Fisher College of Business
Working Paper Series
Charles A. Dice Center for
Research in Financial Economics
Do ETFs Increase Volatility?
Itzhak Ben-David,
The Ohio State University and NBER
Francesco Franzoni,
USI Lugano and the Swiss Finance Institute
Rabih Moussawi,
Villanova University and WRDS, University of Pennsylvania
Dice Center WP 2011-20
Fisher College of Business WP 2011-03-20
Revised: November 2017
This paper can be downloaded without charge from:
http://ssrn.com/abstract=1967599
An index to the working papers in the Fisher College of Business Working Paper Series is located at:
http://www.ssrn.com/link/Fisher-College-of-Business.html
fisher.osu.edu
Electronic copy available at: https://ssrn.com/abstract=1967599
Do ETFs Increase Volatility?
Itzhak Ben-David
Fisher College of Business, The Ohio State University, and NBER
Francesco Franzoni
USI Lugano and the Swiss Finance Institute
Rabih Moussawi
Villanova School of Business, Villanova University
and WRDS, The Wharton School, University of Pennsylvania
November 2017
Abstract
Due to their low trading costs, ETFs are potentially a catalyst for short-horizon liquidity traders. The liquidity
shocks can propagate to the underlying securities through the arbitrage channel, and ETFs may increase the
non-fundamental volatility of the securities in their baskets. We exploit exogenous changes in index
membership and find that stocks with higher ETF ownership display significantly higher volatility. ETF
ownership increases the negative autocorrelation in stock prices. The increase in volatility appears to
introduce undiversifiable risk in prices, because stocks with high ETF ownership earn a significant risk
premium of up to 56 basis points monthly.
Keywords: ETFs, volatility, arbitrage, fund flows
JEL Classification: G12, G14, G15
*
We are especially grateful to Andrew Ellul, Marco Di Maggio, Robin Greenwood (AFA discussant), and Martin Oehmke (NBER discussant). We
thank Pierre Collin-Dufresne, Chris Downing, Vincent Fardeau, Thierry Foucault, Rik Frehen, Denys Glushkov, Jungsuk Han, Johan Hombert,
Augustin Landier, David Mann, Rodolfo Martell, Massimo Massa, Albert Menkveld, Robert Nestor, Marco Pagano, Ludovic Phalippou, Anton
Tonev, Tugkan Tuzun, Dimitri Vayanos, Scott Williamson, Hongjun Yan, and participants at seminars and conferences at the NBER Summer
Institute (Asset Pricing), Toulouse School of Economics, Insead, HEC Paris, the Cambridge Judge Business School, Villanova University, USI
Lugano, the 4th Paris Hedge Funds Conference, the 5th Paul Woolley Conference (London School of Economics), the 8th Csef-IGIER Symposium
(Capri), the 5th Erasmus Liquidity Conference (Rotterdam), the 1st Luxembourg Asset Pricing Summit, the Center for Financial Policy Conference
at the University of Maryland, Jacobs Levy’s Quantitative Financial Research Conference at the Wharton School, the Geneva Conference on
Liquidity and Arbitrage, the 20th Annual Conference of the Multinational Finance Society, the 7th Rothschild Caesarea Conference, the Swedish
House of Finance, the FIRS conference (Toronto), and SAC Capital Advisors for helpful comments and suggestions. Ben-David acknowledges
support from the Neil Klatskin Chair in Finance and Real Estate and from the Dice Center at the Fisher College of Business. Franzoni acknowledges
support from the Swiss Finance Institute. An earlier version of this paper circulated under the title “ETFs, Arbitrage, and Shock Propagation.” The
authors do not have any material disclosure to make. The Internet Appendix for this paper is at
http://www.people.usi.ch/franzonf/ETFs_Internet_Appendix.pdf.
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Exchange-traded funds (ETFs) are gaining increasing popularity in financial markets. Introduced
in the early nineties, this asset class today boasts $2.5 trillion in AUM (assets under management)
in the United States, and $3.5 trillion globally, accounting for about 35% of volume in US equity
markets. The increased access to liquidity and diversification is undoubtedly the greatest benefit
for investors, and justifies ETFs’ popularity. ETFs innovate in multiple dimensions relative to
traditional index funds. First, they provide intraday liquidity. As a result, they can satisfy highfrequency demands for trading. Moreover, investment strategies from which retail investors were
typically precluded, such as the use of leverage and the possibility to short sell, have become widely
available thanks to ETFs.
One wonders, however, whether the same ease of trade that makes ETFs so popular does
not lead to unintended consequences for the securities in the ETF baskets. The liquidity of ETFs
likely attracts high-frequency demand. This demand can migrate to the underlying securities’
prices because ETFs and their basket are tied by arbitrage.1 Therefore, the ETF-underlying
securities might be exposed to a new layer of demand shocks, which can make the prices of these
securities more volatile. The paper explores this conjecture and its asset-pricing implications.
As a first step in testing this hypothesis, one must first understand the difference between
the conjectured mechanism and the impact that other institutional investors can have on asset
prices (e.g., Coval and Stafford (2007), Lou (2012), Vayanos and Woolley (2013)). Analogous to
the effect of mutual-fund or hedge-fund flows on stock prices, the demand for ETF shares
translates into price pressure on the underlying securities. What makes ETFs special is that they
1
If the ETF price deviates from the net asset value (NAV) of the portfolio holdings because of a demand shock,
arbitrageurs trade the underlying securities in the same direction as the initial shock to the ETF price. Thus, the
underlying securities can inherit the shocks that occur in the ETF market.
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allow investors to access the market continuously and at a low trading cost. Hence, they
potentially attract more high-frequency demand than other institutional portfolios, including
traditional index funds. Moreover, although active managers have leeway in the extent to which
they track their benchmark, which gives them control over the price impact of their trades,
arbitrage trading between ETFs and the underlying securities is mechanical and therefore prone to
generate a bigger price impact. Indeed, ETFs track specified indices, meaning that ETF
arbitrageurs have almost no discretion in terms of the timing and composition of their trades.
Hence, although the channel of shock propagation we conjecture is not qualitatively different
from the price impact other institutional investors could trigger as a response to flows, the
frequency at which ETFs operate and the passive nature of their strategies make the ETF arbitrage
a distinctive mechanism that warrants separate attention.
The natural alternative hypothesis is that ETFs provide a buffer for demand shocks that
would otherwise directly hit the underlying securities’ prices. Grossman (1989) makes this point
about the introduction of futures, which in this respect are analogous to ETFs. He argues the
existence of futures provides additional market-making power to absorb the impact of liquidity
shocks. As a result, volatility in the spot market is reduced (see also Danthine (1978), Turnovsky
(1983)). To disentangle the two hypotheses, one needs to measure the direction of the link
between the presence of ETFs and stock-level volatility.
The empirical analysis starts by providing suggestive evidence that ETFs attract shortterm investors. ETFs are, on average, significantly more liquid than the basket of underlying
securities in terms of bid-ask spread, price impact, and turnover. Consistent with theories positing
that short-horizon clienteles self-select into assets with lower trading costs (Amihud and
Mendelson (1986)), using trade-level data, we find that the institutions holding ETFs have a
significantly shorter horizon than those holding the underlying securities.
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Then we move on to the main test of the effect of ETFs on stock-level volatility, and show
a positive and significant link in ordinary least squares (OLS) regressions. ETF ownership is the
total fraction of a stock’s capitalization that is held by ETFs. A normal shock to ETF ownership
shifts the volatility of the median stock in the S&P 500 to a place between the 55th and 64th
percentiles.
Although the OLS regressions control for observable stock characteristics and include
stock fixed effects, ETF ownership might be an endogenous variable. To address this concern, we
rely on the natural experiment provided by the annual reconstitution of the Russell indexes
(Appel, Gormley, and Keim (2015), Chang, Hong, and Liskovich (2015)). Exploiting the
mechanical rule allocating stocks between the Russell 1000 and 2000 indexes, we use the indexswitching event as an instrument for ETF ownership. This methodology confirms the impact of
ETF ownership on volatility is positive and statistically significant. The shift in ETF ownership
that follows the index reconstitution pushes the median stock’s volatility up to the 65th percentile
of the distribution. The instrumental variable (IV) estimates somewhat exceed the OLS ones,
which suggests a negative omitted-variable bias in the latter. However, the local nature of the
experiment that we use for identification does not allow us to generalize these magnitudes to the
entire sample. Finally, we corroborate the validity of the exclusion restriction by showing that
switching indexes has a stronger impact in months when ETF ownership is greater, and for stocks
with a higher ratio of ETF ownership to mutual-fund ownership (index or active) and hedge-fund
ownership.
Next, we take on the task of separating the hypothesis that the observed increase in
volatility reflects the improvement in price discovery brought about by ETFs from the hypothesis
that it arises from non-fundamental demand for liquidity, which ETFs attract. In the former case,
the increased volatility would be the result of stock prices more promptly responding to
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fundamental news, as in Andrei and Hasler (2015). In the latter case, the new volatility would
amount to noise.
To separate these two alternatives, we rely on the premise that liquidity shocks
subsequently revert, whereas fundamental information leads to permanent price changes. First, we
estimate predictive regressions of stock returns as a function of ETF flows at the stock level and
daily frequency. We find that most of the contemporaneous stock-price impact of ETF flows
reverts over the next 40 days, corroborating the view that the demand shocks in the ETF market
translate into non-fundamental price changes for the underlying securities. Second, using variance
ratios, we find that ETF ownership leads stock prices to deviate from a random walk at the daily
frequency, and that the autocorrelation of returns becomes more negative. These findings support
the conjecture that ETFs add noise to stock prices.
Next, we explore the channel linking ETF ownership to stock volatility. First, using tradelevel data from Ancerno in OLS and IV regressions, we show that ETF ownership of stocks
attracts traders with higher turnover. We interpret this evidence as consistent with the argument
that ETFs attract a new clientele of investors, whose demand is passed on to underlying securities
through the arbitrage channel. Second, we provide indirect evidence on the role of ETF arbitrage
in increasing stock volatility. In particular, the effect of ETFs on volatility is weaker for stocks
with higher limits of arbitrage (i.e., bid-ask spread and short-selling fees) and is stronger during
times of more intense arbitrageur trading activity.
Finally, we study the implications of ETF ownership for expected returns. If the volatility
ETFs impound in stock prices is partly non-diversifiable, for example, because most listed stocks
are included in ETF baskets, investors may require compensation for bearing this risk. Consistent
with this conjecture, we find that a long-short portfolio of the top minus the bottom quintile of
stocks by ETF ownership earns a return premium of up to 56 basis points (bps) per month. This
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alpha survives in models that include up to seven risk factors, and the result is confirmed in Fama
and McBeth (1973) regressions that control for the price impact of ETF flows. Ultimately, the
evidence qualifies ETFs as a new source of systematic risk.
Our study relates to several strands of the literature. Evidence is mounting that institutions
have a role in impounding non-fundamental demand shocks into asset prices because of flows
from their investors (Coval and Stafford (2007), Greenwood and Thesmar (2011), Lou (2012),
Basak and Pavlova (2013, 2016), Vayanos and Woolley (2013), Anton and Polk (2014), Hombert
and Thesmar (2014), Lou and Polk (2014)). We highlight a previously unexplored channel:
arbitrage activity between ETFs and the underlying baskets.2
Recent empirical literature also studies the effect of ETFs on asset prices. Da and Shive
(2015) find that ETF ownership is associated with higher comovement of the underlying
securities. This idea is consistent with our results: ETFs impound the same shocks into all the
stocks in their basket and therefore make them comove. Israeli, Lee, and Sridharan (2015) claim
increased ETF ownership can lead to higher trading costs and lower benefits from information
acquisition for the basket securities, a combination that results in less informative stock prices.
Leippold, Su, and Ziegler (2015) build a model in which the impact of ETFs on return
correlations exceeds the effect of futures, and they provide consistent empirical evidence in timeseries tests. Relative to these studies, our paper provides causal evidence of the shocktransmission channel and explores the implications for expected returns. Combining theory and
2
Our paper indirectly relates to the rich literature on the effect of indexing (Shleifer (1986), Barberis, Shleifer, and
Wurgler (2005), Greenwood (2005), Wurgler (2011), Chang, Hong, and Liskovich (2015)). The trigger for the effect
we measure is trading in ETFs, as opposed to index reconstitution. Index membership matters only in defining the
stocks that ETFs affect.
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empirics, Chinco and Fos (2016) describe the rebalancing cascades that follow from shocks to a
non-fundamental stock price, and test this theory in the context of ETFs. Bhattacharya and
O’Hara (2017) show theoretically that ETFs can increase price fragility due to information
linkages. Finally, Malamud (2015) develops a model in which ETFs can affect volatility through
the liquidity-shock-transmission channel as well as through the time-varying risk premiums
investors require as compensation for exposure to these shocks. Both of these claims are
consistent with our empirical evidence.3
Our study relates to the long-running debate on the effect of derivatives on the quality of
the underlying securities’ prices. For example, Stein (1987) argues that imperfectly informed
speculators in futures markets can destabilize spot prices. Grossman (1989) supports the
alternative view that futures improve price efficiency.4 We contribute to this debate by providing
systematic evidence from ETFs, an asset class similar to futures but potentially more attractive to
liquidity traders due to the lack of margin requirements and the absence of rollover risk. In
December 2014, the AUM in ETFs tracking the S&P 500 surpassed the open interest in futures on
the same index, suggesting that investors use ETFs as a way to achieve exposure to the stock
market (Amery (2015)).
3
We refer to Ben-David, Franzoni, and Moussawi (2017) for a detailed treatment of the growing literature on ETFs.
4
Earlier studies that examined the impact of derivatives on volatility focused on futures. Bessembinder and Seguin
(1992) find that high trading volume in the futures market is associated with lower equity volatility. They also find
that unexpected futures trading volume is positively correlated with equity volatility. Chang, Cheng, and Pinegar
(1999) document that the introduction of futures trading increased the volatility of stocks in the Nikkei index stocks.
Roll, Schwartz, and Subrahmanyam (2007) find evidence of Granger causality between prices in the futures and
equity markets.
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The study proceeds as follows. Section I provides institutional details and data description.
Section II develops the hypotheses. Section III documents the effects of ETF ownership on stock
volatility. Section IV explores the channel through which ETF ownership impacts stock volatility.
Section V investigates the asset-pricing implications of the impact of ETF ownership on stock
volatility. Section VI concludes the study.
I.
A.
Institutional Details and Data Description
Institutional Details
ETFs are investment companies whose objective is to replicate the performance of an
index, analogously to index mutual funds. Unlike index funds, ETFs are listed on an exchange
and trade throughout the day. ETFs were first introduced in 1990 in Canada, and entered the
United States with the issuance in January 1993 of the Standard & Poor’s Depository Receipts
(SPDR) tracking the S&P 500 (ticker: SPY). SPY is currently the largest ETF in the world, with
about $224 billion in assets. The number of ETFs and other exchange-traded products (ETPs) in
the United States subsequently exploded to more than 1,969 (6,625 globally) by the end of 2016,
spanning various asset classes.
To illustrate the growing importance of ETFs in the ownership of common stocks, we
present descriptive statistics for the S&P 500 and Russell 3000 universes in Table I. For S&P 500
stocks, the average fraction of a stock’s capitalization held by ETFs has risen almost 50 times,
from 0.14% in 2000 to 7.05% in 2015. The statistics for the Russell 3000 universe paint a similar
picture. The growth of ETFs appears even more drastic when compared to index funds, which are
the closest substitute, and active funds. Index fund average stock ownership, although higher in
the early years, was remarkably stable in this sample. At the end of the period, ETFs held more
than twice as much as index funds in the average stock. In terms of AUM in S&P 500 stocks,
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index funds grew by about 73%, which is a large number, but orders of magnitude smaller than
the growth in ETFs’ AUM. The size of active funds, although still significantly larger than for the
passive vehicles throughout the sample, grew significantly less than ETFs.
Futures are similar to ETFs in that they track an index. Unlike futures, ETFs do not
involve a rollover of the expiring contract, which can erode performance for investors with
horizons spanning beyond the short maturity of a futures contract. According to BlackRock, the
annualized rollover cost of a futures position in large-cap stocks (S&P 500, Euro Stoxx 50, FTSE
100) ranges from 0.9% to 1.4%. The total expense ratio for an ETF on the same indexes can be as
low as 0.05% (e.g., the Vanguard S&P 500 ETF). Hence, ETFs provide a more cost-efficient way
to track an index, especially for investors with uncertain trading horizons.
ETFs are traded in the secondary market by retail and institutional investors, in a fashion
similar to closed-end funds. However, unlike closed-end funds, new ETF shares can be created
and redeemed. Because the supply and demand in the secondary market determines the price of
ETF shares, the ETF price can diverge from the value of the underlying securities (the NAV).5
Some institutional investors called “authorized participants” (APs), who are dealers that have
signed an agreement with the ETF provider, can trade bundles of ETF shares (called “creation
units,” typically 50,000 shares) with the ETF sponsor. An AP can create new ETF shares by
transferring to the ETF sponsor the securities underlying the ETF. These transactions constitute
the primary market for ETFs. Similarly, the AP can redeem ETF shares and receive the
5
Unlike premiums and discounts in closed-end funds (e.g., Lee, Shleifer, and Thaler (1991), Pontiff (1996)), price
divergence between the ETF and the NAV can be more easily arbitraged away thanks to the possibility of
continuously creating and redeeming ETF shares. As a result, ETF premiums/discounts are orders of magnitude
smaller than for closed-end funds.
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underlying securities in exchange. For some funds, ETF shares can be created and redeemed in
cash.6,7
If an ETF trades at a premium relative to the NAV, APs have an incentive to buy the
underlying securities, submit them to the ETF sponsor, and ask for newly created ETF shares in
exchange. Then the AP sells the new supply of ETF shares on the secondary market. This process
puts downward pressure on the ETF price and potentially leads to an increase in the NAV,
reducing the premium. In the case of a discount, APs buy ETF units in the market and redeem
them for the basket of underlying securities from the ETF sponsor. Then the APs can sell the
securities in the market. This process generates positive price pressure on the ETF and possibly
negative pressure on the NAV, which reduces the discount.
ETF arbitrage also takes place continuously throughout the day and is carried out by
hedge funds and high-frequency traders. These investors do not need to engage in primary market
trades. On the secondary market, they can buy the inexpensive asset and short sell the more
expensive one between the ETF and the basket of underlying securities. They hold the positions
until prices converge, at which point they close down the positions to realize the profit. Of course,
the uncertainty involved in these profits does not qualify these trades as an arbitrage in a strict
sense. ETF sponsors facilitate arbitrage activity by disseminating NAV values at a 15-second
frequency throughout the trading day. They do so because the smooth functioning of arbitrage is
what brings about the low tracking error of these instruments. Because of the low trading costs
6
Creation and redemption in cash is especially common with ETFs on foreign assets or for illiquid assets, for
example, fixed-income ETFs.
7
Petajisto (2013) describes the fixed creation/redemption costs as ranging in absolute terms from $500 to $3,000 per
creation/redemption transaction, irrespective of the number of units involved.
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and availability of information, arbitraging ETFs against the NAV has become a popular trading
strategy in recent years. According to some industry participants, statistical arbitrage accounts for
50% of the volume in the SPY, which is the most traded security in the United States, with a $24
billion average daily volume (last three months of 2015). Over our sample period, secondarymarket volume in ETFs accounted for about 93% of total trading volume, which includes primary
market creation and redemption activity.
These institutional details, with some modifications, also apply to synthetic ETFs, which
replicate the performance of the index using total return swaps and other derivatives, and for
which creation and redemption occur in cash. The secondary-market arbitrage still involves
transactions in the underlying securities. Similarly, the arbitrage process is an inherent
characteristic of all types of ETFs. Hence, one should expect the effects we describe in this paper
to hold for all types of underlying assets, irrespective of the replication mechanism.
B.
The Data
We use Center for Research in Security Prices (CRSP), Compustat, Bloomberg, and
OptionMetrics data to identify ETFs traded on the major US exchanges and to extract returns and
prices. We first draw information from CRSP for all securities that have a historical share code of
73, which exclusively defines ETFs. We then screen all US-traded securities in the Compustat
XpressFeed and OptionMetrics data, identifying ETFs using the security-type variables, and
merge this sample with the CRSP ETF sample.
In our analysis, we focus on ETFs that are listed on US exchanges and whose baskets
contain US stocks. Further, we restrict our sample to “plain vanilla” products that engage in
physical replication; that is, they hold the securities of the basket they aim to track. We omit from
our sample leveraged and inverse-leveraged ETFs that use derivatives to deliver the performance
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of the index, which represent about 2% of the assets in the sector according to BlackRock
(December 2014). We also omit active ETFs that are still below 1% of AUM in the sector.8
We use the Thomson-Reuters Mutual Fund Ownership database as the source of the ETF
holdings data in our sample. Our final dataset contains 454 distinct equity ETFs, providing
holdings information for 93% of all domestic equity ETFs in the United States between January
2000 and December 2015, with around 92% coverage of all US equity ETFs in December 2015,
and a maximum coverage of 97.1% of all domestic equity ETFs during our sample period. The
Internet Appendix (I.A.) details how we address the issue of unreliable Thomson holdings data
starting in June 2015. We use total shares outstanding at day-end to compute the daily market
capitalization of each ETF and to measure the net share creations/redemptions (i.e., flows) for
each ETF daily. Bloomberg is our primary source for shares outstanding, being more accurate,
and we complement it with Compustat and OptionMetrics in case of data gaps. As a dependent
variable of our main tests, we compute daily stock volatility at the monthly frequency as the
standard deviation of daily returns within a month. For some of our tests, we compute intraday
volatility at a daily frequency using second-by-second data from the Trade and Quote (TAQ)
database. We compute stock-level order imbalance at the daily frequency. We use the daily TAQ
millisecond feed to classify every trade between 2007 and 2015, and the monthly TAQ feed at the
second-by-second granularity for the previous period (2000–2006). We follow Holden and
Jacobsen (2014) and modify the Lee and Ready (1991) algorithm, according to the logic in Ellis,
8
We restrict our sample to the following Lipper Objective Codes: Broad Based US Equity: CA, EI, G, GI, MC, MR,
SG, and SP. We also include Sector Funds that invest in US companies with codes BM, CG, CS, FS, H, ID, NR, RE,
TK, TL, S, and UT.
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Michaely, and O’Hara (2000), in order to classify every trade into a buy or sell trade (more details
are in the I.A.).
We extract stock-lending fees from the Markit Securities Finance (formerly Data
Explorers) database. We use the average lending fee over the prior seven days. For some of our
tests, we use the Ancerno institutional trade-level data from the firm Abel Noser.9 Ancerno
provides information on all the trades of a portfolio during the period in which the manager
reports to the database.
Table II reports summary statistics for the variables we use in the analysis. Panel A
presents summary statistics for the monthly stock-level sample of our main regressions; Panel B
reports the correlations for the same variables. Panel C presents summary statistics for the
variables that are used in the return regressions at the daily frequency. Panel D presents statistics
for the variables derived from the trade-level Ancerno dataset. We further describe these variables
in later sections and provide definitions in the I.A. Table AI.
II.
A.
Hypotheses Development and Evidence on Trading Horizon
Hypotheses Development
The main testable hypothesis of the paper is that ETFs are a catalyst for liquidity trading,
and the ensuing price pressure propagates to the underlying securities via arbitrage. According to
this hypothesis, stocks with higher ETF ownership should display higher volatility, all else being
equal. We label this conjecture the liquidity-trading hypothesis.
We provide a simple illustration of this channel. We imagine a situation in which the ETF
price and the NAV of its portfolio are aligned at the level of the fundamental value, as in Figure
9
Previous studies, such as Puckett and Yan (2011) and Anand et al. (2012, 2013), have argued convincingly for the
representativeness of the institutions in Ancerno for the broader universe of institutional investors.
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1a. Then a liquidity shock, namely, one that is unrelated to information about future cash flows,
hits the ETF market. Arbitrageurs absorb the liquidity demand by shorting the ETF. Because they
are risk averse, as in Grossman and Miller (1988), arbitrageurs require compensation for the
(negative) inventory in the ETF they are taking on. Hence, the ETF price has to rise (Figure 1b).
To hedge their short ETF position, arbitrageurs take a long position in the securities in the ETF
basket. To compensate market makers, the prices of the basket securities have to rise, as in Figure
1c. Eventually, when other sources of liquidity materialize, prices revert to fundamentals (Figure
1d). This prediction also emerges in Malamud’s (2015) dynamic model of the ETF market.
For example, the trades of hedge funds that carry out high-frequency ETF arbitrage
conform to the mechanism described in Figure 1. In addition, hedge funds can impound
mispricing indirectly through their use of ETFs in statistical arbitrage. Suppose hedge funds short
sell an overpriced stock and hedge the industry risk by going long in the corresponding sector
ETF. This trade puts upward pressure on the ETF price (as in Figure 1b). Then ETF arbitrageurs
transfer the price pressure to the securities in the ETF basket (as in Figure 1c). Thus, ETFs can
propagate mispricing to the underlying securities not only because they are traded directly by
uninformed investors, but also because they participate in long-short strategies that involve other
mispriced securities (similar to the propagation mechanism in Hong, Kubik, and Fishman (2012)).
The liquidity-trading hypothesis predicts an increase in the demand shocks hitting the
underlying securities because of increased ETF ownership. However, if the same amount of
liquidity traders merely shifted from trading a given stock to trading the ETFs holding that
security, the volatility in the stock’s price would not increase. To observe an increase in volatility,
ETFs would need to attract a new layer of liquidity demand. This scenario could happen if ETFs
allowed a new breed of short-horizon investors to express their liquidity demand, with more ease
than using stocks. To explore this conjecture, the first part of our analysis is devoted to comparing
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the trading horizons of stock and ETF investors (subsection II.B). Moreover, subsection IV.A
investigates the effect of ETF ownership on the investor churn ratio at the stock level.
The most natural alternative hypothesis to the liquidity-trading hypothesis is that ETFs
actually decrease volatility. Grossman (1989) makes such a claim about futures, which we extend
by analogy to ETFs. The argument is that the introduction of a correlated asset class, such as
ETFs, adds a new layer of market-making power, which acts as a liquidity buffer. Investors who
would originally satisfy their liquidity demands using the ETF-underlying stocks can now find
satisfaction in the ETF market. Consequently, the liquidity shocks hitting the underlying
securities are dampened and volatility becomes smaller. We label this conjecture the liquiditybuffer hypothesis. To separate these two hypotheses, we measure the causal effect of ETF
ownership of stocks on stock-level volatility. Section III contains this analysis.
The liquidity-trading hypothesis partly differs from an alternative hypothesis that claims
ETFs are vehicles for improved price discovery (e.g., Glosten, Nallareddy, and Zou (2016),
Madhavan and Sobczyk (2016)). In this alternative scenario, the starting point is a fundamental
shock, that is, a permanent change in the value of the underlying securities. If ETFs facilitate
price discovery, ETF prices adjust immediately to the new information, while the underlying
securities’ prices remain temporarily fixed (“stale pricing”). We illustrate this situation in Figure
2. A shock to the fundamental value of the ETF components (Figure 2b) perturbs the initial
equilibrium (Figure 2a). The ETF price moves first because of price discovery (Figure 2c), and
the prices of the underlying securities move with a delay because of stale pricing (Figure 2d). In
this alternative situation, the presence of ETFs allows prices to react more quickly to
fundamentals. As a result, a positive link could exist between ETF ownership and volatility, but
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the increased volatility would result from the faster impounding of fundamental information into
prices. We label this conjecture the price-discovery hypothesis.10
To disentangle the liquidity-trading hypothesis from the price-discovery hypothesis, we
need to test whether ETFs are associated with increased mean reversion in prices, which follows
from the propagation of liquidity shocks (as per Figure 1). Analogously, one can measure the
effect of ETF ownership on price efficiency. Finally, to corroborate the liquidity-trading
hypothesis, one should show that non-fundamentally motivated ETF trading has an impact on
stock volatility. Sections IV and V deal with these issues.
B.
ETFs vs. Stocks: Liquidity, Investor Types, and Trading Horizon
The liquidity-trading hypothesis posits that ETFs increase the volatility of the securities in
their baskets because of the propagation of liquidity shocks. This conjecture requires the
condition that, in a world without ETFs (i.e., the counterfactual world), less liquidity trading in
the underlying securities would occur. Although we directly test this conjecture in subsection
IV.A, here we provide suggestive evidence in its support by contrasting the liquidity of ETFs with
that of their portfolio constituents and by comparing investor turnover in the two asset classes.
Drawing inspiration from the theory in Subrahmanyam (1991), one can argue the bid-ask
spreads on ETFs are on average low because of a less severe information asymmetry than in
10
Theoretical underpinning for this hypothesis can be found, for example, in Amihud and Mendelson (1987), who
provide a simple model in which the volatility of trading prices is positively related to the speed at which prices
adjust to fundamentals. In addition, Andrei and Hasler (2015) prove theoretically and empirically that investor
attention increases the sensitivity of prices to fundamentals and therefore volatility. If ETF arbitrage makes prices
adjust more promptly to fundamentals, or if stocks in ETFs are exposed to higher investor attention, the fundamental
volatility of the underlying securities can increase.
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stocks. Indeed, investors with stock-level private information are more likely to trade individual
securities, and market makers impose higher bid-ask spreads to overcome adverse selection. By
contrast, investors who place uninformed directional bets or trade for hedging purposes are more
likely to trade entire baskets, such as ETFs. As a result, ETF spreads are less likely to contain an
adverse-selection premium.
Table III, Panel A, presents systematic evidence on the difference in liquidity between
ETFs and the underlying portfolios along three dimensions: the percentage of the bid-ask spread,
the Amihud (2002) measure of price impact, and daily turnover. For all the ETFs in our sample,
we compute the average of each liquidity measure across all the stocks in the basket in a given
quarter. Then, to replicate the strategy of an investor who allocates funds to all ETFs according to
their market capitalization, we take the value-weighted mean of these measures across all ETFs in
a given quarter. The table reports the time-series average of these means in the 64 quarters of the
sample, along with the results of tests for the statistical significance of their difference. Along all
three dimensions, the average ETF is significantly more liquid than its basket stocks. The bid-ask
spread is lower by about 20 bps. Price impact, as measured by the Amihud (2002) ratio, is also
significantly lower for ETFs. Finally, ETF turnover is about 7.5% higher.
A corollary of the conjecture that ETFs are more liquid than the underlying baskets is that
ETF investors should display higher turnover. This prediction stems, for example, from Amihud
and Mendelson’s (1986) clientele effect, whereby short-horizon investors choose to trade in more
liquid securities. Table III, Panel B, supports this conjecture. We compare the churn ratio of
different institutional classes in common stocks and ETFs.11 The churn-ratio measure comes from
Cella, Ellul, and Giannetti (2013), who compute an institutional investor-level churn ratio as the
11
Institutional category definitions from Thomson O.P. (Ownership and Profiles) are in I.A. Table AII.
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sum of quarterly absolute changes in dollar holdings over average AUM. For all investor classes,
the churn ratio is significantly larger for ETFs than for stocks.
Also interesting, the panel reports shares held by each group as a fraction of total shares
outstanding. The first notable fact is that throughout the entire sample period, the institutional
ownership of ETFs is far smaller (at 50.7% on average) than the institutional ownership of stocks
(at 65.4% on average). Based on Stambaugh’s (2014) argument that uninformed traders are
mostly present among retail investors, this evidence suggests a higher density of liquidity traders
in the ETF investor base. Second, research firms, which include broker-dealers, have greater ETF
ownership (17.6%) than stock ownership (2%). This class of owners, along with hedge funds,
corresponds to ETF arbitrageurs and market makers (including APs).
The churn-ratio statistics in Table III, Panel B, may underestimate the real extent of
investor turnover, because the quarterly frequency at which they are computed conceals intraquarter trading. To overcome this limitation, we rely on the Ancerno dataset, which contains
institutional trade-level data. We compute two measures of the manager-level churn ratio, noting
Ancerno does not provide information on AUM. For each manager and security within a quarter,
our first measure compares the total dollar value of buy-and-sell trades with the absolute value of
the difference between buy-and-sell trades. Hence, for manager k, security i, during quarter q, the
churn ratio is
,,
1
$
$
,,
,,
$
$
,,
,,
.
(1)
This variable ranges between 0 and 1: 0 if the trades in the quarter are in only one direction (either
buy or sell), and 1 if as much buying activity as selling activity occurs in that security over the
quarter. This variable is averaged across all the securities that are traded by a manager in a
quarter, for ETFs and stocks, to obtain the manager-level measure of the churn ratio.
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This definition of the churn ratio yields the same number when the manager sells and buys
the security only once during the quarter as when the manager flips the security several times.
Hence, we modify this variable and take into account the number of times the trade in the security
changes from buy to sell during the quarter, and vice versa:
,,
where
,,
,,
∗
1
,,
2
,
(2)
is the number of times the direction of a given trade is different from that of the
preceding trade during the quarter.12 I.A. Table AIII provides summary statistics for the two
churn-ratio variables, splitting the manager-quarter-level sample between stocks and ETFs.
Across subsamples, we note that both measures of the churn ratio give a significantly higher score
for ETFs. The raw churn-ratio measure is 0.105 for stocks and 0.299 for ETFs, a 2.8 times
difference. The adjusted churn ratio is 0.137 for stocks and 0.450 for ETFs, a 3.3 times difference.
In Table III, Panel C, we regress the two churn-ratio variables on a dummy for whether the
security is an ETF. Standard errors are clustered at the quarter and manager levels. Across all
specifications, including different types of fixed effects, the difference in the churn ratio between
ETFs and stocks is statistically significant.
Overall, the empirical evidence in this section suggests institutions trade ETFs at a
substantially higher frequency than stocks. This result provides initial support for the main
assumption behind the liquidity-trading hypothesis, namely, the idea that ETFs are a catalyst for
short-horizon investors. In subsection IV.A, we test whether this clientele of high-turnover
investors is passed on to the underlying securities.
12
With this measure, for example, a manager that has the sequence of trades [+100, -100, +100, -100] in a given
security has an adjusted churn ratio of 2, which is double that of a manager with the sequence trades [+100, -100].
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III.
A.
The Effect of ETF Ownership on Volatility
ETF Ownership and Volatility: OLS Regressions
To separate the liquidity-trading from the liquidity-buffer hypothesis, we test whether ETF
ownership leads to higher volatility of the underlying securities. ETF ownership of stock i in
month t is defined as the sum of the dollar value of holdings by all ETFs investing in the stock,
divided by the stock’s capitalization at the end of the month:
∑
, ,
,
where J is the set of ETFs holding stock I;
,
,
, ,
(3)
,
is the weight of the stock in the portfolio of ETF
j, which is extracted from the most recent quarterly report; and
,
is the AUM of ETF j at the
end of the month. The I.A. provides more details on the construction of this variable.
Based on equation (3), variation in ETF ownership comes from three sources. First, stocks
are typically part of multiple indices (e.g., a stock might be part of the S&P 500, the S&P 500
Value, the Russell 3000, and a sector index). Second, variation in ETFs’ AUM occurs over time
and across products. Third, variation exists in weighting schemes. For example, the S&P 500 and
the Russell 2000 are capitalization-weighted, but the Dow Jones is price-weighted; also, our
sample contains 17 products that explicitly mention equal-weighting in their names.
The three sources of variation in ETF ownership present different types of potentially
spurious correlation with stock volatility. For instance, if the weights at the numerator do not
grow at the same pace as the market capitalization at the denominator (e.g., for equal-weighted
indexes), a spurious link could exist between ETF ownership and volatility resulting from the
correlation between stock size and volatility. To avoid this issue, we control for logged market
capitalization. ETFs’ AUM and the number of ETFs covering a stock also present some potential
endogeneity issues. For example, investors’ demand for existing or new ETFs may relate to how
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popular a given sector or asset class is. This popularity also affects the trading intensity and the
volatility of the underlying securities. If this argument is valid, popularity could generate a
positive relation between ETF ownership and volatility that confounds the causal effect we are
trying to identify. On the other hand, the number of ETFs tracking a given stock depends on the
number of indexes in which a stock appears. If more established, less volatile firms are more
likely to be members of an index, the correlation between ETF ownership and volatility might be
negatively biased.
We take several steps to guard against potentially omitted variables. First, we include
stock and month fixed effects. Second, we control for stock size and liquidity, which is measured
by the inverse of the stock price, the Amihud (2002) illiquidity measure of price impact, and the
bid-ask spread. Finally, we include standard predictors of returns that could also relate to
volatility, such as the book-to-market ratio, past-12-month returns, and gross profitability (gross
income scaled by total assets, as in Novy-Marx (2013)).
We start by reporting the results of OLS regressions of daily volatility in a given month on
ETF ownership at the end of the prior month. Table IV, Panel A, presents separate regressions for
S&P 500 stocks and for Russell 3000 stocks. The goal is to assess how the effect of interest varies
for stocks of different size. All the controls date from the end of the prior month. We also include
stock and month fixed effects in all regressions. Standard errors are double clustered at the stock
and month levels. To ease interpretation, we standardize volatility and ETF ownership by
subtracting the sample mean and dividing by the sample standard deviation in the entire sample.
From column (1) of Table IV, Panel A, we infer that the relationship between ETF
ownership and volatility is positive and strongly statistically significant. The magnitude seems
economically important, because a one-standard-deviation move in ownership is associated with
16.4% of a standard deviation change in daily volatility. In section III.C, we provide a more
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detailed discussion of economic magnitudes. The positive and significant link between ETF
ownership and stock volatility provides the first piece of evidence in support of the liquiditytrading hypothesis and against the liquidity-buffer hypothesis.
Next, we test whether ETF ownership captures a different effect from the ownership by
other institutional investors. Among these, open-end mutual funds are the most similar to ETFs
because they also tend to receive flows on a daily frequency. Given that hedge funds are also
likely to trade at a high frequency, similar to ETF arbitrageurs with which they partly overlap, we
also control for hedge-fund ownership. In column (2) of Table IV, Panel A, we include lagged
ownership by active and index mutual funds, as well as by hedge funds, measured in the same
way as ETF ownership (and standardized). The coefficients on both mutual-fund-ownership
variables are positive (significant only for active funds), whereas hedge-fund ownership is
insignificant. The point estimates of both mutual-fund-ownership variables are significantly
smaller in magnitude than the slope on ETF ownership, which remains intact. Thus, ETF
ownership appears to have an independent and stronger tie to volatility.
In column (3) of Panel A, we replicate the analysis of column (2) using the subsample for
which three lags of the dependent variable are available. We find that the slope on ETF ownership
is not materially impacted. In column (4), we include three lags of volatility to address the
concern that the persistence in volatility could introduce reverse causality. The coefficient on ETF
ownership is significant with a magnitude of 7.7% of a standard deviation.
Extending the universe to smaller stocks (columns (5) to (8)), the relationship between
ETF ownership and volatility is somewhat weaker: 5.3% to 8.7% of a standard deviation. The
lower sensitivity of volatility to ETF ownership in a sample that is dominated by small stocks is
consistent with the channel behind the liquidity-trading hypothesis. In the secondary market,
arbitrageurs can choose to minimize transaction costs by concentrating on larger stocks in the
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ETF baskets when constructing the replicating portfolio. Such behavior, called “optimized
replication,” can explain why smaller stocks inherit fewer shocks from the ETF market.
To confirm that the relation of interest is a pervasive phenomenon throughout the sample
period, in Table IV, Panel B, we carry out the analysis for the 2000–2006 (early period), 2007–
2008 (crisis period), and 2009–2015 (late period) subsamples. In this case, the variables of
interest are standardized using their standard deviation in the relevant sample. The crisis period
aside, the estimates tend to be somewhat larger in the late period, especially in the specifications
that do not control for lagged volatility. Moreover, the effect on Russell 3000 stocks, which are on
average smaller, is more important in the late than in the early period. Arguably, this fact results
from ETFs covering smaller and smaller corners of the market. Overall, the evidence resonates
with the idea that, as ETFs become a more important asset class, their impact on the underlying
securities becomes stronger. The most striking result is that during the crisis, the effect of interest
is about three times as large as in the other periods. Consistent with the liquidity-trading
hypothesis, this fact suggests market liquidity modifies the impact of ETFs on the underlying
securities. The crisis led to an illiquid market, so that ETF arbitrage had a bigger impact on stock
prices.
In I.A. Table AIV, we study whether the presence of ETFs leads to increased tail risk for
the underlying stocks. We find that stocks with higher ETF ownership display larger negative
skewness at times of market stress, measured by the VIX index and by aggregate selloffs of ETFs
by institutional investors. This result suggests that not only do ETFs increase stock volatility on a
daily basis, but they also can destabilize stock prices in periods of market turmoil, when they
experience a negative order imbalance.
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B.
Identification Using a Quasi-Natural Experiment
An identification based on cross-sectional and time-series variation in ETF ownership,
which underlies the OLS results in Table IV, can be questionable if the controls and fixed effects
fail to capture characteristics that co-determine ETF ownership and volatility. For this reason, we
next present results from a more robust identification approach.
