Three essays on exchange traded funds

THREE ESSAYS ON EXCHANGE-TRADED FUNDS

Ramabhadran S. Thirumalai

Submitted to the Faculty o f the University Graduate School
in Partial Fulfillment o f the Requirements
for the Degree
Doctor o f Philosophy
in the Kelley School o f Business
Indiana University

May, 2004

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UMI Number: 3134050

Copyright 2004 by
Thirumalai, Ramabhadran S.

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ACCEPTANCE

Accepted by the Graduate Faeulty, Indiana University, in partial fulfillment o f the
requirements of the Degree of Doctor of Philosophy in Business.

/
V
Craig W. Holden,
Bo
Chairman

Robert H. Jennings
Doctoral Committee

(December 17, 2003)

11

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© 2004

Ramabhadran S. Thirumalai
ALL RIGHTS RESERVED

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ACKNOWLEDGMENTS
I would like to thank my committee members, Craig Holden, Robert Jennings, Heejoon Kang,
and Charles Trzcinka, for their help and guidance towards the completion o f this dissertation.
I would also like to thank Neal Galpin, Scott Smart, and Chad Zutter for helpful discussions and
comments. I am grateful to the Finance faculty for their support over the years. I appreciate the
encouragement from my fellow doctoral students.
I would also like to thank m y friends for urging me on to finish this dissertation. I am thankful to
my parents and my sister for their constant support and words o f encouragement. My deepest
thanks go to my wife, Gayathri, for her patience, support, and understanding.

IV

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ABSTRACT
Essay one compares the pricing and liquidity o f passive exchange-traded funds (ETFs) to those o f
active ETFs. Consistent with predictions, I find that average absolute price deviations from net
asset value (N A V ) are larger for a non-arbitrageable basket security (active ETFs) than for an
arbitrageable one (passive ETFs). Flowever, the mean price deviations are positive for passive
ETFs and not different from zero for active ETFs. Further, contrary to predictions from theory, 1
find that the bid-ask spreads for active ETFs, which have one market maker each, who has an
information advantage relative to the rest o f the market, are significantly narrower than those for
passive ETFs, which have multiple market makers.
Essay two examines the performance o f four bond ETFs relative to their underlying indices.
Since all four ETFs hold only a representative sample o f bonds from their underlying indices,
ETF performance may differ from index performance. I find that all four ETFs underperform
their respective indices, which may be attributed to the ETFs holding only the most liquid bonds
from their indices. I also examine the deviations o f market price from N A V . I find that the short­
term Treasury ETF has the smallest deviations and the corporate bond ETF has the largest
deviations. This difference may be attributed to the difference in the underlying bonds’ liquidity.
One puzzling result, however, is the positive premiums that these ETFs trade at on average.
Essay three studies the effect o f ETF option listings on the underlying ETFs. Earlier studies have
documented negative abnormal returns in equity around the introduction o f equity options, which
have been attributed to the alleviation o f short-sale constraints on the underlying stocks. One
short-sale constraint faced by investors is the uptick rule that prohibits investors from short
selling on a downtick. Flowever, since ETFs are exempt from this rule, they may face lower
short-sale constraints. This suggests that there may be no abnormal returns in ETFs around
options listings. Consistent with this, I find no abnormal returns around options listings
suggesting that ETFs are not short-sale constrained. I also find that there is no change in short
interest around options listings.

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TABLE OF CONTENTS
Essay One: Active vs. Passive ETFs

1

I.

Introduction

2

II.

Data and Methodology

10

III.

Results and Discussion

11

IV.

Conclusions

25

Essay Two: The Bond ETF Market

28

I.

Introduction

29

II.

Bond ETFs and Data

31

III.

Results

34

IV.

Conclusions

41

Essay Three: D oes Exemption from the Uptick Rule Effectively Alleviate

43

Short-Sale Constraints?
I.

Introduction

44

II.

Data and M ethodology

47

III.

Results

50

IV.

