Information Asymmetry about the Firm and the
Permanent Price Impact of Trades:
Is there a Connection?
Gideon Saar
Lei Yu1
First Draft: July 2001
This Version: July 2002
1 Both
authors are from the Stern School of Business, New York University, 44 West Fourth
Street, Suite 9-190, New York, NY 10012-1126. Saar can be reached at Tel: 212-998-0318, Fax:
212-995-4233, E-mail: [email protected], and Yu can be reached at Tel: 212-998-0321, Fax:
212-995-4233, E-mail: [email protected]. The authors thank I/B/E/S for providing the data on
analysts’ earnings forecasts, Frank Russell Company for data on the 1999 reconstitution of the
Russell 1000 index, and Foster Provost for helping with the matching procedure used in the paper.
The authors are grateful for helpful comments from Hendrik Bessembinder, Ekkehart Boehmer,
Joel Hasbrouck, and seminar participants at Babson College, University of Utah, and NYU.
Abstract
We investigate whether permanent price impact measures describing intra-day price movements are helpful in characterizing information asymmetry about the fundamentals of firms.
We conduct an event study of the Russell 1000 index reconstitution and find that the permanent price impact measures change around the event despite the fact that Russell 1000
membership is based on market capitalization and therefore the event is not associated with
any change in private information about the firms. We also examine a large cross-sectional
sample and find that the permanent price impact measures do not consistently reflect uncertainty about future earnings or relate to price informativeness about future earnings in a
manner that is compatible with their use as proxies for information asymmetry about firms’
fundamentals.
Information Asymmetry about the Firm and the Permanent Price Impact of Trades: Is there a Connection?
The literature examining price movements on trades often makes a distinction between
“temporary” and “permanent” price movements. Short-horizon temporary price movements
have been attributed, for example, to inventory management on the part of market makers;
the most common reason cited for the permanent price impact of trades has been the presence
of investors with private information about the future cash flows of the firm who trade to
profit from their information.
A number of papers have put forward econometric specifications for estimating the permanent and temporary price impacts of trades using intra-day data comprised of trades
and quotes (see, for example, Glosten, 1987; Glosten and Harris, 1988; Hasbrouck, 1988;
Stoll, 1989; Hasbrouck, 1991a; Hasbrouck, 1991b; Madhavan and Smidt, 1991; Huang and
Stoll, 1997; Madhavan, Richardson, and Roomans, 1997).1 While the aforementioned papers focused on quantifying the relative importance of temporary and permanent factors in
explaining price movements, researchers have soon found a rich set of applications for these
new tools. Since theoretically the permanent price impact of trades was associated with the
incorporation into prices of private information about fundamentals, measures of the permanent price impact were used to quantify the extent of information asymmetry about a firm.
These measures proved attractive in areas outside market microstructure (e.g., corporate finance) where researchers have been interested in characterizing the information asymmetry
environment of a firm, which is inherently unobservable.2
There are two potential problems with using measures of permanent price impact estimated from trade and quote data to tell a story about the future cash flows, or fundamentals,
1
George, Kaul, and Nimalendran (1991) propose a methodology for estimating components of the spread
that uses daily and weekly rather than intra-day data.
2
For example, these measures were used to investigate information asymmetry in the contexts of corporate
events (Brooks, 1994; Jennings, 1994; Barclay and Dunbar, 1996; Krinsky and Lee, 1996; Desai, Nimalendran,
and Venkataraman, 1998), the debt-equity mix (Illesy and Shastri, 2000), corporate diversification (Fee and
Thomas, 1999), disclosure quality (Heflin, Shaw, and Wild, 2000), the opaqueness of banking firms’ assets
(Flannery, Kwan, and Nimalendran, 2000), the size of the analyst following (Brennan and Subrahmanyam,
1995), and ownership structure (Heflin and Shaw, 2000a; Sarin, Shastri, and Shastri, 2000, Dennis and
Weston, 2001; Dey and Radhakrishna, 2001).
1
of a firm. The first problem is that many elements in the trading environment of a stock
can affect the estimation procedures and bias the estimates. For example, specific rules that
govern trading, like the price continuity requirement at the NYSE, affect the adjustment of
prices to order flow and therefore the measures of permanent price impact estimated from
trades and quotes. A slowly moving target inventory level of NYSE specialists (see, for
example, Hasbrouck and Sofianos, 1993) can also affect the estimates. This may partially
explain the fact that, in our large cross-sectional sample, the magnitude of permanent price
impact measures for NYSE stocks is on average three times that of NASDAQ stocks. Does it
really mean that there is so much more information asymmetry about NYSE firms relative
to Nasdaq firms? When elements that conceptually should not affect prices permanently
get incorporated into the permanent price impact measures, it is unclear whether differences in the measures reflect differences in the information asymmetry environment or other
influences.
Even if we are certain that the permanent price impact measures indeed capture only
things that should affect the price permanently, the second potential problem is that not only
information asymmetry about the future cash flows of a firm can give rise to the permanent
price impact of trades. The “discount rate” effect documented in the literature for longer
horizon returns (e.g., Fama, 1990; Campbell and Ammer, 1993) demonstrates how return
variation is partly caused by shocks to future expected returns, not just shocks to expected
future cash flows.3 Saar (2001) shows in a sequential trade model how uncertainty about
the distribution of preferences and endowments of investors affects the risk premium and
generates a permanent price impact for trades even in the absence of information asymmetry
about future cash flows. Therefore, the permanent price impact measures may be picking
up information about investors that is unrelated to the fundamentals of firms.
3
Fama (1990), for example, finds that the discount rate effect accounts for about 30% of the variance
of annual real returns on a value-weighted portfolio of NYSE stocks. Campbell and Ammer (1993) use a
vector autoregression (VAR) decomposition of monthly stock excess returns and find that only 15% of the
variance of returns is attributed to the variance of news about future dividends, while 70% is attributed to
the variance of news about future excess returns.
2
Both problems weaken the link between the permanent price impact measures and information asymmetry about the firm. To have confidence in using these measures to make an
inference about the level of information asymmetry, it is important to investigate empirically
how close is the association between them. The objective of this paper is to examine the
question whether measures constructed from trade and quote data to describe intra-day price
movements are helpful in characterizing information asymmetry about the fundamentals of
firms.
Four papers in particular are related to our investigation: Neal and Wheatley (1998)
and Clarke and Shastri (2001) are two papers looking at close-end funds; Clarke and Shastri
(2000) and Van Ness, Van Ness, and Warr (2001) conduct “horse races” among different
permanent price impact measures. Neal and Wheatley postulate that since the net asset
value of a closed-end fund is reported every week, there can be little information asymmetry
about its current liquidation value. They find large permanent price impact measures, and
conclude that the estimates may be unreliable. Clarke and Shastri (2001) reach a different
conclusion, arguing that uncertainty about private benefits paid to blockholders creates
adverse selection costs.
Clarke and Shastri (2000) use six econometric methodologies to estimate permanent price
impact measures for 320 NYSE firms. They look at how these measures relate to each other,
and also at the correlations between the measures and certain firm characteristics. The correlations with firm characteristics are statistically significant only for net sales and a dummy
for regulated firms. Similarly, Van Ness, Van Ness, and Warr (2001) conduct a horse race of
five permanent price impact measures using 856 NYSE stocks and examine their relations
with corporate finance variables, volatility measures, and measures that involve analysts
and institutional holdings. They find mixed results, with no single econometric methodology producing estimates that are consistently correlated with the variables they consider as
information proxies. The strongest relation they document is between the permanent price
impact measures and volatility.
3
Both “horse race” papers mentioned above are subject to the same conceptual problem.
Since information asymmetry is unobservable, they use a variety of proxies about which
they have stories of how the proxies relate to information asymmetry about fundamentals.
However, since the permanent price impact measures also have a story that relates them to
information asymmetry, the exercise turns into looking at relations among proxies without
the ability to determine whether lack of relation between the permanent price impact measures and the other information proxies is the fault of the measures or the other proxies.
The design in the present paper is more powerful since we use an event study that allows
for a characterization of changes (or their absence) in the information asymmetry environment without the need to rely on proxies. We additionally provide a cross-sectional analysis
for three reasons. First, it allows us to examine whether a weaker link exists between the
measures and other information asymmetry proxies that would justify using the measures
under some conditions. Second, we look at a much larger sample (2,797 stocks) than the
other two papers and use stocks from the NYSE, AMEX and Nasdaq as opposed to only
NYSE in these studies. Third, we are able to test the measures even without information
asymmetry proxies by examining the cross-sectional relation between the measures and price
informativeness about future earnings.
While the measures used in the aforementioned papers have different names, such as the
“permanent impact of the order flow innovation” or the “adverse selection component of
the spread” or the “trade-correlated component of the efficient price variance,” they all use
intra-day data to estimate the permanent changes in price induced by trades.4 Using any
estimate of permanent price impact as a measure of information asymmetry about fundamentals is subject to the same two problems identified above. Thus instead of examining all
possible measures, we choose two of the methodologies that impose different degree of structure on the trading process: a more structured trade-indicator model and a less structured
variance decomposition procedure. The trade-indicator model, from Madhavan, Richard4
See Huang and Stoll (1997) for a discussion of the relationships among some of the measures.