Chang, Hong, and Liskovich (2015) devise an identification strategy that exploits the
exogenous variation in membership in the Russell 1000 and the Russell 2000 indexes. In our
implementation, we closely follow Appel, Gormley, and Keim (2015), who cast this experiment
within an IV framework.13
The Russell 1000 index comprises the top 1,000 stocks by market capitalization, and the
Russell 2000 includes the next 2,000 stocks. Russell Inc. reconstitutes the indexes on the last
Friday of June every year, based only on end-of-May stock capitalization; hence, no discretion is
typically involved in index assignment. Index composition remains constant for the rest of the
year. For stocks in close proximity to the cutoff, changes in index membership are random events,
once we control for the assignment variable, namely, market capitalization, because they result
from random variation in stock prices at the end of May.
Chang, Hong, and Liskovich (2015) show that although the amount of passive assets
benchmarked to the Russell 1000 is 2 to 3.5 times larger than those tracking the Russell 2000, the
weights of the top stocks in the Russell 2000 are about 10 times larger than those of the bottom
stocks in the Russell 1000. Consequently, a significantly larger amount of passive money tracks
the top Russell 2000 stocks than the bottom Russell 1000 stocks.
13
Other papers that exploit the Russell reconstitution are Cao, Gustafson, and Velthuis (2014), Crane, Michenaud,
and Weston (2014), Lu (2014), Mullins (2014), and Fich, Harford, and Tran (2015).
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Figure 3a provides evidence consistent with the latter claim in the context of ETFs. The
figure plots average ETF ownership as a function of market-capitalization rankings for the Russell
3000 universe, in bins of 10 stocks, for 500 stocks to the right and 500 to the left of the cutoff (the
1,000th position). We note that stocks immediately after the cutoff appear to display
discontinuously higher ownership than stocks immediately to the left. Some evidence of
discontinuity is also present for index funds (Figure 3b), although no such evidence exists in the
case of active funds (Figure 3c) and hedge funds (Figure 3d). The index-fund evidence motivates
us to control for index-fund ownership in our tests and to carry out additional tests to ensure that
ETF ownership, and not index-fund ownership, is driving our findings.
We carry out a two-stage least-squares estimation. In each stage, we run our regressions
on two separate groups of stocks: those that in May, before index reconstitution, are in the Russell
1000 and those that are in the Russell 2000. The sample composition remains constant for all the
months between June, the first month after index reconstitution, and May of the next year. The
first stage consists of a regression of ETF ownership on an indicator variable for whether the
stock switches index membership in June. For the Russell 1000 sample, the indicator variable
flags stocks that switch to the Russell 2000, and vice versa for the Russell 2000 sample; the
dummy captures a switch to the Russell 1000. In regression form, the first stage is
(4)
∗
.
In the second stage, for the same two separate groups of stocks, we regress volatility on
the fitted value of ETF ownership from the first stage. The regression is
∗
.
In addition to the control for market capitalization, that is, the assignment variable, we
include the same set of controls as in the OLS regressions. Time fixed effects are part of the
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(5)
regression, but we do not include stock fixed effects, because identification in this experiment is
inherently cross sectional; in other words, identification results from comparing switchers to nonswitchers in a given time period. Standard errors are double clustered at the stock and month
levels. We standardize the ownership variables and volatility in the relevant samples to ease
interpretation. We experiment with different specifications of the ranking variable: first-, second-,
and third-degree polynomials.14
The identifying assumption that needs to be satisfied is the exclusion restriction, that is,
the requirement that the event affects the outcome variable only through the treatment variable. In
our context, this assumption translates into the condition that a switch in index membership only
affects volatility through ETF ownership. Later in this section, we discuss the reasons this
assumption might fail, and conclude that this concern does not appear to be relevant in our
context.
We cast our analysis at the monthly frequency because every month we have a different
observation on the dependent variable (i.e., daily volatility). The first index reconstitution in our
sample occurs in May 2000. Until the June 2006 reconstitution, the cutoff for reclassification was
simply the 1,000th position in terms of market capitalization. Thus, in our main tests, we include
end-of-month data between June 2000 and May 2007. We consider several bandwidths: 100, 200,
300, 400, and 500 stocks on each side of the cutoff. The validity of the Russell experiment
becomes questionable after 2006, when Russell Inc. adopted a banding rule whereby stocks only
switch from their current index if they move beyond a 5% range around the market-capitalization
percentile of the 1,000th stock. As expected, switches are more frequent before the introduction of
the banding rule (I.A. Table AV). In I.A. Table AVII, we show that our results hold even in the
14
Results for the second- and third-degree polynomials are in I.A. Table AVII.
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longer sample period, but are noisier in the late subsample (Table AVIII). Given that during the
migration of stocks across indexes, spurious effects on volatility might occur, in I.A. Table AVI,
we provide results excluding the months of May and June. The conclusions remain unaffected.
Table V, Panel A, shows the first-stage regressions. We separately consider stocks that
belong to the Russell 1000 before index reconstitution (columns (1)–(5)) and stocks belonging to
the Russell 2000 before index reconstitution (columns (6)–(10)). The results of this test show that
switching indexes has a strong impact on ETF ownership. The slope on the switch indicator in
column (1) suggests ETF ownership in the 12 months after reconstitution increases for the stocks
switching to the Russell 2000 by about 19.6% of a standard deviation. Across columns (1)
through (5), the average effect is larger at about 35.7%. Column (6) focuses on stocks that start
out in the Russell 2000 in May prior to reconstitution, with the same bandwidth (100 stocks to the
left and 100 stocks to the right of the cutoff between the Russell indexes). For the stocks that
switch to the Russell 1000 after reconstitution, ETF ownership decreases by about 18% of a
standard deviation. Across columns (6) through (10), the average estimate is about -33.9%. The
strong statistical significance in the first stage reassures us about the validity of the instrument.
Table V, Panel B, reports the second-stage estimates of the effect of ETF ownership on
volatility in the next month. Analogous to the layout in Panel A, the instruments are indicators for
a switch to either index, and the sample is restricted to members of either index pre-reconstitution.
The effect of ETF ownership on volatility is significant across all samples and bandwidths. The
coefficients range between 16.9% and 71.7%, about 31% of a standard deviation on average.
The larger IV estimates from Table V suggest the endogeneity of ETF ownership induces
a negative bias in the OLS estimates in Table IV. A negative bias can occur if, for example,
higher ETF ownership signals companies that belong to multiple indexes, which have less volatile
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stocks because they are more established companies. In section III.C, we provide a more detailed
discussion of the economic magnitude of these estimates.
Finally, we come back to assessing the validity of the exclusion restriction. This
assumption is violated if a correlated omitted variable exists that varies with index switches and
affects volatility. For example, a violation occurs if, after appearing among the top stocks in the
Russell 2000, a firm becomes more visible to investors. Prices can then react more quickly to
fundamental information and returns become more volatile, as Andrei and Hasler (2015) show.
Appel, Gormley, and Keim (2015) find analyst coverage is largely unaffected after inclusion in
the Russell 2000. Similarly, Crane, Michenaud, and Weston (2014) show that a switch to the
Russell 2000 does not lead to increased media coverage. These results are important for our study
because they suggest a rise in information production following switching is not likely to cause
the increase in volatility associated with the increase in ETF ownership. Moreover, in later results,
we show that ETFs increase mean reversion in stock prices, suggesting that the driver of the
increase in volatility is not only improved price discovery. Therefore, the evidence seems to rule
out this specific violation of the exclusion restriction.
Further corroboration of the validity of the exclusion restriction comes from combining
the cross-sectional identification from the index-switching experiment with time-series variation
in ETF ownership. In particular, if the IV estimates are truly measuring the causal effect of ETF
ownership, we should observe a stronger impact of index switching on volatility at times when
aggregate ETF ownership is larger. Following this argument, we regress stock-level volatility on
the interaction between the index-switching indicator and the (equally weighted) average of ETF
ownership across Russell 2000 stocks. If the exclusion restriction is satisfied, we would expect
switching to the Russell 2000 (Russell 1000) to have a more positive (negative) effect on
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volatility at times when ETF ownership is overall higher.15 The regressions include additional
interactions to control for aggregate ownership by other mutual funds (index and active) and
hedge funds, and for a time trend, given that ETF ownership increases over time. We also include
the non-interacted variables as well as the usual stock-level controls and month fixed effects. The
estimates in Table V, Panel C, broadly support the validity of the exclusion restriction. In
columns (1)–(5), the addition to the Russell 2000 has a larger impact on volatility at times of
higher average ETF ownership. In two cases, the effect is statistically significant. In all five
specifications focusing on the switch to the Russell 1000 (columns (6)–(10)), the decrease in
volatility is significantly larger in months when ETF ownership is higher.16
One may still wonder to what extent ETF ownership captures an independent effect from
that of ownership by other institutions. In particular, the concern exists that index-switching
stocks experience an overall migration of institutional owners, which in turn causes the change in
volatility. This concern is relevant given the evidence in Figure 3 suggesting that some
discontinuity in ownership is also present for index funds around the cutoff for index
15
Note that we expect a switch to the Russell 2000 (Russell 1000) to increase (decrease) volatility because that
switch increases (decreases) ETF ownership, based on the evidence in Table V, Panel A.
16
Note that in the sample consisting of 100 stocks around the cutoff, the effect of active fund ownership is
comparable in sign and magnitude to that of ETF ownership. Following the index reconstitution, other institutions
might rebalance their portfolios. Especially for the stocks closer to the cutoff, which are more likely to be involved in
the rebalancing, this trading activity can have an impact on volatility. We are, however, confident this effect is
separate from the effect of ETF ownership we document. ETF ownership remains significant as an independent driver
of volatility in specifications that also include active fund ownership (e.g., Table V, Panels B and C). Further
reassuring evidence comes from Table V, Panel D, discussed below.
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reconstitution. To address this issue, in Table V, Panel D, we provide a formal test of the
importance of ETF ownership relative to ownership by other funds in driving the volatility effect.
We study whether stocks switching to the Russell 1000, for which ETF ownership goes down,
experience a larger decrease in volatility if in May, before reconstitution, they have a higher ratio
of ETF ownership to ownership by other fund types. Reassuringly, the tests in Panel D reveal the
ownership ratio, with either index-fund or active-fund or hedge-fund ownership in the
denominator, magnifies the decrease in volatility for stocks exiting the Russell 2000. For a move
into the Russell 2000, which entails an increase in ETF ownership, we do not have a clear-cut
prediction on the sign of the interaction between the switch indicator and the ratio of ETF
ownership to other funds’ ownership. Hence, carrying out the test only for switches to the Russell
1000 makes sense.
Given the evidence in Table V, we feel more confident in a causal interpretation of the
positive relation between ETF ownership and stock-level volatility. This causal evidence provides
support for the liquidity-trading hypothesis and against the liquidity-buffer hypothesis.
C.
Discussion of the Economic Magnitude of OLS and IV Estimates
In I.A. Table AIX, we provide a thorough analysis of the economic magnitude of the
effect of ETF ownership on stock-level volatility. Here, we summarize the main conclusions.
For the OLS analysis, we assess the economic magnitude by measuring the shift in
volatility relative to the median stock in the sample following a one-standard-deviation change in
ETF ownership. The median stock shifts to a place between the 58th and 64th percentiles of the
volatility distribution for S&P 500 stocks, the upper bound coinciding with the less accurate
specification that does not include lagged volatility. For the Russell 3000 universe, the effects are
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more contained. The median stocks move to a position between the 55th and 57th percentiles of
the distribution.
In interpreting the economic magnitude of the IV estimates, one issue is especially
relevant. The estimated IV coefficients reflect a local average treatment effect (Imbens and
Angrist (1994)). In particular, the IV estimate, resulting from a natural experiment inducing a
switch between a control and a treatment group, measures the effect of treatment only on the units
that switch groups because of the outcome of the natural experiment. These units would not
otherwise receive treatment. Applied to our context, the IV estimates capture the effect of ETF
ownership on the stocks that enter the ETF basket only because of the index switch. These stocks
drastically change status from being intensively utilized by arbitrageurs in their replication of the
index (when they are at the top of the Russell 2000) to being neglected by arbitrageurs (when they
are at the bottom of the Russell 1000), and vice versa for a switch in the other direction.
Arguably, this drastic change of status results in a greater impact of a given amount of ETF
ownership than for the average stock. This argument can explain why the local average treatment
effect (LATE) is larger than the OLS effect.
Also important, the index-switching stocks experience, on average, a change in ETF
ownership of about 50 bps (Figure 3a). Therefore, the amount of “treatment” for these stocks
corresponds to the actual change in ETF ownership to which they are exposed because of the
index switch. Therefore, a more natural approach in this context is to compute the economic
magnitude by multiplying the IV estimates by the change in ETF ownership that results from the
index switch. When we do so, the median stock’s volatility shifts to between the 55th and 65th
percentiles (on average, to the 60th percentile). These magnitudes are comparable to those from
OLS regressions.
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Although economically significant, these effects do not seem out of proportion relative to
the average magnitude of ETF ownership in the sample, which is not large.17 On the other hand,
ETF trading volume is an important fraction of total trading volume in the stock market (on
average 32% in the whole sample). According to the liquidity-trading hypothesis, trading activity
in ETFs impounds price shocks, which are then passed up to the prices of the underlying
securities via arbitrage. Hence, under this hypothesis, an economically important effect of ETFs
on volatility would be consistent with the large volume of ETF trading.18
IV.
Exploring the Channel: ETF Flows and Arbitrage
This section explores the channel through which ETFs affect volatility. The empirical
analysis also attempts to separate the liquidity-trading hypothesis from the price-discovery
hypothesis.
A.
ETFs Attract a High-Turnover Clientele
As detailed in section II, for ETFs to impound a new layer of liquidity shocks, absent the
ETFs, the liquidity traders must not have directly traded the underlying stocks or gotten indirect
access to them through other vehicles, such as futures. In subsection II.B, we provide suggestive
evidence that ETFs attract higher turnover investors than the common stocks. These investors are
likely to express their liquidity demands at a higher frequency. If the liquidity-trading hypothesis
17
Average ETF ownership is about 2.6% in the whole sample for S&P 500 stocks (2.8% for Russell 3000 stocks) and
about 7% for the S&P 500 sample in 2015 (7.5% for Russell 3000 stocks).
18
In I.A. Table AX, using Ancerno trade-level data, we confirm that institutional investors generate significantly
higher turnover when trading stocks than when trading ETFs.
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is correct, this demand propagates to the underlying stocks through arbitrage activity, exposing
the stock prices to a new layer of liquidity shocks. The open question is therefore whether the
stocks in ETF baskets are exposed to this high-turnover clientele through ETF ownership.
To address this question, we study whether the stock-level churn ratio of the investors that
trade in a given stock increases with ETF ownership. Using Ancerno trade-level data, for each
manager-stock-quarter, we compute the adjusted churn ratio as in equation (2). Then we
aggregate this variable at the quarter-stock level by taking the volume-weighted average across
managers. Finally, we regress the stock-quarter-level churn ratio on ETF ownership at the end of
the previous quarter. Both the dependent and the main explanatory variables are standardized.
Consistent with the conjecture that ETFs attract high-turnover investors to the underlying
securities, in Panel A of Table VI, we find a positive and significant relation between ETF
ownership and the adjusted churn ratio. In column (2), a one-standard-deviation increase in ETF
ownership for an S&P 500 stock is associated with a 12% of a standard deviation increase in the
investor churn ratio. In line with the results in Table IV, the effect is smaller for the Russell 3000.
The concern about endogeneity of ETF ownership applies here as well. Hence, we also
cast the test within the IV framework that relies on the switch across Russell indexes. In Panel B
of Table VI, we find broad support for a positive link between ETF ownership and the investor
churn ratio. The estimates are mostly significant for the additions to the Russell 2000, whereas
significance is weaker for the deletions from the Russell 2000.
Overall, we interpret this evidence as corroborating the view that a new clientele of highturnover investors is attracted to the stocks in the ETF baskets. Under a causal interpretation of
these regressions, these investors would not trade the stocks if they were not in the ETF
portfolios.
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B.
The Price Impact of ETF Flows
A comparison between Figures 1 and 2 suggests a way to disentangle the two hypotheses.
According to the liquidity-trading hypothesis (Figure 1), following a demand shock in the ETF
market, the prices of the underlying securities should move in the same direction as the initial
shock, but then prices should revert to the initial level as the effect of the shock vanishes. Instead,
the price-discovery hypothesis (Figure 2) posits that stock prices should stay at the new level after
the demand shock. This simple argument motivates us to study the behavior of stock prices
following changes in the demand for ETFs.
For this analysis, we identify demand shocks in the ETF market by measuring daily flows
in ETFs. As explained above, ETF flows (redemptions and creations) are the result of APs’
activity. Stock-level flows are defined as the weighted average of the daily flows in the ETFs that
own the stock. The weights are the fraction of ownership in the stock held by each ETF. Daily
dollar ETF flows are a fraction of average daily trading volume over the prior month:
∑
,
, ,
$
∗$
,
,
.
(6)
Focusing on the S&P 500, from the summary statistics in Table II, Panel C, we learn that,
on average, (absolute) flows are $2 million per stock-day (1.5% of daily volume). Hence, flows
by far exceed the size of the National Best Bid and Offer ($517), suggesting the demand shock
from flows needs to climb up or down the order book, and likely causes prices to move.
On the day flows occur, we expect a price move in the same direction as the flows,
irrespective of whether the motive for trade is new information or liquidity demand. To the extent
that at least part of the originating shock is due to liquidity demand, a reversal should occur in the
subsequent days. To capture this behavior, we regress returns over different horizons (5, 10, 20,
and 40 days) on stock-level flows measured on the first day of each of these horizons. We include
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the usual stock-level controls and time fixed effects, in addition to order imbalance, calculated as
the dollar value of buy-minus-sell trades from TAQ, divided by market capitalization. Order
imbalance is a natural control in this context because daily flows in ETFs could merely be a proxy
for aggregate demand in the underlying securities, which induces negative autocorrelation in
returns (Chordia and Subrahmanyam (2004)). The standard errors are clustered at the day and
stock level.
In Table VII, Panel A, Daniel et al. (1997, DGTW)-adjusted returns are expressed as
percentages, whereas net flows are standardized. From column (1), we note that on the same day,
ETF flows and returns move in the same direction. The contemporaneous price move is 12.2 bps
for a one-standard-deviation change in net flows for S&P 500 stocks. The high significance is not
surprising, because flows and returns are measured on the same day (hence, this regression is not
predictive). In addition, we note the magnitude of the change in prices exceeds the half-spread,
which is about 8.5 bps for the sample of large stocks. This magnitude rules out the possibility that
flows cause a simple bid-ask bounce.
More relevant to separating the hypotheses of interest, ETF flows predict a reversal of the
underlying stocks’ prices in the 40 days starting on day t (columns (2)–(5)). This evidence is
consistent with the conjecture that the demand shocks in the ETF market add a mean-reverting
component to stock prices. As in the prior tables, the absolute effects are smaller in the extended
universe of Russell 3000 stocks, but we still observe a complete reversal over 40 days.
In sum, the evidence of a full reversal of the price impact of ETF flows is consistent with
the liquidity-trading hypothesis and tends to rule out the conjecture that ETFs are the vehicle of
choice for expressing fundamental demand, as posited by the price-discovery hypothesis.
In the I.A., we also provide results from a test that aims to show that non-fundamental
demand for ETFs affects stock-level volatility, consistent with the liquidity-trading hypothesis.
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The identifying assumption is that total daily ETF flows contain a part that reflects net influxes of
money into the ETFs that hold that stock and a part that is, instead, due to the reallocation of
capital across the ETFs holding the stock. The former, which is captured by the net stock-level
flows, may reflect fundamental information that concerns the securities in the ETF basket.
Instead, the latter part depends on investors’ decision to reshuffle money across the ETFs holding
a given stock, which has non-fundamental explanations such as the fact that some ETFs revise
their fees downward. Based on this decomposition, we show in I.A. Table AXII that nonfundamental flows are the main driver of stock volatility, whereas fundamental flows play a
smaller role.19
C.
Making Sense of the Size and Persistence of the Price Impact
Next, we show that the magnitude of the price impact of flows in Table VII, Panel A, is
consistent with microstructure evidence. To this purpose, we follow an established practice in the
literature and compute a market-impact function from trade-level data (e.g., Hasbrouck (1991),
Hausman, Lo, and MacKinlay (1992), Keim and Madhavan (1996), Frazzini, Israel, and
Moskowitz (2012), Landier, Simon, and Thesmar (2015)). Hence, we use the trade-level data in
Ancerno, with observations at the day-stock-side-broker-manager level (where “side” is either
buy or sell). Following the literature, we construct a measure of price impact as the percentage
difference between the execution price and a pre-trade trade benchmark, specifically, the price at
the time of order placement (e.g., Anand et al. (2012)). From the summary statistics in Table II,
19
Also consistent with the idea that ETFs propagate non-fundamental demand shocks, in I.A. Table AXIV, we show
that the relation between ETF ownership and volatility is stronger at times of high sentiment, as measured by the
Baker and Wurgler (2006) index and the Michigan Survey of Consumer Sentiment index.
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Panel D, we learn that in the sample of S&P 500 (Russell 3000) stocks, the average price impact
is 3.76 (5.35) bps, whereas the average turnover as a fraction of daily volume is 0.45% (0.94%).
Table VII, Panel B, reports estimates from a regression of the trade-level price impact on
turnover, measured as a fraction of the average daily volume over the prior month, and turnover
squared. The quadratic function is motivated by prior literature that finds a concave relation (e.g.,
Keim and Madhavan (1996)). For each universe of stocks, we provide two specifications: with day
and stock fixed effects and without them. Standard errors are double clustered at the day and stock
level. The estimates are similar irrespective of the fixed effects, and they confirm the evidence in
prior literature about the convexity of the relation between price impact and turnover.
Using these estimates, we can give a microstructure foundation to the price impact of flows.
In Table VII, Panel A, we note that a one-standard-deviation change in flows, which is 2.7% for
S&P 500 stocks (see Table II, Panel C), correlates with a 12 bps change in prices on the same day.
Based on the price-impact estimates in Table VII, Panel B, column (1), we obtain that a 2.7%
change in turnover leads to a price impact of about 11 bps (= 2.6 + 3.6×2.7 – 0.15×2.72), which is
fully consistent with the price impact of flows from Table VII, Panel A.20,21
20
Similar conclusions emerge from I.A. Figure A1.
21
The evidence in Table VII, Panel A, of smaller price pressure in the universe of Russell 3000 apparently does not
conform with the intuition that because these stocks are less liquid and exposed to larger flows as a fraction of daily
volume (see Table II, Panel C), they should react more strongly to ETF flows. However, the smaller price impact we
measure in Table VII, Panel A, could be the result of the larger measurement error in the flows into small stocks,
because of the higher volatility in these stocks’ returns.
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The evidence in Table VII, Panel A, suggests that, following ETF flows, the half-life to
convergence of prices to the initial level is about 10 days. This finding is apparently in contrast to
the microstructure evidence pointing to high resiliency of the limit-order book.22
Two considerations help us reconcile the evidence. First, the settlement of the shares of US
domestic-equity ETFs works on a t+3 basis and, in some circumstances, it can be extended to t+6,
if the AP is also a market maker for ETFs, which happens in the large majority of cases (see ICI
(2014)). This institutional framework implies APs have time to buy (in case of creation) or short
(in case of redemption) the underlying securities up to t+6. Consequently, when we measure flows
on day t, we should expect the price pressure on the underlying securities to continue over the
following days as well. This fact can explain the slow reversal of prices to the initial level. If this
explanation is really behind the persistence of the price impact, we should observe that flows on
day t predict order imbalance on the following days. This conjecture finds confirmation in I.A.
Table AXI, Panel A, which shows that day-t flows significantly predict order imbalance in the same
direction for at least up to seven days in the future.
Second, ETF flows are themselves persistent. Because flows on a given day are followed
by flows in the same direction on the subsequent days, price pressure on the underlying stocks can
continue after day t. In I.A. Table AXI, Panel B, we show significant persistence in ETF flows. For
example, for the entire sample of ETFs, the first-order daily autocorrelation is about 9% and the
higher-order autocorrelations remain significant for at least 20 days.
22
For example, the empirical work in Biais, Hillion, and Spatt (1995), Dufour and Engle, (2000), Degryse et al.
(2005), and Large (2007) suggests liquidity is replenished in a few minutes, if not seconds. More recently,
Hendershott and Menkveld (2014) estimate a half-life of convergence following price pressure of 0.92 days.
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Overall, we recognize that these arguments only provide suggestive explanations for the
persistence of the effect of ETF flows. Therefore, further research should delve deeper into these
channels and explore other potential explanations.
D.
Indirect Evidence on the Arbitrage Channel
To assess the relevance of arbitrage activity in driving the impact of ETFs on volatility, we
search for an interaction of this effect with measures of limits to arbitrage. We proxy the intensity
of arbitrage activity using the ETF mispricing. Then we conjecture that the proxy for expected
arbitrage activity should have a weaker effect on prices for stocks that are harder to arbitrage.
At the daily frequency, the stock-level mispricing is computed by summing the absolute
dollar mispricing (i.e., the difference between the ETF price and NAV, as a fraction of the ETF
price, multiplied by the dollar holdings in the stock) across all ETFs holding stock , and we express
this quantity as a fraction of a stock’s capitalization:
∑
, ,
∗
,
,
∗
,
,
.
In the computation of mispricing, the ETF price and the NAV are measured using daily
closing prices. Thus, mispricing on a given day is a good predictor of next-day mispricing.23
We raise the caveat that ETF mispricing could instead proxy for a lack of arbitrage activity.
That is, more mispricing is present when arbitrageurs refrain from entering the market. For instance,
Gagnon and Karolyi (2010) show that the price deviation between ADRs and the corresponding
home market shares are positively related to measures of holding costs, foremost among which is
23
In the I.A. Table AXIII, we provide evidence that mispricing predicts next-day volume and order imbalance in the
right direction at the stock level (i.e., a positive mispricing predicts positive order). Hence, these results confirm that
mispricing is a signal on which arbitrageurs condition their trading strategies.
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(7)
idiosyncratic volatility. This channel could affect our inference if arbitrageurs abstain from trading
high-volatility securities. To address this concern, we control for the lagged volatility so that we
study the impact of mispricing on innovations in volatility. This choice helps attenuate the
endogeneity concern, because arbitrage trades are not likely to condition on innovations in volatility
in the next period. Further, this potential endogeneity would lead to the opposite sign of the
coefficient on the interaction variables relative to what we find.
We use two proxies for limits to arbitrage. First, because ETF arbitrage involves a roundtrip transaction in the stock, a large stock-level bid-ask spread reduces the profitability of arbitrage
trades and therefore the incidence of arbitrage trading in a given stock. Second, when an arbitrage
transaction involves shorting the stock, higher stock-lending fees discourage arbitrageurs. Also, a
high share-lending fee can reflect a shortage of shares for lending, meaning some arbitrageurs may
simply not be able to carry out the trade (Cohen, Diether, and Malloy (2007)).
Given the high-frequency fluctuations in arbitrage activity, we carry out our tests at the daily
frequency, which allows us to measure the variables of interest in a more timely way. Thus, the
dependent variable for these tests is intraday volatility, which is estimated from second-by-second
returns within a day. The main explanatory variable is the stock-level measure of absolute ETF
mispricing in the prior day, defined in equation (7).
In Table VIII, the sample consists of S&P 500 stocks, where, according to our prior results,
the effect of ETFs is stronger. In column (1), we test whether absolute mispricing at the close of
day t–1, which is a proxy for arbitrage activity on day t, has an incremental effect on volatility for
a given level of ETF ownership. In addition to the usual controls, we include the mispricing on day
t–2 and the lagged dependent variable. The goal is to capture the effect of the innovation in
mispricing on the innovation in volatility, given that mispricing on day t–1 could itself depend on
volatility (i.e., ETFs holding stocks that are more volatile are more likely to be mispriced, as
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discussed above). We also include the return on the stock on day t–1 to capture variation in
mispricing that is exogenous to movements in the stock price itself. We note the effect of absolute
mispricing is positive and significant. This evidence lends further support to the view that arbitrage
activity is the transmission channel for the effect of ETF ownership on volatility.
We next report specifications that include interactions of absolute mispricing with the
proxies for arbitrage costs. For each measure of limits to arbitrage, we define a dummy variable for
stocks that are in the top half of the distribution of the variable in the prior period.24 We leave out
stock fixed effects, because we wish to achieve identification from the cross-sectional variation in
the proxies. From Table VIII, column (2), we infer that the effect of arbitrage on volatility, as
proxied by absolute mispricing, is significantly weaker for stocks with a high bid-ask spread,
consistent with a role for limits of arbitrage. Next, we break up the sample by the sign of net
mispricing. A priori, we do not expect the sign of mispricing to matter for the interaction with the
bid-ask spread, because the arbitrage trade involves a round-trip transaction in the underlying stock
in any case. The results in columns (3) and (4) confirm this conjecture.
In column (5), share-lending fees have a marginally significant impact on attenuating the
effect of arbitrage on volatility. More importantly, we now expect this effect to differ based on the
sign of net mispricing. Only when mispricing is negative (i.e., the ETF price is below the NAV)
does the arbitrage trade involve a short sale of the underlying stocks. The estimates in columns (6)
and (7) square nicely with this prediction and provide strong evidence for the role of arbitrage
activity in generating the effect of interest.
24
Information on share-lending fees is sparse, especially in the initial part of the sample. Therefore, we use the
average fee in the month.
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Importantly, the sign of the interactions with the proxies for arbitrage costs tends to rule out
concerns about the endogeneity of mispricing. If mispricing were capturing the fact that arbitrageurs
abstain from trading because volatility discourages them, we would expect this effect to be even
stronger for illiquid stocks or for stocks that are hard to short, given that these characteristics
correlate positively with volatility. That is, the sign on the interactions with arbitrage costs should
be positive as opposed to negative and significant.25
In I.A. Table AXVI, we show that the relationship between ETF ownership and volatility is
stronger at times of more availability of arbitrage capital, which we measure using trading activity
of institutional investors and hedge funds, in particular.
Overall, the results point to a role of arbitrage in driving the link between ETF ownership
and stock volatility. We recognize, however, that the evidence in this subsection is only suggestive
of a role of arbitrage in causing the increase in volatility. First, the evidence is indirect. For example,
institutional investors and hedge funds might trade ETFs for reasons other than arbitrage. Moreover,
a lot of arbitrage is done by high-frequency-trading firms, whose trading activity we do not capture.
Second, estimation for Table VIII relies on OLS regressions because of the requirement of
sufficiently large cross-sectional variation in stock characteristics, which the index-switching
experiment does not satisfy due to its local nature. Hence, future research should study more closely
the role of arbitrage in propagating liquidity shocks between ETFs and the underlying stocks.
25
In I.A. Table AXVII, we report the analysis for the Russell 3000. As expected, the effects in this sample are weaker
or nonexistent. These results confirm our prior belief that arbitrageurs tend to focus on the larger stocks in the ETF
baskets when doing optimized replication.
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V.
Asset-Pricing Implications
In this section, we explore two different dimensions of the effect of ETFs on stock prices:
(1) the impact of ETFs on price efficiency, and (2) the effect of ETF ownership on expected returns.
A.
Implications for Pricing Efficiency
The liquidity-trading and the price-discovery hypotheses have different implications for
price efficiency. According to the former, transitory demand shocks in the ETF market migrate to
the underlying security prices in the form of a mean-reverting component. As a result, prices
become noisier. For the latter hypothesis, prices of stocks with higher coverage by ETFs adjust
more promptly to fundamentals. The fundamental demand in the ETF market propagates to the
underlying basket, impounding a permanent shock. In this scenario, ETF ownership makes prices
closer to a random walk. Thus, we can test for the effect of ETFs on the transitory component of
stock prices.
Lo and MacKinlay (1988) and O’Hara and Ye (2011), among others, use variance ratios to
measure the transitory component of stock prices. The variance ratio is defined as the variance of
k-period returns divided by k times the variance of the single-period returns in the same window.
When prices follow a random walk, the variance ratio equals 1. If the autocorrelation of returns at
the chosen frequency differs from zero, the variance ratio diverges from 1.
Given that ETF arbitrageurs operate on a daily basis to exploit ETF mispricing, we test for
their effect on the autocorrelation of daily returns. Accordingly, we define
,
where
,,
is the five-day return and
,,
5∙
,,
1,
(8)
,,
is the one-day return. If ETFs cause stock prices to deviate
from a random walk, the statistic in equation (8) should increase with ETF ownership.
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The liquidity-trading hypothesis makes an even tighter prediction about the effect of ETFs
on the variance ratio. The conjecture is that ETFs impound a mean-reverting component into prices,
which in turn should make returns more negatively autocorrelated. Due to this negative
autocorrelation, the numerator of the variance ratio shrinks relative to the denominator. Hence, if
we redefine our test statistic as
,
,,
5∙
,
(9)
,,
we expect a negative relation between the quantity in equation (9) and ETF ownership.
We conduct our tests using stock-quarter-level observations. More specifically, we estimate
the variance ratios using non-overlapping observations during a quarter, and regress them on ETF
ownership at the beginning of the quarter. The quarterly frequency responds to the need for a
sufficiently long period over which we can estimate the five-day variance ratio.
Table IX reports tests using the usual IV framework. Both dependent variables, as well as
the ownership variables, are standardized. Panel A shows that the absolute value of the variance
ratio increases with ETF ownership, consistent with lower price efficiency for stocks owned by
ETFs. Panel B suggests ETF ownership correlates with a lower variance ratio, which supports the
conjecture that ETF arbitrage induces negative autocorrelation in daily returns.
Overall, this analysis suggests the increase in stock volatility we identify in section III is
likely the result of the fact that ETFs impound a mean-reverting component in stock prices. The
evidence, therefore, provides further corroboration for the liquidity-trading hypothesis and makes
the price-discovery hypothesis less plausible.
B.
Implications for Expected Returns
A potential implication of the finding that ETFs affect stock volatility is that ETF ownership
introduces a new source of risk to the investors of the underlying stocks. This risk may not be
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diversifiable, given that ETFs invest across the entire universe of stocks. Thus, asking whether the
expected returns of the stocks in the ETF baskets pay a premium to compensate investors for this
risk is natural. This question is even more relevant in light of the finding that the impact of ETFs
on volatility is greater at times of market turmoil (Table IV, Panel B) and when aggregate volatility
is high (I.A. Tables AXIV and AXV), and that in bad times, the skewness of ETF-owned stocks
becomes more negative (I.A. Table AIV). The ETF-induced shocks tend to cancel out over time, as
indicated by the evidence of mean reversion in returns. However, short-horizon investors may still
consider this volatility a source of risk for which they require a reward.
We follow the standard approach in asset pricing to test whether some characteristic
correlates with a premium in returns. For every month, we form portfolios based on the level of
ETF ownership in the prior month. We allocate stocks to five quintiles and equally weight the
portfolios. Thus, we obtain time series of portfolio returns ranging from February 2000 to December
2015.26
Table X, Panel A, reports the average excess returns over the sample period for the five
ETF-ownership quintile portfolios. The average returns increase almost uniformly with the amount
of ETF ownership. Following the literature standard, we form a portfolio that is long in the top
quintile and short in the bottom quintile of ETF ownership. We use this long-short portfolio to test
whether ETF ownership commands a premium.
In Table X, Panel B, we report the raw returns and alphas from different factor models for
the long-short portfolio, using the whole sample. In terms of raw returns, the high-minus-low ETFownership portfolio earns about 35 bps per month, which is statistically different from zero. The
26
We also experimented with value-weighted portfolios and found qualitatively similar results but lower magnitudes
and statistical significance.
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alpha with respect to the market model is of a somewhat smaller magnitude (30 bps) but still
significant. Using the Fama and French (1993) three factors increases the significance and the
magnitude of the alpha, given that the loading on HML is negative. The momentum factor does not
affect the alpha in a four-factor model (Carhart (1997)). Next, we gradually introduce the two new
Fama and French (2015) factors (RMW, CMA), which make the alpha somewhat larger. Finally,
we test whether liquidity risk can explain the premium we observe. After including the Pástor and
Stambaugh (2003) liquidity risk factor (PS_VWF), the magnitude and significance of alpha do not
change.
One way to verify whether the effect we measure is indeed related to ETF ownership, as
opposed to some omitted risk factor, is to test whether the alphas are larger in recent years, when
ETFs have become more important. In I.A. Table AXVIII, Panels A and B, we estimate the factor
models by splitting the sample at the end of 2007. Consistent with the conjecture that the effect we
capture is related to the presence of ETFs in the market, the alphas are larger and more statistically
significant in the recent sample. In this period, the magnitude ranges from 44 to 56 bps.
The results are consistent with the conjecture that ETF ownership impounds some
undiversifiable source of risk into the underlying securities, which is priced ex ante. An alternative
interpretation of these results hinges on the price pressure deriving from ETF flows. Over the
sample period, ETF ownership has grown consistently. Based on the results in Table VII, we know
ETF flows impart price pressure on the basket securities. Hence, according to this alternative view,
the price pressure from ETF flows, which are larger for stocks with more ETF ownership, would
lead ex post to the abnormal returns for high-ETF-ownership portfolios.
To disentangle the two explanations, we run Fama and MacBeth (1973) regressions of
abnormal returns on the explanatory variable of interest, that is, lagged ETF ownership, and controls
for other potential explanations, including ETF flows. The dependent variable is the monthly four46
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factor model-adjusted (Carhart (1997)) stock return expressed in percent. In Table X, Panel C, the
first specification reveals a positive and significant relation between returns and standardized ETF
ownership. A one-standard-deviation increase in ETF ownership correlates with an increase of 14
bps in returns. The next specification includes ownership by other types of institutions, whose effect
is not significant, although it is positive in the case of active mutual funds and hedge funds. Then
we add controls for liquidity and stock characteristics typically associated with returns. We note a
significant profitability effect, consistent with Novy-Marx (2013), whereas the other asset-pricing
effects are insignificant, probably due to the four-factor adjustment of the dependent variable. In
column (4), ETF flows display a significant correlation with returns, when ETF ownership is not
included. However, a horse race between the two variables reveals ETF ownership is the dominant
determinant of stock returns (column (5)). This finding rules out the explanation that the alphas we
identify are due to the price pressure of ETF flows.
Overall, these results contribute to the argument that ETFs significantly modify the
underlying stocks’ return distribution. As ETFs increase the volatility of stock returns, they appear
to induce a non-diversifiable source of risk, at least in the short term, for which investors require a
premium in expected returns.
VI.
Conclusion
The success of ETFs is justified by the fact that these investment vehicles offer an
unprecedented source of diversification at low cost and high liquidity. This aspect of ETFs is
undeniably beneficial for investors. On the other hand, due to their ease of trade, ETFs can be a
catalyst for a new breed of high-frequency investors, whose demand shocks can pass on to the
underlying securities via the arbitrage activity continuously taking place between the ETFs and
their baskets. This mechanism can lead to higher volatility for the underlying securities. The
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increase in volatility would not be a desirable effect of ETFs if it were merely the reflection of
increased noise trading.
The paper starts by showing ETFs are indeed the preferred habitat of investors with
relatively higher turnover, consistent with the view that they attract high-frequency demand. One
of the main results of the paper is that the stocks with more ownership by ETFs display higher
volatility than otherwise similar securities. Through a quasi-natural experiment based on the
reconstitution of the Russell indexes, we ascribe a causal interpretation to this finding.
Next, we show that the demand shocks in the ETF market impound a mean-reverting
component in asset prices, which plays out at the daily frequency, suggesting the increase in stock
return volatility is hardly imputable to an improvement in price discovery brought about by ETFs.
More likely, it is the reflection of the transmission of non-fundamental demand shocks from the
ETF market to the prices of the underlying stocks via arbitrage. Further supporting this view, we
show that proxies for the intensity of arbitrage activity between the ETFs and their baskets magnify
the effect of ETFs on volatility.
Lastly, the paper addresses the asset-pricing implications of ETFs for stocks. If the increase
in stock volatility brought about by ETFs is partly non-diversifiable, it may represent systematic
risk for some investors, especially for those with a short trading horizon. As such, ETF ownership
may warrant a risk premium. Consistent with this conjecture, we show that portfolios of stocks with
high ETF ownership display positive alphas relative to a variety of asset-pricing models. These
alphas are about 50 bps in the more recent sample. We confirm this finding in a regression setting
and rule out the possibility that it is the ex-post reflection of the growing demand for ETFs.
Future research should delve deeper into the channels linking ETF ownership to stock
volatility. At this point, the evidence on the role of arbitrage trades is admittedly indirect. Relatedly,
further investigation seems necessary on the role of ETFs in attracting a different clientele of
48
Electronic copy available at: https://ssrn.com/abstract=1967599
traders. Consistent with the clientele effect, we find that the composition of traders shifts toward
higher-turnover investors in stocks with more ETF ownership. Whether this modification in the
client base is the result of ETF arbitrage remains to be established.
