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DOES PASSIVE INVESTING HELP RELAX SHORT-SALE
CONSTRAINTS?
Darius Paliaa,b and Stanislav Sokolinskia`
August 2019
Abstract
Prior literature argues that passive investing mainly introduces price inefficiencies. This article
presents a channel through which passive investing leads to more informative prices. We study the
impact of passive investors’ security lending on short-sale constraints. Stocks with higher passive
ownership exhibit larger short positions, lower lending fees and longer loan durations. This effect
is significantly larger for passive than for active investors. Higher passive ownership is associated
with lower cross-autocorrelations with negative market returns, less skewness, and a smaller value
premium, especially among hard-to-borrow stocks. These results suggest that passive investing
contributes to price efficiency by relaxing short-sale constraints.
_____________________________________________________________________________________ a Rutgers Business School and b Columbia Law School, respectively. We thank Azi Ben-Rephael, Nittai Bergman,
Menahem Brenner, Lauren Cohen, Liyuan Cui, Valentin Dimitrov, Todd Gormley, Ron Kaniel, Pradeep Yadav, David
Yermack and seminar participants at NYU, Oklahoma, Rutgers, IDC Summer Finance Conference, CUHK
International Finance Conference, and the Triple Crown Conference for helpful discussions and comments. We are
grateful to the Whitcomb Center for Research in Financial Services for providing funds to obtain data. All errors
remain our responsibility. Corresponding author: Darius Palia; [email protected]
1
“Fidelity Investments is cutting out its middleman – Goldman Sachs – when dealing with
Wall Street short sellers. … The move comes as Fidelity and its rivals compete to cut fees on index
funds, luring assets that can be used for more profitable businesses like securities lending”.
Bloomberg, May 2019
“Large funds with large passive portfolios, such as ETFs and index funds, are more likely than
active funds to lend securities. The nature of their portfolios enables these funds to lend more
securities for longer periods, making them preferred counterparties for their loans”.
Callan: Institutional Investor Consulting
1. Introduction
Modern portfolio theory and the efficient market paradigm 1 has resulted in a large
increase in assets managed by passive investors (index mutual funds and ETFs) when compared
to actively managed assets. For example, 15% of total assets in the U.S. mutual funds were
managed passively in 2007, which went up to 25% by the end of 2018.2 The shift to passive
management was especially dramatic in the U.S. equity markets wherein the proportion of mutual
fund assets managed passively was over 40% in 2017.3 One of the potential reasons for this shift
is that investors in index funds pay significantly smaller fees, and many active mutual funds do
not generate significantly higher net-of-fee returns for their investors than comparable passive
funds.4
Recent literature argues that the shift to passive investing mainly introduces price
inefficiencies. The existing theoretical work shows that passive investing can generating price
pressure and increase volatility. Since passive investors do not actively seek security-level
1 See Fama (1970). 2 See 2018 Investment Company Fact Book available at www.icifactbook.org. 3 See Cremers, Fulkerson and Riley (2018) 4 Jensen (1968), Carhart (1997), Sharpe (1991), French (2008), Fama and French (2010) and Lewellen (2011) find
that the average active manager cannot outperform her benchmark net of fees. Some papers have found positive returns
to “conditional skill,” i.e., response to news events, industry specialization, education, etc. (see Daniel, Grinblatt,
Titman and Wermers (1997), Kosowski, Timmermann, Wermers and White (2006), Kacpercsyk, Sialm and Zheng
(2005), Kacperczyk, Van Nieuwerburgh and Veldkamp (2014), Pastor, Stambaugh and Taylor (2017)).
2
information, the shift to passive investing can also reduce the amount of information incorporated
in stock prices.5 Some of these concerns have found empirical support. In particular, passive
investing has been shown to increase volatility, auto-correlations, return co-movement, and
transaction costs as well as to weaken stock earnings response.6 While the existing literature has
not reached an overall consensus on the effects of passive investing, the prevailing view suggests
that an increased share of index funds and ETFs mostly “make markets dumb”.
In this paper, we propose and analyze a specific channel through which a shift to passive
investing leads to more information being embedded in prices and contributes to price efficiency.
In particular, we study of the impact of passive investors on short-sale constraints through their
security lending activities.7 In doing so, we bring together and extend two strands of literature. The
first strand of literature suggests that short-sale constraints represent a crucial limit to arbitrage
restricting incorporation of negative information into security prices and generating short-term
overvaluation (Miller (1977), Hong and Stein (2003)).8 The second strand of literature argues that
institutional investors are an important source of supply of lendable securities to short-sellers
(D'Avolio (2002), Geczy, Musto and Reed (2002), Nagel (2005), Asquith, Pathak and Ritter
(2005)). If passive investing helps relax short-sales constraints through the supply of lendable
securities, it can facilitate the incorporation of information in prices and improve efficiency. While
5 See, for example, Basak and Pavlova (2013), Brown and Davies (2017), Bond and Garcia (2017), Baruch and
Zhang (2018) and Garleanu and Pedersen (2018). 6 See Israeli, Lee and Sridharan (2017), Ben-David, Franzoni and Moussawi (2018), Coles, Heath and Ringgenberg
(2018) and Glosten, Nallareddy and Zou (2019). We provide a detailed literature review in Section 2. 7 We refer to index mutual funds and index ETFs as passive funds throughout this paper. We refer to passive ownership
as the combined ownership of index mutual funds and index ETFs. 8 Many empirical papers have shown that short selling helps predict stock returns (see Desai, Hemang, Thiagarajan
and Balachandran (2002), Jones and Lamont (2002), Ofek, Richardson and Whitelaw (2004), Asquith, Pathak and
Ritter (2005), Cohen, Diether and Malloy (2007), Diether, Lee and Werner (2009), Boehmer, Huszar and Jordan
(2010), Engelberg, Reed and Ringgenberg (2012, 2018), and Muravyev, Pearson and Pollet (2018)).
3
passive investors do not directly conduct informed trading, they can complement information-
seeking efforts of active investors who employ short-selling strategies.
The extant literature suggests that passive funds participate significantly in stock lending
programs. Prado, Saffi and Sturgess (2016) document a positive relationship between the fraction
of stock held by index funds and lending supply, and Evans, Ferreira and Prado (2017) find that
indexers report to the SEC more frequent participation in security lending relative to active funds.
It seems reasonable that passive fund managers make more prominent security lenders due to the
lack of managerial discretion over the fund’s asset allocation as they only have to limit lending in
response to fund outflows or index reconstitutions. In contrast, actively managed funds might
prefer to retain stocks as a part of their trading strategy and the opportunity to sell shares in the
future. In addition, they are also more likely to recall shares due to the change in the market
conditions other than fund flows or change in index composition (D'Avolio (2002)).
Using a comprehensive dataset of stock lending outcomes in the U.S. over 2007-2017, we
analyze whether the increased supply of lendable stock due to passive investing helps relax short-
sale constraints and increases stock price efficiency. In doing so, we examine: i) the relationship
between passive ownership and security lending outcomes; ii) the economic impact of passive
indexers relative to other institutional investors (active and non-mutual fund institutional investors
such as pension funds, banks/insurance companies, and endowments), iii) the relationship between
passive investing and the price impact of short-sale constraints; and iv) investigate whether the
relationships are casual.
4
We present four principal findings. First, stocks with higher levels of passive fund
ownership exhibit higher levels of short interest9 accompanied by lower lending fees and longer
duration of securities loans. These effects are economically meaningful, namely, a one standard
deviation increase in passive fund ownership increases short interest by 0.8% relative to the
average short interest of 3%, and has similarly large economic effects on other security loan
outcomes such as lending fees and loan durations. We also find that that passive ownership
increases lending supply as in Prado, Saffi and Sturgess (2016).
Second, we document that the effect of passive funds is larger by a factor of two-to-three
relative to actively managed funds, and by a factor of two-to-six relative to non-mutual fund
lenders. A one percent increase in passive fund ownership leads to an increase of 0.7 percent in
lending supply, a reduction of four basis points in lending fees, and an increase of 1.4 days in loan
duration. On the other hand, a one percent increase in active fund ownership leads to an increase
of 0.25 percent in lending supply, a reduction of two basis points in lending fees and an increase
of 0.6 days in loan duration. These differences are statistically significant and establish a clear
hierarchy: passive indexers appear to participate the most in their custodian’s lending programs,
followed by actively managed mutual funds and least by other institutional investors such as
pension funds, banks/insurance companies, and endowments. Splitting the sample across sub-
periods reveals that passive investing produces an especially large effect on short interest and loan
duration earlier in the sample, when passive investing was less popular.
Third, we study how passive investing affects the price impact of short-sale constraints.
We employ three measures of price impact developed in the literature on short selling. Our first
9 Note that short interest proxies for the actual quantity of stock borrowed in equilibrium, whereas lending supply
represents the amount of stock that can be borrowed (i.e., borrowing capacity).
5
measure is the cross-autocorrelation between lagged market returns and stock returns conditional
on market returns being negative (Bris, Goetzmann and Zhu (2007), Saffi and Sigurdsson (2011)).
Diamond and Verrecchia (1987) theorize that in the presence of short-sale constraints, stock prices
do not fully incorporate past negative information. Accordingly, we hypothesize that if stocks with
higher passive fund ownership benefit from relaxed short-sale constraints, then we can expect them
to exhibit lower cross-autocorrelations with lagged market returns conditional on market returns
being negative. Our second measure of price impact is the skewness of stock returns. The empirical
research on short-sale constraints have shown that when these constraints are relaxed, large
negative price movements become less likely, and stock returns exhibit less skewness (Chang,
Cheng and Yu (2007), Xu (2007)). Accordingly, we expect to observe a negative relationship
between skewness and passive fund ownership. Our third test is based on Nagel (2005). He finds
that stocks that are owned by two passive-oriented institutional investors, namely, the Vanguard
S&P 500 Index Fund and Dimensional Fund Advisors, exhibit a lower value premium. Nagel
(2005) suggests that this effect exists because security lending activities of these insitutional
investors allow short-sellers to trade on the value effect. Extending his argument, we hypothesize
that stocks with higher passive fund ownership will have a lower value premium. Finally, across
all the tests we expect to observe stronger price effects for stocks that are harder to borrow (i.e.,
with high lending fees or otherwise known as “specials”) where short-sale constraints are likely to
be severe (D'Avolio (2002) and Geczy, Musto and Reed (2002)).
All the tests indicate that the price impact of increased passive fund ownership is similar
to the effects of relaxing short-sale constraints, and this effect is stronger for special hard-to-
borrow stocks. The first series of tests show that increased passive fund ownership significantly
lowers downside cross-autocorrelation for specials but it has not effect on upside cross-
6
autocorrelation. In addition, passive fund ownership has no effect on either upside or downside
cross-autocorrelations for stocks with low fees (“general collateral” stocks). The second set of tests
illustrates that passive fund ownership is associated with reduced skewness in stock returns and
this effect is significantly larger for specials. The third test extends Nagel’s (2005) findings by
showing that stocks with more passive institutional ownership exhibit a lower value premium.
Finally, we find that active mutual fund ownership and non-mutual fund ownership have no
significant price impact for the hard-to-borrow stocks or “specials”. The combined evidence on
price impact of passive fund ownership suggests that indexers relax short-sale constraints and
facilitate incorporation of negative information in stock prices contributing to market efficiency.
Our main results hold in a large sample of heterogeneous U.S. stocks across a variety of
specifications controlling for stock and quarter fixed effects as well as for a number of time-
varying variables that have been shown to affect both lending supply and lending demand. At the
same time, identification still remains a concern as certain time-varying factors that determine
supply and demand for shorting can be unobserved.10 To examine whether the effects passive
ownership are casual, we use instrumental variables methodologies that are based on the
reconstitution of Russell 1000 and Russell 2000 indices. While these methodologies help mitigate
identification concerns, they have two important shortcomings for the purposes of our analysis.