Conclusions

56

Appendix

58

References

60

Tables

65

Figures

93

VI

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L IST OF T A B L E S A N D FIG U R E S
Table I; Differences between passively and actively managed exchange-traded funds
Table II: Summary statistics on ETFs
Table III: Summary statistics on ETF premiums
Table IV: Summary statistics on premiums o f ETFs matched on benchmark indices
Table V: Summary statistics on premiums o f ETFs matched on geographic region o f benchmark
indices
Table VI: Linear regression o f premium measures on characteristics o f ETFs
Table VII: Tests for persistence in ETF premiums
Table VIII: Summary statistics for liquidity measures o f ETFs
Table IX: Linear regression o f liquidity measures on trading characteristics o f ETFs

Table X: Correlation coefficients
Table XI: Daily turnover o f ETF shares
Table XII: Creation and redemption o f bond ETF units
Table XIII: Performance o f bond ETFs relative to their underlying indices
Table XIV: Pricing o f bond ETFs relative to their net asset values
Table XV: Linear regression o f premiums on lagged premiums
Table XVI: Linear regression o f premium measures on characteristics o f ETFs
Table XVII: N ew listings by options exchange and year
Table XVIII: Cumulative abnormal returns around option listing date
Table XIX: Cumulative abnormal returns for the 11-day window around options listings
Table XX: Test for other short-sale constraints
Table XXI: Change in short interest in ETFs around options listing
Table XXII: Volume-return regressions
Figure la: Time series plot o fppremium.
Figure lb: Time series plot o f qpremium.

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Figure 2: Histogram o f premiums for the four bond ETFs.
Figure 3: Time-series plot o f bond ETF premiums.
Figure 4: ETF versus equity DARs and CARs.

V lll

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Essay One:
Active vs. Passive ETFs

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I.

Introduction
An exchange-traded fund (ETF) comprises o f a basket o f either stocks or bonds. It

has characteristics common to both closed- and open-end funds. ETFs trade on an
intraday basis on major exchanges like closed-end funds. Like open-end funds, the
number o f ETF shares outstanding can change on a daily basis depending on whether
there is a net creation or redemption o f shares in the ETF. ETFs are either passively or
actively managed. Passive ETFs track an equity or bond index, whereas active ETFs
attempt to outperform an equity or bond index.
A comparison o f active and passive ETFs provides valuable insights about pricing
efficiency because o f institutional features which either facilitate (in the case of passive
ETFs) or limit (in the case o f active ETFs) arbitrage. Theory and evidence from option
pricing literature (e.g. Black and Scholes (1973), Galai (1977, 1978), Phillips and Smith
(1980)) and interest rate parity literature (e.g. Frenkel and Levich (1975), Rhee and
Chang (1992), Fletcher and Taylor (1996)) suggest that when arbitrage, using financial
securities, is possible, we should not observe large deviations from theoretical values.
Moreover, evidence from purchasing power parity literature (e.g. Frenkel (1981), Adler
and Lehmann (1983), Taylor (1988)) and closed-end fund literature (e.g. Pontiff (1996))
show that when there are limits to arbitrage using financial securities, large deviations

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from theoretical values can persist.'’^ Prior literature does not directly compare the
mispricing o f arbitrageable and non-arbitrageable securities. Passive and active ETFs
provide such an opportunity leading to the following hypothesis.
Hypothesis 1: Mispricing fo r active ETFs, which are not arbitrageable, should be greater
than mispricing fo r passive ETFs, which are arbitrageable.
This study also exploits structural differences in active and passive ETF markets
to test theories of liquidity. Active ETFs have only one market maker whereas passive
ETFs have multiple market makers. Theory predicts that liquidity improves as the
number o f market makers increases (Glosten (1989), Grossman and Miller (1988)).
Empirical tests o f the effect o f the number o f market makers on bid-ask spreads (one
measure of liquidity) find that hid-ask spreads decrease as the number o f market-makers
increase (e.g. Wahal (1995), Fluang and Masulis (1999)). This literature indicates that the
bid-ask spread should be wider for active ETFs than for passive ETFs. Further, only the
market maker knows the active ETF’s net asset value (NAV) at all times, whereas the
passive ETF’s NAV is public knowledge. If the active ETF market maker attempts to
profit from his information advantage, liquidity will be lower for active ETFs than for
passive ETFs (see Bhattacharya and Spiegel (1991)). This also suggests that hid-ask
spreads should be wider for active ETFs than for passive ETFs. Empirical studies that
examine the effect o f information asymmetry on market liquidity show that liquidity is
inversely related to information asymmetry (e.g. Lee, Mucklow, and Ready (1993), Koski