49
Electronic copy available at: https://ssrn.com/abstract=1967599
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56
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Table I. ETF Ownership Statistics
Russell 3000
S&P 500
The table presents descriptive statistics for stock ownership by ETFs, index mutual funds, and active mutual funds, for
the S&P 500 and Russell 3000 universes. For each year, across months and stocks, we average the number of institutions
and the percentage of each stock owned by an institution type. We also report cumulative assets owned by these
institutions in the stocks in our sample, as reported in Thomson-Reuters Mutual Fund Ownership data.
ETFs
Year # of funds % of Market Cap $ Market Cap
2000
4.5
0.14%
$16.6
2001
12.6
0.18%
$18.0
2002
14.2
0.46%
$39.6
2003
15.1
0.69%
$62.4
2004
18.4
0.86%
$90.6
2005
20.2
1.16%
$129.5
2006
21.5
1.29%
$157.2
2007
38.5
2.50%
$336.2
2008
54.2
4.18%
$430.6
2009
56.0
4.66%
$412.1
2010
54.7
4.77%
$506.6
2011
54.9
5.21%
$604.6
2012
51.5
5.58%
$717.6
2013
53.4
6.30%
$958.0
2014
47.7
6.47%
$1,140.7
2015
48.3
7.05%
$1,214.2
2000
2.2
0.12%
$17.5
2001
7.5
0.19%
$23.3
2002
8.1
0.48%
$48.9
2003
8.7
0.73%
$80.6
2004
10.6
0.93%
$121.2
2005
11.5
1.24%
$173.2
2006
12.5
1.39%
$210.8
2007
22.4
2.65%
$445.4
2008
31.0
4.34%
$555.8
2009
31.2
4.95%
$534.2
2010
30.1
5.14%
$677.5
2011
30.0
5.56%
$803.4
2012
28.2
5.94%
$942.1
2013
29.7
6.70%
$1,267.7
2014
27.6
6.83%
$1,502.4
2015
28.3
7.48%
$1,611.3
Index Funds
# of funds % of Market Cap $ Market Cap
111.6
2.61%
$318.6
126.7
2.65%
$269.7
137.6
2.76%
$239.9
141.7
2.92%
$262.9
142.4
3.23%
$341.2
139.3
3.44%
$383.8
130.4
3.64%
$444.4
128.6
3.04%
$407.8
131.1
2.28%
$237.5
125.8
2.51%
$223.0
113.7
2.60%
$275.9
108.6
2.61%
$303.2
99.9
2.73%
$351.2
97.0
2.87%
$437.2
91.7
2.90%
$512.0
92.9
3.20%
$550.9
40.4
2.33%
$343.1
46.6
2.49%
$298.7
51.5
2.65%
$276.5
56.3
2.83%
$310.4
57.2
3.15%
$413.4
56.2
3.38%
$473.3
55.4
3.66%
$555.7
55.3
3.09%
$518.2
57.9
2.26%
$291.7
58.5
2.51%
$271.3
52.2
2.59%
$339.5
51.4
2.61%
$375.5
49.1
2.71%
$427.0
47.9
2.86%
$537.2
45.4
2.89%
$632.2
44.6
3.14%
$673.6
Active Funds
# of funds % of Market Cap $ Market Cap
240.5
15.22%
$1,872.1
277.8
15.65%
$1,616.9
288.4
16.07%
$1,416.2
286.0
16.16%
$1,471.9
284.3
16.83%
$1,804.4
287.6
17.55%
$1,980.4
281.2
18.10%
$2,231.2
307.5
19.66%
$2,658.5
345.2
21.18%
$2,214.3
357.2
21.56%
$1,913.9
337.2
21.44%
$2,281.3
326.6
21.72%
$2,527.8
299.8
20.90%
$2,695.8
284.5
21.41%
$3,265.6
260.1
20.96%
$3,697.0
257.3
21.70%
$3,741.8
80.3
16.44%
$2,456.3
92.7
16.59%
$2,006.3
97.4
17.00%
$1,777.8
98.4
17.11%
$1,882.0
102.6
17.95%
$2,361.5
105.5
18.74%
$2,637.3
105.1
19.14%
$2,932.8
124.8
21.02%
$3,563.3
144.0
22.54%
$2,941.7
147.9
23.07%
$2,498.0
139.8
23.07%
$3,050.8
134.2
23.28%
$3,382.7
122.9
22.40%
$3,572.6
119.2
22.93%
$4,370.6
109.8
22.21%
$4,917.8
109.4
22.92%
$4,974.1
57
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Table II. Summary Statistics
The table presents summary statistics for the variables used in the study. Panel A shows summary statistics for the
stock-month sample. Panel B reports correlations for the same sample, and Panel C shows summary statistics for the
stock-day sample. Panel D shows summary statistics for the Ancerno transaction-level data. The samples range between
January 2000 and December 2015.
Panel A: Monthly Sample
S&P 500
Daily stock volatility (%)
Skewness
Log(abs(VR 5 days/(5*1 day)))
ETF ownership
Index Fund ownership
Active Fund ownership
Hedge Fund ownership
log(Mktcap ($m))
1/Price
Amihud
Bid-ask spread (%)
Book-to-Market
Past 12-month Return
Gross Profitability
N
81,243
81,243
81,243
81,243
81,243
81,243
81,243
81,243
81,243
81,243
81,243
81,243
81,243
81,243
Mean
2.010
0.109
-1.810
0.026
0.062
0.176
0.034
9.360
0.039
0.000
0.207
0.524
0.113
0.301
Std Dev
1.400
2.490
0.895
0.019
0.020
0.063
0.045
1.060
0.040
0.001
0.462
0.385
0.366
0.224
Min
0.581
-8.900
-3.850
0.000
0.004
0.008
0.000
5.230
0.004
0.000
0.000
0.038
-0.823
-0.399
Median
1.600
0.114
-1.600
0.023
0.061
0.173
0.019
9.300
0.029
0.000
0.048
0.420
0.100
0.262
Max
11.000
8.900
-0.582
0.112
0.120
0.354
0.354
11.400
0.556
0.036
3.700
2.360
2.180
1.120
N
418,748
418,745
418,748
418,748
418,748
418,748
418,748
418,748
418,748
418,748
418,748
418,748
418,748
418,748
Mean
2.610
0.123
-1.740
0.028
0.047
0.151
0.058
7.120
0.073
0.015
0.293
0.588
0.133
0.293
Std Dev
1.760
2.490
0.902
0.023
0.025
0.083
0.070
1.540
0.083
0.037
0.527
0.414
0.485
0.258
Min
0.581
-8.900
-3.850
0.000
0.002
0.002
0.000
4.250
0.004
0.000
0.000
0.038
-0.823
-0.399
Median
2.120
0.130
-1.520
0.023
0.045
0.149
0.031
6.900
0.047
0.002
0.113
0.498
0.089
0.262
Max
11.000
8.900
-0.582
0.112
0.120
0.354
0.354
11.400
0.556
0.278
3.700
2.360
2.180
1.120
Russell 3000
Daily stock volatility (%)
Skewness
Log(abs(VR 5 days/(5*1 day)))
ETF ownership
Index Fund ownership
Active Fund ownership
Hedge Fund ownership
log(Mktcap ($m))
1/Price
Amihud
Bid-ask spread (%)
Book-to-Market
Past 12-month Return
Gross Profitability
58
Electronic copy available at: https://ssrn.com/abstract=1967599
Panel B: Correlations
Daily stock volatility (%)
Skewness
Log(abs(VR 5 days/(5*1 day)))
ETF ownership (%)
Index Fund ownership (%)
Active Fund ownership (%)
Hedge Fund ownership (%)
log(Mktcap ($m))
1/Price
Amihud
Bid-ask spread (%)
Book-to-Market
Past 12-month Return
Gross Profitability
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10) (11) (12) (13)
(1) 1.000
(2) -0.004 1.000
(3) 0.027 0.000 1.000
(4) -0.074 -0.021 -0.022 1.000
(5) -0.092 -0.007 -0.060 0.355 1.000
(6) -0.102 -0.004 -0.097 0.160 0.428 1.000
(7) 0.071 0.008 -0.025 0.055 -0.005 -0.052 1.000
(8) -0.343 -0.001 -0.083 0.041 0.325 0.382 -0.147 1.000
(9) 0.402 0.001 0.040 -0.074 -0.169 -0.287 0.094 -0.459 1.000
(10) 0.312 -0.003 0.104 -0.174 -0.262 -0.377 -0.035 -0.473 0.439 1.000
(11) 0.273 0.000 0.058 -0.270 -0.212 -0.222 -0.084 -0.265 0.281 0.428 1.000
(12) 0.104 0.001 0.036 0.088 0.089 -0.164 -0.010 -0.227 0.234 0.190 0.132 1.000
(13) -0.191 -0.007 -0.031 -0.009 -0.015 0.024 0.028 0.134 -0.240 -0.187 -0.147 -0.264 1.000
(14) -0.029 0.001 -0.030 -0.015 0.025 0.201 0.010 0.033 -0.061 -0.082 -0.054 -0.297 0.083
59
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Table II. Summary Statistics (Cont.)
Panel C: Variables Used in Return Regressions (Daily Frequency)
S&P 500
Net Flows ($ million)
abs(Net Flows) ($ million)
Net Flows/Daily Volume
abs(Net Flows)/Daily Volume
NBBO size ($)
DGTW Ret[t] (%)
DGTW Ret[t, t+4] (%)
DGTW Ret[t, t+9] (%)
DGTW Ret[t, t+19] (%)
DGTW Ret[t, t+39] (%)
N
1,501,051
1,501,051
1,501,056
1,501,056
1,437,745
1,501,056
1,501,056
1,501,056
1,501,056
1,501,056
Mean
0.250
2.050
0.002
0.015
517
0.015
0.070
0.127
0.209
0.352
Std Dev
40.700
40.700
0.027
0.022
1813
1.700
3.660
5.070
7.090
10.000
Min
-12.400
0.000
-0.081
0.000
54
-4.820
-10.000
-13.500
-18.400
-25.400
Median
0.027
0.609
0.001
0.007
295
-0.013
-0.004
0.018
0.061
0.136
Max
13.200
18.300
0.088
0.111
3433
5.150
10.800
14.700
20.200
28.500
abs(Net Flows)×106/Mkt Cap
1,542,880
0.012
0.016
0.000
0.006
0.078
sum(abs(Flows))×106/Mkt Cap
Intraday Price Range (%)
Intraday Volatility (%)
Abs(mispricing) (bps)
Net(mispricing) (bps)
Share lending fee (%)
1,542,880
1,542,880
1,542,880
1,686,822
1,660,396
1,029,618
0.018
0.028
0.020
0.174
-0.004
0.213
0.020
0.021
0.018
0.147
0.125
1.110
0.000
0.006
0.005
0.013
-0.499
0.000
0.012
0.022
0.014
0.129
0.006
0.099
0.096
0.111
0.100
0.859
0.369
72.400
Net Flows ($ million)
abs(Net Flows) ($ million)
Net Flows/Daily Volume
abs(Net Flows)/Daily Volume
NBBO size ($)
DGTW Ret[t] (%)
DGTW Ret[t, t+4] (%)
DGTW Ret[t, t+9] (%)
DGTW Ret[t, t+19] (%)
DGTW Ret[t, t+39] (%)
N
7,812,071
7,812,071
7,812,107
7,812,107
7,733,982
7,812,107
7,812,107
7,812,107
7,812,107
7,812,107
Mean
0.081
0.617
0.002
0.029
226
0.007
0.021
0.026
0.021
0.007
Std Dev
23.300
23.300
0.051
0.042
1057
2.070
4.410
6.090
8.540
12.100
Mix
-4.600
0.000
-0.166
0.000
16
-5.750
-11.800
-15.800
-21.600
-29.900
Median
0.000
0.091
0.000
0.011
100
-0.038
-0.095
-0.138
-0.206
-0.359
Max
5.130
7.770
0.176
0.197
1886
6.360
13.000
17.400
23.800
33.900
abs(Net Flows)×106/Mkt Cap
8,546,816
0.017
0.022
0.000
0.008
0.094
sum(abs(Flows))×106/Mkt Cap
Intraday Price Range (%)
Intraday Volatility (%)
Abs(mispricing) (bps)
Net(mispricing) (bps)
Share lending fee (%)
8,546,816
8,546,297
8,546,816
8,572,503
8,454,831
4,554,404
0.022
0.036
0.024
0.211
-0.015
0.444
0.026
0.028
0.019
0.169
0.153
2.240
0.000
0.006
0.005
0.013
-0.499
0.000
0.013
0.028
0.018
0.162
-0.001
0.132
0.108
0.143
0.102
0.859
0.369
132.000
N
28,291,346
28,291,346
Mean
3.757
0.446
Std Dev
Min
98.373 -463.063
1.689
0.000
Median
1.242
0.031
Max
489.987
24.758
N
54,250,928
54,250,928
Mean
5.355
0.939
Std Dev
Min
114.126 -463.063
2.676
0.000
Median
1.685
0.077
Max
489.987
24.758
Russell 3000
Panel D: Ancerno Data
S&P 500
Price Impact (bps)
Turnover (%)
Russell 3000
Price Impact (bps)
Turnover (%)
60
Electronic copy available at: https://ssrn.com/abstract=1967599
Table III. ETFs versus Stocks: Liquidity, Institutional Ownership, Churn Ratio
The table reports statistics for ETF- and stock-level liquidity, investor turnover, and ownership. The sample includes
S&P 500 stocks and ETFs. Panel A shows the security-level liquidity measures (bid-ask spread, Amihud (2002) ratio,
and daily turnover). For all ETFs in our sample, we compute the average measure of liquidity across the stocks in the
basket in a given quarter. Then we value-weight the ETF-level and basket-level measures across all ETFs at the quarter
level using ETF market capitalization. Panel B presents information about institutional ownership averaged across all
64 quarters, in the first quarter of the sample, and in the last quarter of the sample. Ownership averages are presented
for the ETFs in our sample and all the stocks in the CRSP dataset. Churn Ratio is also in this panel, computed as the
sum of quarterly absolute changes in dollar holdings over average AUM. Panel C uses trade-level data from Ancerno,
aggregated at the manager-stock-quarter level to present regressions of the churn ratio and adjusted churn ratio on an
ETF indicator. Summary statistics for Panel C are presented in I.A. Table AIII. t-statistics for the test of the null
hypothesis that the difference is equal to zero are presented in parentheses. ***, **, and * represent statistical significance
at the 1%, 5%, and 10% levels, respectively. The sample ranges between 2000:Q1 and 2015:Q4.
Panel A: Liquidity and Investors’ Churn-Ratio Measures
Liquidity measures
Bid-Ask Spread
Amihud ratio
Daily turnover
Quarters
64
64
64
ETFs
0.002
0.002
0.085
Stocks
0.004
0.007
0.010
Difference t-stat
-0.002
(-3.611)
-0.004
(-7.408)
0.075
(13.682)
Common Stocks
Ownership
Q1.2000 Q4.2015
1.5%
1.9%
0.8%
0.9%
32.6%
43.0%
11.0%
15.6%
0.9%
4.2%
2.7%
3.4%
0.8%
2.9%
Churn
Ratio
17.9%
11.3%
18.5%
26.7%
74.8%
13.3%
39.7%
ETFs
Ownership
Average Q1.2000 Q4.2015
3.3%
2.5%
4.8%
0.5%
1.1%
0.4%
16.1%
14.2%
25.2%
8.7%
13.7%
6.3%
1.9%
1.0%
0.7%
1.4%
1.6%
1.1%
17.6%
7.4%
17.6%
Churn
Ratio
31.2%
37.6%
45.1%
48.5%
100.8%
58.5%
51.0%
23.7%
22.6%
1.3%
50.7%
62.7%
47.8%
Panel B: Types of Institutional Ownership
Type of Institution
Bank and Trust
Insurance Company
Investment Advisor / Investment Company
Investment Advisor / Hedge Fund
Hedge Fund
Pension Fund
Research Firm
Other Institutions
All Institutions
Total
1.7%
0.8%
38.9%
14.7%
2.8%
3.7%
2.0%
0.7%
65.4%
0.4%
50.9%
0.7%
72.4%
0.8%
42.2%
61
Electronic copy available at: https://ssrn.com/abstract=1967599
0.1%
56.3%
Panel C: Churn-Ratio Regressions
Dependent variable:
Security is ETF
Churn Ratio
(1)
(2)
(3)
0.194*** 0.197*** 0.146***
(13.764) (14.584) (11.060)
Adj. Churn Ratio
(4)
(5)
(6)
0.571*** 0.570*** 0.372***
(10.258) (10.142) (7.246)
Date FE
Manager FE
No
No
Yes
No
Yes
Yes
No
No
Yes
No
Yes
Yes
Observations
32,371
32,371
32,329
32,371
32,371
32,329
2
0.154
0.168
0.358
0.098
0.101
0.396
Adjusted R
62
Electronic copy available at: https://ssrn.com/abstract=1967599
Table IV. ETF Ownership and Stock Volatility
The table reports estimates from ordinary least squares (OLS) regressions of daily volatility on ETF ownership and
controls. In Panel A, columns (1) to (4), the sample consists of S&P 500 stocks, and in columns (5) to (8), the sample
consists of Russell 3000 stocks. Panel B presents the same regressions but with the sample split by period. The
frequency of the observations is monthly, and volatility is computed using all daily returns within the month. The
controls in all panels include logged market capitalization, the lagged inverse share price, the lagged Amihud (2002)
ratio, the lagged average bid-ask spread, the lagged book-to-market ratio, lagged past 12 month returns, lagged gross
profitability (as in Novy-Marx (2013)), lagged volatility, index-fund ownership, and active-fund ownership. The
dependent variable and the ownership variables have been standardized by subtracting the mean and dividing by the
standard deviation. Standard errors are double clustered at the stock and month levels. t-statistics are presented in
parentheses. ***, **, and * represent statistical significance at the 1%, 5%, and 10% levels, respectively. The sample
ranges between January 2000 and December 2015.
Panel A: OLS Regressions, Whole Sample
Daily volatility (t)
S&P 500
Russell 3000
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
0.164*** 0.163*** 0.158*** 0.077*** 0.087*** 0.078*** 0.079*** 0.053***
(6.446)
(6.415)
(6.436)
(6.072)
(8.445)
(7.741)
(7.873)
(7.548)
Dependent variable:
Sample:
ETF ownership
log(mktcap (t-1))
1/Price (t-1)
Amihud (t-1)
Bid-ask spread (t-1)
Book-to-Market (t-1)
Past 12-month return (t-1)
Gross profitability (t-1)
Index fund ownership (t-1)
Active fund ownership (t-1)
Hedge fund ownership (t-1)
Volatility (t-1)
Volatility (t-2)
Volatility (t-3)
0.019
0.010
-0.011
-0.013
(0.544)
(0.306)
(-0.312) (-0.912)
2.906*** 2.848*** 2.821*** 1.052***
(4.311)
(4.237)
(4.087)
(3.574)
41.750*** 44.412*** 55.318*** 21.548**
(2.728)
(2.897)
(3.265)
(2.540)
-0.601
-0.678
0.422
-0.340
(-0.194) (-0.217) (0.135) (-0.213)
0.111** 0.114*** 0.097**
-0.027
(2.527)
(2.614)
(2.242) (-1.338)
-0.079** -0.083** -0.103*** -0.008
(-2.398) (-2.489) (-3.210) (-0.497)
0.010
0.038
0.010
-0.043
(0.098)
(0.384)
(0.104) (-1.105)
0.014
0.017
0.002
(1.241)
(1.447)
(0.491)
0.046*** 0.045*** 0.016***
(3.594)
(3.517)
(2.983)
-0.013
-0.013 -0.026***
(-1.006) (-0.989) (-4.220)
0.291***
(17.597)
0.176***
(9.689)
0.204***
(14.983)
-0.077*** -0.101*** -0.114*** -0.064***
(-4.848) (-6.216) (-7.258) (-6.953)
1.586*** 1.603*** 1.589*** 0.809***
(10.126) (10.299) (9.961)
(8.625)
2.072*** 2.108*** 2.322*** 1.165***
(8.524)
(8.635)
(9.327)
(6.717)
3.194*** 3.280*** 3.374*** 2.467***
(2.639)
(2.700)
(3.340)
(4.574)
0.118*** 0.115*** 0.115*** 0.006
(5.479)
(5.324)
(5.264)
(0.478)
0.012
0.023
0.015
0.015
(0.751)
(1.452)
(0.926)
(1.587)
-0.141*** -0.137*** -0.130*** -0.083***
(-3.427) (-3.359) (-3.094) (-3.523)
0.016*** 0.017*** 0.009***
(3.038)
(3.157)
(3.022)
0.048*** 0.049*** 0.026***
(6.570)
(6.668)
(5.945)
-0.027*** -0.025*** -0.023***
(-5.598) (-5.262) (-7.985)
0.207***
(20.102)
0.154***
(22.784)
0.177***
(28.001)
Month fixed effects
Stock fixed effects
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Observations
81,243
81,243
77,675
77,675
418,748
418,748
392,684
392,684
0.643
0.644
0.644
0.740
0.607
0.608
0.613
0.670
2
R
63
Electronic copy available at: https://ssrn.com/abstract=1967599
Table IV. ETF Ownership and Stock Volatility (Cont.)
Panel B: OLS Regressions, Sample Split by Period
Dependent variable:
Period:
Sample:
ETF ownership
log(mktcap (t-1))
1/Price (t-1)
Amihud (t-1)
Bid-ask spread (t-1)
Book-to-Market (t-1)
Past 12-month return (t-1)
Gross profitability (t-1)
Index fund ownership (t-1)
Active fund ownership (t-1)
Hedge fund ownership (t-1)
Volatility (t-1)
Volatility (t-2)
Volatility (t-3)
Daily volatility (t)
2000-2006
2007-2008
2009-2015
S&P 500
Russell 3000
S&P 500
Russell 3000
S&P 500
Russell 3000
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
(11)
(12)
0.082*** 0.061*** 0.044*** 0.033*** 0.276*** 0.184*** 0.079*** 0.071*** 0.110*** 0.063*** 0.077*** 0.057***
(3.728) (4.557) (5.193) (5.434) (5.192) (3.667) (4.790) (4.890)
(4.774) (5.701) (6.544) (7.063)
0.220*** 0.123*** 0.079*** 0.025 -0.513***-0.378*** -0.576***-0.467*** -0.149***-0.102*** -0.163***-0.133***
(5.202) (5.408) (2.977) (1.439) (-4.925) (-3.568) (-8.455) (-7.393) (-2.871) (-3.404) (-6.807) (-6.897)
3.072*** 1.813*** 2.004*** 1.260*** 2.253*** 1.171** 1.048*** 0.761*** 3.896*** 2.186*** 1.492*** 0.826***
(3.754) (3.525) (7.812) (5.810) (4.236) (2.734) (4.583) (3.930)
(4.417) (3.798) (7.183) (5.755)
38.208***25.647** 1.224*** 0.992*** 34.758 19.100 3.779*** 2.848*** 249.919**209.336*** 2.761*** 1.681***
(2.965) (2.565) (5.916) (5.842) (0.833) (0.530) (5.611) (3.608)
(4.631) (3.507) (7.334) (5.436)
0.410
0.912 2.511*** 1.621*** 11.121 2.433 10.244*** 6.391** 43.292**29.276*** 14.190***10.889***
(0.197) (0.596) (3.350) (4.187) (1.700) (0.522) (3.313) (2.686)
(2.574) (3.217) (6.365) (5.834)
-0.036 -0.086** -0.027 -0.059**
0.269
0.040
0.093 -0.036
0.046 -0.037 0.179*** 0.068***
(-0.615) (-2.384) (-0.747) (-2.226) (1.486) (0.231) (1.190) (-0.501) (0.806) (-0.913) (5.199) (2.858)
-0.112***-0.056** -0.029 -0.007
-0.036 0.031 0.189*** 0.171***
0.007
0.047 0.095*** 0.074***
(-3.186) (-2.631) (-1.642) (-0.585) (-0.613) (0.529) (7.071) (6.354)
(0.169) (1.603) (5.547) (5.573)
0.290** 0.074 -0.142** -0.104** -0.486** -0.284
-0.064 -0.117 -0.276** -0.063
-0.078 -0.054
(2.185) (1.054) (-2.527) (-2.434) (-2.091) (-1.296) (-0.654) (-1.251) (-2.175) (-0.841) (-1.520) (-1.277)
-0.014 0.001
-0.000 0.001
0.017
0.010
0.029** 0.028** -0.025* -0.013*
0.011
0.007
(-0.935) (0.117) (-0.068) (0.205) (0.678) (0.421) (2.360) (2.441) (-1.783) (-1.680) (1.502) (1.189)
0.047*** 0.027** 0.058*** 0.038*** 0.097*** 0.066** 0.066*** 0.046**
0.010 0.021** 0.046*** 0.040***
(2.657) (2.469) (4.499) (4.142) (3.106) (2.502) (4.364) (2.788)
(0.497) (2.053) (5.006) (6.157)
-0.043**-0.038*** -0.063***-0.045*** -0.073* -0.055 -0.051***-0.040** -0.035** -0.025** -0.027***-0.025***
(-2.214) (-2.826) (-9.175) (-8.850) (-1.868) (-1.453) (-3.148) (-2.209) (-2.243) (-2.565) (-3.244) (-4.084)
0.227***
0.160***
0.201***
0.141***
0.126***
0.111***
(15.165)
(16.477)
(3.624)
(4.116)
(7.373)
(11.971)
0.113***
0.107***
0.135*
0.076***
0.092***
0.098***
(9.920)
(16.664)
(2.068)
(2.993)
(5.869)
(14.677)
0.155***
0.129***
0.081*
0.076***
0.178***
0.147***
(10.438)
(13.769)
(1.828)
(4.721)
(12.213)
(18.416)
Month fixed effects
Stock fixed effects
Yes
Yes
Yes
Yes
Observations
33,731
29,478
160,298 132,219
0.656
0.709
0.629
2
R
Yes
Yes
Yes
Yes
0.661
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
10,237
8,366
55,549
45,477
36,349
34,338
197,867 184,458
0.780
0.794
0.732
0.739
0.657
0.641
0.609
64
Electronic copy available at: https://ssrn.com/abstract=1967599
Yes
Yes
Yes
Yes
0.576
Table V. Quasi-Natural Experiment Based on the Russell Index Reconstitution
The table reports estimates from a quasi-natural experiment relying on the reconstitution of the Russell 1000 and Russell
2000 indexes. The sample is at the stock-month stock level. Panel A presents the first stage where the dependent
variable is ETF ownership. The explanatory variables (instruments) are a dummy for inclusion in the Russell 2000, for
stocks in the Russell 1000 before index reconstitution (columns (1)–(5)), and a dummy for inclusion in the Russell
1000, for stocks in the Russell 2000 before index reconstitution (columns (6)–(10)). Stocks are ranked by market
capitalization in May of each year. Columns (1)–(5) and (6)–(10) present bandwidths ranging from 100 to 500 stocks.
The same stocks enter the sample in the June after index reconstitution and remain in the sample until the following
May, except if delisted. The controls in all panels are logged market capitalization, lagged inverse share price, lagged
Amihud (2002) ratio, lagged average bid-ask spread, lagged book-to-market ratio, lagged past 12 month returns, lagged
gross profitability (as in Novy-Marx (2013)), lagged volatility, index-fund ownership, active-fund ownership, hedgefund ownership, and a linear specification of the ranking variable (not reported). In Panels B, C, and D, the dependent
variable is daily stock volatility (computed using daily returns within a month). The main explanatory variable is
instrumented ETF ownership. The instruments are the switching indicators. In Panel C, the main explanatory variable
is an interaction between the dummy variables for index inclusion and average ETF ownership (for Russell 2000
stocks). Panel C also includes controls for average ETF ownership as well as average ownership for index funds, active
funds, and hedge funds (for Russell 2000 stocks). In Panel D, the main explanatory variable is an interaction between
the dummy variable for Russell 1000 inclusion and the stock-level ratio of ETF ownership to other fund (index, active,
and hedge fund) ownership in May before reconstitution. The dependent variable and the ownership variables are
standardized by subtracting the mean and dividing by the standard deviation. Standard errors are double clustered at
the stock and month level. t-statistics are in parentheses. ***, **, and * represent statistical significance at the 1%, 5%,
and 10% levels, respectively. The sample covers June 2000 to May 2007.
Panel A: First-Stage Regressions, First-Degree Polynomial
Dependent variable:
Instrument:
Bandwidth:
Switch indicator
log(mktcap (t-1))
1/Price (t-1)
Amihud (t-1)
Bid-ask spread (t-1)
Book-to-Market (t-1)
Past 12-month return (t-1)
Gross profitability (t-1)
Volatility (t-1)
Index fund ownership (t-1)
Active fund ownership (t-1)
Hedge fund ownership (t-1)
ETF ownership
Switch to the Russell 2000
Switch to the Russell 1000
± 100
± 200
± 300
± 400
± 500
± 100
± 200
± 300
± 400
± 500
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
0.196*** 0.294*** 0.407*** 0.456*** 0.433*** -0.180*** -0.405*** -0.397*** -0.356*** -0.359***
(6.214)
(7.122)
(7.887)
(8.986)
(9.099)
(-3.210) (-8.935) (-10.052) (-8.246) (-8.581)
-0.193*** -0.284*** -0.231*** -0.191*** -0.195*** -0.184*** -0.090*** -0.094*** -0.097*** -0.100***
(-3.259) (-5.868) (-4.763) (-4.894) (-5.366) (-5.925) (-5.078)
(-5.343) (-5.946) (-5.373)
-0.680**
-0.449 -0.797*** -0.652*** -0.746*** -0.184
-0.084
0.039
-0.566*** -0.692***
(-2.488) (-1.611) (-3.568) (-3.812) (-4.668) (-0.863) (-0.598)
(0.294)
(-6.409) (-9.377)
-6.708*** -10.189***-11.042***-10.321*** -10.819*** -18.391*** -18.242*** -18.757*** -15.080*** -10.444***
(-6.112) (-8.164) (-7.266) (-7.338) (-7.485) (-11.623) (-13.283) (-11.000) (-8.550) (-9.445)
-2.787
-1.098
-0.755
-2.438** -4.318*** 6.201*** 3.892** 2.989*** 2.989*** 1.949**
(-1.354) (-1.088) (-0.785) (-2.383) (-3.833)
(2.853)
(2.203)
(2.742)
(3.058)
(2.005)
0.037
-0.008
0.023
0.022** 0.017** 0.283*** 0.336*** 0.318*** 0.351*** 0.353***
(1.403) (-0.416) (1.628)
(2.029)
(2.009)
(7.261)
(13.789) (18.003) (19.998) (19.685)
0.045
0.039*
0.024
0.052**
0.016
-0.064*** -0.019* -0.020**
-0.013
-0.017*
(1.264)
(1.868)
(1.171)
(2.386)
(0.758)
(-2.928) (-1.963)
(-2.155) (-1.400) (-1.692)
-0.160*** -0.171*** -0.162*** -0.175*** -0.128*** -0.071 -0.101*** -0.042**
-0.007
-0.004
(-4.142) (-4.685) (-5.130) (-5.889) (-3.965) (-1.239) (-3.836)
(-2.185) (-0.430) (-0.259)
-0.034*** -0.042*** -0.033*** -0.028*** -0.027*** -0.133*** -0.124*** -0.132*** -0.127*** -0.124***
(-4.816) (-5.069) (-4.144) (-3.816) (-3.280) (-13.026) (-16.633) (-14.908) (-15.266) (-13.747)
0.116*** 0.163*** 0.165*** 0.179*** 0.197*** 0.138*** 0.159*** 0.165*** 0.163*** 0.167***
(12.537) (16.642) (15.637) (19.056) (20.545)
(7.803)
(8.066)
(9.682)
(10.292) (10.655)
-0.093*** -0.049*** -0.022*** -0.011 -0.020*** 0.095*** 0.066*** 0.057*** 0.056*** 0.068***
(-9.811) (-7.210) (-3.236) (-1.569) (-3.006)
(5.916)
(8.050)
(8.366)
(8.046)
(10.713)
-0.118*** -0.105*** -0.102*** -0.100*** -0.104*** -0.093*** -0.106*** -0.080*** -0.070*** -0.072***
(-11.806) (-20.185) (-23.143) (-22.697) (-20.998) (-9.375) (-12.085) (-16.223) (-19.097) (-21.804)
Month fixed effects
Linear polynomials of rank
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Observations
4,857
10,103
16,101
22,303
28,599
6,495
12,735
18,293
23,647
29,060
65
Electronic copy available at: https://ssrn.com/abstract=1967599
Table V. Quasi-Natural Experiment Based on the Russell Index Reconstitution (Cont.)
Panel B: Second-Stage Regressions, First-Degree Polynomial
Dependent variable:
Instrument:
Bandwidth:
ETF ownership
log(mktcap (t-1))
1/Price (t-1)
Amihud (t-1)
Bid-ask spread (t-1)
Book-to-Market (t-1)
Past 12-month return (t-1)
Gross profitability (t-1)
Volatility (t-1)
Index fund ownership (t-1)
Active fund ownership (t-1)
Hedge fund ownership (t-1)
Daily volatility (t)
± 100
(1)
0.512**
(2.224)
Switch to the Russell 2000
± 200
± 300
± 400
(2)
(3)
(4)
0.384*** 0.268*** 0.176**
(2.649)
(3.269)
(2.631)
± 500
(5)
0.249***
(3.656)
± 100
(6)
0.717**
(2.409)
Switch to the Russell 1000
± 200
± 300
± 400
(7)
(8)
(9)
0.249*** 0.198*** 0.222***
(3.572)
(3.252)
(3.486)
-0.346*** -0.404*** -0.478*** -0.512*** -0.533*** -0.606*** -0.731***
(-3.995) (-5.576) (-7.079) (-7.366) (-7.322) (-7.121) (-9.075)
2.758*** 1.815*** 1.550*** 1.326*** 1.461*** 1.759*** 1.395***
(5.928)
(6.649)
(8.570)
(8.651)
(9.395)
(6.464)
(6.511)
1.241
5.238** 4.392*** 5.737*** 6.139*** 13.736** 6.568***
(0.493)
(2.413)
(2.876)
(3.501)
(3.845)
(2.251)
(3.293)
-0.484
0.696
-2.117
-2.833
-3.004 -12.445*** -9.365***
(-0.163)
(0.319) (-1.293) (-1.654) (-1.571) (-3.084) (-2.662)
0.063** 0.082*** 0.095*** 0.088*** 0.109*** -0.291*** -0.248***
(2.113)
(3.117)
(4.458)
(4.376)
(5.189)
(-3.162) (-4.827)
-0.014
-0.029
0.027
0.008
0.038
0.309*** 0.156***
(-0.227) (-0.735) (0.749)
(0.214)
(1.101)
(5.908)
(3.318)
0.004
0.049
0.064**
0.035
0.069*** 0.173** 0.109***
(0.051)
(1.084)
(2.167)
(1.265)
(2.852)
(2.421)
(3.443)
0.229*** 0.263*** 0.260*** 0.267*** 0.270*** 0.376*** 0.290***
(14.041) (19.465) (20.091) (18.905) (17.987)
(9.317)
(17.415)
-0.002
-0.022
-0.013
0.001
-0.020
-0.059
-0.003
(-0.074) (-0.795) (-0.807)
(0.073)
(-1.354) (-1.461) (-0.238)
0.105*** 0.083*** 0.082*** 0.088*** 0.092***
0.024
0.093***
(3.878)
(5.868)
(9.452)
(9.880) (11.305)
(0.957)
(10.297)
0.088*** 0.076*** 0.054*** 0.048*** 0.050*** 0.075**
0.013
(2.778)
(4.236)
(5.291)
(5.997)
(6.117)
(2.308)
(1.061)
-0.766***
(-9.783)
1.322***
(8.198)
7.135***
(5.038)
-8.741***
(-3.349)
-0.245***
(-5.323)
0.152***
(4.150)
0.080***
(3.176)
0.287***
(18.014)
0.005
(0.444)
0.098***
(12.991)
0.011
(1.228)
± 500
(10)
0.169***
(3.394)
-0.761*** -0.728***
(-9.504) (-9.266)
1.411*** 1.435***
(8.382)
(9.383)
7.249*** 6.084***
(6.163)
(7.869)
-9.558*** -10.449***
(-3.411) (-3.641)
-0.235*** -0.184***
(-5.208) (-4.293)
0.153*** 0.140***
(4.738)
(5.024)
0.072***
0.033
(3.339)
(1.500)
0.297*** 0.294***
(18.037) (19.731)
0.001
0.010
(0.043)
(0.974)
0.092*** 0.088***
(12.698) (12.378)
0.011
0.011
(1.332)
(1.487)
Month fixed effects
Linear polynomials of rank
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Observations
4,857
10,103
16,101
22,303
28,599
6,495
12,735
18,293
23,647
29,060
66
Electronic copy available at: https://ssrn.com/abstract=1967599
Table V. Quasi-Natural Experiment Based on the Russell Index Reconstitution (Cont.)
Panel C: Identification from Time-Series Variation in Aggregate Fund Ownership
Dependent variable:
Instrument:
Bandwidth:
Daily stock volatility
ETF ownership × Switch
Index funds ownership × Switch
Active funds ownership × Switch
Hedge funds ownership × Switch
Switch indicator
log(mktcap (t-1))
Switch to the Russell 2000
± 100
± 200
± 300
± 400
(1)
(2)
(3)
(4)
0.231
0.401** 0.351**
0.219
(1.289)
(2.450)
(2.430)
(1.574)
-0.087*** -0.060** -0.053** -0.046**
(-3.271) (-2.493) (-2.461) (-2.248)
0.237***
0.041
0.046
0.053
(3.136)
(0.657)
(0.763)
(0.856)
0.176
0.079
-0.059
-0.041
(1.237)
(0.671)
(-0.566) (-0.384)
11.776** 12.236*** 7.772**
6.098*
(2.448)
(3.404)
(2.431)
(1.943)
Switch to the Russell 1000
± 500
± 100
± 200
± 300
± 400
± 500
(5)
(6)
(7)
(8)
(9)
(10)
0.216
-0.287* -0.431*** -0.496*** -0.592*** -0.671***
(1.390)
(-1.866) (-3.849) (-4.169) (-4.068) (-3.769)
-0.049** 0.067***
0.016
-0.011
-0.006
-0.008
(-2.196)
(3.201)
(0.876)
(-0.707) (-0.358) (-0.399)
0.056
-0.092
0.020
0.083
0.082
0.125*
(0.925)
(-1.554)
(0.358)
(1.337)
(1.404)
(1.770)
-0.086
-0.121
-0.053
-0.093
-0.003
0.040
(-0.758) (-0.972) (-0.710) (-1.320) (-0.033)
(0.483)
4.730 -9.630*** -10.797*** -11.743*** -11.380*** -11.272***
(1.282)
(-2.716) (-4.242) (-4.811) (-4.108) (-3.645)
-0.570*** -0.590*** -0.612*** -0.619*** -0.652*** -0.849*** -0.846*** -0.877*** -0.860*** -0.837***
(-6.259) (-8.189) (-9.086) (-9.037) (-9.856) (-9.943) (-9.605) (-11.168) (-11.611) (-11.912)
2.117*** 1.640*** 1.373*** 1.252*** 1.440*** 1.649*** 1.492*** 1.374*** 1.324*** 1.358***
(7.012)
(9.095) (10.241)
(8.823)
(8.869)
(8.182)
(6.777)
(6.884)
(7.106)
(7.813)
-1.524
0.713
1.136
3.570** 3.223**
-1.118
0.228
2.469*** 3.405*** 4.304***
(-0.897)
(0.518)
(1.282)
(2.560)
(2.508)
(-0.742)
(0.161)
(2.643)
(4.281)
(7.037)
-0.658
0.442
-1.969
-2.372
-3.742** -8.000*** -9.079*** -8.493*** -9.282*** -10.094***
(-0.203)
(0.242)
(-1.290) (-1.384) (-2.210) (-2.775) (-3.007) (-3.538) (-3.718) (-3.976)
0.079** 0.081*** 0.099*** 0.091*** 0.113***
-0.066 -0.171*** -0.188*** -0.150*** -0.115***
(2.186)
(2.873)
(4.045)
(4.015)
(5.346)
(-1.144) (-3.108) (-3.684) (-3.385) (-2.750)
0.062
0.019
0.055
0.045
0.065* 0.274*** 0.160*** 0.161*** 0.169*** 0.166***
(1.024)
(0.528)
(1.542)
(1.203)
(1.880)
(5.727)
(3.160)
(4.152)
(4.701)
(4.935)
-0.086*
-0.021
0.023
0.010
0.044** 0.117*** 0.083*** 0.072*** 0.074*** 0.040**
(-1.748) (-0.555)
(0.889)
(0.409)
(2.082)
(3.033)
(3.121)
(3.507)
(3.809)
(2.008)
2.214*** 1.596*** 1.339*** 1.371*** 1.255*** 1.258** 1.217*** 1.343*** 1.243*** 1.295***
(4.114)
(3.653)
(4.186)
(4.542)
(4.535)
(2.458)
(3.244)
(3.377)
(3.303)
(3.966)
0.793*** 0.852*** 0.992*** 1.053*** 1.068*** 1.012*** 1.267*** 1.280*** 1.256*** 1.190***
(5.733)
(7.937) (10.225) (10.143) (11.490)
(6.437) (11.668) (13.062) (13.154) (13.254)
0.676*** 0.817*** 0.612*** 0.722*** 0.606***
0.172
-0.173
0.040
0.071
0.144
(3.480)
(6.219)
(5.629)
(6.892)
(6.468)
(1.031)
(-1.429)
(0.360)
(0.685)
(1.523)
0.221*** 0.247*** 0.251*** 0.263*** 0.262*** 0.275*** 0.255*** 0.261*** 0.268*** 0.271***
(17.959) (21.347) (21.154) (20.220) (19.184) (16.202) (15.773) (18.007) (18.555) (19.530)
1/Price (t-1)
Amihud (t-1)
Bid-ask spread (t-1)
Book-to-Market (t-1)
Past 12-month return (t-1)
Gross profitability (t-1)
Volatility (t-1)
Index fund ownership (t-1)
Active fund ownership (t-1)
Hedge fund ownership (t-1)
Time trend, interacted with switch
Linear polynomials of rank
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Observations
4,858
10,107
16,107
22,315
28,615
6,499
12,744
18,304
23,663
29,077
0.634
0.609
0.604
0.594
0.594
0.495
0.473
0.476
0.484
0.489
R
2
67
Electronic copy available at: https://ssrn.com/abstract=1967599
Table V. Quasi-Natural Experiment Based on the Russell Index Reconstitution (Cont.)