First, Russell-based methodologies do not provide any instruments for active and non-mutual fund
ownership which does not allow to compare the effects of different types of ownership within the
same stock. Second, these methodologies operate in a small restricted sample of large and liquid
Russell stocks which are less likely to face short-sale constraints.
10 For example, ownership by passive investors might be correlated with other factors such as the firm’s investment
opportunities -- that are observed by short-sellers but not by the econometrician -- and can directly affect security loan
characteristics.
7
We implement the procedures suggested by Appel, Gormely and Keim (2018) and by Coles,
Heath and Ringgenberg (2018). The main idea is that firms cannot control small variations in their
market capitalization, and therefore index assignment near Russell thresholds are plausibly
exogenous. This process leads to significant differences in index weights around the thresholds
resulting in substantial variation in index ownership and mitigating concerns related to unobserved
heterogeneity across stocks.11
For lending outcomes, we find that our results generally hold in a reasonably causal
framework which attempts to isolate the supply effect across two different samples and
methodologies. Instrumenting passive fund ownership by assignment to Russell 2000, we find
that passive fund ownership increases lending supply and short interest as well as reduces lending
fees. The relationship between loan duration and index fund ownership is positive but not
statistically significant.
When we examine the effects of passive fund ownership on price impact of short-sale
constraints in the sample of large and liquid Russell stocks, we are limited to a very small number
of specials. In particular, our large sample tests involve about 12,000 observations of specials,
whereas in the Russell reconstitution sample we have only 126 to 235 observations of specials.
However, we are still able to document that passive fund ownership lowers downside cross-
autocorrelations for specials. At the same time, we are unable to confirm our large sample results
on skewness and value premium. Finally, we present a battery of tests to show that our findings
11 Other studies that have used various index reassignment methodologies are Chang, Hong, Liskovich (2015), Boone
and White (2015), Crane, Michemaud, and Weston (2016), Schmidt and Fahlenbrach (2017), Wei and Young (2017)
and Heath, Macciocchi, Michaely and Ringgenberg (2019).
8
across Russell reconstitution methodologies are unlikely to be driven by unobserved demand for
shorting.
This paper proceeds as follows. Section 2 explains our contributions to the related literature.
Section 3 describes our data and variables. Section 4 reports our main empirical results. Our
supplemental results based on the Russell index reconstitution are reported in Section 5, and
Section 6 presents our conclusions.
2. Relevant Literature and Our Contribution
Our primary contribution is to show that passive investors play an important role in
relaxing short-sale constraints relative to other institutional investors as measured by multiple
security lending and price impact outcomes across three different samples and methodologies. A
number of studies have analyzed supply and demand in the market for securities lending (D’Avolio
(2002), Asquith, Pathak and Ritter (2005), Cohen, Dietner and Malloy (2007), Blocher, Reed and
Wesep (2013)). These studies focus on an equilibrium framework and they also examine
differential effects of shorting supply and demand. Blocher and Whaley (2016) show that the
security lending by indexers is profitable to fund families and affects fund holdings while Johnson
and Weitzner (2018) argue that this practice leads to distortions in asset allocation impacting fund
returns. Prado, Saffi and Sturgess (2016) study the relationship between various characteristics of
institutional ownership structure and short-sale constraints documenting positive relationship
between holdings of indexers and lending supply among their other results. Our article solely
focuses on passive investing due to its rapidly growing importance and provides a comprehensive
apples-to-apples comparison between the effects of passive funds, active mutual funds and other
institutional investors on short-sale constraints. In addition, we present direct evidence on the
effects of passive investing on actual equilibrium lending outcomes such as short interest, lending
9
fees and loan durations, as well as on price impact of short-sale constraints. We also address
causality concerns implementing multiple Russell reconstitution methodologies.
Our second contribution is to propose a new channel through which a shift to passive
investing can affect securities prices. The theoretical literature in this area focuses on the effects
of passive investing on price pressure and volatility (Basak and Pavlova (2013)), on incorporation
of systemic information in prices (Cong and Xu (2019)), on effort exerted by active managers
(Brown and Davies (2017)), and on reduced informational content of prices due to reduced active
investing (Bond and Garcia (2017), Baruch and Zhang (2018), Garleanu and Pedersen (2018)).
Overall, the theories of asset management typically do not consider the implications of an increase
in passive investing for securities lending and short-sale constraints.
The empirical literature on the price impact of passive investors evolves around the price
pressure effects on volatility and autocorrelations (Ben-David, Franzoni and Moussawi (2018))
together with correlation with index prices movements and trading costs (Israeli, Lee and
Sridharan (2017), Glosten, Nallareddy and Zou (2019), Choi (2017), Coles, Heath and
Ringgenberg (2018)). Most of these papers focus on exchange-traded funds (ETF) with Coles,
Heath and Ringgenberg (2018) being an exception (who focus on all passive investors including
index mutual funds). Unlike these studies, we focus on a different channel through which passive
fund investors can affect security prices. As our study is organized around the effects of passive
fund ownership on the relaxation for short-sale constraints, we depart from the literature on price
pressure and focus on the specific measures of price impact as suggested by the literature on short-
sales constraints (see, for example, Hong and Stein (2003), Geszy, Musto and Reed (2002), Bris,
Goetzman and Zhu (2007), Chang, Cheng and Yu (2007), Xu (2007), and Saffi and Sigurdsson
(2011)).
10
Our final contribution is to examine the causal effect of passive fund ownership on lending
outcomes and on stock prices. Methodologically, we employ the instrumental variables
frameworks suggested by Appel, Gormley and Keim (2018) and Coles, Heath and Ringgenberg
(2018).12 In doing so, we complement the nascent literature on the causal effects of passive
investing on stock prices as well as the literature that studies the effects of passive investing on
other outcomes such as firm value and CEO power (Schnidt and Fahlenbrach (2017)), corporate
governance (Appel, Gormley and Keim (2018)), and product market competition (Azar, Schmalz
and Tecu (2018)).
3. Data and Variables
We combine stock-level mutual fund ownership data together with security lending data
from Markit, accounting and pricing data from CRSP and Compustat as well as Russell index
membership. We describe the construction of the main sample and variables in this section. We
also create a significantly smaller Russell assignment sample that is described in Section 5.
3.1 Fund Holdings
We follow the procedure similar to Iliev and Lowry (2015) and Appel, Gormley and Keim
(2016, 2018). We begin with the CRSP Mutual Fund database and classify domestic equity funds
as passive if CRSP indicates that the fund is an index fund. All the rest of the funds are classified
as active. Next we match fund classification to the mutual fund quarterly holdings from Thomson
Reuters Mutual Fund Holdings S12 database. We calculate stock ownership within each category
by aggregating the holdings of all passive and active funds for each stock-quarter observation. The
12 Among the studies on causal effects of securities lending, Kolasinski, Reed and Ringgenberg (2013) use instruments
for loan demand, whereas Kaplan, Moskowitz and Sensoy (2013) study the effect of supply shocks in an experimental
setting.
11
fund holdings are defined as proportion of shares held by the fund relatively to the total number of
shares outstanding. The number of shares outstanding within each stock-quarter is calculated by
using the information on shares outstanding from CRSP stock data.
We next turn to Thomson Reuters Institutional Ownership S34 database to obtain the
holdings of all 13F institutional investors. We follow Frazzini (2006) and Brav, Jiang and Li (2018)
and drop all the observations where the number of shares held by institutions exceeds the number
of shares outstanding in CRSP. Having this information, we calculate non-mutual fund ownership
as the difference between total institutional ownership and the ownership of passive and active
mutual funds. This definition captures the ownership of other institutional investors such as
pension funds, banks/insurance companies, and endowments. Non-passive ownership is defined
as the difference between total institutional ownership and the ownership of passive mutual funds.
3.2 Security Lending Data
We obtain security lending data from Markit. This daily dataset includes the key security
lending indicators from the vast majority of the U.S. stocks over the period of 2007-2017. We
focus on four key variables: “Active Lendable Quantity” which is a measure of lending supply,
“Quantity on Loan” which is a measure of short interest, “Indicative Fee” which is a measure of
lending fees,13 and “Average Tenure” which measures the average loan duration. We merge Markit
dataset to daily CRSP stock file and keep only U.S. common stocks (share codes 10 and 11).
For each daily stock observation, we first calculate lending supply and short interest as a
proportion of shares reported by Markit relative to total number of outstanding shares from CRSP
13 As in Muravyev, Pearson, and Pollet (2018) we use “Indicative Fees” which are the fees paid by short sellers to
prime brokers. They show that these fees are much greater than fees received by either the custodian or the ultimate
lender, frequently used in the literature.
12
stock data. We next average both quantity variables within each stock-quarter to match with
quarterly holdings data. Lending fees and loan maturity are computed in a similar manner by
averaging the daily Markit data within each stock-quarter.
3.3 Price Impact Measures and Accounting Data
We have hypothesized that passive fund investors help to relax short-sales constraints.
Accordingly, we employ measures of price impact suggested by the literature on shorting. In
particular, we hypothesize that ownership by passive fund investors affect stock prices in the same
manner as relaxing short-sale constraints.
Our first measure of price impact is the downside cross-autocorrelation between lagged
market returns and stock returns (Hou and Moskowitz (2005), Bris, Goetzman and Zhu (2007),
Saffi and Sigurdsson (2011)). For each stock-quarter we calculate the downside cross-auto
correlation using daily stock returns and lagged market return as follows:
𝜌𝑖,𝑡− = 𝑐𝑜𝑟𝑟(𝑟𝑖,𝑑,𝑡, 𝑟𝑑−1,𝑡
𝑀− ), (1)
where 𝑟𝑖,𝑑,𝑡 is the return on stock i in quarter t on day d, and 𝑟𝑑−1,𝑡𝑀− is market returns on
day d-1 in quarter t conditional on market returns being negative. We follow Hou and Moskowitz
(2005) by using the CRSP value-weighted stock market index to obtain daily market returns. The
larger is the correlation of stock returns with past negative market returns, the larger is the delay
in price response to negative information.
Using a similar approach, we also compute upside cross-autocorrelations using positive
market returns and the difference between the downside and the upside autocorrelations as follows:
𝜌𝑖,𝑡+ = 𝑐𝑜𝑟𝑟(𝑟𝑖,𝑑,𝑡, 𝑟𝑑−1,𝑡
𝑀+ ), 𝜌𝑖,𝑡𝐷𝑖𝑓𝑓
= 𝜌𝑖,𝑡− − 𝜌𝑖,𝑡
+ . (2)
13
These measures help to quantity the asymmetry in price adjustment. As short-sale
constraints are not expected to affect the incorporation of positive information in prices, it is useful
to separately analyze upside and downside autocorrelations as well as the difference between them.
As correlations are bounded by -1 and 1, we apply the ln [(1 + 𝜌)/(1 − 𝜌)] transformation to both
of measures of cross-autocorrelations.
Our second measure of price impact is skewness of stock returns. We follow Bris,
Goetzman and Zhu (2007) applying log-transformation to returns, and calculate the skewness of
daily returns within each stock-quarter observation.14 Bris, Goetzman and Zhu (2007), Xu (2007),
Chang, Cheng and Yu (2007) and Saffi and Sigurdsson (2011) find that relaxing short sales
constraints is associated with less skewness in stock returns. We adopt the positive association
between short-sales constraints and skewness when testing the effects of ownership by passive
investors on individual stock returns.
Finally, we merge holdings data to securities lending data as well as the pricing information
from CRSP and accounting variables from Compustat to obtain the final dataset. The definitions
of our variables are provided in the Appendix.
3.4. Summary statistics
Table 1 presents our summary statistics. We observe that passive fund investors own 6%
of shares outstanding for the average U.S. stock. At the same time, the average level of active fund
ownership is 18%, and the average level of non-mutual fund ownership is 45%. While passive
funds are becoming more popular, they still own significantly less shares of the average company
relative to other institutional investors.