' See Pakko and Pollard (1996) for list o f reasons for violation o f purchasing power parity.
^ Possible explanations for the closed-end fund discount include overvaluation o f illiquid or restricted
assets in N A V calculation (Malkiel (1977)), managerial ability reflected in the market price but not in the
N A V (Boudreaux (1973), Chay and Trzcinka (1999)), and/or tax liabilities on unrealized capital gains not
reflected in the N A V (Roenfeldt and Tuttle (1973)). Alternatively, behavioral explanations o f the closedend fund puzzle attribute the discount to risk due to the presence o f noise traders (e.g. Z w eig (1973), De
Long, Shleifer, Summers, and Waldman (1990) and Lee, Shleifer, and Thaler (1991)).

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and Michaely (2000)). These studies show that uninformed market makers reduce
liquidity when exposed to informed traders. Contrary to this approach, this study tests
how liquidity is affected when the market maker is informed relative to the rest o f the
market. The second hypothesis is as follows.
Hypothesis 2: Bid-ask spreads are greater fo r active ETFs than fo r passive ETFs.
The insight gained from this study has significant policy implications. The
Securities and Exchange Commission (SEC) is considering proposals to introduce active
ETFs in the US (see DJNS (2001), SEC (2001)). Though it has been more than two years
since the first o f these proposals were filed with the SEC and more than a year since the
SEC requested public comments on its concept release, the SEC is yet to permit active
ETFs in the US. The delay is due to the SEC’s concern about an appropriate structure for
the active ETFs. An appropriate structure for an active ETF should, among other things,
ensure that its shares are priced efficiently and have a liquid market (SEC (2001)). This
paper examines such a structure for active ETFs by studying those listed on the Deutsche
Borse.
The first ETF was introduced on the Toronto Stock Exchange (TSE) in 1990
under the name TIPS (Toronto Index Participation units). It tracks the 35 largest stocks
on the TSE. TIPS were introduced to attract small investors who stayed away from the
market since the 1987 crash (Globe and Mail (1989)). The SPDR (the first ETF in the
U.S.) was introduced in 1993 to attract retail investors who wanted to invest in the S&P
500 Index (DJNS (1993)).^ Since then ETFs have grown dramatically both in number and
size. A study by Merrill Lynch in 2002 finds that there are 246 ETFs listed worldwide

SPDR stands for Standard and Poor’s Depositary Receipts and is pronounced spider.

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with nearly $130 billion in assets."^ All ETFs issued worldwide prior to 2000 were
passively managed. The Deutsche Bdrse introduced eleven active ETFs in November
2000.^ One of the key reasons for introducing active ETFs was to give investors a
security that could outperform an index since passive ETFs could only match the
performance o f an index. In the time since, others followed and currently there are 24
active ETFs listed on the Deutsche B o r s e . ’
Table I lists the main characteristics o f passive and active ETFs on the Deutsche
Borse. One o fth e key differences between passive and active ETFs is that the portfolio
composition o f passive ETFs is released every day prior to start o f trading, whereas the
composition o f active ETFs is never known to the market. This helps arbitrageurs to
profit from mispricing in passive ETF shares since they know what shares to trade but
rules out the same for active ETF shares. The exchange disseminates an indicative net
asset value (INAV) all through the trading day that represents the true value o f a share in
the passive ETF. The market makers post bid and offer prices based on the supply and
demand for the passive ETF shares and the NAV. If the quoted prices deviate from the
NAV o f the passive ETF, arbitrageurs can take advantage of the deviation using the
creation/redemption process. The creation/redemption process allows traders to create
shares in the passive ETF by putting together a portfolio consisting o f the individual
securities of the passive ETF and exchanging this portfolio for shares in the passive ETF.
The trust that manages the passive ETF issues the new shares to the traders. Similarly,
The Merrill Lynch report quoted figures as o f the end o f May 2002, at which time the US had 102 ETFs
with over $90 billion in assets. Investment Company Institute (2003a) reports that there are 118 ETFs in the
US as o f April 2003 with over $110 billion in assets.
^ On the Deutsche BOrse, the passive ETFs are referred to as index funds and the active ETFs are called
actively managed funds.
®N o active ETF has been closed down over my sample period.
’ Currently, the Australian Stock Exchange (A SX ) is the only other exchange to have active ETFs listed.
On the A SX , active ETFs are called hybrid ETFs. Nine hybrid ETFs are currently listed on the A SX .