Panel D: Ratio of ETF to Ownership by Other Fund Types
Dependent variable:
Instrument:
Ratio:
Bandwidth:
Ratio × Switch
Switch indicator
Ratio
log(mktcap (t-1))
1/Price (t-1)
Amihud (t-1)
Bid-ask spread (t-1)
Book-to-Market (t-1)
Past 12-month return (t-1)
Gross profitability (t-1)
Volatility (t-1)
Month Fixed Effects
Linear polynomials of rank
Observations
R
2
Daily stock volatility
Switch to the Russell 1000
ETF / Index Fund
ETF / Active Fund
ETF / Hedge Fund
± 100
± 200
± 300
± 400
± 500
± 100
± 200
± 300
± 400
± 500
± 100
± 200
± 300
± 400
± 500
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
(11)
(12)
(13)
(14)
(15)
-0.033
-0.091** -0.094** -0.109*** -0.106*** -0.352
-0.268
-0.391** -0.372*** -0.345*** -0.040*** -0.034*** -0.018** -0.020*** -0.014*
(-0.526) (-2.143) (-2.418) (-3.025) (-3.047) (-1.485) (-1.441) (-2.551) (-2.772) (-2.857) (-2.748) (-3.251) (-2.417) (-2.674) (-1.936)
-0.081**
-0.042
-0.038
-0.022
-0.010
-0.089** -0.064* -0.052**
-0.035
-0.024
-0.061* -0.067** -0.078*** -0.059*** -0.048***
(-2.159) (-1.482) (-1.580) (-0.960) (-0.509) (-2.284) (-1.955) (-2.033) (-1.547) (-1.249) (-1.891) (-2.471) (-3.347) (-2.874) (-2.925)
-0.203*** -0.202*** -0.211*** -0.206*** -0.208*** -0.689*** -0.946*** -0.870*** -0.880*** -0.902*** -0.013 -0.020** -0.029*** -0.029*** -0.036***
(-3.397) (-5.489) (-7.512) (-9.611) (-9.998) (-3.043) (-8.164) (-9.967) (-10.959) (-11.838) (-1.059) (-2.376) (-4.904) (-5.143) (-6.674)
-0.597*** -0.577*** -0.590*** -0.567*** -0.553*** -0.587*** -0.567*** -0.567*** -0.531*** -0.526*** -0.608*** -0.581*** -0.585*** -0.569*** -0.555***
(-8.027) (-7.372) (-8.590) (-8.970) (-8.978) (-7.966) (-7.257) (-8.267) (-8.463) (-8.739) (-8.493) (-7.355) (-8.470) (-8.969) (-9.151)
1.459*** 1.599*** 1.509*** 1.395*** 1.461*** 1.787*** 1.486*** 1.456*** 1.399*** 1.505*** 1.653*** 1.778*** 1.523*** 1.324*** 1.360***
(6.483)
(9.247) (11.075) (10.267) (12.839)
(7.141)
(5.305)
(6.607)
(6.956)
(8.933)
(6.952) (10.698) (11.255) (9.977) (11.778)
-1.319*** -1.802*** -1.874*** -1.479*** -0.584
-1.850
0.867
-0.488
-0.483
0.617
-3.615** -4.469*** -3.340*** -2.023**
1.087
(-2.704) (-4.049) (-4.139) (-3.790) (-1.377) (-0.852)
(0.661)
(-0.451) (-0.731)
(0.954) (-2.083) (-3.219) (-2.969) (-2.303)
(1.347)
1.040
1.791
0.164
0.049
-0.678
1.334
0.337
-0.561
0.536
-1.138
-0.850
-0.619
-2.713
-2.053 -3.577***
(0.416)
(0.724)
(0.078)
(0.031)
(-0.522)
(0.538)
(0.137)
(-0.271)
(0.358) (-0.928) (-0.287) (-0.220) (-1.228) (-1.235) (-2.807)
-0.030
-0.113** -0.129*** -0.078**
-0.057
-0.038
-0.081
-0.093**
-0.050
-0.049
-0.058 -0.125** -0.130*** -0.111*** -0.089**
(-0.662) (-2.254) (-3.280) (-2.024) (-1.553) (-0.834) (-1.613) (-2.451) (-1.340) (-1.262) (-1.333) (-2.565) (-3.397) (-3.193) (-2.406)
0.240*** 0.137*** 0.147*** 0.154*** 0.151*** 0.246*** 0.136*** 0.146*** 0.157*** 0.153*** 0.247*** 0.135*** 0.144*** 0.153*** 0.148***
(6.969)
(2.851)
(3.459)
(3.877)
(4.279)
(7.335)
(2.844)
(3.404)
(3.862)
(4.265)
(7.377)
(2.753)
(3.364)
(3.830)
(4.254)
0.148*** 0.128*** 0.100*** 0.126*** 0.097*** 0.094* 0.094*** 0.084*** 0.102*** 0.052** 0.139*** 0.131*** 0.114*** 0.134*** 0.090***
(3.262)
(4.154)
(4.087)
(6.414)
(4.576)
(1.907)
(2.923)
(3.381)
(4.973)
(2.395)
(2.937)
(4.219)
(4.712)
(6.920)
(4.301)
0.298*** 0.264*** 0.264*** 0.271*** 0.274*** 0.293*** 0.250*** 0.256*** 0.261*** 0.265*** 0.299*** 0.268*** 0.268*** 0.272*** 0.275***
(19.127) (16.553) (18.653) (20.554) (21.726) (19.193) (16.097) (18.566) (20.066) (20.100) (20.070) (16.962) (19.600) (21.771) (22.366)
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
5,609
10,850
15,520
19,957
0.437
0.396
0.401
0.402
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
24,355
5,459
10,574
15,067
19,496
0.414
0.433
0.391
0.397
0.396
23,874
5,532
10,635
15,194
19,478
23,609
0.404
0.435
0.396
0.399
0.401
0.409
68
Electronic copy available at: https://ssrn.com/abstract=1967599
Table VI. ETF Ownership and Churn Ratio of Stock Traders
The table presents evidence about the relation between ETF ownership and the churn ratio of the underlying stocks,
using Ancerno data. Panel A reports estimates from ordinary least squares (OLS) regressions where the dependent
variable is the adjusted churn ratio at the stock-quarter level, computed as the volume-weighted average of the managerstock-level-adjusted churn ratio, which in turn is defined as
$
1
$
,,
,,
,,
1
∗
.
,,
$
2
$
,,
,,
The main explanatory variable is ETF ownership. Both variables are standardized. Panel B reports second-stage, IV
estimates from a quasi-natural experiment relying on the reconstitution of the Russell 1000 and Russell 2000 indexes.
The frequency of the data is quarterly at the stock level. The explanatory variable is ETF ownership instrumented by a
dummy for inclusion in the Russell 2000, for stocks in the Russell 1000 before index reconstitution (columns (1)–(5))
and a dummy for inclusion in the Russell 1000, for stocks in the Russell 2000 before index reconstitution (columns
(6)–(10)). Stocks are ranked in terms of market capitalization in May of each year. Different ranges of this rank around
the cutoff are used for inclusion in the sample: 100 stocks on each side (columns (1) and (6)), 200 stocks on each side
(columns (2) and (7)), 300 stocks on each side (columns (3) and (8)), 400 stocks on each side (columns (4) and (9)),
and 500 stocks on each side (columns (5) and (10)). The same stocks enter the sample in the June after index
reconstitution and remain in the sample until May of the next year, except if delistings occur. In all panels, the dependent
variable and the ownership variables have been standardized by subtracting the mean and dividing by the standard
deviation. The controls in Panels A and B include logged market capitalization, the lagged inverse share price, the
lagged Amihud (2002) ratio, the lagged average bid-ask spread, the lagged book-to-market ratio, the lagged past 12
month returns, lagged gross profitability (as in Novy-Marx (2013)), the lagged dependent variable in some of the
columns, index-fund ownership, active-fund ownership, and hedge-fund ownership. Stock and quarter fixed effects are
included. Standard errors are double clustered at the stock and quarter level. t-statistics are presented in parentheses.
*** **
, , and * represent statistical significance at the 1%, 5%, and 10% levels, respectively. The sample ranges between
January 2000 and December 2014.
Panel A: OLS Specification
Dependent variable:
Adjusted Churn Ratio (t)
(2)
(3)
0.123***
0.084***
(3.330)
(4.950)
(4)
0.059***
(4.359)
0.555***
(13.870)
0.320
(0.611)
28.446*
(1.825)
-1.529
(-0.498)
-0.033
(-0.655)
0.117***
(2.664)
0.077
(0.505)
1.425
(0.576)
1.361***
(5.010)
-0.600
(-1.637)
0.420***
(13.023)
0.215
(0.557)
26.453**
(2.024)
-1.095
(-0.400)
-0.013
(-0.319)
0.111***
(2.895)
0.045
(0.382)
1.108
(0.548)
0.963***
(4.628)
-0.406
(-1.325)
0.170***
(18.923)
0.361***
(16.231)
0.405***
(3.182)
0.323
(1.350)
-1.753
(-1.333)
0.005
(0.247)
0.003
(0.205)
-0.024
(-0.551)
-1.444**
(-2.045)
0.909***
(7.748)
-0.226***
(-2.667)
0.261***
(12.898)
0.295***
(2.746)
0.189
(0.936)
-1.153
(-1.085)
0.010
(0.589)
0.017
(1.341)
-0.021
(-0.648)
-0.951*
(-1.725)
0.581***
(6.466)
-0.184***
(-2.879)
0.202***
(15.215)
Quarter fixed effects
Stock fixed effects
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Observations
25,641
25,641
130,267
130,267
0.469
0.500
0.489
0.529
ETF ownership (t-1)
log(mktcap (t-1))
1/Price (t-1)
Amihud (t-1)
Bid-ask spread (t-1)
Book-to-Market (t-1)
Past 12-month return (t-1)
Gross profitability (t-1)
Index fund ownership (t-1)
Active fund ownership (t-1)
Hedge fund ownership (t-1)
(1)
0.165***
(3.511)
Adjusted Churn Ratio (t-1)
R
2
69
Electronic copy available at: https://ssrn.com/abstract=1967599
Table VI. ETF Ownership and Churn Ratio of Stock Traders (Cont.)
Panel B: IV Specification
Dependent variable:
Instrument:
Bandwidth:
Switch indicator
Adjusted Churn Ratio (t)
± 100
(1)
0.741***
(3.172)
Switch to the Russell 2000
± 200
± 300
± 400
(2)
(3)
(4)
0.462*** 0.200**
0.051
(3.514)
(2.444)
(0.814)
log(mktcap (t-1))
0.600*** 0.582*** 0.484*** 0.438***
(7.095)
(9.580)
(9.725)
(11.642)
1/Price (t-1)
1.832*** 1.842*** 1.558*** 1.207***
(5.270)
(5.424)
(7.152)
(7.551)
Amihud (t-1)
-0.215
-1.628
-2.585*** -3.355***
(-0.116)
(-1.152)
(-2.924)
(-4.536)
-11.618*** -6.860*** -11.585*** -9.646***
Bid-ask spread (t-1)
(-3.467)
(-2.883)
(-5.616)
(-5.516)
Book-to-Market (t-1)
0.094
0.082
0.064**
0.038
(1.203)
(1.605)
(2.028)
(1.559)
Past 12-month return (t-1) -0.141**
-0.001
0.030
0.036
(-2.290)
(-0.020)
(0.691)
(0.882)
Gross profitability (t-1)
0.073
0.094*
0.037
-0.015
(1.175)
(1.795)
(0.954)
(-0.507)
Lagged Adj. Churn Ratio 0.194*** 0.209*** 0.211*** 0.218***
(9.353)
(14.526) (14.598) (19.861)
Index fund ownership (t-1) 0.055*
0.063*** 0.084*** 0.106***
(1.769)
(3.039)
(6.322)
(11.103)
Active fund ownership (t-1) 0.175*** 0.119*** 0.131*** 0.130***
(7.490)
(9.857)
(14.279) (13.914)
Hedge fund ownership (t-1) 0.136*** 0.073*** 0.042*** 0.027**
(4.030)
(3.549)
(2.976)
(2.354)
± 500
(5)
0.137**
(2.139)
± 100
(6)
0.321
(1.619)
Switch to the Russell 1000
± 200
± 300
± 400
(7)
(8)
(9)
-0.049
-0.080
-0.025
(-0.785)
(-1.381)
(-0.420)
± 500
(10)
-0.029
(-0.497)
0.425*** 0.286*** 0.345*** 0.254*** 0.294*** 0.309***
(12.825)
(5.245)
(7.868)
(6.475)
(8.569)
(9.834)
1.316*** 2.360*** 1.522*** 1.326*** 1.432*** 1.390***
(7.701)
(9.152)
(7.769)
(7.564)
(8.199)
(9.642)
-1.337*
1.257
-3.382
-3.439* -3.769** -2.287**
(-1.810)
(0.252)
(-1.386)
(-1.845)
(-2.370)
(-2.117)
-9.865*** -16.447*** -14.999*** -11.984*** -13.128*** -14.539***
(-5.801)
(-6.111)
(-8.700)
(-8.748)
(-9.024)
(-9.776)
0.041** -0.171** -0.095** -0.095** -0.098** -0.063**
(2.560)
(-2.126)
(-2.281)
(-2.543)
(-2.523)
(-2.209)
0.060
0.199*** 0.127*** 0.144*** 0.142*** 0.134***
(1.621)
(4.132)
(4.570)
(6.062)
(6.782)
(6.519)
-0.002
0.135**
-0.043* -0.054*** -0.040**
-0.033*
(-0.084)
(2.501)
(-1.844)
(-3.061)
(-2.109)
(-1.718)
0.219*** 0.292*** 0.264*** 0.242*** 0.236*** 0.239***
(19.900) (14.108) (22.414) (27.167) (25.865) (28.048)
0.089***
0.026
0.108*** 0.106*** 0.085*** 0.080***
(7.469)
(0.871)
(7.707)
(7.766)
(6.732)
(6.725)
0.135*** 0.156*** 0.172*** 0.160*** 0.148*** 0.148***
(15.288) (11.823) (13.826) (15.730) (15.222) (15.105)
0.046***
0.045*
0.008
0.015
0.038*** 0.045***
(4.534)
(1.681)
(0.616)
(1.353)
(3.892)
(5.037)
Quarter fixed effects
Linear polynomials of rank
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Observations
4,840
10,077
16,083
22,286
28,574
6,482
12,726
18,286
23,641
29,054
70
Electronic copy available at: https://ssrn.com/abstract=1967599
Table VII. ETF Flows, Stock Returns, and Price Impact
Panel A reports results from regressions of stock-level Daniel et al. (1997, DGTW)-adjusted cumulative returns
computed over different horizons starting on day t on stock-level ETF flows on day t. The analysis is at the stock-day
level. ETF flows are scaled by market capitalization and standardized. The controls in all panels include logged market
capitalization, the lagged inverse share price, the lagged Amihud (2002) ratio, lagged average bid-ask spread, lagged
book-to-market ratio, lagged past 12 month returns, lagged gross profitability (as in Novy-Marx (2013)), stock-level
order imbalance, and lagged returns. Day fixed effects are included. Standard errors are double clustered at the stock
and time level. Panel B reports estimates from ordinary least squares (OLS) regressions of price impact on turnover
and turnover squared. The sample includes trade-level observations from Ancerno data. Price impact is defined as the
percentage difference between the execution price and price at time of placement. Turnover is measured as the dollar
volume as a fraction of daily dollar volume in CRSP. Day and stock fixed effects are included. Standard errors are
double clustered at the stock and time level. The sample ranges between January 2000 and December 2014. t-statistics
are presented in parentheses. ***, **, and * represent statistical significance at the 1%, 5%, and 10% levels,
respectively.
Panel A: ETF Flows and Stock Returns
Sample:
Dependent variable:
ETF flows (t)
log(mktcap (t-1))
1/Price (t-1)
Amihud (t-1)
Bid-ask spread (t-1)
Book-to-Market (t-1)
Past 12-month return (t-1)
Gross profitability (t-1)
Order Imbalance (t-1)
Ret(t-1)
Ret(t)
(1)
0.122***
(13.433)
Ret(t,t+4)
(2)
0.111***
(7.469)
S&P 500
Ret(t,t+9)
(3)
0.062***
(3.233)
Ret(t,t+19)
(4)
0.046*
(1.848)
Ret(t,t+39)
(5)
0.015
(0.416)
Ret(t)
(6)
0.040***
(15.069)
Ret(t,t+4)
(7)
0.034***
(6.649)
Russell 3000
Ret(t,t+9) Ret(t,t+19)
(8)
(9)
0.027***
0.016*
(3.995)
(1.669)
Ret(t,t+39)
(10)
-0.000
(-0.006)
0.048***
(14.352)
-0.870***
(-4.084)
37.332***
(6.715)
-2.450**
(-2.505)
0.039***
(4.750)
0.209
(0.835)
1.842
(0.139)
2.411
(1.132)
0.033**
(2.003)
1.471**
(2.555)
-31.973
(-1.208)
6.631*
(1.759)
0.040
(1.216)
4.131***
(3.365)
-72.013
(-1.332)
19.021***
(2.671)
0.050
(0.736)
9.562***
(3.386)
-159.667
(-1.482)
29.763**
(2.220)
0.008***
(6.956)
-0.316***
(-10.093)
0.135***
(2.777)
0.781*
(1.853)
0.022***
(7.371)
0.100
(1.302)
-0.813***
(-8.169)
0.135
(0.157)
0.044***
(7.942)
0.613***
(4.369)
-1.868***
(-10.661)
0.245
(0.186)
0.090***
(8.579)
1.819***
(6.737)
-3.664***
(-11.816)
1.653
(0.716)
0.181***
(8.896)
4.754***
(8.791)
-6.662***
(-11.964)
4.534
(1.048)
0.020*
(1.702)
-0.014
(-1.591)
0.035**
(2.052)
0.003***
(20.893)
-2.587***
(-8.348)
0.014
(0.565)
-0.016
(-0.567)
0.053
(1.254)
0.003***
(18.073)
0.011
(0.232)
-0.036
(-0.699)
0.045
(0.627)
0.002***
(13.541)
-0.001
(-0.013)
0.067
(0.673)
0.064
(0.481)
0.002***
(9.855)
-0.020
(-0.106)
0.308
(1.490)
0.152
(0.571)
0.002***
(4.915)
0.017***
(3.511)
-0.020***
(-5.325)
0.049***
(5.425)
0.002***
(75.636)
-3.364***
(-19.595)
0.039***
(2.951)
-0.007
(-0.657)
0.222***
(9.468)
0.002***
(61.639)
0.062***
(2.622)
-0.006
(-0.306)
0.403***
(10.277)
0.002***
(53.132)
0.107**
(2.333)
0.017
(0.452)
0.690***
(9.918)
0.002***
(41.312)
0.177**
(1.986)
0.043
(0.581)
1.210***
(9.200)
0.002***
(27.932)
Ret(t-1,t-5)
-2.199***
(-7.195)
Ret(t-1,t-10)
-1.571***
(-10.302)
-2.266***
(-7.337)
Ret(t-1,t-20)
-1.861***
(-12.330)
-2.496***
(-7.010)
Ret(t-1,t-40)
Observations
R2
-1.873***
(-11.240)
-3.008***
(-6.340)
-1.609***
(-7.837)
1,492,313
1,492,313
1,492,313
1,492,313
1,492,313
7,759,143
7,759,143
7,759,143
7,759,143
7,759,143
0.033
0.013
0.011
0.011
0.013
0.039
0.009
0.007
0.006
0.006
71
Electronic copy available at: https://ssrn.com/abstract=1967599
Table VII. ETF Flows, Stock Returns, and Price Impact (Cont.)
Panel B: Price Impact
Price Impact
Dependent variable:
Sample:
Turnover (%)
Turnover (%) ^2
Constant
Day FE
Stock FE
Observations
R
2
S&P 500
Russell 3000
(3)
(4)
3.426***
3.465***
(47.787)
(41.592)
-0.131***
-0.131***
(-39.559)
(-35.681)
3.199***
(15.126)
(1)
3.609***
(34.627)
-0.148***
(-29.961)
2.598***
(15.909)
(2)
3.621***
(36.255)
-0.148***
(-30.910)
No
No
Yes
Yes
No
No
Yes
Yes
27,960,051
27,960,051
53,167,782
53,167,760
0.001
0.009
0.002
0.011
72
Electronic copy available at: https://ssrn.com/abstract=1967599
Table VIII. Limits of Arbitrage
The table reports estimates from OLS regressions of intraday volatility (Panel A) and intraday variance ratios (Panel
B) on absolute stock-level mispricing in the prior period, interacted with measures of arbitrage costs. The frequency is
daily, and the observations are at the stock level. The sample includes S&P 500 stocks. In columns (2)–(4), arbitrage
cost is captured by the bid-ask spread in the prior day, and in columns (5)–(7), by the average share-lending fee in the
month. For both measures of arbitrage costs, we construct dummy variables denoting whether the stock is in the top
half of the distribution of that measure in the relevant period. In columns (3) and (6), we restrict the sample to
observations for which the stock-level mispricing is positive. In columns (4) and (7), we restrict the sample to
observations for which the stock-level mispricing is negative. The controls in all panels include logged market
capitalization, the lagged inverse share price ratio, the lagged Amihud (2002) ratio, the lagged average bid-ask spread,
the lagged book-to-market ratio, lagged past 12 months’ returns, lagged gross profitability (as in Novy-Marx, 2013),
lagged returns, the lagged dependent variable, and the absolute mispricing in period t - 2. Variable descriptions are
provided in Appendix Table A1. Standard errors are double clustered at the stock and day level. t-statistics are presented
in parentheses. ***, **, and * represent statistical significance at the 1%, 5%, and 10% levels, respectively. The sample
ranges between January 2000 and December 2015.
Dependent variable:
Abs(Mispricing) (t-1)
All
(1)
0.023***
(6.897)
× I(High bid-ask spread)
All
(2)
0.043***
(8.025)
Intraday stock volatility
Misp > 0 Misp < 0
All
(3)
(4)
(5)
0.076*** 0.035*** 0.020***
(10.300)
(6.988)
(4.642)
Misp > 0
(6)
0.048***
(7.530)
Misp < 0
(7)
0.018***
(4.302)
-0.009*
(-1.956)
0.003
(0.444)
-0.010**
(-2.548)
0.031***
(5.531)
0.041***
(5.720)
4.718***
(12.275)
-13.726
(-0.634)
7.552
(1.085)
0.081***
(4.220)
0.036***
(3.269)
0.038
(1.525)
0.249***
(3.104)
0.541***
(24.546)
0.004
(1.060)
-0.005
(-1.565)
0.021***
(4.042)
0.034***
(4.945)
4.568***
(11.996)
-15.911
(-0.712)
9.859
(1.515)
0.078***
(4.136)
0.027***
(2.668)
0.033
(1.342)
-0.235***
(-4.704)
0.565***
(24.739)
0.018***
(4.597)
-0.003
(-0.957)
-0.006
(-1.227)
0.035***
(5.110)
4.300***
(11.333)
-9.579
(-0.427)
9.416
(1.551)
0.075***
(4.046)
0.020**
(2.056)
0.037
(1.542)
-0.697***
(-9.612)
0.578***
(24.044)
0.059***
(9.901)
-0.005
(-1.433)
0.031***
(5.417)
0.033***
(4.719)
4.805***
(12.505)
-21.039
(-0.942)
14.033**
(1.989)
0.081***
(4.244)
0.036***
(3.243)
0.035
(1.398)
0.264***
(3.280)
0.545***
(24.734)
0.000
(0.061)
Yes
No
Yes
No
Yes
No
Yes
No
Yes
No
509,240
513,308
1,022,548
509,240
513,308
0.505
0.498
0.499
0.504
0.497
-0.053*** -0.055*** -0.043***
(-6.554) (-4.257) (-6.392)
× I(High lending fee)
High bid-ask spread
0.042***
(7.186)
0.038***
(6.318)
0.045***
(7.130)
High lending fee
ETF ownership (t-1)
0.022***
(3.611)
log(mktcap (t-1))
0.086***
(4.060)
1/Price (t-1)
5.767***
(7.882)
Amihud (t-1)
-19.124
(-0.795)
Bid-ask spread (t-1)
5.128
(0.796)
Book-to-Market (t-1)
0.110***
(3.231)
Past 12-month return (t-1)
0.009
(0.805)
Gross profitability (t-1)
-0.018
(-0.230)
Return (t-1)
-0.196***
(-3.984)
Dependent variable (t-1)
0.408***
(20.800)
Abs(Mispricing) (t-2)
0.024***
(7.081)
Day fixed effects
Stock fixed effects
Observations
R
2
Yes
Yes
0.022***
-0.004
(4.217)
(-0.692)
0.042*** 0.042***
(5.940)
(6.017)
4.479*** 4.216***
(11.778) (11.131)
-8.636
-3.039
(-0.399) (-0.139)
4.059
4.005
(0.636)
(0.670)
0.078*** 0.075***
(4.102)
(3.997)
0.027*** 0.020**
(2.703)
(2.078)
0.035
0.038
(1.443)
(1.579)
-0.246*** -0.707***
(-4.956) (-9.759)
0.561*** 0.575***
(24.501) (23.836)
0.021*** 0.059***
(5.305)
(9.870)
Yes
No
1,022,548 1,022,548
0.549
0.500
73
Electronic copy available at: https://ssrn.com/abstract=1967599
Table IX. Variance Ratio
The dependent variable in this table is Abs(Variance Ratio), which is the absolute variance ratio over five days, and is
defined as
,,
∙
,,
,
,,
∙
,,
1 . Variance Ratio is the variance ratio over five days, and is defined as
,
. In Panels A (for the absolute value of VR) and B (for the level of VR), we report instrumental variable (IV)
estimates from a quasi-natural experiment relying on the reconstitution of the Russell 1000 and Russell 2000 indexes.
The frequency of the data is monthly at the stock level. The explanatory variable is ETF ownership instrumented by a
dummy for inclusion in the Russell 2000, for stocks in the Russell 1000 before index reconstitution (columns (1)–(5)),
and a dummy for inclusion in the Russell 1000, for stocks in the Russell 2000 before index reconstitution (columns
(6)–(10)). Stocks are ranked in terms of market capitalization in May of each year. Different ranges of this rank around
the cutoff are used for inclusion in the sample: 100 stocks on each side (columns (1) and (6)), 200 stocks on each side
(columns (2) and (7)), 300 stocks on each side (columns (3) and (8)), 400 stocks on each side (columns (4) and (9)),
and 500 stocks on each side (columns (5) and (10)). The same stocks enter the sample in the June after index
reconstitution and remain in the sample until May of the next year, except if delistings occur. In all panels, the dependent
variable and the ownership variables have been standardized by subtracting the mean and dividing by the standard
deviation. The controls include the lag of logged market capitalization, the lagged inverse share price, the lagged
Amihud (2002) ratio, the lagged average bid-ask spread, the lagged book-to-market ratio, lagged past 12 months’
returns, lagged gross profitability (as in Novy-Marx (2013)), index-fund ownership, active-fund ownership, and hedgefund ownership. Stock and quarter fixed effects are included. Standard errors are double clustered at the stock and
quarter level. t-statistics are presented in parentheses. ***, **, and * represent statistical significance at the 1%, 5%, and
10% levels, respectively. The sample ranges between January 2000 and December 2015.
Panel A: Second-Stage IV Regressions for abs(Variance Ratio)
Dependent variable:
Instrument:
Bandwidth:
abs(Variance Ratio)
± 100
(1)
0.305
(1.182)
Switch to the Russell 2000
± 200
± 300
± 400
(2)
(3)
(4)
0.207
0.243*
0.235*
(1.320)
(1.810)
(2.033)
0.058
(0.414)
-0.573
(-0.854)
3.342
(1.315)
-4.951
(-1.063)
-0.025
(-0.610)
-0.154
(-1.143)
0.087
(0.640)
-0.079*
(-1.765)
-0.043
(-1.031)
-0.008
(-0.212)
0.015
(0.161)
-0.719**
(-2.387)
3.802
(1.611)
-0.072
(-0.032)
-0.018
(-0.629)
-0.092
(-1.635)
0.133
(1.560)
-0.076**
(-2.101)
-0.054**
(-2.058)
-0.016
(-0.585)
Month fixed effects
Linear polynomials of rank
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Observations
1,535
3,204
5,115
7,097
9,116
2,064
4,038
5,801
7,498
9,221
ETF ownership
log(mktcap (t-1))
1/Price (t-1)
Amihud (t-1)
Bid-ask spread (t-1)
Book-to-Market (t-1)
Past 12-month return (t-1)
Gross profitability (t-1)
Index fund ownership (t-1)
Active fund ownership (t-1)
Hedge fund ownership (t-1)
Switch to the Russell 1000
± 200
± 300
± 400
(7)
(8)
(9)
0.494** 0.511*** 0.563**
(2.494)
(2.917)
(2.711)
± 500
(10)
0.550**
(2.767)
0.036
-0.022
-0.040
0.174
0.048
0.044
0.042
(0.546)
(-0.447) (-1.189)
(1.347)
(0.603)
(0.786)
(1.029)
-0.626** -0.801*** -0.831*** 0.095
0.164
-0.176
-0.016
(-2.429) (-3.139) (-3.446)
(0.214)
(0.533)
(-0.784) (-0.052)
5.148** 4.697** 5.254**
10.753 11.557** 13.500*** 14.604***
(2.078)
(2.173)
(2.326)
(1.418)
(2.295)
(3.400)
(4.017)
1.400
2.757*
1.713
-0.480
3.577
2.104
1.302
(0.741)
(1.771)
(1.105) (-0.118)
(1.063)
(0.998)
(0.683)
-0.025
-0.022
-0.005
-0.081
-0.082
-0.085
-0.128
(-1.454) (-1.072) (-0.369) (-0.537) (-0.917)
(-1.164) (-1.449)
-0.057
-0.034
0.008
0.060
-0.002
-0.007
-0.017
(-1.263) (-0.769)
(0.169)
(0.895)
(-0.052)
(-0.165) (-0.447)
0.099
0.113
0.094
0.040
0.137*
0.046
0.028
(1.444)
(1.683)
(1.624)
(0.401)
(1.838)
(0.688)
(0.500)
-0.065* -0.066** -0.069**
-0.069
-0.069** -0.088*** -0.092***
(-2.043) (-2.368) (-2.340) (-1.437) (-2.327)
(-3.461) (-3.595)
-0.061*** -0.060*** -0.054*** -0.152*** -0.127*** -0.115*** -0.124***
(-3.307) (-3.953) (-4.122) (-4.217) (-5.411)
(-5.834) (-6.237)
0.009
0.012
0.023
0.066
0.057**
0.031
0.038*
(0.371)
(0.559)
(1.134)
(1.595)
(2.090)
(1.668)
(1.893)
-0.009
(-0.209)
0.160
(0.520)
10.343***
(3.309)
1.325
(0.513)
-0.196**
(-2.767)
0.002
(0.070)
-0.002
(-0.041)
-0.098***
(-3.751)
-0.139***
(-6.847)
0.029
(1.493)
± 500
(5)
0.227*
(1.992)
± 100
(6)
0.524
(1.383)
74
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Table IX. Variance Ratio (Cont.)
Panel B: Second-Stage IV Regressions for Variance Ratio
Dependent variable:
Instrument:
Bandwidth:
ETF ownership
log(mktcap (t-1))
1/Price (t-1)
Amihud (t-1)
Bid-ask spread (t-1)
Book-to-Market (t-1)
Past 12-month return (t-1)
Gross profitability (t-1)
Index fund ownership (t-1)
Active fund ownership (t-1)
Hedge fund ownership (t-1)
Variance Ratio
Switch to the Russell 2000
± 100
± 200
± 300
± 400
± 500
± 100
(1)
(2)
(3)
(4)
(5)
(6)
-1.191*** -0.867*** -0.743*** -0.676*** -0.678*** -1.231*
(-3.003) (-3.322)
(-2.977) (-2.903) (-2.833) (-1.834)
-0.409
-0.404** -0.218**
-0.071
-0.067
(-1.570) (-2.559)
(-2.363) (-1.280) (-1.656)
-0.649
0.191
0.101
0.383
0.313
(-0.829)
(0.436)
(0.262)
(1.470)
(1.213)
-8.841** -8.987*** -10.598*** -9.537*** -8.800***
(-2.229) (-3.237)
(-3.453) (-3.451) (-3.177)
10.485
5.122
5.812
3.444
0.711
(1.280)
(1.216)
(1.549)
(1.195)
(0.299)
-0.002
0.015
0.018
0.018
0.042**
(-0.027)
(0.327)
(0.650)
(0.871)
(2.591)
-0.016
0.011
-0.043
-0.043
-0.055
(-0.112)
(0.139)
(-0.628) (-0.692) (-0.980)
-0.248*
-0.154*
-0.088
-0.123*
-0.079
(-1.858) (-1.811)
(-1.266) (-2.013) (-1.193)
0.165*** 0.172*** 0.140*** 0.139*** 0.157***
(2.810)
(3.570)
(3.043)
(3.180)
(3.226)
0.011
0.050**
0.048** 0.059*** 0.055***
(0.199)
(2.077)
(2.595)
(3.358)
(2.984)
-0.107*
-0.038
-0.049
-0.033
-0.043
(-1.956) (-1.083)
(-1.434) (-1.095) (-1.520)
Switch to the Russell 1000
± 200
± 300
± 400
± 500
(7)
(8)
(9)
(10)
-0.975*** -1.051*** -1.160*** -1.202***
(-3.286)
(-3.309) (-3.127)
(-3.096)
-0.448*
-0.225
-0.211
-0.169
-0.117
(-1.998) (-1.588)
(-1.700) (-1.577)
(-1.173)
-0.851
-0.534
-0.247
-0.864
-0.967*
(-1.047) (-1.192)
(-0.563) (-1.605)
(-1.844)
-24.204* -20.393*** -23.756*** -25.530*** -17.594***
(-1.739) (-3.509)
(-4.111) (-4.323)
(-2.836)
8.025
3.549
0.951
2.288
1.040
(1.158)
(1.176)
(0.344)
(0.805)
(0.329)
0.379
0.376**
0.304** 0.378** 0.447***
(1.569)
(2.647)
(2.352)
(2.527)
(2.935)
-0.046
-0.019
-0.027
-0.025
-0.037
(-0.468) (-0.399)
(-0.530) (-0.548)
(-0.789)
-0.106
-0.100
-0.048
-0.027
0.003
(-0.537) (-0.915)
(-0.522) (-0.307)
(0.032)
0.162** 0.157*** 0.172*** 0.179*** 0.197***
(2.198)
(4.466)
(4.322)
(3.810)
(3.834)
0.150** 0.119*** 0.141*** 0.148*** 0.189***
(2.438)
(3.371)
(4.100)
(4.242)
(4.804)
-0.124* -0.086**
-0.059*
-0.066*
-0.053
(-1.800) (-2.447)
(-2.041) (-1.900)
(-1.483)
Month fixed effects
Linear polynomials of rank
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Observations
1,535
3,204
5,115
7,097
9,116
2,064
4,038
5,801
7,498
9,221
75
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Table X. ETF Ownership Portfolios
The table reports statistics and regression analysis for portfolios based on ETF ownership. Each month, five equally
weighted portfolios are formed on the basis of the five quintiles of the distribution of ETF ownership in the previous
month. Panel A presents the raw returns. Panel B presents factor model regressions for the High-ETF-ownership minus
the Low-ETF-ownership portfolio. The factors are the five Fama and French (2015) factors (MKTRF, HML, SMB,
RMW, CMA), Momentum (UMD), and the Pástor and Stambaugh (2003) traded liquidity factor (PS_VWF). Panel C
reports estimates from Fama and MacBeth (1973) regressions of four-factor-model-adjusted (Carhart (1997)) monthly
stock returns on ETF ownership in the previous month, contemporaneous ETF stock-level flows, index-, active-, and
hedge-fund ownership, and control variables. The dependent variable is expressed as a percentage, and both the
ownership variables and the flows are standardized. The controls include logged market capitalization, the laggedinverse-share-price ratio, the lagged Amihud (2002) ratio, the lagged average bid-ask spread, the lagged book-to-market
ratio, lagged past 12 months’ returns, and lagged gross profitability (as in Novy-Marx (2013)). t-statistics are presented
in parentheses. ***, **, and * represent statistical significance at the 1%, 5%, and 10% levels, respectively. The sample
ranges between January 2000 and December 2015.
Panel A: Raw Excess Returns for the Quintile Portfolios
Raw excess returns
Low
0.389
(1.051)
# Months
191
Quintiles based on ETF Ownership
(2)
(3)
(4)
High
0.618*
0.696* 0.739** 0.737*
(1.736) (1.941) (2.040) (1.828)
191
191
191
191
Panel B: High Minus Low Portfolio, Whole Sample
Dependent variable:
Alpha
(1)
0.347**
(2.296)
MKTRF
HML
SMB
UMD
RMW
CMA
PS_VWF
# Months
2
R
ret(High-minus-Low ETF Ownership)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
0.303** 0.334** 0.355** 0.364** 0.350** 0.383** 0.383**
(2.074)
(2.294)
(2.429)
(2.477)
(2.287)
(2.482)
(2.461)
0.130*** 0.126*** 0.136*** 0.125*** 0.132*** 0.119*** 0.119***
(4.012)
(3.915)
(4.126)
(3.437)
(3.204)
(2.847)
(2.829)
-0.089** -0.095** -0.101** -0.111**
-0.051
-0.051
(-1.996) (-2.127) (-2.223) (-2.046) (-0.749) (-0.738)
-0.061
-0.054
-0.044
-0.036
-0.036
(-1.316) (-1.132) (-0.778) (-0.645) (-0.620)
-0.021
-0.023
-0.014
-0.014
(-0.747) (-0.787) (-0.475) (-0.474)
0.025
0.016
0.016
(0.340)
(0.220)
(0.219)
-0.136
-0.136
(-1.460) (-1.455)
-0.001
(-0.021)
191
191
191
191
191
191
191
191
0.000
0.078
0.098
0.106
0.109
0.109
0.119
0.119
76
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Table X. ETF Ownership Portfolios (Cont.)
