Active vs. Passive Investing and the Efficiency of
Individual Stock Prices
Russ Wermers and Tong Yao∗
May 2010
∗
Wermers is from Department of Finance, Robert H. Smith School of Business, University of Maryland.
Email: [email protected]. Yao is from Department of Finance, Tippie College of Business, University of
Iowa. Email: [email protected]. We gratefully thank INQUIRE-UK for financial support and Marlies
vanBoven of Baring Asset Management for helpful comments on prior revisions of this work. All errors are
our own.
Active vs. Passive Investing and the Efficiency of
Individual Stock Prices
Abstract
In equilibrium, active investing must be compensated with returns from gathering costly
information about stock values (e.g., Grossman and Stiglitz, 1980). In return, active investors serve to promote price discovery in stocks. However, substantial trading is required
by active, informed investors, who may prefer to trade in the same stocks as passive, uninformed investors to hide their intentions and better profit from their private information
(e.g., Admati and Pfleiderer, 1988). Thus, both active and passive investors must coexist in
the market for a stock to allow the efficient transfer of information into the stock price. This
paper analyzes the relation between active and passive mutual fund ownership and trading
activity in U.S. stocks during 1993 to 2006, and the resulting efficiency of stock prices. Our
study finds that active funds are drawn to the same stocks as passive funds, and that active
funds increase the price efficiency of stocks through their trades. We also find that stocks
with “excessive” levels of passive fund ownership and trading exhibit more long-term pricing
anomalies as well as a larger price reversal following trades.
I.
Introduction
The efficient market paradigm, coupled with modern portfolio theory, has brought a huge
increase in index products to securities markets. For instance, by year-end 2008, assets
in ETFs and index mutual funds exceeded $1.1 trillion–growing about tenfold over the past
decade, and accounting for almost 12 percent of all mutual fund assets.1 In some sectors, passive investing has a much bigger presence. For instance, among large-blend domestic equity
funds, passively managed money accounts for 40 percent of all assets. While some studies
have documented that passive funds demand significant liquidity, little empirical research
has been conducted to directly examine the impact of this increased passive management on
the efficiency of stock prices.2
Some useful insights can be drawn from a comparison of passive funds to the “noise
traders” of microstructure models (e.g., Kyle, 1985)). Similar to noise traders, passive funds
reflect the decisions of (mainly) individual investors, who do not usually possess superior
information about the stocks in which they invest. The seminal paper by Grossman and
Stiglitz (1980) describes an equilibrium that requires trading by informed (active) investors
for the efficient transmission of costly information to stock prices. Their model would predict
that an “excess” fraction of uninformed (passive) traders would result in inefficient stock
markets, with mispricings significant enough to attract further active traders. On the other
hand, Admati and Pfleiderer (1988) and Milgrom and Stokey (1982) show how an excess
of active traders could result in a market breakdown, which could lead to inefficient price
discovery.
Passive funds and noise traders are also distinct in important ways. One such difference
is in their liquidity provision roles. Noise trades take place randomly across stocks, as well
as over time. In models of market structure, such as Kyle (1985), noise traders provide
liquidity to the market by pooling with informed traders. That is, market makers can set
1
See Investment Company Institute Fact Book (2009) at www.ici.org.
For example, Madhavan (2003) and Carino and Pritamani (2007) document a significant price-pressure
effect when the Russell 2000 stock index is reconstituted, presumably from the demand for liquidity by index
funds. Further, Goetzmann and Massa (2003) find a price impact of the daily flows of three Fidelity index
funds. Also, using institutional transactions data, Keim and Madhavan (1997) and Jones and Lipson (1999,
2001) document that, at short horizons, index funds generate a larger price impact when they trade, relative
to active funds.
2
1
prices to offset their losses to informed traders with profits from uninformed traders, thus,
market makers are willing to trade when they do not know whether their counter-party is
informed or not. Index funds, however, tend to trade in the same direction at the same
time, as well as trading in a persistent direction over time, due to the persistent flows
from investors. In addition, index funds trade to accommodate index reconstitutions in a
correlated manner. As a consequence, index funds may generate a larger and longer-lasting
price impact than typical noise traders. This gives rise to the question of whether index funds
are much of a liquidity provider to the market, and, in particular, to active funds. Perhaps
index funds sometimes increase liquidity by pooling with active funds, and, at other times
decrease liquidity through their impatient and correlated trades. In turn, as shown by Da,
Gao, and Jagannathan (2010), actively managed funds can be liquidity-absorbing impatient
traders or liquidity suppliers, depending on the relative profits of these two competing trade
motivations.
In this paper, we empirically investigate the relation between passive and active institutional trading and stock price efficiency. Following the predictions of the aforementioned
papers, we conjecture the following “causal effect” of the presence of passive vs. active institutional investors: stocks with “too many” passive investors should have a greater level
of persistent mispricing, such as momentum- (Jegadeesh and Titman, 1993) or accrualbased (Sloan, 1996) stock anomalies (due to the influence of flows from individuals with
predictable behavioral investing patterns) that are not adequately arbitraged by active institutional traders.3 On the other hand, stocks having too many active investors may exhibit
short-term illiquidity, as active traders must wait longer for uninformed investors with which
to pool their trades.
Complicating our analysis is the presence of a “preference effect”, which is also based
on the aforementioned papers. That is, although uninformed (passive) investors add noise
to stock prices, they are, by nature, attracted to stocks whose prices are informationally
efficient. On the other hand, when stock prices become noisy due to the presence of un3
It is not clear why the aggregate of all passive funds does not equal the market portfolio, thus, creating
cross-sectional differences in the proportion of stocks held or traded by passive funds. However, it is likely
due to either frictions in setting up or trading passive funds or to investor preferences for certain types of
stocks.
2
informed traders, active investors have a strong incentive to acquire information and trade
stocks. Therefore, passive investing is associated with higher liquidity by preference, and
active funds may have a similar preference in order to strategically pool with the uninformed,
as modeled by Admati and Pfleiderer (1988).
Our study investigates the effect of active and passive fund holdings and trades using
mutual fund holdings during the period from 1993 to 2006. Our analysis compares the
liquidity and price efficiency of stocks held and traded by passive funds and active funds
using these holdings data. To facilitate our analysis, we construct measures of stock-level
passiveness, based on total shares owned, total shares traded, and net trading (buys minus
sells) of a given stock by all passive funds. We also construct similar stock-level activeness
measures, based on holdings and trades by all active funds.
Our analysis shows that active and passive funds hold and trade similar stocks. Specifically, equity holdings of passive funds exhibit a strong positive cross-sectional correlation
with equity holdings of active funds, controlling for stock characteristics known to attract
institutional investors in general (e.g., stock liquidity). Further, stocks traded more heavily
by passive funds are also traded more heavily by active funds. These findings suggest that
active funds purposely trade the same stocks as passive funds. It also suggests that the
interaction between passive and active funds is important when assessing the relation of passive funds with liquidity and efficiency. Interestingly, the correlation between net purchases
(buys minus sells) of a particular stock by passive funds and by active funds, although still
significantly positive, has a much smaller magnitude. That is, while passive and active funds
tend to trade the same stocks, their trades are often in different directions. This finding
indicates that, while active funds often strategically choose to trade in the same direction in
the same stocks as passive funds to hide their private information (Admati and Pfleiderer,
1988), they also sometimes supply liquidity to passive funds, consistent with Da, Gao, and
Jagannathan (2010).
Stock price efficiency is multi-faceted, and existing studies have analyzed this issue in
multiple dimensions. To provide a relatively comprehensive perspective, we measure price
efficiency in terms of liquidity, price impact, price informativeness, and magnitude of longterm systematic mispricing (i.e., stock “anomalies”). That is, we measure price efficiency
3
at high and low frequencies. We find that, first, there is a strong positive relation between
active-fund presence and stock liquidity. The relation between passive fund presence and
stock liquidity is also positive, but not as strong as that for active funds in terms of magnitude
in a model that includes both passive and active fund holdings of a stock. Recall that the
“preference effect” predicts a positive correlation between passiveness and liquidity, while
the “causality effect” suggests a negative relation. The results therefore suggest that the
preference effect dominates, in a way consistent with the equilibrium predictions mentioned
earlier.
We also find evidence of synchronized trading and a large price impact by passive funds.
Specifically, across stocks, trades by passive funds are much more often in the same direction
than trades made by active funds due to the highly correlated flows of passive funds and
the ensuing forced trades of all stocks within an index. Further, trading by passive funds
generates significant price reversals during subsequent quarters. For example, a higher dollar
value of shares bought by passive funds during a particular quarter results in lower returns
during subsequent quarters. By contrast, trading by active funds tend to generate return
continuations during the next quarter. This result is robust to controlling for the effect
of past stock returns and lagged stock liquidity. These findings are evidence of a causality
effect–passive fund trading has a negative impact on stock liquidity, while active fund trading
aids price discovery.
To further examine the effect of passive/active funds on the informational efficiency of
stock prices, we consider two price informativeness measures from the existing literature. The
first is the R2 that results from regressing stock returns onto market returns (e.g., Morck,
Yeung, and Yu, 2001; Durnev et al., 2003; and Durnev, Morck, and Yeung, 2004). The
second is the probability of informed trading, or PIN (e.g., Easley et al. 1996; Easley, Kiefer,
and O’Hara, 1997a and 1997b; Easley, Hvidkjaer, and O’Hara, 2002). We find that, after
controlling for stock liquidity characteristics, passive funds tend to hold stocks with a lower
R2 and lower PIN. The former suggests that passive funds prefer stocks when firm-specific
information is already substantially impounded into the stock price. The latter suggests that
trading in stocks preferred by passive funds does not contain substantial private information.
Both are consistent with the theoretical equilibrium predictions, which is that passive funds
4
prefer stocks with a high degree of informational efficiency.4 We also find that active funds
tend to hold and trade stocks with a lower R2 and higher PIN; the former suggests the
causal effect that active funds improve efficiency by impounding firm-specific information
into stock prices, while the latter suggests a preference effect–active funds pursue stocks
with rich private information, and their presence might be the reason for the high PIN of
some stocks.