4
son, and Roomans (1997), provides an estimate of the permanent price impact of the order
flow innovation (henceforth, MRR). The variance decomposition procedure from Hasbrouck
(1991b) provides two measures: (i) the trade-correlated efficient price variance component
that is used as an “absolute” measure of information asymmetry (HASAB), and (ii) the
ratio of the trade-correlated component to the total efficient price variance that is taken as
a measure of the amount of private information relative to the total amount of information
(HASR).
We formulate the investigation of the association between the permanent price impact
measures and information asymmetry about fundamentals in terms of “necessary” and “sufficient” links. The strongest possible association is when changes in information asymmetry
about fundamentals are necessary to produce changes in the permanent price impact measures (holding constant the amount of uninformed trading). While such a claim is difficult
to prove (as it requires considering all possible circumstances in which future cash flows can
change), its converse is not. Showing that changes in private information about fundamentals are not necessary for the permanent price impact measures to change requires only one
example.
The Russell 1000 index reconstitution event provides a suitable environment in which
we can test this issue. The composition of the index changes once a year and the new
component stocks are determined solely based on their market capitalization at a single
point in time (the last trading day of May), which is public information. Therefore, the event
does not add information to what the market already knows, and we expect no change in
information asymmetry about fundamentals. The permanent price impact measures should
not change when controlling for the amount of uninformed trading if the measures indeed
reflect information asymmetry about fundamentals.
We look at how the permanent price impact measures change from the last trading week
in May (before the new ranking of the Russell 1000 is established) to the first trading week in
July (when the new index takes effect). We find that both MRR (the permanent price impact
5
of the order flow innovation) and HASAB (the trade-correlated component of the randomwalk variance of quote midpoint changes) decrease significantly around the event. The design
of the test also enables us to demonstrate that these results cannot be attributed just to
changes in liquidity trading or analyst activity around the event. We test the robustness of
our findings with respect to alternative estimation intervals, price level effects, and possible
changes in market-wide liquidity, and find that these do not change our conclusions.
The event study is a strong test of the relation between the permanent price impact
measures and information asymmetry about the firm since it does not require us to use
other variables to independently characterize information asymmetry. But while the MRR
and HASAB measures fail to pass the “necessary” test, it is still possible that a weaker
“sufficient” relation exists. More specifically, we would like to know whether differences
across stocks in the degree of information asymmetry about fundamentals are sufficient to
generate differences in the estimates of the permanent price impact measures that are used as
proxies for information asymmetry. Generally speaking, it is difficult to find good proxies for
information asymmetry about future cash flows, a reason that no doubt contributed to the
popularity of the permanent price impact measures. We choose for our cross-sectional tests
only proxies that are constructed using earnings or their forecasts. Intuitively, variables
that explicitly incorporate information about the firm’s future earnings should be more
tightly connected to the firm’s future cash flows than measures that do not use such direct
information (like the estimated permanent price impact measures).
To implement the test we use uncertainty about future cash flows to represent information
asymmetry since the greater the uncertainty, the more room (and incentives) there is for
investors to acquire private information and trade on it profitably. Two of our proxies for
uncertainty about future cash flows are based on dispersion in analysts’ earnings forecasts and
two others are based on past earnings variability. We find that MRR provides conflicting
results since it is negatively related to dispersion in analysts’ earnings forecasts but also
negatively related to earnings predictability (as it should be). HASAB is related to one
6
of the analysts’ forecasts variables in the predicted direction in univariate tests, but gives
conflicting results when the two types of proxies are used together. HASR is not related to
any of the proxies for future cash flows uncertainty.5
We then conduct a cross-sectional test that bypasses the need for information asymmetry
proxies by examining the relation between the permanent price impact measures and price informativeness about future earnings (i.e., how much of the information about future earnings
is impounded into current prices). Ceteris paribus, the more trading on private information
about the firm, the more informative should prices be with respect to future earnings (see,
for example, Grossman and Stiglitz, 1980). We find that none of the permanent price impact
measures relates to price informativeness in the predicted manner.
By utilizing a variety of designs and tests, we offer a comprehensive assessment of the
relation between the permanent price impact measures and information asymmetry about
fundamentals. The results we present do not invalidate the use of measures estimated from
intra-day data to examine the price impact of trades. However, they cast doubt on the use of
very short-horizon price movements for making inferences concerning information asymmetry
about the fundamentals of firms.
The rest of the paper proceeds as follows. Section 1 describes the permanent price impact
measures we use. Section 2 examines changes in the permanent price impact measures around
the Russell 1000 index reconstitution. Section 3 presents cross-sectional analysis that relates
the permanent price impact measures to proxies for uncertainty about future cash flows.
Section 4 investigates the relation between the permanent price impact measures and price
informativeness, and Section 5 is a conclusion.
5
For robustness, we also look at how the permanent price impact measures relate to analysts’ forecast
errors, another common proxy for information asymmetry that uses earnings information. The analysis using
this proxy points to the same conclusions as the analysis of uncertainty about future cash flows.
7
1
Permanent Price Impact Measures
In this section we provide some details on the estimation of the permanent price impact
measures. For a more comprehensive exposition of these methodologies we refer the readers
to the original papers that developed them.
1.1
Madhavan, Richardson, and Roomans (1997)
Let xt denote an indicator variable taking the value of 1 if the transaction at time t is buyer
initiated and −1 if it is seller initiated, and let µt denote the post-trade expected value of
a stock. The revision of beliefs following a trade is the sum of the change in beliefs due to
public information and the change in beliefs due to the order flow innovation:
µt = µt−1 + θ (xt − E[xt |xt−1 ]) +
t
(1)
where θ is the permanent impact of the order flow innovation and is a measure of the degree
of information asymmetry, and
t
is the innovation in beliefs between times t−1 and t due to
public information. Let pt denote the transaction price at time t, and φ denote the market
makers’ cost per share of supplying liquidity (compensating them for order processing costs,
inventory costs, and so on). The transaction price can then be expressed as:
pt = µt + φxt + ξt
(2)
where ξt captures the effects of stochastic rounding errors induced by price discreteness or
possibly time-varying returns.
Equations (1) and (2) can be used to obtain:
ut = pt − pt−1 − (φ + θ)xt + (φ + ρθ)xt−1
(3)
where ρ is the first-order autocorrelation of the trade initiation variable. Then, the measure of
permanent price impact θ, alongside φ, ρ, λ (the unconditional probability that a transaction
occurs within the quoted spread), and a constant α can be estimated using GMM applied
8
to the following moment conditions:




E



xt xt−1 − x2t−1 ρ
|xt | − (1 − λ)
ut − α
(ut − α)xt
(ut − α)xt−1








=0
(4)
We use data from the TAQ database to estimate (4).6 Following Madhavan et al., the
classification into buys and sells is done as follows: (i) if a trade price is greater than or
equal to the prevailing ask then xt = 1, (ii) if the trade price is less than or equal to the bid
then xt = −1, and (iii) if the trade price falls between the bid and the ask then xt = 0. We
use the log transaction price for pt , and refer to the estimate of θ, the permanent impact of
the order flow innovation, as the “MRR” measure.7
1.2
Hasbrouck (1991b)
Hasbrouck models the quote midpoint qt as the sum of two unobservable components:
qt = mt + st
(5)
where mt is the efficient price (i.e., expected end-of-trading security value conditional on all
time-t public information) and st is a residual discrepancy term that is assumed to incorporate inventory control, price discreteness, and other influences that cause the midquote to
6
We apply various filters to clean the data. We only use trades for which TAQ’s CORR field is equal to
either zero or one, and for which the COND field is either blank or equal to B, J, K, or S. We eliminate
any trades with non-positive prices or where the change from the last trade price is greater than $5 ($20 for
stocks with average price greater than $100). We also exclude a trade if its price is greater (less) than 150%
(50%) of the price of the previous trade. We only use quotes from the exchange on which a stock is listed.
We eliminate quotes for which TAQ’s MODE field is equal to 4, 5, 7, 8, 9, 11, 13, 14, 15, 16, 17, 19, 20, 27,
28, or 29. We exclude quotes with non-positive ask or bid prices, where the bid is greater than the ask, and
where the ask is more than $9999. We require that the difference between the bid and the ask be smaller
than 25% of the sum of the bid and the ask. We also eliminate a quote if the bid or the ask are greater (less)
than 150% (50%) of the bid or ask of the previous quote. When signing trades, we employ yet an additional
filter that requires the difference between the price and the prevailing midquote to be smaller than $8.
7
Madhavan et al. estimate (4) using the transaction price, rather than its logarithmic transformation,
and therefore the components they estimate are in dollar terms (i.e., components of the dollar spread). In
the event study (Section 2), we estimate two versions of θ: one using dollar prices and the other using log
prices to get components in percentage terms (i.e., components of the relative spread). The results from
both specifications are similar. In the cross-sectional part of the paper (both in Section 3 and Section 4), we
use log transaction prices since a component of the relative spread seems to be better suited for comparisons
across stocks.
