one containing 127 normal ETF with data from January 2006 until December 2013, the

other one contains 62 LIETFs also with data from January 2006 until December 2013. The first

dataset contains a total number of 10626 observations and the second one a total of 4222.

One of the purposes of this paper is to analyze the tracking and pricing efficiency of equity ETFs

and LIETFs. For this reason all the chosen funds only track equity indices priced in U.S dollars,

and therefore currency, bond and commodity ETFs are excluded. Also ETN and other ETP,

excepting leveraged and inverse ETFs, are not included as they are not in the scope of this

research.

Regarding the selection of the ETFs or LIETFs that will be part of the chosen data, the Blackrock

Global Handbook Q4 2012 was used. This document contains a comprehensive directory of all

4748 Exchanged Traded Products with 1.8 US$ trillion in assets from 195 providers on 54

exchanges around the world. Using this report, 150 normal ETFs and 70 LIETFs were selected

based in the following criteria:

For the normal ETFs dataset only funds that follow a passive investing approach, based

on replicating a market index, were selected.

For LIETFs only funds that follow a passive leveraged or inverse replication approach

were selected.


Funds have to trade in U.S exchanges. The reason of this is because U.S is the biggest

market of ETPs as it accounts for 71% of the global ETP market.

ETFs have to track a broad and general market index well-known in the investment

world. For this reason, the datasets are mainly composed by well-known index provider

companies like MSCI, S&P, FTSE, Stoxx and Russell among others. Table 1 in appendix

2 shows the selected benchmarks.

For data availability purposes, only ETFs created before January 2010 were selected.

The selection tries to get the maximum diversity respecting countries and index providers

given the other criteria. An overview of selected ETFs by ETF provider can be consulted

in table 2 in appendix 2.

The time period selected for the analysis runs from January 2006 until December 2013. The

reason for this selection is due to data and fund’s availability. As ETF and LIETFs are very

recent products, not many were created before 2006 and this paper tries to extract general

conclusions for the equity ETF and LIETF markets. For this reason it was necessary to have

enough funds working and data available since the beginning. However, due to this constrain it is

difficult to get overall conclusions as the available data comprises a concrete period of time

characterized by high volatility in financial markets as a consequence of the economic crisis of

2007-2008.

Once, the funds were selected, it was time to get all the relevant variables that would be used for

the empirical analysis. The datasets are constructed using four different sources of data with

different variables collected in each of them:


CRSP database: Many of the variables used in this paper come directly or indirectly from

the mutual fund tool in CRSP database. The variables obtained in CRSP are Price, Net

Asset Value (NAV), Total return per share, Total Net Assets (TNA), dividend cash

payments, volume, bid, ask, shares outstanding, percentage of the fund’s asset held in

cash, year first offered, expense ratio, and fund turnover ratio (aggregated sales of

securities divided by the average TNA of the fund).

Thompson Datastream: This tool was used in order to get the total return of the index

benchmark and also the total return of the risk free rate, in this case the 3 Months U.S T-

Bill.

Morningstar webpage: This web page specialized in funds was used in order to generate

dummy variables for style and size and also in order to classify the ETFs and LIETFs in

geographic areas. It was also necessary in order to find out which index benchmark each

fund tracks.

Fund’s prospectus: In order to find out which type of replication each ETF uses it was

necessary to check the prospectus of all ETFs included in the dataset. In the LIETFs case

this was not necessary because all of these funds use synthetic replication.

Once all the data was collected and assembled into two datasets, one for normal ETF and the

other for LIETFs, it was time to create the variables that would be used in the empirical analysis.

Apart of the dependent variables, tracking error and price deviation, described in part 3 of this

paper, there are other important variables, for a description of them please look at the appendix

3: list of variables and definitions.


Due to missing data and other difficulties in completing the data, the final datasets are composed

by 134 ETFs and 61 LIETFs supposing 10626 and 4222 observations respectively.

5.2- Sample and descriptive statistics

5.2.1- ETFs

In this part, a summary statistics analysis for ETFs will be performed. In table 3 of the appendix

2 a selection of summary statistics for ETFs can be found. The results are shown in a monthly

basis, so it is necessary to multiply by 12 the results in order to get comparable annual numbers.

The first thing that can be seen in the table is that average index monthly returns are higher than

ETFs returns by 4 basis points (bp) with similar conclusion when the median is .This means that

ETFs underperform their benchmarks by 50 bp each year on average. This difference in returns

is also responsible for the annual average tracking error of 2.4% which is a considerable amount

to be taken into account by investors when choosing a fund given the fact that, on average,

tracking errors are translated into underperformance, even when the underperformance is

partially offset by mean-reversion. These results are similar to related papers in which ETFs

usually suffer from similar underperformance figures.

In a similar analysis we can also check the price deviation variable. On average the price of a

fund is higher (premium) that the assets backing the ETF share in near 0.01 dollars in absolute

terms or 1.8 bp in relative terms (the median is 0). This value is low giving a first impression that

ETFs are doing a good job in keeping premiums or discounts low as designed to.


Other interesting variable is Total Net Assets (TNA) with an average of 3.6 billion per fund

which decreases to 0.6 billion when using the median. The difference indicates an important

concentration of capital into the top up funds in the distribution.

Also expense ratio is an important variable as it indicates how much it does cost to invest in the

fund in a monthly basis. The average is 0.034% per month or 0.40% per year (the median is very

similar) which is lower than an average equivalent mutual fund.

It is also interesting to know that the average ETF is 12 years old indicating that they are very

recent products that have become very important in a short period of time. The variable cash

shows the percentage of the TNA ETFs have in cash and indicates that they have an average of

0.25% of their funds in cash (0.19% median) evidencing that, as was expected, funds keep the

majority of their capital invested in the respective market index.

Finally if we take a look to volume figures, it can be seen that the average fund has a number of

825,000 transactions every month (almost 10 million in year terms) with value of 66,862,000

U.S dollars (800 million in yearly terms). Again, the median of these variables suffer from severe

Skewness to the right and kurtosis showing and important concentration of transactions in some

funds and dates.

After this superficial analysis it is time to take a look at the correlation between the main

variables used in the paper. Table 4 in appendix 2 shows the correlation matrix of selected

variables. From this table it can be extracted that: first, return and benchmark have, as expected,

a very high correlation of 99.8%. Second, the rest of the variables like tracking error, TNA, Cash

Dividends, Liquidity, among others, are not very highly related as correlations are below 0.33.


The second highest correlation is between Amihud’s illiquidity measure and spread, both

measures of liquidity.

5.2.2-LIETF

In the case of LIETFs the statistics are substantially different. In table 5 in appendix 2 a table

with summary statistics for LIETFs can be found. The first thing that can be appreciated is that

the LIETF monthly return over the period is negative -0.78% (9.5% in annual terms) and also

that the return of the benchmarks times the multiple is also negative but smaller -0.28% (-

3.46%). These returns can lead to misleading conclusions as the sample includes inverse ETFs

that show positive returns when the market is bearish. What it is informative is the difference

between both of them, LIETFs underperform their benchmarks by almost 50 bp on average per

month (64 bp if the median is considered) causing considerable tracking errors of 1.38% per

month or 16.5% per year (0.64% and 7.7% respectively, indicating concentration of tracking

errors in some funds and dates).

If we take a look a price deviation, the average deviation is -2 bp in relative terms or -0.01

dollars in absolute terms with even lower figures for the median. The number is negative which

means that the NAV is higher than the fund’s market price, meaning that LIETFs products sell

with discount. Investors value the product less than the value of the assets that back them.