Finally, we quantify the informational role of passive funds by examining their impact on
the cross-sectional return predictive power of a large set of stock characteristics that have
been shown to predict returns by past research. These predictors are combined into eight
variables, including value, investment and financing activities, earnings quality, intangible
investments, price and earnings momentum, information uncertainty, profitability, and liquidity. We find that the presence of active funds in stocks tends to reduce the predictive
power of these variables. By contrast, the presence of passive funds tends to increase their
predictive power. To the extent that such stock return predictability reflects market mispricing rather than a risk-return trade-off, this can be interpreted as evidence that active
funds enhance, while passive funds reduce, the informational efficiency of stock prices. This
finding is consistent with the equilibrium predictions of Grossman and Stiglitz (1980).
Our study shows how the coexistence of active and passive management in stocks affects
price discovery. Active funds prefer to either trade together with passive funds–to hide the
intentions of their trades from market-makers–or to trade against active funds to supply
liquidity. In either case, active funds are mostly drawn to the same stocks as passive funds.
In turn, active funds increase the price efficiency of stocks by arbitraging mispricings. When
passive funds dominate the holdings or trades of a given stock, relative to active funds, price
discovery in that stock is hindered. Thus, a balance of active and passive funds is necessary
for the price discovery process.
Our paper is related to Boehmer and Kelley (2007), who find that stocks with greater
institutional ownership are priced more efficiently in the sense that their high-frequency
transaction prices more closely follow a random walk. In addition, Shu (2007) finds that
low-frequency pricing anomalies, such as price momentum, post-earnings announcement drift,
4
There is a different interpretation on the PIN results. Some would argue that a low PIN indicates price
inefficiency; see, Chen, Goldstein, and Jiang, 2007).
5
and the value premium, are mitigated in stocks with a higher fraction of institutional traders.
Our paper is the first to show the separate and joint effects of active and passive funds on
stock price efficiency.
The rest of the paper is organized as follows. Section II describes mutual fund sample
and empirical methodology for identifying passive funds. Section III examines the effect
of passive investing on stock liquidity and price impact. Section IV analyzes the effect of
passive investing on price informativeness and magnitude of systematic mispricing. Section
V concludes.
II.
II.A.
Data and Methodology
Data Sources
Data on mutual fund portfolio holdings are from Thomson Reuters. Data on fund returns and
fund characteristics such as expense ratio and turnover are from CRSP. These two datasets
are merged together via MFLINKs, which is obtained from WRDS (Wharton Research
Data Service). We additionally obtain stock pricing data from CRSP and data on financial
statements from COMPUSTAT. Analyst forecast data are from IBES.
II.B.
Passive Fund Identification
Thomson Reuters and CRSP do not provide direct information on whether a mutual fund
is an index fund or active fund. The MFLINKS dataset provides an index fund indicator.
However, we find that there are still many apparent index funds not classified as such by
this indicator. Many index funds have names that contain identifiable words such as “index”
and “S&P 500”. However, some index funds do not have informative names. In addition,
there are many “closet indexers”. These are mutual funds that claim to be active funds, but
actually behave quite similarly to index funds when forming portfolios.
We take two approaches to identify passive funds. In the first approach, we take all index
funds identified via the MFLINKS index fund indicator, then add index funds manually
identified based on suggestive fund names.
6
In the second approach, we attempt to include index funds with non-informative names
and “closet indexers” based on several fund characteristics. The fund characteristics we
consider include 1) annual turnover, 2) expense ratio, 3) R-square from regressing past 12month fund returns in excess of the riskfree rate onto the Fama-French three factors (i.e.,
MKTRF, SMB, and HML), 4) the absolute value of estimated fund alpha from the same
regression, 5) Herfindahl index of portfolio weights, and 6) Herfindahl index of portfolio
weight changes.5 In each quarter, we first estimate a Probit model, where the dependent
variable equals one for index funds identified by the first approach, onto these fund characteristics. Then, we classify funds in the highest quartile in terms of the fitted probability,
together with those index funds identified by the first approach, as passive funds.6 Unlike
the permanent index fund identification in the first approach, the identity of passive funds
from the second approach may change from quarter to quarter, depending on the variations
of fund characteristics.
We select a large sample of U.S. domestic equity funds based on the Thomson data. We
start with all funds in the Thomson data whose reported investment objectives are aggressive
growth, growth, growth and income. For each fund, we calculate the average ratio of equity
value to reported total net assets across all reporting quarters. Funds with the average ratio
below 0.75 are excluded from the sample, since such funds are likely either non-equity funds
or have significant unreported holdings. The sample period is from 1993 to 2006. We start
from 1993 because the number of index funds identified via the first approach is below 20
prior to this year.
The above procedure leaves us 2,405 unique funds altogether, among which 187 are
identified as index funds via the first approach. In Table I, we provide year-by-year statistics
5
The Herfindahl index for portfolio weights is a measure of portfolio concentration:
H=
N
X
2
wit
i=1
where w is the portfolio weight and N is the number of stocks held by the fund. The Herfindahl index for
portfolio weight changes is similarly measured, by replacing wit with ∆wit , the weight change during the
six-month period ending at quarter t.
6
For funds with missing characteristics, we first use cross-sectional regressions to project these characteristics onto the remaining (observed) characteristics, and then replace the missing characteristics with fitted
values. Finally, we compute the implied probability using the parameters estimated for the Probit model.
This procedure is performed during each quarter.
7
on passive funds and active funds – funds in our sample that are not classified as passive
funds. In 1993, there are 35 passive funds identified via the first approach, with a median
of 427 stocks held per fund, and a median value of equity holdings of $243 million. By
2006, there are 98 passive funds; the median number of stocks held is 484 and the median
equity value held is $1,734 million. Both the number of index funds and their assets under
management have grown substantially. During the same period, the number of active funds
grows from 788 to 1179. The median number of stocks held by active funds is much lower,
at between 63 and 77. The size of active funds is also smaller, with a median equity value
of $467 million in 2006.
The number of index funds in the sample is smaller than the actual number known in
the market. According to ICI Fact Book (2007), by year-end 2006 there are 290 domestic
equity index funds. There are a few possible reasons for the lower fund number in our
sample. The first is that many index funds hold derivatives contracts (e.g., futures) instead
of holding underlying stocks. Such funds are not tracked by the Thomson data. Second,
Thomson Reuters focuses on active funds, and may have incomplete data collection for index
funds.7 Third, there are index funds with non-revealing names and thus not identified by
our first approach. Such funds are likely captured by our second approach based on fund
characteristics. The second approach will further capture “closet indexers”, whose holdings
and trades are close to index funds despite self-claimed active investment styles.
There are 144 passive fund identified via the Probit model in 1993, with a median number
of 119 stocks held per fund and median value of equity holdings of $678 million. By 2006,
the number of passive funds grows to 287, approximately the same as the number of index
funds reported by ICI. The median number of stocks held per fund is 146 and the median
equity value per fund is $1,506 million. During the same period, the number of active funds
grows from 679 to 990. The number of stocks held by active funds range between 59 and 72.
The median value of equity holdings stands at $367 million in 2006, much smaller than that
of passive funds.
Table 2 provides a description of characteristics of funds classified as passive and active,
respectively. The fund characteristics are those used in the Probit model – Rsquare, ab7
Note that a few index funds are excluded from our sample because their average equity value to total
assets ratio is below 0.75 due to incomplete reporting of holdings.
8
solute value of alpha, turnover ratio, expense ratio, concentration of portfolio holdings and
concentration of trades. The characteristics are averaged for passive funds and active funds
in each quarter, and then averaged over time. Relative to active funds, passive funds have
a higher R-square, lower absolute value of alpha, lower turnover, lower expense ratio, and a
lower concentration of fund holdings and fund trades. This holds whether passive funds are
classified by the index fund indicator or by the Probit model.
II.C.
Stock Level Measures of Passiveness and Activeness
We use several measures to quantify how heavily a stock is held or traded by passive funds
and active funds. ACTIVEHOLD is the total number of shares of a stock held by all active
funds at the end of a calendar quarter, divided by total shares outstand at quarter-end.
PASSIVEHOLD is similarly calculated, for shares held by passive funds. ACTIVETRADE is
the total number of shares bought plus total number of shares sold by all active funds during
the six months ending at the current quarter-end, divided by total shares outstanding at
the current quarter-end. PASSIVETRADE is similarly calculated, for the combined number
of shares bought and sold by all passive funds. Finally, ACTIVEBUY is the net shares
purchased – number of shares bought minus the number of shares sold by all active funds
– during the past six months, divided by total shares outstanding at current quarter-end,
while PASSIVEBUY is similarly calculated for the net purchases by all passive funds.
In this study, fund trades are computed over past six months instead of quarterly, for the
reason that many funds report holdings semi-annually.8 Further, a fund that reports semiannually may have holdings reported for the previous quarter but does not report holdings
for the current quarter. In this case, we include its holdings and trades at the end of the
previous quarter when calculating the above statistics for the current quarter.
Funds report holdings for their fiscal quarter-ends, which may not coincide with the
calendar quarter-ends. We assume that the shares in fund holdings reported for their fiscal
quarter-ends are valid for the immediate coming calendar quarter-ends, after adjusting for
8
The SEC-mandated frequency for mutual fund portfolio disclosure is quarterly before 1984, semiannually
afterwards, and switched back to quarterly after May 2004. Many funds voluntarily report holdings quarterly
during the period when the mandatory disclosure frequency was semiannual. However, during mid to late
1990s the proportion of funds reporting semiannually is quite high.
9
stock splits using the CRSP share adjustment factor. The number of shares traded are also
split-adjusted to reflect the share basis of the current calendar quarter-end.
The stock sample analyzed in this study includes all stocks held by at least one fund in
our sample, in a given quarter. For convenience we refer to this stock sample as “stocks
held by funds.” Within this sample, if there is no holding or trading by any group of funds
(active or passive) during a quarter, we set the resulting stock-level passiveness or activeness
measures to zero. Table 3 reports cross-sectional distribution of these stock level passiveness
and activeness measures. The distribution statistics include the 5th and 95th percentile, 1st
and 3rd quartile, median, and standard deviation. These statistics are first calculated in
each quarter, then averaged over time.
One clear pattern is that active funds hold and trade more shares than do passive funds.