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when traders want to redeem shares in the passive ETF, they surrender ETF shares to the
trust and receive a portfolio consisting o f the underlying securities in return.*
The portfolio composition o f active ETFs is not public knowledge and they do not
have the creation/redemption feature.^ However, the fund manager makes public the top
ten holdings o f the active ETF at the end of each month. She decides on which stocks to
select and how to weight them. This decision is based on the fund’s investment objectives
and the fund manager’s private information about the future performance o f securities.
For investors to be involved in a creation/redemption process for active ETFs, they will
have to know the active ETF’s portfolio composition. The fund manager will not share
her portfolio composition with other investors since they may attempt to free ride on her
information. Consequently, arbitrageurs cannot take advantage o f arbitrage opportunities
and bring prices back to p a r i t y . " The onus o f maintaining parity between the market

Under the creation/redemption feature, arbitrageurs face negligible holding costs since their positions may
last a few seconds or minutes. If transaction costs to replicate the entire portfolio o f a passive ETF are high,
it is possible that arbitrageurs trade a representative sample o f securities in the index, in which case creation
or redemption is not possible. In this case, arbitrageurs may face significant holding costs and mispricing
may not disappear completely.
®The fund manager o f the active ETF reveals the portfolio composition to the market maker and the
exchange daily. Additionally, she informs the other two parties if she makes any change to the portfolio
during the trading day.
In addition to being able to trade active ETF shares on the exchange, investors can also buy or sell shares
directly from the fund manager at the closing N A V at the end o f the trading day (similar to open-end
funds). This suggests that one possible way to take advantage o f mispricing in active ETF shares is to buy
(sell) shares on the exchange and sell (buy) shares directly to (from) the fund manager if the market price is
at a discount (premium) relative to the N A V (shares can be purchased on the exchange and redeemed from
the fund manager and vice versa). In this scenario, investors do not have to know the true com position o f
the active ETFs portfolio. To profit from this strategy, investors must be able to buy and sell

simultaneously in the two markets, which is not possible due to restrictions. The two markets are the
primary and secondary markets. The primary market is the one in which investors trade directly with the
fund manager. The secondary market is the exchange where trades take place between investors. To trade
with the manager, investors are required to place their orders prior to the opening o f markets. This suggests
that investors w ill place orders based on the previous day’s closing market price and closing N A V . But
their orders w ill be executed by the fund manager at the follow ing day’s closing N A V , by which tim e the
market price would have also changed. Hence investors who attempt to profit from possible arbitrage
opportunities w ill base their strategies on stale prices and may end up making loses instead o f profits.
'' Passive ETFs are arbitrageable in the pure riskless sense whereas active ETFs are not. Since a part o f the
com position o f the active ETF is made public every month, som e investors may attempt to profit from
mispricing using their partial knowledge o f the composition o f the active ETF. Other investors may try to

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price and the NAV falls on the market maker.