14 Our results hold even if we do not log-transform the daily returns.
14
*** Table 1***
The security lending data implies that, for the average stock, much of the lending supply
is not utilized by short sellers; specifically, average supply of lendable shares equals to 19% while
the average aggregate short position equals to only 3%. However, lending fees exhibit a high
degree of variability, wherein the average fee is 2% but the median fee is only 0.05%.15 These
results are consistent with Asquith, Pathak and Ritter (2005) who suggest that borrowing is not too
difficult for most stocks, but there exists some hard-to-borrow-stocks. We also find that the
average loan duration is 80 days.
We observe that individual stock returns are positively skewed and exhibit negative
downside cross-autocorrelation. Finally, the average stock has a market-to-book ratio of three and
a bid-ask spread of 1%.
4. Empirical Results
4.1 Effect of Passive Fund Ownership on Security Lending Outcomes
We begin by investigating the relationship between the ownership of passive funds and
security lending outcomes. In order to do so, we create 20 bins of passive fund ownership and plot
our loan outcomes against these 20 bins. We residualize all the variables on a set of control
variables such as ln (market capitalization), ln (book value of assets), market-to-book, bid-ask
spread as well as stock and quarter fixed effects. Figure 1 illustrates the relationships between
passive fund ownership and security lending variables, i.e., lending supply, short interest, lending
fees and loan duration. We observe a strong positive correlation between passive fund ownership,
lending supply, short interest and loan durations as well as a substantial negative correlation
15 In the case of cash collateral, the lending fee is calculated as the difference between returns on reinvested collateral
(typically, the fed fund rate) and the rebate received by the borrower.
15
between passive fund ownership and lending fees. Our preliminary analysis suggests that stocks
with higher passive fund ownership are cheaper to borrow, exhibit larger aggregate short positions
and are borrowed for longer time periods.
***Figure 1***
We next conduct formal tests by regressing the security lending variables on passive fund
ownership using the following specification:
𝑦𝑖,𝑡 = 𝛼𝑖 + 𝛼𝑡 + 𝛽 ∙ 𝑃𝑎𝑠𝑠𝑖𝑣𝑒𝑖,𝑡 + 𝛾𝑋𝑖,𝑡 + 휀𝑖,𝑡 (3)
where 𝑦𝑖,𝑡 is a security lending outcome for stock i in quarter t, 𝑃𝑎𝑠𝑠𝑖𝑣𝑒𝑖,𝑡 is a level of
passive fund ownership of stock i in quarter t, 𝛼𝑖 are stock fixed effects, 𝛼𝑡 are quarter fixed effects
and 𝑋𝑖,𝑡 is a vector of stock-specific control variables (namely, ln (market capitalization), ln (book
value of assets), market-to-book and bid-ask spread). All the variables are defined in Appendix A.
Standard errors are clustered at the stock level.
Table 2 confirms the stylized facts previously shown in Figure 1. Panel A presents the
evidence for the quantity variables: lending supply and equilibrium short interest. Column (1)
presents the baseline specification only with quarter fixed-effects suggesting that an increase of
one percent in passive fund ownership is associated with a two percent increase in the equilibrium
level of short interest. Column (2) introduces the control variables and the estimated elasticity
slightly declines to 1.83. This column also shows that larger and more liquid stocks have higher
levels of lending supply. Adding stock fixed effects in column (3) and employing within stock
variation in passive fund ownership reduces the elasticity to 0.82. In column (4) we control for
ownership of non-passive funds (actively managed mutual funds and other 13F institutions) and
the estimated elasticity basically remains at the same level. The effect is economically sizable,
16
namely, a one standard deviation increase in passive fund ownership is associated with an increase
in half-standard deviation in lending supply.
*** Table 2***
We hence examine whether the supply increase driven by passive fund ownership results
in a higher level of short interest. The results are reported in columns (5) – (9). As can be seen, the
coefficient on passive fund ownership is always positive and significant at the one percent level.
The most restrictive specification in column (8) indicates that a one percent increase in passive
fund ownership results into an increase of 18 basis points in the level of short interest. These results
indicate that for the average stock, 25% of the additional supply produced by passive investors (18
basis points out of 78 basis points) is utilized by short sellers.
Panel B repeats the analysis and studies the effects passive fund ownership on lending fees
and security loan durations. The baseline specification (column (1)) indicates that an increase of
one percent in passive fund ownership is associated with a reduction of 31 basis points in lending
fees. Introducing additional control variables as well as stock fixed-effects leads to a considerable
decline in the estimated coefficient to three basis points. However, this effect is still economically
meaningful as moving from the 25th percentile (one percentage point) to the 75th percentile (10
percentage points) of the passive fund ownership reduces lending fees by 27 basis points.
We then examine the effect of passive fund ownership on security loan duration. Columns
(5) – (8) of Panel B demonstrate that higher level of passive fund ownership results in longer
duration of stock loans. According to the most restrictive specification in column (8), a change of
one-standard deviation in passive fund ownership results in the increase of seven days in average
stock loan duration.
17
In sum, the results presented in Figure 1 and Table 2 suggest that stocks with higher levels
of passive fund ownership face weaker short-sale constraints as measured by multiple security
lending outcomes.
4.2 Differential Impact of Passive Funds and Other Securities Lenders
Having established the baseline effects of passive funds on security lending, we hence
examine if passive funds have a larger economic impact on lending outcomes than other
institutional investors. The size of lendable assets by types of beneficial owners is not precisely
known (Balkanova, Copeland and McCaughrin (2015)). However, the typical security lender is a
large institutional investor managing a low-levered portfolio of securities. Mutual funds, pension
funds, endowments and insurance companies represent the majority of lenders (Balkanova, Caglio,
Keane and Porter (2016)).
To address this question, we split institutional ownership of a given stock into three
categories: ownership by passive funds, ownership by active mutual funds and ownership by non-
mutual fund 13F institutions such as pension funds, endowments, and banks/insurance companies.
We use the following regression model:
𝑦𝑖,𝑡 = 𝛼𝑖 + 𝛼𝑡 + 𝛽1 ∙ 𝑃𝑎𝑠𝑠𝑖𝑣𝑒𝑖,𝑡 + 𝛽2 ∙ 𝐴𝑐𝑡𝑖𝑣𝑒𝑖,𝑡 + 𝛽3 ∙ 𝑁𝑜𝑛𝑀𝐹𝑖,𝑡 + 𝛾𝑋𝑖,𝑡 + 휀𝑖,𝑡 (4)
where 𝑦𝑖,𝑡 is a security lending outcome for stock i in quarter t, 𝑃𝑎𝑠𝑠𝑖𝑣𝑒𝑖,𝑡 is the level of
passive fund ownership of stock i in quarter t, 𝐴𝑐𝑡𝑖𝑣𝑒𝑖,𝑡 is the level of active mutual fund
ownership of stock i in quarter t, 𝑁𝑜𝑛𝑀𝐹𝑖,𝑡 is the ownership by non-mutual fund institutions of
stock i in quarter t, 𝛼𝑖 are stock fixed effects, 𝛼𝑡 are quarter fixed effects and 𝑋𝑖,𝑡 is a vector of
stock-specific control variables (namely, ln( market capitalization), ln(book value of assets),
market-to-book- and bid-ask spreads).
18
Table 3, Panel A presents the results. The first two columns show that passive funds have
a significantly larger effect on lending supply relatively to both active funds and non-mutual funds.
Specifically, an increase of one percent in passive fund ownership results in an increase of 0.76%
in lending supply, while an increase of one percent in active fund ownership contributes 0.25% to
lending supply. Non-mutual funds have the smallest impact as an increase of one percent in their
ownership results in 0.17% increase in lending supply.
*** Table 3***
The dominating effects of passive investors on security lending can be seen throughout the
rest of the outcomes. Passive funds have twice the effects on lending fees and loan durations
relative to active mutual funds. The larger effect on loan durations suggest that short-sellers may
prefer passive investors as stock lenders who are less likely to recall the stock for their own needs.
Passive investors also have larger effects on equilibrium short interest relative to both actively
managed mutual funds and non-mutual funds. Panel B formally evaluates the differences in the
magnitude of the coefficients and confirms the importance of passive funds. In particular, the
difference between coefficients of passive versus active funds is statistically significant at one
percent level for lending supply and loan duration. It is also statistically significant at the 10
percent level for short interest and lending fees. Non-mutual funds appear to have the least impact,
having substantially smaller coefficients when compared to both passive and active funds.
Our sample spans over 2007-2017 when passive investing was consistently gaining market
share. In particular, in the early sample period index funds and ETFs represented a significantly
lower share of the U.S. mutual fund market. In Table 4, we examine the effects across sub-samples
by interacting the ownership variables with a dummy that equals one if the observation belongs to
the pre-2012 period. The main effects remain similar to Table 3 and passive investing still produces
19
the largest impact on all the lending outcomes. In addition, the interaction terms reveal that passive
investing had an especially large effects on short interest and loan duration earlier in the sample.
This result suggests that at times of relatively scarce passive ownership, it had an even stronger
impact on selected lending outcomes.
*** Table 4***
Overall, the findings establish a clear hierarchy among various institutional investors in
their impact on securities lending outcomes. Passive funds appear to participate the most in lending
programs, followed by active mutual funds, and lastly by other institutional asset managers.
4.3 Effect of Passive Fund Ownership on Price Impact of Short-Sale Constraints
Having established the effects of passive investors on securities lending outcomes, we turn
to pricing implications. Given the results in Tables 2 and 3, we hypothesize that the price impact
of the increased passive fund ownership is similar to the effects of relaxing short-sale constraints.
We test this hypothesis using three different approaches from the literature on short selling.
In addition, the relaxation of short-sale constraints will generate stronger effect on stock
prices when these constraints are initially more severe. Capitalizing on this idea, we expect to
observe larger price consequences for the stocks that are harder to borrow. We follow D’Avolio
(2002) and Gezcy, Musto and Reed (2003) using the lending fee as a proxy for the severity of the
short-sale constraints. In our regression analysis, we split the sample into the following two types
of stocks based on their lending fees: “general collateral” (GC) stocks with a fee of less than 2%,
and “specials” or hard-to-borrow stocks with a lending fee larger than 2%.16 Our hypothesis across
16 The 2% cutoff implies that roughly 10% of stocks are defined as specials consistent with D’Avolio (2002). Our
results are also robust to the cutoff fee of 1% from D’Avolio (2002) or to the cutoff fee of 3%.
20
all the tests is that the effect of passive fund ownership on price impact of short-sale constraints is
more pronounced for the hard-to-borrow stocks when compared to other stocks.
4.3.1 Cross-autocorrelations
Following Bris, Goetzmann and Zhu (2007), and Saffi and Sigurdsson (2011), we
hypothesize that if stocks with higher passive fund ownership benefit from relaxed short-sale
constraints, then they would be expected to exhibit lower cross-autocorrelations with lagged
market returns conditional on market returns being negative. The top graphs of Figure 2 provide
the initial descriptive evidence presenting the relationship between passive fund ownership and
downside cross-autocorrelations separately for special and general collateral stocks using an
approach similar to the construction of Figure 1. Consistent with the literature, the figure shows
that hard-to-borrow stocks have higher downside cross-autocorrelation in comparison with other
stocks. We can also see that when passive fund ownership within a stock increases, downside
cross-autocorrelation declines for specials at a much higher rate than for GC stocks. This
descriptive evidence suggests that specials with high level of passive fund ownership exhibit faster
price discovery conditional on negative information.
***Figure 2***
Table 5 presents the formal regression results using econometric specifications based on
equation (4) across “special” and “GC” stocks. Column (1) shows that a within stock increase in
passive fund ownership results in lower downside cross-autocorrelation for specials and this effect
is statistically significant at the five percent level. We also see that neither active fund ownership
nor non-mutual fund ownership affects downside cross-autocorrelation for specials. Column (2)
shows that there is no effect of passive fund ownership on downside cross-autocorrelation for
21
general collateral stocks. Columns (3) – (4) analyze the upside cross-autocorrelations and finds
that the impact of passive fund ownership on the speed of incorporation of positive information
into stock prices is statistically insignificant. Columns (5) - (6) report the results for the difference
between the upside and the downside cross-autocorrelations and find that the asymmetric effect is
especially pronounced for specials.