For example, when funds are classified using the index fund indicator, for a median stock,
active funds collectively hold 6.64% of shares outstanding, while the holding by passive funds
is only 0.91%. The fraction of shares traded by active funds is 2.89%, while that by passive
funds is 0.13%. When the Probit model is used to identify passive funds, the difference
narrows, but remains quite large. For a median stock, active funds hold 3.94% of total
shares outstanding while passive funds hold 2.70%. The fraction of shares traded by active
funds is 1.85% while that by passive funds is 0.76%. The net purchases by active and passive
funds for the median stock are both slightly positive, reflecting the growth of the mutual
fund industry.
Another pattern to note is the cross-sectional standard deviation of these measures. For
passive funds identified by index fund indicator, the standard deviations of holding- and
trading-based activeness measures, ACTIVEHOLD and ACTIVETRADE, are 24.34% and
22.06%, while those for PASSIVEHOLD and PASSIVETRADE are only 1.68% and 1.10%.
Under the Probit model, the standard deviations of ACTIVEHOLD and ACTIVETRADE
are 19.46% and 17.69%, while those for PASSIVEHOLD and PASSIVETRADE are 8.44%
and 7.02%. This suggests a higher degree of homogeneity among passive funds in terms of
their holdings and trades, than among active funds.
An issue arises when interpreting the results from analysis based on these activeness
and passiveness measures. Due to possible incomplete identification of passive funds and
10
incomplete reporting by some passive funds, the passiveness measures likely understate the
fraction of shares held and traded by all passive funds in the stock market. Across stocks,
the passiveness measures constructed using sample passive funds are likely to have a strong
positive correlation with the “true” passiveness measures had we observe and correctly identify all passive funds.9 Given potential incomplete reporting by active funds, the activeness
measures may also be understated. The complication this causes can be illustrated via the
following example. Suppose one wishes to measure funds’ price impact, by regressing future stock returns onto net-purchase-based passiveness and activeness measures. Further,
suppose that for every identified passive fund, there is another identical passive fund not observed in the data. As a result, the real coefficient for the passiveness measure after taking
into account the unreported funds, should be only half of the estimated coefficient in the
regression based on reported data. Therefore, while one can read sensibly from the signs
of the coefficients, one may not be able to infer much by comparing the magnitude of the
coefficients.10
Panel A of Table 4 reports the cross-sectional correlations between pairs of activeness
and passiveness measures. We compute both Pearson correlations and Spearman rank correlations each quarter, and then average them over the sample period. In general, the correlations are significantly positive – between ACTIVEHOLD and PASSIVEHOLD, between
ACTIVETRADE and PASSIVETRADE, and between ACTIVEBUY and PASSIVEBUY.
Some of the correlations are rather high. For example, the Spearman rank correlation between ACTIVEHOLD and PASSIVEHOLD is 0.46 under the Probit model for passive fund
identification. This suggests that it is important to control for the effect of active funds
when analyzing the effect of passive funds. On the other hand, the correlation between
ACTIVEBUY and PASSIVEBUY, although statistically significant, becomes much lower in
magnitude, compared to the other two pairs. This suggests that while passive and active
funds cluster on the stock they trade, they don’t agree very highly on the direction of their
trades.
9
The idea of identifying all truly passive funds may be actually unrealistic, given the existence of “closet
indexers” with a continuum of degree of passiveness and activeness.
10
In empirical analysis we mainly rely on a transformation of these measures, i.e., their cross-sectional
ranks. This makes their regression coefficients somewhat more comparable.
11
There could be several reasons for the high correlations in the holding and trading between
passive and active funds. One apparent reason is that active funds, for the purpose of
reducing tracking errors, would hold stocks that are members of the passive benchmarks. As
a result, part of active fund portfolio holdings and their trades resemble passive funds. This
particular cause of the correlation is perhaps not a concern when we examine the impact of
active and passive funds separately on stock price efficiency. Another possible explanation
is the strategic liquidity choice by active funds, in a way similar to how informed investors
cluster their trades with large noise trades in the intraday trading pattern (Admati and
Pfleiderer, 1988). A third explanation is the efficiency preference by passive funds – stocks
with strong active fund presence may be more efficiently priced, and thus attracting passive
funds. All these reasons suggest that the interaction between passive and active funds may
be important when examining the effects of these funds on market efficiency.
To see if liquidity fully drives the correlation between the two groups of funds, we perform
a cross-sectional regression with activeness measures as dependent variables. The explanatory variables include the corresponding passiveness measures, and two measures of liquidity
as control variables: log market cap, and cross-sectional rank of stock trading turnover.11
The time series averages of the regression coefficients are reported in Panel B of Table 4.
For the passiveness and activeness measures, we use both their raw measures, and their
cross-sectional percentile ranks in regressions. The result suggests that the relation between
activeness and passiveness measures remain significantly positive even after controlling for
liquidity. Although not tabulated, we also include a few other liquidity measures employed
subsequently in this study and obtain similar results here. Therefore, liquidity is not the
only reason for the clustering of holdings and trades of passive and active funds.
III.
Empirical Analysis: Liquidity and Price Impact
The textbook definition of market efficiency is that that security prices fully reflect all available information (Fama 1970). To make this definition operational for empirical analysis,
researchers have used various measures to quantify efficiency. In this paper, we provide a
11
Turnover is ranked separately within NYSE/AMEX and within NASDAQ, to take into account the
different trading volume reporting practices by exchanges.
12
relative comprehensive analysis on price efficiency from in the following four perspectives:
liquidity, price impact, price informativeness, and magnitude of systematic mispricing. They
capture the multi-facet nature of stock price efficiency.
III.A.
The Effect on Stock Liquidity
Stock liquidity can be viewed as a measure of efficiency, in the sense that the price of a more
liquid stock is less swayed by temporarily demand-supply imbalance, thus reflecting more
information about its fundamentals. We employ the following five measures of liquidity:
1) ILLIQ, the cross-sectional percentile rank of Amihud (2002) illiquidity ratio, 2) LDV,
the latent dependent variable estimate of transaction cost, following Lesmond, Ogden, and
Trzcinka (1999), 3) SIZE, the log of market capitalization at the end of a quarter, 4) TURN,
turnover ratio, measured by the monthly trading volume divided by total shares outstanding,
averaged over a quarter, and 5) VR, the variance ratio between 5-day return and 1-day return.
We provide a detailed description on the construction of ILLIQ, LDV, and VR in Appendix
A.
To gauge the relation between active/passive fund presence and stock liquidity, we perform the following Fama-MacBeth regressions:
LIQi,t+1 = b0 + b1 ACTIVEHOLDi,t + b2 PASSIVEHOLDi,t + eit+1
(1)
LIQi,t+1 = b0 + b1 ACTIVETRADEi,t + b2 PASSIVETRADEi,t + eit+1
(2)
where LIQi,t+1 is one of the five liquidity variables, measured in quarter t+1 (using quartert liquidity measures yields similar results). The explanatory variables, while denoted as
ACTIVEHOLD, PASSIVEHOLD, ACTIVETRADE, and PASSIVETRADE, are actually
transformed version of these variables. Two forms of transformations are considered. In the
first, we use the cross-sectional percentile rank of the variables as regressors. In the second,
we divide the original variables by their cross-sectional standard deviations, before using
them as regressors. The cross-sectional regressions are performed during each quarter, and
we obtain their time series averages and corresponding t-statistics.
The results are shown in Table 5. Across the different liquidity measures, across the
holding-based and trade-based passiveness/activeness measures, and across the two different
13
approaches for defining passive funds, the coefficients obtained from regressions are generally
consistent with the following interpretation: both higher activeness and passiveness measures
are associated with higher stock liquidity. For example, when ILLIQ is the liquidity measure
(higher ILLIQ means lower liquidity), the coefficients for ACTIVEHOLD, PASSIVEHOLD,
ACTIVETRADE, PASSIVETRADE are all significantly negative.12
As discussed earlier, due to incomplete reporting, it is difficult to compare the magnitude
of the coefficients when the original passiveness and activeness measures are used as regressors. After the transformations, the magnitude of the coefficients are no longer dependent
on the average magnitude of the passiveness and activeness measures. To some extent this
makes it feasible to compare the magnitude of the coefficients. That is, the difference in
the coefficients between the passiveness and activeness measures can be interpreted as the
differential effect on liquidity caused by per unit of ranking change or per standard deviation
change in the measures. For example, the coefficient for PASSIVEHOLD is always higher
(less negative) than that for ACTIVEHOLD, in both panels and under both approaches
for identifying passive funds. This suggests that passive funds’ holding and trading has a
weaker association with stock liquidity, relative to that of active funds, on the basis of per
unit ranking change and per unit standard deviation change of the measures.
Recall that the coefficients are the net of two effects: a preference effect and a causal
effect. The preference effect of active funds suggests a positive relation between active fund
holding/trading and liquidity, while the causal effect suggests a negative relation as informed
trading by active funds demands liquidity. The positive empirical relation indicates that the
preference effect dominates. Passive funds also prefer holding and trading on liquid stocks.
Further, the causal effect of noise trading is to provide liquidity to the market. These two
effects combined seem to suggest a stronger positive relation between passive fund presence
and stock liquidity than that for active funds. However, the empirical result is to the
opposite. One possible explanation is that despite a positive preference effect, passive funds
has actually a negative causal effect on liquidity – their passive holding reduces liquidity and
their trading demands liquidity.
The reason for this negative causal effect is that, as discussed earlier, passive funds are
12
The only exception is in Panel A, the coefficient for PASSIVEHOLD when the liquidity measure is
TURN. It is negative, but statistically insignificant.
14
different than noise traders in the conventional sense. First, since passive funds hold stocks
with low frequency of trading, a high proportion of stocks held by passive funds means
that shares available for trading in the market is low. Further, trades by noise traders are
uncoordinated and often offset each other, but passive funds often trade in the same direction
and at around the same time, because they tend to have similar response to index change,
have similar re-balancing needs, and experience similar investment flows driven by investors’
market expectations and sentiments. This means that index funds may not be much of a
liquidity provider to the market, but rather demand liquidity when they trade.
In the following, we further analyze this issue, by looking at the synchronicity of trades
and price impact of trades.
III.B.
Trading Synchronicity and Price Impact
We construct two measures of trading synchronicity among passive funds and among active
funds. The first, a dollar-based measure, is the dollar value of net purchases (purchase sale) on a stock during the six months prior to the current quarter end, divided by the total
value of trades (purchase + sale), by all passive funds and by all active funds respectively.