Panel C: Fama and MacBeth (1973) Regressions
Dependent variable:
ETF ownership (t-1)
ETF Flows (t)
Four-Factor Model Adjusted Returns (t)
(1)
(2)
(3)
(4)
(5)
0.144** 0.161** 0.195***
0.199***
(2.382)
(2.536)
(2.862)
(2.642)
0.099**
0.080
(2.009)
(1.452)
Hedge fund ownership (t-1)
Index fund ownership (t-1)
Active fund ownership (t-1)
0.062
(1.198)
-0.055
(-1.145)
0.075
(1.231)
0.024
0.026
0.021
(0.444)
(0.474)
(0.376)
-0.065
-0.025
-0.067
(-1.363) (-0.575) (-1.398)
0.049
0.053
0.040
(0.973)
(1.048)
(0.819)
0.109*
0.029
0.078
(1.895)
(0.450)
(1.310)
6.458*** 6.440*** 6.206***
(5.197)
(5.209)
(5.011)
3.074
-10.612
6.454
(0.182)
(-0.607)
(0.364)
-18.181
-21.054
-17.810
(-1.281) (-1.479) (-1.254)
-0.068
-0.095
-0.067
(-0.311) (-0.440) (-0.304)
-0.430
-0.408
-0.417
(-1.495) (-1.442) (-1.453)
0.709** 0.659** 0.702**
(2.332)
(2.181)
(2.321)
log(mktcap (t-1))
1/Price (t-1)
Amihud (t-1)
Bid-ask spread (t-1)
Book-to-Market (t-1)
Past 12-month return (t-1)
Gross profitability (t-1)
Observations
350,237
350,237
350,237
350,237
350,237
R2
# Months
0.003
191
0.011
191
0.037
191
0.036
191
0.039
191
77
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Figure 1: Illustration of the Propagation of Liquidity Shocks via Arbitrage
ETF
ETF
NAV
NAV
Fundamental Value
Fundamental Value
Figure 1a. Initial equilibrium
ETF
Figure 1b. Liquidity shock to ETF
NAV
ETF
Fundamental Value
Fundamental Value
Figure 1c. Initial outcome of arbitrage:
the shock is propagated to the NAV, and
the ETF price starts reverting to the
fundamental value.
NAV
Figure 1d. Equilibrium reestablished: after
some time, both the ETF price and the NAV
revert to the fundamental value.
78
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Figure 2: Illustration of the Propagation of a Fundamental Shock with Price Discovery
Occurring in the ETF Market
New Fundamental Value
ETF
NAV
ETF
NAV
Fundamental Value
Figure 2a. Initial equilibrium
ETF
Figure 2b. Shock to fundamental value
New Fundamental Value
ETF
NAV
New Fundamental
NAV
Figure 2c. Price discovery takes place in
the ETF market. The ETF price moves to
the new fundamental value.
Figure 2d. After a delay, the NAV
catches up with the new fundamental.
79
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Figure 3: Fund Ownership around the Russell Cutoff
3.5
Index Fund Ownership (%)
ETF Ownership (%)
4
3.5
3
2.5
3
2.5
2
500
1000
Rank
500
1500
Figure 3a. ETF Ownership
1500
Figure 3b. Index-Fund Ownership
8
28
27
7
HF Ownership (%)
Active Fund Ownership (%)
1000
Rank
26
25
6
5
24
4
23
500
1000
Rank
500
1500
Figure 3c. Active-Fund Ownership
1000
Rank
1500
Figure 3d. Hedge-Fund Ownership
The figure reports average ownership (in %) by ETFs (3a), index funds (3b), active funds (3c), and hedge funds (3d)
for stocks ranked by market capitalization and included in the Russell 3000. The average is computed first by ranking
over time, and then across the ranking in bins of 10 stocks. The vertical line denotes the 1,000th rank. The sample
ranges between January 2000 and May 2007.
80
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Do ETFs Increase Volatility?
Internet Appendix
Itzhak Ben-David
Fisher College of Business, The Ohio State University, and NBER
Francesco Franzoni
USI Lugano and the Swiss Finance Institute
Rabih Moussawi
Villanova School of Business, Villanova University
and WRDS, The Wharton School, University of Pennsylvania
The Internet Appendix (I.A.) includes a more detailed description of the data and the additional
results that are referenced in the main text. In addition, it reports ancillary results that do not
appear in the main paper.
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Holdings Data Construction
We proceed as follows to identify and clean ETF holdings data in Thomson. First, we
identify the Thomson’s fundno of the ETFs in our sample by using a historical ticker-date
merging with the s12type8 table in Thomson, which contains the historical tickers of each mutualfund share class. Then we double-check this link by manually verifying the names of the fund in
the Thomson-Reuters database and in our sample to ensure those links are valid.
Because the fund holdings in the Thomson data are at the portfolio level, many of the links
between the ETF share class and the associated fund portfolio can include the holdings of nonETF open-end share classes. For example, many Vanguard ETFs are not standalone ETFs,
because they are structured as share classes within the overall fund portfolio.27 To address this
issue, we adjust the holdings of the fund portfolio to reflect only the holdings of the ETF share
class as follows. First, we compute the ownership of each stock in the fund portfolio as a
percentage of the total assets of all the equity holdings in that portfolio. Then we multiply these
portfolio weights by the market capitalization of the ETF share class to compute the accurate
ownership in that stock by the ETF share class exclusively. Using the updated market
capitalization of the ETF at the end of every period, we also follow this approach to update the
ETF ownership in that stock every period until the next available quarterly holding snapshot by
this ETF.
At the end of every period, to create the total ETF ownership measure in the shock, we
sum the ownership in each stock across all ETFs that own it. Therefore, the ETF ownership
variable is computed as
27
https://advisors.vanguard.com/iwe/pdf/standAloneTrans.pdf
82
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∑
,
In this equation,
, ,
, ,
,
,
.
(A.1)
is computed as the most recently available fund portfolio weight of ETF j
in stock i (i.e., the dollar ownership by the fund portfolio in the stock, divided by the total equity
assets in the fund portfolio). These fund-portfolio weights are computed from the most recent
quarterly investment company report (at fiscal period end), available in the Thomson-Reuters
Mutual Fund Ownership database.
Importantly, we noticed some errors in the Thomson-Reuters Mutual Fund Ownership
data after June 2015 (e.g., Apple Inc. is missing in mid-2015). Hence, we decided to rely on other
sources, such as the Thomson-Reuters Global Ownership database, as a cleaner source of
holdings data.
,
in equation (A.1) is the daily updated market capitalization of ETF j, which equals
the assets under management. Due to daily creation and redemption, the total shares outstanding
of the ETF change on a daily basis, and we use the more accurate Bloomberg information.
The product
, ,
,
in equation (A.1) reflects the dollar ownership of ETF j in stock i
updated to the current period, assuming the weight of each stock in the ETF portfolio is constant
between fiscal-period end and current-period end, which is a legitimate assumption given that
most ETFs track index portfolios. This approach provides cleaner separation of many index-fund
assets from ETF assets, especially for non-standalone ETFs.
Finally,
,
is the market capitalization of stock i at the end of the period.
Identification of Buy/Sell Orders in TAQ
We use the TAQ intraday data to properly classify every trade between 2000 and 2015
into buy or sell. We use the legacy TAQ Monthly database in the earlier period between 2000 and
2006, and the TAQ Daily database with millisecond timestamps in the period between 2007 and
83
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2015, and classify every trade using the following algorithm. First, for each trade, we compute the
prevailing National Best Bid and Offer (NBBO) quote at the end of the previous millisecond.
Then we compare the trade price for every trade in the next millisecond to the prevailing best bid
and best offer. The midpoint reference inherent to the Lee and Ready (1991) algorithm does not
take into consideration the “outside trades” that are not permitted under the Reg NMS rules, and
therefore are less likely to occur in recent years, especially after 2007. For this reason, we follow
Holden and Jacobsen (2014) and use a modified quote test based on Ellis, Michaely, and O’Hara
(2000), because the quote test is less accurate when trades are not executed at the ask or the bid.
Therefore, once an executed trade price crosses the prevailing NBBO within a millisecond, we
stop using the quote test for the rest of the millisecond. Instead, and for the remaining trades
during this millisecond, we rely on the tick test. Therefore, our modified Ellis, Michaely, and
O’Hara (2000) algorithm takes into consideration that buys are more likely to be executed at the
ask, and sales on the bid price, and whenever an outside trade is observed during that millisecond,
the algorithm relies instead on the tick test until the end of the millisecond.
Internet Appendix Tables Description
Internet Appendix Table AI. Variable Definitions
The table describes the variables used in the empirical analysis of the paper, including the
data sources.
Internet Appendix Table AII. Institution Type Definitions
The table lists the institutional types as defined by Thomson-Reuters Global Ownership
database Owner Types.
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Internet Appendix Table AIII. Churn Ratio from Trade-Level Data
The table reports statistics for the data that are used in Table IV, Panel C, including the
churn ratio and adjusted churn ratio for ETFs and stocks using trade-level data from Ancerno,
aggregated at the manager-stock-quarter level.
Internet Appendix Table AIV. ETF Ownership and Tail Risk
The table tests whether ETF ownership increases tail risk in the underlying stocks. We
construct the daily marginal expected shortfall at the 5% level as the worst daily return in a given
month. Note that a month contains about 20 trading days; hence, the worst daily return represents
the bottom 5% of the observations. Then, in an ordinary least squares (OLS) framework, we
regress the marginal expected shortfall on ETF ownership at the end of the prior month. The
results are in column (1) of I.A. Table AIV. We find that a one-standard-deviation increase in
ETF ownership is related to a decrease of about 13.7% of a standard deviation in the marginal
expected shortfall. This finding suggests left-tail risk is significantly higher for stocks that are
more exposed to ETFs.
Next, we investigate whether the right tail is affected as well. In column (2), we regress
the best daily return in a month on ETF ownership and the usual controls. The positive and
significant slope suggests the right tail is also stretched out as ETF ownership increases.
At first sight, then, both the left and right tails seem to move out by a similar magnitude
with ETF ownership. This result finds confirmation in column (3), where we find that, although
negative, the relationship between ETF ownership and daily skewness, estimated nonparametrically as in Ghysels, Plazzi, and Valkanov (2016), is not significant. Hence, this evidence
suggests our main result of an increase in volatility for ETF-owned securities translates into a
symmetric outward stretch of the return distribution.
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However, a more rigorous formulation of the hypothesis behind these tests suggests return
asymmetries should emerge in cases of large liquidations of ETFs by the institutions that hold
them. These fire sales are not likely to happen in normal times. Rather, we should expect
institutional investors to massively dump ETFs in turbulent markets.
To test this refined conjecture, we use two proxies for bad times. First, focusing on the
VIX index, which captures dry-ups in aggregate liquidity (e.g., Nagel (2012)), we define bad
months as those lying in the bottom quartile of the VIX distribution. In column (4) of I.A. Table
AIV, we regress skewness on the interaction between ETF ownership and the dummy that
identifies bad times. The negative and significant slope on the interaction suggests that in highVIX periods, ETF ownership is associated with significantly more negatively skewed returns,
consistent with the conjecture. In these months, a one-standard-deviation increase in ownership
makes skewness more negative by 4.3% of a standard deviation.
Second, we take a more direct route and focus on aggregate ETF flows, which are
measured as the quarterly change in ETF holdings by all institutional investors, using the 13F
filings in the Thomson-Reuters Global Ownership dataset. Periods of liquidations are those with a
negative aggregate value of institutional trades in all US-listed ETFs. In column (5), we regress
skewness on the interaction of ETF ownership and the dummy for quarters of institutional
liquidations. Confirming the conjecture, we find that returns of stocks with higher ETF ownership
are significantly more negatively skewed during periods of ETF liquidations by institutional
investors. The magnitude of this effect is non-negligible, at about 4.7% of a standard deviation of
daily skewness.
Focusing on the Russell 3000 sample, columns (6)–(10) of I.A. Table AIV, the results on
the marginal expected shortfall remain significant, whereas the results on skewness do not. The
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lack of significance in this sample resonates with the rest of the evidence in the paper, where the
effects are mostly significant in the S&P 500 sample.
Internet Appendix Table AV. Number of Index Switchers
The table reports the number of companies moving across indexes at each yearly
reconstitution. The years range between 2000 and 2015.
Internet Appendix Table AVI. Regression Discontinuity, Excluding May and June
The table shows instrumented results that exclude the months of May and June. The
estimates in I.A. Table AVI show this choice does not affect the conclusions.
Internet Appendix Table AVII. Regression Discontinuity, Linear, Quadratic, and Cubic
Specifications
In addition to the main specification in the main body of the study, we provide two
additional versions of the instrumental setting. In particular, in I.A. Table AVII, Panel A, we
control for a linear polynomial of the rank variable, extending the sample to 2015. The results are
comparable to Table X, Panel B. In I.A. Table AVII, Panel B, we control for quadratic
polynomials of the rank variable. In I.A. Table AVII, Panel C, we control for cubic polynomials
of the rank variable.
Internet Appendix Table AVIII. Russell Switching Instrument, Sample Splits
The table presents the IV analysis using sample splits. Panel A of I.A. Table AVIII has the
results of the sample ending in May 2007. Panel B of Table AVIII shows the estimates for the
subsample that starts with the reconstitution of June 2007. In this case, the estimates are more
unstable, and significance is not consistent across specifications. We tend to attribute this
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instability to the noise that the banding procedure introduces in this experiment. Because of the
banding procedure, fewer stocks become eligible for switching indexes (see Table AV).
Internet Appendix Table AIX. Magnitude Estimation
To gauge the economic significance of the OLS estimates in Table IV, we allocate stocks
to the percentiles of the distribution of daily volatility in each month. Then we compute the
standard deviation of ETF ownership within each percentile, across stocks and over time. We
focus on the 50th and 51st percentiles, because they provide an estimate of the variation in ETF
ownership to which the median stock in the sample is exposed. Then we ask the question: What is
the effect of a one-standard-deviation change in ETF ownership for the median stock in the
sample? To address this question, we multiply the estimated OLS coefficient by the estimated
standard deviation of ETF ownership in those percentiles. Then we add this term to the volatility
of the median stock in the last month of the sample.28 The result is expressed in terms of the
percentiles of the distribution volatility, in the last month of the sample. In Panel A of I.A. Table
AIX, we report the median volatility, which is the starting point before applying the variation in
ETF ownership, the estimated standard deviation of ETF ownership, the new level of volatility
after applying the variation, and the new percentile in the volatility distribution that is achieved
after applying the change in ETF ownership. For the S&P 500 sample, when the regressions do
not contain lags of the dependent variable (corresponding to column (2) of Table IV), the standard
deviation in ETF ownership is about 1.8%, which leads the daily volatility of the median stock to
increase by about 20 bps to 2.3%. This new level corresponds to the 64th percentile of the
28
We focus on the end of the sample because we need the entire sample to estimate the standard deviation of ETF
ownership for a given percentile. Hence, these estimates of standard deviation can only be known at the end of the
sample.
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volatility distribution. Including three lags of the dependent variable (as in column (4) of Table
IV) reduces the economic magnitude of the effect of a one-standard-deviation change in ETF
ownership, as the median stock shifts to the 58th percentile of the volatility distribution. The
effects are smaller in the Russell 3000 sample, consistent with the smaller OLS estimates. When
no lags are included, the median stock shifts to the 57th percentile, and when controlling for the
lags, it moves to the 55th percentile.
Although the economic magnitudes appear significant, they do not seem excessively large.
Of course, one can make a more informed claim about their size when they are compared to a
benchmark. To this purpose, we refer to the asset-pricing literature to identify another determinant
of volatility. In particular, we focus on the well-known negative relation between realized returns
and volatility (see, e.g., French, Schwert, and Stambaugh (1987)). Although the direction of the
causality in this relationship is unknown, strong evidence suggests realized returns are a
significant predictor of volatility (Schwert (1989), Campbell and Hentschel (1992)). Accordingly,
we estimate monthly regressions with volatility as the dependent variable and replace ETF
ownership with the prior-month return, keeping the same controls as in the original regressions.
The estimated coefficients, reported in I.A. Table AIX, Panel C, are negative and significant,
consistent with the literature. Using an identical approach to the one used for ETF ownership, we
compute the economic magnitude of these estimates and report them at the bottom of I.A. Table
AIX, Panel A. Especially when the specifications include the lagged dependent variable, we note
that the shift in volatility induced by a one-standard-deviation move in the prior-month return is in
the same ballpark as the effect of ETF ownership. Therefore, we conclude the economic
magnitude of the effect of ETF ownership in this setup is comparable to that of a well-known
determinant of volatility.
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To assess the economic magnitude of the IV estimates, two issues are relevant. First, the
estimated coefficients reflect a local average treatment effect (LATE; Imbens and Angrist
(1994)). In brief, the IV estimate, resulting from a natural experiment inducing a switch between a
control and a treatment group, measures the effect of treatment only on the units that switch
groups because of the outcome of the natural experiment. These units would not otherwise receive
treatment. Applied to our context, the IV estimates capture the effect of ETF ownership on the
stocks that enter the ETF basket only because of the index switch. As discussed in the paper, these
stocks drastically change status from being intensively utilized by arbitrageurs in their replication
of the index (when they are at the top of the Russell 2000) to being neglected by arbitrageurs
(when they are at the bottom of the Russell 1000), and vice versa for a switch in the other
direction. Arguably, this drastic change in status results in a greater impact of a given amount of
ETF ownership than for the average stock in the sample. This argument can explain why the
LATE effect is larger than the OLS effect.
The second issue is the computation of the economic magnitude of the IV estimates. The
index-switching stocks experience, on average, a change in ETF ownership of about 50 bps.
Therefore, multiplying the IV estimates by the standard deviation of ETF ownership in computing
the economic magnitude makes little sense. The amount of “treatment” for these stocks
corresponds to the actual change in ETF ownership to which they are exposed because of the
index switch. Therefore, a more natural approach in this context is to compute the economic
magnitude by multiplying the IV estimates by the change in ETF ownership that results from the
index switch.
In I.A. Table AIX, Panel B, we compute economic magnitudes by assessing the shift in
volatility for the median stock in the last month of the sample period. The organization of the
table mirrors the outline of Table V in terms of the bandwidth of the experiment and the direction
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of the index switch. Moreover, it includes specifications for the different polynomial degrees of
the ranking variable that are included in the regressions (linear, quadratic, and cubic). In a first set
of rows, for comparability purposes, we replicate the methodology from Panel A; that is, we
apply a change in ETF ownership corresponding to the standard deviation of this variable for the
median stock. These results highlight the large magnitude of the LATE estimates in comparison
to the OLS estimates. Across specifications, after the shock to ETF ownership, volatility ranges
between the 65th and the 85th percentile (on average, the 76th percentile).29 The second set of
rows reports the more conservative results in which the median volatility is perturbed by (the
absolute value of) the change in ETF ownership triggered by the index switch. In this case, the
median stock’s volatility shifts to between the 55th and 65th percentiles (on average, to the 60th
percentile). These economic magnitudes are arguably more realistic and consistent with the
magnitude of the shock to ETF ownership these stocks undergo. Moreover, these magnitudes are
comparable to those from OLS regressions.
We conclude that a normal shock to ETF ownership causes the median stock volatility to
shift to between the 55th and 65th percentiles of the volatility distribution. This conclusion is
drawn using the more conservative approaches, which are the OLS regressions including lagged
volatility and the IV estimates interacted with the shock to ETF ownership induced by the index
switch. We also note the upper bound of this range coincides with estimates that are subject to the
LATE interpretation and therefore are not necessarily generalizable to the entire sample. Overall,
while remaining economically significant, these effects appear more realistic when compared to
29
We indeed group stocks into 20 vigintiles according to the volatility distribution each month, because the reduced
number of stocks that appear in the sample would not allow us to create 100 groups every month. We express the
results in percentiles by multiplying them by 5.
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the average magnitude of ETF ownership in the sample and are of similar size to the effect of
another known determinant of volatility, namely, the lagged stock return.
Internet Appendix Table AX. Turnover Analysis
Given that retail investors tend to generate smaller-sized trades, the liquidity demand they
direct to the ETF market could be manageable by market makers, and the resulting price pressure
could be limited. This fact would limit the amount of noise that migrates from the ETF market to
the underlying securities.
To address this possibility, we start from the observation that the level of institutional
ownership in ETFs matters as far as it generates trading volume. Trading volume is the ultimate
determinant of price pressure. For this reason, we need an assessment of institutional investors’
turnover in ETFs. Using Ancerno data, we compute turnover at the security-day level,
aggregating the share volume generated by all the institutions in the dataset and normalizing it by
the security’s shares outstanding. From I.A. Table AX, Panel A, we note the institutional daily
turnover in ETFs is 42.7 bps. This magnitude is striking in comparison to the turnover of the same
institutions in common stocks, which is 9.5 bps and 12.7 bps, for the S&P 500 and Russell 3000
samples, respectively. I.A. Table AX, Panel B, confirms the difference in institutional turnover
between ETFs and stocks is also statistically significant, with and without day fixed effects and
standard errors clustered at the security and day level. Thus, under the assumption that Ancerno
institutions’ behavior is representative of the broader universe, we find institutions generate a
very large turnover in ETFs.
However, a large turnover is not enough to conclude that institutions cause a significant
price impact. In fact, ETFs might be so liquid that this large trading volume does not alter prices
significantly. To investigate the impact of institutional trades on ETF prices, we again use the
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Ancerno dataset. In a trade-level sample, we regress the price impact for trade d in stock i on day t
on the corresponding volume of the trade,
, ,
where
, ,
, ,
, , ,
(A.2)
is defined as the percentage difference between the trading price and the
price at the time of order placement, as in Anand et al. (2012).
, ,
is the number
of shares that are traded divided by the number of shares outstanding. The regressions include day
(
) and security fixed effects ( ), and the standard errors are clustered at the security and day
level. Panel C of I.A. Table AX reports the results. The 0.203 estimate for the ETF sample reveals
that a volume of 1% of shares outstanding moves prices by 20.3 bps. To gauge this magnitude, we
can contrast it with the price-impact estimates for S&P 500 stocks, 1.54%, and Russell 3000
stocks, 1.27%. Hence, ETFs are significantly more liquid than stocks, because the price impact of
the same amount of trading volume in stocks is between 6.3 and 7.6 times larger than in ETFs.
Therefore, on the one hand, institutional trading volume in ETFs is large; on the other
hand, ETFs are very liquid. The relevant question is how large the overall institutional price
impact is when the two elements are combined. To address this question, we compute the
cumulative daily price impact on ETFs as the product of the estimated price-impact coefficient
from equation (A.2) and the daily institutional turnover, reported in I.A. Table AX, Panel A. This
computation returns a cumulative daily impact of Ancerno institutions on ETF prices of about 8.6
bps (i.e., 0.203×0.00427). To assess this magnitude, we provide the cumulative impact of
Ancerno institutions on stock prices, which is 14.6 bps in the S&P 500 sample (i.e.,
1.544×0.00095) and 16.1 bps in the Russell 3000 sample (i.e., 1.273×0.00127).
Although the cumulative price impact institutions impart on ETFs is smaller than the price
impact on stocks, the former is still a sizeable fraction of the latter, being at least half of it. The
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paper’s main conjecture is that the pressure on ETF prices represents an additional layer of
volatility that eventually propagates to the underlying stocks through arbitrage activity. Therefore,
the non-fundamental volatility that institutional turnover indirectly adds to stock prices through
the ETF channel is potentially a non-negligible part of the noise they impound by directly trading
in stocks.
A natural benchmark against which we can contrast the price impact of institutional trades
in ETFs is the daily volatility of ETFs, which in our sample is on average 1.4% (estimated from
daily returns within a month). Hence, the average price impact of Ancerno institutions’ ETF trades
is about 6.1% of the total daily volatility of ETFs (i.e., 8.6/140). This magnitude seems reasonably
important.
Internet Appendix Table AXI. Predictability of Order Imbalance
We attempt to reconcile the difference between our results about how long stock prices
take to revert following ETF flows and the empirical studies on the resiliency of the limit-order
book. In particular, the empirical work in Biais, Hillion, and Spatt (1995), Dufour and Engle,
(2000), Degryse et al. (2005), and Large (2007) points out high resiliency for the order book of
large stocks, suggesting liquidity is replenished in a few minutes, if not seconds. More recently,
Hendershott and Menkveld (2014) estimate a half-life of convergence following price pressure of
0.92 days. By contrast, our evidence on the price impact of ETF flows, which we have updated
through 2015 and reported in Table VII, suggests that, following ETF flows, the half-life to
convergence of prices to the initial level is about 10 days. In Table VII, flows are expressed as a
fraction of average daily turnover over the prior month, and they are measured in units of standard
deviations.
Two considerations help us solve this apparent inconsistency. The first argument arises
from the description of the institutional details of the primary market for ETFs. We refer the
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interested reader to the detailed discussion in the ICI Research Perspective (2014) (see, in
particular, pp. 14–19). For the present purposes, we note the settlement of the shares of US
domestic equity ETFs works on a T+3 basis and, in some circumstances, can be extended to T+6.
In particular, when an authorized participant (AP) issues a creation/redemption order on day T,
the ETF manager responds on the same day by issuing new shares or withdrawing existing shares
through the National Securities Clearing Corporation (NSCC). Thus, on day T, the ETF flows are
recorded. However, the AP has to deliver the underlying securities (in the case of creation) or the
ETF shares (in the case of redemption) only on day T+3. The AP can then choose to spread the
trade of the underlying securities over a few days to reduce the price impact. Furthermore, if the
AP is also a market maker for ETFs, which happens in the large majority of cases, the delivery
date can be extended to T+6, in case the failure to deliver by T+3 is the result of bona fide market
making.
This institutional framework implies APs have time to buy (in the case of creation) or
short (in the case of redemption) the underlying securities up to T+6. Consequently, when we
measure flows on day T, we should expect the price pressure on the underlying securities to
continue over the following days as well. In case of failures to deliver on day T+6, day-T flows
can induce persistence beyond T+6. Overall, these arguments can explain the slow reversal of
prices to the initial level.
If this explanation is behind the persistence of the price impact, we should observe that
flows on day T predict order imbalance on the following days. This conjecture finds confirmation
in I.A. Table AXI, Panels A and B, which report results from regressions of contemporaneous and
future stock-level order imbalance on stock-level ETF flows measured on day T. The table shows
that day-T flows significantly predict order imbalance in the same direction for at least up to
seven days in the future. Hence, the evidence is consistent with the view that APs spread their
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transactions across multiple days. This prolonged price pressure can slow the reversal of prices
following ETF flows.
The second important element that can help us explain the persistence in the price impact
of flows is the persistence in flows themselves. If flows on a given day are followed by flows in
the same direction on the subsequent days, price pressure on the underlying stocks can continue
after day T. The predictability of order imbalance in I.A. Table AXI, Panels A and B, would also
support this claim. In I.A. Table AXI, Panel C, we provide statistics on the autocorrelation of
flows at different lags, for all ETFs in the US market and by style. Overall, the evidence reveals
significant persistence in ETF flows. For example, for the entire sample of ETFs, the first-order
autocorrelation is about 9%, whereas it is 4.3% for the sample of US large-cap ETFs. In the whole
sample, the higher-order autocorrelations remain significant for at least 20 days.
To summarize, we find two reasons for a sustained price pressure of flows. First, the
settlement on T+3 (on T+6 for market makers) allows the APs to continue trading the underlying
securities beyond the day on which flows are recorded. Second, flows are persistent, so that price
pressure on day T is likely to be followed by price pressure in the same direction on the
subsequent days.
Internet Appendix Table AXII. Intraday Volatility and Range, and ETF Flows
We develop another strategy to identify the price impact of non-fundamental ETF trades.
We observe that daily ETF flows at the stock level can be decomposed into two parts: one that
reflects net influxes of money into the ETFs that hold that stock and another that is instead due to
the reallocation of capital across the ETFs holding a given stock. The former, which is captured
by the net stock-level flows, may partly reflect fundamental information that concerns the
securities in the ETF basket. Instead, the latter part depends on investors’ decisions to reshuffle
money across the ETFs holding a given stock. For example, investors may withdraw money from
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the State Street’s SPDR S&P 500 ETF and pour it into the IShares S&P 500 ETF. Arguably, these
reallocations have non-fundamental explanations, such as the fact that some ETFs change their
fees and become more attractive. We measure this component of flows as the sum of the absolute
stock-level flows. That is, we do not net the flows at the stock level. Only the part of this variable
that exceeds the absolute value of net flows captures reallocations across ETFs. Hence, in our
analysis, we also need to control for the absolute value of net stock-level flows.
Based on these considerations, we make the identifying assumption that, controlling for
net stock-level flows, the sum of absolute stock-level flows captures the across-ETF reallocation
of capital that is due to non-fundamental reasons. Then we test whether this non-fundamental
component of flows has an impact on stock-level volatility. Because we measure flows daily, we
also need measures of price variation at the daily frequency. Thus, we use as dependent variables
either intraday volatility computed from second-by-second returns or the price range, computed as
the high price minus the low price divided by the average of the two.
I.A. Table AXII reports estimates from regressions of intraday volatility, or price range,
on the absolute value of net stock-level flows and the sum of absolute stock-level flows. For these
regressions, we standardize flows by stock-level market capitalization. The specifications include
stock and day fixed effects, and the standard errors are double clustered. The dependent and
explanatory variables are expressed in units of standard deviations. The analysis is carried out for
the S&P 500 and Russell 3000 universes.
From column (1), we note the absolute value of net stock-level flows is positively and
significantly related to intraday volatility. This relation could be due to both fundamental and
non-fundamental ETF flows. In column (2), we implement our strategy to identify nonfundamental flows. We note the sum of absolute flows is significantly related to intraday stocklevel volatility, controlling for the absolute value of net flows, which in turn loses much of its
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explanatory power. Hence, under our identifying assumption, we conclude that the nonfundamental component of flows is a significant determinant of volatility. Given the magnitude
and significance of the different flow variables, we also infer that non-fundamental flows are the
most important determinant of volatility, consistent with our evidence in Table VII that the price
impact of flows is fully reversed.
A concern about our identification strategy may arise if, for example, investors aiming to
reduce exposure to large stocks and increase exposure to small stocks switch from large-cap ETFs
(e.g., those covering the S&P 500) to ETFs tracking a broader universe (e.g., the Russell 3000). A
large-cap stock that is in both indexes will then experience low net flows but a large sum of
absolute flows. Information about the relative prospects of the two groups of stocks could
motivate this rebalancing decision. In this case, our identifying assumption will fail. We argue,
however, that investors wishing to get exposure to small stocks are unlikely to invest in Russell
3000 ETFs, given that the Russell 3000 index has over a 94% exposure to large stocks. Rather,
these investors will buy ETFs tracking the Russell 2000 index, which is fully invested in small
stocks.
The argument is more general. If we think about ETFs as tracking investment themes, a
stock will enter into only one among the industry themes (e.g., technology vs. automotive), only
one among the style themes (e.g., value vs. growth), only one among the size themes, and so on.
This stock will then only be exposed to the ETFs following those themes. The net flows into
ETFs covering those themes should capture fundamental flows. Controlling for net flows, the sum
of absolute flows should measure within-theme reallocation of capital, which is due to nonfundamental considerations.
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Internet Appendix Table AXIII. Evidence of Arbitrage Activity
The liquidity-trading hypothesis posits that price pressure in ETFs migrates to stock prices
through arbitrage activity. The following analysis searches for evidence of the arbitrage channel.
In both the primary and secondary markets, arbitrageurs respond to a price signal. They
compare the ETF price with the NAV of its underlying basket. If this difference, which we label
mispricing, is positive, the arbitrage trade involves buying the underlying stocks and selling ETF
shares in the secondary market. The ETF shares can be short-sold if they are not already available.
On the contrary, if the mispricing is negative, the arbitrage trade consists of buying the ETF and
selling the underlying basket. Overall, a positive shock to the ETF price, which causes the
mispricing to rise, translates into buying pressure in the underlying stocks, and vice versa for a
negative shock. Hence, mispricing is the signal upon which arbitrageurs condition their trading
strategies.
To prove the significance of this arbitrage channel, we regress trading volume on priorday mispricing at the stock level and daily frequency. In some specifications, in which we want to
measure the effect on the overall amount of arbitrage activity, we use the absolute value of
mispricing as the determinant of arbitrage activity, as in equation (7), noting that both positive
and negative gaps between ETF prices and the NAV trigger arbitrage activity. In this case, the
dependent variable is share turnover, defined as shares traded over shares outstanding. In another
set of tests in which we want to capture the direction of arbitrage activity, we focus on net
mispricing as the determinant of arbitrage activity. Net mispricing differs from absolute
mispricing for the omission of the absolute value in its definition, so that positive and negative
mispricing values net out. For these tests, the dependent variable is the stock-level order
imbalance, which is defined as the difference between shares bought and sold, over the sum of the
two, for a given stock-day.
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In I.A. Table AXIII, we report the estimates of these regressions. The dependent variables
are expressed as percentages. For each day, we define a high-mispricing dummy for whether the
level of mispricing is above the daily median. To filter out aggregate time variation in mispricing,
we use these dummies as our main explanatory variables. Given the persistence of the dependent
variables, we also include their lagged value among the controls. Then we have the usual controls
and the daily return. The specifications include different combinations of day and stock fixed
effects. The standard errors are clustered at the day and stock level.
In columns (1)–(4), we note that high absolute mispricing on a given day predicts higher
turnover on the next day. Because we control for the lagged dependent variable and for stock
fixed effects, this evidence is unlikely to result from some unobserved source of cross-sectional
heterogeneity. Instead, it is consistent with the conjecture that mispricing at the end of a trading
day determines the amount of arbitrage trading taking place on the next day.
In columns (5)–(8), we provide a tighter test of the arbitrage channel by measuring the
correlation of mispricing and trading. We recall that positive mispricing entails arbitrageurs
buying the underlying securities, and vice versa for negative mispricing. Consistent with this
explanation, high positive mispricing (i.e., a level of mispricing above the daily median of
positive mispricing) predicts an increase in buy trades over sell trades on the next day, whereas
the opposite occurs for high negative mispricing (i.e., a level of mispricing below the daily
median of negative mispricing). When we extend the sample to the Russell 3000 universe, the
results are robust, but the magnitudes are smaller, possibly because short selling is more difficult
for small stocks.
These results help address the concern that ETFs affect the underlying securities only
during extreme events, such as the Flash Crashes of May 6, 2010, and August 24, 2015. Because
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mispricing occurs on a daily basis, the evidence suggests arbitrage activity can also affect the
underlying securities’ prices on normal trading days.
Internet Appendix Table AXIV. ETF Ownership and Volatility, Moderated by Investor
Sentiment
We investigate whether the effect of ETFs on the underlying securities is stronger during
periods of high sentiment, when non-fundamental trading should be heightened. We define
periods of high sentiment as the months that fall in the top quintile of the realizations of the Baker
and Wurgler (2006) index and of the index of Consumer Sentiment from the Michigan Survey
Research Center (Lemmon and Portniaguina (2006)). Then we construct interactions between the
high-sentiment dummy and ETF ownership. I.A. Table AXIV reports results from OLS
regressions of daily stock volatility on the interaction and the usual controls. For both measures of
sentiment, we find the relation between ETF ownership and volatility to be significantly stronger
during times of high sentiment. The effect is also economically significant for S&P 500 stocks.
The relation is three times as large during high-sentiment periods with the Baker and Wurgler
(2006) index, and twice as large with the Michigan index.
To summarize, sentiment shocks constitute non-fundamental motivated demand for
stocks. As such, they are part of the liquidity shocks that are propagated through ETF arbitrage to
the underlying securities. Therefore, we conjecture that sentiment trading is an important driver of
the effects we document. This conjecture finds confirmation in the evidence that the relation
between ETF ownership and volatility is stronger at times of high sentiment.
Internet Appendix Table AXV. ETF Ownership and Stock Volatility, Moderated by
Arbitrage Capital
The availability of arbitrage capital should increase the trading activity of ETF
arbitrageurs. As a result, the effects of ETF ownership on volatility and of ETF flows on price
reversal should be larger when arbitrage capital is more abundant. We test this conjecture by
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interacting the measures of institutional investors’ wealth from Adrian, Etula, and Muir (2014)
and He, Kelly, and Manela (2017) with our measures of ETF ownership and flows. In I.A. Table
AXV, Panels A and B, we focus on the relation between ETF ownership and volatility. We
interact ETF ownership with the variables proposed by He, Kelly, and Manela (2017), columns
(1)–(2), and the variable proposed by Adrian, Etula, and Muir (2014), column (3). Contrary to our
prior, we find that the interactions tend to be negative and significant, which means the effect of
interest is weaker when arbitrage capital is plentiful. Panel B of the table paints a similar picture
for the sample of Russell 3000 stocks.
In columns (1)–(5) of I.A. Table AXV, Panels C, D, and E, we study the relationship
between ETF flows and stock returns. In particular, we regress returns computed over different
horizons, starting on day 0, on flows at day 0. We find the interaction of the three measures of
arbitrage capital with ETF flows to be negative and, in some specifications, significant. Again, the
evidence runs against our prior, because it suggests ETF flows have a smaller impact on stock
prices in periods when arbitrage capital is more abundant.
Given that the evidence tends to be very distant from our prior, we feel compelled to
entertain an alternative hypothesis that could explain the results. The proposed measures capture
the availability of capital to primary dealers (He, Kelly, and Manela (2017)) and broker-dealers’
leverage (Adrian, Etula, and Muir (2014)). Within the theoretical framework of the institutional
asset-pricing literature, to which these papers belong, these intermediaries are the marginal price
setters in security markets. A direct implication of these theories is that when broker-dealers’
capital is more abundant, the price-setting process is more efficient. Then, according to this
alternative view, the price dislocations caused by ETFs are smaller when the broker-dealers have
more capital.
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This explanation resonates with theories that relate liquidity and price efficiency to the
availability of arbitrageurs’ capital (e.g., Gromb and Vayanos (2002), Brunnermeier and Pedersen
(2009)). In these models, shocks to arbitrageurs’ capital reduce liquidity and make prices deviate
from fundamentals. In particular, in bad times, market makers are less able to absorb noise-trader
shocks, and price concessions are larger. Therefore, these theories can also explain why the price
pressure of ETF-related demand on the underlying securities is larger when arbitrageurs’ capital is
scarcer.
The empirical tests of these theories relate liquidity provision by financially constrained
intermediaries to aggregate uncertainty. In particular, Nagel (2012) shows that market liquidity is
lower at times when the VIX spikes. The explanation is that risk limits on arbitrageurs’ strategies
become binding when aggregate volatility increases, so their ability to correct mispricing is
impaired.
We draw inspiration for a test of the alternative hypothesis from Nagel’s (2012) evidence.
In particular, if arbitrageurs’ liquidity provision counteracts ETF price pressure, the dislocations
caused by ETFs should be stronger when the VIX is higher. We test this conjecture in I.A. Table
AXV, Panels A and B, by including an interaction between ETF ownership and the VIX, columns
(4)–(6). The interaction is positive and strongly statistically significant, consistent with the
conjecture. Moreover, the interactions of ETF ownership and the measures of arbitrage capital
lose their significance. The latter finding suggests that, indeed, these variables capture liquidity
provision, which explains the negative sign on their interactions with ETF ownership. In columns
(6)–(10) of I.A. Table AXV, Panels C, D, and E, we similarly modify the specifications in which
we estimate the effect of ETF flows on stock prices. Although not always significant, the price
pressure of ETF flows tends to be larger at times of higher VIX, consistent with the results in I.A.
Table AXV, Panels A and B.
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A further test of this alternative hypothesis focuses on the relation between ETF
mispricing and the availability of arbitrage capital. If arbitrageurs absorb the shocks coming from
ETF demand, the deviation of ETF prices from the NAV should be smaller when arbitrage capital
is more abundant. To test this conjecture, in I.A. Table AXV, Panel F, we report estimates from
time-series regressions of the monthly average of stock-level absolute ETF mispricing on the
proxies of arbitrage capital and the VIX. Confirming the intuition, we find that arbitrage capital is
negatively related to the absolute value of ETF mispricing. This relation, however, is driven out
when we include the VIX index, which seems to be more directly related to liquidity provision by
financial intermediaries.
To summarize, the measures of arbitrageurs’ capital can capture two distinct phenomena.
First, arbitrageurs generate more volume in ETFs when they have more capital. This channel
should magnify the impact of ETFs on the underlying security prices. Second, an increase in
arbitrageurs’ capital translates into the broker-dealer’s ability to provide liquidity, which dampens
the price pressure of ETF shocks on the underlying security. The evidence seems to support this
alternative hypothesis.
Internet Appendix Table AXVI. The Availability of Arbitrage Capital
To strengthen the argument that the volatility effects we identify in section III are the
result of ETF arbitrage activity, we investigate whether these effects are larger when arbitrageurs
are more actively trading in ETFs.
To this purpose, we conjecture that the aggregate amount of institutional trading activity
in all listed ETFs provides a measure of the turnover in arbitrage capital. In particular, among all
institutions, hedge funds are especially interesting because they are the prototypical arbitrageurs.
Hence, using quarterly holdings in Thomson-Reuters OP (Ownership & Profiles) data, we
construct the trades in each ETF as the quarterly change in ownership by each institution. Then
104
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we aggregate these trades across all institutions, and separately for hedge funds only, and express
them as a fraction of the aggregate market capitalization of ETFs. In aggregating the institutionlevel trades, we follow two routes. First, we sum positive and negative trades and take the
absolute value of the net trade. This definition captures the net amount of institutional capital that
moves in and out of the ETF sector. Second, we sum the absolute value of all trades. This
approach measures the total amount of volume institutions generate in ETFs.
We interact these aggregate ETF institutional trading factors with our measure of ETF
ownership at the stock-month level. The institutional trading factors are standardized, as are the
ownership variables and volatility. We also control for the interaction with the VIX, which
correlates with aggregate market liquidity (Nagel (2012)) and can confound the identification. For
the remaining part, the specifications mirror those in Table IV.