Regarding TNA, the average assets of a LIETF is 0.25 billion dollar with a smaller median of 44

million dollars, again this difference shows an important concentration of assets in a few funds

and dates. When these results are compared with the ones we found for ETFs, it can be seen that

LIETFs are much smaller in size that normal ETFs. This is due to their relative youth and

speculative nature that makes them short term financial instruments.


Furthermore, LIETFs are on average only 7 years old, which confirms our previous statements

talking about how recent an innovative these funds are, even compared with ETFs. Taking a look

to cash, the table tells us that funds usually keep 63% of their funds in cash (32% if we look at

the median) indicating that an important percentage of their assets are kept in cash. This is not a

surprise as cash serves as a guarantee when using derivatives to achieve the desired leverage.

Finally, if we take a look to volume figures, the average fund has 0.62 million transactions every

month (almost 7.5 million every year) valued in 24 million U.S dollars (almost 300 million in

yearly terms). Again the median is considerably smaller indicating a severe concentration of

assets in some funds. If this data is compared with the data obtained for normal ETFs, volumes

are relatively high, as ETFs volumes are only three times higher than LIETFs but the value of

their assets is 15 times the TNA of LIETFs. This last fact reassures the short term nature of the

product.

Table 6 of appendix 2 shows the correlation coefficients of selected variables for LIETFs.

LIETF’s and benchmark returns are correlated by 98.8%, slightly lower than for normal ETFs.

For the rest of the variables an increase in correlations compared with ETFs can be appreciated,

but still lower than 37%.The second highest correlation is between turnover and fund age

indicating that older funds have less turnover that younger ones.


6-Empirical results

From last section some interesting results were obtained indicating that, in general, ETFs and

LEITFs are successful in keeping price deviations low. These funds are created to keep price

deviation low and it seems that they are achieving it. However, they struggle significantly when

tracking benchmark returns.

In this section of the paper a more formal analysis will be performed, the objective is to find out

if both products can be considered as substitutes for market indices and finding out which are the

reasons of their deviations in returns and prices (even though the last one has been shown as

quite low). The structure of the section is the following, first ETFs will be analyzed followed by

LIETFs. For each product a CAPM test will be performed to check if ETFs or LIETFs replicate

their respective benchmarks correctly followed by an econometric analysis of tracking errors and

price deviations.

6.1- ETFs

6.1.1-Capital Asset Pricing Model test

In this subsection I will check if ETFs returns follow the CAPM model from equation 1 in

section 4. The results of the regression are shown in the first specification of table 7 in appendix

2. As explained in section 3, in this regression the variable Beta is expected to be equal to 1 and

the constant negative and similar to the monthly average expense ratio of 0.03% as, in theory, the

returns of ETFs should replicate perfectly the returns of their benchmarks excepting for the fees

charged to investors. The coefficient for Beta is equal to 0.995 which is approximately 1

although if a t-test is performed, the results indicate that the coefficient is statistically different

from 1 (t-statistic is equal to -6.7). It is more interesting to look at the coefficient of the constant,


its value is -0.04% and it is significant at 1% level indicating underperformance of 48 bp per

year. The ETFs underperformance is, as expected, near the average expense ratio of 0.03%,

possibly indicating that much of the underperformance is due to the fees charged by the ETF.

More discussion about this will be done in next paragraph and in next section when analyzing

tracking errors. This result is very similar to the one extracted from the summary statistics ( table

3), which adds more evidence to the fact that ETFs underperform their benchmarks indices for an

amount slightly higher than the expense ratio. Regarding the goodness of fit, the is 0.996

which means that almost all movements in ETF returns are explained by movements in the

benchmark returns.

Also in table 7 in specification 2 a CAPM test with a new variable added, expense ratio, can be

found. This test is made in order to confirm if the underperformance is mainly due to the expense

ratio or there are more variables responsible. Checking the results it can be confirmed that much

of the underperformance measured in specification 1 by the constant disappears when including

the expense ratio as α becomes insignificantly different form 0 and the expense ratio is negative

and significant. Moreover, does not change with the inclusion of the expense ratio indicating

that the it absorbs the effect previously captured by the constant. Given this, we can confirm that

an important amount of the underperformance is due to the fees charged by the ETFs.

6.1.2-ETF Tracking errors

As stated before, ETFs have problems in tracking index benchmarks and this causes average

annual tracking errors of 2.4% that are directly responsible for the underperformance of 48 bp

per year analyzed in section 6.1.1 In this part we are going to study this problem deeper by


analyzing tracking errors (for a more detailed explanation of the variables, look at appendix 3:

List of variables and definitions).

As stated by Elton et al. (2002), two of the most important sources of tracking errors and price

deviations are the expense ratio and dividends. In order to capture these effects, the expense ratio

and one dummy variable that signals if the fund has paid dividends during the month are

included in the regressions. These variables are expected to be economically and statistically

significant.

One of the most important hypotheses of this paper is that the method of replication matters

regarding tracking errors and price deviation. For the testing of this hypothesis, a dummy

variable signaling if the replication approach selected by the provider is sampling replication is

included. Sampling is cheaper but more prone to systematic errors; physical replication is more

expensive (higher expenses are related to higher tracking errors) as it implies more transactions

but is less likely to suffer tracking errors. Depending on which effect is stronger the variable will

have a positive or negative sign.

Other variables which are expected to have a significant impact are the ones related with

liquidity like Amihud’s illiquidity measure and the variable called liquidity (check appendix 3

for more details). Liquidity is one of the fundamental reasons why ETFs were created, it is

expected that more liquid funds have less problems in tracking their indices and also in keeping

price deviations low.

Turnover is also expected to be significant as it captures the number of transactions a fund does

when buying or selling stock mainly due to rebalancing purposes. Fund’s that make more


transactions, pay more costs and are more prone to underperform. Other variables like age and

cash can also play a role, even though smaller in determining tracking errors and price

deviations.

Table 8 in appendix 2 shows the results of several regressions performed using tracking errors as

the dependent variable. The table is separated in 4 specifications, the first shows the most usual

variables used in research to determine tracking errors and the sampling dummy, specification 2

includes the variables of the first one and adds more variables (extended model), specifications 3

and 4 contain the same variables than 1 and 2 but with date fixed effects and provider effects4.

The variable Sampling dummy is positive and significant at 5%, which means that funds with

sampling replication suffer 4 bp higher tracking errors per month than funds with physical

replication (48 bp in annual terms). This value supposes 20% of the average tracking errors

which does not seem extremely important but if the median is used as a comparison, the

coefficient supposes around 60% of it, which is a more considerable fraction. Even though, it is a

considerable percentage, the value of 48 bp per year seems at first sight low to be considered

economically significant.

Regarding the other variables, as expected the expense ratio is positive and significant with a

coefficient of 2.91 indicating than if the expense ratio increases by 1% the tracking errors

increase by 35 bp per year. The sign is positive meaning that higher expenses cause higher

tracking errors, in line with previous research. The value seems significant, but taking into

account that the average expense ratio is around 0.34%, it makes us think that maybe is not

4 One dummy variable per index provider.


economically significant after all. Expense ratio seems to be less important in explaining tracking

errors than expected, giving room to other variables than can be potentially significant.

Amihud illiquidity measure is significant economically and statistically, confirming our

hypotheses of higher tracking errors when the stock is illiquid. Divdummy and fund Age have

the expected sign as the payment of dividends is usually a cause of errors and Age’s negative

sign is associated with more experience in the business and better results. Even though

Divdummy and Age are statistically significant at 1%, their values are rather low to be

considered economically significant.