The second, a trades-based measure, is the net number of funds purchasing a stock (number
of purchasing funds - number of selling funds) divided by the total number of funds trading
the stock. We calculate these two measures for each stock in each quarter, among passive
funds and among active funds separately. We then calculate their averages across stocks in
each quarter, and finally take the time series means. For both dollar-based and trades-based
measures, a higher value indicates a higher degree that funds trade on the same direction.13
The results are reported in Table 6. When passive funds are identified by the index
fund indicator, the dollar-based synchronicity measure for passive funds is 0.81, and the
trades-based synchronicity measure is 0.58. By comparison, both synchronicity measures for
active funds are significantly lower, at 0.61 and 0.42, respectively. When passive funds are
identified by the probit model, the dollar-based measure and trades-based measure are 0.71
and 0.50 for passive funds, respectively, significantly higher than those for active funds, at
13
Despite differences in the scaling factor, the dollar-based synchronicity measure is similar to the herding
measure of Sias (2004) and the trades-based synchronicity measure is similar to the herding measure of
Lakonishok, Shleifer, and Vishny (1992).
15
0.63 and 0.43. These results is consistent with the notion that passive funds trade in a much
more concerted way than active funds.
Concerted trading by passive funds has a potentially large impact on stock prices. We
investigate this using the following Fama-MacBeth regressions:
Ri,t+k = b0 + b1 ACTIVEBUYi,t + b2 PASSIVEBUYi,t
+b3 Ri,t + b4 SIZEi,t + b5 TURNi,t + eit+1
(3)
where Ri,t+k is stock return during quarter t+k. We look at the four quarters of returns
after the current quarter, i.e., k=1, ...,4. Again, we transform the explanatory variables by
using their cross-sectional percentile ranks and cross-sectionally standardized values. Control
variables include stock return in current quarter(Ri,t ), log market capitalization at current
quarter-end (SIZE), and cross-sectional percentile rank of trading turnover during the current
quarter (TURN), with NASDAQ stocks ranked separately from NYSE-AMEX stocks. The
regression is performed quarterly and the time series averages of the estimated coefficients
are reported in Table 7.
The coefficient of ACTIVEBUY is initially positive for the stock return during quarter
t+1, and turns negative for returns in the next three quarters, suggesting an initial continuation and subsequent reversal. The initial continuation could be due to information as well
as delayed herding behavior by some investors. The subsequent reversal is consistent with
the recent evidence on the impact of herding, e.g., Brown, Wei, and Wermers (2009). By
contrast, the coefficient for PASSIVEBUY is significantly negative for quarter t+1. That is,
stocks heavily purchased by passive funds experience strong and immediate return reversals.
Note that the coefficient remains mostly negative and in many cases significantly negative
for quarter t+2 to t+4.
A few studies, such as Keim and Madhavan (1997) and Jones and Lipson (1999, 2001),
have found that index funds generate large price impact at relatively short horizons. What
is striking about our finding is that the price impact of passive funds is quite long-lasting –
the negative impact on stock return is significant for several quarters. This indicates that
excess trading by passive funds reduces price efficiency.
16
IV.
Empirical Analysis: Price Informativeness and Return Predictability
We now turn to two other aspects of price efficiency. The first is based on measures of
price informativeness that we adopt from the existing literature. In the second set of analysis, we examine whether passive fund presence has an impact on cross-sectional stock return
predictability. Many forms of stock return predictability are considered anomalies or systematic patterns of mispricing, and stronger predictability is indicative of lower price efficiency.
Therefore, by examining the effect of passive/active funds on these anomalies, we can infer
the relation between passive/active fund presence and stock price efficiency.
IV.A.
Analysis based on Price Informativeness Measures
We consider two measures of price informativeness. The first is R2, the R-square obtained
from regressing weekly stock returns onto weekly market returns. Morck, Yeung, and Yu
(200l) argue that a low R2 means that a large dose of firm-specific information is impounded
into stock prices, hence an indication of price efficiency.The second is PIN, or probability of
informed trading. The PIN is estimated from a model of informed trading (Easley, Hvidkjaer,
and O’Hara, 2002), and a higher PIN implies that a stronger proportion of trades arrived are
informed trades. Both measures have been used in the existing studies (e.g., Chen, Goldstein,
and Jiang, 2007). It is interesting to point out a nuance between the two measures. R2 reflect
the degree to which firm-specific information is impounded into stock prices; on the other
hand, PIN measures the intensity of informed trading, and such information may or may
not be immediately impounded into stock prices.
We estimate R2 in each quarter, using data starting from 12 months before the current
quarter-end and ending 12 months after the current quarter-end. The PIN data are directly
obtained from Soren Hvidkjaer’s website. Because Hvidkjaer’s data are for the period from
1983 to 2001, correspondingly our analysis involving PIN is for the period from 1993 to 2001.
The PIN is an annual measure – i.e., one observation per year for each stock. We therefore
assign the same annual PIN value to the four quarters with the year.
To examine the link between passive fund presence and price informativeness, we per17
form Fama-MacBeth regressions by regressing R2 or PIN onto activeness and passiveness
measures, as well as a set of control variables that are related to stock liquidity. In Table
8, we report the results when we use market capitalization and stock turnover as control
variables.14
When we use R2 as the price information measure, the coefficients for ACTIVEHOLD
and ACTIVETRADE are always significantly negative. The coefficients for PASSIVEHOLD
and PASSIVETRADE are also significantly negative. This suggests that holding and trading
by both active funds and passive funds are positively related to information efficiency. It is
not clear the association for passive funds is stronger or weaker than that for active funds,
as the difference between the coefficients take both positive and negative signs, depending
on model specifications.
When PIN is used as dependent variable, the coefficients for ACTIVEHOLD and ACTIVETRADE are always significantly positive, suggesting that stocks pursued by active
funds are more likely to have informed trading (perhaps by active funds themselves). The
coefficients for PASSIVEHOLD and PASSIVETRADE, on the other hand, are almost always
significantly negative, suggesting that there are less informed trades on these stocks.
How do we interpret the PIN-based results in terms of price informativeness? Some
would argue that a higher PIN means a higher degree of private information incorporated
into the stock price, hence higher price efficiency. Others would say that informed trades
are attracted by less informed stock price, hence a negative relation between PIN and price
informativeness. Their difference appears to be the difference between the preference effect
and the causal effect.
IV.B.
Analysis based on Stock Return Predictability
The literature has documented many market anomalies, or cross-sectional stock return predictability by firm specific characteristics. To the extent that these anomalies reflect mispricing with respect to publicly available information, stronger anomalies means lower price
efficiency. Therefore, by examining whether passive/active fund presence alleviates or exac14
We have also performed the analysis using other liquidity measures as control variables, such as the
Amhihud illiquidity ratio, variance ratio, LDV trading cost. We obtained similar results with these alternate
specifications.
18
erbates anomalies, we can infer the role of these funds in price efficiency.
We consider an extensive set of market anomalies – 25 in total. In Appendix B, we
provide detailed descriptions of each firm-specific variable associated with the anomalies.
While large in number, many variables are related to each other. Based on their nature, we
further group them into eight categories: 1) value (VALUE), 2) investment and financing
activities (INVFIN), 3) earnings quality (EQAL), 4) intangible investments (INTANG), 5)
momentum (MOM), 6) information uncertainty (UNCERT), 7) profitability (PROF), and
8) liquidity (LIQ). We combine variables in each group by a simple average of their crosssectional percentile ranks, into 8 summary variables. The variables are signed so that they
should be positively related to stock returns, according to existing literature. These eight
variables are the focus of our analysis. The details for constructing these measures are also
explained in Appendix B.
In Table 9, we report the univariate Fama-MacBeth regression of stock returns during
the next four quarters (Q1 to Q4) onto each of the eight predictive variables. Most variables
exhibit predictive power on stock returns as indicated by the existing literature.
It is also noted that the predictive power of each variable varies across the four quarterly
holding periods (Q1 to Q4). To obtain a summary measure of the return predictive power
across all four quarters, we take an approach that is similar to the “overlapping portfolio”
approach of Jegadeesh and Titman (1993) for the analysis of momentum portfolios. In the
context of Fama-MacBeth regressions, the specific procedure is as follows. First, in each
quarter, we perform the following four cross-sectional regressions:
RETi,t = a + bk Xi,t−k + ei,t,k
(4)
for k=1, 2, 3, and 4. Xi,t−k is the predictive variable in quarter t-k. That is, we predict stock
returns during quarter t by the k-quarter-lagged predictive variable X. Second, we take the
average of the coefficients bk (k=1, ..., 4), and compute its time series mean. The result is
reported in the last column of Table 9, referred to as the “JT-Average”.
Most “JT-Average” coefficients are significant except two, for UNCERT and LIQ. The
main reason for the insignificant result is the relative short sample period (1993-2006).
Nonetheless, we include them as return predictor, as we are interested in whether passive/active fund presence makes a difference in the predictive power of these variables.
19
To see the impact of passive and active fund presence on the return predictive power of
these variables, we perform the following Fama-MacBeth regressions:
RETi,t = b0,k + b1,k Xi,t−k + b2,k Xi,t−k ∗ ACTIVEi,t−k + b3,k Xi,t−k ∗ PASSIVEi,t−k
+b4,k Xi,t−k ∗ SIZEi,t−k + b5,k Xi,t−k ∗ TURNi,t−k + ei,t,k
(5)
where k=1, ..., 4. Xi,t is one of the eight firm-specific predictive variables. ACTIVEi,t is the
one of the activeness measures and PASSIVEi,t is the corresponding passiveness measure.
SIZE and TURN are log market cap and stock turnover ranks, respectively. When LIQ is
the dependent variable, we do not include SIZE or TURN as explanatory variable.
For the purpose of reporting brevity, we only compute the JT-average of the coefficients,
that is, the average of bj,k (k=1, ...., 4). Further, the results on the “JT-Average” coefficients
are by and large similar when the passiveness and activeness measures are based on holdings
(e.g., PASSIVEHOLD) or based on trades (e.g., PASSIVETRADE). To save space we only
tabulate the results for the holding-bases passiveness and activeness measures and when they
are rank-transformed.
The results are in Table 10. The patterns are as follows. First, the coefficients for the
predictive variables are significant except for two (INTANG and LIQ). Second, a majority
coefficients for the product term X*ACTIVE are negative, and a few are significantly negative. Third, most coefficients for X*PASSIVE are positive, with quite a few significantly
positive. It is also worth-noting that although UNCERT and LIQ per se are not significant in
predicting returns in univariate regressions (Table 9), their interaction terms with activeness
and passiveness are significant predictors.