9
deviate from the efficient price. The efficient price evolves as a random walk:
mt = mt−1 + wt
(6)
where the innovation wt reflects updates to the public information set including the information in the order flow.
The market’s signal of private information is the current trade innovation defined as xt −
E[xt |Φt−1 ], where xt is signed volume and Φt−1 is the public information set prior to the trade.
The impact of the trade innovation on the efficient price innovation is E [wt |xt − E[xt |Φt−1 ]].
Two measures of information asymmetry that Hasbrouck proposes are:
2
σw,x
≡ Var (E [wt |xt − E[xt |Φt−1 ]])
2
Rw
≡
2
σw,x
Var (E [wt |xt − E[xt |Φt−1 ]])
=
2
σw
Var(wt )
(7)
(8)
2
where σw,x
is the trade-correlated component of the random-walk variance of quote midpoint
2
changes representing an absolute measure of information asymmetry, and Rw
is a measure
of the amount of private information relative to the total amount of information.
Let x0t be an indicator variable that takes the values {−1, 0, +1}, and define: x1t =
log(xt + 1) (the log volume), and xt = {x0t , x1t }. Let rt = log qt − log qt−1 . The absolute
and relative permanent price impact measures are estimated using the vector autoregressive
(VAR) model:
5
rt =
5
ai rt−i +
i=1
5
xt =
bi xt−i + v1,t
(9)
Di xt−i + v2,t
(10)
i=0
5
ci rt−i +
i=1
i=1
where bi is a 2 × 1 vector of coefficients, Di is a 2 × 2 matrix of coefficients, and v2,t is a
2 × 1 vector of error terms.8
8
Hasbrouck (1991b) uses a specification with volume and volume squared instead of log volume. Applying his exact specification to our analysis did not materially affect the results. We chose to present the
specification using log volume because it seems to fit better the concave relation between trade size and price
impact.
10
We use data from the TAQ database for the estimation of the VAR model in (9) and (10).
Following Hasbrouck, the trade classification into buys and sells is done as follows: (i) if a
trade price is greater than the prevailing midquote then x0t = 1, (ii) if the trade price is less
than the prevailing midquote then x0t = −1, and (iii) if the trade price is at the prevailing
midquote then x0t = 0. We estimate the VAR system using OLS. A finite VAR generally
possesses a vector moving average (VMA) representation of an infinite order. The random
walk variance and the trade-correlated component are calculated from the coefficients of
the VMA representation truncated after 100 lags. Throughout the paper, we refer to the
estimate of the absolute measure, expressed in the form of standard deviation per hour, as
2
“HASAB” and to the estimate of the relative measure (Rw
) as “HASR.”9
2
Event Study: Russell 1000 Reconstitution
In this section we investigate whether changes in information about the firm are necessary
for the permanent price impact measures to change, holding constant the amount of liquidity
trading. The Russell 1000 index reconstitution provides us with a natural experiment for
testing the “necessary” connection.10
The Russell 1000 index is comprised of the largest 1000 firms in terms of market capitalization.11 Membership in the Russell 1000 index is determined strictly by market capitalization
at the end of the last trading day in May and reconstitution occurs once a year. During June,
Frank Russell Company issues a list of firms to be added to and deleted from the indexes.
The new indexes become effective on July 1. The more heavily studied changes to the S&P
equity indexes, in contrast, involve a committee of nine people who make their decision taking into account attributes such as liquidity, profitability of the firm, market capitalization,
9
We also conduct the analysis using the raw estimates of the trade-correlated component of the randomwalk variance without conversion to standard deviation per hour. The results are very similar in both sign
and significance level, and are therefore omitted from the presentation.
10
Madhavan (2001) examines return effects of the Russell reconstitution.
11
Excluded from all Russell indexes are foreign firms, limited partnerships, limited liability companies,
royalty trusts, closed-ended investment management companies, ADRs, preferred stocks, pink-slipped companies, OTC bulletin board companies, and warrants and rights. The indexes also exclude stocks trading at
below $1.
11
and sector representation of the stock.12 Revisions to the S&P indexes also occur continuously throughout the year on a stock-by-stock basis. As such, the Russell reconstitution
differs from changes to the S&P indexes in that the criterion used is public information (market capitalization on May 28) and all changes occur at the same time. More importantly,
additions to and deletions from the Russell 1000 index convey no new information about
the firm, while S&P revisions might be viewed as expressing an opinion about a firm. Thus
if the measures arise solely from private information about the fundamentals of firms, they
should not change around the Russell 1000 reconstitution when controlling for the amount of
uninformed or liquidity trading. If these measures are affected by other factors, like changes
in the characteristics of investors that are unrelated to being informed or uninformed about
the fundamentals of firms, we might detect changes around the reconstitution event.
Controlling for the amount of uninformed trading is important because it has direct effect
on the permanent price impact measures. However, it is difficult to identify trades as being
initiated by liquidity traders (being uninformed is not an observable attribute). We use two
variables in the regressions in an attempt to control for the amount of normal or liquidity
trading. The analysis of both the addition and deletion samples, however, provides us with
a more powerful robustness check on the effects of liquidity trading. The reason is that most
stocks in our sample that were added to the Russell 1000 index (89 out of 105) were deleted
from the Russell 2000 index, and all stocks that were deleted from the Russell 1000 index
were added to the Russell 2000. Say we believe that a move from the Russell 1000 to the
Russell 2000 index increases the amount of liquidity trading (perhaps more passive funds
follow the Russell 2000 index). If the proxy for normal volume is not good enough, some of
the increase in liquidity trading will be captured by the intercept in the regression we use to
examine changes in the measures around the event, making it negative. At the same time,
stocks that move from the Russell 2000 to the Russell 1000 should experience a decrease in
liquidity trading. For them, insufficient control for liquidity trading will result in a positive
12
For papers examining changes to S&P equity indexes see Harris and Gurel (1986), Shleifer (1986), Jain
(1987), Dhillon and Johnson (1991), and Lynch and Mendenhall (1997).
12
intercept. If the intercepts of the addition and the deletion samples have the same sign,
however, the effect cannot be solely due to insufficient control for uninformed or liquidity
trading.
It is clear that the Russell reconstitution event is fairly transparent, and it is possible
to predict prior to the last trading day in May which stocks are more likely to be added or
deleted. In fact, firms like Investment Technology Group, Inc. offer the service of predicting
the changes in order to assist fund managers who wish to begin rebalancing their portfolios in
advance of the announced index changes. While some fund managers could be trading ahead
of time based on a certain assessment as to which stocks will switch indexes, others could
be trading based on a different assessment or waiting until the new composition is made
known. Rebalancing before May 28 does not necessarily bias the results against finding
any change between the permanent price impact measures estimated just before the end of
May and immediately after July 1 if such behavior does not reduce the uncertainty about
final membership. If the uncertainty is reduced, any effect that we detect is likely to be an
underestimate of the real change in the measures.
2.1
Sample and Methodology
The initial sample is constructed from a list of 157 stocks that were added to the Russell
1000 index in 1999 and 103 stocks that were deleted from the index.13 We restrict the
sample to common stocks (for compatibility with the cross-sectional tests in Section 3 and
Section 4) with data from April 1 through mid-July. We use CRSP and Dow Jones Interactive
to identify firms with corporate events including mergers and acquisitions, share offerings,
earnings announcements, dividends distributions, and stock splits within the sample period.
These firms are eliminated from the sample in order not to confound the results (if a corporate
event occurs within the sample period, the information environment of a firm can change).
13
The preliminary list of the changes was published by the Frank Russell Company on June 11 and the final
list was published on July 7 (though the new composition of the index took effect on July 1). To construct
the sample, we eliminate 12 stocks that were not present in both the preliminary and final lists. Note that
the number of additions and deletions can be different due to bankruptcies and mergers that decrease the
number of firms in the Russell 1000 index throughout the year.
13
The final sample consists of 105 additions and 70 deletions.14
Table 1 presents summary statistics for the firms used in the event study. There seems
to be a slight increase in mean price between May 28 (the last trading day in May) and July
1 (when the new composition of the index takes effect). Average turnover increases slightly
from the last week of May to the first week of July for both samples, but the cross-sectional
mean of the average number of trades decreases for the addition sample. Dollar spreads and
percentage spreads decrease for both additions and deletions.
Our event study methodology is an adaptation of standard specifications.15 Let ψi,τ
denote the permanent price impact measure for stock i estimated over time interval τ ∈
{pre, post} (i.e., either the pre-event interval or the post-event interval). The simplest specification assumes that the permanent price impact measure can be described as the sum of
a stock-specific unconditional mean (µi ), an event effect (α), and an error term (
ψi,τ = µi + αδτ +
i,τ ):
(11)
i,τ
where δτ is an indicator variable that takes the value zero in the pre-event interval and one
in the post-event interval, and
i,τ
is assumed i.i.d and normally distributed with mean zero
and variance σi2 /2.