The market maker posts bid and offer

prices based on the supply and demand for the active ETF shares and his private
information about the active BTF’s portfolio composition.
The Deutsche Borse requires all ETFs to declare a benchmark index. In the case
of passive ETFs, each one explicitly tracks its benchmark index. Investors expect the
passive ETF’s performance to match its benchmark’s performance. On the other hand,
the exchange requires the active ETF’s fund manager to select a benchmark index,
subject to its approval, such that investors can compare the active ETF’s composition and
performance to its benchmark. This does not imply that the fund must only hold
securities that are a subset of the securities in the index. For example, the fund may hold
securities that are in the same sector or geographic region as some securities in the
benchmark but not necessarily the same seeurities. The Deutsche Dorse’s stated purpose

for requiring each active ETF to select a benchmark index is to have a yardstick against
which to compare the active ETF’s performance. Since there are only a limited number of
indices available, it is possible that more than one ETF has the same benchmark index.
Prior studies have investigated the pricing and liquidity o f only passive ETFs.
Ackert and Tian (2000) find that the degree o f mispricing on the SPDR, which has low
arbitrage costs, is insignificant suggesting that speculators successfully arbitrage any
discrepancies. Contrary to their finding for the SPDR, they find that the level o f
infer the com position through a style analysis by regressing past active ETF returns on various benchmarks
(see Sharpe (1992)). These attempts by investors may still fall short o f being able to replicate the active
ETF exactly. A t best, these w ill be speculative arbitrages.
The fund manager o f the active ETF reveals the portfolio composition to the market maker and the
exchange daily. Additionally, she informs the other two parties if she makes any change to the portfolio
during the trading day. The market maker and/or the fund manager could potentially profit from deviations
between N A V and market price o f active ETF shares i.e. they could act as arbitrageurs since they know the
portfolio com position o f the fund. Rules and regulations on the Deutsche Borse preclude the market maker
and the fund manager from acting as arbitrageurs. The rules and regulations also prohibit the market maker
from disclosing the portfolio com position to third parties.

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mispricing for the Midcap SPDR (ETF in the US that tracks the S&P Midcap 400 Index),
which has higher arbitrage costs, is significant indicating that pricing errors are
insufficient to cover trading costs. Engle and Sarkar (2002) study a large sample o f US
passive ETFs (passive ETFs that track domestic US indices) and find that on average they
are priced efficiently, the only exception being short-lived and minor deviations from the
NAV during the trading day. Contrary to their finding for US passive ETFs, they find
large and persistent deviations for a sample of international ETFs (passive ETFs that
track foreign indices) listed in the US. Engle and Sarkar attribute these differences to the
larger transaction costs associated with trading shares listed in other countries.

Hegde and McDermott (2003) examine the liquidity o f Diamonds and Qubes,'^
which are both passive ETFs, and their underlying stocks. Consistent with
Subrahmanyam (1991), they find that adverse selection is lower for the ETF shares than
for the underlying individual stocks. They also find that the introduction o f ETFs
improves the liquidity o f the underlying stocks and increases the volume o f trading and
open interest in the related futures markets.
This is the first study that examines the pricing efficiency and liquidity o f both
active and passive ETFs. In particular it compares the pricing efficiency and liquidity of
active ETFs to that o f passive ETFs listed on the Deutsche Borse. The sample includes
ETFs that trade on the Xetra system of the Deutsche Borse. Xetra is a hybrid trading
system where liquidity is provided by market maker(s) and limit orders. ETF market
makers are obliged to maintain fair prices and liquid markets. Additionally, market
makers are required to post quotes for at least 90 percent o f the effective trading time.''^

Diamonds track the D ow Jones Industrial Average and Qubes track the Nasdaq 100.
The effective trading time is the time o f continuous trading only and excludes auctions.

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They also face restrictions on the maximum quoted spread and minimum quoted size.
The limit order book is open but trader identity remains anonymous. The Xetra exists
side-by-side with a trading floor where trades execute using a fixed number o f intraday
call auctions. Further, trading on Xetra begins and ends with a call auction. There may be
additional auctions during the day on Xetra during which the exchange halts continuous
trading.'^ By comparing the pricing efficiency and liquidity o f active ETFs to those of
passive ETFs listed on the same exchange, I am able to control for the effects o f market
structure (other than the number o f market makers) and other market-wide factors on
pricing and liquidity. Consequently, resulting differences in pricing efficiency and
liquidity are attributable to differences in the structures o f active and passive ETFs. This

study’s results permit conclusions with direct policy implications regarding the merits of
different ETF structures.
Consistent with my hypothesis, I find that absolute deviations in market price
from NAV are larger for active ETFs than for passive ETFs. However, I find that the
mean deviations are positive and significant for passive ETFs but insignificant for active
ETFs. I also find persistence in these deviations for passive ETFs but no persistence for
active ETFs. Contrary to expectations, I find that the bid-ask spreads for active ETFs are
smaller than those for passive ETFs. This result persists even after controlling for
differing characteristics o f active and passive ETFs. This suggests that a single informed
market maker is better able to maintain liquid markets than multiple uninformed market
makers.