Therefore, once we control for stock liquidity and for the respective effect on each other
by active vs. passive funds, there is some evidence that the presence of active funds reduces
stock return predictability, and even stronger evidence that the presence of passive funds
exacerbates stock return predictability. This is consistent with the causal effect for both the
passive funds and active funds.
20
V.
Conclusions
This paper investigates the interaction in ownership and trading activity on individual stocks
between active and passive mutual fund, and analyzes the resulting impact on the efficiency
of stock prices. Our study finds that active funds are drawn to the same stocks as passive
funds, and that active funds increase the price efficiency of stocks through their trades. We
also find that stocks with high levels of passive fund ownership and trading exhibit more
long-term pricing anomalies as well as a larger price reversal following trades. Our study is
the first to analyze the separate as well as joint roles of active and passive fund ownership
and trades of U.S. stocks. Our results suggest that further research should account for the
mix of these two institutional types in studying the price discovery process as well as the
tendency of stocks to exhibit pricing anomalies.
21
APPENDIX A: Stock Liquidity Measures
We investigate five measures of stock liquidity. Among the five, SIZE and TURN are readily
explained in the main text. Below we provide details of the remaining three: ILLIQ, LDV, and
VR.
A.1 ILLIQ
The Amihud illiquidity ratio (IR) is based on Amihud (2002) and is further used in Acharya and
Pedersen (2005). IR is computed as
dt
X
|rik |
,
IRit =
dvolik
k=1
where rik is the return on stock i during day k of quarter t; dvolik is the dollar volume traded in
stock i during that day, and dt is the number of trading days in quarter t. We require stock i to
be traded during at least 44 days during quarter t to compute Ait . Note that a more illiquid stock
will have a larger (absolutely value of) return for the same level of dollar volume traded, since the
price impact will be larger.
Since the structure of the Nasdaq market is different from that of the NYSE and AMEX, we
rank stocks, at the end of each quarter, on their IR measure relative to all same-market stocks. That
is, Nasdaq-listed stocks are ranked against all other Nasdaq stocks, and NYSE/AMEX stocks are
ranked against all other NYSE/AMEX stocks. Then, we express the ranking, ILLIQ, in percentile
terms, so that the most illiquid stock receives a ranking of 100 and the most liquid receives a
ranking of 1.
A.2 LDV
Lesmond, Ogden, and Trzcinka (1999) develop a model that exploits the idea that less-liquid stocks
are more likely to have zero return days. Specifically, using a single-index market model for the
∗
true day t return on stock j, Rjt , the measured stock return is nonzero only if the true return Rjt
exceeds the trading cost (in absolute value). That is,
∗
Rjt
= βj Rmt + jt
∗ −α
Rjt = Rjt
1j
if
∗ <α
Rjt
1j
Rjt = 0
if
∗ <α
α1j < Rjt
2j ,
∗ −α
Rjt = Rjt
2j
if
∗ >α
Rjt
2j
where α1j and α2j are the trade costs of selling and buying a stock, respectively. Note that larger
trade costs, α1j and α2j , result in a larger set of true return values over which measured returns are
zero. Then, α1j and α2j are estimated using maximum liklihood estimation methods that assume
that jt is normally distributed. The LDV measure of trading costs (or illiquidity) for stock j is
∗ ), we
then computed as (α2j − α1j ) /2. Since this model assumes a latent dependent variable (Rjt
refer to trading costs estimated using this model as LDV estimates of trading costs.
22
A.3 VR
Another measure we use is the variance ratios as applied in early market efficiency research. If
prices are a random walk, then this implies that the ratio of long-term to short-term variances
should be one. If prices are strongly mean-reverting, then long-term variance should be much lower
than short-term variance.
The m- to n-day (m > n) variance ratio is defined as
V Rmn =
2
σm
m
2
σn
n
,
2 and σ 2 are the volatility of daily log returns over m- and n-days, respectively. Stock
where σm
n
prices following a random walk have an expected variance ratio of one over all values of m and n;
stock prices that are mean-reverting have an expected variance ratio between zero and one. Higher
levels of mean reversion in stock returns (less efficient stock prices) give lower expected values of
V Rmn .
23
APPENDIX B: Return Predictive Variables
We construct the following 24 stock characteristic variables based on data from CRSP, COMPUSTAT, and IBES. The variables are measured at the end of each quarter t. When COMPUSTAT
data is involved, a variable of quarter t means a variable for the fiscal quarter reported in calendar
quarter t. The reporting date is from the COMPSTAT quarterly file. If the COMPUSTAT reporting date is missing, we assume a two month time lag between fiscal quarter end and reporting
date.
1. Value (VALUE)
1) Book-to-Market ratio (BM): book value of equity of quarter t divided by the market capitalization of common shares at end of quarter t
2) Earnings to price ratio (E/P): net income of quarter t divided by market capitalization of
common shares at the end of quarter t.
3) Long term growth forecast (LTG): analyst consensus forecast for long term growth rate
during last month of quarter t.
4) Sales growth (SG): Sales revenue of quarter t divided by sales revenue of quarter t-3.
2. Investment and Financing Activities (INVFIN)
5) Capital expenditure (CAPEX): capital expenditure during quarter t-3 to quarter t, divided
by the total assets of quarter t.
6) Asset growth (AG): total assets of quarter t divided by total assets of quarter t-3.
7) Net share issues (NS): total shares outstanding at the end of quarter t divided by total shares
outstanding 4 quarters ago, adjusting for stock splits.
3. Earnings Quality (EQAL)
8) Accruals (ACC): balance-sheet measure of accruals from quarter t-3 to quarter t, divided
by the average total assets of quarter t-3 and quarter t. The balance-sheet measure of accruals
is change in current assets, minus change in cash and short-term investments, minus change in
current liabilities, plus change in debt in current liabilities, plus change in deferred taxes, minus
depreciation.
9) Net operating assets (NOA): operating assets of quarter t minus operating liabilities of
quarter t, divided by total assets of quarter t. Operating assets is total assets minus cash and
short-term investments. Operating liabilities is total assets minus debt in current liabilities, long
term debt, minority interests, preferred shares, and common equity.
4. Intangible Investments (INTANG)
10) R&D expenditure (RD): R$D expenditure of most recently reported fiscal year, divided by
market cap at the end of the reported fiscal year. Annual data is used because R&D data reported
in COMPUSTAT quarterly file tends to be sporadic.
11) Selling, general, and administrative expenditure (SGA): SGA expenditure of quarter t,
divided by market cap at the end of quarter t. We use SGA to proxy for advertising expenditure,
which is not available in the COMPUSTAT quarterly file.
5. Momentum (MOM)
12) Price momentum (PRRET): stock returns during the 12 months prior to the last month of
quarter t.
13) Analyst forecast revision (FREV): analyst consensus EPS forecast for the currently unreported fiscal year during last month of quarter t, in excess of the consensus EPS forecast for the
same fiscal year made three months ago, divided by stock price at the time the current quarter
consensus forecast is measured.
14) Standardized unexpected earnings (SUE): EPS change from 4-quarter ago (i.e., EPS for
quarter t minus EPS for quarter t-3), divided by the standard deviation of EPS changes from
4-quarter ago. The standard deviation is measured using EPS change of past 8 quarters, with a
minimum of 4 quarters of observations required.
24
15) Earnings surprise (SUR): reported EPS for quarter t minus the last consensus EPS forecast
prior to earnings announcement, divided by stock price when the forecasts are measured.
6. Information uncertainty (UNCERT)
16) Return standard deviation (STDR): standard deviation of daily returns during quarter t.
17) Idiosyncratic volatility (IVOL): standard deviation of residuals from regressing daily stock
returns during quarter t onto daily market returns and 3 lags of market returns. CRSP valueweighted index is used as proxy for the market.
18) Analyst forecast dispersion (DISP): the cross-sectional standard deviation of EPS forecast
for the currently unreported fiscal year, made during month m, divided by the stock price measured
at the time of forecast.
7. Profitability (PROF)
19) Return on assets (ROA): net income of quarter t divided by the total assets at beginning
of quarter t.
20) Change in return on assets (DROA): ROA of quarter t minus ROA of quarter t-3.
8. Liquidity (LIQ)
21) Size (SIZE): log market capitalization at end of quarter t.
22) Trading turnover (TURN): average monthly trading volume during quarter t divided by
total shares outstanding at end of quarter t.
23) Dollar turnover: (DTURN): average monthly dollar trading volume (shares traded multipled
by month-end stock price) during quarter t divided by total shares outstanding at end of quarter
t.
24) Amihud illiquidity ratio (AMIHUD): the absolute daily return divided by the dollar amount
of trading (number of shares traded multiplied by end-of-day stock price), averaged over quarter t.
A minimum of 44 daily observations are required.
After constructing the 24 characteristic variables, we take the following steps to convert them
into 8 predictors.
First, we adjust the sign of each variable so that variables of similar nature are in the same
direction. For example, a high value of TURN is an indication of liquidity, while a high value of
AMIHUD is an indication of illiquidity. So is the relationship between EP and SG. To make these
variables consistent with each other, we add a negative sign in front of the following variables:
LTG, SG, CAPEX, AG, NS, ACC, NOA, STDR, IVOL, DISP, TURN, DTURN. After adjusting
the signs, all the variables are expected to be positively correlated with stock returns during the
subsequent quarter, based on evidence from existing literature.
Second, in each quarter we cross-sectionally rank all 18 signed variables into percentiles to
make them comparable. For the two variables involving trading volume – TURN, DTURN, and
AMIHUD, since NYSE/AMEX and NASDAQ report trading volume differently, we rank stocks
mainly traded on NYSE/AMEX separately from those traded on NASDAQ.
Third, we combine 18 variables into 8 characteristic measures by taking the average of the
percentile ranks. Specifically, VALUE is the average of percentile ranks of BM, EP, -LTG, -SG.
INVFIN is the average percentile ranks of -CAPEX, -AG, and -NS. EQAL is the average percentile
ranks of -ACC and -NOA. INTANG is the average percentile ranks of RND and SGA. MOM is the
average of percentile ranks of PRRET, FREV, SUE, and SUR. UNCTN is the average percentile
ranks of -STDR, -IVOL and -DISP. PROF is the percentile rank of ROA and DROA. Finally, LIQ
is the average percentile ranks of -TURN, -DTURN, and AMIHUD. The negative signs in front of
the variables indicate that we have changed the signs of these variables in the first step.