Theoretical models that show how information asymmetry causes trades to have permanent price impacts also demonstrate how the price impact of trades can be affected by
changes to normal or liquidity trading (i.e., volume due to uninformed traders that is unrelated to information events). A formulation that takes normal trading into account can be
written as:
ψi,τ = µi + αδτ + βVi,τ +
i,τ
(12)
where Vi,τ is a proxy for the amount of normal volume.
By examining differences between the pre- and post-event intervals, we can eliminate the
14
15
Similar results are obtained without eliminating firms with major corporate events.
See, for example, Schipper and Thompson (1983) and Thompson (1985).
14
firm-specific mean. Equation 11 can be written in terms of differences as:
∆ψi ≡ ψi,post − ψi,pre = α +
where
i
(13)
i
is normally distributed with mean zero and variance σi2 . Similarly, the formulation
in terms of differences of Equation 12 is:
∆ψi = α + β ∆Vi +
(14)
i
where ∆Vi ≡ Vi,post − Vi,pre .16
Testing that the Russell 1000 reconstitution event affects the permanent price impact
measures is therefore equivalent to testing whether the intercept (α) of either Equation 13
or Equation 14 is statistically different from zero.
Figure 1 shows the timeline for the event study. We use one week as the length of the
interval over which the permanent price impact measures are estimated. Since the ranking
of firms for the reconstitution is based on the closing prices on May 28, we use the week
ending May 28 as the pre-event interval. Similarly, since the effective date of the changes is
July 1, we use five trading days beginning July 1 as the post-event interval.17 For a start,
we assume that the error terms are identically distributed across stocks and Equation 13 is
implemented as a simple t-test. We also use the non-parametric Wilcoxon signed rank test
to perform the analysis under less restrictive assumptions. Equation 14 is estimated using
OLS with White’s heteroscedasticity-consistent standard errors.
16
We also used a specification with an interaction between the event dummy and the volume measure:
ψi,τ = µi + αδτ + βVi,τ + γδτ Vi,τ +
i,τ
Thus,
∆ψi = α + β ∆Vi + γVi,post +
i,τ
Tests under this formulation give similar results to those without the interaction.
17
Unlike the pre-event interval, the five days beginning July 1 do not include all days of the week (due to
Independence Day). Since there may be a day-of-the-week effect in the estimated permanent price impact
measures (see, for example, Foster and Viswanathan, 1993), we also conducted the analysis with the first
five days in July that comprise a full set of the days of the week (dates 1, 2, 6, 7, and 12). The results
obtained were very similar to the results using the first five trading days in July, and are therefore omitted
for brevity of exposition.
15
Figure 1: Timeline for Event Study
5-day pre-event interval
5-day post-event interval
May 28
July 1
Market capitalization
calculated from closing
prices is used to determine
membership in the new
Russell 1000 index.
New Russell 1000 index
takes effect.
We use two proxies to control for changes in normal volume: the average daily turnover
and the average daily number of trades in the interval. We fully acknowledge that these may
not be perfect controls. However, the internal check discussed in Section 2 enables us to test
whether our results are driven by insufficient adjustment for liquidity trading by examining
the intercepts of the addition and deletion samples to see if they have opposite signs.
While throughout the paper we use the MRR measure estimated using log prices to get a
measure that can be interpreted as a component of the percentage spread, in the event study
part of the paper we also use the same methodology with dollar prices to get the permanent
price impact measure in terms of dollars, MRR$. This is done to examine the robustness of
our results to possible changes in the level of prices induced by the event that are unrelated
to the information asymmetry environment.
2.2
Results
Panel A of Table 2 presents the results of the event study for the addition sample. The t-tests
indicate that the decrease in the mean measure between the pre- and post-event intervals is
statistically different from zero for MRR$, MRR, and HASAB. The non-parametric Wilcoxon
statistics are also highly significant. Normalizing by the pre-event magnitude of the measures,
the median percentage changes in MRR$, MRR, and HASAB are −27.41%, −45.78%, and
−25.80%, respectively. The fourth column of Panel A shows the intercept from the regression
with AvgTurn as a proxy for normal volume and the sixth column shows the intercept from
the regression with AvgTrd as a proxy for normal volume. The intercepts in the regressions
16
with MRR$, MRR, and HASAB are all negative and statistically significant. The mean,
median, and intercepts in the HASR regressions are all positive but insignificant.
The results for the deletion sample are presented in Panel B of Table 2. The means and
medians of differences between the pre- and post-event measures are negative and statistically
different from zero for the two MRR measures. HASAB also decreases after the event, though
the t-test is only marginally significant (with a p-value of 0.0529); the Wilcoxon signed rank
test is significant. Normalizing by the pre-event magnitude of the measures, the median
percentage changes in MRR$, MRR, and HASAB are −21.50%, −17.44%, and −9.55%,
respectively. The intercepts of the regressions with the proxies for normal volume tell the
same story: significant negative intercepts for MRR$, MRR and HASAB. Again, HASR does
not show any significant change around the event.
The results from both the addition and deletion samples point to the same conclusion:
the Russell 1000 reconstitution event is associated with a decrease in the permanent price
impact measures (with the exception of HASR). This cannot be due to a change in private information about the fundamentals of the firms since the only criterion used for the
reconstitution–market capitalization on May 28–is public information. The finding of a
decrease in the measures for both the addition and deletion samples also rules out an explanation based on insufficient control for changes in liquidity trading. As the discussion
in Section 2 points out, even if the proxies for normal volume are not perfect, a change in
normal trading would produce opposite results in the addition and deletion samples. The
reason is that if a membership in a certain index is associated with a particular amount of
uninformed trading, we would expect that being added to the Russell 1000 and deleted from
the Russell 2000 would produce the opposite effect to being added to the Russell 2000 and
deleted from the Russell 1000. Finding that the permanent price impact measures decrease
in both addition and deletion samples is evidence that the result is not being driven by
changes in liquidity trading.
This feature of the test also enables us to rule out that the effects on the permanent
17
price impact measures are due to changes in the production of fundamental information by
analysts induced by changes in index membership. It is possible that analysts are more
willing to follow stocks that are included in a certain index, say the Russell 1000. This can
be due to more trading activity in these stocks by index funds, or just because of a larger
market capitalization that induces more mutual funds to own the stock. If this is the case,
it could be that the amount of fundamental information production would increase after
inclusion in the Russell 1000 index. But at the same time, a stock leaving the Russell 1000
index should experience a decrease in fundamental information production. The fact that
we get a similar decrease in the permanent price impact measures for both addition and
deletion samples means that our results cannot be solely due to a change in fundamental
information production by analysts.
We conducted several tests to evaluate the robustness of our results. First, we used interval lengths other than five days. Two-day intervals displayed a similar significant decrease
in the permanent price impact measures MRR$, MRR, and HASAB.18 We also used onemonth intervals and obtained results similar to those presented in Table 2 (i.e., a statistically
significant decrease in MRR$, MRR, and HASAB).19
Since MRR$ and MRR behave in a similar fashion, it seems unlikely that the results
are due to possible changes in the price level that may affect the estimated measures due to
discreteness of the price gird. Nonetheless, we added the change in AvgPrc as a regressor to
the specification in Equation 14 to account for changes in the price level, and found that it
did not alter our results. We also used a dummy variable to examine whether the 16 stocks
that were added to the Russell 1000 index but were not previously in the Russell 2000 index
behave differently from the rest of the stocks. The coefficient of the dummy variable was not
significant and similar results were obtained. For MRR$ and MRR, we repeated the tests
18
We used May 27 and 28 for the pre-event interval and July 1 and 2 for the post-event interval. Both
intervals are comprised of the days Thursday and Friday, and hence the results are not due to a day-of-theweek effect.
19
The only difference was with respect to the HASR measure, which was significantly negative in the
deletion sample and significantly positive in the addition sample.
18
using only positive estimates and only estimates that were statistically different from zero.
This was done to eliminate the influence of stocks that did not have sufficient amount of
trading to produce reliable estimates of the permanent price impact measures. The results
were similar to those reported in Table 2.
Lastly, we constructed a matched sample of stocks based on both market capitalization
and average turnover in April 1999.20 The motivation behind constructing the matched
sample was to investigate whether the Russell 1000 reconstitution event coincided with a
market-wide change in liquidity that could have affected the estimates of the permanent
price impact measures of all stocks. Unlike the results for the addition and deletion samples,
all permanent price impact measures except one showed no statistically significant decrease in
the matched sample. The decrease in HASAB in the addition-matched sample was significant
but smaller in magnitude than the decrease in the addition sample, and a paired t-test (as
well as a Wilcoxon signed rank test) showed that the difference between them was statistically
significant.
To summarize the results so far: the event study shows that the “necessary” link between
information asymmetry about future cash flows and the permanent price impact measures
does not exist. The estimated measures should not have changed around the Russell 1000
reconstitution event if they only reflect the information asymmetry environment, but we
have found a significant decrease in all measures (except for HASR).