*** Table 5***
These results confirm that price discovery conditional on negative information is faster for
constrained stocks when passive fund ownership is higher. Consistent with the short-selling
literature, the effect of passive fund ownership on adjustment of prices to information is
asymmetric, namely, the speed of incorporation of positive information is not affected.
4.3.2 Skewness
We next analyze the effect of passive fund ownership on skewness of stock returns. The
bottom panel of Figure 2 presents the relationship between passive fund ownership and skewness
similarly to our analysis of cross-autocorrelations. Consistent with the predictions by Xu (2007),
we can see that hard-to-borrow stocks exhibit higher skewness relatively to other stocks. We also
observe that when passive fund ownership increases, skewness steadily declines and this
relationship is stronger for specials. The figure suggests that higher passive fund ownership is
associated with less skewness in individual stock returns - which is in accordant with the relaxation
of short-sale constraints.
Table 6 confirms the result through regression tests. Columns (1) and (2) present the effects
of passive fund ownership on the skewness of stock returns separately for special and GC stocks.
We can see that the coefficient on passive fund ownership is negative and the magnitude of the
22
effect is significantly larger for specials. Both coefficients are statistically significant at the one
percent level. In addition, the effect of active mutual fund ownership on skewness is more than
twice smaller while the effect of non-mutual fund investors is positive.
*** Table 6***
In sum, the evidence on the relationship between passive fund ownership and stock return
skewness is in line with the papers that document a negative relationship between relaxation of
short-sale constraints and skewness (Bris, Goetzman and Zhu (2007), Xu (2007), Chang, Cheng
and Yu (2007) and Saffi and Sigurdsson (2011)).
4.3.3 Value Premium
Our final test is based on Nagel (2005), who shows that ownership by two prominent
security lenders, namely, the Vanguard S&P 500 Index Fund, and Dimensional Fund Advisors, is
associated with a reduced value premium. He suggests that this effect exists because security
lending activities of these insitutional investors allow short-sellers to trade on known price
anomalies. Conequently, we hypothesize that stocks with higher ownership by passive indexers
might exhibit a reduced value premium.
We closely follow Nagle’s (2005) methodology. As in his paper, we transform all return
predictors into decile ranks each quarter and scale them such that their values fall into interval
between 0 and 1. Our dependent variable is the return over four quarters from t+1 to t+4, which
is regressed on quarter t stock characteristics. To be consistent with our previous results, we use
the same stock characteristics that we employed in the previous analysis.
Table 7 presents the results. Columns (1)-(2) show the results for the hard-to-borrow
special stocks, and columns (3)-(4) show the results for the general collateral stocks. In column
23
(1), the returns are regressed on the ownership variables, on market-to-book, controlling for other
stock characteristics as well as quarter and stock fixed-effects. The coefficient on market-to-book
is negative and significant which confirms the presence of the value premium. Consistently with
Nagel (2005) and Asquith, Pathak and Ritter (2005), we also observe that stocks with higher
institutional ownership of any type have lower future returns. In Column (2) we interact market-
to-book with the different types of institutional ownership. The coefficient on market-to-book
implies that if a given stock is moved into the lowest ownership decile across all the investor types,
the difference in returns between top and bottom market-to-book deciles becomes 56% per year.17
However, if we go to the highest decile of passive fund ownership, holding ownerships by other
funds fixed, the value effect is reduced by more than two-thirds (44%). We note that neither
ownership by active mutual funds nor by non-mutual fund institutional investors has a significant
effect on the value premium in the sample of hard-to-borrow stocks. Consistent with our results
on other measures of price impact of short-sale constraints, we observe that the effect of passive
fund ownership on the value premium is twice smaller for general collateral stocks.
*** Table 7***
Overall, our results in Tables 4-6 provide consistent evidence that increased passive fund
ownership generates price impact similar to the impact of relaxing short-sale constraints
documented by the literature. We confirm that passive investors improve the speed of
incorporation of negative information into stock prices, reduce the likelihood of large negative
returns as well as diminish value premium. These effects are more pronounced for the constrained,
17 Note that our regression specifications include stock fixed effects. Therefore, we interpret the economic magnitude
of the coefficient as moving the same stock from the extreme growth decile to the extreme value decile, and conversely.
24
hard-to-borrow, special stocks as suggested by D’Avolio (2002) and Gezcy, Musto and Reed
(2003).
5. Russell Indices Reconstitution Test
While our results are robust to the inclusion of a rich set of control variables as well as
quarter and stock fixed-effects, identification still remains a concern. Specifically, certain stock–
specific time-varying parameters that determine supply and demand for shorting, such as
valuations of marginal investors and short-sellers, are unobserved. For example, ownership by
passive investors can be correlated with other factors such as the firm’s investment opportunities
that might be observed by short-sellers but are not observed by econometrician, and can directly
affect security loan characteristics. In this section, we develop an identification strategy that draws
from the literature on Russell indices reconstitution and the effects of passive fund ownership.
Methodologically, we present the instrumental variables framework suggested by Appel, Gormley
and Keim (2018) who study the effects of passive investors on corporate governance.18 While
Russell-based methodologies help mitigate identification concerns, they have two important
shortcomings for the purposes of our analysis. First, Russell-based methodologies do not provide
any instruments for active and non-mutual fund ownership which does not allow to compare the
effects of different types of ownership within the same stock. Second, these methodologies operate
in a small restricted sample of large and liquid Russell stocks which are less likely to face short-
sale constraints.
18 See Appel, Gormley and Keim (2019) for a discussion of various methodologies based on Russell indices
reconstitutions.
25
5.1 Sample construction
Our sample construction procedure follows Appel, Gormely and Keim (2018). Markit
provides data on security lending starting in 2007, and in the same year Russell implemented a
new assignment regime known as “banding.” First, stocks are sorted based on May market
capitalizations and then two bands around the stock ranked 1000th are generated. Each band’s
width is equal to 2.5% of the total May market capitalization of the entire Russell 3000 index. The
stocks within the band do not change their index assignment from the last year.
Consider the following example. After the Russell banding procedure, the two following
thresholds around the 1000 rank were created.: an upper threshold of 875 and a lower threshold of
1100. In this example, all 225 stocks ranked in between 875-1100 are not predicted to change their
index assignment as they fall within the band (the variable Band equal to one and zero otherwise,
in Equation (5) below). The stocks ranked above 875 are predicted to be reassigned to Russell
1000 only if they were assigned to Russell 2000 in the previous year. The stocks ranked below
1100 are predicted to be reassigned to Russell 2000 only if they were included in Russell 1000 in
the previous year. Effectively, the banding procedure generates two cutoffs instead of one (a rank
of 1000) and creates an assignment process that is relatively difficult to manipulate.
Following Appel, Gormely and Keim (2018) we construct our sample selecting top 250
stocks in Russell 2000 and bottom 250 stocks in Russell 1000. Table 8 presents the descriptive
statistics for this sample. The variables of interest are calculated for the 3rd quarter in any given
year as this quarter exactly follows the annual June reconstitution.19 For the average stock, 9% are
owned by passive funds and 18% are owned by active funds. The overall level of institutional
19 Our results are also robust to calculating variables of interest over the 4th quarter.
26
ownership is 78%. All these variables are higher than at the larger sample of stocks used in the
analysis of the previous sections. These differences come from the fact that the cutoff sample
stocks are relatively large due to being highly ranked members of the Russell indices and therefore
exhibit much higher level of institutional ownership.
*** Table 8***
5.2 Methodology
We follow Appel, Gormley and Keim (2018) to identify the effects of passive fund
ownership on securities lending and price impact of short-sale constraints. In particular, we use
the inclusion into Russell 2000 as an instrument for ownership of passive funds. The assignment
into Russell 2000 is determined by the following factors: i) end-of May market capitalization of
the stock, ii) whether the stock is “banded” by Russell and does not switch indices in a given year,
iii) whether the stock was included in Russell 2000 during the last reconstitution year, iv) the
interaction between the two indicators. In addition, stock index weights are determined by end-of-
June float-adjusted market capitalization calculated by Russell. Therefore, we include the above
determinants of index assignment in our specifications. In particular, we estimate the following
first stage regression:
𝑃𝑎𝑠𝑠𝑖𝑣𝑒𝑖,𝑡 = 𝛼 + 𝛽𝑅𝑢𝑠𝑠𝑒𝑙𝑙2000𝑖,𝑡 + ∑ 𝜃𝑛(ln(𝑀𝑎𝑟𝑘𝑒𝑡𝐶𝑎𝑝𝑖,𝑡))𝑛
𝑁
𝑛=1
+ 𝛾 ln(𝐹𝑙𝑜𝑎𝑡𝑖,𝑡)
+ 𝜇1𝑅𝑢𝑠𝑠𝑒𝑙𝑙2000𝑖,𝑡−1 + 𝜇2𝐵𝑎𝑛𝑑𝑖,𝑡 + 𝜇3𝑅𝑢𝑠𝑠𝑒𝑙𝑙2000𝑖,𝑡−1 × 𝐵𝑎𝑛𝑑𝑖,𝑡 + 𝜏𝑡+휀𝑖,𝑡 (5)
where 𝑃𝑎𝑠𝑠𝑖𝑣𝑒𝑖,𝑡 is the amount of passive ownership for stock i in year t, 𝑅𝑢𝑠𝑠𝑒𝑙𝑙2000𝑖,𝑡 is an
indicator variable equal to one if the stock is included in Russell 2000 in year t, 𝑀𝑎𝑟𝑘𝑒𝑡𝐶𝑎𝑝𝑖,𝑡 is
the end-of-May market capitalization from CRSP, 𝐹𝑙𝑜𝑎𝑡𝑖,𝑡 is the end-of-June float-adjusted market
27
capitalization calculated by Russell, 𝐵𝑎𝑛𝑑𝑖,𝑡 is an indicator variable equals one if the stock i is
within the band in year t and 𝑅𝑢𝑠𝑠𝑒𝑙𝑙2000𝑖,𝑡−1 is an indicator variable equal to one if the stock is
included in Russell 2000 in year t-1. Finally, we cluster our standard errors at the individual stock
level.
Our second stage estimation mirrors the specification from the first-stage and estimates the
effects of passive fund ownership on security lending and price impact variables. In particular, we
implement the following regression model:
𝑦𝑖,𝑡 = 𝜗 + 𝛿𝑃𝑎𝑠𝑠𝑖𝑣𝑒𝑖,𝑡̂ + ∑ 𝜑𝑛(ln(𝑀𝑎𝑟𝑘𝑒𝑡𝐶𝑎𝑝𝑖,𝑡))
𝑛𝑁
𝑛=1
+ 𝜌 ln(𝐹𝑙𝑜𝑎𝑡𝑖,𝑡) + 𝜎1𝑅𝑢𝑠𝑠𝑒𝑙𝑙2000𝑖,𝑡−1
+ 𝜎2𝐵𝑎𝑛𝑑𝑖,𝑡 + 𝜎3𝑅𝑢𝑠𝑠𝑒𝑙𝑙2000𝑖,𝑡−1 × 𝐵𝑎𝑛𝑑𝑖,𝑡 + 𝜖𝑡 + 𝑢𝑖,𝑡 (6)
where 𝑦𝑖,𝑡 is an outcome of interest for stock i in year t and 𝑃𝑎𝑠𝑠𝑖𝑣𝑒̂𝑖,𝑡 is the predicted level of
passive fund ownership for stock i in year t from the first stage estimation.
Our methodology is based on two identification assumptions. First, inclusion in Russell
2000 should affect the level of passive fund ownership after controlling for the criteria used by
Russell when determining index assignment in any given year. This condition is verified below
through the first-stage estimation. Second, inclusion in Russell 2000 should not directly affect our
outcomes of interest except through its impact on ownership by passive funds. As we argue that
the effect of passive fund ownership operates only through the increase of supply of lendable
shares, our primary concern is the effect of inclusion on shorting demand in the next three months
following index reconstitution. Chang, Hong and Liskovich (2014) demonstrate that inclusion in
Russell 2000 generates predictable short-term price increase. If market participants act on this and
28
reduce their short positions around the inclusion, our results cannot be solely attributed to the
increased supply provided by passive investors.