If any of the 24 variables is missing, it is not used to compute the corresponding characteristic
measure. We require a minimum of 12 non-missing characteristic variables for a stock to be included
in our sample. If any of the resulting 8 predictors is still missing, we replace it with the crosssectional mean (across all valid stocks during the quarter t). However, if more than four resulting
characteristic measures are missing the stock is excluded from the sample.
25
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Markets: Why Do Emerging Markets Have Synchronous Stock Price Movements? Journal
of Financial Economics 59, 215-260.
33. Shu, Tao, 2007, Trader composition, price efficiency, and the cross-section of stock returns,
Working Paper, University of Georgia.
34. Sloan, R., 1996, Do stock prices fully reflect information in accruals and cash flows about
future earnings? Accounting Review 71, 280-315.
27
35. Sias, R., 2004, Institutional Herding, Review of Financial Studies 17, 165-206.
28
29
142
148
140
137
123
109
106
96
90
98
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
69
1995
97
53
1996
35
484
489
438
409
363
397
390
393
396
383
487
488
493
427
Number
Funds
1994
Stock
Median
Equity
Median
1734
1572
1121
639
357
445
755
436
334
363
374
252
286
243
1179
1157
1212
1245
1258
1317
1433
1492
1538
1476
1301
1152
967
788
Funds
of
Number
indicator
Value ($m)
Passive funds
of
Number
1993
Year
Identification
70
72
72
77
71
72
68
65
66
69
69
67
64
63
Number
Stock
Median
Equity
Median
467
481
401
271
338
388
513
348
307
284
249
176
210
193
Value ($m)
Active funds
287
286
281
325
331
329
379
350
369
371
287
226
192
144
Funds
of
Number
146
147
128
123
114
121
118
113
116
111
119
134
123
119
Number
Stock
Median
Equity
Median
1506
1418
1002
676
622
752
1303
1010
824
644
580
395
618
678
990
961
1027
1026
1036
1111
1191
1282
1317
1247
1111
995
828
679
Funds
of
Number
probit
Value ($m)
Passive funds
64
65
66
72
67
66
62
61
60
65
64
62
60
59
Number
Stock
Median
Equity
Median
376
386
354
235
287
326
415
287
257
232
222
160
176
159
Value ($m)
Active funds
This table reports summary statistics of passive and active mutual funds in each year from 1993 to 2006. Passive funds are identified by
either the index fund indicator in the MFLINK data combined with those manually identified, or by a probit model that are based on fund
characteristics. In each year, for passive funds and active funds separately, we report the total number of funds, median number of stocks
held by funds, and the median value of equity held by funds. Number of stocks and value of equity holdings are based on end-of-year observations. If a fund do not report holdings for the last quarter of a year, we use their latest reported holdings of the year to compute these statistics.
Table 1. Summary Statistics: Annual Snapshots of Passive and Active Funds
30
0.36
0.52
0.71
1.36
0.03
Turnover
Expense (%)
HHOLD (%)
HTRADE (%)
0.93
0.01
0.88
0.60
0.22
0.18
0.97
median
0.09
1.18
0.50
1.12
0.46
0.12
2.00
2.40
1.28
0.87
0.59
0.87
mean
indicator
stdev
Passive funds
mean
|α| (%)
R
2
Identification
0.05
1.98
1.22
0.66
0.43
0.91
median
Active funds
56.25
2.22
0.42
0.79
0.58
0.13
stdev
0.03
1.47
0.87
0.47
0.35
0.93
mean
0.02
1.32
0.89
0.34
0.24
0.95
median
0.05
0.97
0.37
0.71
0.39
0.09
stdev
Passive funds
2.49
2.57
1.35
0.96
0.65
0.85
mean
probit
0.05
2.13
1.29
0.76
0.49
0.89
median
Active funds
62.87
2.35
0.41
0.83
0.61
0.13
stdev
This table reports characteristics of passive and active mutual funds. Passive funds are identified by either the index fund indicator or by
a probit model. Fund characteristics include the R-square (R2 ) and the absolute value of fund alpha (|α|), both obtained from regressing
pre-expense fund returns onto the Fama-French 3-factor model using rolling past 12 month returns, fund annual turnover ratio (Turnover),
annual expense ratio (Expense), Herfindahl index of fund holdings (HHOLD), and Herfindahl index of fund trading (HTRADE). We first
calculate the mean, median, and standard deviation of these characteristic measures in each quarter for passive and active funds separately,
and then average them over the sample years from 1993 to 2006.
Table 2. Fund Characteristics: Passive vs. Active Funds
31
0.00
-0.27
PASSIVETRADE
PASSIVEBUY
-4.49
ACTIVEBUY
0.00
0.00
ACTIVETRADE
PASSIVEHOLD
0.16
P5
ACTIVEHOLD
Identificatoin
-0.01
0.02
0.30
-0.63
0.68
2.15
Q1
0.03
0.13
0.91
0.11
2.89
6.64
Median
0.16
0.32
1.65
1.53
6.77
12.86
Q3
indicator
0.63
0.95
3.05
6.59
15.26
23.93
P95
0.10
0.27
1.13
0.80
5.02
8.94
Mean
1.05
1.10
1.62
20.95
22.06
24.34
Std
-2.10
0.00
0.00
-3.57
0.00
0.02
P5
-0.10
0.14
0.89
-0.45
0.34
1.12
Q1
0.05
0.76
2.70
0.04
1.85
3.94
Median
0.60
2.18
6.04
1.06
4.71
8.31
Q3
probit
3.14
5.87
12.67
5.10
11.58
16.93
P95
0.35
1.70
4.20
0.58
3.58
5.87
Mean
6.62
7.02
8.44
16.93
17.69
19.46
Std
This table reports cross-sectional distribution of stock level passiveness and activeness measures. Passive funds are identified by either the
index fund indicator or by a probit model. PASSIVEHOLD (ACTIVEHOLD) is the total number of shares of a stock held by all passive
(active) funds in current quarter divided by shares outstanding at current quarter-end. PASSIVETRADE (ACTIVETRADE) is the total
purchase plus total sale of a stock by all passive (active) funds during the current and previous quarter, divided by total shares outstanding.
PASSIVENETBUY (ACTIVENETBUY) is the net purchase – total purchase minus total sale – by all passive (active) funds on a stock during
the current and previous quarter, divided by the total shares outstand. The cross-sectional statistics include the 5th percentile, 1st quartile,
median, 3rd quartile, 95th percentile, and standard deviation. We first calculate these statistics for each quarter, and then take the average
over the sample period from 1993 to 2006.
Table 3. Cross-sectional Distribution of Stock Level Activeness and Passiveness Measures
Table 4. Correlations between Stock-level Passiveness and Activeness Measures
This table reports relations between the stock-level measures of passiveness and activeness. Passive funds
are identified by either the index fund indicator or by a probit model. The three activeness measures
are ACTIVEHOLD, ACTIVETRADE, ACTIVENETBUY, and the corresponding passiveness measures are
PASSIVEHOLD, PASSIVETRADE, and PASSIVENETBUY. Panel A report the pairwise correlations. We
first calculate the pairwise correlation between a passiveness measure and the corresponding activeness
measure across all stocks in each quarter. We then report the time series averages and the corresponding
t-statistics (in parenthesis) over the sample years from 1993 to 2006. In Panel B, we perform quarterly
cross-sectional regressions and report the time-series averages of the estimated coefficients. The dependent
variable is one of the activeness measure and the explanatory variables include the corresponding passiveness
measure, log market cap (SIZE), and cross-sectional rank of trading turnover (TURN). Regression intercept
is not reported.
Panel A: Correlations
indicator
Identification
probit
Pearson
Spearman
Pearson
Spearman
(PASSIVEHOLD, ACTIVEHOLD)
0.16 (4.85)
0.25 (10.95)
0.29 (11.54)
0.46 (48.51)
(PASSIVETRADE, ACTIVETRADE)
0.16 (4.94)
0.33 (10.21)
0.28 (11.52)
0.48 (37.89)
(PASSIVENETBUY, ACTIVENETBUY)
0.11 (3.31)
0.04 (1.83)
0.17 (5.56)
0.12 (18.10)
Panel B: Cross-sectional Regressions with Control for Liquidity
Dependent variables: activeness measures
Identification
indicator
HOLD
TRADE
probit
NETBUY
HOLD
TRADE
NETBUY
Raw activeness and passiveness measures
PASSIVE
SIZE
TURN
1.04
0.95
0.62
0.36
0.35
0.27
(4.62)
(2.75)
(2.08)
(12.03)
(8.42)
(4.55)
3.98
-4.81
-3.51
-2.07
-5.72
-3.04
(1.43)
(-1.53)
(-1.23)
(-0.73)
(-1.84)
(-1.10)
1.12
1.26
0.24
0.86
0.91
0.18
(12.65)
(11.84)
(2.81)
(10.55)
(9.14)
(2.22)
Rank-transformed activeness and passiveness measures
PASSIVE
SIZE
TURN
0.21
0.14
0.02
0.33
0.30
0.11
(14.27)
(15.59)
(1.99)
(47.56)
(40.87)
(17.12)
4.70
3.94
0.30
2.52
2.24
0.02
(50.71)
(39.04)
(2.05)
(21.41)
(28.00)
(0.12)
0.31
0.51
0.09
0.33
0.45
0.07
(44.75)
(69.89)
(11.36)
(38.39)
(57.51)
(10.51)
32
Table 5. Passiveness, Activeness, and Stock Liquidity
This table reports the results of Fama-MacBeth regressions that examine the effect of activeness and passiveness on stock liquidity. The dependent variables include five stock liquidity measures: cross-sectional
percentile rank of Amihud illiquidity ratio (ILLIQ), the latent dependent variable estimate of trading cost
(LDV), log market capitalization (SIZE), cross-sectional percentile rank of stock trading turnover (TURN),
and five-day vs. one-day variance ratio (VR). In Panel A, the explanatory variables are the cross-sectional
percentile rank of activeness and passiveness measures PASSIVEHOLD, ACTIVEHOLD, PASSIVETRADE
and ACTIVETRADE. In Panel B, the explanatory variables are the cross-sectional standardized measures
of activeness and passiveness. DIF is the difference in estimated coefficients between the passiveness measure
and the corresponding activeness measure. Passive funds are identified by either the index fund indicator or
by a probit model. Stock liquidity measures are for the quarter subsequent to the passiveness and activeness
measures. The cross-sectional regressions are performed in each quarter. Reported are the time series means
and the corresponding t-statistics (in parenthesis) of the estimated coefficients. Regression intercept is not
reported. Reported coefficients are multiplied by 100 when LDV is the dependent variable.