For comparisons o f the trading floor and the computerized trading systems o f the Deutsche Borse, see
Theissen (2002). Hau (2001) has a brief description o f the Xetra. For a detailed description o f the Xetra, see
DB (2002).

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The remainder o f the paper proceeds as follows. In the next section, I describe my
data and methodology. In Section III, I present empirical results and discussions.
Conclusions and implications follow in Section IV.

II.

Data and Methodology
Data is collected from Bloomberg. It consists o f daily closing market prices, daily

closing NAVs, daily closing bid and offer prices, and daily volumes for all active and
passive ETFs starting from the listing date on Deutsche Borse to the end o f August 2002.

Additionally, data on the number o f market makers for each ETF is collected from the
Deutsche Bdrse Web site. The final sample consists o f 57 passive ETFs and 15 active
ETFs. The oldest passive ETF started in April 2000 and latest passive ETF in July 2002.
Similarly, the oldest active ETF in the sample started in November 2000 and the latest in
May 2002. The Appendix lists all the ETFs used in this study along with their listing
date.
I define two measures o f premium for ETF i at close o f trading on day t as
follows:

ppremium^ = In

and

(1)

qpremium^i = In

(2)

where In is the natural logarithm, Pu is the closing per-share market price o f ETF i on day
t, Qit is the midpoint o f the closing bid and offer prices o f ETF i on day t, and NA Vu is the
closing per-share net asset value o f ETF i on day t. ppreminmu is a market price-based
measure o f ETF premium, whereas qpremiurriit is a quote-based measure o f ETF

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premium. The logarithmic premium measure is commonly used in closed-end fund and

ETF literature to measure mispricing (e.g. Chay and Trzcinka (1999), Engle and Sarkar
(2002)).'^ For both measures, a negative premium indicates a discount.
I use the percentage quoted and effective spreads as measures o f liquidity, which
are defined for ETF i on day t as follows:

p g s p r e a d „ ^ ^ S 3 id ^ _

(3)

Qii

pespread

2x\ Pn - Q u \

(4)

Q il

where offern is the closing offer price for ETF i on day t, bidu is the closing bid price for
ETF i on day t and Pu and Qu are the same as defined earlier. These measures are
commonly used in microstructure literature to measure liquidity (e.g. Stoll (2000), Hegde
and McDermott (2003)). A wider spread implies lower liquidity since they measure
investors’ transaction costs on a round-trip transaction.

III.

Results and Discussion
Table II presents summary statistics on the ETFs. Table II shows that relative to

passive ETFs, active ETFs are larger and have share prices that are twice as large. The
higher price o f active ETFs suggests that using a percentage spread is better than using a
euro spread because it adjusts for price clustering effects (see Harris (1991)). One
explanation for the larger size of active ETFs is the minimum size requirement o f €50
million for active ETFs at start-up but no such requirement for passive ETFs (see Table

If premium is measured as the difference between price and N A V expressed as a percentage o f N A V ,
this results in a skewed distribution for the premium measure, where premium takes values between -1 and
infinity. The logarithmic measure has a symmetric distribution that takes values between negative and
positive infinity. This is more conducive to using standard statistical tests.