Turnover ratio is positive economically and statistically significant implying that funds that do

more transactions perform worse that the ones that keep turnover low.

It is also important to highlight the fact that the natural logarithm of the fund’s Total Net Assets

(lgTNA) is completely insignificant with a coefficient of almost 0. This signals that the value of

the assets under management is completely irrelevant when choosing among funds.

Regarding the investment style variables, neither size (large, small) or investment style (value,

growth) perform better or worse than the medium size and blend style. The last variables signal

the geographical areas the index is tracking and we can highlight that Europe, Latin America and

Asia suffer from higher tracking errors than the rest of the geographical areas. However, the

dummy for U.S is insignificant, even thought it was expected to be negative as it is usually easier

for funds located in the U.S to track national indices.

Finally, a lagged value of the tracking error is included in the regression to check whether there

is persistence in the data. The coefficient is positive and significant implying that when last


month tracking errors are 1% higher, this month’s error is likely to increase by 29 bp. This is

interesting an interesting result as it can help investors to get more efficient portfolios investing

in fund’s that have done good in the recent past regarding tracking errors.

6.1.3-ETF Price efficiency

In this subsection a very similar analysis than in the point above will be performed but using

relative price deviation as the dependent variable. Table 9 in appendix 2 shows the results of

these regressions. The first thing that can be appreciated is that fewer variables are significant;

this is due to the fact that price deviations are relatively small compared with tracking errors.

The variable Sampling dummy is significant in specifications 1 and 3 when only a few variables

are in the model, but when the extended model is used; it becomes insignificantly different from

0. However, it should caught attention the fact that it is negative, meaning that sampling

replication is less prone to deviations, just the opposite conclusion we extracted from last section

regarding tracking errors.

The important variables for price deviations are Divdummy, expense ratio, Small dummy and the

geographical dummies for the U.S and Asia. Divdummy is a peculiar case as it is first positive

but it becomes negative when including fixed effects. A negative number supposes that ETFs

that pay dividend have less deviation that the ones that not, when the opposite was expected. Age

is again significant implying that for each year the fund is in the market the deviation between

the market price and the NAV decreases by 1 bp which does not seem high, but it supposes 55%

of the average deviation.


The expense ratio is statistically and economically significant. The sign of the variable is

negative meaning that higher expenses cause smaller price deviations. This result is not in line

with much of the literature related with fund’s analysis as more expenses are usually linked with

poorer performance and higher price deviations. In this case an increase of 1% in the expense

ratio is associated with a reduction of price deviations of 3.5 bp; this value is economically

significant taking into account that the average price deviation is lower than 2 bp.

The variable lgTNA is insignificant as in the tracking error case signalling that the size of the

fund’s asset is completely irrelevant for both tracking errors and price deviations. Moreover, the

variable p_dev_lag is insignificant signalling that past deviations have no influence in

determining today’s deviations.

The dummy signalling small stocks is also significant and negative indicating that small stocks

have less price deviations. Regarding the geographic dummies, only the U.S and Asia dummies

are significant indicating a decrease in deviations when ETF’s track indices located in these areas.

Especially important seems the value of U.S dummy as ETFs tracking indices in these countries

experience deviations 12 bp lower when the average deviation is 1.8 bp.

6.2-LIETFs

6.2.1-Capital Asset Pricing Model test

In this part a CAPM test will be performed for LIETFs returns using equation 2 in section 4 of

this paper. The results of the regression are shown in specification 1 of table 10 in appendix 2. In

this case benchmark returns are not used, but the returns multiplied by the relevant LIETF

multiple (2, 3,-1-2,-3). As it can be deducted from table 10, LIETFs have serious problems to


track their index benchmarks. First of all, the Beta of the regression is equal to 0.97 that is not

equal to 1 when a t-test is performed (t-statistic of -5.71) although the final number is not that

distant from 1. But more interesting is the fact that the constant is negative and rather high

evidencing that LIETF have abnormal lower returns of 51 bp per month or 6.12% per year. This

result reassures the conclusion extracted from the sample description analysis (section 4.2.2) that

LIETFs underperform their benchmarks notably around 6% every year. Furthermore, the

underperformance is much larger than the average expense ratio of 0.08% per month, or 0.95%

per year, indicating that there are more variables that are responsible of the LIETFs

underperformance.

Following the methodology used for ETFs, a second specification is included in table 10 where

the expense ratio is added. In this case, the expense ratio does not absorb the negative value of

the intercept but makes it higher and insignificant. As a consequence, our previous conclusion

that expense ratio is not the source of the underperformance is confirmed.

CAPM is a long term model and as a consequence LIETFs perform badly as they are short term

products. Even when for many LIETFs investors this long term underperformance is not a source

of concern as their time horizons are usually a few months or shorter, the fact that the

underperformance is 51 bp per month can affect them notably. Regarding the goodness of fit, the

is 0.96 in both models meaning that the movements of the funds are almost completely

explained by movements in the multiplied indices. is nonetheless smaller than the normal

ETF case indicating that the benchmark returns have less explanatory power.


6.2.2-LIEFTs tracking errors

Given the vast underperformance and tracking errors LIETFs suffer, it is time to analyse which

factors are responsible for this fact. Table 11 in appendix 2 shows a selection of regressions

performed using tracking errors as the dependent variable. The presence of variables is smaller

than the ETF case as for some variables there was no data available (turnover), others were not

applicable to LIETFs (sampling dummy as all LIETFs use synthetic replication) and selected

funds were less disperse geographically and among providers (only two providers Proshares and

Direxion).

First, expense ratio is significant when only a few variables are in the model but becomes

insignificant when using the extended model; this confirms the conclusion of section 6.2.1 that

the expense ratio is not an essential variable for tracking efficiency in LIETFs.

The variable liquidity5 is positive and significant indicating that more liquid LIETFs suffer from

higher tracking errors which is an unusual conclusion. This is supported with the negative but

insignificant sign (with date fixed effects) of the Amihud variable, indicating that illiquid stocks

have smaller tracking errors. This result is unusual but it can be due to the fact that holders of

these funds are short term speculative investors, when they expect high volatility they take

higher positions in these funds increasing liquidity and volatility that is associated with higher

tracking errors.

Other relevant variables are divdummy that signals that, when funds pay dividends, they have 43

bp higher monthly tracking errors that funds that not. This value is critical because it supposes 31%

of the average tracking error and 49% of the median. Furthermore, it is economically and

5 It is formally defined as the ETF/LIETF turnover ratio but in this paper it is given that name to avoid possible

confusions with the other turnover variable.


statistically significant. The age of the fund also matters, each year the fund is in the market

monthly tracking errors are reduced by 20 bp indicating that experience is an important factor in

order to get better results. As in the ETF case, lgTNA is not significant.

Regarding our model’s dummies, firstly, style and size dummies matter, being Large Blend

stocks the ones the offer better performance translated in lower tracking errors. Also the

Proshares dummy, that indicates when a fund pertains to the Proshares family, is significant and

negative signalling that Proshares funds have lower tracking errors of 54 bp in monthly terms (40%

the average) than Direxion’s Funds.

I have also included a specific variable in this regression that indicates whether a fund is a

leveraged fund or an inverse fund called inverse dummy. Its positive sign indicates that inverse

funds perform worse than common leveraged funds. This is probably due to the fact that inverse

multiples are more difficult and costly to achieve.