Panel A: Rank-transformed passiveness and activeness measures
Identification
indicator
ILLIQ
ACTIVEHOLD
PASSIVEHOLD
ACTIVETRADE
PASSIVETRADE
LDV
SIZE
probit
TURN
VR
ILLIQ
LDV
SIZE
TURN
VR
-34.05
-0.32
1.84
34.83
0.19
-30.57
-0.22
1.24
35.77
0.16
(-41.14)
(-9.77)
(55.46)
(56.55)
(19.25)
(-26.86)
(-10.92)
(15.42)
(46.48)
(20.17)
-1.90
-0.04
0.20
-0.35
0.03
-12.39
-0.21
1.18
4.75
0.06
(-1.74)
(-2.66)
(2.48)
(-0.43)
(3.33)
(-10.96)
(-7.77)
(12.75)
(6.68)
(5.13)
-40.23
-0.27
1.77
48.21
0.22
-34.29
-0.17
1.14
44.81
0.17
(-45.73)
(-10.25)
(35.16)
(79.76)
(16.83)
(-32.68)
(-10.49)
(14.35)
(69.12)
(19.25)
-14.79
-0.12
0.83
7.09
0.02
-21.62
-0.24
1.58
12.56
0.10
(-12.36)
(-8.72)
(9.26)
(7.32)
(2.64)
(-23.38)
(-9.83)
(20.56)
(16.14)
(6.78)
Panel B: Cross-sectionally standardized passiveness and activeness measures
Identification
indicator
ILLIQ
ACTIVEHOLD
PASSIVEHOLD
ACTIVETRADE
PASSIVETRADE
LDV
SIZE
probit
TURN
VR
ILLIQ
LDV
SIZE
TURN
VR
-27.36
-0.27
1.47
30.06
0.15
-25.92
-0.20
0.93
33.31
0.13
(-4.67)
(-3.92)
(4.57)
(4.73)
(4.39)
(-4.19)
(-3.70)
(4.42)
(4.14)
(4.37)
-0.53
-0.00
0.03
1.82
0.01
-6.20
-0.09
0.60
4.06
0.02
(-0.44)
(-0.35)
(0.48)
(1.75)
(1.36)
(-5.15)
(-4.63)
(5.18)
(4.69)
(3.19)
-50.28
-0.33
2.05
65.48
0.24
-42.45
-0.20
1.07
61.37
0.19
(-4.82)
(-4.03)
(4.66)
(4.72)
(4.41)
(-3.90)
(-3.45)
(3.73)
(3.84)
(3.61)
-9.33
-0.03
0.36
11.40
0.03
-18.72
-0.16
1.32
18.79
0.11
(-2.14)
(-1.26)
(1.65)
(2.35)
(1.71)
(-4.53)
(-4.27)
(4.10)
(4.08)
(2.85)
33
Table 6. Trading Synchronicity: Passive Funds vs. Active Funds
This table reports synchronicity of trades among passive funds and among active funds. Passive funds are
identified by either the index fund indicator in the MFLINK data or by a probit model. Two synchronicity
measures are used. |net $trades|/total $trades is the absolute value of net purchase by all passive or active
funds on a stock during the current quarter and the previous quarter, divided by the total purchase plus
total sale, over the current quarter and the prior quarter. |net #trades|/total #trades is the absolute value of
net number of funds purchasing a stock during the current quarter and the previous quarter, divided by the
total number of funds trading on the stock, over the current quarter and the prior quarter. In each quarter,
we calculate these measures on each individual stock, for passive funds and for active funds separately, and
then average them across stocks. Their time series means over the sample years from 1993 to 2006, and the
corresponding t-statistics (in parenthesis) are reported. Passive-Active is the difference of the synchronicity
measures between the passive funds and active funds.
Identification
indicator
probit
Passive
Active
Passive-Active
Passive
Active
Passive-Active
|net $trades|/total $trades
0.81
0.61
0.20 (29.37)
0.71
0.63
0.09 (17.09)
|net #trades|/total #trades
0.58
0.42
0.16 (9.88)
0.50
0.43
0.08 (7.48)
34
Table 7. Price Impact of Passive Funds and Active Funds
This table reports the results of Fama-MacBeth regressions that examine the price impact of active and passive funds. The dependent variables are stock returns in subsequent four quarters (RETQ1 to RETQ4). The
main explanatory variables are PASSIVENETBUY and ACTIVENETBUY. These variables are transformed
into cross-sectional percentile ranks (Panel A) and cross-sectionally standardized (Panel B), before used in
regressions. DIF is the coefficient for PASSIVENETBUY minus the coefficient for ACTIVENETBUY. Control variables include stock return during the current quarter (RETQ0), log market capitalization (SIZE),
and exchange-specific cross-sectional percentile rank of stock trading turnover (TURN). Identification of
passive funds is based on either the index fund indicator or the probit model. The cross-sectional regressions
are performed in each quarter from 1993 to 2006. Reported are the time series means and the corresponding
t-statistics (in parenthesis) of the estimated coefficients. Regression intercept is not reported.
Panel A: Rank-transformed passiveness and activeness measures
Identification
indicator
RETQ1
ACTIVEBUY
PASSIVEBUY
RETQ0
SIZE
TURN
RETQ2
probit
RETQ3
RETQ4
RETQ1
RETQ2
RETQ3
0.56
-0.54
-1.23
-0.83
0.89
-0.34
-0.97
-0.64
(0.95)
(-0.87)
(-2.18)
(-1.87)
(1.54)
(-0.60)
(-1.85)
(-1.49)
-0.91
-0.59
-0.41
-0.38
-0.38
-0.62
-0.73
-0.60
(-2.56)
(-1.82)
(-1.17)
(-1.16)
(-0.98)
(-1.65)
(-2.27)
(-2.01)
2.18
4.59
2.36
0.03
2.16
4.60
2.36
0.03
(1.52)
(4.65)
(1.88)
(0.02)
(1.51)
(4.66)
(1.88)
(0.03)
-0.11
-0.08
-0.08
-0.05
-0.12
-0.07
-0.07
-0.04
(-0.66)
(-0.46)
(-0.48)
(-0.28)
(-0.70)
(-0.43)
(-0.42)
(-0.22)
-0.95
-1.29
-1.49
-1.41
-1.01
-1.32
-1.49
(-0.49)
(-0.67)
(-0.80)
(-0.81)
(-0.53)
(-0.68)
(-0.81)
Panel B: Cross-sectionally standardized passiveness and activeness measures
Identification
ACTIVENETBUY
PASSIVENETBUY
RETQ0
SIZE
TURN
RETQ4
indicator
-1.42
(-0.82)
probit
RETQ1
RETQ2
RETQ3
RETQ4
RETQ1
RETQ2
RETQ3
0.23
-0.02
-0.18
-0.02
0.13
-0.04
-0.10
RETQ4
-0.03
(0.96)
(-0.15)
(-1.60)
(-0.28)
(0.81)
(-0.28)
(-1.15)
(-0.31)
-0.37
-0.22
0.01
-0.02
-0.23
-0.18
-0.08
-0.09
(-1.66)
(-2.25)
(0.09)
(-0.39)
(-2.01)
(-2.24)
(-0.96)
(-1.61)
2.17
4.54
2.27
-0.03
2.18
4.54
2.28
-0.01
(1.51)
(4.63)
(1.80)
(-0.02)
(1.51)
(4.62)
(1.81)
(-0.01)
-0.12
-0.07
-0.08
-0.05
-0.12
-0.07
-0.08
-0.05
(-0.70)
(-0.44)
(-0.46)
(-0.25)
(-0.68)
(-0.44)
(-0.48)
(-0.25)
-1.01
-1.40
-1.64
-1.55
-1.01
-1.42
-1.65
-1.54
(-0.52)
(-0.71)
(-0.87)
(-0.88)
(-0.52)
(-0.72)
(-0.87)
(-0.87)
35
36
-35.22 (-3.68)
-29.16 (-2.29)
0.02 (14.02)
0.09 (10.97)
ACTIVE
PASSIVE
SIZE
TURN
R2
0.10 (10.89)
TURN
-0.24 (-12.59)
0.08 (9.95)
0.02 (16.34)
-0.39 (-8.03)
-0.05 (-18.10)
-0.03 (-57.90)
-0.24 (-11.30)
0.04 (2.68)
PIN
trading-based
-0.16 (-5.14)
R2
0.10 (11.09)
0.02 (16.58)
-0.29 (-6.95)
-0.10 (-4.24)
PIN
-0.06 (-20.68)
-0.03 (-55.64)
-6.78 (-3.42)
31.91 (4.51)
R2
0.08 (9.96)
0.02 (15.43)
-17.66 (-3.57)
-0.06 (-18.62)
-0.03 (-54.75)
-7.17 (-2.47)
6.52 (4.25)
PIN
trading-based
-8.26 (-3.84)
indicator
R2
0.09 (11.19)
0.02 (14.48)
-11.05 (-2.40)
-30.23 (-3.16)
-0.06 (-21.32)
-0.03 (-56.64)
-1.50 (-0.41)
39.12 (3.16)
PIN
holding-based
0.08 (9.94)
0.02 (15.76)
-10.63 (-3.98)
-4.32 (-1.64)
R2
-0.08 (-3.65)
-0.05 (-19.33)
-0.02 (-62.10)
-0.05 (-18.89)
-0.03 (-58.86)
-1.79 (-1.19)
10.24 (3.78)
PIN
trading-based
0.08 (9.84)
0.02 (16.80)
0.06 (3.35)
PIN
trading-based
-0.29 (-6.43)
probit
-0.05 (-25.95)
-0.02 (-64.87)
R2
-0.14 (-4.50)
probit
0.09 (4.12)
PIN
holding-based
-0.26 (-7.95)
R2
Panel B: Cross-sectionally standardized passiveness and activeness measures
-0.05 (-24.52)
-0.03 (-56.55)
holding-based
0.02 (15.82)
SIZE
Identification
-0.37 (-10.91)
PASSIVE
0.07 (3.13)
indicator
Panel A: Rank-transformed passiveness and activeness measures
PIN
holding-based
-0.28 (-9.23)
R2
ACTIVE
Identification
This table reports the results of Fama-MacBeth regressions that examine the effect of stock level activeness and passiveness on stock price
informativeness. The dependent variables include R2, the Rsquare of regressing weekly individual stock returns onto weekly market returns,
and PIN, the measure of probability of informed trading as per Easley et al. (2002). The main explanatory variables, ACTIVE and PASSIVE, refer to stock level activeness and passiveness that are either holding-based (ACTIVEHOLD and PASSIVEHOLD), or trading-based
(ACTIVETRADE and PASSIVETRADE). PASSIVEHOLD (ACTIVEHOLD) is the total number of shares of a stock held by all passive
(active) funds in current quarter divided shares outstanding end of current quarter. PASSIVETRADE (ACTIVETRADE) is the sum of total
purchase and total sale of a stock by all passive (active) funds during the current quarter and the previous quarter divided by total shares
outstanding. These variables are either cross-sectionally rank-transformed (Panel A) or cross-sectionally standardized (Panel B), before used
in regressions. Passive funds are identified by either the index fund indicator or by a probit model. The two control variables are log market
cap (SIZE) and cross-sectional rank of trading turnover (TURN). The cross-sectional regressions are performed in each quarter from 1993
to 2006. Reported are the time series means and the corresponding t-statistics (in parenthesis) of the estimated coefficients. Regression
intercept is not reported. DIF is the difference in estimated coefficients between PASSIVE and ACTIVE. Reported coefficient for TURN is
pre-multiplied by 1,000.