In I.A. Table AXVI, we find that aggregate institutional trading and hedge-fund trading in
ETFs magnify the impact of ETF ownership on stock volatility, consistent with the view that the
volume of arbitrageurs’ activity matters for the impact of ETFs on stock prices. Incidentally, in
some specifications, the VIX magnifies the effect of ETFs on volatility. This evidence resonates
with the results in Table IV, Panel B, showing that the effect of interest is larger during the crisis
period.
Overall, these results provide supporting evidence for the arbitrage channel as a driver of
the effects of ETFs on volatility.
Internet Appendix Table AXVII. Evidence on the Arbitrage Channel (Russell 3000 Sample)
In this table, we replicate the analysis of Table VIII in the paper for the sample of Russell
3000 stocks.
Internet Appendix Table AXVIII. ETF Ownership Portfolios, Subsamples
The table presents subsample analysis for the tests in Table X, Panel B, in the main paper.
105
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Internet Appendix Figure A1. Price Impact of Trade Turnover
I.A. Figure A1 presents evidence for the correlation between price impact and trade
turnover. It is constructed by averaging the price impact in each of the 30 bins of the daily
distribution of turnover. Price impact is computed as the percentage difference between execution
price and price at time of placement. The quadratic function is motivated by prior literature that
finds a concave relation (e.g., Keim and Madhavan (1996)). For each universe of stocks, we
provide two specifications: without fixed effects and with day and stock fixed effects. Standard
errors are double clustered at the day and stock level. The estimates are very similar irrespective
of the fixed effects. We confirm the evidence in prior literature about the convexity of the relation
between price impact and turnover.
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Variable
ETF ownership
Index (or
active) mutualfund ownership
Hedge-fund
ownership
Daily volatility
Variance ratio 5
days
Intraday price
range
Intraday
volatility
Skewness
NBBO size
Order
imbalance
Internet Appendix Table AI. Variable Definitions
Description
The sum of the ownership of all ETFs holding the stock,
using the most recent quarterly investment company
reports for equity ETFs. Using each individual ETF
portfolio weight at the end of the most recent report, daily
ETF ownership in each stock of the ETF portfolio is
inferred by multiplying the weight by the day-end ETF
AUM and daily stock capitalization to compute daily ETF
ownership in the stock. ETF ownership in each stock is
then aggregated across all ETFs that hold the stock in their
portfolios. The monthly variable is defined accordingly.
The sum of the ownership by all index (or active) mutual
funds holding the stock, using the most recent quarterly
investment company reports. Index funds are identified
using CRSP Mutual Fund database index fund dummy, and
by identifying fund names containing “index,” “S&P,”
“Russell,” NASDAQ,” and “Dow Jones.”
The sum of the ownership by all hedge funds holding the
stock, using the most recent quarterly.
Standard deviation of daily stock returns within a month.
The ratio of 5-day return variance divided by 5 times the 1day return variance minus 1. The numerator and
denominator are computed using daily and 5-day returns
within a quarter. The dependent variable in the regressions
is the logarithm of the absolute value of this difference.
Highest trading price during the day minus the lowest
trading price, scaled by closing price of the previous day.
Standard deviation of second-by-second intraday returns.
Non-parametric skewness measure of daily returns
estimated following Ghysels, Plazzi, and Valkanov (2016).
Average daily measure of the highest bid (offer) quote size
of the highest prevailing bid price, i.e., best bid (lowest
prevailing offer price, i.e., best offer) computed every
second using all prevailing quotes issued by all exchanges
where the security is traded.
(Buy Shares – Sell Shares) scaled by the daily share
volume between 9:30 am and 4:00 pm. Trades are
classified to buy and sell using a modified algorithm that
combines the methods of Lee and Ready (1991) and Ellis,
Michaely, and O’Hara (2000).
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Source
ThomsonReuters,
CRSP,
Bloomberg
ThomsonReuters,
CRSP Mutual
Fund, and
MFLinks
ThomsonReuters
Global
Ownership
CRSP
CRSP
CRSP
TAQ Monthly
and Daily
(millisecond)
CRSP
TAQ Monthly
and Daily
(millisecond)
TAQ Monthly
and Daily
(millisecond)
Net(ETF flows)
Stock-day-level measure. Weighted average of the
percentage change in ETF shares outstanding across the
ETFs holding the stock. The weight is ETF ownership of
the stock.
Abs(mispricing) Sum of absolute dollar mispricing across all the ETFs
holding the stock divided by stock capitalization (equation
(5)). Dollar mispricing is the product of ETF mispricing
(i.e., the difference between the ETF price and its NAV, as
a fraction of the ETF price) times dollar holdings of an
ETF in the stock.
Net(mispricing) Similar construction to abs(mispricing). The only
difference is that the ETF-level mispricing is not in
absolute value.
log(Mktcap)
Bloomberg,
Compustat
ThomsonReuters,
CRSP,
Bloomberg
ThomsonReuters,
CRSP,
Bloomberg
CRSP
Turnover
The logged market capitalization of the stock (in $
millions).
The inverse of the nominal share price.
Measure of price impact computed as the absolute daily
return divided by the total dollar daily volume in $
millions, following Amihud (2002).
Share volume divided by total shares outstanding.
Bid-ask spread
The quoted spread divided by the bid-ask midpoint.
CRSP,
Compustat,
Bloomberg
CRSP
Share-lending
fee
Book-to-market
Share-lending fee at the security level, 7-day average.
Markit
Book value of assets / market value of assets.
CRSP,
Compustat
Compustat
1/Price
Amihud ratio
Gross
profitability
Past 12-month
return
DGTW return
Ret(t1, t2)
Churn ratio
Churn ratio
(Ancerno)
(Revenue – cost of goods sold) / total assets, following
Novy-Marx (2013).
Cumulative returns in the previous 12 months.
Risk-adjusted excess return computed by subtracting from
the total return of every stock, the benchmark return of the
matching portfolio of stocks with similar characteristics,
namely, size, industry-adjusted book-to-market ratio, and
momentum, following Daniel et al. (1997).
The total return of the stock between the close of t1 and the
close of t2.
This measure follows Cella, Ellul, and Giannetti (2013) in
computing the investor-level churn ratio, which is then
aggregated at the stock level using ownership weights.
Equations (1) and (2) in the paper.
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CRSP
CRSP
CRSP
CRSP,
Compustat
CRSP
CRSP,
ThomsonReuters
Global
Ownership
Ancerno
Price impact
Turnover
(Ancerno)
The percentage difference between execution price and
price at time of placement.
Dollar volume of a trade as a fraction of daily dollar
volume in CRSP.
111
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Ancerno
Ancerno,
CRSP
Internet Appendix Table AII. Institution Type Definitions
Source: Thomson-Reuters Owner Types – Global Equity Ownership Feed
Institution Type
Bank and Trust
Insurance Company
Investment Advisor
/Investment
Company
Hedge Fund
Investment Advisor /
Hedge Fund
Pension Fund
Research Firm
Other Institutions
and 13-F Entities
Definition from Thomson-Reuters Global Ownership Database
These firms perform all of the functions of a retail bank. As a retail bank, a portfolio of
investments is put together by an investment adviser and sold in units to investors by brokers.
They may also handle Trust Accounts, which are outside companies or individuals that have
a bank manage their money for their own pensions or for various other reasons. They invest
the money their customers hold in their accounts in order to make interest payments and their
own profits.
Insurance companies invest in a similar fashion as investment advisors. They reinvest the
money they take in, in order to make coverage payouts as well as their own profits.
This group includes buy-side institutions that typically invest in stocks (equities) or bonds
(fixed income). They are registered with the Securities and Exchange Commission and
manage assets for private clients and institutions. They have discretionary power over their
assets under management and actually make buy/sell decisions. They include traditional
mutual fund management companies, which raise money from shareholders and invest in a
groups of assets in accordance with a stated set of objectives.
A pure-play hedge fund management firm that, through its hedge fund products, is permitted
to use aggressive strategies that are unavailable to mutual funds, including selling short,
leverage, program trading, swaps, arbitrage, and derivatives. Many times, they are highly
secretive because they use risky investment styles and also involve high-net investors.
An investment firm that uses both “traditional” and hedge fund (i.e., “alternative”)
investment techniques.
A qualified retirement plan set up by a corporation, labor union, government, or other
organization for its employees. To be included in the Thomson-Reuters database, the pension
fund must manage a portion of its assets internally.
Sell-side research firm that also has an investment-banking side with underwriting business
and a proprietary trading operation in some cases. This group includes brokerage firms
defined as a sell-side investment firm that acts as an intermediary between a buyer and seller,
usually charging a commission. Brokerage firms in the Thomson-Reuters database are
typically those that service the institutional investment community. Some sell-side firms
have ownership attached to them as a result of a 13F filing. This group also includes
independent research firms that write research intended for the buy-side community.
Other institutions include endowments, corporations, private equity, venture capital,
sovereign wealth funds, 13F reporting investors, and others.
Corporations: Typically a business organization that is given many legal rights as an entity
separate from its owners. For ownership purposes, these entities will typically be set up to
represent its strategic investments.
Individual Investors (in 13-F): Individual investors that file the 13-F because they exercise
investment discretion over the account of any other natural person or entity.
Venture Capital: A firm that specializes in providing money to startup firms and small
businesses with exceptional growth potential.
Private Equity: Firm that invests solely in private equity investments (i.e., privately held
companies). They provide equity financing to small- and middle-market companies engaged
in a variety of industries. They often focus on management buyouts, industry consolidations,
recapitalization of existing business, and other private equity opportunities.
Sovereign Funds: State-owned institutions that invest public resources to reduce the
unpredictability of government revenues, offset the boom-bust cycles' adverse effect on
government spending and the national economy, or foster savings for future generations.
Endowments: Endowment funds are permanent gifts, often to universities or colleges, that
are re-invested to ensure continuing profit.
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Internet Appendix Table AIII. Churn Ratio from Trade-Level Data
The table reports statistics for the churn ratio and adjusted churn ratio for ETFs and stocks using trade-level data from
Ancerno, aggregated at the manager-stock-quarter level.
Type of Security
Stocks
Variable
Churn Ratio
Adj. Churn Ratio
N
26,276
26,276
Mean
0.105
0.209
St. Dev.
0.123
0.452
Min
0.000
0.000
Median
0.068
0.074
Max
1.000
12.500
ETFs
Churn Ratio
Adj. Churn Ratio
6,095
6,095
0.299
0.780
0.319
1.250
0.000
0.000
0.206
0.337
1.000
18.800
All
Churn Ratio
Adj. Churn Ratio
32,371
32,371
0.141
0.316
0.193
0.714
0.000
0.000
0.075
0.084
1.000
18.800
113
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Internet Appendix Table AIV. ETF Ownership and Tail Risk
The table reports estimates from regressions of measures of tail risk on ETF ownership, interacted with measures of
aggregate conditions, in a stock-month sample. The dependent variable is the worst return in a month, capturing the
5% marginal expected shortfall (columns (1) and (6)), the best return in a month (columns (2) and (7)), and a nonparametric measure of skewness (column (3)–(5) and (8)–(10)). ETF ownership is standardized. Aggregate conditions
are measured using indicators for the months in which the VIX is in the bottom quartile (I(High VIX)) and months of
aggregate ETF liquidations by 13F institutions (I(Aggregate ETF liquidations)). The controls in all panels are logged
market capitalization, the lagged inverse share price, the lagged Amihud (2002) ratio, the lagged average bid-ask
spread, the lagged book-to-market ratio, lagged past 12 month returns, lagged gross profitability (as in Novy-Marx
(2013)), lagged volatility, index-fund ownership, active-fund ownership, and hedge-fund ownership. Month and stock
fixed effects are included. Variable descriptions are provided in I.A. Table AI. Standard errors are double clustered at
the stock and time level. t-statistics are presented in parentheses. ***, **, and * represent statistical significance at the
1%, 5%, and 10% levels, respectively. The sample ranges between January 2000 and December 2015.
S&P 500
Sample:
Dependent Variable:
ETF ownership (standardized)
5% Left
Tail
(1)
-0.137***
(-5.673)
5% Right
Tail
(2)
0.156***
(6.157)
Skewness
(3)
-0.009
(-0.654)
× I(High VIX)
Russell 3000
Skewness
(4)
0.003
(0.223)
-0.043**
(-2.464)
× I(Aggregate ETF liquidations)
log(mktcap (t-1))
Skewness
(5)
0.006
(0.488)
5% Left
Tail
(6)
-0.002***
(-6.392)
5% Right
Tail
(7)
0.003***
(7.450)
Skewness
(8)
0.001
(0.374)
Skewness
(9)
0.000
(0.015)
0.005
(0.795)
-0.046**
(-2.340)
Skewness
(10)
0.001
(0.197)
-0.000
(-0.043)
-0.068**
(-2.147)
-2.220***
(-4.231)
-26.624**
(-2.208)
0.416
(0.152)
-0.142***
(-3.427)
0.052*
(1.771)
-0.071
(-0.786)
0.020
(1.367)
-0.014
(-1.313)
-0.038***
(-3.188)
-0.052
(-1.578)
2.920***
(3.887)
49.172***
(3.022)
1.277
(0.449)
0.082*
(1.879)
-0.089***
(-2.795)
0.016
(0.169)
0.003
(0.283)
0.008
(0.747)
0.037***
(2.980)
-0.023
(-1.421)
-0.215
(-1.266)
4.303
(0.728)
-0.323
(-0.263)
-0.018
(-0.825)
-0.039***
(-2.699)
-0.092
(-1.405)
0.013
(1.273)
-0.004
(-0.563)
0.002
(0.273)
-0.023
(-1.433)
-0.205
(-1.214)
4.681
(0.795)
-0.506
(-0.410)
-0.018
(-0.815)
-0.040***
(-2.736)
-0.092
(-1.405)
0.013
(1.270)
-0.004
(-0.521)
0.003
(0.351)
-0.019
(-1.216)
-0.177
(-1.058)
3.937
(0.665)
-0.267
(-0.216)
-0.017
(-0.783)
-0.038***
(-2.627)
-0.079
(-1.201)
0.013
(1.268)
-0.005
(-0.625)
0.001
(0.151)
0.001**
(2.264)
-0.039***
(-7.048)
-0.061***
(-6.584)
-0.099*
(-1.774)
-0.005***
(-6.394)
-0.002***
(-3.664)
0.003**
(2.276)
0.001***
(6.354)
-0.001***
(-3.123)
-0.002***
(-5.823)
-0.007***
(-9.592)
0.083***
(10.971)
0.091***
(8.527)
0.119**
(2.335)
0.004***
(3.888)
0.001
(0.711)
-0.006***
(-3.368)
-0.001***
(-3.458)
0.001**
(2.329)
0.002***
(5.291)
-0.026***
(-4.047)
0.125**
(2.532)
0.036
(0.378)
0.210
(0.421)
-0.024***
(-2.768)
-0.010*
(-1.939)
-0.014
(-0.739)
0.006**
(2.322)
-0.003
(-0.923)
0.003
(0.924)
-0.026***
(-4.043)
0.123**
(2.495)
0.041
(0.433)
0.210
(0.423)
-0.024***
(-2.771)
-0.010*
(-1.946)
-0.014
(-0.740)
0.006**
(2.312)
-0.003
(-0.916)
0.003
(0.906)
-0.025***
(-3.824)
0.138***
(2.838)
0.029
(0.304)
0.192
(0.385)
-0.023***
(-2.671)
-0.010*
(-1.943)
-0.014
(-0.708)
0.006**
(2.299)
-0.003
(-0.914)
0.003
(0.825)
Month FE
Stock FE
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Observations
83,348
83,348
83,348
83,348
82,508
431,244
431,244
431,244
431,244
426,555
0.465
0.480
0.028
0.028
0.028
0.437
0.441
0.025
0.025
0.025
1/Price (t-1)
Amihud (t-1)
Bid-ask spread (t-1)
Book-to-Market (t-1)
Past 12-month return (t-1)
Gross profitability (t-1)
Hedge fund ownership
Index fund ownership
Active fund ownership
2
R
114
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Internet Appendix Table AV. Number of Index Switchers
The table reports the number of companies moving across indexes at each yearly reconstitution. The sample ranges
between June 2000 and December 2015.
Switch to:
Year
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
2015
In 2000
126
106
103
79
63
80
52
9
38
37
15
22
28
26
24
46
In 1000
114
148
126
82
63
82
85
17
42
39
23
35
26
24
27
27
115
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Internet Appendix Table AVI. Regression Discontinuity, Excluding May and June
The table reports IV estimates from a quasi-natural experiment relying on the reconstitution of the Russell 1000 and
Russell 2000 indexes. The frequency of the data is monthly at the stock level. The dependent variable is daily stock
volatility. The explanatory variable is ETF ownership instrumented by a dummy for inclusion in the Russell 2000, for
stocks in the Russell 1000 before index reconstitution (columns (1)–(5)), and a dummy for inclusion in the Russell
1000, for stocks in the Russell 2000 before index reconstitution (columns (6)–(10)). Stocks are ranked in terms of
market capitalization in May of each year. Different ranges of this rank around the cutoff are used for inclusion in the
sample: 100 stocks on each side (columns (1) and (6)), 200 stocks on each side (columns (2) and (7)), 300 stocks on
each side (columns (3) and (8)), 400 stocks on each side (columns (4) and (9)), and 500 stocks on each side (columns
(5) and (10)). The same stocks enter the sample in the June after index reconstitution and remain in the sample until
May of the next year, except if delistings occur. The controls in all panels are logged market capitalization, the lagged
inverse share price, the lagged Amihud (2002) ratio, the lagged average bid-ask spread, the lagged book-to-market
ratio, lagged past 12 month returns, lagged gross profitability (as in Novy-Marx (2013)), lagged volatility, index-fund
ownership, and active-fund ownership. The regressions include linear, quadratic, and cubic specifications of the ranking
variable in Panels A, B, and C, respectively (not reported). The dependent variable and the ownership variables have
been standardized by subtracting the mean and dividing by the standard deviation. Month fixed effects are included.
Standard errors are double clustered at the stock and month level. t-statistics are presented in parentheses. ***, **, and *
represent statistical significance at the 1%, 5%, and 10% levels, respectively. The sample ranges between July 2000
and April 2015. The sample omits observations in May and June.
Panel A: Second-Stage Regressions, First-Degree Polynomial
Dependent variable:
Instrument:
Bandwidth:
ETF ownership (standardized)
log(Mktcap (t-1))
1/Price (t-1)
Amihud (t-1)
Bid-ask spread (t-1)
Book-to-Market (t-1)
Past 12-month Return (t-1)
Gross Profitability (t-1)
Volatility (t-1)
Index Fund Ownership
Active Fund Ownership
Daily stock volatility
± 100
(1)
0.584
(1.426)
Switch to the Russell 2000
± 200
± 300
± 400
(2)
(3)
(4)
0.530** 0.363*** 0.235**
(2.602)
(3.151)
(2.478)
-0.291**
(-2.083)
2.220***
(7.835)
-1.678*
(-1.790)
3.354
(0.927)
0.122***
(4.382)
-0.073
(-1.264)
0.062
(0.681)
0.255***
(9.421)
-0.044
(-0.772)
0.039***
(3.116)
-0.386*** -0.506*** -0.607*** -0.645***
(-4.844)
(-9.421) (-10.648) (-11.319)
1.789*** 1.460*** 1.389*** 1.484***
(8.847)
(10.858)
(11.645)
(13.265)
0.026
1.161
1.550
1.586
(0.029)
(1.215)
(1.429)
(1.411)
2.913
-0.767
-0.848
-0.938
(1.112)
(-0.395)
(-0.366)
(-0.358)
0.108*** 0.108*** 0.090*** 0.090***
(5.358)
(7.089)
(5.743)
(5.689)
-0.064*
-0.030
-0.018
-0.003
(-1.888)
(-1.101)
(-0.645)
(-0.160)
0.093
0.055
0.035
0.054
(1.606)
(1.362)
(0.935)
(1.598)
0.270*** 0.259*** 0.261*** 0.263***
(15.450)
(19.797)
(20.479)
(20.635)
-0.085** -0.057***
-0.030
-0.035**
(-2.149)
(-2.613)
(-1.573)
(-1.986)
0.049*** 0.060*** 0.068*** 0.070***
(6.115)
(10.859)
(12.135)
(13.487)
± 500
(5)
0.276***
(2.997)
± 100
(6)
0.495***
(3.299)
Switch to the Russell 1000
± 200
± 300
± 400
(7)
(8)
(9)
0.297*** 0.272*** 0.279***
(3.293)
(3.268)
(3.377)
± 500
(10)
0.153**
(2.271)
-0.719*** -0.779*** -0.818*** -0.831*** -0.823***
(-8.961)
(-9.395) (-10.234) (-10.437) (-10.945)
1.689*** 1.104*** 1.175*** 1.530*** 1.562***
(7.697)
(6.320)
(7.237)
(9.165)
(10.967)
-0.585
0.920
2.228**
1.787**
1.631**
(-0.918)
(1.164)
(2.216)
(2.417)
(2.606)
-7.281*
-6.885
-6.961*
-7.633*
-9.057**
(-1.831)
(-1.510)
(-1.727)
(-1.866)
(-2.284)
0.000
-0.053** -0.089*** -0.085*** -0.082***
(0.008)
(-2.153)
(-4.061)
(-4.764)
(-4.941)
0.278*** 0.199*** 0.214*** 0.215*** 0.203***
(8.847)
(4.284)
(5.632)
(6.335)
(6.946)
0.139**
0.084**
0.065** 0.062***
0.034
(2.516)
(2.555)
(2.384)
(2.846)
(1.560)
0.292*** 0.273*** 0.273*** 0.273*** 0.260***
(17.006)
(17.720)
(17.905)
(18.120)
(19.810)
-0.067** -0.048** -0.036** -0.037**
-0.008
(-2.407)
(-2.356)
(-2.103)
(-2.091)
(-0.537)
0.048*** 0.074*** 0.070*** 0.062*** 0.058***
(3.892)
(9.505)
(10.944)
(10.086)
(10.377)
Month fixed effects
Linear polynomials of rank
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Observations
6,849
14,378
23,110
32,869
43,652
8,487
17,123
25,691
34,925
44,240
R2
0.478
0.475
0.539
0.566
0.551
0.440
0.478
0.486
0.490
0.516
116
Electronic copy available at: https://ssrn.com/abstract=1967599
Internet Appendix Table AVI. Regression Discontinuity, Excluding May and June (Cont.)
Panel B: Second-Stage Regressions, Second-Degree Polynomial
Dependent variable:
Instrument:
Bandwidth:
ETF ownership (standardized)
log(Mktcap (t-1))
1/Price (t-1)
Amihud (t-1)
Bid-ask spread (t-1)
Book-to-Market (t-1)
Past 12-month Return (t-1)
Gross Profitability (t-1)
Volatility (t-1)
Index Fund Ownership
Active Fund Ownership
Daily stock volatility
± 100
(1)
4.823
(0.182)
Switch to the Russell 2000
± 200
± 300
± 400
(2)
(3)
(4)
0.647** 0.650*** 0.555***
(2.227)
(2.630)
(2.947)
1.126
(0.127)
3.331
(0.456)
3.253
(0.107)
32.011
(0.182)
0.335
(0.250)
-0.511
(-0.185)
0.856
(0.171)
0.508
(0.322)
-0.614
(-0.172)
0.069
(0.342)
-0.341*** -0.413*** -0.511*** -0.604***
(-3.241)
(-5.005)
(-7.365)
(-9.311)
1.829*** 1.520*** 1.457*** 1.560***
(8.112)
(9.810)
(11.497)
(12.531)
0.216
2.214
2.889**
2.411*
(0.206)
(1.638)
(1.980)
(1.803)
3.705
0.155
0.425
-0.028
(1.242)
(0.073)
(0.164)
(-0.010)
0.117*** 0.125*** 0.108*** 0.097***
(5.168)
(6.859)
(6.228)
(5.939)
-0.071*
-0.040
-0.030
-0.005
(-1.914)
(-1.346)
(-1.048)
(-0.232)
0.123
0.132*
0.132**
0.102**
(1.600)
(1.851)
(2.183)
(2.156)
0.277*** 0.279*** 0.283*** 0.274***
(11.567)
(12.780)
(15.239)
(16.300)
-0.106*
-0.109** -0.093** -0.071**
(-1.909)
(-2.405)
(-2.516)
(-2.257)
0.049*** 0.058*** 0.069*** 0.072***
(5.778)
(9.361)
(11.372)
(12.981)
± 500
(5)
0.456***
(2.832)
± 100
(6)
0.377***
(3.666)
Switch to the Russell 1000
± 200
± 300
± 400
(7)
(8)
(9)
0.345*** 0.425*** 0.453***
(3.407)
(3.907)
(4.002)
± 500
(10)
0.455***
(3.728)
-0.742*** -0.770*** -0.795*** -0.802*** -0.774***
(-9.705)
(-9.331)
(-9.830) (-10.131) (-10.557)
1.627*** 1.109*** 1.216*** 1.647*** 1.804***
(7.717)
(6.269)
(7.141)
(8.756)
(10.759)
-0.646
1.061
2.816**
2.356** 2.590***
(-1.080)
(1.240)
(2.310)
(2.568)
(3.118)
-7.533*
-6.719
-6.666
-7.374*
-8.736**
(-1.923)
(-1.470)
(-1.614)
(-1.744)
(-2.140)
0.000
-0.056** -0.102*** -0.097*** -0.111***
(0.008)
(-2.199)
(-4.297)
(-4.853)
(-5.259)
0.274*** 0.200*** 0.216*** 0.217*** 0.205***
(8.800)
(4.289)
(5.614)
(6.317)
(6.910)
0.122** 0.091*** 0.085*** 0.078*** 0.063**
(2.501)
(2.659)
(2.899)
(3.278)
(2.525)
0.283*** 0.278*** 0.290*** 0.291*** 0.287***
(19.258)
(17.803)
(17.790)
(18.470)
(18.852)
-0.045** -0.058*** -0.069*** -0.076*** -0.075***
(-2.129)
(-2.613)
(-3.040)
(-3.115)
(-2.859)
0.054*** 0.073*** 0.067*** 0.060*** 0.056***
(4.646)
(9.120)
(10.057)
(9.666)
(9.884)
Month fixed effects
Quadratic polynomials of rank
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Observations
6,849
14,378
23,110
32,869
43,652
8,487
17,123
25,691
34,925
44,240
R2
0.436
0.413
0.400
0.442
0.486
0.486
0.463
0.438
0.436
0.437
117
Electronic copy available at: https://ssrn.com/abstract=1967599
Internet Appendix Table AVI. Regression Discontinuity, Excluding May and June (Cont.)
Panel C: Second-Stage Regressions, Third-Degree Polynomial
Dependent variable:
Instrument:
Bandwidth:
Daily stock volatility
± 100
(1)
-1.391
(-1.386)
Switch to the Russell 2000
± 200
± 300
± 400
(2)
(3)
(4)
1.411
0.690** 0.655***
(1.310)
(2.233)
(2.609)
-0.948***
(-2.776)
1.685***
(3.619)
-4.059**
(-2.404)
-9.599
(-1.116)
0.026
(0.459)
0.124
(1.128)
-0.321
(-1.637)
0.141**
(2.314)
0.215
(1.647)
0.027
(1.504)
-0.060
(-0.158)
2.080***
(4.455)
1.798
(0.749)
7.026
(1.192)
0.160***
(2.727)
-0.110
(-1.427)
0.304
(1.230)
0.333***
(4.170)
-0.252
(-1.221)
0.049***
(4.232)
Month fixed effects
Cubic polynomials of rank
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Observations
6,849
14,378
23,110
32,869
43,652
8,487
17,123
25,691
34,925
44,240
R2
0.402
0.395
0.374
0.383
0.446
0.483
0.480
0.474
0.457
0.453
ETF ownership (standardized)
log(Mktcap (t-1))
1/Price (t-1)
Amihud (t-1)
Bid-ask spread (t-1)
Book-to-Market (t-1)
Past 12-month Return (t-1)
Gross Profitability (t-1)
Volatility (t-1)
Index Fund Ownership
Active Fund Ownership
± 500
(5)
0.537**
(2.230)
-0.399*** -0.481*** -0.584***
(-4.025)
(-5.712)
(-6.994)
1.530*** 1.482*** 1.582***
(9.456)
(10.871)
(11.352)
2.382
3.349**
2.789*
(1.559)
(2.006)
(1.734)
0.308
0.763
0.486
(0.139)
(0.277)
(0.147)
0.127*** 0.114*** 0.101***
(6.302)
(5.836)
(5.633)
-0.042
-0.035
-0.005
(-1.354)
(-1.154)
(-0.262)
0.144*
0.163**
0.124*
(1.660)
(2.096)
(1.788)
0.282*** 0.289*** 0.279***
(10.864)
(12.913)
(12.914)
-0.116** -0.112**
-0.087*
(-2.044)
(-2.297)
(-1.867)
0.057*** 0.069*** 0.073***
(9.073)
(10.989)
(12.284)
± 100
(6)
0.387***
(3.122)
Switch to the Russell 1000
± 200
± 300
± 400
(7)
(8)
(9)
0.293*** 0.320*** 0.394***
(2.615)
(3.099)
(3.487)
± 500
(10)
0.409***
(3.766)
-0.741*** -0.780*** -0.812*** -0.812*** -0.782***
(-9.328)
(-9.299) (-10.091) (-10.033) (-10.101)
1.614*** 1.103*** 1.189*** 1.605*** 1.768***
(7.523)
(6.307)
(7.238)
(8.529)
(10.388)
-0.665
0.949
2.438**
2.174** 2.439***
(-1.122)
(1.139)
(2.153)
(2.382)
(3.054)
-7.574*
-6.953
-7.021*
-7.503*
-8.781**
(-1.963)
(-1.496)
(-1.737)
(-1.791)
(-2.152)
0.001
-0.054** -0.094*** -0.093*** -0.107***
(0.023)
(-2.221)
(-4.119)
(-4.846)
(-5.613)
0.276*** 0.199*** 0.214*** 0.217*** 0.204***
(8.701)
(4.279)
(5.617)
(6.320)
(6.909)
0.124**
0.084**
0.074** 0.073*** 0.059**
(2.564)
(2.493)
(2.548)
(3.036)
(2.406)
0.284*** 0.273*** 0.279*** 0.285*** 0.283***
(16.727)
(17.368)
(18.024)
(18.482)
(19.850)
-0.046*
-0.047*
-0.046** -0.063** -0.064***
(-1.743)
(-1.838)
(-2.154)
(-2.509)
(-2.663)
0.053*** 0.074*** 0.068*** 0.060*** 0.056***
(4.495)
(9.388)
(10.365)
(9.734)
(9.910)
118
Electronic copy available at: https://ssrn.com/abstract=1967599
Internet Appendix Table AVII. Regression Discontinuity, Quadratic and Cubic
Specifications
The table reports estimates from regressions of daily stock volatility on the variable of interest (ETF ownership)
controlling for hedge-fund ownership. The table presents instrumental variable (IV) regressions around the
Russell1000/2000 cutoff. The other controls in all panels are the lag of logged market capitalization, the lagged inverse
share price, the lagged Amihud (2002) ratio, the lagged average bid-ask spread, the lagged book-to-market ratio, lagged
past 12 month returns, lagged gross profitability (as in Novy-Marx (2013)), lagged volatility, index-fund ownership,
active-fund ownership, and hedge-fund ownership. The dependent variable and the ownership variables are
standardized. Month fixed effects are included. Panel A includes a linear specification of rank. Panel B includes a
quadratic specification of rank. Panel C includes a cubic specification of rank. Standard errors are double clustered at
the stock and time level. t-statistics are presented in parentheses. ***, **, and * represent statistical significance at the
1%, 5%, and 10% levels, respectively. The sample ranges between July 2000 and April 2015.
Panel A: Linear Function of Rank
Dependent variable:
Instrument:
Bandwidth:
ETF ownership (standardized)
log(mktcap (t-1))
1/Price (t-1)
Amihud (t-1)
Bid-ask spread (t-1)
Book-to-Market (t-1)
Past 12-month return (t-1)
Gross profitability (t-1)
Volatility (t-1)
Index fund ownership
Active fund ownership
Hedge fund ownership
± 100
(1)
0.491*
(1.930)
Daily volatility (t)
Switch to the Russell 2000
Switch to the Russell 1000
± 200
± 300
± 400
± 500
± 100
± 200
± 300
± 400
± 500
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
0.479*** 0.382*** 0.241*** 0.303*** 0.400*** 0.275*** 0.257*** 0.301*** 0.201***
(2.875)
(3.827)
(2.886)
(3.704)
(3.680)
(3.661)
(3.643)
(4.097)
(3.195)
-0.296*** -0.387*** -0.456*** -0.550*** -0.587*** -0.696*** -0.728*** -0.752*** -0.764*** -0.754***
(-3.344) (-6.080) (-9.371) (-11.111) (-11.918) (-10.361) (-10.288) (-11.376) (-11.574) (-11.947)
1.920*** 1.695*** 1.413*** 1.389*** 1.477*** 1.802*** 1.327*** 1.354*** 1.707*** 1.736***
(9.698) (10.702) (12.183) (12.746) (13.920)
(7.393)
(6.970)
(8.291) (10.403) (12.248)
1.041
3.532* 4.600*** 5.327*** 5.636***
4.657* 6.537*** 8.897*** 8.001*** 5.672***
(0.480)
(1.920)
(3.020)
(3.360)
(3.530)
(1.902)
(4.002)
(6.039)
(6.169)
(6.898)
0.466
1.497
-1.326
-1.914
-1.791
-9.690*** -9.459** -9.397*** -10.251*** -10.686***
(0.184)
(0.773)
(-0.865) (-1.127) (-0.919)
(-3.136) (-2.590) (-3.451) (-3.612) (-3.710)
0.121*** 0.104*** 0.112*** 0.092*** 0.093***
-0.002
-0.054** -0.083*** -0.085*** -0.085***
(5.684)
(6.050)
(8.304)
(6.469)
(6.401)
(-0.070) (-2.278) (-4.028) (-4.936) (-5.236)
-0.011
-0.024
-0.002
0.007
0.015
0.291*** 0.208*** 0.219*** 0.220*** 0.207***
(-0.255) (-0.785) (-0.093)
(0.276)
(0.741)
(9.218)
(4.459)
(5.878)
(6.605)
(7.176)
0.004
0.057
0.047
0.025
0.046*
0.133*** 0.085*** 0.070*** 0.070*** 0.040**
(0.072)
(1.301)
(1.459)
(0.805)
(1.673)
(2.778)
(2.820)
(2.771)
(3.362)
(2.006)
0.236*** 0.258*** 0.251*** 0.253*** 0.256*** 0.274*** 0.266*** 0.267*** 0.269*** 0.259***
(15.726) (19.061) (21.749) (21.651) (21.732)
(19.026) (19.874) (20.316) (20.277) (21.789)
-0.024
-0.061** -0.048*** -0.020
-0.031** -0.049** -0.037** -0.026* -0.035**
-0.013
(-0.684) (-1.996) (-2.707) (-1.288) (-2.096)
(-2.401) (-2.194) (-1.773) (-2.268) (-0.993)
0.038*** 0.052*** 0.063*** 0.071*** 0.074*** 0.063*** 0.085*** 0.081*** 0.072*** 0.067***
(3.600)
(6.996) (12.674) (13.585) (15.069)
(6.158) (11.737) (13.283) (12.760) (12.366)
0.111*** 0.084*** 0.087*** 0.075*** 0.080*** 0.055*** 0.031*** 0.033*** 0.042*** 0.038***
(3.218)
(4.367)
(7.140)
(7.423)
(8.183)
(4.184)
(3.253)
(4.211)
(5.153)
(5.219)
Month fixed effects
Linear polynomials of rank
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Observations
8,116
17,056
27,420
38,971
51,692
10,204
20,563
30,848
41,888
52,974
119
Electronic copy available at: https://ssrn.com/abstract=1967599
Internet Appendix Table AVII. Regression Discontinuity, Quadratic and Cubic
Specifications (Cont.)
Panel B: Quadratic Function of Rank
Dependent variable:
Instrument:
Bandwidth:
ETF ownership (standardized)
log(mktcap (t-1))
1/Price (t-1)
Amihud (t-1)
Bid-ask spread (t-1)
Book-to-Market (t-1)
Past 12-month return (t-1)
Gross profitability (t-1)
Volatility (t-1)
Index fund ownership
Active fund ownership
Hedge fund ownership
Daily volatility (t)
± 100
(1)
0.469
(0.614)
Switch to the Russell 2000
± 200
± 300
± 400
(2)
(3)
(4)
0.510** 0.591*** 0.531***
(2.387)
(3.067)
(3.365)
-0.305
(-1.264)
1.904***
(9.119)
0.978
(0.212)
0.689
(0.223)
0.120***
(3.068)
-0.009
(-0.112)
-0.004
(-0.038)
0.236***
(6.994)
-0.021
(-0.213)
0.037***
(2.739)
0.108
(1.079)
-0.375*** -0.390*** -0.463*** -0.560***
(-4.906)
(-5.613)
(-7.565) (-10.083)
1.698*** 1.427*** 1.410*** 1.510***
(10.374)
(11.275)
(12.154)
(13.519)
3.752*
6.306*** 7.802*** 6.731***
(1.832)
(2.960)
(3.710)
(3.521)
1.786
-0.940
-1.141
-1.374
(0.888)
(-0.603)
(-0.638)
(-0.667)
0.108*** 0.124*** 0.109*** 0.097***
(5.911)
(8.256)
(7.015)
(6.540)
-0.028
-0.013
-0.010
0.013
(-0.878)
(-0.455)
(-0.338)
(0.612)
0.065
0.098*
0.104**
0.074**
(1.242)
(1.900)
(2.237)
(2.080)
0.259*** 0.263*** 0.269*** 0.262***
(15.874)
(15.895)
(17.406)
(18.554)
-0.066*
-0.083** -0.073** -0.054**
(-1.691)
(-2.500)
(-2.509)
(-2.180)
0.051*** 0.062*** 0.073*** 0.076***
(6.917)
(11.992)
(13.077)
(14.311)
0.086*** 0.111*** 0.110*** 0.094***
(3.703)
(5.008)
(5.884)
(5.995)
± 500
(5)
0.424***
(3.177)
± 100
(6)
0.300***
(3.772)
Switch to the Russell 1000
± 200
± 300
± 400
(7)
(8)
(9)
0.324*** 0.413*** 0.458***
(3.880)
(4.451)
(4.582)
± 500
(10)
0.487***
(4.364)
-0.717*** -0.718*** -0.726*** -0.734*** -0.704***
(-10.976) (-10.168) (-10.878) (-11.267) (-11.450)
1.757*** 1.334*** 1.414*** 1.826*** 1.983***
(7.475)
(6.866)
(7.954)
(9.734)
(11.576)
3.851*
7.203*** 10.727*** 9.600*** 7.660***
(1.714)
(4.093)
(6.335)
(6.452)
(6.598)
-9.590*** -9.537** -9.740*** -10.619*** -11.028***
(-3.163)
(-2.583)
(-3.462)
(-3.560)
(-3.658)
-0.001
-0.057** -0.095*** -0.096*** -0.112***
(-0.046)
(-2.323)
(-4.294)
(-5.039)
(-5.522)
0.287*** 0.208*** 0.221*** 0.220*** 0.205***
(9.141)
(4.466)
(5.865)
(6.590)
(7.126)
0.119*** 0.094*** 0.092*** 0.085*** 0.068***
(2.747)
(2.960)
(3.348)
(3.736)
(2.926)
0.268*** 0.270*** 0.282*** 0.283*** 0.281***
(20.101)
(20.114)
(20.566)
(21.016)
(21.098)
-0.030*
-0.047** -0.058*** -0.069*** -0.076***
(-1.792)
(-2.583)
(-3.078)
(-3.309)
(-3.248)
0.067*** 0.084*** 0.080*** 0.072*** 0.067***
(6.654)
(11.497)
(12.829)
(12.626)
(12.208)
0.048*** 0.034*** 0.044*** 0.054*** 0.060***
(4.290)
(3.385)
(4.630)
(5.344)
(5.633)
Month fixed effects
Quadratic polynomials of rank
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Observations
8,116
17,056
27,420
38,971
51,692
10,204
20,563
30,848
41,888
52,974
120
Electronic copy available at: https://ssrn.com/abstract=1967599
Internet Appendix Table AVII. Regression Discontinuity, Quadratic and Cubic
Specifications (Cont.)
