master thesis: the efficiency of exchange-traded funds as
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Master Thesis: The Efficiency of Exchange-Traded Funds as a market investment Page 1
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
Master Thesis: The Efficiency of Exchange-Traded Funds as a market investment Page 2
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.
Master Thesis: The Efficiency of Exchange-Traded Funds as a market investment Page 3
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
Master Thesis: The Efficiency of Exchange-Traded Funds as a market investment Page 4
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,
Master Thesis: The Efficiency of Exchange-Traded Funds as a market investment Page 5
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
Master Thesis: The Efficiency of Exchange-Traded Funds as a market investment Page 6
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.
Master Thesis: The Efficiency of Exchange-Traded Funds as a market investment Page 7
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
Master Thesis: The Efficiency of Exchange-Traded Funds as a market investment Page 8
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.
Master Thesis: The Efficiency of Exchange-Traded Funds as a market investment Page 9
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.
Master Thesis: The Efficiency of Exchange-Traded Funds as a market investment Page 10
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.
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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
Master Thesis: The Efficiency of Exchange-Traded Funds as a market investment Page 12
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:
Master Thesis: The Efficiency of Exchange-Traded Funds as a market investment Page 13
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).
Master Thesis: The Efficiency of Exchange-Traded Funds as a market investment Page 14
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
Master Thesis: The Efficiency of Exchange-Traded Funds as a market investment Page 15
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,
Master Thesis: The Efficiency of Exchange-Traded Funds as a market investment Page 16
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.
Master Thesis: The Efficiency of Exchange-Traded Funds as a market investment Page 17
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
Master Thesis: The Efficiency of Exchange-Traded Funds as a market investment Page 18
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.
Master Thesis: The Efficiency of Exchange-Traded Funds as a market investment Page 19
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).
√( )
Master Thesis: The Efficiency of Exchange-Traded Funds as a market investment Page 20
: 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.
Master Thesis: The Efficiency of Exchange-Traded Funds as a market investment Page 21
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.
Master Thesis: The Efficiency of Exchange-Traded Funds as a market investment Page 22
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:
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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.
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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.
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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.
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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.
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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.
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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,
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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
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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
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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.
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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
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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.
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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
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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.
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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.
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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.
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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.
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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,
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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
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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
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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.
Master Thesis: The Efficiency of Exchange-Traded Funds as a market investment Page 43
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http://www.blackrockinternational.com/home
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https://pressroom.vanguard.com/nonindexed/6.14.2013_Understanding_Synthetic_ETFs.pdf
Master Thesis: The Efficiency of Exchange-Traded Funds as a market investment Page 46
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
Master Thesis: The Efficiency of Exchange-Traded Funds as a market investment Page 47
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)
Master Thesis: The Efficiency of Exchange-Traded Funds as a market investment Page 48
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)
Master Thesis: The Efficiency of Exchange-Traded Funds as a market investment Page 49
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
Master Thesis: The Efficiency of Exchange-Traded Funds as a market investment Page 50
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
Master Thesis: The Efficiency of Exchange-Traded Funds as a market investment Page 51
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
Master Thesis: The Efficiency of Exchange-Traded Funds as a market investment Page 52
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
Master Thesis: The Efficiency of Exchange-Traded Funds as a market investment Page 53
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
Robust standard errors in parentheses
*** p<0.01, ** p<0.05, * p<0.1
Master Thesis: The Efficiency of Exchange-Traded Funds as a market investment Page 54
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
Robust standard errors in parentheses
*** p<0.01, ** p<0.05, * p<0.1
Master Thesis: The Efficiency of Exchange-Traded Funds as a market investment Page 55
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
Robust standard errors in parentheses
*** p<0.01, ** p<0.05, * p<0.1
Master Thesis: The Efficiency of Exchange-Traded Funds as a market investment Page 56
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
Robust standard errors in parentheses
*** p<0.01, ** p<0.05, * p<0.1
Master Thesis: The Efficiency of Exchange-Traded Funds as a market investment Page 57
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
Robust standard errors in parentheses
*** p<0.01, ** p<0.05, * p<0.1
Master Thesis: The Efficiency of Exchange-Traded Funds as a market investment Page 58
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.
Master Thesis: The Efficiency of Exchange-Traded Funds as a market investment Page 59
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.
Master Thesis: The Efficiency of Exchange-Traded Funds as a market investment Page 60
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.
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