Table 8. Passiveness, Activeness, and Price Informativeness
Table 9. Fama-MacBeth Regressions of Stock Returns onto Return Predictors
This table reports the results of Fama-MacBeth regressions of stock returns onto each return-predictive variable. In each regression, the dependent variable is stock return during one of the subsequent four quarters
(RETQ1 to RETQ4); the explanatory variable is one of the following eight stock return predictors: value
(VALUE), investment and financing activities (INVFIN), earnings quality (EQAL), intangible investments
(INTANG), momentum (MOM), uncertainty (UNCERT), profitability (PROF), and liquidity (LIQ). In the
column “JT-Average”, we report the average coefficients of regressions with predictors lagged by one to four
quarters. The explanatory variables are signed so that their correlations with next-quarter stock returns,
according to existing literature, are positive. The cross-sectional regressions are performed in each quarter
from 1993 to 2006. Reported are the time series means and the corresponding t-statistics (in parenthesis)
of the estimated coefficients. Regression intercept is not reported. Reported coefficients are multiplied by 100.
RETQ1
RETQ2
RETQ3
RETQ4
JT-Average
VALUE
4.41 (1.28)
4.72 (1.79)
4.98 (1.77)
4.19 (1.26)
4.42 (2.88)
INVFIN
3.04 (2.15)
3.61 (2.50)
3.19 (2.08)
2.45 (1.63)
2.89 (3.52)
EQAL
2.22 (2.71)
2.13 (2.37)
1.93 (2.18)
2.10 (2.53)
1.92 (3.58)
INTANG
3.09 (2.94)
3.23 (3.19)
3.70 (3.60)
3.05 (3.08)
3.18 (5.70)
MOM
6.39 (5.43)
4.90 (4.59)
0.99 (0.77)
-0.21 -(0.22)
3.10 (7.06)
UNCERT
2.48 (1.87)
1.63 (0.56)
1.60 (0.67)
1.41 (0.51)
1.78 (1.38)
PROF
5.23 (3.74)
4.29 (2.95)
3.18 (2.17)
1.77 (1.29)
3.61 (5.33)
LIQ
1.42 (0.76)
1.98 (1.69)
1.94 (1.45)
1.41 (0.78)
1.56 (1.50)
37
38
0.13 (0.52)
1.24 (1.12)
X*TURN
-2.07 (-1.79)
X*ACTIVE
-0.21 (-1.35)
5.81 (2.94)
X
X*SIZE
1.28 (1.22)
X*TURN
X*PASSIVE
1.43 (0.43)
-0.23 (-1.48)
X*SIZE
-1.56 (-0.28)
X*ACTIVE
X*PASSIVE
6.13 (3.09)
X
VALUE
-0.16 (-0.10)
-0.22 (-1.39)
1.32 (2.02)
-1.48 (-1.27)
5.20 (2.62)
-0.38 (-0.24)
-0.30 (-1.83)
1.46 (2.74)
0.51 (0.74)
5.62 (2.88)
INVFIN
-1.19 (-0.61)
-0.32 (-1.93)
2.22 (2.93)
-1.05 (-0.87)
6.04 (3.22)
-1.46 (-0.72)
-0.42 (-2.44)
2.44 (2.93)
1.76 (2.64)
6.23 (3.33)
EQAL
-0.81 -(0.51)
0.09 (0.62)
0.77 (1.23)
-1.43 (-1.67)
2.19 (1.27)
probit
-0.82 (-0.51)
0.06 (0.40)
0.48 (0.92)
-0.53 (-0.94)
2.57 (1.43)
indicator
INTANG
-1.70 (-0.93)
-0.43 (-2.46)
1.92 (2.53)
-2.78 (-1.90)
9.17 (4.90)
-1.96 (-1.05)
-0.53 (-2.88)
2.42 (3.25)
0.73 (1.05)
9.50 (5.11)
MOM
0.85 (1.92)
-0.36 (-2.94)
0.83 (2.19)
-1.95 (-1.61)
6.10 (2.35)
0.51 (1.09)
-0.37 (-3.06)
0.87 (2.40)
-0.13 (-0.29)
5.87 (2.39)
UNCERT
Panel A: Rank-transformed passiveness and activeness measures
-1.31 (-0.76)
-0.32 (-2.15)
1.04 (2.19)
-1.82 (-1.87)
8.23 (3.85)
-1.43 (-0.82)
-0.41 (-2.68)
2.04 (3.08)
-0.24 (-0.44)
8.91 (4.34)
PROF
1.19 (1.92)
-4.20 (-2.53)
1.32 (1.46)
2.11 (4.22)
-0.14 (-0.21)
0.80 (0.93)
LIQ
This table reports the results of Fama-MacBeth regressions that examine the effect of passive and active funds on return-predictive power
of firm characteristics. In each regression, the dependent variable is stock return during one of the subsequent four quarters (RETQ1 to
RETQ4). The main explanatory variables include X, one of the eight stock return predictors, and two product terms X*ACTIVE and
X*PASSIVE, where, ACTIVE is the cross-sectional rank of the activeness measure ACTIVEHOLD, and PASSIVE is the cross-sectional
rank of the corresponding passiveness measure PASSIVEHOLD. The return-predictors (X) are, respectively, value (VALUE), investment and
financing activities (INVFIN), earnings quality (EQAL), intangible investments (INTANG), momentum (MOM), uncertainty (UNCERT),
profitability (PROF), and liquidity (LIQ). These predictive variables are signed so that their correlations with next-quarter stock returns,
according to existing literature, are positive. In addition, we include two control variables X*SIZE and X*TURN, where SIZE is the log market
cap and TURN is the exchange-specific cross-sectional percentile rank of trading turnover. The cross-sectional regressions are performed in
each quarter from 1993 to 2006. The explanatory variables are lagged by one to four quarters and in each quarter we take the averages of
the coefficients across the four regressions (i.e., the “JT-Average” coefficient). Reported are the time series means and the corresponding
t-statistics (in parenthesis) of the estimated quarterly-average coefficients. Regression intercept is not reported. Coefficients in the table are
all multiplied by 100.
Table 10. Passiveness, Activeness, and Cross-sectional Stock Return Predictability
39
0.13 (0.52)
-0.21 (-1.35)
1.24 (1.12)
X*PASSIVE
X*SIZE
X*TURN
X*TURN
5.81 (2.94)
1.28 (1.21)
X*SIZE
-2.07 (-1.79)
-0.21 (-1.42)
X*PASSIVE
X*ACTIVE
-0.17 (-0.65)
X*ACTIVE
X
6.03 (3.05)
-1.42 (-1.63)
X
VALUE
-0.16 (-0.10)
-0.22 (-1.39)
1.32 (2.02)
-1.48 (-1.27)
5.20 (2.62)
-0.43 (-0.27)
-0.27 (-1.69)
0.57 (1.36)
-1.15 (-1.14)
5.70 (2.89)
INVFIN
-1.19 (-0.61)
-0.32 (-1.93)
2.22 (2.93)
-1.05 (-0.87)
6.04 (3.22)
-1.47 (-0.73)
-0.37 (-2.17)
0.95 (2.20)
0.07 (0.08)
6.41 (3.33)
EQAL
-0.81 -(0.51)
0.09 (0.62)
0.77 (1.23)
-1.43 (-1.67)
2.19 (1.27)
probit
-0.87 (-0.54)
0.08 (0.50)
0.19 (0.46)
-1.39 (-1.79)
2.36 (1.32)
indicator
INTANG
-1.70 (-0.93)
-0.43 (-2.46)
1.92 (2.53)
-2.78 (-1.90)
9.17 (4.90)
-2.03 (-1.09)
-0.48 (-2.66)
0.99 (2.11)
-1.27 (-1.14)
9.59 (5.02)
MOM
0.85 (1.92)
-0.36 (-2.94)
0.83 (2.19)
-1.95 (-1.61)
6.10 (2.35)
0.50 (1.10)
-0.34 (-2.90)
0.22 (0.72)
-1.09 (-1.25)
5.69 (2.29)
UNCERT
Panel B: Cross-sectionally standardized passiveness and activeness measures
-1.31 (-0.76)
-0.32 (-2.15)
1.04 (2.19)
-1.82 (-1.87)
8.23 (3.85)
-1.56 (-0.89)
-0.37 (-2.45)
0.66 (1.73)
-1.17 (-1.48)
8.82 (4.20)
PROF
1.19 (1.92)
-4.20 (-2.53)
1.32 (1.46)
0.61 (1.74)
-2.72 (-2.06)
1.18 (1.32)
LIQ