Finally, Developed dummy signals that indices located in developed countries have less tracking

errors, being even lower in the U.S and higher in Asia. These coefficients are very high

(developed dummy supposes 62% of the average tracking errors and U.S 52%) indicating that

LIETFs tracking indices in developed countries have much better performance, especially in the

U.S.

Like in the normal ETF case, it seems that there is persistence in the tracking errors as shown by

the t_error_ lag variable. The coefficient is reasonably relevant ( 1% increase in last month

tracking errors causes and increase of 18 bp today) in explaining current errors but lower than

the normal ETF case.


6.2.3-LIETFs price efficiency

It is time to look now to the price deviations of LIETFs, if a similar regressions as in the section

above is performed, we get the results shown in table 12 of appendix 2. As commented in the

sample description, the price deviations are low so it is not expected to find many relevant

variables. Only 4 variables and the constant are significant in specification 4 of table 12, giving

the other specifications similar results. Expense ratio is the most important determinant of price

deviations as it supposes a substantial part of the total deviations. As in the ETF case, its

coefficient is negative meaning that higher expenses cause lower deviations between market

price and NAV which, as commented before, is an unexpected result that should be analyse more

intensively in future research.

Fund Age is again significant and negative indicating that older funds are more efficient in

reducing deviations. Small based indices seem to have smaller pricing errors with similar

conclusions than in the general ETF case. Finally, inverse funds seem to have higher deviations

as their assets are more complex which can make more difficult to keep prices differences low.


7-Conclusions

In this thesis, I investigated whether ETFs and LIETFs are efficient products substitute for

market indices, or multiples of the market indices, around the globe and which factors are

responsible for the mismatches in the tracking and pricing functions.

Summary statistics showed that ,in general, both ETFs and LIETFs, seem to be rather efficient in

keeping their market prices close to their NAV. Price deviations are on average only 1.8 bp

(premium) for normal ETFs and -2,1 bp (discount) for LIETFs. On the other hand, both ETFs

and LIETFs seem to have more problems when replicating the returns of their target indices with

considerable average annual tracking errors of 2.4% for ETFs and 16.5% for LIETF. It is true

that for LIETFs investors these tracking errors are less important as these products are usually

held for short time periods (typically a few months). Even when this is true, average monthly

tracking errors of 1.38% are still too high to be ignored.

After this, a CAPM test was performed to check whether the returns of ETFs and LIETFs track

correctly the returns of the benchmarks. I confirmed previous results as both ETFs and LIETFs

have negative alphas with values near their average underperformance. Even when their betas are

relatively near to 1 (0.99 for ETFs and 0.97 for LIETFs) their alphas indicate that these products

have underperformance inherent in their construction. In the case of ETFs, expense ratio is

responsible of much of the underperformance, but in the LIETFs case expense ratio alone does

not explain much of it.

Once it has been checked that ETFs and LIETFs have problems replicating their respective

indices, it was time to analyse the reasons behind tracking errors. We could check that both type

of funds had several variables that helped to explain their tracking errors like illiquidity,


dividends, age, turnover and geographical dummies among others. One of the main hypotheses

of this paper is that the type of replication matters for ETF’s tracking errors; this is true as

sampling replication has higher tracking errors of almost 50 bp per year compared with physical

replication strategies. This value, however, is rather low tacking into account that the average

annual tracking error is 2.4%. Due to all of this, I conclude that the method of replication matters

for the tracking errors but economically it does not suppose an important difference. Moreover,

the expense ratio seems to have less economic importance in explaining tracking errors for both

ETFs and LIETFs. Finally, it seems that there is a significant persistence in tracking errors as

the lagged value is statistically significant with a considerable coefficient. This signals that funds

with high tracking errors in the near past tend to perform worse.

Then, a price deviation analysis was performed finding that the expense ratio and the fund’s age

explain much of the variability of both ETFs and LIETFs, being also significant for ETFs other

variables like the spread, dividend dummy and some geographical (U.S, Asia) and investment

style dummies (Small). Moreover for LIETFs, inverse funds perform worse than simple

leveraged funds. Furthermore, for both ETFs and LIETFs, the expense ratio is negative

indicating that funds with higher expense ratio perform better in terms of price deviations. This

result suggests that more expensive funds are better in adjusting the market price to the value of

the fund’s assets when the opposite was expected. I arrive to the conclusion that the creation-

redemption process works properly for ETFs and LIETS and that when misprices occur they are

small and short lived.

In general, and after this research, I can affirm that in general ETFs are good index trackers but

suffer from natural underperformance of around 50 bp per year, much of it due to management


fees. This underperformance can be important because holders of ETF funds are usually long

term investors that practise a passive investment approach. An underperformance of 50 bp per

year can become much higher when accruing for long periods of time if mean-reversion does not

happen (on average it seems that it does not happen with much intensity). When pursuing a long

term investment it is necessary to do research about funds and choose the ones with the

following characteristics: good liquidity, experience in the market, no dividends, low expense

ratio, low tracking errors in the past , low turnover and with physical replication. If investors

choose funds with these characteristics is very likely that they outperform other similar portfolios.

Leveraged/Inverse funds have shown to be a very bad investment, especially for longer periods

of time. Their monthly underperformance is near 50 bp per month, which is even worrying for

short term investors with investment horizons of some months. With LIETFs is even more

important to choose the correct fund than for ETFs. In general investors should follow our

previous recommendation for ETFs but trying to buy funds that track large and blend indices

based in the U.S if they want to minimize their tracking errors. It is also recommendable to avoid

inverse exchange-traded funds as their performance is worse than general leveraged funds. Based

on this we can reaffirm the conclusions of Li, Wang and Zhang (2009) that LIETFs are not long

term substitutes for long or short positions in an index.

Taking into account all this conclusions it would interesting for investors to have some kind of

measure that help them to choose the funds with the best performance concerning tracking errors.

For this measure I would suggest the creation of a star-based index similar to the Morginstar star

rating. This rating uses past information of return and risk and compares it with peers in specific

investment categories. Then, given the results, funds are assigned a stars-based ranking


depending on their position in the distribution compared with other similar funds. The

distribution of starts is based as following: 10% of funds within each category receive 5 stars,

22.5% receive 4 stars, 35% receive 3 stars, 22.5% receive 2 stars, and 10% receive 1 star. I

would suggest the creation of a new a star-base rating that would be constructed using the

methodology explained above for all the variables that this paper has found relevant6. Then, the

final fund rating would be calculated using the average of all the individual variable’s rating.

This measure would improve the existing rating considerably, giving investors a very good ETF

and LIETF performance-based indicator that is guaranteed to minimize tracking errors.

6 Expense ratio, past tracking errors, liquidity measures (Amihud, spread, liquidity), dividends, turnover ,sampling

replication, fund age and index location.


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exchange-traded funds and closed-end country funds. Journal of International Financial Markets,

Institutions and Money, 16(2), 104-122.

Haubrich, J. G. (1994). Risk aversion, performance pay, and the principal-agent

problem. Journal of Political Economy, 258-276.

Lu, L., Wang, J., & Zhang, G. (2009). Long Term Performance of Leveraged ETF. working

paper series.


Malkiel, B. G. (1995). Returns from investing in equity mutual funds 1971 to 1991. The Journal

of Finance, 50(2), 549-572.

Markowitz,H.M.(1952), Portfolio Selection, Journal of Finance,Vol.7, No.1, page 77-91.