Panel C: Cubic Function of Rank
Dependent variable:
Instrument:
Bandwidth:
ETF ownership (standardized)
log(mktcap (t-1))
1/Price (t-1)
Amihud (t-1)
Bid-ask spread (t-1)
Book-to-Market (t-1)
Past 12-month return (t-1)
Gross profitability (t-1)
Volatility (t-1)
Index fund ownership
Active fund ownership
Hedge fund ownership
Daily volatility (t)
± 100
(1)
-5.647
(-0.595)
Switch to the Russell 2000
± 200
± 300
± 400
(2)
(3)
(4)
0.574
0.608** 0.611***
(1.428)
(2.566)
(3.094)
-2.253
(-0.745)
1.529*
(1.733)
-34.431
(-0.617)
-17.004
(-0.592)
-0.156
(-0.375)
0.522
(0.636)
-0.783
(-0.636)
-0.006
(-0.015)
0.737
(0.624)
-0.028
(-0.270)
-0.708
(-0.566)
-0.353*** -0.383*** -0.439*** -0.541***
(-2.630)
(-4.750)
(-6.273)
(-7.807)
1.715*** 1.430*** 1.419*** 1.518***
(8.933)
(11.171)
(11.858)
(13.076)
4.173
6.452*** 8.531*** 7.458***
(1.389)
(2.666)
(3.527)
(3.158)
1.832
-0.870
-0.973
-0.998
(0.866)
(-0.553)
(-0.530)
(-0.448)
0.112*** 0.125*** 0.113*** 0.100***
(4.445)
(7.780)
(6.810)
(6.378)
-0.031
-0.015
-0.015
0.011
(-0.811)
(-0.491)
(-0.507)
(0.518)
0.078
0.102*
0.127**
0.093*
(0.912)
(1.687)
(2.258)
(1.853)
0.262*** 0.264*** 0.273*** 0.265***
(10.054)
(14.119)
(15.812)
(15.683)
-0.077
-0.086** -0.087**
-0.068*
(-1.071)
(-2.100)
(-2.432)
(-1.921)
0.052*** 0.062*** 0.074*** 0.077***
(6.404)
(11.894)
(12.744)
(13.743)
0.093** 0.113*** 0.120*** 0.103***
(2.223)
(4.117)
(5.116)
(4.628)
± 500
(5)
0.500**
(2.602)
± 100
(6)
0.282***
(3.038)
Switch to the Russell 1000
± 200
± 300
± 400
(7)
(8)
(9)
0.275*** 0.304*** 0.380***
(3.014)
(3.581)
(4.022)
± 500
(10)
0.404***
(4.303)
-0.724*** -0.727*** -0.744*** -0.749*** -0.720***
(-10.933) (-10.133) (-11.122) (-11.170) (-11.110)
1.737*** 1.324*** 1.373*** 1.763*** 1.911***
(7.401)
(6.926)
(8.196)
(9.721)
(11.486)
3.567
6.677*** 9.476*** 8.844*** 7.073***
(1.516)
(3.653)
(5.888)
(5.999)
(6.661)
-9.498*** -9.550** -9.660*** -10.499*** -10.904***
(-3.287)
(-2.601)
(-3.502)
(-3.612)
(-3.710)
-0.002
-0.055** -0.088*** -0.091*** -0.105***
(-0.078)
(-2.334)
(-4.118)
(-5.021)
(-5.854)
0.289*** 0.208*** 0.219*** 0.220*** 0.206***
(9.159)
(4.451)
(5.869)
(6.604)
(7.162)
0.115*** 0.086*** 0.079*** 0.077*** 0.060***
(2.756)
(2.819)
(2.953)
(3.456)
(2.686)
0.266*** 0.266*** 0.272*** 0.276*** 0.275***
(18.285)
(19.839)
(20.965)
(21.209)
(22.130)
-0.026
-0.037*
-0.035** -0.052** -0.058***
(-1.309)
(-1.762)
(-2.022)
(-2.540)
(-2.785)
0.067*** 0.085*** 0.080*** 0.072*** 0.067***
(6.766)
(11.686)
(13.118)
(12.790)
(12.349)
0.047*** 0.030*** 0.036*** 0.048*** 0.054***
(3.798)
(2.924)
(4.129)
(5.007)
(5.748)
Month fixed effects
Cubic polynomials of rank
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Observations
8,116
17,056
27,420
38,971
51,692
10,204
20,563
30,848
41,888
52,974
121
Electronic copy available at: https://ssrn.com/abstract=1967599
Internet Appendix Table AVIII. Russell Switching Instrument, Sample Splits
The table reports estimates from a quasi-natural experiment relying on the reconstitution of the Russell 1000 and Russell
2000 indexes. The frequency of the data is monthly at the stock level. The table presents the second stage of the analysis.
The variable of interest is ETF ownership instrumented by a dummy for inclusion in the Russell 2000, for stocks in the
Russell 1000 before index reconstitution (columns (1)–(5)), and a dummy for inclusion in the Russell 1000, for stocks
in the Russell 2000 before index reconstitution (columns (6)–(10)). The dependent variable and the ownership variables
have been standardized by subtracting the mean and dividing by the standard deviation. Stocks are ranked in terms of
market capitalization in May of each year. Different ranges of this rank around the cutoff are used for inclusion in the
sample: 100 stocks on each side (columns (1) and (6)), 200 stocks on each side (columns (2) and (7)), 300 stocks on
each side (columns (3) and (8)), 400 stocks on each side (columns (4) and (9)), and 500 stocks on each side (columns
(5) and (10)). The same stocks enter the sample in the June after index reconstitution and remain in the sample until
May of the next year, except if delistings occur. The controls in all panels are logged market capitalization, the lagged
inverse share price, the lagged Amihud (2002) ratio, the lagged average bid-ask spread, the lagged book-to-market
ratio, lagged past 12 month returns, lagged gross profitability (as in Novy-Marx (2013)), lagged volatility, index-fund
ownership, active-fund ownership, and hedge-fund ownership. Month fixed effects are included. Panel A uses years
2000 to 2006. Panel B uses years 2007 to 2015. Standard errors are double clustered at the stock and month level. tstatistics are presented in parentheses. ***, **, and * represent statistical significance at the 1%, 5%, and 10% levels,
respectively. The whole sample ranges between July 2000 and April 2015.
Panel A: Sample Period: 2000–2006
Dependent variable:
Instrument:
Bandwidth:
ETF ownership (standardized)
log(mktcap (t-1))
1/Price (t-1)
Amihud (t-1)
Bid-ask spread (t-1)
Book-to-Market (t-1)
Past 12-month return (t-1)
Gross profitability (t-1)
Volatility (t-1)
Hedge fund ownership
Index fund ownership
Active fund ownership
Daily volatility (t)
± 100
(1)
0.512**
(2.224)
Switch to the Russell 2000
± 200
± 300
± 400
(2)
(3)
(4)
0.384*** 0.268*** 0.176**
(2.649)
(3.269)
(2.631)
± 500
(5)
0.249***
(3.656)
± 100
(6)
0.717**
(2.409)
Switch to the Russell 1000
± 200
± 300
± 400
± 500
(7)
(8)
(9)
(10)
0.249*** 0.198*** 0.222*** 0.169***
(3.572)
(3.252)
(3.486)
(3.394)
-0.346*** -0.404*** -0.478*** -0.512*** -0.533*** -0.606*** -0.731*** -0.766*** -0.761*** -0.728***
(-3.995) (-5.576) (-7.079) (-7.366) (-7.322)
(-7.121) (-9.075) (-9.783) (-9.504) (-9.266)
2.758*** 1.815*** 1.550*** 1.326*** 1.461*** 1.759*** 1.395*** 1.322*** 1.411*** 1.435***
(5.928)
(6.649)
(8.570)
(8.651)
(9.395)
(6.464)
(6.511)
(8.198)
(8.382)
(9.383)
1.241
5.238** 4.392*** 5.737*** 6.139*** 13.736** 6.568*** 7.135*** 7.249*** 6.084***
(0.493)
(2.413)
(2.876)
(3.501)
(3.845)
(2.251)
(3.293)
(5.038)
(6.163)
(7.869)
-0.484
0.696
-2.117
-2.833
-3.004 -12.445*** -9.365*** -8.741*** -9.558*** -10.449***
(-0.163)
(0.319)
(-1.293) (-1.654) (-1.571)
(-3.084) (-2.662) (-3.349) (-3.411) (-3.641)
0.063** 0.082*** 0.095*** 0.088*** 0.109*** -0.291*** -0.248*** -0.245*** -0.235*** -0.184***
(2.113)
(3.117)
(4.458)
(4.376)
(5.189)
(-3.162) (-4.827) (-5.323) (-5.208) (-4.293)
-0.014
-0.029
0.027
0.008
0.038
0.309*** 0.156*** 0.152*** 0.153*** 0.140***
(-0.227) (-0.735)
(0.749)
(0.214)
(1.101)
(5.908)
(3.318)
(4.150)
(4.738)
(5.024)
0.004
0.049
0.064**
0.035
0.069***
0.173** 0.109*** 0.080*** 0.072***
0.033
(0.051)
(1.084)
(2.167)
(1.265)
(2.852)
(2.421)
(3.443)
(3.176)
(3.339)
(1.500)
0.229*** 0.263*** 0.260*** 0.267*** 0.270*** 0.376*** 0.290*** 0.287*** 0.297*** 0.294***
(14.041) (19.465) (20.091) (18.905) (17.987)
(9.317) (17.415) (18.014) (18.037) (19.731)
0.088*** 0.076*** 0.054*** 0.048*** 0.050***
0.075**
0.013
0.011
0.011
0.011
(2.778)
(4.236)
(5.291)
(5.997)
(6.117)
(2.308)
(1.061)
(1.228)
(1.332)
(1.487)
-0.002
-0.022
-0.013
0.001
-0.020
-0.059
-0.003
0.005
0.001
0.010
(-0.074) (-0.795) (-0.807)
(0.073)
(-1.354)
(-1.461) (-0.238)
(0.444)
(0.043)
(0.974)
0.105*** 0.083*** 0.082*** 0.088*** 0.092***
0.024
0.093*** 0.098*** 0.092*** 0.088***
(3.878)
(5.868)
(9.452)
(9.880) (11.305)
(0.957) (10.297) (12.991) (12.698) (12.378)
Month fixed effects
Linear polynomials of rank
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Observations
4,857
10,103
16,101
22,303
28,599
6,495
12,735
18,293
23,647
29,060
122
Electronic copy available at: https://ssrn.com/abstract=1967599
Internet Appendix Table AVIII. Russell Switching Instrument, Sample Splits (Cont.)
Panel B: Sample Period: 2007–2015
Dependent variable:
Instrument:
Bandwidth:
Daily volatility (t)
± 100
(1)
ETF ownership (standardized) -0.454
(-1.119)
log(mktcap (t-1))
Switch to the Russell 2000
± 200
± 300
± 400
(2)
(3)
(4)
0.347
0.249** 0.209**
(1.073)
(2.171)
(2.378)
± 500
(5)
0.185**
(2.510)
± 100
(6)
0.184**
(2.435)
Switch to the Russell 1000
± 200
± 300
± 400
(7)
(8)
(9)
0.103*
0.061
0.038
(1.750)
(1.143)
(0.761)
± 500
(10)
-0.064
(-1.238)
-0.785***
(-3.078)
1.697***
(3.638)
-13.936
(-1.255)
-15.864
(-0.707)
0.053
(1.006)
0.120*
(1.983)
-0.203
(-1.604)
0.227***
(7.903)
-0.031
(-0.434)
0.112
(1.272)
0.005
(0.296)
-0.455**
(-2.570)
1.142***
(4.561)
0.010
(0.002)
43.692*
(1.661)
0.106***
(2.867)
0.020
(0.511)
0.087
(0.571)
0.249***
(9.242)
0.062*
(1.711)
-0.092
(-1.038)
0.018
(1.534)
Month fixed effects
Linear polynomials of rank
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Observations
3,259
6,953
11,319
16,668
23,093
3,709
7,828
12,555
18,241
23,914
1/Price (t-1)
Amihud (t-1)
Bid-ask spread (t-1)
Book-to-Market (t-1)
Past 12-month return (t-1)
Gross profitability (t-1)
Volatility (t-1)
Hedge fund ownership
Index fund ownership
Active fund ownership
-0.527*** -0.635*** -0.707*** -0.758*** -0.852*** -0.852*** -0.882*** -0.887***
(-7.093) (-8.964) (-10.581) (-6.005) (-6.635) (-7.368) (-8.023) (-8.371)
0.817*** 0.936*** 1.105*** 1.980*** 1.448*** 1.456*** 1.755*** 1.570***
(4.785)
(6.348)
(8.168)
(3.319)
(4.799)
(5.036)
(7.411)
(6.784)
5.260
4.033
2.735
24.798*** 7.993** 11.753*** 10.296*** 4.583*
(1.586)
(1.322)
(0.931)
(2.721)
(2.373)
(3.149)
(3.053)
(1.754)
51.758*** 57.599*** 52.860*** 39.211** 17.908* 21.637** 26.479*** 22.907**
(4.148)
(6.660)
(7.106)
(2.275)
(1.707)
(2.316)
(2.758)
(2.349)
0.100*** 0.084*** 0.070***
-0.008
-0.028 -0.043*** -0.051*** -0.053***
(5.413)
(4.961)
(3.703)
(-0.441) (-1.568) (-2.923) (-4.167) (-4.297)
-0.008
0.020
0.017
0.305*** 0.332*** 0.318*** 0.310*** 0.302***
(-0.237)
(0.621)
(0.802)
(6.746)
(7.729)
(8.503)
(7.492)
(8.191)
0.011
0.030
0.007
-0.026
-0.043
-0.044
-0.024
-0.032
(0.169)
(0.498)
(0.137)
(-0.411) (-0.829) (-0.947) (-0.658) (-0.869)
0.230*** 0.236*** 0.227*** 0.188*** 0.196*** 0.195*** 0.191*** 0.181***
(13.275) (16.505) (17.044)
(13.340) (15.538) (16.235) (18.480) (20.562)
0.083*** 0.084*** 0.083*** 0.064*** 0.035*** 0.025*** 0.031*** 0.028***
(5.099)
(6.064)
(6.881)
(4.288)
(3.513)
(2.862)
(3.280)
(3.101)
-0.057*
-0.041*
-0.027
-0.063**
-0.037
-0.012
0.004
0.041**
(-1.937) (-1.753) (-1.394)
(-2.108) (-1.533) (-0.594)
(0.195)
(2.114)
0.044*** 0.053*** 0.057*** 0.054*** 0.051*** 0.045*** 0.033*** 0.028***
(6.051)
(8.863)
(9.706)
(5.199)
(6.739)
(7.204)
(5.698)
(5.188)
123
Electronic copy available at: https://ssrn.com/abstract=1967599
Internet Appendix Table AIX. Magnitude Estimation
The table presents assessments of the economic magnitude of the effects of ETFs on stock volatility. Panel A reports
the median volatility, which is the starting point before applying the variation in ETF ownership, the estimated standard
deviation of ETF ownership for the median stock, the new level of volatility after applying the variation, and the new
percentile in the volatility distribution that is achieved after applying the change in ETF ownership. Panel B computes
the economic magnitudes by assessing the shift in volatility for the median stock using estimates from instrumental
variable (IV) regressions. In this panel, first we consider the effect of a one-standard-deviation change in ETF
ownership. Then we consider the effect of the change in ETF ownership that is induced by the Russell index switch.
The organization of the table mirrors the outline of Table V in terms of the bandwidth of the experiment and the
direction of the index switch. Panel C reports estimates from a regression of daily stock volatility (estimated within the
month) on previous month stock returns and controls. The controls are the lag of logged market capitalization, the
lagged inverse share price, the lagged Amihud (2002) ratio, the lagged average bid-ask spread, the lagged book-tomarket ratio, lagged past 12 month returns, lagged gross profitability (as in Novy-Marx (2013)), lagged volatility,
index-fund ownership, and active-fund ownership. Stock and month fixed effects are included. Standard errors are
double clustered at the stock and time level. t-statistics are presented in parentheses. ***, **, and * represent statistical
significance at the 1%, 5%, and 10% levels, respectively. The sample ranges between January 2000 and December
2015.
Panel A: Summary Statistics
Sample:
Lags of dep. variable in regression:
Median volatility
S&P 500
No lags Three lags
0.021
0.021
Russell 3000
No lags Three lags
0.027
0.027
Std. dev. of ETF ownership
New level of volatility
New quantile of volatility
0.018
0.023
64
0.018
0.022
58
0.023
0.028
57
0.023
0.028
55
Std. dev. of prior month return
New level of volatility
New quantile of volatility
0.085
0.022
57
0.085
0.022
57
0.114
0.027
54
0.114
0.028
54
124
Electronic copy available at: https://ssrn.com/abstract=1967599
Internet Appendix Table AIX. Magnitude Estimation (Cont.)
Panel B: Estimation of Effect Magnitude, per Window Size
Switch to the Russell 2000
± 200 ± 300 ± 400 ± 500
± 100
Switch to the Russell 1000
± 200 ± 300 ± 400 ± 500
Bandwidth:
± 100
Median volatility
0.026
0.024
0.025
Linear Function of Rank
0.025 0.024
0.031 0.028
0.027
0.027
0.027
Std.dev. of ETF ownership
New level of volatility
New quantile of volatility
0.023
0.035
80
0.023
0.031
80
0.022
0.031
75
0.022
0.029
70
0.022
0.029
75
0.020
0.038
75
0.021
0.033
70
0.022
0.031
70
0.023
0.031
70
0.024
0.030
65
Abs(ETF ownership due to switch (%)) 0.304
New level of volatility
0.027
New quantile of volatility
65
0.460
0.025
60
0.576
0.027
60
0.663
0.026
60
0.649
0.026
60
0.490
0.033
60
0.592
0.029
60
0.565
0.028
60
0.522
0.028
60
0.553
0.028
55
Median volatility
0.026
0.024
0.025
Quadratic Function of Rank
0.025 0.024
0.031 0.028
0.027
0.027
0.027
Std.dev. of ETF ownership
New level of volatility
New quantile of volatility
0.023
0.041
85
0.023
0.032
80
0.022
0.035
80
0.022
0.033
80
0.022
0.031
75
0.020
0.036
75
0.021
0.033
70
0.022
0.033
80
0.023
0.034
80
0.024
0.034
80
Abs(ETF ownership due to switch (%)) 0.059
New level of volatility
0.027
New quantile of volatility
60
0.369
0.025
60
0.374
0.027
60
0.448
0.027
65
0.485
0.026
60
0.641
0.033
60
0.598
0.030
60
0.578
0.029
60
0.531
0.028
60
0.496
0.029
60
Median volatility
0.026
0.024
0.025
Cubic Function of Rank
0.025 0.024
0.031 0.028
0.027
0.027
0.027
Std.dev. of ETF ownership
New level of volatility
New quantile of volatility
0.023
.
.
0.023
0.035
85
0.022
0.035
80
0.022
0.035
85
0.022
0.032
80
0.020
0.036
75
0.021
0.032
70
0.022
0.032
75
0.023
0.032
75
0.024
0.033
75
Abs(ETF ownership due to switch (%)) 0.066 0.186 0.309 0.355
New level of volatility
.
0.025 0.026 0.026
New quantile of volatility
.
55
60
65
Note: missing values in quintiles correspond to insignificant IV estimates
0.377
0.026
60
0.594
0.033
60
0.598
0.029
60
0.623
0.028
60
0.593
0.028
60
0.599
0.029
60
125
Electronic copy available at: https://ssrn.com/abstract=1967599
Internet Appendix Table AIX. Magnitude Estimation (Cont.)
Panel C: Comparing Magnitude or Volatility-Return Regressions
Dependent variable:
Return (t-1)
Daily stock volatility
S&P 500
Russell 3000
(1)
(2)
(3)
(4)
-0.012*** -0.012*** -0.006*** -0.008***
(-4.731) (-8.432)
(-3.843) (-7.045)
Volatility (t-1)
0.288***
(17.693)
Volatility (t-2)
0.183***
(10.118)
Volatility (t-3)
0.210***
(16.009)
log(Mktcap (t-1))
0.001
0.000
(0.993) (0.382)
1/Price (t-1)
0.055*** 0.017***
(4.472) (3.622)
Amihud (t-1)
0.682** 0.451***
(2.508) (2.897)
Bid-ask spread (t-1)
-0.037
-0.020
(-0.680) (-0.726)
Book-to-Market (t-1)
0.002*** -0.000
(3.066) (-0.290)
Past 12-month Return (t-1) -0.002** -0.000
(-2.481) (-1.332)
Gross Profitability (t-1)
0.000
-0.001
(0.108) (-1.360)
Index Fund Ownership
0.026 0.023***
(1.084) (2.660)
Active Fund Ownership
0.007*** 0.004***
(2.866) (3.549)
0.215***
(21.338)
0.157***
(23.013)
0.179***
(28.830)
-0.002*** -0.001***
(-4.990) (-5.255)
0.029*** 0.013***
(9.624) (7.437)
0.033*** 0.019***
(7.302) (6.383)
0.046* 0.043***
(1.934) (4.502)
0.003*** 0.001***
(7.901) (4.024)
0.000
0.000
(1.031) (0.311)
-0.003*** -0.002***
(-3.700) (-3.591)
-0.033*** -0.006
(-4.969) (-1.556)
0.008*** 0.005***
(7.340) (7.794)
Observations
2
R
84,261
78,428
446,608
404,861
0.638
0.743
0.604
0.670
126
Electronic copy available at: https://ssrn.com/abstract=1967599
Internet Appendix Table AX. Turnover Analysis
The table presents analysis of the turnover in ETFs and stocks using Ancerno data. Turnover is computed as dollar
volume over market capitalization. Panel A presents summary statistics. Panel B shows regressions of turnover on an
indicator for whether a security is an ETF. Panel C reports estimates from regressions of price impact on trade volume.
Price impact is calculated as the percentage difference between the execution price and the price at the time of
placement. Trade volume is the number of shares that are traded divided by the number of shares outstanding. The
analysis is at the stock-day level in Panels A and B, and at the trade level in Panel C. Standard errors are double clustered
at the security and day level. t-statistics are presented in parentheses. ***, **, and * represent statistical significance at
the 1%, 5%, and 10% levels, respectively. The sample ranges between 2000 and 2014.
Panel A: Summary Statistics
N
58,778
1,198,411
3,647,470
ETFs
S&P 500 Stocks
Russell 3000 Stocks
Turnover (%)
St. Dev.
Min
1.740
0.000
0.127
0.001
0.167
0.001
Mean
0.427
0.095
0.127
Median
0.050
0.050
0.065
Max
25.200
1.170
1.170
Panel B: Turnover Regressions
Dependent variable:
Sample:
Security is ETF
Turnover (%)
S&P 500
Russell 3000
(1)
(2)
(3)
(4)
0.332*** 0.337*** 0.300*** 0.314***
(3.678)
(3.863)
(3.321)
(3.521)
Date FE
No
Observations
Adjusted R
Yes
No
1,257,189 1,257,189
2
0.030
Yes
3,706,248 3,706,248
0.034
0.018
0.032
Panel C: Price-Impact Regressions
Dependent variable:
Sample:
Trade Volume
Price Impact of Trade
ETFs
S&P 500 Russell 3000
(1)
(2)
(3)
0.203***
1.544***
1.273***
(8.560)
(48.252)
(57.229)
Date FE
Security FE
Yes
Yes
Yes
Yes
Yes
Yes
Observations
843,158
18,867,594
44,374,985
2
0.018
0.008
0.010
Adjusted R
127
Electronic copy available at: https://ssrn.com/abstract=1967599
Internet Appendix Table AXI. Predictability of Order Imbalance
The table reports estimates from regressions of different leads of order imbalance on ETF flows, at the stock-day level.
Panel A uses S&P 500 stocks. Panel B uses Russell 3000 stocks. Order imbalance is defined as the difference between
shares bought and sold, over the sum of the two, for a given stock-day. The controls in all panels are the lag of logged
market capitalization, the lagged inverse share price, the lagged Amihud (2002) ratio, the lagged average bid-ask
spread, the lagged book-to-market ratio, lagged past 12 month returns, and lagged gross profitability (as in Novy-Marx
(2013)). Day fixed effects are included. Panel C reports different lags of the autocorrelation of ETF flows across
different ETF styles at the daily frequency. Standard errors are double clustered at the stock and day level. t-statistics
are presented in parentheses. ***, **, and * represent statistical significance at the 1%, 5%, and 10% levels,
respectively. The sample ranges between January 2000 and December 2015.
Panel A: Predictability of Order Imbalance (S&P 500)
Dependent variable:
Day:
ETF flows (t)
log(mktcap (t-1))
1/Price (t-1)
Amihud (t-1)
Bid-ask spread (t-1)
Book-to-Market (t-1)
Past 12-month return (t-1)
Gross profitability (t-1)
Observations
2
R
t
(1)
0.006***
(12.637)
t+1
(2)
0.002***
(4.719)
t+2
(3)
0.001**
(2.088)
t+3
(4)
0.001***
(2.712)
Stock-level order imbalance
t+4
t+5
t+6
(5)
(6)
(7)
0.001**
0.000
0.001**
(2.150)
(0.365)
(1.969)
t+7
(8)
0.001**
(2.048)
-0.003***
(-2.993)
-0.023
(-1.053)
-5.781*
(-1.760)
0.398**
(2.144)
0.005**
(2.470)
0.004**
(2.339)
-0.004
(-0.998)
-0.003***
(-3.512)
-0.011
(-0.528)
-7.516**
(-2.270)
0.465**
(2.581)
0.005**
(2.296)
0.004**
(2.325)
-0.004
(-1.098)
-0.004***
(-3.597)
-0.008
(-0.381)
-7.974**
(-2.325)
0.559***
(2.801)
0.005**
(2.206)
0.004**
(2.322)
-0.005
(-1.112)
-0.004***
(-3.710)
-0.008
(-0.376)
-8.232**
(-2.412)
0.559***
(2.892)
0.005**
(2.220)
0.004**
(2.346)
-0.004
(-1.059)
-0.004***
(-3.735)
-0.007
(-0.336)
-8.390**
(-2.469)
0.633***
(3.335)
0.005**
(2.190)
0.004**
(2.316)
-0.004
(-1.048)
-0.004***
(-3.749)
-0.009
(-0.419)
-8.413**
(-2.495)
0.617***
(3.382)
0.005**
(2.225)
0.004**
(2.206)
-0.004
(-1.054)
-0.004***
(-3.692)
-0.007
(-0.335)
-8.234**
(-2.430)
0.620***
(3.223)
0.005**
(2.204)
0.004**
(2.242)
-0.004
(-1.075)
-0.004*** -0.004***
(-3.674)
(-3.639)
-0.007
-0.005
(-0.328)
(-0.237)
-8.118**
-7.878**
(-2.397)
(-2.359)
0.576***
0.470**
(3.028)
(2.541)
0.005**
0.005**
(2.191)
(2.163)
0.004**
0.004**
(2.219)
(2.240)
-0.004
-0.004
(-1.068)
(-1.067)
-0.004*** -0.004***
(-3.610)
(-3.691)
-0.008
-0.007
(-0.340)
(-0.293)
-7.635** -7.955**
(-2.284)
(-2.279)
0.585***
0.361**
(3.070)
(1.968)
0.005**
0.005**
(2.208)
(2.192)
0.004**
0.004**
(2.268)
(2.220)
-0.004
-0.004
(-1.076)
(-1.085)
1,171,675
1,171,597
1,166,409
1,164,448
1,163,007
1,161,873
1,160,493
1,159,176
1,158,006
1,156,991
1,156,097
0.131
0.130
0.130
0.130
0.130
0.130
0.130
0.130
0.130
0.129
0.130
t+8
(9)
0.000
(0.589)
t+9
(10)
0.000
(0.800)
t+10
(11)
0.000
(0.197)
t+8
(9)
0.000
(0.519)
t+9
(10)
0.000
(1.109)
t+10
(11)
0.000
(1.521)
Panel B: Predictability of Order Imbalance (Russel 3000)
Stock-level order imbalance
Dependent variable:
Stock-level order imbalance
is measured on day:
ETF flows (t)
log(mktcap (t-1))
1/Price (t-1)
Amihud (t-1)
Bid-ask spread (t-1)
Book-to-Market (t-1)
Past 12-month return (t-1)
Gross profitability (t-1)
Observations
2
R
t
(1)
0.004***
(8.601)
t+1
(2)
0.007***
(14.377)
t+2
(3)
0.001*
(1.870)
t+3
(4)
0.000
(0.048)
t+4
(5)
0.000
(0.649)
t+5
(6)
-0.000
(-0.504)
t+6
(7)
-0.000
(-0.214)
t+7
(8)
0.000
(0.795)
0.007***
(17.587)
-0.037***
(-6.851)
-0.052***
(-4.392)
-0.867***
(-7.374)
0.008***
(8.451)
0.007***
(10.795)
0.007***
(4.274)
0.007***
(17.755)
-0.023***
(-4.320)
-0.061***
(-5.225)
-0.906***
(-7.749)
0.008***
(8.033)
0.007***
(10.927)
0.007***
(4.325)
0.007***
(17.264)
-0.021***
(-3.931)
-0.062***
(-4.934)
-0.954***
(-8.037)
0.008***
(8.045)
0.007***
(11.064)
0.007***
(4.362)
0.007***
(17.079)
-0.021***
(-3.827)
-0.062***
(-4.966)
-0.938***
(-7.397)
0.008***
(7.960)
0.007***
(10.915)
0.007***
(4.203)
0.007***
(17.118)
-0.021***
(-3.783)
-0.062***
(-5.022)
-0.916***
(-7.246)
0.008***
(7.927)
0.007***
(10.932)
0.007***
(4.300)
0.007***
(16.999)
-0.020***
(-3.663)
-0.071***
(-5.687)
-0.936***
(-7.513)
0.008***
(7.990)
0.007***
(10.866)
0.007***
(4.339)
0.007***
(17.015)
-0.020***
(-3.731)
-0.066***
(-5.013)
-0.774***
(-6.185)
0.008***
(8.010)
0.007***
(10.752)
0.007***
(4.231)
0.007*** 0.007***
(16.862)
(16.773)
-0.019*** -0.020***
(-3.541)
(-3.673)
-0.079*** -0.074***
(-5.605)
(-5.304)
-0.763*** -0.873***
(-6.069)
(-6.868)
0.008*** 0.008***
(7.852)
(8.037)
0.007*** 0.007***
(10.572)
(10.630)
0.007*** 0.007***
(4.357)
(4.360)
0.007*** 0.007***
(16.787)
(16.928)
-0.020*** -0.019***
(-3.634)
(-3.362)
-0.069*** -0.070***
(-4.989)
(-5.188)
-0.864*** -0.919***
(-7.059)
(-7.177)
0.008*** 0.007***
(7.876)
(7.814)
0.007*** 0.007***
(10.484)
(10.326)
0.007*** 0.007***
(4.222)
(4.220)
6,342,140
6,341,040
6,271,888
6,246,749
6,228,970
6,214,873
6,197,962
6,181,891
6,168,824
6,158,129
6,148,945
0.059
0.058
0.059
0.059
0.058
0.059
0.058
0.059
0.059
0.058
0.059
128
Electronic copy available at: https://ssrn.com/abstract=1967599
Internet Appendix Table AXI. Predictability of Order Imbalance (Cont.)
Panel C: Autocorrelation in ETF Flows
N=
Lag 1
Lag 2
Lag 3
Lag 4
Lag 5
Lag 6
Lag 7
Lag 8
Lag 9
Lag 10
Lag 11
Lag 12
Lag 13
Lag 14
Lag 15
Lag 16
Lag 17
Lag 18
Lag 19
Lag 20
All Funds US Large Cap US Small Cap US Sector
4000
56
65
492
0.090***
0.042***
0.043***
0.087***
0.075***
0.016
0.042***
0.066***
0.061***
0.030***
0.017
0.048***
0.056***
0.022**
0.018
0.037***
0.053***
0.034***
0.008
0.036***
0.047***
0.022**
0.002
0.032***
0.042***
0.029***
0.017
0.030***
0.043***
0.022***
0.004
0.033***
0.044***
0.030***
0.028***
0.034***
0.043***
0.025***
0.009
0.031***
0.039***
0.018***
0.019***
0.029***
0.036***
0.018***
0.023***
0.028***
0.036***
0.024***
0.021***
0.029***
0.033***
0.026***
0.026***
0.021***
0.033***
0.018*
0.023***
0.024***
0.033***
0.024***
0.014
0.026***
0.029***
0.019**
0.010**
0.022***
0.029***
0.024***
0.008
0.021***
0.032***
0.021**
0.025***
0.023***
0.029***
0.030***
0.006
0.022***
US Style-based Foreign Equity
535
626
0.091***
0.104***
0.076***
0.096***
0.060***
0.088***
0.063***
0.078***
0.056***
0.078***
0.042***
0.071***
0.037***
0.061***
0.038***
0.066***
0.036***
0.062***
0.040***
0.059***
0.034***
0.057***
0.026***
0.054***
0.029***
0.046***
0.031***
0.046***
0.032***
0.045***
0.028***
0.047***
0.021***
0.045***
0.026***
0.039***
0.032***
0.038***
0.032***
0.037***
Mixed
Fixed Income
189
311
0.086***
0.087***
0.073***
0.073***
0.061***
0.062***
0.059***
0.066***
0.051***
0.064***
0.054***
0.060***
0.034***
0.053***
0.044***
0.049***
0.052***
0.053***
0.044***
0.050***
0.044***
0.045***
0.033***
0.047***
0.036***
0.044***
0.025***
0.041***
0.032***
0.036***
0.023***
0.041***
0.033***
0.041***
0.026***
0.036***
0.031***
0.038***
0.015*
0.032***
129
Electronic copy available at: https://ssrn.com/abstract=1967599
Other
1726
0.084***
0.077***
0.063***
0.053***
0.038***
0.039***
0.036***
0.037***
0.035***
0.042***
0.035***
0.031***
0.029***
0.020***
0.025***
0.020**
0.013
0.018*
0.023***
0.023***
Internet Appendix Table AXII. Intraday Volatility and Range, and ETF Flows
The table reports estimates from regressions of intraday volatility, or price range, on the absolute value of net stocklevel flows and the sum of absolute stock-level flows. Flows are standardized by stock-level market capitalization. The
controls in all panels are the lag of logged market capitalization, the lagged inverse share price, the lagged Amihud
(2002) ratio, the lagged average bid-ask spread, the lagged book-to-market ratio, lagged past 12 month returns, and
lagged gross profitability (as in Novy-Marx (2013)). Date and stock fixed effects are included. Standard errors are
double clustered at the stock and time level. t-statistics are presented in parentheses. ***, **, and * represent statistical
significance at the 1%, 5%, and 10% levels, respectively. The sample ranges between January 2000 and December
2015.
Dependent variable:
Sample:
Intraday volatility (standartized)
S&P 500
Russell 3000
(1)
(2)
(3)
(4)
abs(Net Flows)/Mkt Cap 0.048*** 0.007
0.000 -0.005**
(8.751) (1.400)
(0.057) (-2.487)
Sum abs(Flows)/Mkt Cap
0.065***
0.007**
(5.910)
(2.363)
log(Mktcap (t-1))
0.151*** 0.152***
(3.809) (3.841)
1/Price (t-1)
5.515*** 5.514***
(5.657) (5.660)
Amihud (t-1)
4.265
5.150
(0.304) (0.367)
Bid-ask spread (t-1)
-5.441*** -5.477***
(-2.730) (-2.750)
Book-to-Market (t-1)
0.092** 0.091**
(2.532) (2.528)
Past 12-month Return (t-1) -0.164*** -0.164***
(-8.233) (-8.246)
Gross Profitability (t-1)
-0.128
-0.127
(-0.781) (-0.780)
Intraday range (standartized)
S&P 500
Russell 3000
(5)
(6)
(7)
(8)
0.036*** -0.004
0.006*** -0.004***
(11.779) (-0.975)
(5.573) (-2.918)
0.062***
0.015***
(8.384)
(6.589)
-0.025** -0.025**
0.006
0.007
-0.061*** -0.061***
(-2.118) (-2.123)
(0.352) (0.408)
(-8.512) (-8.533)
1.925*** 1.926*** 1.970*** 1.969*** 0.955*** 0.956***
(18.842) (18.838)
(5.206) (5.217)
(14.099) (14.108)
0.124*** 0.124*** 29.898*** 30.731*** 0.314*** 0.314***
(3.166) (3.167)
(4.292) (4.407)
(8.022) (8.023)
7.776*** 7.777***
0.503
0.467
7.348*** 7.348***
(14.666) (14.665)
(0.541) (0.502)
(21.766) (21.759)
0.090*** 0.090***
0.034
0.034
0.059*** 0.058***
(6.940) (6.930)
(1.580) (1.566)
(7.213) (7.179)
-0.041*** -0.041*** -0.070*** -0.070*** -0.009** -0.009**
(-6.525) (-6.517)
(-7.033) (-7.063)
(-2.140) (-2.111)
-0.169*** -0.169***
-0.070
-0.069
-0.114*** -0.114***
(-4.624) (-4.623)
(-1.152) (-1.153)
(-5.396) (-5.390)
Stock FE
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Calendar day FE
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Observations
2
R
1,542,880 1,542,880
0.589
0.589
8,546,816 8,546,816
0.530
0.530
1,549,715 1,549,715
0.507
0.509
130
Electronic copy available at: https://ssrn.com/abstract=1967599
8,575,670 8,575,670
0.434
0.434
Table AXIII. Evidence of Arbitrage Activity
The table reports estimates from regressions of turnover and order imbalance on measures of mispricing at the end of
the prior day, at the day-stock level. Turnover is defined as shares traded over shares outstanding. Order imbalance is
defined as the difference between shares bought and sold, over the sum of the two, for a given stock-day. The analysis
is at the stock-day level. The controls in all panels include the lagged dependent variable, the lag of logged market
capitalization, the lagged inverse share price, the lagged Amihud (2002) ratio, the lagged average bid-ask spread, the
lagged book-to-market ratio, lagged past 12 month returns, and lagged gross profitability (as in Novy-Marx (2013)).
Stock and day fixed effects are included. Standard errors are double clustered at the stock and day level. t-statistics are
presented in parentheses. ***, **, and * represent statistical significance at the 1%, 5%, and 10% levels, respectively.
The sample ranges between January 2000 and December 2015.
Dependent variable:
Sample:
High absolute mispricing
Turnover (%) (t-1)
Turnover (%)
S&P 500
(1)
0.026***
(5.243)
0.733***
(95.255)
(2)
0.021***
(7.282)
0.577***
(112.957)
Russell 3000
(3)
(4)
0.033*** 0.017***
(12.803) (9.095)
0.725*** 0.583***
(201.923) (196.332)
Negative mispricing
Positive mispricing
Order Imbalance (t-1)
log(mktcap (t-1))
-0.060*** -0.155***
(-11.107)
(-13.786)
1/Price (t-1)
0.841***
0.519**
(6.272)
(2.101)
Amihud (t-1)
-124.811*** -132.838***
(-8.167)
(-8.456)
Bid-ask spread (t-1)
0.507
0.452
(0.735)
(0.909)
Book-to-Market (t-1)
0.035***
0.035**
(3.745)
(2.472)
Past 12-month return (t-1) 0.030***
0.019***
(3.880)
(2.923)
Gross profitability (t-1)
0.077***
0.044
(4.091)
(1.048)
Return (t-1)
-0.825*** -0.604***
(-11.313)
(-8.814)
Date FE
Stock FE
Observations
2
R
Yes
No
Yes
Yes
1,306,791
1,306,791
0.664
0.695
0.016*** 0.016***
(9.761)
(3.306)
0.135*** -0.037**
(8.508) (-2.217)
-0.411*** -0.311***
(-7.305) (-7.379)
-2.659*** -1.213***
(-8.519) (-6.978)
0.006
0.025***
(1.639)
(6.339)
0.026*** 0.026***
(4.086)
(5.441)
0.061*** 0.055***
(8.312)
(3.597)
-0.568*** -0.411***
(-19.405) (-15.857)
Yes
No
Yes
Yes
7,071,752 7,071,751
0.586
0.621
Order Imbalance (%)
S&P 500
Russell 3000
(5)
(6)
(7)
(8)
-0.137*** -0.121***
(-2.621)
(-2.705)
0.154*** 0.132***
(3.412)
(3.504)
0.125*** 0.112***
(47.448)
(53.297)
-0.024
(-0.463)
0.363***
(6.932)
0.124***
(91.414)
-0.078
(-1.586)
0.244***
(4.840)
0.112***
(98.638)
-0.305*** -0.341**
(-5.955)
(-1.974)
-0.715
-1.846
(-0.567)
(-0.760)
-555.273*** -234.613
(-3.390)
(-1.564)
5.685
2.929
(0.896)
(0.731)
0.164
-0.121
(1.492)
(-0.939)
0.301*** 0.223**
(3.224)
(2.334)
-0.732***
0.075
(-3.077)
(0.104)
5.702*** 6.628***
(6.902)
(7.998)
0.501*** 0.449***
(15.609)
(6.061)
-0.871***
-0.239
(-4.255)
(-1.145)
-1.353***
0.317
(-3.039)
(0.606)
-39.070*** -15.549***
(-5.855)
(-3.609)
0.236***
-0.001
(5.342)
(-0.017)
0.166*** 0.136***
(2.886)
(3.507)
0.223** 0.553***
(2.560)
(2.669)
6.865*** 7.904***
(14.035)
(16.345)
Yes
No
Yes
Yes
Yes
No
Yes
Yes
1,297,863
1,297,862
7,024,827
7,024,825
0.118
0.128
0.072
0.081
131
Electronic copy available at: https://ssrn.com/abstract=1967599
Internet Appendix Table AXIV. ETF Ownership and Volatility, Moderated by Investor
Sentiment
The table reports estimates from regressions of daily stock volatility on ETF ownership, interacted with investor
sentiment. The dependent variable is stock-level volatility measured across days within each month. The measures of
investor sentiment are top-quartile indicators derived from the distributions of the Baker and Wurgler (2006) index and
the Michigan Survey of Consumer Sentiment index. Volatility and ETF ownership are standardized. The controls in all
panels are logged market capitalization, the lagged inverse share price, the lagged Amihud (2002) ratio, the lagged
average bid-ask spread, the lagged book-to-market ratio, lagged past 12 month returns, lagged gross profitability (as in
Novy-Marx (2013)), lagged volatility, index-fund ownership, active-fund ownership, hedge-fund ownership, and lags
of stock volatility. Month and stock fixed effects are included. Standard errors are double clustered at the stock and
time level. t-statistics are presented in parentheses. ***, **, and * represent statistical significance at the 1%, 5%, and
10% levels, respectively. The sample ranges between January 2000 and December 2015.
