Excess Comovement and Limits-to-Arbitrage - European Financial

41 Pages·2013·0.6 MB·English

by  Markus Broman

Excess Comovement and Limits-to-Arbitrage:
Evidence from Exchange-Traded Funds

Markus S. Broman*

First draft: November 28, 2012
This draft: May 20, 2013

Abstract

The prices of Exchange-Traded Funds can deviate from their Net Asset Values by the magnitude of
arbitrage costs, such as transaction and holding costs. Despite the explicit “in-kind” arbitrage
mechanism that exists for ETFs, I find that ETF mispricing mean-reverts only partially; moreover,
mispricing increases not only with proxies for aggregate market illiquidity, but also for ETFs with high
arbitrage costs, particularly during the financial crisis. As long as mispricing remains within the
arbitrage costs boundaries, there is limited pressure to correct for any price discrepancies, which may
leave the ETF partially exposed to a common factor. Consistent with this prediction and with recent
theoretical work on the effects of commonality in trading patterns, I find strong evidence of
comovement among excess ETF returns (i.e. after correcting for movements in the fundamentals, the
NAV) within three investment styles – size, value-growth and ETF liquidity.

JEL Classification: G10, G12, G14, G15, G20, G23
Keywords: Excess Comovement, ETF, mispricing, limits to arbitrage, style investing.