The decrease in the measures is consistent with changes to the extent of uncertainty about
the investor population in the spirit of Saar (2000, 2001). The Russell indexes are popular
benchmarks of stock market performance in the United States. In 2001, an estimated 117
billion dollars in investment were indexed to the Russell 1000, 2000, and 3000 indexes.21
Therefore, the annual reconstitution event can generate buying and selling pressures on
20
The universe of stocks that was used for the matching consisted of all common stocks in the CRSP
database with information from April 1 to July 12 that were not added to or deleted from the Russell 1000
index.
21
This estimate is taken from a report by Investment Technology Group, Inc. on the 2001 Russell index
reconstitution.
19
stocks that are added to or deleted from the indexes. Uncertainty about whether a stock
will end up in the Russell 1000 index or the Russell 2000 index during the last week of May
creates uncertainty with respect to the characteristics of the investors (e.g., the amount of
money in index funds) who trade the stock. This increased uncertainty for stocks that may
be added to or deleted from the index increases the price impact of trades and is picked up
by the permanent price impact measures. In the post-event interval, there is less uncertainty
about the investor population since the changes to the index are announced and therefore
the permanent price impact of trades decreases.
3
Uncertainty about Future Cash Flows
In this section we conduct a cross-sectional investigation of the relation between the permanent price impact measures and proxies for uncertainty about future cash flows that we
use to represent information asymmetry about the firm. We test whether differences across
stocks in the degree of information asymmetry about future earnings are sufficient to generate
differences in the estimates of the permanent price impact measures.
3.1
Sample
The initial sample for the cross-sectional analysis is constructed from all common stocks with
information in the CRSP database for the entire year of 1999 that had, on average, more than
one analyst covering them in the I/B/E/S database. The reason for requiring more than one
analyst is to allow the calculation of the standard deviation of analysts’ earnings forecasts.
This screen leaves 3,144 stocks. The sample is further restricted to firms with information in
TAQ, COMPUSTAT, and Value Line Investment Survey in order to allow the computation
of the permanent price impact measures and the construction of other variables that will be
explained in greater detail below. This requirement eliminates 268 firms from the sample.
We also eliminate firms that switched exchanges during the sample period, leaving a final
sample of 2,797 firms.
20
Table 3 presents summary statistics for the sample. The average daily market capitalization (AvgCap) over the sample period (January 4 through December 31, 1999) for firms
in our sample ranges from $6.05M to $446.16B, testifying to its heterogeneous nature. The
sample also spans a range of trading activity and price levels. The most active firm has on
average 29,845.81 daily trades (AvgTrd), while the average firm has 459.26 daily trades, and
the least actively traded firm in the sample has 3.28 trades per day. Average daily closing
prices (AvgPrc) range from $0.24 to $550.05. The sample is also diverse with respect to
analyst following and institutional holdings. NumEst is the average of 12 monthly observations (January through December, 1999) of the number of analysts with end-of-fiscal-year
earnings forecasts for the current year in I/B/E/S. While the mean of NumEst is 8.80, it
ranges from a minimum of 2 to a maximum of 40.18. The percentage institutional holdings
from Value Line Investment Survey (InstHol) ranges from 0.23% to 99.59%.
For eight stocks in the sample, the MRR estimates came out negative. While there is
nothing in the estimation to constrain the MRR measure from being negative, it is unclear
how to interpret these estimates. The negative measures do not affect our results as our
findings are practically identical with and without these eight stocks. The estimation of
the Hasbrouck (1991b) specification proved infeasible for two stocks in the sample for which
the VMA could not converge. These stocks are eliminated from the sample for the tests
involving the HASAB and HASR measures.
3.2
Methodology
The first test we run examines whether cross-sectional differences in MRR, HASAB, and
HASR reflect differences in information asymmetry about future cash flows. Since we do
not have a way to directly measure information asymmetry, we focus instead on uncertainty
about future cash flows.
We use two definitions of dispersion of analysts’ forecasts to represent uncertainty about
future cash flows: the standard deviation of analysts’ forecasts (StdEst) and the coefficient
21
of variation (CoefEst).22 The logic behind the test is that the greater the uncertainty about
future cash flows, the more room (and incentives) there is for investors to acquire private
information and trade on it profitably. A theoretical treatment of the information environment of analysts is provided by Barron, Kim, Lim, and Stevens (1998). They show that
an increase in private information about the firm, ceteris paribus, will increase the dispersion of analysts’ forecasts. Monthly observations for the standard deviation and the mean
of analysts’ earnings forecasts for the upcoming end-of-fiscal-year are taken from I/B/E/S.
StdEst is the simple average of the monthly standard deviation observations for all months
in 1999, and CoefEst is the ratio of StdEst to the absolute value of the average monthly
mean observations. Time left until the end-of-fiscal-year seems to exert an influence on the
monthly observations of the standard deviation of the forecasts in I/B/E/S (as well as the
number of estimates). However, since we use twelve consecutive months of data, the average
should have similar properties across firms with different end-of-fiscal-year dates.
We also use two proxies for uncertainty about future cash flows constructed from past
earnings information. The first is the earning predictability measure provided by Value
Line Investment Survey (VLPred). This variable, available for 2016 stocks in our sample,
is derived from the standard deviation of percentage changes in quarterly earnings over
an eight-year period, with special adjustments for negative observations and observations
around zero. VLPred takes the values 1 to 100, where higher values are associated with
less variability of past earnings and hence higher predictability of future earnings. We also
compute the standard deviation of past annual earnings from COMPUSTAT using the five
years prior to 1999 (StdEPS).23 The idea behind both measures is that higher past earnings
variability makes it more likely that future earnings cannot be predicted with great precision
(allowing more room for private information production and profitable informed trading).
22
We also used the difference between the high and the low forecasts as an additional definition of uncertainty about future cash flows. The results using this definition were very similar to the results using the
standard deviation of earnings’ forecasts, and are therefore omitted for brevity.
23
We repeated the analysis with the standard deviation of annual earnings computed using five years that
include 1999. The results were very similar to those obtained using StdEPS.
22
We then estimate regressions with the permanent price impact measures as dependent
variables and the proxies for uncertainty about future cash flows as independent variables
using OLS with White’s Heteroscedasticity-consistent standard errors. The choice of control
variables to add to the regressions is guided by the proxies we use for future cash flows
uncertainty. More dispersion among analysts may reflect the nature of the industry or the
number of analysts that typically follow firms in a specific industry. Therefore, we add
to the regressions a set of 2-digit SIC dummies to control for industry effects. To relate
our measures of uncertainty about future cash flows to information asymmetry we need to
control for public information, and we (partially) do it by including the standard deviation
of daily returns in 1999 from CRSP as a control variable. Similarly, there are more public
information events (e.g., news articles) about larger firms. So, we add a second control for
public information flow by including AvgCap, the average market capitalization in 1999 from
CRSP (in log form), to the regressions.
Two other controls are motivated by the market microstructure literature. First, the
impact of informed trading on prices diminishes as the amount of liquidity trading or normal
trading increases (see, for example, Kyle, 1985; Easley and O’Hara, 1987). Hence, we want
to hold constant the amount of liquidity trading when we compare across firms. As a proxy
for normal trading, we use the median daily turnover (daily number of shares traded over the
number of shares outstanding) in 1999 from CRSP (MedTurn). The median is less sensitive
to informational shocks that generate a lot of trading, and therefore is a better description of
“normal” volume.24 Lastly, we use dummies for the three primary markets (NYSE, AMEX,
and Nasdaq) to control for differences in the manner specialists or market makers set prices
in these markets. The motivation behind this control is that on the NYSE, for example,
the price continuity requirement affects the way in which specialists change prices, and this
may be picked up by the spread decomposition and variance decomposition procedures (for
a discussion of this point see Hasbrouck, 1991a). Table 4 presents summary statistics for
24
We use median turnover in log form, and add a small constant (0.00001) to the raw data before making
the transformation to be able to accommodate stocks with zero median turnover.
23
the analysts’ forecasts and past earnings proxies, as well as correlations among the (log
transformed) proxies and control variables that are used in the regressions.
A potential econometric problem with the OLS estimation for the two proxies that use
analysts’ forecasts is that the dispersion in forecasts can be endogenous.25 In other words,
the amount of time analysts spend on producing their estimates (which may affect the
dispersion), the number of estimates or the frequency of their updates may be influenced
by how much profit can be made from this information. The profit opportunity, in turn,
depends on the permanent price impact of trades–the same permanent price impact that
the econometric methodologies estimate and that we use as a dependent variable. This
rationale suggests that the dispersion of analysts’ forecasts may be correlated with the error
term, causing OLS to be inconsistent. To examine this potential problem, we also estimate
the cross-sectional relation using two-stage-least-squares (2SLS) and conduct Durbin-WuHausman tests.26
3.3
Results
Panel A of Table 5 presents the results of the cross-sectional regressions with the permanent
price impact of the order flow innovation, MRR, as the dependent variable. Of the two
proxies using analysts’ forecasts, only StdEst is statistically significant, and it is negative.