Dependent variable:
Sample:
Daily volatility (t)
0.072**
(2.095)
Russell 3000
(3)
(4)
0.053***
0.052***
(7.368)
(7.434)
0.070*
(1.709)
0.018
(1.270)
-0.012
(-0.856)
1.036***
(3.272)
22.127**
(2.544)
0.461
(0.300)
-0.027
(-1.315)
-0.004
(-0.264)
-0.040
(-1.041)
-0.026***
(-4.296)
0.002
(0.513)
0.015***
(2.927)
0.291***
(17.276)
0.174***
(9.534)
0.201***
(14.852)
-0.013
(-0.902)
1.049***
(3.533)
21.773**
(2.558)
-0.265
(-0.168)
-0.027
(-1.338)
-0.008
(-0.540)
-0.042
(-1.093)
-0.026***
(-4.228)
0.002
(0.458)
0.016***
(2.999)
0.291***
(17.583)
0.176***
(9.682)
0.204***
(14.975)
-0.064***
(-6.805)
0.809***
(8.536)
1.157***
(6.659)
2.529***
(4.763)
0.005
(0.413)
0.016*
(1.731)
-0.081***
(-3.442)
-0.023***
(-7.988)
0.009***
(3.058)
0.026***
(5.874)
0.208***
(20.112)
0.154***
(22.617)
0.175***
(28.218)
-0.064***
(-6.948)
0.809***
(8.624)
1.165***
(6.713)
2.470***
(4.588)
0.006
(0.478)
0.015
(1.586)
-0.083***
(-3.520)
-0.023***
(-7.985)
0.009***
(3.016)
0.026***
(5.949)
0.207***
(20.097)
0.154***
(22.781)
0.177***
(27.999)
Month FE
Stock FE
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Observations
76,834
77,675
388,054
392,684
0.742
0.740
0.671
0.670
ETF ownership (standardized)
× Top BW sentiment
S&P 500
(1)
0.072***
(5.643)
0.157***
(2.924)
× Top Michigan sentiment
log(Mktcap (t-1))
1/Price (t-1)
Amihud (t-1)
Bid-ask spread (t-1)
Book-to-Market (t-1)
Past 12-month Return (t-1)
Gross Profitability (t-1)
Hedge fund ownership
Index fund ownership
Active fund ownership
Volatility (t-1)
Volatility (t-2)
Volatility (t-3)
2
R
(2)
0.076***
(5.976)
132
Electronic copy available at: https://ssrn.com/abstract=1967599
Internet Appendix Table AXV. ETF Ownership and Stock Volatility, Moderated by
Arbitrage Capital
The table reports estimates from regressions of daily stock volatility on ETF ownership, interacted with measures of
the availability of arbitrage capital. The dependent variable is stock-level volatility measured using daily returns within
a month. ETF ownership and volatility are standardized. ETF ownership is interacted with the variables proposed by
He, Kelly, and Manela (2017) in columns (1)–(2), and with the variable proposed by Adrian, Etula, and Muir (2014) in
column (3). Columns (4)–(6) add the average VIX as a control. Panel A uses a sample of S&P 500 stocks. Panel B uses
a sample of Russell 3000 stocks. Month and stock fixed effects are included. Panels C, D, and E report estimates from
regressions of daily stock returns on ETF flows, interacted with measures of the availability of arbitrage capital. The
dependent variable is the stock-level DWGT-adjusted return measured across different horizons. The ETF-flows
variable is expressed as a fraction of the stock’s market capitalization and is standardized. The ETF-flows variable is
interacted with the variables proposed by He, Kelly, and Manela (2017) in Panel C and Panel D, and with the variable
proposed by Adrian, Etula, and Muir (2014) in Panel E. The controls in all panels include logged market capitalization,
the lagged inverse share price, the lagged Amihud (2002) ratio, the lagged average bid-ask spread, the lagged book-tomarket ratio, lagged past 12 month returns, lagged gross profitability (as in Novy-Marx (2013)), index-fund ownership,
active-fund ownership, hedge-fund ownership, and lags of stock volatility. Day fixed effects are included. Standard
errors are double clustered at the stock and time level. Panel F reports estimates from time-series regressions of the
monthly cross-sectional average of stock-level mispricing on measures of arbitrage capital. In columns (1)–(4),
arbitrage capital is measured using the variables proposed by He, Kelly, and Manela (2017): intermediary capital and
the traded factor based on intermediary capital. In columns (5)–(6), arbitrage capital is measured using the variable
proposed by Adrian, Etula, and Muir (2014). In some specifications, the (average within the month) VIX index is also
included. t-statistics are presented in parentheses. ***, **, and * represent statistical significance at the 1%, 5%, and
10% levels, respectively. The sample ranges between January 2000 and December 2012, due to the availability of the
measures of arbitrage capital.
133
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Internet Appendix Table AXV. ETF Ownership and Stock Volatility, Moderated by
Arbitrage Capital (Cont.)
Panel A: S&P 500
Sample:
Dependent variable:
ETF ownership (standardized)
× Intermediary capital risk factor
× Intermediary capital traded factor
× AEM leverage factor
× VIX
log(Mktcap (t-1))
1/Price (t-1)
Amihud (t-1)
Bid-ask spread (t-1)
Book-to-Market (t-1)
Past 12-month Return (t-1)
Gross Profitability (t-1)
Hedge fund ownership
Index fund ownership
Active fund ownership
Volatility (t-1)
Volatility (t-2)
Volatility (t-3)
S&P 500
Daily volatility (t)
(1)
(2)
(3)
(4)
(5)
(6)
0.074*** 0.073*** 0.074*** 0.065*** 0.065*** 0.064***
(5.012) (5.080) (5.079) (4.869) (4.847) (4.851)
-0.020***
-0.012*
(-2.740)
(-1.760)
-0.019***
-0.007
(-2.863)
(-1.232)
-0.014
0.001
(-1.613)
(0.151)
0.021*** 0.022*** 0.027***
(3.345) (3.338) (3.261)
-0.000
-0.000
-0.000
-0.000
-0.000
-0.000
(-0.688) (-0.714) (-0.713) (-0.675) (-0.692) (-0.692)
0.020*** 0.020*** 0.020*** 0.020*** 0.020*** 0.020***
(3.440) (3.429) (3.437) (3.413) (3.403) (3.395)
0.351** 0.350** 0.351** 0.335** 0.336** 0.336**
(2.226) (2.221) (2.233) (2.138) (2.141) (2.139)
-0.006
-0.005
-0.007
-0.003
-0.003
-0.003
(-0.198) (-0.172) (-0.227) (-0.117) (-0.106) (-0.099)
-0.000
-0.000
-0.000
-0.000
-0.000
-0.000
(-1.015) (-1.032) (-1.020) (-1.036) (-1.043) (-1.039)
-0.000
-0.000
-0.000
-0.000
-0.000
-0.000
(-0.315) (-0.326) (-0.343) (-0.292) (-0.297) (-0.288)
-0.000
-0.000
-0.000
-0.000
-0.000
-0.000
(-0.188) (-0.211) (-0.167) (-0.200) (-0.206) (-0.195)
-0.008*** -0.008*** -0.008*** -0.008*** -0.008*** -0.008***
(-3.654) (-3.645) (-3.672) (-3.646) (-3.647) (-3.658)
0.003
0.004
0.003
0.004
0.004
0.004
(0.808) (0.849) (0.775) (0.880) (0.895) (0.886)
0.004*** 0.004*** 0.004*** 0.004*** 0.004*** 0.004***
(3.001) (3.020) (3.009) (2.932) (2.939) (2.929)
0.304*** 0.303*** 0.304*** 0.303*** 0.302*** 0.303***
(18.010) (18.054) (18.078) (18.074) (18.072) (18.097)
0.174*** 0.175*** 0.175*** 0.174*** 0.174*** 0.174***
(8.888) (8.911) (8.908) (8.879) (8.888) (8.881)
0.195*** 0.195*** 0.196*** 0.195*** 0.195*** 0.195***
(13.223) (13.220) (13.255) (13.279) (13.263) (13.299)
Month FE
Stock FE
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Observations
62,508
62,508
62,508
62,508
62,508
62,508
0.747
0.747
0.747
0.747
0.747
0.747
2
R
134
Electronic copy available at: https://ssrn.com/abstract=1967599
Internet Appendix Table AXV. ETF Ownership and Stock Volatility, Moderated by
Arbitrage Capital (Cont.)
Panel B: Russell 3000
Sample:
Dependent variable:
ETF ownership (standardized)
× Intermediary capital risk factor
× Intermediary capital traded factor
× AEM leverage factor
× VIX
log(Mktcap (t-1))
1/Price (t-1)
Amihud (t-1)
Bid-ask spread (t-1)
Book-to-Market (t-1)
Past 12-month Return (t-1)
Gross Profitability (t-1)
Hedge fund ownership
Index fund ownership
Active fund ownership
Volatility (t-1)
Volatility (t-2)
Volatility (t-3)
Russell 3000
Daily volatility (t)
(1)
(2)
(3)
(4)
(5)
(6)
0.074*** 0.073*** 0.075*** 0.065*** 0.065*** 0.064***
(5.013) (5.081) (5.082) (4.852) (4.823) (4.819)
-0.021***
-0.012*
(-2.740)
(-1.760)
-0.020***
-0.007
(-2.863)
(-1.232)
-0.014
0.001
(-1.613)
(0.151)
0.022*** 0.022*** 0.027***
(3.345) (3.338) (3.261)
-0.000
-0.000
-0.000
-0.000
-0.000
-0.000
(-0.688) (-0.714) (-0.713) (-0.675) (-0.692) (-0.692)
0.020*** 0.020*** 0.020*** 0.020*** 0.020*** 0.020***
(3.440) (3.429) (3.437) (3.413) (3.403) (3.395)
0.351** 0.350** 0.351** 0.335** 0.336** 0.336**
(2.226) (2.221) (2.233) (2.138) (2.141) (2.139)
-0.006
-0.005
-0.007
-0.003
-0.003
-0.003
(-0.198) (-0.172) (-0.227) (-0.117) (-0.106) (-0.099)
-0.000
-0.000
-0.000
-0.000
-0.000
-0.000
(-1.015) (-1.032) (-1.020) (-1.036) (-1.043) (-1.039)
-0.000
-0.000
-0.000
-0.000
-0.000
-0.000
(-0.315) (-0.326) (-0.343) (-0.292) (-0.297) (-0.288)
-0.000
-0.000
-0.000
-0.000
-0.000
-0.000
(-0.188) (-0.211) (-0.167) (-0.200) (-0.206) (-0.195)
-0.008*** -0.008*** -0.008*** -0.008*** -0.008*** -0.008***
(-3.654) (-3.645) (-3.672) (-3.646) (-3.647) (-3.658)
0.003
0.004
0.003
0.004
0.004
0.004
(0.808) (0.849) (0.775) (0.880) (0.895) (0.886)
0.004*** 0.004*** 0.004*** 0.004*** 0.004*** 0.004***
(3.001) (3.020) (3.009) (2.932) (2.939) (2.929)
0.304*** 0.303*** 0.304*** 0.303*** 0.302*** 0.303***
(18.010) (18.054) (18.078) (18.074) (18.072) (18.097)
0.174*** 0.175*** 0.175*** 0.174*** 0.174*** 0.174***
(8.888) (8.911) (8.908) (8.879) (8.888) (8.881)
0.195*** 0.195*** 0.196*** 0.195*** 0.195*** 0.195***
(13.223) (13.220) (13.255) (13.279) (13.263) (13.299)
Month FE
Stock FE
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Observations
62,508
62,508
62,508
62,508
62,508
62,508
0.747
0.747
0.747
0.747
0.747
0.747
2
R
135
Electronic copy available at: https://ssrn.com/abstract=1967599
Internet Appendix Table AXV. ETF Ownership and Stock Volatility, Moderated by
Arbitrage Capital (Cont.)
Panel C: Arbitrage Capital Proxied by Intermediary Capital Risk Factor
DGTW returns over…
(t)
(t, t+5) (t, t+10) (t, t+20) (t, t+40)
(t)
(t, t+5)
(1)
(2)
(3)
(4)
(5)
(6)
(7)
ETF flows (standartized)
0.118*** 0.102*** 0.052**
0.033
0.017
0.117*** 0.101***
(11.374) (6.160) (2.319) (1.134) (0.406)
(11.479) (6.173)
× Intermediary capital risk factor -0.015 -0.065*** -0.057** -0.081** -0.073*
-0.011 -0.058***
(-1.475) (-3.401) (-2.011) (-2.431) (-1.652)
(-1.012) (-3.091)
× VIX
0.027** 0.044**
(1.991) (2.037)
Dependent variable:
log(Mktcap (t-1))
1/Price (t-1)
Amihud (t-1)
Bid-ask spread (t-1)
Book-to-Market (t-1)
Past 12-month Return (t-1)
Gross Profitability (t-1)
Lagged dependent variable
Day FE
Observations
R
2
0.034*** 0.025*** 0.015
0.022
0.032
(11.410) (2.732) (0.862) (0.603) (0.428)
-0.678*** 0.275
1.454** 4.049*** 9.341***
(-3.903) (1.090) (2.471) (3.218) (3.217)
29.054*** -5.936
-40.582 -81.454 -169.202
(5.557) (-0.437) (-1.499) (-1.483) (-1.541)
-1.512*
3.110
7.050* 19.413*** 29.602**
(-1.659) (1.476) (1.881) (2.737) (2.208)
0.039*** 0.020
0.004
-0.013
-0.046
(4.231) (0.741) (0.088) (-0.135) (-0.226)
-0.020** -0.031
-0.073
0.022
0.250
(-2.204) (-1.047) (-1.284) (0.203) (1.099)
0.040**
0.039
0.009
0.016
0.041
(2.255) (0.865) (0.120) (0.112) (0.140)
-2.397*** -2.296*** -2.348*** -2.737*** -3.401***
(-7.126) (-6.941) (-7.079) (-7.167) (-6.753)
Yes
Yes
Yes
Yes
Yes
1,250,631 1,250,631 1,250,631 1,250,631 1,250,631
0.010
0.009
0.009
0.011
0.014
(t, t+10) (t, t+20) (t, t+40)
(8)
(9)
(10)
0.050**
0.033
0.017
(2.292) (1.155) (0.403)
-0.050* -0.082** -0.072
(-1.755) (-2.489) (-1.633)
0.043
-0.006
0.010
(1.438) (-0.155) (0.192)
0.034*** 0.025*** 0.015
0.022
0.032
(11.392) (2.719) (0.856) (0.603) (0.428)
-0.678*** 0.275
1.455** 4.048*** 9.341***
(-3.896) (1.093) (2.473) (3.218) (3.217)
29.007*** -6.014
-40.656 -81.444 -169.219
(5.553) (-0.442) (-1.502) (-1.483) (-1.541)
-1.507*
3.118
7.058* 19.412*** 29.604**
(-1.654) (1.480) (1.883) (2.737) (2.208)
0.039*** 0.020
0.004
-0.013
-0.047
(4.214) (0.731) (0.082) (-0.135) (-0.226)
-0.020** -0.032
-0.073
0.022
0.250
(-2.210) (-1.050) (-1.286) (0.203) (1.099)
0.040**
0.039
0.010
0.016
0.041
(2.259) (0.867) (0.121) (0.112) (0.140)
-2.397*** -2.296*** -2.348*** -2.737*** -3.401***
(-7.122) (-6.942) (-7.080) (-7.167) (-6.753)
Yes
Yes
Yes
Yes
Yes
1,250,631 1,250,631 1,250,631 1,250,631 1,250,631
0.010
0.009
0.009
136
Electronic copy available at: https://ssrn.com/abstract=1967599
0.011
0.014
Internet Appendix Table AXV. ETF Ownership and Stock Volatility, Moderated by
Arbitrage Capital (Cont.)
Panel D: Arbitrage Capital Proxied by Intermediary Capital Traded Factor
Dependent variable:
(t)
(t, t+5) (t, t+10)
(1)
(2)
(3)
ETF flows (standartized)
0.118*** 0.105*** 0.054**
(11.394) (6.259) (2.410)
× Intermediary capital traded factor
-0.002
-0.034
-0.036
(-0.224) (-1.557) (-1.361)
× VIX
log(Mktcap (t-1))
1/Price (t-1)
Amihud (t-1)
Bid-ask spread (t-1)
Book-to-Market (t-1)
Past 12-month Return (t-1)
Gross Profitability (t-1)
Lagged dependent variable
Day FE
Observations
2
R
(t, t+20)
(4)
0.036
(1.244)
-0.060*
(-1.838)
DGTW returns over…
(t, t+40)
(t)
(t, t+5) (t, t+10) (t, t+20) (t, t+40)
(5)
(6)
(7)
(8)
(9)
(10)
0.021
0.117*** 0.103*** 0.052**
0.037
0.021
(0.476)
(11.506) (6.270) (2.369) (1.283) (0.482)
-0.062
0.008
-0.019
-0.022 -0.065** -0.062
(-1.407)
(0.801) (-0.854) (-0.867) (-2.054) (-1.420)
0.032** 0.047**
0.043
-0.015
-0.000
(2.375) (2.062) (1.498) (-0.436) (-0.007)
0.034*** 0.025*** 0.015
0.022
0.032
(11.428) (2.738) (0.862) (0.602) (0.427)
-0.679*** 0.275
1.455** 4.050*** 9.342***
(-3.905) (1.092) (2.471) (3.218) (3.217)
29.074*** -5.906
-40.570 -81.449 -169.214
(5.561) (-0.435) (-1.499) (-1.483) (-1.541)
-1.515*
3.100
7.042* 19.403*** 29.593**
(-1.663) (1.471) (1.879) (2.736) (2.208)
0.039*** 0.020
0.004
-0.013
-0.046
(4.237) (0.747) (0.090) (-0.134) (-0.225)
-0.020** -0.031
-0.072
0.022
0.251
(-2.197) (-1.037) (-1.280) (0.207) (1.101)
0.040**
0.039
0.010
0.017
0.041
(2.257) (0.869) (0.122) (0.113) (0.141)
-2.398*** -2.295*** -2.347*** -2.738*** -3.402***
(-7.128) (-6.938) (-7.076) (-7.169) (-6.755)
Yes
Yes
Yes
Yes
Yes
1,250,631 1,250,631 1,250,631 1,250,631 1,250,631
0.010
0.009
0.009
0.011
0.014
0.034*** 0.025*** 0.015
0.022
0.032
(11.414) (2.730) (0.859) (0.603) (0.427)
-0.679*** 0.275
1.455** 4.050*** 9.342***
(-3.898) (1.092) (2.472) (3.217) (3.217)
29.032*** -5.967
-40.626 -81.429 -169.213
(5.556) (-0.439) (-1.501) (-1.483) (-1.541)
-1.510*
3.108
7.050* 19.400*** 29.593**
(-1.657) (1.475) (1.881) (2.736) (2.208)
0.039*** 0.020
0.004
-0.013
-0.046
(4.217) (0.736) (0.085) (-0.133) (-0.225)
-0.020** -0.031
-0.072
0.022
0.251
(-2.206) (-1.042) (-1.282) (0.207) (1.101)
0.040**
0.039
0.010
0.017
0.041
(2.261) (0.871) (0.123) (0.113) (0.141)
-2.398*** -2.295*** -2.347*** -2.738*** -3.402***
(-7.125) (-6.940) (-7.077) (-7.169) (-6.755)
Yes
Yes
Yes
Yes
Yes
1,250,631 1,250,631 1,250,631 1,250,631 1,250,631
0.010
0.009
0.009
137
Electronic copy available at: https://ssrn.com/abstract=1967599
0.011
0.014
Internet Appendix Table AXV. ETF Ownership and Stock Volatility, Moderated by
Arbitrage Capital (Cont.)
Panel E: Arbitrage Capital Proxied by AEM Leverage Factor
Dependent variable:
ETF flows (standartized)
× AEM leverage factor
(t)
(t, t+5)
(1)
(2)
0.119*** 0.107***
(11.366) (6.241)
-0.018
-0.044*
(-1.417) (-1.800)
× VIX
DGTW returns over…
(t, t+10) (t, t+20) (t, t+40)
(t)
(t, t+5) (t, t+10) (t, t+20) (t, t+40)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
0.057**
0.041
0.025
0.117*** 0.104*** 0.055**
0.042
0.026
(2.518) (1.391) (0.593)
(11.551) (6.252) (2.498) (1.476) (0.625)
-0.069** -0.099** -0.114**
-0.007
-0.025
-0.055 -0.109** -0.119*
(-2.125) (-2.458) (-1.975) (-0.505) (-1.009) (-1.617) (-2.580) (-1.911)
0.027* 0.047**
0.035
-0.024
-0.013
(1.899) (2.068) (1.121) (-0.638) (-0.242)
log(Mktcap (t-1))
0.034*** 0.025*** 0.016
0.022
0.032
0.034*** 0.025*** 0.015
0.022
0.032
(11.417) (2.747) (0.865) (0.606) (0.429)
(11.402) (2.735) (0.860) (0.607) (0.429)
1/Price (t-1)
-0.678*** 0.275
1.455** 4.050*** 9.343*** -0.678*** 0.275
1.455** 4.050*** 9.343***
(-3.900) (1.091) (2.473) (3.219) (3.218)
(-3.896) (1.092) (2.474) (3.219) (3.218)
Amihud (t-1)
29.076*** -5.840
-40.508 -81.343 -169.104 29.023*** -5.930
-40.574 -81.298 -169.078
(5.561) (-0.430) (-1.497) (-1.482) (-1.541)
(5.557) (-0.436) (-1.499) (-1.481) (-1.541)
Bid-ask spread (t-1)
-1.545*
3.020
6.919* 19.226*** 29.392** -1.520*
3.063
6.951* 19.204*** 29.379**
(-1.697) (1.433) (1.847) (2.712) (2.193)
(-1.672) (1.455) (1.856) (2.709) (2.192)
Book-to-Market (t-1)
0.039*** 0.020
0.004
-0.014
-0.047
0.039*** 0.020
0.004
-0.013
-0.047
(4.224) (0.741) (0.083) (-0.139) (-0.228)
(4.213) (0.733) (0.080) (-0.137) (-0.228)
Past 12-month Return (t-1) -0.020** -0.031
-0.072
0.022
0.250
-0.020** -0.031
-0.073
0.022
0.250
(-2.202) (-1.041) (-1.283) (0.204) (1.099)
(-2.207) (-1.044) (-1.284) (0.204) (1.099)
Gross Profitability (t-1)
0.040**
0.039
0.009
0.016
0.041
0.040**
0.039
0.010
0.016
0.041
(2.255) (0.867) (0.120) (0.112) (0.140)
(2.260) (0.870) (0.122) (0.112) (0.140)
Lagged dependent variable -2.398*** -2.295*** -2.346*** -2.737*** -3.401*** -2.397*** -2.296*** -2.347*** -2.736*** -3.401***
(-7.129) (-6.938) (-7.075) (-7.166) (-6.754) (-7.125) (-6.940) (-7.076) (-7.165) (-6.754)
Day FE
Observations
2
R
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
1,250,631 1,250,631 1,250,631 1,250,631 1,250,631 1,250,631 1,250,631 1,250,631 1,250,631 1,250,631
0.010
0.009
0.009
0.011
0.014
0.010
0.009
0.009
138
Electronic copy available at: https://ssrn.com/abstract=1967599
0.011
0.014
Internet Appendix Table AXV. ETF Ownership and Stock Volatility, Moderated by
Arbitrage Capital (Cont.)
Panel E: ETF Mispricing and Arbitrage Capital
Dependent variable:
Arbitrage factor:
Arbitrage factor
VIX
Constant
Intermediary capital
(1)
(2)
-0.000**
-0.000
(-2.391)
(-0.471)
0.000***
(7.703)
0.000***
0.000
(18.534)
(0.726)
Average Mispricing
Traded Factor
(3)
(4)
-0.000***
-0.000
(-3.374)
(-0.045)
0.000***
(7.194)
0.000***
0.000
(19.248)
(0.572)
AEM leverage
(5)
(6)
-0.000***
-0.000
(-3.701)
(-1.189)
0.000***
(7.127)
0.000***
0.000
(19.470)
(1.071)
Observations
156
156
156
156
156
156
R2
0.036
0.305
0.069
0.304
0.082
0.311
139
Electronic copy available at: https://ssrn.com/abstract=1967599
Internet Appendix Table AXVI. The Availability of Arbitrage Capital
The table reports estimates from regressions of daily stock-level volatility within the month on ETF ownership
interacted with aggregate factors. Volatility and the ownership variables are standardized. The aggregate factors are the
VIX, absolute net trades, and the sum of absolute trades, where trades are of all institutional investors (columns (1),
(2), (5), (6)), or of hedge funds (columns (3), (4), (7), (8)). Columns (1)–(4) restrict the sample to S&P 500 firms.
Columns (5)–(8) use a sample of Russell 3000 stocks. The controls in all panels are logged market capitalization, the
lagged inverse share price, the lagged Amihud (2002) ratio, the lagged average bid-ask spread, the lagged book-tomarket ratio, lagged past 12 month returns, lagged gross profitability (as in Novy-Marx (2013)), lagged volatility,
index-fund ownership, active-fund ownership, and hedge-fund ownership, and lags of stock volatility. Panel A uses a
sample of S&P 500 stocks. Panel B uses a sample of Russell 3000 stocks. Month and stock fixed effects are included.
Standard errors are double clustered at the stock and time level. t-statistics are presented in parentheses. ***, **, and *
represent statistical significance at the 1%, 5%, and 10% levels, respectively. The sample ranges between January 2000
and December 2015.
Daily volatility (t)
Dependent variable:
Sample:
Institutions in the factor:
S&P 500
All
Hedge Funds
All
Russell 3000
Hedge Funds
Abs(net
trades)
Sum(abs
trades)
Abs(net
trades)
Sum(abs
trades)
Abs(net
trades)
Sum(abs
trades)
Abs(net
trades)
Sum(abs
trades)
(1)
0.075***
(7.111)
0.031***
(3.432)
0.025***
(3.918)
(2)
0.078***
(6.967)
0.038***
(4.210)
0.008
(1.295)
(3)
0.072***
(6.980)
0.028**
(2.365)
0.025***
(4.080)
(4)
0.080***
(7.562)
0.050***
(4.418)
0.010
(1.532)
(5)
0.046***
(9.564)
0.007**
(2.319)
0.018***
(6.456)
(6)
0.048***
(9.047)
0.011***
(2.650)
0.014***
(4.058)
(7)
0.049***
(9.340)
0.017***
(3.060)
0.019***
(6.216)
(8)
0.053***
(9.530)
0.025***
(4.216)
0.011***
(3.218)
-0.000
(-0.592)
0.020***
(3.371)
0.396**
(2.448)
0.006
(0.203)
-0.000
(-1.284)
-0.000
(-0.436)
-0.001
(-0.986)
-0.000
(-0.025)
0.003***
(2.761)
-0.007***
(-4.249)
0.289***
(17.691)
0.174***
(9.585)
0.201***
(14.929)
-0.000
(-0.547)
0.020***
(3.355)
0.399**
(2.463)
0.009
(0.333)
-0.000
(-1.286)
-0.000
(-0.403)
-0.001
(-1.064)
0.000
(0.070)
0.003***
(2.754)
-0.007***
(-4.161)
0.288***
(17.755)
0.174***
(9.601)
0.201***
(14.864)
-0.000
(-0.671)
0.019***
(3.340)
0.392**
(2.434)
0.006
(0.205)
-0.000
(-1.272)
-0.000
(-0.393)
-0.001
(-0.914)
-0.000
(-0.042)
0.003***
(2.769)
-0.007***
(-4.267)
0.289***
(17.725)
0.174***
(9.534)
0.201***
(14.849)
-0.000
(-0.681)
0.019***
(3.091)
0.402**
(2.450)
0.018
(0.637)
-0.000
(-1.181)
-0.000
(-0.311)
-0.001
(-0.905)
-0.000
(-0.078)
0.003***
(2.766)
-0.007***
(-4.198)
0.287***
(17.558)
0.173***
(9.519)
0.199***
(14.762)
-0.001***
(-6.749)
0.015***
(8.551)
0.023***
(6.831)
0.047***
(4.650)
0.000
(0.430)
0.000
(1.592)
-0.002***
(-3.425)
0.007***
(3.138)
0.006***
(5.736)
-0.006***
(-8.110)
0.207***
(20.299)
0.154***
(22.477)
0.175***
(28.240)
-0.001*** -0.001*** -0.001***
(-6.750)
(-6.777)
(-6.793)
0.015*** 0.015*** 0.015***
(8.543)
(8.540)
(8.482)
0.023*** 0.023*** 0.023***
(6.825)
(6.890)
(6.901)
0.048*** 0.048*** 0.049***
(4.683)
(4.669)
(4.810)
0.000
0.000
0.000
(0.420)
(0.437)
(0.429)
0.000
0.000
0.000
(1.579)
(1.620)
(1.597)
-0.002*** -0.002*** -0.002***
(-3.427)
(-3.421)
(-3.420)
0.007*** 0.007*** 0.007***
(3.164)
(3.109)
(3.143)
0.005*** 0.006*** 0.005***
(5.677)
(5.745)
(5.657)
-0.006*** -0.006*** -0.006***
(-8.126)
(-8.124)
(-8.159)
0.207*** 0.207*** 0.206***
(20.304)
(20.282)
(20.279)
0.154*** 0.154*** 0.154***
(22.482)
(22.483)
(22.515)
0.175*** 0.175*** 0.175***
(28.278)
(28.249)
(28.286)
Month FE
Stock FE
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Observations
76,834
76,834
76,834
76,834
388,054
388,054
388,054
388,054
0.743
0.743
0.743
0.743
0.672
0.672
0.672
0.672
Type of factor:
ETF ownership
× Trading factor
× VIX
log(mktcap (t-1))
1/Price (t-1)
Amihud (t-1)
Bid-ask spread (t-1)
Book-to-Market (t-1)
Past 12-month return (t-1)
Gross profitability (t-1)
Index fund ownership
Active fund ownership
Hedge fund ownership
Volatility (t-1)
Volatility (t-2)
Volatility (t-3)
2
R
140
Electronic copy available at: https://ssrn.com/abstract=1967599
Internet Appendix Table AXVI. Evidence on the Arbitrage Channel (Russell 3000 Sample)
The table reports estimates from ordinary least squares (OLS) regressions of intraday volatility (Panel A) and the
intraday variance ratio (Panel B) on absolute stock-level mispricing in the prior period interacted with measures of
arbitrage costs. The frequency is daily, and the observations are at the stock level. The sample contains Russell 3000
stocks. In columns (2)–(4), the arbitrage cost is captured by the bid-ask spread from the prior day, and in columns (5)–
(7), by the average share-lending fee in the month. For both measures of arbitrage costs, we construct dummy variables
denoting whether the stock is in the top half of the distribution of that measure in the relevant period. In columns (3)
and (6), we restrict the sample to observations for which the stock-level mispricing is positive. In columns (4) and (7),
we restrict the sample to observations for which the stock-level mispricing is negative. The controls in all panels are
logged market capitalization, the lagged inverse share price, the lagged Amihud (2002) ratio, the lagged average bidask spread, the lagged book-to-market ratio, lagged past 12 month returns, lagged gross profitability (as in Novy-Marx
(2013)), lagged returns, the lagged dependent variable, and the absolute mispricing in period t - 2. Variable descriptions
are provided in I.A. Table AI. Standard errors are double clustered at the stock and day levels. t-statistics are presented
in parentheses. ***, **, and * represent statistical significance at the 1%, 5%, and 10% levels, respectively. The sample
ranges between January 2000 and December 2015.
All
(2)
0.005***
(3.424)
Intraday stock volatility
Misp > 0
Misp < 0
All
(3)
(4)
(5)
0.017***
0.001
0.002
(8.650)
(0.326)
(1.220)
-0.010***
(-2.950)
-0.022***
(-6.015)
Dependent variable:
Abs(Mispricing) (t-1)
All
(1)
0.006***
(6.452)
× I(High bid-ask spread)
0.077***
(18.020)
0.077***
(18.166)
0.005*
(1.867)
log(Mktcap (t-1))
-0.074***
(-9.929)
1/Price (t-1)
1.268***
(14.093)
Amihud (t-1)
-0.826***
(-5.635)
Bid-ask spread (t-1)
22.967***
(11.449)
Book-to-Market (t-1)
0.105***
(8.495)
Past 12-month Return (t-1) 0.045***
(11.865)
Gross Profitability (t-1)
-0.038*
(-1.712)
Ret (t-1)
-0.175***
(-8.972)
Dependent variable (t-1)
0.422***
(70.202)
Abs(Mispricing) (t-2)
0.003***
(2.751)
Day fixed effects
Stock fixed effects
Observations
2
R
0.004**
(2.305)
0.000
(0.086)
1.967***
(29.945)
-1.060***
(-8.281)
16.286***
(9.004)
0.040***
(6.712)
0.052***
(13.486)
0.011
(1.254)
-0.233***
(-11.616)
0.559***
(73.167)
-0.001
(-1.357)
-0.001
(-0.635)
0.001
(0.376)
-0.003
(-1.566)
0.040***
(16.488)
0.002
(1.357)
-0.008***
(-3.661)
2.007***
(30.126)
-1.283***
(-9.798)
23.517***
(11.946)
0.041***
(6.911)
0.052***
(13.119)
0.004
(0.512)
-0.225***
(-11.221)
0.561***
(72.839)
-0.002**
(-2.091)
0.041*** 0.039***
(16.471)
(15.455)
-0.001
0.003
(-0.433)
(1.635)
-0.006*** -0.010***
(-2.629)
(-4.237)
1.953*** 2.051***
(28.995)
(30.335)
-1.092*** -1.454***
(-8.591)
(-10.352)
22.162*** 25.081***
(11.784)
(11.704)
0.038*** 0.044***
(6.100)
(7.426)
0.052*** 0.053***
(13.571)
(12.276)
0.005
0.004
(0.553)
(0.514)
-0.568*** 0.085***
(-20.130)
(3.114)
0.574*** 0.549***
(70.634)
(73.617)
0.005*** -0.006***
(3.359)
(-5.360)
0.075***
(17.012)
High lending fee
ETF ownership (t-1)
Misp < 0
(7)
-0.001
(-0.573)
-0.005
(-1.391)
× I(High lending fee)
High bid-ask spread
Misp > 0
(6)
0.008***
(4.531)
0.001
0.004**
(0.684)
(2.277)
0.003
-0.001
(1.109)
(-0.552)
1.919*** 2.009***
(28.858)
(30.159)
-0.882*** -1.229***
(-7.084)
(-8.955)
14.740*** 18.118***
(8.328)
(9.305)
0.036*** 0.043***
(5.935)
(7.218)
0.052*** 0.053***
(13.872)
(12.655)
0.011
0.011
(1.297)
(1.230)
-0.577*** 0.077***
(-20.462)
(2.806)
0.572*** 0.547***
(71.125)
(73.810)
0.006*** -0.005***
(3.838)
(-4.198)
Yes
Yes
Yes
No
Yes
No
Yes
No
Yes
No
Yes
No
Yes
No
4,333,078
4,333,078
2,050,177
2,282,901
4,333,078
2,050,177
2,282,901
0.513
0.466
0.468
0.465
0.465
0.467
0.464
141
Electronic copy available at: https://ssrn.com/abstract=1967599
Internet Appendix Table AXVIII. ETF-Ownership Portfolios, Subsamples
The table reports raw returns and alphas for portfolios based on ETF ownership, split by periods. Each month, five
equally weighted portfolios are formed monthly on the basis of the five quintiles of the distribution of ETF ownership
in the previous month. The panels present factor model regressions for the High-ETF-ownership minus the Low-ETFownership portfolio. The factors are the five Fama and French (2015) factors (MKTRF, HML, SMB, RMW, CMA),
Momentum (UMD), and the Pástor and Stambaugh (2003) traded liquidity factor (PS_VWF). Panels A and B present
the regressions for the subsamples 2000–2007 and 2008–2015, respectively. t-statistics are presented in parentheses.
***, **, and * represent statistical significance at the 1%, 5%, and 10% levels, respectively. The sample ranges between
January 2000 and December 2015.
Panel A: High Minus Low Portfolio, 2000–2007
Dependent variable:
Alpha
(1)
0.158
(0.589)
MKTRF
HML
SMB
UMD
RMW
CMA
ret(High-minus-Low ETF Ownership)
(2)
(3)
(4)
(5)
(6)
(7)
0.148
0.304
0.420*
0.417
0.309
0.327
(0.596)
(1.216)
(1.663)
(1.637)
(1.192)
(1.247)
0.244*** 0.175*** 0.177*** 0.184** 0.260*** 0.248***
(4.063)
(2.697)
(2.777)
(2.627)
(3.158)
(2.915)
-0.185** -0.235*** -0.234*** -0.337*** -0.288**
(-2.483) (-3.025) (-3.001) (-3.445) (-2.230)
-0.133** -0.139*
-0.049
-0.045
(-1.991) (-1.944) (-0.552) (-0.502)
0.012
0.004
0.007
(0.253)
(0.084)
(0.156)
0.203*
0.184
(1.710)
(1.494)
-0.078
(-0.586)
PS_VWF
(8)
0.229
(0.856)
0.220**
(2.549)
-0.337**
(-2.552)
-0.098
(-1.031)
0.018
(0.376)
0.168
(1.367)
-0.037
(-0.272)
0.122
(1.538)
# Months
95
95
95
95
95
95
95
95
R2
0.000
0.151
0.204
0.237
0.238
0.262
0.265
0.284
142
Electronic copy available at: https://ssrn.com/abstract=1967599
Internet Appendix Table AXVIII. ETF Ownership Portfolios, Subsamples (Cont.)
Panel B: High Minus Low Portfolio, 2008–2015
Dependent variable:
Alpha
MKTRF
HML
SMB
UMD
RMW
CMA
PS_VWF
# Months
2
R
ret(High-minus-Low ETF Ownership)
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
0.535*** 0.507*** 0.563*** 0.565*** 0.564*** 0.447*** 0.441*** 0.445***
(3.792)
(3.587)
(4.266)
(4.256)
(4.239)
(3.436)
(3.345)
(3.415)
0.043
0.001
0.004
0.009
0.052
0.053
0.050
(1.471)
(0.031)
(0.136)
(0.297)
(1.602)
(1.626)
(1.563)
0.201*** 0.205*** 0.218*** 0.235*** 0.218*** 0.272***
(4.013)
(3.974)
(3.936)
(4.474)
(3.317)
(3.788)
-0.020
-0.021
0.021
0.021
-0.010
(-0.334) (-0.348)
(0.370)
(0.360)
(-0.162)
0.019
0.015
0.012
0.009
(0.670)
(0.567)
(0.444)
(0.315)
0.311*** 0.304*** 0.304***
(3.464)
(3.324)
(3.367)
0.050
0.060
(0.430)
(0.528)
0.060*
(1.766)
96
96
96
96
96
96
96
96
0.000
0.022
0.167
0.168
0.172
0.269
0.271
0.296
143
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Internet Appendix Figure A1. Price Impact of Trade Turnover
The figure plots non-parametric estimates of the price impact of trade turnover (measured as a fraction of daily volume)
from Ancerno data. The figure reports the average price impact in each of the 30 bins of daily turnover. The sample is
trades in S&P 500 stocks (Figure A1a) and Russell 3000 stocks (Figure A1b). The trade-level sample ranges between
1999 and 2014.
Figure A1a. S&P 500 stocks
Figure A1b. Russell 3000 stocks
144
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