* Finance Department, Schulich School of Business, York University, 4700 Keele St., Toronto, Ontario
M3J 1P3, Tel: [phone] ext. 44655, e-mail: [email protected]. I wish to thank
Pauline Shum, Yisong Tian, Kee-Hong Bae and Mark Kamstra for discussions and suggestions, as
well as seminar participants at York University, Schulich School of Business.
© by the author.
1 Introduction
In frictionless markets with rational investors, the market price of an Exchange-Traded
Fund (ETF) will equal its fundamental price (the Net Asset Value), and any comovement in
ETF returns must be due to comovement in fundamentals. However, in economies with
frictions or with irrational investors, and in which there are limits to arbitrage, comovement
in ETF returns may be partially delinked from fundamentals giving rise to what is known as
excess comovement (see Barberis and Shleifer (2003); Barberis, Shleifer and Wurgler
(2005) and Greenwood (2008)). The two main non-fundamentals based explanations of
excess comovement are articulated in Barberis, Shleifer and Wurgler (2005): The first is
related to correlated investor demand (e.g. when ETF investors engage in style investing or
habitat formation), while the second arises from differences among securities in their rate of
information diffusion (e.g. ETFs incorporate information faster than the underlying
portfolio).
A unique feature of the ETF market is the “in-kind” share creation/redemption
process, an explicit arbitrage mechanism, which allows select investors (known as
Authorized Participants) to trade on price differentials between the ETF and the NAV by
exchanging (or receiving) a portfolio of securities similar to the ETF’s benchmark index for
new ETF shares. Arbitrage is, however, limited by two types of costs: transaction costs
(such as bid-ask spreads, market-impact costs and creation/redemption fees) and holding
costs (delays in the execution of the arbitrage trade). Moreover, these arbitrage costs are
expected to be magnified by the large size and relative infrequency of typical
creation/redemption transactions. As long as mispricing remains within the arbitrage costs
boundaries, there is limited pressure to correct for any price discrepancies, which may leave
the ETF partially exposed to a common, non-fundamental, factor.
The goal of this paper is twofold. First, I investigate the existence of limits-to-
arbitrage among U.S. ETFs investing in U.S. equity. Specifically, I examine the extent to
which arbitrage costs affect mispricing both in the cross-section and in the time-series.
Second, I analyze whether ETF returns comove excessively with other ETFs in similar
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styles. In this effort, I examine three style dimensions: size (large-, mid- and small-cap),
value-growth and ETF liquidity (high-, medium- and low).
To preview my results, I find that, despite the existence of an explicit arbitrage
mechanism, mispricing mean-reverts only partially; roughly by 25.2 %, 24.6 % and 21 %
over a 1-day, 1-week, 4-week period respectively. A decomposition of this effect shows
that mispricing stems mainly from the ETF, particularly at longer horizons suggesting that
it is the ETF, rather than the NAV, that is the source of mispricing. I then analyze the extent
to which proxies for arbitrage costs (transaction and holding costs) can explain the
magnitude of mispricing. I find that mispricing increases with proxies for aggregate
illiquidity, i.e. with the uncertainty in U.S. equity markets (VIX), with the volatility of the
ETF’s benchmark return and during the financial crisis (09/2008-03/2009). As an example,
mispricing increased by 7 bps (or 24 % of the Std. Dev. of mispricing) for the average ETF
during the crisis. Cross-sectional differences in ETF transaction costs seem to matter even
more; the average difference in mispricing between funds in the top and bottom tercile of
Amihud’s illiquidity is 7.9 bps (30 % of Std. Dev.). Moreover, these cross-sectional
differences are amplified during the financial crisis when the most illiquid ETFs
experienced an increase in mispricing by 21 bps (72 % of Std. Dev.). Combined, the
arbitrage cost proxies can explain more than 43 % of the variation in the magnitude of
mispricing.
Mispricing is notoriously difficult to measure and it is not surprising that there is little
direct evidence of its existence in prior studies, except for a handful of special cases such as
closed-end country funds, dual-listed companies (or “Siamese twins”), index
inclusions/exclusions and internet carve-outs and spin-offs (see the survey of Barberis and
Thaler, 2003). Moreover, in all of these cases fundamental risk may still remain as
arbitrageurs cannot fully hedge their portfolio due to a lack of perfect substitutes. My
contribution is to remedy this deficiency in the literature by investigating ETFs, where
mispricing is directly observable as the difference between the ETF market price and the
fundamental NAV price, recorded synchronously at the end of each trading day. The U.S.
ETF market can also be considered representative of the broader financial market based on:
1) its size ($1.2 trillion in total assets, out of which $632.5 billion in domestic U.S. equity
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in September 2012), 2) its share of U.S. equity dollar trading volume (roughly 30 % in
20122) and disturbingly also because 3) ETFs have been shown to increase the volatility of
the underlying assets and to propagate liquidity shocks to the underlying assets (Ben-
David, Franzoni and Moussawi (2012); Shum et al. (2013)) .
To examine whether ETF returns comove excessively with each other, I begin by
constructing excess ETF returns, defined as the difference between the ETF and the
fundamental (NAV) returns. I then estimate a regression of excess ETF returns on the
equally-weighted excess return of other ETFs with similar investment styles, and use the
regression beta as my measure of excess comovement. The information diffusion view
predicts excess comovements among the returns of ETFs with the highest liquidity
differential vis-à-vis the underlying portfolio. Small-cap ETFs fit this description, while
large-cap ETFs are not expected to have any significant liquidity improvement since the
underlying securities are among the most liquid in the world. In contrast, the correlated
investor demand view predicts excess comovement among ETF returns in similar
investment styles. My results can differentiate between these two hypotheses; I find strong
comovement patterns among both small- and large-cap ETFs, and limited comovement
across categories. The economic magnitudes are also considerable. To illustrate, a 1 Std.
Dev. increase in the equally-weighted excess return of own category ETF returns is, on
average, associated with an increase in excess ETF returns by 8.5 bps (or 32 % of Std.
Dev.) and 12.9 bps (or 59 % of Std. Dev.) for large- and small-cap ETFs respectively. After
controlling for size-related excess comovement, I also find that the returns of value and
growth focused ETFs covary excessively with each other. Similarly, ETFs with high and
low liquidity seem to comove more strongly with other ETFs in their respective categories
compared with the benchmark group of medium liquidity funds. This pattern also appears
to be unrelated to either size, or value-growth related comovement. These results, along
with the stability of excess comovements across return horizons, favor the correlated
investor demand view of excess comovement.