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I). Expense ratios are higher for active ETFs than for passive ETFs. A reason for the
higher expense ratio o f active ETFs is compensation for the manager’s expertise in
picking securities. Expense ratios are lower for passive ETFs since manager’s expertise is
not required to pick stocks because passive ETFs track indices.
Table III presents summary statistics on ETF premiums. In Panel A, each
premium measure is averaged across all days for each passive ETF (active ETF) and the
summary statistics o f the resulting series are shown. Absolute deviations from NAV are
larger for active ETFs than for passive ETFs. There is also evidence o f passive ETFs
trading at significant premiums relative to their NAVs, whereas active ETFs do not trade
at a premium. However, there is little evidence o f any difference between premiums for
passive and active ETFs. Evidence from option pricing, interest rate parity, and
purchasing power parity literature suggests that the magnitude o f mispricing should be
larger for non-arbitrageable securities than for arbitrageable securities but does not
predict a direction for the mispricing (discount or premium). Examining the volatility o f

the premium measures will provide insights about the magnitude o f active and passive
ETFs’ mispricing. A comparison o f the volatility o f ppremium and qpremium for passive
ETFs and active ETFs is presented in Table III. In the cross-section (Panel A o f Table
III), the standard deviations for ppremium {qpremium) are 88 (28) basis points for passive
ETFs and 54 (59) basis points for active ETFs.'^ The measures are significantly different
for passive ETFs and active ETFs, though ppremium suggests that volatility is higher for
passive ETFs whereas qpremium suggests that volatility is higher for active ETFs.
ppremium may suffer from stale closing prices for less liquid ETFs and hence

These measures are higher than the 15 basis points that Engle and Sarkar (2002) report for passive ETFs
in the US.

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interpretations based on qpremium are more appropriate. There is less variation in the
premiums o f passive ETFs than o f active ETFs. This result is consistent with the
hypothesis that non-arbitrageable securities have larger mispricing than arbitrageable
securities.
All ETFs do not have the same length o f time-series. As a result some ETFs with
shorter time-series o f data receive larger weights in Panel A. If mispricing is related to
the age o f the ETF, it will introduce a bias in the results. To check for such biases, I
determine time-series statistics o f the premium measures. Equally-weighted portfolios of
passive ETFs (active ETFs) are formed on every calendar date and the mean premium
measures for these portfolios are calculated for each day. The daily mean premiums are
plotted against calendar time in Figure 1. Figure la is for ppremium and Figure lb is for
qpremium. There are no discernable patterns in the deviations o f market price from NAV
for both active and passive ETFs. ppremium appears to be similar for both active and

passive ETFs. qpremium appears to be more volatile for active ETFs than for passive
ETFs. This is consistent with the hypothesis that non-arbitrageable securities have larger
deviations from NAY. The summary statistics o f the daily mean premiums o f the equallyweighted portfolios are presented in Panel B o f Table III. The time-series data show
results consistent with those from Panel A. This indicates that absolute deviations from
NAV are smaller for passive ETFs than for active ETFs. This is consistent with the
hypothesis that arbitrageable securities have lower mispricing than non-arbitrageable
securities.
The volatility o f premium measures does not show if either type o f ETF trades
more often at a premium or discount. If an ETF trades consistently at a premium or

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discount, the mean and median should be significantly different from zero. Evidence
from option pricing and interest rate parity literature suggests that passive ETFs should
trade at insignificant premiums. Results from Brickley and Schallheim (1985) suggest
that active ETFs should also trade at insignificant premiums. They find that the closedend fund discount disappears between when a closed-end fund announces that it will
reorganize as an open-ended fund and the actual reorganization.'* They also find a large
reduction in the discount around the announcement o f the reorganization. They attribute
part of the reduction in discount over time to the resolution o f the uncertainty about fund
reorganization. This evidence suggests that investors’ ability to trade with the fund
manager at the NAV eliminates the closed-end fund discount. Though investors can trade
active ETFs intraday, investors can also trade directly with the fund manager at the NAV
at the close o f trading. Active ETFs are, in effect, open-ended funds that trade intraday.
The ability o f investors to trade active ETF shares with the fund manager at the NAV
suggests that active ETF shares will not trade at significant deviations from NAV.
In the cross-section (Panel A o f Table III), the mean ppremium and qpremium for
passive ETFs are 32 and 9 basis points, respectively, and 14 and 22 basis points,

respectively, for active ETFs. Both the premium measures for passive ETFs are
significantly different from zero, though the mean qpremium is not economically
significant. The premium measures for active ETFs are not significant. The premium
measures for passive and active ETFs are not significantly different from each other.
Further, the median ppremium and qpremium for passive ETFs are 22 and 5 basis points,
respectively, and -10 and -6 basis points, respectively, for active ETFs. A nonparametric
After reorganization, in most cases, the closed-end fund ceases to trade intraday. Investors will have to
trade directly with the fund manager once a day at the close o f trading and all trades are executed at the
NAV.