25
This is not a problem with the proxies that use actual earnings data since it is hard to imagine how the
permanent price impact of trades can affect the firms’ earnings per share.
26
See Wu (1973), Hausman (1978), and Davidson and MacKinnon (1989) for a discussion of this test. Using
data in COMPUSTAT and CRSP, we construct six instruments for the dispersion in analysts’ forecasts. The
first instrument is the log standard deviation of EPS for the five years prior to 1999 (available for 2767 firms
in our sample). The second instrument is the one year lagged EPS growth (percentage change in EPS from
1997 to 1998), using the absolute value of EPS in the denominator to maintain consistent signs when EPS
is negative (available for 2744 firms in our sample). The motivation for this instrument is that growth firms
are associated with more uncertainty about future earnings. The third instrument is the average absolute
value of quarterly sales growth in 1999 from COMPUSTAT (available for 2701 firms in our sample). This is
a measure of the magnitude of change in the firm’s operations that presumably is correlated with uncertainty
about its sales and earnings potential. The fourth instrument is the number of days with listing records
in CRSP, which is a measure of the maturity of the firm. Presumably, it is easier to estimate the future
earnings of more mature firms. The fifth instrument is the log number of SIC codes that are associated with
the businesses of the firm (available for 2677 firms in our sample). Firms comprised of more businesses may
be more difficult for analysts to evaluate, and this should increase the dispersion of the forecasts. The sixth
instrument is the dividend payout ratio for 1999 (available for 2610 firms in our sample). The idea behind
this instrument is that the more money is paid out, the less money is spent of new projects and therefore
the less uncertainty there is about earnings.
24
This implies a greater permanent price impact for stocks with less uncertainty about future
cash flows, which goes against the predicted direction. As for the two proxies using past
earnings, VLPred is negative and (weakly) statistically significant. Here the direction is
consistent with our expectation: higher predictability is associated with lower information
asymmetry and therefore a smaller permanent price impact.
Panel B of Table 5 presents the results with the trade-correlated component of the efficient
price variance, HASAB, as the dependent variable. Here StdEst is negative but not significant
by itself (though it gains weak statistical significance when it is in the regression alongside
VLPred). CoefEst is positive and statistically significant. The positive relation between
HASAB and uncertainty about future cash flows is in line with the role of this measure a
proxy for information asymmetry. Both of the proxies using past earnings (VLPred and
StdEPS) are negative but insignificant. Panel C of Table 5 presents the results using the
amount of private information relative to the total amount of information, HASR, as the
dependent variable. None of the proxies for uncertainty about future cash flows is statistically
significant.27
The Durbin-Wu-Hausman exogeneity tests and the coefficients of the two-stage-leastsquares (2SLS) estimation are presented in Table 6. For all three measures, the exogeneity
tests are insignificant (with very low chi-squared statistics). This gives us confidence that
the results of the OLS estimations provide an accurate picture of the relationships among
the variables. To further test the robustness of our results, we examined another variable
constructed from earnings that had been used in the literature as a proxy for information
asymmetry about future cash flows: analysts’ forecast errors.28 The findings using forecast
errors were similar in nature to those reported in Table 5 for uncertainty about future cash
flows.
27
Since HASR is a proportion, we also estimated the regressions with a logit transformation of HASR as
the dependent variable. The results were qualitatively similar to those reported in Panel C and are therefore
not presented here.
28
We define a forecast error as the absolute value of the difference between the actual annual earnings and
the median forecast one month prior to the earnings announcement, deflated by the stock price five days
prior to the announcement. See, for example, Thomas (2002).
25
To summarize the results of the analysis in this section: HASAB is related to one of the
analysts’ forecasts proxies for uncertainty about future cash flows in the predicted direction in
univariate tests, but gives conflicting results when the two types of proxies are used together.
MRR provides conflicting results that are difficult to interpret, and HASR is unrelated to
any of the proxies.
4
Price Informativeness about Future Earnings
4.1
Methodology
We use the same sample to perform a different kind of cross-sectional analysis that does
not require a proxy for information asymmetry about future cash flows. Our tests involve
two measures of the informativeness of prices about future earnings that were developed in
the accounting literature (see, Kothari, 1992; Kothari and Sloan, 1992; Collins, Kothari,
Shanken, and Sloan, 1994; Durnev, Morck, Yeung, and Zarowin, 2001). Let rt = (Pt −
Pt−1 )/Pt−1 be the current quarterly return and rt+τ be the return τ quarters ahead. Similarly,
let ∆Et be the current quarterly earnings-per-share change and ∆Et+τ be the earnings change
τ quarters ahead, where all earnings changes are scaled by the price at the beginning of the
current quarter, Pt−1 . To measure stock price informativeness, we regress current stock
returns on current and future earnings changes:
rt = a + b0 ∆Et +
bτ ∆Et+τ +
τ
cτ rt+τ + ut
(15)
τ
Future stock returns are included among the regressors to control for the measurement error
problem described by Collins et al. (1994).
The two measures of price informativeness are:
FERC ≡
bτ
(16)
τ
2
FINC ≡ Ra+b
0 ∆Et +
τ
bτ ∆Et+τ +
τ
cτ rt+τ +ut
− R2a+b0 ∆Et +ut
(17)
FERC (Future Earnings Response Coefficients) is defined as the sum of the coefficients on
the future earnings changes, and FINC (Future earnings INCremental) is the incremental
26
explanatory power of the future earnings changes (given that current earnings are already in
the model). Both FERC and FINC are designed to detect the extent to which current stock
prices capitalize information about future earnings.
The general intuition behind using FERC and FINC to test the permanent price impact
measures is that the more trading on private information, holding constant the extent of
public information, the more informative are prices with respect to future earnings (for a
theoretical justification see, for example, Grossman and Stiglitz, 1980). The need to control
for public information arises since if we take the extreme case where all future cash flow
information is revealed publicly, then both FERC and FINC will be at their maximum but
there will be no information asymmetry. However, once we control for public information,
the relation between trading on private information and FERC and FINC should be monotonically increasing. This is true in particular since MRR and HASAB (or HASR) are not
just measures of information asymmetry, but are constructed as measures of trading based
on private information that moves prices. Therefore, these measures relate directly to information incorporation into prices and thus should be more tightly related to FERC and
FINC.
Since we are interested in evaluating how much information about future earnings is
incorporated into prices during our sample period, we use returns for the four calendar
quarters in 1999. Our earnings data is taken from COMPUSTAT, and we have earnings
up to and including the second quarter of 2000. To be able to use all four quarterly return
observations, we set τ = 2 and estimate the information that is impounded into current
prices about earnings two quarters in the future. Since each firm has only four observations,
we cannot estimate FERC and FINC for individual firms. We group stocks with similar
permanent price impact measures and estimate the specification in Equation (15) for each
group. The motivation behind this procedure is that each group of stocks that have the same
level of informed trading (holding public information constant) should have similar FERC
and FINC estimates, and hence can be estimated together.
27
For example, to estimate FERC and FINC for the MRR measure we sort all stocks
according to MRR and form 279 groups of ten stocks each.29 Each such group has approximately 40 firm-quarter observations that can be used for the estimation of FERC and FINC.
We estimate Equation (15) using OLS with White’s heteroscedasticity-consistent standard
errors. We then use the mean of the MRR coefficients of stocks in each group (MRRG ) to
represent the level of permanent price impact for the group. FERCMRR and FINCMRR are
computed according to (16) and (17). We perform separate estimations of Equation (15) for
groups formed by sorting on HASAB and HASR. We then use correlations to examine the relationship between the price informativeness measures and the group measures of permanent
price impact.
Ideally, one should control for cross-sectional differences in public information and liquidity trading when looking at the relation between the permanent price impact measures
and price informativeness. However, since we group stocks according to their permanent
price impact measures, we cannot simply use a regression and plug in control variables. The
mean of the market capitalization (or the volatility of returns) of stocks in a group has no
real economic content. To exercise some control, we divide the stocks into four categories.
First, we sort the 2,789 stocks according to their market capitalization. We then separate
them into two categories, Low AvgCap and High AvgCap, with equal number of stocks.
Each category is then sorted according to MedTurn and divided into two equal categories,
Low MedTurn and High MedTurn. This procedure produces four control categories. Within
each category, we sort according to the permanent price impact measure, create 70 groups
of ten stocks each, and estimate FERC and FINC for the groups. We then compute the
correlations separately for each category. Such a structure provides (partial) control for
public information and liquidity trading. We use a similar procedure to control for public
information and liquidity trading with StdRet and MedTurn, respectively.
29
We dropped the eight stocks for which the MRR measures were negative. Inclusion of these stocks in
the groups does not materially affect the results.
28
4.2
Results
The results of the FERC and FINC analysis are provided in Table 7. The predicted direction
is that more informed trading is associated with a higher degree of price informativeness,
which means larger magnitudes of FERC and FINC. The results of the unconditional analysis, where we look at the correlations for the entire sample, seem to go the other way.
MRR and HASR are not significantly correlated with either FERC or FINC; HASAB has a
negative correlation with FINC (-0.1316) that is statistically significant.