2 Financial Times on January 8th, 2013
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In the existing literature, researchers are not in agreement on whether the asset
pricing anomalies related to size or value-growth are the result of fundamental risk (e.g. the
value premium is related to relative distress; Fama and French, 1993, 1994 and 1996) or
unmodeled irrational behavior (as argued by Barberis and Thaler, 2003). Brav, Heaton, Li
(2010) make an attempt to explain the factor premiums related to size and value-growth by
arbitrage costs (as proxied by idiosyncratic volatility), but the results are mixed suggesting
that limits to arbitrage may only provide a partial explanation for the survival of these
factor premiums. Even if some of the common variation in size or value-growth stocks is
related to fundamental risk, that is not a concern here as I have a direct way to control for
variation in fundamentals. My contribution in this regard is to provide direct evidence of
excess comovement in the returns of ETFs grouped by similar styles.
Style investing can lead to excess comovements in security returns. Barberis and
Shelifer (2003) present a model where investors, to simplify decision making, first group
assets into categories, and then allocate funds at the level of the category as opposed to at
the individual asset level. If some of these category investors are also noise traders with
correlated sentiment, and if their trading can impact prices, then as these investors move
from one category to another based on past relative performance, their coordinated demand
will induce a common factor in the returns of assets in the same category. The tendency to
engage in category-based investing can result from an individual’s need to categorize for
the purpose of developing compact representations (or mental models) of the complex
environment in which she is in (Mullainathan, 2002). An alternative interpretation of the
style investing model is given by Barberis, Shleifer and Wurgler (2005), where investors
have preferred habitats leading them to trade only a subset of all the available securities.
When these investors’ risk aversion, sentiment or liquidity needs change, they will adjust
their exposure to the securities in their habitat, which will induce a common factor in the
returns of these securities.
The strong demand for investment categories is evident from the large number of
mutual funds, ETFs and hedge funds that follow distinct styles such as growth, value, and
small-cap, and which are used by both individual and institutional investors (see e.g. Brown
and Goetzmann (1997), Fung and Hsieh (1997), and Chan, Chen, and Lakonishok (2002)).
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Cooper, Gulen and Rau (2005) find that mutual funds take advantage of current “hot”
investment styles by renaming their fund to match the current hot style. These funds
subsequently experience abnormal inflows with no improvement in performance. This hold
even for cosmetic name changes, i.e. where the holdings of the fund do not change.
Consistent with the intuition that common variation in stock returns can be explained
by correlated investor demand, there is growing empirical evidence suggesting that
comovement in asset returns is related to the trading patterns of groups of investors. Kumar
(2009) show how individual investors systematically shift their preferences across extreme
style portfolios (small vs. large, value vs. growth) in response to past style returns, earnings
differentials and advice from investment newsletters, while these shifts are found to be
unaffected by innovations in macroeconomic fundamentals or changes in security specific
expectations about cash-flows. Froot and Teo (2009) find evidence of style investing
among institutional investors, whose reallocations across style groupings are found to be
more intense than across random groupings of stocks. Moreover, they also find that own
(distant) category inflows and returns predict future category returns positively (negatively)
consistent with Barberis and Shleifer (2003). One important implication of too much short-
run comovement in stock returns is that comovements must become negative at
intermediate horizons so that, in the long run, prices reflect fundamentals. Consistent with
this prediction, Greenwood (2008) constructs a simple trading strategy that bets on the
reversion of the prices of over-weighted Nikkei 225 stocks that comove too much in the
short-run and finds this trading strategy to yield significant risk-adjusted profits. Finally,
Boyer (2011) find that economically meaningless value and growth index labels causes
stock returns to covary excessively with each other following index reclassifications.
The article proceeds as follows. Section 2 gives a brief background on ETFs, their
importance and the arbitrage mechanism. Section 3 describes the data and provides a
definition of the key variables used in this study. Section 4 describes potential arbitrage
costs in the ETF market and examines their importance for mispricing. Section 5 begins
with a description of the key hypotheses and concludes with the main empirical findings.
Section 6 provides additional robustness checks. Section 7 concludes.
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2 Background on ETFs and Arbitrage
Exchange Traded Funds (ETFs) are investment vehicles that typically focus on replicating
the performance of a pre-specified asset class, industry or geographical area. The first ever
ETF, the Toronto Index Participation Unit (TIP) was created on March 9, 1990 in Toronto,
though ETFs became popular only after the introduction of the S&P 500 ETF by State
Street in 1993. This market has grown tremendously in the past 10 years with ETFs
gathering more than $1.2 trillion in assets in the U.S., and $1.8 trillion globally, as of
September 2012. This asset class is also capturing a large fraction of the transactions taking
place in the financial markets. In the U.S., ETFs and other exchange traded products have
been reported to account for roughly 30 % of all trading volume in 2012.
Before the proliferation of ETFs, most individual investors were limited to open- or
closed-end funds and individual stocks. ETFs are hybrid instruments that combine the best
features of both open- and closed-end funds. They combine the creation and redemption
process of the former with the continuous tradability of the latter. ETFs have several other
important advantages over open- and closed-end funds. Short-selling is often easier and
cheaper than for the underlying assets due to the higher liquidity of ETFs, they generally
have lower expense ratios than index funds and are considered tax efficient as the in-kind
mechanism is a “non-taxable” event3. The main disadvantage of open-end funds is that they
can be traded only once a day and they typically also suffer from a cash drag as the fund
manager needs to keep some cash in hand for investor redemptions. In contrast, ETFs and
closed-end funds can be traded throughout the day and both fund types avoid the cash-drag
as investors can exit simply by selling the fund shares on the exchange at the prevailing
market price. The main issue with closed-end funds is the lack of a creation or redemption
mechanism – the number of shares is fixed, hence excess demand or supply may result in
significant price deviations from the NAV. In fact, closed-end funds typically trade at a
sizeable premium surrounding the IPO and move to a large discount within 6-months after