A related concern is that short-selling activity can affect index inclusion rather than the
other way around. Stocks are ranked by their market capitalization at the end of May to determine
index assignments. If an increased demand for shorting reduces stock price and market
capitalization around the rank day, stocks with higher levels of short interest might be assigned to
Russell 2000 due to lower market capitalization.
To address the first concern and bolster our assumption regarding the exclusion restriction,
we will show in latter tests that our instrument is not related to other factors that have been shown
to affect shorting demand including stock characteristics such as the bid-ask spread, market-to-
book and the book value of assets. We will also present evidence that our instrument is not related
to long positions of other institutions suggesting that these investors do not actively trade on the
expected price increase. In addition, we will illustrate that the level of short-selling activity does
not exhibit any irregularities around the reconstitution days for stocks that switch indices.
With respect to the second concern, we control for stock market capitalization in May in
multiple ways using polynomials of various ranks. Additionally, we document the lack of
abnormal short-selling activity around the ranking days for stocks that move between the indices.
5.3. First-Stage
Table 8 presents the first-stage regressions using first-, second-, and third-order
polynomials when controlling for market capitalization. The results confirm that Russell 2000
membership is strongly associated with an increase in passive fund ownership. According to Panel
A, the inclusion in Russell 2000 is translated into an increase of 2% in ownership by passive funds
29
which amounts to half a standard deviation. This effect is consistent across the polynomials of
different orders.
The table also shows that the inclusion in Russell 2000 does not induce statistically
significant change in neither the level of active mutual fund ownership nor the level of non-mutual
fund ownership. These findings suggest that the increase in lending supply and the resultant
changes in fees and short interest are the most likely to come from the effect of increased passive
fund ownership as there is no change in holdings of other potential security lenders. In addition,
this evidence implies that following the inclusion in Russell 2000 actively trading institutions do
not increase their long positions suggesting that the average institutional investor does not actively
trade based on short-term price increase (as documented by Chang, Hong and Liskovich (2014)).
*** Table 9***
5.4 Effects of Passive Fund Ownership on Securities Lending Outcomes: Russell Sample
Table 10 presents the effects of passive fund ownership on security lending outcomes
employing the instrumental variables approach. Panel A focuses on quantities and columns (1)-(3)
show the effect of passive fund ownership on lending supply. Our identification strategy confirms
that higher ownership by passive investors results in greater supply of shares to short-sellers. The
effect is economically meaningful such that an increase in one standard deviation in passive fund
ownership is associated with an increase of one standard deviation in lending supply.20 Columns
20 At the first glance it appears than a 1% increase in passive ownership increases lending supply by more than 1%.
However, one should remember that passive ownership is reported by CRSP at the end of the 3rd quarter, while lending
supply is defined as an average lending supply over the third quarter. For a sake of clarification, consider a simple
example. Lending supply is reported three times per quarter: July 31st - 2%, August 31st - 3% and September 31st –
0.7%. Passive ownership is reported on September 31st only, and equals to 1% such that on this date the lending supply
is significantly smaller than the passive ownership. Due to mutual fund reporting, it is impossible to determine the
level of passive ownership on the rest of the dates. At the same time, the average lending supply over the 3rd quarter
equals to 1.9% and appears to be larger than the passive ownership.
30
(4)- (6) confirm the effects of passive fund ownership on the size of the short positions. This effect
is also both economically and statistically significant as one standard deviation increase in passive
fund ownership leads to one standard deviation increase in short interest.
*** Table 10***
The effects of passive fund ownership on lending fees and loan maturity are shown in Panel
B. Columns (1)-(3) show that passive ownership reduces lending fees with this effect being
statistically significant at the 10 percent level. This effect is economically large, a one standard
deviation increase in passive fund ownership is associated with one standard deviation reduction
in lending fees. Columns (4)-(6) presents the results for loan duration and documents negative
effect of passive fund ownership which is not statistically significant at the conventional levels.
In sum, our instrumental variables approach on the much smaller Russell reconstitution
sample yields results that are generally consistent with those obtained using the fixed-effects
methodology in our much larger sample.
5.5 Effects of Passive fund ownership On Price Impact of Short-Sale Constraints: Russell
Sample
We closely follow the methodology presented in Section 4 and split our sample into hard-
to-borrow specials as well as low-fee general collateral stocks. As our small sample consists of
large and liquid member of Russell indices, the number of stocks with lending fee above 2% per
year is highly limited. In particular, we are constrained to 126 stock-year observations while in the
large sample we use about 12,000 observations of specials. Accordingly, the smaller sample can
substantially restrict our ability to detect the casual effects of passive fund ownership on prices of
hard-to-borrow stocks.
31
Table 11 presents the results for the impact of passive fund ownership on stock prices.
Panel A shows the results for cross-autocorrelation variables and, despite very low number of
specials, confirms our previously documented findings. Column (1) shows that higher levels of
passive fund ownership result into faster incorporation of negative information in prices of special
stocks as measured by downside cross-autocorrelations with past market returns. Consistent with
our previous findings, column (2) confirms that there is no effect of passive fund ownership on
speed of price discovery in the sample of GC stocks that are less likely to experience short-sale
constraints. Columns (3)-(6) show the results are robust to different polynomial specifications.
The analysis of the effects of passive fund ownership on skewness (Panel B) and value premium
(Panel C) does not yield any significant results in our small sample of Russell specials. 21
*** Table 11***
In sum, we find similar results for downside cross-autocorrelations in a much smaller
Russell sample of special stocks, although the statistical significance is weaker relatively to our
initial large sample results.
5.6 Robustness Tests
In our main analysis, we follow Appel, Gormley and Keim (2018), and construct our
sample using 250 top stocks in Russell 2000 and 250 bottom stocks in Russell 1000. However, our
results are robust to using other than the 250 cutoff. Table B.1 in Appendix B examines the
robustness of our results to specifications using samples of 200, 300, 400 and 500 of top Russell
21 In the analysis of value premium, we face two endogenous variables – passive ownership and its interaction with
market-to-book. Consequently, we use two instrumental variables, Russell 2000 dummy and its interaction with
market-to-book in our econometric model.
32
2000 and bottom Russell 1000 stocks. We observe that our estimates as well as their significance
are generally not sensitive to the choice of bandwidth.
*** Table B1 in Appendix B***
To strengthen our assumption regarding the exclusion restriction, we study the relationship
between our instrument and other variables that have been shown to affect demand for shorting.
Table B.2 in Appendix B presents the result for three such variables: bid-ask-spreads, market-to-
book, and book value of assets, as they have been shown to be related to security lending outcomes
in Table 2. We observe that the relationship between inclusion in Russell 2000 and each of these
variables is not statistically significant, which allows us to gain additional confidence in our
identification strategy.
*** Table B2 in Appendix B***
To further support that our results are not contaminated by major variation in shorting
demand, we study the short-selling activity around reconstitution days and rank days. Figure B.1
in Appendix B presents the graphical results and show the lack of abnormal shorting activity
around both reconstitution and rank days. Table B.3 in Appendix B presents the results of
regression of daily short interest on dummy that equals one if a date falls into a 5-day window
around rank day (columns (1)-(2)) or reconstitution day (columns (3)-(4)). The regression results
confirm the previously shown graphical results illustrating the lack of irregular shorting activity
around these days.
*** Figure B1 and Table B3 in Appendix B***
We also implement an additional methodology developed by Coles, Heath and
Ringgenberg (2018) that utilizes Russell assignments thresholds in the post-2007 period similar to
33
that used by Appel, Gormley and Keim (2018). Appendix C briefly describes their approach as
well as presents the results which are generally similar to our previous findings.
Finally, we examine if the financial crisis interferes with our results. As in Fahlenbrach,
Prilmeier and Stulz (2012), we define the crisis period as 2007q3 to 2008q4, and exclude it from
our sample. None of our results changed significantly.
6. Conclusions
In this paper, we propose and analyze a security lending channel through which passive
investors can affect security prices. We find that passive funds operate as significant lenders of
shares to arbitrageurs and by doing so relax short-sale constraints. We empirically confirm the
effects of passive investors by showing that their security lending activities expand the supply of
lendable stock leading to larger short positions, lower lending fees and longer loan durations. As
a result, stocks with more passive fund ownership exhibit faster price discovery, lower likelihood
of large negative returns and a smaller value premium.
Our findings yield two main implications. First, recent research has argued the increase in
passive investing can make prices less efficient as these investors do not actively seek out and
utilize security-specific information when making investment decisions, and generate price
pressure. However, our study suggests that passive investors complement information-seeking
efforts of active investors who employ short-selling strategies. While our results do not resolve the
ongoing debate, they provide a channel by which passive investing increases amount of
information incorporated in prices. Specifically, the relaxation of short-sale constraints can lead to
more information being reflected in stock prices.
Second, our study argues for the inclusion of security lending activity in theoretical models
of passive and active investing. The recent advances in these area focuses on price pressure and
34
information acquisition, and do not take into account the effects of passive investing on short-sale
constraints. The incorporation of these effects into the theories of asset management can lead to a
better understanding of the aggregate effect of passive investing on financial markets.
35
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40
Figure 1
This figure presents the relationships between passive fund ownership and security lending
outcomes: lending supply, short interest, lending fee and loan duration. The figure uses binned-
scatter plots with 20 bins of passive fund ownership. We residualize all the variables on a set of
control variables such as ln (market capitalization), ln (book value of assets), market-to-book, bid-
ask spread as well as stock and quarter fixed effects. Detailed definitions of variables can be found
in the Appendix A.
41
Figure 2
This figure presents the relationships between passive fund ownership, downside cross-
autocorrelations and skewness of daily returns. The figure uses binned-scatter plots with 20 bins
of passive fund ownership. We residualize all the variables on a set of control variables such as ln
(market capitalization), ln (book value of assets), market-to-book, bid-ask spread as well as stock
and quarter fixed effects. Detailed definitions of variables can be found in the Appendix.
42
Table 1: Summary Statistics, Full Sample
This table presents summary statistics for our 2007-2017 quarterly panel of stocks. Detailed definitions of
variables can be found in the Appendix. Ownership variables are calculated using end-of-the-quarter ownership
as reported by Thomson Reuters Mutual Fund Holding database. The definitions of ownership types are based
on CRSP Mutual Fund database. The security lending variables are from Markit and represent daily averages
within each stock-quarter observation. The price impact and control variables are calculated using CRSP and
Compustat.
Stock-quarter level variables N Mean Std.
Dev.
Median Min. Max.
Ownership variables
Passive fund ownership (fraction) 121,405 0.06 0.05 0.06 0.00 0.55
Active fund ownership (fraction) 121,405 0.11 0.09 0.10 0.00 0.87
Total mutual fund ownership (fraction) 121,405 0.18 0.12 0.17 0.00 0.89
Non-mutual fund ownership (fraction) 121,109 0.45 0.20 0.48 0.00 0.99
Total institutional ownership (fraction) 121,405 0.62 0.27 0.69 0.00 1.00
Non-passive ownership (fraction) 121,109 0.56 0.25 0.61 0.00 1.00
Security lending variables
Lending supply (fraction) 121,383 0.19 0.11 0.20 0.00 0.42
Short interest (fraction) 121,326 0.03 0.04 0.02 0.00 0.24
Lending fee (fraction) 121,307 0.02 0.06 0.00 0.00 1.20
Loan duration (days) 121,326 80.53 67.86 63.52 3.17 463.86
Price impact variables
Downside cross-autocorrelation 121,232 -0.06 0.44 -0.05 -13.57 15.72
Upside cross-autocorrelation 121,237 0.00 0.38 -0.01 -9.57 10.46
Downside minus upside 121,209 -0.06 0.57 -0.05 -13.14 15.15
Skewness 121,289 0.24 1.32 0.19 -7.34 7.78
Control variables
Log(market value) 121,305 20.37 1.95 20.20 13.61 27.48
Log(book value) 112,549 19.71 1.83 19.53 6.91 26.59
Market-to-book 113,533 3.00 3.82 1.83 0.30 27.29
Bid-ask spreads (fraction) 121,305 0.01 0.01 0.00 0.00 0.31
43
Table 2: Effects of Passive Fund Ownership On Security Lending Outcomes
This table reports the results from regressing security lending outcomes on passive ownership and a set of control variables. Detailed
definitions of variables can be found in the Appendix. Panel A reports the results on quantity variables. Column (1) reports the baseline
specification for lending supply including quarter fixed-effects, column (2) adds control variables and column (3) adds stock fixed-
effects. Column (4) adds ownership of non-passive institutional investors as an additional control variable. Columns (5) - (8) repeat the
specifications from columns (1) - (4) using short interest as dependent variable. Panel B reports the results for fees (columns (1) - (4))
and loan duration (columns (5) - (8)). *, **, and *** denote statistical significance at 10%, 5% and 1% levels respectively. Standard
errors clustered by stock are in parentheses.