The conditional analysis, where we sort the stocks into four categories according to two
conditioning variables, should lessen the influence of differences across stocks in the degree
of public information or the amount of liquidity trading. Panel B of Table 7 shows the conditional analysis for the MRR measure. When the controls are average market capitalization
(AvgCap) and median turnover (MedTurn), the correlations of MRR with either FERC or
FINC are not statistically different from zero. Similarly, when the controls are the standard
deviation of daily returns (StdRet) and MedTurn, none of the correlations is statistically
different from zero.
Panel C of Table 7 shows the conditional analysis for the HASAB measure. When the
controls are AvgCap and MedTurn, none of the four categories has correlations with FERC
and FINC that are significantly different from zero, and most correlations are negative.
When the controls are StdRet and MedTurn, the only correlation that is statically different
from zero (and negative) is in the High StdRet and High MedTurn category. Panel D of
Table 7 presents the conditional analysis for the HASR measure. There are both positive
and negative correlations of HASR with FERC and FINC, but only one category (small,
inactive stocks) has significant negative correlation with FINC.
The bottom line of the FERC and FINC analysis is that despite our expectation that
more trading by investors who are informed about future cash flows would increase the informativeness of prices with respect to future earnings, all permanent price impact measures
seem to be either negatively correlated or not significantly correlated with the measures of
29
price informativeness.
5
Conclusion
Our goal in this paper was to examine the question whether measures constructed from
trades and quotes that describe very short-horizon price movements are helpful in characterizing information asymmetry about the fundamentals of firms. The most powerful test
we conduct uses the Russell 1000 index reconstitution to look at whether changes in information asymmetry are necessary to produce changes in the estimated measures. We then
investigate whether cross-sectional differences in uncertainty about future cash flows that is
used as a proxy for information asymmetry are sufficient to produce differences in the estimated measures. Finally, we relate the permanent price impact measures directly to price
informativeness about future earnings.
In the introduction we mention two potential problems with the permanent price impact measures. One of the problems is that even if these methodologies capture only real
permanent price changes, these can be due to uncertainty about investors or other factors
that affect the risk premium and not necessarily due to information asymmetry about future
cash flows. The results of the event study seem to suggest that this problem is real. The
MRR (both in dollar and percentage terms) and the HASAB measures decreased significantly around the reconstitution event, and this cannot be attributed to mere changes in
liquidity trading. These findings are consistent with an explanation of the permanent price
impact of trades based on uncertainty about the preferences and endowments of investors
rather than information asymmetry about the firm’s fundamentals.
The cross-sectional results seem to suggest the presence of the other potential problem
mentioned in the introduction: that the estimation procedures may incorporate into the
permanent price impact measures influences of the trading environment that should not
affect the price permanently. Because the various econometric specifications used to generate
the measures differ in the assumptions they make, the resulting measures may incorporate
30
temporary price effects to a different degree. The MRR measure did not relate to uncertainty
about future cash flows in a consistent fashion. HASAB performed slightly better in that it
had a strong relation in the predicted direction with one proxy using analysts’ forecasts. Both
HASAB and MRR, however, did not fare well in the price informativeness analysis, where
more informed trading according to these permanent price impact measures was associated
with less information in prices about future earnings. While HASR showed promise in the
event study analysis in that it did not change around the Russell 1000 reconstitution, it did
not have a significant relation with any of the proxies for uncertainty about future cash flows
or with price informativeness.
If information about the firm indeed affects prices in a more permanent fashion than other
factors, then the better we are at identifying permanent price changes, the stronger will be
the connection between the measures and future cash flow information. The methodology
that generates HASAB uses five lags of price changes to identify permanent effects. The
econometric model that generates the MRR measure essentially uses only one lag. As such,
the MRR measure may incorporate more of the other factors that affect trading, reducing
its effectiveness in identifying information about the firm. Further increasing the number of
lags in the variance decomposition methodology, while preventing its use for thinly traded
stock, may increase its effectiveness. This is especially important after the move to a decimal
price grid, as the reduced tick size dramatically increases the number of quote changes.
It is not clear, however, that very short-horizon price movements can at all be used
effectively to identify information asymmetry about the firm. Callahan, Lee, and Yohn (1997)
claim that the information asymmetry risk faced by a dealer, presumably the one reflected
in the permanent price impact of trades, is not a measure of the long-term fundamental risk
of investing in a particular firm. Market makers are concerned with order imbalances over
very short horizons (often less than an hour), and these need not correspond to the creation
of new information about the firm or the trading by investors with special knowledge about
the firm. Even if information about the firm is one cause for these order flow imbalances, its
31
effects may be miniscule relative to other factors that influence minute-by-minute trading.
Our findings suggest that the two potential problems we have identified with the use of the
permanent price impact measures as proxies for information asymmetry about fundamentals
may be at work. Without necessarily disqualifying the measures as tools for analyzing the
price impact of trades, the overall weight of the evidence points to a conclusion that measures
based on very short-horizon price movements may not be suitable for describing information
asymmetry about the firm.
32
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36
Table 1
Summary Statistics for the Event-study Sample
The initial sample for the event study consists of all stocks that were added to or deleted from the Russell 1000 index in 1999. We restrict the sample to common
stocks with trading data between April and mid-July, and eliminate firms about which we find news reports discussing mergers and acquisitions, share offerings,
earnings announcements, dividends distributions, and stock splits in the months around the Russell reconstitution dates. The following variables are calculated
for each stock using data in CRSP: CapMay28 is the market capitalization on May 28 (the number of shares outstanding multiplied by the closing price),
PrcMay28 and PrcJuly1 are the closing prices on these two dates, BegTurn is the average daily turnover (the number of shares traded divided by the number of
shares outstanding) for the pre-event interval (May 24–28), and EndTurn is the average daily turnover for the post-event interval (July 1–8). The following
variables are calculated for each stock using data in TAQ: BegTrd and EndTrd are the average daily number of trades in the pre- and post-events intervals,
Beg$Sprd and End$Sprd are the average dollar spreads in the pre- and post-event intervals, and Beg%Sprd and End%Sprd are the average relative spreads
(dollars spreads divided by the mid-quotes) in the pre- and post-event intervals, respectively. Panel A presents the statistics for the 105 stocks in the addition
sample, and Panel B presents the statistics for the 70 stocks in the deletion sample.
Panel A: Addition Sample
CapMay28 PrcMay28 PrcJuly1
(in $)
(in million $)
(in $)
Mean
Median
Std. Dev.
Min.
Max.
Obs.
2,456.23
1,704.72
2,628.09
197.75
21,402.83
105
48.98
44.50
25.78
9.88
177.19
105
50.81
46.50
26.88
10.06
149.66
105
BegTurn
(in %)
1.54
0.76
1.77
0.03
8.52
105
EndTurn
(in %)
1.69
0.69
3.24
0.07
25.58
105
BegTrd
EndTrd
1,349.89
417.00
3,020.15
22.00
23,130.60
105
1,252.56
373.00
2,325.53
28.40
12,510.20
105
BegTrd
EndTrd
Beg$Sprd End$Sprd Beg%Sprd End%Sprd
(in $)
(in $)
(in %)
(in %)
0.27
0.22
0.18
0.09
1.13
105
0.22
0.19
0.13
0.08
0.72
105
0.60
0.53
0.28
0.19
2.49
105
0.48
0.43
0.23
0.14
1.97
105
Panel B: Deletion Sample
CapMay28 PrcMay28 PrcJuly1
(in million $)
(in $)
(in $)
Mean
Median
Std. Dev.
Min.
Max.
Obs.
982.01
1,071.70
302.92
310.08
1,346.02
70
19.32
18.94
9.11
3.25
42.69
70
20.44
19.13
9.72
4.81
47.20
70
BegTurn
(in %)
0.61
0.47
0.61
0.02
3.91
70
EndTurn
(in %)
0.65
0.48
0.58
0.07
2.94
70
37
271.25
151.40
337.65
15.80
1,851.60
70
292.45
167.90
397.17
27.20
2,693.80
70
Beg$Sprd End$Sprd Beg%Sprd End%Sprd
(in $)
(in $)
(in %)
(in %)
0.15
0.13
0.07
0.06
0.46
70
0.13
0.11
0.04
0.06
0.31
70
0.87
0.70
0.45
0.41
3.23
70
0.73
0.62
0.30
0.28
1.69
70
Table 2
Event Study Analysis
This table presents the analysis of changes in the permanent price impact measures around the Russell 1000
reconstitution in 1999. The pre-event interval is May 24–28 and the post-event interval is July 1–8 (each contains 5
trading days). ∆MRR$ is the change in the MRR$ measure (similar to MRR but estimated with price differences
rather than log price differences) between the post- and pre-event intervals. Similarly, ∆MRR is the change in the
MRR measure, ∆HASAB is the change in the HASAB measure, and ∆HASR is the change in the HASR measure.