3 In case of redemption, the ETF sponsor can minimize taxes by delivering the stocks with the largest
embedded capital gains. Vanguard takes this one step further by embedding ETFs as a separate share class in
an existing fund family. This allows the fund manager to select the securities with the largest embedded
capital gains among all the funds in the same share class.
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inception (Lee, Shleifer and Thaler, 1993). A unique feature of ETFs compared with other
fund types is the “in-kind” share creation/redemption process, an explicit arbitrage
mechanism that is designed to ensure efficient pricing.
2.1 The Arbitrage Mechanism
In a frictionless economy with rational investors, the market price of an ETF must equal its
fundamental value, which is the market value of the underlying portfolio of securities held
by the fund on a per-share basis (the NAV). The level of ETF mispricing is defined as the
percentage deviation of the ETF price from the NAV:
PREM lnETF  – lnNAV  (2.1)
i,t t t
For simplicity I call this measure a “premium” whether it is positive, or negative. The
market price of an ETF may temporarily deviate from the NAV as a result of excess
demand or supply. Such price deviations should not persist for long due to the in-kind
creation/redemption process.
The in-kind process is only available to a select group of investors, typically large
institutional investors, who have an agreement with the ETF sponsor. These investors,
called Authorized Participants, are allowed to purchase or sell ETF shares in bundles (or
“creation units”) directly from the ETF sponsor in exchange for a basket of securities
similar in composition to the benchmark index4. The creation process works as follows.
During periods of strong demand for an ETF, its market price can be bid up in the market
above the NAV. In order to take advantage of this price discrepancy, an Authorized
Participant can purchase a portfolio of securities underlying the index, exchange this
portfolio for ETF, sell the newly created ETF shares on the secondary market and realize an
arbitrage profit that is equal to the difference between the ETF and NAV price, net of any
transaction costs. Conversely, when there is strong selling pressure for an ETF, the ETF
price can fall below the NAV. Authorized Participants can then purchase existing ETF