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test o f medians suggests that both premium measures are significantly different from zero
for passive ETFs, whereas they are not significant for active ETFs. The median
qpremium for passive ETFs is not economically significant. The median ppremium of
passive ETFs is statistically different from that o f active ETFs whereas the median
qpremiums are not different from each other. Contrary to expectations, there is evidence
that premiums are more common than discounts for passive ETFs. On the other hand, as
expected, premiums and discounts occur randomly for active ETFs. The results from the
time-series data in Panel B o f Table III are similar. The average mispricing o f active
ETFs is not different from zero implying that the active ETF structure on the Deutsche
Borse maintains efficient pricing o f active ETF shares.
The liquidity o f stocks in the benchmark indices may affect the pricing o f ETFs.
If an ETF holds a set o f relatively illiquid securities, then the prices used to calculate its
NAV may be stale resulting in evidence o f large mispricing. To control for this illiquidity
effect, I select active and passive ETFs that have the same benchmark index. This results
in a sample of 9 active and 12 passive ETFs.’^ The summary statistics o f the premium

measures o f this sample are in Table IV. Panel A contains the cross-sectional statistics
and Panel B contains the time-series statistics. Consistent with results from Table III, I
find that the volatility o f premium measures is larger for active than for passive ETFs.
This implies that deviations from NAV are larger for active ETFs than for passive ETFs
even after controlling for some liquidity effects. The mean and median measures for
The number o f active and passive ETFs are not the same since in some cases there is more than one
passive ETF for a given benchmark index. For five active ETFs, I find passive ETFs with exactly the same
benchmark index. For three other active ETFs, the match is not exact. I find passive ETFs w hose
benchmarks are in the same sector or industry as the active ETF’s benchmark. For the last active ETF in the
subsample (benchmark is the D ow Jones STOXX 600), there is no passive ETF that has a similar
benchmark. But there are 18 passive ETFs that track the different sectors o f the D ow Jones STOXX 600. 1
determine the equally-weighted premium measures on a daily basis for these 18 passive ETFs and use this
measure as a match for the corresponding active ETF.

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passive ETFs are statistically significant but not economically significant whereas they
are insignificant for active ETFs. The premium measures for passive ETFs are
significantly different from those of active ETFs. This is also consistent with findings
from Table III suggesting that the positive mean premiums for passive ETFs are not due
to illiquidity effects.
The different trading hours o f the underlying securities and the ETFs may he
another source of stale prices. The ETFs on the Deutsche Borse track indices that hold
securities from all over the world. The ETFs may use stale prices o f securities that trade
on markets which are closed when the NAV is calculated. This could lead to larger
deviations in market price from NAV. To control for this effect, I divide my sample o f
active and passive ETFs into three suhsamples: ETFs based on European indices, ETFs

based on US indices, and ETFs based on global indices.^^ 1 then compare the mispricing
of active and passive ETFs within each o f the three subsamples. Results o f this analysis
are in Table V. For all three subsamples, the results are similar to those in Table III.
Deviations in market price from NAV are larger for active than for passive ETFs. Passive
ETFs trade more often at a premium than at a discount. These results hold even after
controlling for different sources o f stale prices.
The results in Tables III, IV, and V are based on univariate tests. The results may
differ in a multivariate setting. To this end, I run the following linear regression:
PM„ = CTo + a^crl +
where

InF;., + ajG,,. +

,

(5)

is the absolute value o f the premium measure ppremium or qpremium for

ETF i on day t, c>l is the square o f NAV returns for ETF i on day t (a measure of
There is only one ETF based on an Asian index and so I drop this ETF from the analysis.

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