Pontiff, J. (1996). Costly arbitrage: Evidence from closed-end funds. The Quarterly Journal of

Economics, 1135-1151.

Ramaswamy, S. (2011). Market structures and systemic risks of exchange-traded funds (No.

343). Bank for International Settlements.

Rompotis, G. G. (2009). Interfamily competition on index tracking: The case of the vanguard

ETFs and index funds. Journal of Asset Management, 10(4), 263-278.

Williams,O (2012), Country ETF Currency Exposure and International Diversification (June 11,

2012). Available at SSRN 2081981.

Williams,O (2014) “Physically versus Synthetically Replicated Trackers. Is There a Difference

in Terms of Risk? Available at http://williamsmarketanalytics.com/research/.

Internet Sources

http://www.morningstar.com/Cover/ETFs.aspx

http://www.etf.com/

http://www.blackrockinternational.com/home

http://www.ishares.com/global/

https://pressroom.vanguard.com/nonindexed/6.14.2013_Understanding_Synthetic_ETFs.pdf

http://williamsmarketanalytics.com/research/

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http://www.blackrockinternational.com/home

http://www.ishares.com/global/

https://pressroom.vanguard.com/nonindexed/6.14.2013_Understanding_Synthetic_ETFs.pdf


Appendix 1: Figures

Figure1: This figure shows the evolution of ETP assets under management since 2000 until September 2012. Source: Blackrock semi-annual ETP handbook 2012.

Figure 2: This figure shows the evolution of ETP number of funds since 2000 until September 2012. Source: Blackrock semi-annual ETP handbook 2012.

2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011sep-12

Other ETF 5.1 3.9 4.1 6.3 9.3 15.9 32.5 54.6 61.2 119.7 171.3 173.5 201.3

ETF Total 74.3 104.8 141.6 212 309.8 412.1 565.6 796.7 711.1 1036 1311 1351 1644

0

200

400

600

800

1000

1200

1400

1600

1800

2000

Ass

ets

un

de

r m

anag

em

en

t (U

S $

Bn

)

ETP Global Development. Assets (US $Bn)

2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011sep-12

Other ETPs 14 17 17 18 21 63 170 371 625 750 1083 1300 1451

ETFs 92 202 280 282 336 461 713 1170 1595 1944 2460 3011 3297

0

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

Nu

mb

er

of

ETP

s

ETP Global Development. Number of funds


Figure 3: This figure shows ETF providers value of assets as September 2012. . Source: Blackrock semi-annual ETP handbook 2012.

Figure 4: This figure shows the evolution of ETP number of funds in the U.S since 2000 until September 2012. Source: Blackrock semi-annual ETP handbook.

0

100

200

300

400

500

600

700

800

ETF provider by assets(US $Bn)

2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011sep-12

Other ETF 5 3.8 4 6.1 8.9 14.4 25.9 40.5 45.3 88.1 120.8 121.4 142.2

ETF Total 65.6 84.6 102.3 150.7 227.7 299.4 406.8 580.7 497.1 705.5 891 940.4 1159

0

200

400

600

800

1000

1200

1400

Ass

ets

un

de

r m

anag

em

en

t (U

S $

Bn

)

ETP U.S Development. Assets (US $Bn)


Figure 5: This figure shows ETF providers value of assets in the U.S as September 2013. . Source: Blackrock semi-annual ETP handbook.

Figure 6: This figure shows the creation-redemption process for normal ETFs. This image is taken from Ramaswamy(2011)

0

100

200

300

400

500

600

ETF provider by assets in the U.S (US $Bn)


Appendix 2: Tables Table 1: This table shows the benchmark indices of selected ETFs used in the dataset. . The list only contains equity indices replicated by the selected ETF in the dataset.

Benchmark Indices Benchmark Indices

Dow Jones Global Select Real Estate Securities Index Nasdaq Composite

Dow Jones Broad Stock Market NASDAQ OMX Global Agriculture Index

Dow Jones Global Select Dividend Index Benchmark Indices2

Dow Jones Industrial Average NYSE Arca Steel Index

Dow Jones Select micro-cap Russell 1000

Dow Jones U.S. Large-Cap Total Stock Market Index Russell 1000 Growth Dow Jones US Russell 1000 Value

DJ US Financials Russell 2000

Eurostoxx 50 Russell 2000 growth

FTSE AW ex U.S Russell 2000 value

FTSE China 25 Russell 3000

FTSE China HK Russell 3000

FTSE Developed Asia Russell 3000 Growth FTSE Developed Europe Russell 3000 Value

FTSE developed ex North America Russell micro cap

FTSE Developed Small Cap ex-North America Index Russell Mid Cap

FTSE Dev ex U.S Russell Mid Cap Growth

FTSE Emerging Russell Mid Cap Value

FTSE Global all cap Russell Top 50 Mega Cap

FTSE Nordic 30 Index Russell/Nomura Prime Japan

FTSE RAFI Developed ex U.S. Index Russell/Nomura Small cap FTSE RAFI Developed ex U.S. Mid Small 1500 Index S&P SmallCap 600® Pure Growth Index Total Return

FTSE RAFI US 1000 Index S&P 100

MSCI ACWI S&P 1500

MSCI Asia ex Japan S&P 500

MSCI All Country World Index ex USA Index S&P 500® High Quality Rankings Index

MSCI Austria Investable Market Index (IMI) 25/50 S&P 500 equal weighted

MSCI Astralia S&P 500 growth MSCI Brazil 25/50 Index S&P 500 value

MSCI Belgium Investable Market Index (IMI) 25/50 S&P 500® Pure Value Index Total Return

MSCI BRIC S&P Asia Pacific Emerging

MSCI Canada S&P BRIC 40

MSCI Chile Investable Market Index (IMI) 25/50 S&P China BMI

MSCI EAFE S&P completion index

MSCI EAFE Growth S&P Developed Ex-U.S.BMI Index

MSCI EAFE Small Cap S&P developed ex-U.S. under USD 2 billion MSCI EAFE Value S&P Emerging Markets

MSCI EM Eastern Europe S&P Emerging Markets Under USD2 Billion Index

MSCI Emerging Markets S&P Europe 350

MSCI EMU S&P Global 100

MSCI France S&P Global 1200 Energy Sector Index

MSCI Germany S&P Global 1200 SEC/Cons Disc

MSCI Honk Kong S&P Global 1200 SEC/Cons Staples

MSCI Italy 25/50 Index S&P Global 1200 SEC/Financials MSCI Japan S&P Global 1200 SEC/Health Care Index

MSCI Japan Small Cap S&P Global 1200 SEC/Industrials

MSCI Kokusai Index S&P Global 1200 SEC/Info Tech

MSCI Malaysia S&P Global 1200 SEC/Utilities

MSCI Mexico Capped ETF S&P Global 1200 Telecom Index Svcs

MSCI Netherlands Investable Market Index S&P Global Water Index

MSCI Pacific ex Japan S&P International Developed High Quality Rankings Index MSCI Singapore S&P Latin America

MSCI South Africa S&P MidCap 400

MSCI South Korea Capped ETF S&P midcap 400 growth

MSCI Spain 25/50 Index S&P midcap 400 value

MSCI Sweden S&P Small Cap 600

MSCI Switzerland 25/50 Index S&P Small-Cap 600 growth

MSCI Taiwan S&P Small-Cap 600 value

MSCI UK S&P SmallCap 600® Pure Value Index MSCI US Broad Market Stoxx Euro 50

Nasdaq 100 Stoxx Europe Select Dividend

The Global Dow


Table 2: This table shows the number of funds and providers included in the dataset from January 2006 to January 2013. The list only contains selected equity ETFs based in the U.S that follow the conditions explained in section 5.1 of this paper.