(1) (2) (3) (4) (5) (6) (7) (8)
Panel A:Quantities
y = Lending supply y = Short interest
Passive fund ownership 2.12*** 1.83*** 0.82*** 0.78*** 0.29*** 0.35*** 0.20*** 0.18***
(0.02) (0.03) (0.02) (0.02) (0.01) (0.01) (0.02) (0.02)
Non-passive ownership 0.18*** 0.11***
(0.00) (0.00)
Log(market value) 0.01*** 0.01*** 0.00 0.00*** -0.01*** -0.01***
(0.00) (0.00) (0.00) (0.00) (0.00) (0.00)
Log(book value) 0.00** 0.02*** 0.01*** -0.00*** 0.01*** 0.00***
(0.00) (0.00) (0.00) (0.00) (0.00) (0.00)
Market-to-book -0.00*** 0.00*** 0.00*** -0.00*** 0.00*** 0.00***
(0.00) (0.00) (0.00) (0.00) (0.00) (0.00)
Bid-ask spread -1.23*** -0.32*** -0.17*** -0.78*** -0.41*** -0.33***
(0.07) (0.04) (0.03) (0.03) (0.03) (0.02)
Observations 121,383 112,515 112,279 112,098 121,326 112,471 112,237 112,060
𝑅2 0.62 0.65 0.88 0.90 0.12 0.18 0.57 0.61
Quarter fixed-effects Yes Yes Yes Yes Yes Yes Yes Yes
Stock fixed-effects No No Yes Yes No No Yes Yes
44
(1) (2) (3) (4) (5) (6) (7) (8)
Panel B:Fee and Loan
Maturity
y = Lending fee y = Loan duration
Passive fund ownership -0.31*** -0.20*** -0.04*** -0.03*** 159.52*** 325.77*** 146.03*** 140.21***
(0.01) (0.01) (0.01) (0.01) (14.30) (14.88) (21.51) (21.43)
Non-passive ownership -0.02*** 28.53***
(0.00) (4.48)
Log(Market value) 0.00*** -0.01** -0.00*** -7.67*** -18.63*** -20.24***
(0.00) (0.00) (0.00) (0.66) (1.15) (1.14)
Log(Book value) -0.00*** -0.00 -0.00 1.02 3.62*** 2.96***
(0.00) (0.00) (0.00) (0.65) (0.99) (0.98)
Market-to-book -0.00*** -0.00* -0.00* 0.16 0.22 0.21
(0.00) (0.00) (0.00) (0.21) (0.21) (0.20)
Bid-ask spread -0.06 -0.10** -0.12*** -396.53*** 129.94* 156.72**
(0.04) (0.04) (0.04) (67.78) (67.64) (68.54)
Observations 121,307 112,455 112,221 112,044 121,326 112,471 112,237 112,060
𝑅2 0.06 0.11 0.58 0.58 0.03 0.05 0.32 0.32
Quarter fixed-effects Yes Yes Yes Yes Yes Yes Yes Yes
Stock fixed-effects No No Yes Yes No No Yes Yes
45
Table 3: Differential Impact of Institutional Investors on Security Lending Outcomes
This table reports the results from regressing security lending outcomes on ownership of various institutional investors. Detailed
definitions of variables can be found in the Appendix. Panel A reports the regression results. Column (1) reports the baseline
specification for lending supply including stock and quarter fixed-effects and column (2) adds ownership by non-mutual fund
institutional investors. Columns (3) and (4) repeat the specifications using short interest as the dependent variable. Columns (5) and (6)
report the results for lending fees and columns (7) and (8) report the results for loan duration. Panel B reports the p-values of test for the
differences between every pair of coefficients in Panel A. *, **, and *** denote statistical significance at 10%, 5% and 1% levels
respectively. Standard errors clustered by stock are in parentheses.
(1) (2) (3) (4) (5) (6) (7) (8)
Panel A: Regressions
y = Lending supply y = Short interest y = Lending fee y = Loan duration
Passive fund ownership 0.77*** 0.76*** 0.16*** 0.16*** -0.04*** -0.04*** 138.39*** 137.98***
(0.02) (0.02) (0.02) (0.01) (0.01) (0.01) (19.69) (19.66)
Active fund ownership 0.19*** 0.25*** 0.11*** 0.14*** -0.01*** -0.02*** 58.75*** 65.27***
(0.01) (0.01) (0.01) (0.01) (0.00) (0.00) (6.99) (7.16)
Non-mutual fund ownership 0.17*** 0.10*** -0.02*** 20.56***
(0.00) (0.00) (0.00) (4.42)
Observations 112,279 112,098 112,237 112,060 112,221 112,044 112,237 112,060
𝑅2 0.89 0.90 0.59 0.62 0.58 0.58 0.34 0.35
Quarter fixed-effects Yes Yes Yes Yes Yes Yes Yes Yes
Stock fixed-effects Yes Yes Yes Yes Yes Yes Yes Yes
Control variables Yes Yes Yes Yes Yes Yes Yes Yes
Panel B: p-values of tests for differences between coefficients
𝐻𝑜: Active > Passive 0.00 0.07 0.07 0.00
𝐻𝑜: Non-mutual fund > Passive 0.00 0.00 0.09 0.00
𝐻𝑜: Non-mutual fund > Active 0.00 0.00 0.77 0.00
46
Table 4: Differential Impact of Institutional Investors on Security Lending Outcomes: Time-Series Analysis
This table reports the results from regressing security lending outcomes on ownership of various institutional investors. Detailed
definitions of variables can be found in the Appendix. The ownership variables are interacted with the dummy variable that equals one
if the year is 2011 or earlier. Columns (1) - (4) report the results for lending supply, short interest, lending fee and loan duration
respectively. *, **, and *** denote statistical significance at 10%, 5% and 1% levels respectively. Standard errors clustered by stock
are in parentheses.
(1) (2) (3) (4)
y = Lending supply y = Short interest y = Lending fee y = Loan duration
Passive fund ownership 0.81*** 0.16*** -0.03** 115.01***
(0.02) (0.02) (0.01) (22.13)
Active fund ownership 0.23*** 0.12*** -0.01** 75.11***
(0.01) (0.01) (0.01) (9.41)
Non-mutual fund ownership 0.14*** 0.08*** -0.02*** 22.07***
(0.01) (0.00) (0.00) (5.88)
Passive fund ownership × Before 2012 0.01 0.15*** 0.01 76.55***
(0.03) (0.02) (0.01) (25.17)
Active fund ownership × Before 2012 0.02** 0.02** -0.01* -24.92**
(0.01) (0.01) (0.01) (10.04)
Non-mutual fund ownership × Before 2012 0.04*** 0.01*** 0.00 0.40
(0.00) (0.00) (0.00) (5.77)
Observations 112,101 112,063 112,047 112,063
𝑅2 0.90 0.63 0.57 0.34
Quarter fixed-effects Yes Yes Yes Yes
Stock fixed-effects Yes Yes Yes Yes
Control variables Yes Yes Yes Yes
47
Table 5: Effect of Passive Fund Ownership on Cross-Autocorrelations
This table reports the results from regressing cross-autocorrelations on ownership of institutional investors. Detailed definitions of
variables can be found in the Appendix. Column (1) shows the results for specials (lending fee>2%) and column (2) reports the results
for general collateral stocks (lending fee <2%). Columns (3) - (4) repeat the specifications for upside cross-autocorrelations. Columns
(5) – (6) repeat the specification for the difference between the upside and the downside autocorrelations. *, **, and *** denote statistical
significance at 10%, 5% and 1% levels respectively. Standard errors clustered by stock are in parentheses.
(1) (2) (3) (4) (5) (6)
Cross-Autocorrelation Downside Upside Downside Minus Upside
Special GC Special GC Special GC
Passive fund ownership -0.78** -0.12 0.01 -0.03 -0.79* -0.10
(0.31) (0.07) (0.26) (0.06) (0.41) (0.09)
Active fund ownership 0.04 0.09*** -0.07 0.00 0.11 0.08**
(0.13) (0.03) (0.12) (0.03) (0.17) (0.04)
Non-mutual fund ownership 0.06 -0.06*** -0.01 -0.01 0.07 -0.05**
(0.06) (0.02) (0.05) (0.02) (0.07) (0.02)
Observations 11,996 99,595 11,996 99,595 11,996 99,595
𝑅2 0.28 0.42 0.38 0.44 0.20 0.13
Controls Yes Yes Yes Yes Yes Yes
Quarter fixed effects Yes Yes Yes Yes Yes Yes
Stock fixed effects Yes Yes Yes Yes Yes Yes
48
Table 6: Effect of Passive Fund Ownership on Skewness
This table reports the results from regressing skewness on ownership of institutional investors. Detailed
definitions of variables can be found in the Appendix. Column (1) shows the results for specials (lending
fee>2%) and column (2) reports the results for general collateral stocks (lending fee <2%). *, **, and ***
denote statistical significance at 10%, 5% and 1% levels respectively. Standard errors clustered by stock are
in parentheses.
(1) (2)
Skewness
Special GC
Passive fund ownership -2.71*** -1.58***
(0.92) (0.24)
Active fund ownership 0.13 -0.77***
(0.46) (0.10)
Non-mutual fund ownership 0.13 0.25***
(0.19) (0.06)
Observations 12,012 99,616
𝑅2 0.19 0.08
Controls Yes Yes
Quarter fixed effects Yes Yes
Stock fixed effects Yes Yes
49
Table 7: Effects of Passive Fund Ownership on the Value Premium
This table reports the results from regressing annual future stock returns on ownership of institutional investors. In doing so, we closely
follow the methodology of Nagel (2005). Detailed definitions of variables can be found in the Appendix. Columns (1) and (2) show the
results for specials (lending fee>2%). Column (1) presents the baseline results and column (2) includes the interactions between market-
to-book and ownership variables. Columns (3) - (4) repeat the specifications for general collateral stocks (lending fee<2%). *, **, and
*** denote statistical significance at 10%, 5% and 1% levels respectively. Standard errors clustered by stock are in parentheses.
(1) (2) (3) (4)
Special GC
Passive fund ownership -27.20*** -54.15*** -8.27*** -19.96***
(10.30) (18.72) (2.34) (5.13)
Active fund ownership -16.36* -12.10 -5.34** -10.10**
(8.86) (15.86) (2.08) (4.75)
Non-mutual fund ownership -22.27** -9.64 -3.37 -12.57**
(10.15) (14.42) (2.34) (5.35)
Market-to-Book -52.88*** -56.04*** -39.95*** -65.51***
(10.54) (13.63) (3.99) (8.74)
Passive fund ownership × Market-to-Book 44.13* 21.04***
(26.05) (7.57)
Active fund ownership × Market-to-Book -6.98 7.64
(24.09) (7.33)
Non-mutual fund ownership × Market-to-Book -21.97 16.89**
(23.85) (8.00)
Observations 12,005 12,005 99,606 99,606
𝑅2 0.49 0.49 0.38 0.38
Quarter fixed effects Yes Yes Yes Yes
Stock fixed effects Yes Yes Yes Yes
Controls Yes Yes Yes Yes
50
Table 8: Summary Statistics, Russell Sample
This table presents summary statistics for our 2007-2016 annual panel of stocks for Russell sample. For each
year the variables are calculated over the third quarter. Detailed definitions of variables can be found in the
Appendix. The ownership variables are calculated using end-of-the-quarter ownership as reported by Thomson
Reuters Mutual Fund Holding database. The definitions of ownership types are based on CRSP Mutual Fund
database. The security lending variables are from Markit and represent daily averages within each stock-quarter
observation. The price impact variables are calculated using CRSP stock database and Compustat.