4 For some ETFs redemptions occur in cash instead. These cases are mainly limited to some less liquid asset classes, such
as international fixed income or commodities.
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shares (at a discount), redeem them, and sell the securities received from the redemption to
realize an arbitrage profit.
3 Data
My data selection starts with all U.S. traded Exchange-Traded Funds. I keep funds that 1)
invest in domestic (U.S.) equity, 2) have underlying indices that are either equally- or value
weighted5, and 3) that have at least three years of data6. This data, along with NAVs and
prices for the underlying benchmark, is obtained from Bloomberg. As reported by Petajisto
(2011), Bloomberg coverage of ETFs is anywhere from 60 % to 97 % of all ETFs and 90 %
to 99 % of all ETF assets. My second source is CRSP, which I use to obtain price and
return data for all live and dead funds. The third data source is iShares covering daily NAV
data for iShares funds from inception until 12/2012. iShares is the biggest provider of ETFs
and it used to account for more than 50 % of all ETFs until 2005, and it generally still
accounts for about 50 % of all assets. I prioritize NAV data from iShares over Bloomberg.
Finally, I use Morningstar Direct to classify ETFs by market-cap and along the value-
growth dimension. I end up with 159 U.S. equity ETFs; 21 small-, 49 mid- and 89 large-
cap funds.
There are a handful of highly suspicious observations in the CRSP & Bloomberg data
that I filter out. First, whenever ETF or NAV returns are more (less) than plus (minus) 20
% with a large reversal the next day, and no similar movement in the underlying benchmark
index, I set the both the ETF and NAV returns equal to the return of the underlying index.
Second, when mid-point ETF returns are more than 30 % greater than the ETF returns
based on the closing price (in absolute value); I set the former equal to the latter. Third,
when premiums are greater than 20 %, I set them equal to the previous day’s value. Finally,

5 This criterion is to ensure that the ETFs can be classified as “passive”. Many recent ETFs track underlying indices that
are either proprietary, or fundamentally weighted with the goal of achieving superior risk-adjusted returns. These ETFs
blur the line between active and passive fund management.
6 I exclude the first 6 months of a funds history since the data can often be unreliable or extreme. For instance, ETFs are
highly illiquid when they are first created. Also, due to the low number of shares outstanding and the minimum fixed size
of a creation/redemption basket, ETFs can experience dramatic creation/redemption activity early in the funds lifecycle.
By excluding the first 6 months of a funds data, I essentially impose a 3.5 year requirement.
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I winsorize all returns and premiums at seven standard deviations; estimated separately for
each ETF.
The sample period starts on 31 May 2002 and ends on 31 December 2012. I chose
this particular starting date to coincide with the date of a major index revision for all MSCI
equity indices. These indices were adjusted to account for free float and the market
coverage was extended from 60 % to 85 %. Tracking was more complicated before this
index revision because the index was not fully investable as a large fraction of the
outstanding shares are typically privately held and not accessible for trading. More
importantly, the ETF market has undergone a dramatic expansion in scope and size in the
last 10 years and earlier data may not be as representative of current market conditions.
3.1 Definitions of Key Variables
The main focus of this paper is on excess comovement in the returns of ETFs. The first step
is to filter out the fundamental component of returns. One important advantage of using
ETFs is that we don’t need to estimate a Capital Asset Pricing Model. Instead, we can
simply analyze “excess” ETF returns, which are defined as follows:
ETFe RETF RNAV (2.2)
i,t i,t i,t
where the first (second) term is the return on the ETF (the NAV). ETF returns are calculated
from the bid-ask midpoint (plus dividends) rather than using the returns given in CRSP, as
suggested by Engle and Sarkar (2006). As it turns out, this measure of excess returns is
equal to the change in mispricing, with the definition being exact on days when the ETF
does not pay any dividends7. In order to determine whether comovement between ETF
returns are excessive we need to establish that it is the ETF, rather than the NAV leg that is
driving the results (see eq. 2.2). Hence we need to decompose the excess ETF return
further.

7 ETFs typically pay dividends every quarter or semi-annually.
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