Normal ETFs Number

ishares 74

SPDR 26

Vanguard 9

Power Shares 6

Guggenheim 6

First Trust 4

Schwab 3

Fidelity 1

Global X 1

Market vectors 1

Revenue Shares 1

Total Normal 133

Leveraged/Inverse ETFs

Proshares 48

Direxion 13

Total 61

Table 3: This table provides descriptive information on the sample of ETFs including the mean, the standard deviation, the coefficient of variation, the most important percentiles and the number of observations. The process to obtain the data and the variables is described in section 5.1. For a more detailed description of the variables please look in appendix 3: List of variables and definitions.

dvolume 66862.1 481541 7.202002 337.1285 1572.763 9264.33 10626

volume 824.7024 4388.375 5.321162 7.24 33.3635 207.559 10626

Cash .2535084 1.628202 6.422673 .05 .19 .43 10626

FundAge 11.93111 3.968459 .3326143 8 13 14 10626

spread .0876586 .1682388 1.919251 .02 .04001 .1 10626

liquidity .0065189 .0249801 3.831963 .0014506 .0025715 .0053533 10626

Amihud .0002167 .0008891 4.10315 2.81e-06 .0000183 .000102 10626

turnover .1789008 .1643974 .9189307 .07 .12 .24 10626

exp .0003353 .0001543 .4600741 .0002083 .0003333 .00045 10626

TNA 3636268 1.05e+07 2.882269 154200 606000 2723200 10626

liquidity .0065189 .0249801 3.831963 .0014506 .0025715 .0053533 10626

Cash_div .0917682 .2509075 2.734144 0 0 0 10626

t_error .0020353 .0033568 1.649273 .0002204 .0006174 .0021453 10626

p_dev_rel .0001825 .0051954 28.47522 -.0015779 0 .0021704 10626

p_dev .0096691 .2434965 25.183 -.08 0 .096 10626

BReturn .0081218 .0612476 7.541168 -.0211169 .0132563 .0428084 10626

return .0077253 .0610366 7.900878 -.021873 .0128935 .042191 10626

variable mean sd cv p25 p50 p75 N


Table 4: This table shows the correlation between selected variables for ETFs. For a more detailed description of the variables please look in appendix 3: List of variables and definitions.

Table 5: This table provides descriptive information on the sample of LIETFs including the mean, the standard deviation, the coefficient of variation, the most important percentiles and the number of observations. The process to obtain the data and the variables is described in section 5.1. For a more detailed description of the variables please look in appendix 3: List of variables and definitions.

Cash -0.0135 -0.0115 -0.0089 0.0149 0.0086 -0.0120 -0.0493 0.0820 0.0005 0.0094 0.0301 0.0116 1.0000

FundAge 0.0054 0.0057 -0.0870 -0.2260 0.0236 0.0651 0.2338 -0.1127 -0.0636 -0.1989 -0.1846 1.0000

spread -0.0595 -0.0598 0.0712 0.1434 -0.0153 -0.0143 -0.1111 0.1660 0.0570 0.3286 1.0000

Amihud -0.0225 -0.0240 0.0286 0.1357 -0.0318 -0.0403 -0.0823 0.0848 0.1807 1.0000

turnover 0.0260 0.0244 -0.0178 0.0185 -0.0576 -0.0411 -0.1284 0.0435 1.0000

exp -0.0060 -0.0022 0.0024 0.1589 -0.0704 0.0318 -0.2416 1.0000

TNA 0.0164 0.0157 -0.0177 -0.0691 0.0732 0.1674 1.0000

liquidity -0.0139 -0.0135 0.0088 0.0511 0.0089 1.0000

Cash_div 0.0123 0.0108 0.0211 0.0088 1.0000

t_error -0.0230 -0.0200 0.0231 1.0000

p_dev_rel 0.0719 0.0694 1.0000

BReturn 0.9980 1.0000

return 1.0000

return BReturn p_dev_~l t_error Cash_div liquid~y TNA exp turnover Amihud spread FundAge Cash

dvolume 23178.87 74321.69 3.206442 107.6545 679.5583 10398.41 4222

volume 623.7253 2056.299 3.296802 2.724 15.801 261.564 4222

Cash 63.30393 100.2527 1.583673 .04 31.69 100.7 4222

FundAge 6.721696 1.023069 .152204 6 7 7 4222

spread -.1265095 .2589781 -2.047104 -.14 -.05 -.02 4220

liquidity .0419307 .0801043 1.910395 .0062369 .0154678 .0455303 4220

Amihud .0026813 .0179354 6.688975 5.23e-06 .0000809 .0007032 4220

exp .0007946 .0000405 .0509528 .0007917 .0007917 .0007917 4200

TNA 244872.3 488416.5 1.994576 13200 43700 254500 4222

liquidity .0419307 .0801043 1.910395 .0062369 .0154678 .0455303 4220

Cash_div .163864 1.82114 11.11373 0 0 0 4222

t_error .0137687 .0209204 1.519418 .002742 .0064156 .0145822 4222

p_dev_rel -.0002124 .0035884 -16.8972 -.0016002 -.0000128 .0012407 4222

p_dev -.0099929 .2055177 -20.56631 -.07 -.00055 .045 4222

m_bench -.0028892 .1210361 -41.89207 -.0721382 -.0057228 .0682582 4222

return -.0078801 .1203608 -15.27402 -.076818 -.012121 .062934 4222

variable mean sd cv p25 p50 p75 N


Table 6: This table shows the correlation between selected variables for LIETFs. For a more detailed description of the variables look at the appendix 3: List of variables and definitions.

Table 7: This table shows the regressions results using a CAPM model for Exchanged Traded Funds. The formula is the following: ( ) . The variable Beta is of the CAPM model, being the constant . In specification 2 we use the same formula than specification 1 but adding the variable monthly expense ratio (exp) being the formula used: ( ) .

(1) (2)

VARIABLES CAPM CAPM with exp

BenchmarkTbill 0.9945*** 0.9945***

(0.001) (0.001)

exp -1.5228***

(0.284)

Constant -0.0004*** 0.0002

(0.000) (0.000)

Observations 10,626 10,626

R-squared 0.996 0.996

Date FE NO NO

Provider FE NO NO

Adjusted R-squared 0.996 0.996

F test 1.473e+06 735186

Prob > F 0 0

Robust standard errors in parentheses

*** p<0.01, ** p<0.05, * p<0.1

Cash -0.1246 -0.1360 0.0377 0.0733 0.0067 -0.1728 -0.2216 -0.0590 -0.0312 -0.0978 0.0322 0.0394 -0.0595 1.0000

FundAge -0.0420 -0.0423 0.0119 -0.0198 -0.3403 -0.0362 -0.0295 0.3278 -0.2380 -0.3643 -0.1258 0.0827 1.0000

spread 0.1387 0.1374 -0.0395 -0.0184 -0.1212 0.0207 0.2077 0.2195 0.0292 0.0323 -0.1173 1.0000

Amihud 0.0533 0.0440 0.0009 0.0153 -0.1285 -0.0389 -0.2214 -0.1980 -0.0460 -0.1417 1.0000

turnover 0.0585 0.0604 -0.0124 -0.0164 0.1834 0.0467 0.3444 -0.0632 0.0440 1.0000

exp 0.0178 0.0194 -0.0296 -0.0330 0.0430 0.0342 -0.0636 -0.1057 1.0000

TNA -0.0235 -0.0174 -0.0282 -0.0609 -0.0376 -0.0215 0.3287 1.0000

liquidity 0.0218 0.0285 -0.1111 -0.1077 0.0071 0.0188 1.0000

Cash_div 0.0545 0.0394 0.0048 0.0004 0.1136 1.0000

t_error -0.0635 -0.0477 0.0707 0.0506 1.0000

p_dev_rel -0.0651 -0.0670 0.8807 1.0000

p_dev -0.0366 -0.0297 1.0000

m_bench 0.9882 1.0000

return 1.0000

return m_bench p_dev p_dev_~l t_error Cash_div liquid~y TNA exp turnover Amihud spread FundAge Cash


Table 8: This table shows the empirical results for ETFs from a regression being the tracking errors the dependent variable. For a description of the variables please look at appendix 3: list of variables. The third and fourth specifications have time fixed effects and provider fixed effects which suppose one dummy variable per fund family and month.