Stock-3rd quarter level variables N Mean St Dev Median Min Max
Ownership variables
Passive fund ownership (fraction) 4,284 0.09 0.05 0.09 0.00 0.32
Active fund ownership (fraction) 4,283 0.18 0.09 0.17 0.00 0.63
Total mutual fund ownership (fraction) 4,283 0.27 0.12 0.28 0.00 0.81
Non-mutual fund ownership (fraction) 3,543 0.53 0.16 0.54 0.01 0.98
Total institutional ownership (fraction) 3,546 0.78 0.19 0.84 0.00 1.00
Non-passive ownership (fraction) 3,545 0.62 0.16 0.64 0.01 0.99
Security lending variables
Lending supply (fraction) 4,284 0.27 0.09 0.28 0.03 0.50
Short interest (fraction) 4,284 0.06 0.06 0.04 0.00 0.33
Lending fee (fraction) 4,284 0.01 0.02 0.00 0.00 0.51
Loan duration (days) 4,284 80.30 52.11 68.94 11.96 382.05
Price impact variables
Downside cross-autocorrelation 4,284 -0.11 0.43 -0.08 -1.92 1.39
Upside cross-autocorrelation 4,284 0.06 0.37 0.04 -1.38 1.95
Downside minus upside 4,284 -0.18 0.54 -0.15 -3.62 2.48
Skewness 4,284 0.11 1.34 0.05 -6.10 7.72
51
Table 9: Impact of Russell 2000 Membership on Institutional Ownership
This table reports the results from our first stage regressions for the relationship between Russell
2000 index assignment and ownership variables. Detailed definitions of variables can be found in
the Appendix. Panel A reports the result for ownership by passive funds. Column (1) reports the
results from the specification with first order polynomial. Columns (2) and (3) report the results
using the specification with second and third order polynomials. Panels B and C repeat the
specifications for active fund ownership and non-mutual fund ownership. *, **, and *** denote
statistical significance at 10%, 5% and 1% levels respectively. Standard errors clustered by stock
are in parentheses.
(1) (2) (3)
Panel A: y = Passive fund ownership
Russell 2000 0.02*** 0.02*** 0.02***
(0.00) (0.00) (0.00)
Observations 3,715 3,715 3,715
𝑅2 0.68 0.68 0.68
Banding controls Yes Yes Yes
Float controls Yes Yes Yes
Year fixed effects Yes Yes Yes
Polynomial Order, N 1 2 3
(1) (2) (3)
Panel B: y = Active fund ownership
Russell 2000 -0.01 -0.01 -0.01
(0.01) (0.01) (0.00)
Observations 3,714 3,714 3,714
𝑅2 0.23 0.23 0.23
Banding controls Yes Yes Yes
Float controls Yes Yes Yes
Year fixed effects Yes Yes Yes
Polynomial Order, N 1 2 3
(1) (2) (3)
Panel C: y = Non-mutual fund ownership
Russell 2000 -0.03 -0.03 -0.02
(0.02) (0.02) (0.00)
Observations 3,017 3,017 3,017
𝑅2 0.18 0.18 0.18
Banding controls Yes Yes Yes
Float controls Yes Yes Yes
Year fixed effects Yes Yes Yes
Polynomial Order, N 1 2 3
52
Table 10: Effect of Passive Fund Ownership on Security Lending Outcomes: 2SLS Regressions
This table reports the results from our instrumental variables regressions for the relationship between passive fund ownership and securities
lending outcomes. Detailed definitions of variables can be found in the Appendix. Panel A reports the results for quantities. Columns (1) – (3)
report the results for lending supply using polynomials of different orders. Columns (4) – (6) repeat the specifications for short interest. Panel B
presents the results for lending fees (columns (1) – (3)) and loan duration (columns (4) – (6)). *, **, and *** denote statistical significance at
10%, 5% and 1% levels respectively. Standard errors clustered by stock are in parentheses.
(1) (2) (3) (4) (5) (6)
Panel A: Quantities
y = Lending Supply y = Short Interest
Passive fund ownership 2.26*** 2.26*** 1.83*** 1.03*** 1.04*** 0.80**
(0.38) (0.38) (0.35) (0.32) (0.34) (0.33)
Observations 3,715 3,715 3,715 3,715 3,715 3,715
Banding Controls Yes Yes Yes Yes Yes Yes
Float controls Yes Yes Yes Yes Yes Yes
Year fixed effects Yes Yes Yes Yes Yes Yes
Polynomial Order, N 1 2 3 1 2 3
(1) (2) (3) (4) (5) (6)
Panel B: Fee and Loan Maturity
y = Lending Fee y = Loan Duration
Passive fund ownership -0.18* -0.19* -0.19* 276.74 281.82 149.01
(0.10) (0.11) (0.11) (264.91) (264.07) (285.08)
Observations 3,715 3,715 3,715 3,715 3,715 3,715
Banding Controls Yes Yes Yes Yes Yes Yes
Float controls Yes Yes Yes Yes Yes Yes
Year fixed effects Yes Yes Yes Yes Yes Yes
Polynomial Order, N 1 2 3 1 2 3
53
Table 11: Effect of Passive Fund Ownership on Price Impact Variables: 2SLS Regressions
This table reports the results from our instrumental variables regressions for the relationship between passive fund ownership and securities prices.
Detailed definitions of variables can be found in the Appendix. Panel A reports the results for downside cross-autocorrelation. Column (1) report
the results for specials (lending fee>2%) and column (2) reports the results for general collateral stocks (lending fee <2%). Columns (3) – (4)
repeat the specification using second order polynomial and columns (5) – (6) use third order polynomial. Panel B repeats the splits and the
specifications for skewness. Panel C presents the results for future annual stock returns adding market-to-book and its interaction with passive
fund ownership as explanatory variables. *, **, and *** denote statistical significance at 10%, 5% and 1% levels respectively. Standard errors
clustered by stock are in parentheses.
(1) (2) (3) (4) (5) (6)
Panel A: Downside Cross-Autocorrelation Special GC Special GC Special GC
Passive fund ownership -17.03* -0.58 -14.72* -0.58 -14.74* -0.13
(10.19) (1.41) (7.92) (1.42) (8.03) (1.55)
Observations 126 3,589 126 3,589 126 3,589
Banding Controls Yes Yes Yes Yes Yes Yes
Float controls Yes Yes Yes Yes Yes Yes
Year fixed effects Yes Yes Yes Yes Yes Yes
Polynomial Order, N 1 1 2 2 3 3
(1) (2) (3) (4) (5) (6)
Panel B: Skewness Special GC Special GC Special GC
Passive fund ownership 41.33 -1.91 47.08 -1.90 47.19 -4.81
(47.00) (7.29) (47.87) (7.17) (48.06) (7.73)
Observations 126 3,589 126 3,589 126 3,589
Banding Controls Yes Yes Yes Yes Yes Yes
Float controls Yes Yes Yes Yes Yes Yes
Year fixed effects Yes Yes Yes Yes Yes Yes
Polynomial Order, N 1 1 2 2 3 3
54
(1) (2) (3) (4) (5) (6)
Panel C: Value Premium Special GC Special GC Special GC
Passive fund ownership -269.77 -23.40 -284.94 -23.49 -327.53 -25.27
(235.66) (14.61) (234.57) (14.62) (270.92) (16.01)
Market-to-Book 46.21 -4.11 54.67 -4.25 64.66 -3.41
(269.39) (12.88) (304.38) (12.87) (308.94) (13.14)
Passive fund ownership × Market-to-Book -159.21 -1.60 -178.38 -1.32 -209.12 -3.58
(585.12) (25.45) (663.22) (25.38) (678.31) (26.35)
Observations 111 3,403 111 3,403 111 3,403
Banding Controls Yes Yes Yes Yes Yes Yes
Float controls Yes Yes Yes Yes Yes Yes
Year fixed effects Yes Yes Yes Yes Yes Yes
Polynomial Order, N 1 1 2 2 3 3
55
Appendix A
Table A.1: Definition of Variables
Variable name Source Definition
Ownership variables:
Passive fund ownership Thomson Reuters S12
Mutual Fund Holdings
Percentage of shares outstanding held by
passively managed funds
Active fund ownership Thomson Reuters S12
Mutual Fund Holdings
Percentage of shares outstanding held by
actively managed funds
Total mutual fund
ownership
Thomson Reuters S12
Mutual Fund Holdings
Percentage of shares outstanding held by
mutual funds
Total institutional
ownership
Thomson Reuters S34
Institutional Holdings
Percentage of shares outstanding held by
institutional investors
Non-mutual fund ownership Thomson Reuters S34
Institutional Holdings
Difference between total institutional
ownership and total mutual fund ownership
Non-passive ownership Thomson Reuters S34
Institutional Holdings
Difference between total institutional
ownership and passive fund ownership
Security lending variables:
Lending supply Markit Percentage of shares actively available for
lending, as indicated by “Active Lending
Supply” in Markit
Short interest Markit Percentage of shares on loan as indicated by
“Quantity on Loan” in Markit
Lending fee Markit Lending fee as indicated by “Indicative Fee”
in Markit
Loan duration Markit Duration of the average loan for a given
security as indicated by “Average Tenure” in
Markit
Price impact variables:
Downside cross-
autocorrelation
CRSP Correlation between stock returns in time t
and CRSP value-weighted index returns in
time t-1, conditional on index return being
negative
56
Variable name Source Definition
Upside cross-
autocorrelation
CRSP Correlation between stock returns in time t
and CRSP value-weighted index returns in
time t-1, conditional on index return being
positive
Downside minus upside
cross-autocorrelation
CRSP Difference between downside cross-
autocorrelation and upside cross-
autocorrelation
Skewness CRSP Skewness of daily log-returns
Other variables:
Log(market value) CRSP Natural logarithm of market capitalization
Log(book value) Compustat Natural logarithm of book value of equity
Market-to-book CRSP, Compustat Ratio of market capitalization to book value
of equity
Bid-ask spread CRSP Closing daily bid-ask spread scaled by price
R2000 Russell Investments Indicator equals one if firm is in the Russell
2000, and zero otherwise
57
Appendix B
Table B.1: Impact of Passive Fund Ownership on Security Lending Outcomes: 2SLS Regressions - Different Sample Cutoffs
This table reports the results from our instrumental variables regressions for the relationship between passive fund ownership and securities
lending outcomes using different Russell cutoffs. Detailed definitions of variables can be found in the Appendix. In all the specifications, we
control for market capitalization using second order polynomials. Panel A reports the results for lending supply. Columns (1) shows the
estimates for a sample of 200 top stocks in Russell 2000 and 200 bottom stocks in Russell 1000. Columns (2) – (3) repeat the specifications
using 300, 400 and 500 cutoffs. The further panels repeat the specification for short interest, lending fees, loan duration as well as for downside
cross-autocorrelation and skewness in the samples of special stocks (lending fee>2%). *, **, and *** denote statistical significance at 10%,
5% and 1% levels respectively. Standard errors clustered by stock are in parentheses.