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

VARIABLES Tracking error Tracking error Tracking error Tracking error

t_error_lag 0.2871*** 0.2807***

(0.018) (0.018)

Amihud 0.2186*** 0.1994*** (0.057) (0.058)

Liquidity 0.0051 0.0036

(0.003) (0.003) Spread 0.0811*** 0.0155** 0.0543*** -0.0027

(0.012) (0.007) (0.010) (0.009)

lgTNA -0.0000* -0.0000 (0.000) (0.000)

Cash -0.0000 -0.0000

(0.000) (0.000) Divdummy -0.0001 0.0001 -0.0002* 0.0003**

(0.000) (0.000) (0.000) (0.000)

FundAge -0.0001*** -0.0001*** (0.000) (0.000)

exp 2.9609*** 2.8806*** 3.0231*** 2.9139***

(0.250) (0.450) (0.256) (0.444) Turnover 0.0007*** 0.0006**

(0.000) (0.000)

Samplingdummy 0.0001 0.0003* 0.0001 0.0004** (0.000) (0.000) (0.000) (0.000)

LargeDummy 0.0001 0.0000

(0.000) (0.000) SmallDummy -0.0001 -0.0001

(0.000) (0.000)

ValueDummy -0.0001* -0.0001* (0.000) (0.000)

GrowthDummy -0.0001* -0.0001

(0.000) (0.000)

USDummy -0.0000 -0.0001

(0.000) (0.000)

EuropeDummy 0.0004** 0.0006*** (0.000) (0.000)

NorthAmericaexUSDu

mmy

-0.0000 0.0001

(0.000) (0.000)

LatinAmericaDummy 0.0012*** 0.0013***

(0.000) (0.000) AsiaDummy 0.0005*** 0.0007***

(0.000) (0.000)

OceaniaDummy -0.0001 0.0001 (0.000) (0.000)

AfricaDummy -0.0009*** -0.0008***

(0.000) (0.000) WorldDummy 0.0000 0.0001

(0.000) (0.000) Constant 0.0009*** 0.0010** 0.0009*** 0.0007

(0.000) (0.000) (0.000) (0.000)

Observations 10,626 10,472 10,626 10,472

R-squared 0.040 0.325 0.068 0.347

Date FE NO NO YES YES Provider FE NO NO YES YES

Adjusted R-squared 0.0393 0.323 0.0596 0.339

F test 65.26 97.91 66.37 96.31 Prob > F 0 0 0 0


*** p<0.01, ** p<0.05, * p<0.1


Table 9: This table shows the empirical results for ETFs from a regression being the price deviation the dependent variable. For a description of the variables please look at appendix 3: list of variables. The third and fourth specifications have time fixed effects and provider fixed effects which suppose one dummy variable per fund family and month.

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

VARIABLES Price deviation Price deviation Price deviation Price deviation

p_dev_lag 0.0035 0.0050

(0.006) (0.006)

Amihud -0.0408 0.0277 (0.097) (0.103)

Liquidity 0.0053 0.0063*

(0.004) (0.003) Spread 0.0734*** 0.0496*** 0.0530*** 0.0196

(0.018) (0.017) (0.016) (0.016)

lgTNA -0.0000 -0.0000 (0.000) (0.000)

Cash -0.0000* -0.0000

(0.000) (0.000) Divdummy 0.0005*** 0.0007*** -0.0008*** -0.0004**

(0.000) (0.000) (0.000) (0.000)

FundAge -0.0000* -0.0001*** (0.000) (0.000)

exp -0.0306 -2.7651*** -0.4377 -3.5169***

(0.344) (0.794) (0.323) (0.691) Turnover -0.0002 0.0008*

(0.000) (0.000)

Samplingdummy -0.0006*** -0.0001 -0.0007*** -0.0002 (0.000) (0.000) (0.000) (0.000)

LargeDummy -0.0001 -0.0000

(0.000) (0.000) SmallDummy -0.0003* -0.0003**

(0.000) (0.000)

ValueDummy 0.0001 0.0000 (0.000) (0.000)

GrowthDummy 0.0000 -0.0002

(0.000) (0.000)

USDummy -0.0012*** -0.0012***

(0.000) (0.000)

EuropeDummy -0.0002 -0.0000 (0.000) (0.000)

NorthAmericaexUSDu

mmy

0.0000 0.0001

(0.001) (0.000)

LatinAmericaDummy 0.0002 0.0002

(0.000) (0.000) AsiaDummy -0.0007** -0.0008***

(0.000) (0.000)

OceaniaDummy -0.0007 -0.0007 (0.001) (0.001)

AfricaDummy 0.0007 0.0006

(0.001) (0.001) WorldDummy 0.0004 0.0005**

(0.000) (0.000) Constant 0.0004*** 0.0025*** 0.0010*** 0.0033***

(0.000) (0.001) (0.000) (0.001)

Observations 10,626 10,472 10,626 10,472

R-squared 0.009 0.027 0.203 0.224

Date FE NO NO YES YES Provider FE NO NO YES YES

Adjusted R-squared 0.00872 0.0242 0.195 0.215

F test 16.68 10.74 17.08 12.62 Prob > F 0 0 0 0


*** p<0.01, ** p<0.05, * p<0.1


Table 10: This table shows the regressions results using a CAPM model for Leveraged/Inverse Exchanged Traded Funds. The formula is the following formula ( ) .The variable mBeta is the of the CAPM model, being the constant . In specification 2 we use the same formula than specification 1 but adding the variable monthly expense ratio (exp) being the formula: ( ) .

(1) (2)

VARIABLES CAPM CAPM with exp

mBeta 0.9739*** 0.9721***

(0.005) (0.005)

exp 2.1314

(6.894)

Constant -0.0051*** -0.0068

(0.000) (0.006)

Observations 4,222 4,200

R-squared 0.959 0.959

Date FE NO NO

Provider FE NO NO

Adjusted R-squared 0.959 0.959

F test 45209 22514

Prob > F 0 0


*** p<0.01, ** p<0.05, * p<0.1


Table 11: This table shows the empirical results for LIETFs from a regression being the tracking errors the dependent variable. For a description of the variables please look at appendix 3: list of variables. The third and fourth specifications have time fixed effects.