(1) (2) (3) (4)
Panel A: Lending Supply 200 300 400 500
Passive fund ownership 2.27*** 2.17*** 2.07*** 2.03***
(0.53) (0.35) (0.31) (0.31)
Observations 2,977 4,457 5,927 7,428
(1) (2) (3) (4)
Panel B: Short Interest 200 300 400 500
Passive fund ownership 1.13** 0.82*** 1.25*** 1.47***
(0.50) (0.27) (0.25) (0.25)
Observations 2,977 4,457 3,715 7,428
(1) (2) (3) (4)
Panel C: Lending Fee 200 300 400 500
Passive fund ownership -0.11 -0.13* -0.14* -0.13*
(0.10) (0.07) (0.07) (0.07)
Observations 2,977 4,457 5,927 7,428
58
(1) (2) (3) (4)
Panel D: Loan Duration 200 300 400 500
Passive fund ownership 119.35 344.39 526.59*** 503.10***
(360.81) (220.88) (190.20) (182.78)
Observations 2,977 4,457 5,927 7,428
(1) (2) (3) (4)
Panel E: Downside Cross-
Autocorrelation-Specials
200 300 400 500
Passive fund ownership -6.79*** -12.53** -4.57* -6.87**
(1.81) (5.40) (2.50) (3.19)
Observations 112 142 192 235
(1) (2) (3) (4)
Panel F: Skewness-Specials 200 300 400 500
Passive fund ownership 4.35 49.93 33.71 35.85
(5.68) (40.08) (23.35) (25.12)
Observations 112 142 192 235
59
Table B.2: Impact of Russell 2000 Membership on Stock Characteristics
This table reports the results from our first stage regressions for the relationship between Russell 2000 index
assignment and stock characteristics. Detailed definitions of variables can be found in Appendix. Panel A reports the
result for bid-ask spread. Column (1) reports the results from the specification with first order polynomial. Columns
(2) and (3) report the results using the specification with second and third order polynomials. Panels B and C repeat
the specifications for market-to-book and for book value. *, **, and *** denote statistical significance at 10%, 5% and
1% levels respectively. Standard errors clustered by stock are in parentheses.
(1) (2) (3)
Panel A: y = Bid-ask spread
Russell 2000 -0.00 -0.00 -0.00
(0.00) (0.00) (0.00)
Observations 3,715 3,715 3,715
𝑅2 0.33 0.33 0.33
Banding controls Yes Yes Yes
Float controls Yes Yes Yes
Year fixed effects Yes Yes Yes
Polynomial Order, N 1 2 3
(1) (2) (3)
Panel B: y = Market-to-book
Russell 2000 -0.23 0.01 0.44
(0.84) (1.43) (0.81)
Observations 3,715 3,715 3,715
𝑅2 0.01 0.02 0.04
Banding controls Yes Yes Yes
Float controls Yes Yes Yes
Year fixed effects Yes Yes Yes
Polynomial Order, N 1 2 3
(1) (2) (3)
Panel B: y = Log(Book value)
Russell 2000 -0.16 -0.16 -0.19
(0.11) (0.11) (0.00)
Observations 3,715 3,715 3,715
𝑅2 0.19 0.19 0.19
Banding controls Yes Yes Yes
Float controls Yes Yes Yes
Year fixed effects Yes Yes Yes
Polynomial Order, N 1 2 3
60
Figure B.1: Short Interest Around Rank Days and Reconstitution Days
This figure shows the average daily short interest around rank days and reconstitution days. Detailed definitions of
variables can be found in the Appendix.
61
Table B.3: Short Interest Around Rank Days and Reconstitution Days
This table reports the results from regressing short interest on a dummy variable that equals one if a date falls into a
5-day window around Russell rank day or Russell reconstitution day in a given year. Detailed definitions of variables
can be found in the Appendix. Column (1) reports the baseline results for rank days and Column (2) adds stock fixed
effects. Columns (3) and (4) repeat the specifications for reconstitution days. *, **, and *** denote statistical
significance at 10%, 5% and 1% levels respectively. Standard errors clustered by stock are in parentheses.
(1) (2) (3) (4)
Rank day Rank day Reconstitution
day
Reconstitution
day
y=Short Interest y=Short Interest y=Short Interest y=Short Interest
(0,1) In 5-day window -0.00 -0.00 -0.00 -0.00
(0.00) (0.00) (0.00) (0.00)
Observations 2,296 2,296 2,296 2,296
𝑅2 0.04 0.96 0.05 0.96
Year fixed effects Yes Yes Yes Yes
Stock fixed effects No Yes No Yes
62
Appendix C
Description of Methodology Based on Coles, Heath and Rinngenberg (2018)
1. Sample selection
We select our sample following the procedure described in Coles, Heath and Rinngenberg (2018; further
referred to as CHR). Table C.1 presents the descriptive statistics for this sample. The variables of interest are
calculated for the 3rd quarter in any given year as this quarter exactly follows the annual June reconstitution. For
the average stock, 9% are owned by passive funds and 19% are owned by active funds. The overall level of
institutional ownership is 78%.
2. Estimation
We use the inclusion into Russell 2000 as an instrument for ownership of passive funds. As the stocks are
ranked based on their market capitalization and the sampling is based on the two different cutoffs, the rank and the
cutoff (which changes from year to year) can directly affect the level of passive fund ownership irrespective of
index assignment. Therefore, we include both stock ranks and year fixed- effects interacted with the assignment
cutoffs in our specifications. In particular, we estimate the following first stage regression:
𝑃𝑎𝑠𝑠𝑖𝑣𝑒𝑖,𝑡 = 𝛽 ∙ 𝑅𝑢𝑠𝑠𝑒𝑙𝑙2000𝑖,𝑡 + 𝑓(𝑅𝑎𝑛𝑘𝑖,𝑡) ∙ 𝑈𝑝𝑝𝑒𝑟𝐶𝑢𝑡𝑜𝑓𝑓𝑖,𝑡 + 𝛾𝑡 ∙ 𝑈𝑝𝑝𝑒𝑟𝐶𝑢𝑡𝑜𝑓𝑓𝑖,𝑡 + 휀𝑖,𝑡
where 𝑃𝑎𝑠𝑠𝑖𝑣𝑒𝑖,𝑡 is the amount of passive ownership for stock i in year t, 𝑅𝑢𝑠𝑠𝑒𝑙𝑙2000𝑖,𝑡 is an indicator
variable equal to one if the stock is included in Russell 2000 in year t, 𝑈𝑝𝑝𝑒𝑟𝐶𝑢𝑡𝑜𝑓𝑓𝑖,𝑡 is an indicator variable equal
to one if the stock i belongs to the upper cutoff sample in year t and 𝛾𝑡 is a year fixed effect. 𝑓(𝑅𝑎𝑛𝑘𝑖,𝑡) is a
polynomial control function of rank of stock i in year t. Finally, we cluster our standard errors at the individual
stock level.
63
Our second stage estimation mirrors the specification from the first stage and estimates the effects of
passive fund ownership on security lending and efficiency variables. In particular, we implement the following
regression model:
𝑦𝑖,𝑡 = 𝛽 ∙ 𝑃𝑎𝑠𝑠𝑖𝑣𝑒̂𝑖,𝑡 + 𝑓(𝑅𝑎𝑛𝑘𝑖,𝑡) ∙ 𝑈𝑝𝑝𝑒𝑟𝐶𝑢𝑡𝑜𝑓𝑓𝑖,𝑡 + 𝛾𝑡 ∙ 𝑈𝑝𝑝𝑒𝑟𝐶𝑢𝑡𝑜𝑓𝑓𝑖,𝑡 + 휀𝑖,𝑡
where 𝑦𝑖,𝑡 is an outcome of interest for stock i in year t and 𝑃𝑎𝑠𝑠𝑖𝑣𝑒̂𝑖,𝑡 is the predicted level of passive fund
ownership for stock i in year t from the first stage estimation.
Table C.2 presents the effects of passive fund ownership on security lending outcomes employing the CHR
approach. Panel A focuses on quantities and columns (1) - (3) show the effect of passive fund ownership on lending
supply. Our identification strategy confirms that more ownership by passive investors results in greater supply of
shares to short-sellers. The effect is economically meaningful such that an increase in one standard deviation in
passive fund ownership is associated with an increase of one standard deviation in lending supply. Columns (4) –
(6) confirm the effects of passive fund ownership on the size of the short positions. This effect is also both
economically and statistically significant.
The effect of passive fund ownership on lending fees and loan maturity are shown in Panel B. Columns (1)
- (3) show that more ownership by passive investors generally lowers the lending fees. While the coefficient is
economically sizable and is even larger than the coefficient obtained in the full sample, it is not statistically
significant at conventional levels. Columns (4) - (6) presents the results for loan duration but the coefficients are not
statistically significant.
64
Table C.1: Summary Statistics, Russell Sample, CHR Approach
This table presents summary statistics for our 2007-2016 annual panel of stocks for the cutoff sample using CHR
approach. For each year the variables are calculated over the third quarter. Detailed definitions of variables can be
found in the Appendix. The ownership variables are calculated using end-of-the-quarter ownership as reported by
Thomson Reuters Mutual Fund Holding database. The definitions of ownership types are based on CRSP Mutual
Fund database. The security lending variables are from Markit and represent daily averages within each stock-
quarter observation. The price impact variables are calculated using CRSP stock database and Compustat.
Stock-3rd quarter level variables N Mean Std.
Dev.
Median Min. Max.
Ownership variables
Passive fund ownership (fraction) 801 0.09 0.05 0.09 0.00 0.32
Active fund ownership (fraction) 800 0.19 0.10 0.18 0.00 0.63
Total mutual fund ownership (fraction) 800 0.28 0.12 0.28 0.00 0.76
Non-mutual fund ownership (fraction) 631 0.53 0.16 0.55 0.03 0.97
Total institutional ownership (fraction) 630 0.78 0.21 0.85 0.01 1.00
Non-passive ownership (fraction) 631 0.62 0.19 0.75 0.03 0.99
Security lending variables
Lending supply (fraction) 801 0.26 0.09 0.27 0.02 0.45
Short interest (fraction) 801 0.07 0.06 0.04 0.00 0.36
Lending fee (fraction) 801 0.01 0.03 0.00 0.00 0.51
Maturity (days) 801 76.68 48.87 65.88 11.17 270.26
Price impact variables
Downside cross-autocorrelation 801 -0.12 0.43 -0.10 -2.09 1.26
Upside cross-autocorrelation 801 0.04 0.38 0.04 -1.00 1.30
Downside minus upside 801 -0.18 0.60 -0.15 -4.53 2.48
Skewness 801 0.19 1.42 0.08 -5.44 6.93
65
Table C.2: Impact of Passive Fund Ownership on Security Lending Outcomes: 2SLS Regressions, CHR
Approach
This table reports the results from our instrumental variables regressions for the relationship between passive fund
ownership and securities lending outcomes using CHR approach. Detailed definitions of variables can be found in the
Appendix A. Panel A reports the results for quantities. Columns (1) – (3) report the results for lending supply using
polynomials of different orders. Columns (4) – (6) repeat the specifications for short interest. Panel B presents the
results for lending fees (columns (1) – (3)) and loan duration (columns (4) – (6)). *, **, and *** denote statistical
significance at 10%, 5% and 1% levels respectively. Standard errors clustered by stock are in parentheses.
(1) (2) (3) (4) (5) (6)
Panel A: Quantities
y = Lending Supply y = Short Interest
Passive fund ownership 2.05*** 2.23*** 2.23*** 0.89** 0.93** 0.94**
(0.37) (0.37) (0.40) (0.35) (0.37) (0.40)
Observations 797 797 797 797 797 797
Year x band fixed-effects Yes Yes Yes Yes Yes Yes
Polynomial order, N 1 2 3 1 2 3
(1) (2) (3) (4) (5) (6)
Panel B: Fee and Loan Maturity
y = Lending Fee y = Loan Duration
Passive fund ownership -0.12 -0.12 -0.11 -51.71 -76.39 -57.39
(0.11) (0.12) (0.12) (273.92) (272.35) (281.38)
Observations 797 797 797 797 797 797
Year x band fixed-effects Yes Yes Yes Yes Yes Yes
Polynomial order, N 1 2 3 1 2 3