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

VARIABLES Tracking error Tracking error Tracking error Tracking error

t_error_lag 0.2166*** 0.1791***

(0.025) (0.026)

Amihud -0.0309*** -0.0078 (0.008) (0.005)

Liquidity 0.0477*** 0.0288***

(0.009) (0.005) Spread -0.7534*** -0.5998*** -0.3227*** -0.1806

(0.132) (0.133) (0.115) (0.112)

Cash -0.0000 -0.0000 (0.000) (0.000)

lgTNA 0.0001 0.0001

(0.000) (0.000) Divdummy 0.0044*** 0.0052*** 0.0023* 0.0043***

(0.001) (0.001) (0.001) (0.001)

FundAge -0.0012*** -0.0020*** (0.000) (0.000)

exp 19.8436*** 3.4812 20.9418*** -2.3907

(5.596) (5.440) (4.559) (4.604) LargeDummy -0.0023*** -0.0020***

(0.001) (0.001)

SmallDummy -0.0012* -0.0003 (0.001) (0.001)

ValueDummy 0.0022*** 0.0022***

(0.001) (0.001) GrowthDummy 0.0014** 0.0015***

(0.001) (0.001)

Prosharesdummy -0.0039*** -0.0054*** (0.001) (0.001)

InverseDummy 0.0057*** 0.0053*** 0.0052*** 0.0051***

(0.001) (0.001) (0.001) (0.001)

DevelopedDummy -0.0235*** -0.0079*** -0.0244*** -0.0086***

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

USDummy -0.0078*** -0.0072*** (0.001) (0.001)

EuropeDummy -0.0002 -0.0002

(0.004) (0.003) LatinAmericaDummy 0.0047 0.0047

(0.004) (0.004)

AsiaDummy 0.0053*** 0.0065*** (0.002) (0.002)

Constant 0.0124*** 0.0232*** 0.0139*** 0.0370***

(0.005) (0.006) (0.004) (0.005)

Observations 4,198 4,127 4,198 4,127

R-squared 0.188 0.363 0.396 0.521 Date FE NO NO YES YES

Adjusted R-squared 0.187 0.360 0.382 0.508 F test 93.23 49.60 97.01 60.34

Prob > F 0 0 0 0


*** p<0.01, ** p<0.05, * p<0.1


Table 12: This table shows the empirical results for LIETFs from a regression being the price deviation the dependent variable. For a description of the variables please look at appendix 3: list of variables. The third and fourth specifications have time fixed effects.

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

VARIABLES Price deviation Price deviation Price deviation Price deviation

p_dev_lag -0.0080 -0.0089

(0.015) (0.015)

Amihud -0.0023 -0.0021 (0.002) (0.002)

Liquidity -0.0022* -0.0021*

(0.001) (0.001) Spread 0.0036 -0.0026 -0.0019 -0.0030

(0.023) (0.026) (0.027) (0.031)

Cash 0.0000 0.0000 (0.000) (0.000)

lgTNA 0.0000 0.0001

(0.000) (0.000) Divdummy 0.0001 0.0001 0.0000 -0.0000

(0.000) (0.000) (0.000) (0.000)

FundAge -0.0001* -0.0002** (0.000) (0.000)

exp -1.9789** -2.6678*** -2.0302** -2.7501***

(0.885) (1.023) (0.835) (0.976) LargeDummy -0.0000 -0.0000

(0.000) (0.000)

SmallDummy -0.0005** -0.0005** (0.000) (0.000)

ValueDummy -0.0001 -0.0001

(0.000) (0.000) GrowthDummy 0.0001 0.0002

(0.000) (0.000)

Prosharesdummy 0.0001 0.0001 (0.000) (0.000)

InverseDummy 0.0004*** 0.0004** 0.0004*** 0.0003**

(0.000) (0.000) (0.000) (0.000)

DevelopedDummy -0.0004*** -0.0004* -0.0004*** -0.0004

(0.000) (0.000) (0.000) (0.000)

USDummy 0.0003 0.0002 (0.000) (0.000)

EuropeDummy -0.0006 -0.0007

(0.001) (0.001) LatinAmericaDummy -0.0001 -0.0001

(0.000) (0.000)

AsiaDummy -0.0000 -0.0001 (0.000) (0.000)

Constant 0.0015** 0.0024** 0.0016** 0.0026**

(0.001) (0.001) (0.001) (0.001)

Observations 4,198 4,127 4,198 4,127

R-squared 0.006 0.011 0.020 0.026 Date FE NO NO YES YES

Adjusted R-squared 0.00433 0.00605 -0.00224 7.59e-05 F test 6.218 2.657 6.746 2.824

Prob > F 9.43e-06 0.000119 2.86e-06 2.70e-05


*** p<0.01, ** p<0.05, * p<0.1


Appendix 3: List of variables and definitions

is the market price of the fund i at the end of the month t. Data in U.S dollars.

the Net Asset Value of fund i assets at time t. Data in U.S dollar.

: the NAV monthly returns.

: the index benchmark monthly returns.

the leveraged fund’s promised multiple. For common ETF this number is 1.

|

|

Cash: Percentage of the fund’s TNA kept in cash in a month.

Cash_div: Amount in U.S dollars paid by the fund as cash dividends.

Divdummy: Dummy that signals if the fund has paid any cash dividend during the month.

dVolume: Average value of the shares traded in a month. Data is in thousands U.S dollars.

Exp Ratio: Expense Ratio as of the most recently completed fiscal year. Ratio of total

investment that shareholders pay for the fund’s operating expenses, which include 12b-1 fees. It

is calculated as the year expense ratio divided by 12. Data is in decimal format.

FundAge: Amount of years passed since the creation of the fund.

lgTNA: Natural Logarithm of the Total Net Assets of the fund at the end of the month.


It is formally defined as the ETF/LIETF turnover ratio but it is given this name to

avoid possible confusions with the other turnover variable. Its formula is:

( )

p_dev_lag: One lagged value in the relative price deviation.

Samplingdummy: Signals when the fund follows a sampling replication strategy.

(

)

TNA: Total Net Assets of the fund in thousand US dollars.

√( )

t_error_lag: One lagged value in the tracking error.

Turnover: Fund Turnover Ratio. Minimum of aggregated sales or aggregated purchases of

securities divided by the average 12-month Total Net Assets of the fund.

Volume: Amount of shares trade in a month. Data is in thousands of observations.

LargeDummy: Signals when the benchmark index is formed mainly by stocks with large

capitalizations as defined by the Morginstar grid.

SmallDummy: Signals when the benchmark index is formed mainly by stocks with small

capitalizations as defined by the Morginstar grid.

ValueDummy: Signals when the benchmark index is mainly formed by value stocks as defined

by the Morginstar grid.


GrowthDummy: Signals when the benchmark index is mainly formed by growth stocks as

defined by the Morginstar grid.

USDummy: Signals when the index tracked by the fund is based in the United States.

EuropeDummy: Signals when the index tracked by the fund is based in Europe.

NorthAmericaexUSDummy: Signals when the index tracked by the fund is based in North

America expecting United States.

LatinAmericaDummy: Signals when the index tracked by the fund is based in Latin American

countries.

AsiaDummy: Signals when the index tracked by the fund is based in Asia.

OceaniaDummy: Signals when the index tracked by the fund is based in Oceania.

AfricaDummy: Signals when the index tracked by the fund is based in Africa.

WorldDummy: Signals when the index tracked consists of a portfolio of world stocks.

DevelopedDummy: Signals if the fund pertains to an index located in a developed country as

defined by Morginstar.

Prosharesdummy: Indicates if the LIETF bellows to the Proshares family.

InverseDummy: Signals if the LIETF is an inverse fund.

master thesis: the efficiency of exchange-traded funds as

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