The second column reports the mean of the change in measures and the p-value (in parentheses) of a t-test against
the hypothesis of zero change. The third column reports the median of the change in measures and the p-value (in
parentheses) of a Wlicoxon signed rank test against the hypothesis of zero change. Regressions 1 and 2 (columns
four through seven) both have the following form:
∆ψ i = α + β ∆Vi + ε i
where ∆ψi is the change in the permanent price impact measure and ∆Vi is the change in a proxy for normal volume.
In Regression 1, the proxy for normal volume is the average daily turnover over the interval (i.e., ∆Vi = EndTurn BegTurn). In Regression 2, the proxy for normal volume is the average daily number of trades over the interval (i.e.,
∆Vi = EndTrd - BegTrd). The estimation of the regressions is done using OLS, and p-values (in parentheses) are
calculated using White's heteroskedasticity-consistent standard errors. Panel A presents the results for the 105 stocks
in the addition sample, and Panel B presents the results for the 70 stocks in the deletion sample. "**" indicates
significance at the 1% level and "*" indicates significance at the 5% level (both against a two-sided alternative).
Panel A: Addition Sample
Dependent
Variable
∆MRR$
∆MRR
∆HASAB
∆HASR
Mean
(p-value of
t-test)
-0.004127**
(0.0040)
-0.009407**
(0.0031)
-0.144830**
(0.0000)
0.000829
(0.9245)
Median
(p-value of
Wilcoxon test)
-0.001497**
(0.0029)
-0.005500**
(0.0002)
-0.126247**
(0.0000)
0.003620
(0.8629)
Regression 1
α
(p-value)
-0.004100**
(0.0046)
-0.009341**
(0.0037)
-0.146163**
(0.0000)
0.001268
(0.8854)
β(Turn)
(p-value)
-0.000179
(0.2825)
-0.000433
(0.2250)
0.008628
(0.4067)
-0.002844**
(0.0014)
Regression 2
α
(p-value)
-0.004183**
(0.0037)
-0.009525**
(0.0030)
-0.143406**
(0.0000)
0.000421
(0.9618)
β(Trd)
(p-value)
-0.000001*
(0.0130)
-0.000001**
(0.0044)
0.000015
(0.2207)
-0.000004
(0.0709)
Panel B: Deletion Sample
Dependent
Variable
∆MRR$
∆MRR
∆HASAB
∆HASR
Regression 1
Regression 2
Mean
(p-value of
t-test)
Median
(p-value of
Wilcoxon test)
α
(p-value)
β(Turn)
(p-value)
α
(p-value)
β(Trd)
(p-value)
-0.004670**
(0.0020)
-0.029490**
(0.0010)
-0.059153
(0.0529)
-0.030318
(0.0701)
-0.001836**
(0.0002)
-0.012100**
(0.0000)
-0.076776*
(0.0147)
-0.014745
(0.0782)
-0.004608**
(0.0023)
-0.029137**
(0.0011)
-0.062035*
(0.0354)
-0.029879
(0.0743)
-0.001603
(0.1534)
-0.009135*
(0.0404)
0.074634
(0.3375)
-0.011379
(0.6531)
-0.004666**
(0.0021)
-0.029322**
(0.0011)
-0.063433*
(0.0323)
-0.030479
(0.0703)
-0.000000
(0.8929)
-0.000008
(0.4310)
0.000202*
(0.0322)
0.000008
(0.6354)
38
Table 3
Summary Statistics for the Cross-sectional Sample
The cross-sectional sample is constructed by including all common stocks with information in the CRSP database between January 4 and December 31, 1999
(the sample period) that have at least one analyst covering them in the I/B/E/S database. The sample is further restricted to stocks with information in TAQ,
COMPUSTAT, and Value Line Investment Survey. The following variables are calculated for each stock over the sample period using data in CRSP: AvgCap is
the average daily market capitalization (the number of shares outstanding multiplied by the daily closing price), StdRet is the standard deviation of daily returns,
MedTurn is the median daily turnover (the number of shares traded divided by the number of shares outstanding), AvgVol is the average daily number of shares
traded, and AvgPrc is the average daily closing price of the stock. From the TAQ database, AvgTrd is calculated as the average daily number of trades, and
%Sprd is the average relative spread (the bid-ask spread divided by the midquote) calculated from all quote observations. NumEst is the average of 12 monthly
observations in 1999 of the number of analysts with end-of-fiscal-year earnings forecasts for the current year in I/B/E/S. InstHol is the percentage of shares held
by institutions from Value Line Investment Survey. The table presents summary statistics for the entire sample, as well as means for four equal groups sorted by
AvgCap, StdRet, and MedTurn, respectively.
Entire
Sample
Means
For
AvgCap
Groups
Means
for
StdRet
Groups
Means
for
MedTurn
Groups
Mean
Median
Std. Dev.
Min.
Max.
Obs.
Q1 (Low)
Q2
Q3
Q4 (High)
Q1 (Low)
Q2
Q3
Q4 (High)
Q1 (Low)
Q2
Q3
Q4 (High)
AvgCap
(in million $)
4,403.02
549.40
19,124.85
6.05
446,161.27
2,797
105.54
349.29
1,033.10
16,107.41
7,236.77
7,347.18
2,138.52
894.62
3,410.40
5,773.78
4,894.88
3,534.26
StdRet MedTurn
(in %)
(in %)
3.62
0.50
3.32
0.31
1.70
0.65
0.50
0.00
25.73
15.64
2,797
2,797
4.46
0.37
3.90
0.50
3.27
0.55
2.86
0.59
1.89
0.20
2.81
0.31
3.90
0.53
5.89
0.97
2.84
0.11
2.99
0.24
3.69
0.42
4.98
1.24
AvgVol
(in 100s)
5,152.00
1,606.85
14,028.88
11.00
280,833.61
2,797
829.05
1,812.48
3,014.31
14,938.17
3,602.80
6,023.61
5,775.37
5,206.16
1,180.33
3,818.48
5,150.48
10,451.15
39
AvgPrc
(in $)
26.59
20.84
24.58
0.24
550.05
2,797
10.11
18.53
28.98
48.71
36.50
28.37
21.56
19.96
21.50
26.33
27.34
31.18
AvgTrd
459.26
121.50
1,614.92
3.28
29,845.81
2,797
75.78
163.50
258.08
1,338.40
239.24
446.16
499.57
651.79
83.08
240.11
346.37
1,166.46
%Sprd
NumEst
(in %)
8.80
1.25
6.45
0.88
6.78
1.19
2.00
0.07
40.18
19.47
2,797
2,797
3.87
2.63
5.71
1.26
8.58
0.74
17.01
0.38
10.28
0.70
10.01
1.02
8.39
1.43
6.50
1.85
5.84
1.86
9.55
1.17
9.79
1.12
0.86
10.00
InstHol
(in %)
50.30
51.06
22.70
0.23
99.59
2,797
36.71
47.86
55.52
61.10
51.34
56.31
52.63
40.94
36.98
52.87
57.43
53.91
Table 4
Summary Statistics for Future Cash Flows Uncertainty Proxies
We use as proxies for uncertainty about future cash flows two definitions of dispersion of analysts' earnings
forecasts: log of the standard deviation of analysts' forecasts (StdEst) and log of the coefficient of variation of
analysts' forecasts (CoefEst). I/B/E/S provides monthly observations of the standard deviation and mean of the
analysts' forecasts for the current end-of-fiscal-year. StdEst is the simple average of the monthly standard deviation
observations for all months in 1999, and CoefEst is the ratio of the average standard deviation to the average
absolute mean forecast. We also use two proxies for uncertainty about future cash flows based on past earnings:
VLPred is an earning predictability measure provided by Value Line Investment Survey derived from the standard
deviation of percentage changes in quarterly earnings over an eight-year period, and StdEPS is log of the standard
deviation of annual earnings for the five years prior to 1999. Panel A presents summary statistics for the entire
sample (before taking the log transformations), as well as for four equal groups sorted by AvgCap (average daily
market capitalization), StdRet (the standard deviation of daily returns), and MedTurn (the median daily turnover),
respectively. Panel B presents pairwise correlations and p-values of the four future cash flows uncertainty proxies
and the three control variables used in the cross-sectional regressions (where LAvgCap and LMedTurn are the log
transformations of AvgCap and MedTurn, respectively). The two-sided p-values for the asymptotic test of zero
correlations are shown in parentheses. "**" indicates significance at the 1% level and "*" indicates significance at
the 5% level.
Panel A: Summary statistics of untransformed variables
StdEst
CoefEst
Mean
Entire
0.0875
0.3825
Median
Sample
0.0482
0.0405
Std. Dev.
0.1254
7.1752
Min.
0.0008
0.0008
Max.
2.5400
363.0000
Obs.
2,797
2,797
Q1 (Low)
Means
0.0939
1.0636
Q2
for
0.0863
0.2035
Q3
AvgCap
0.0783
0.1374
Q4 (High)
Groups
0.0913
0.1260
Q1 (Low)
0.0483
Means
0.0816
Q2
for
0.0706
0.0844
Q3
StdRet
0.0850
0.7530
Q4 (High)
Groups
0.1127
0.6440
Q1 (Low)
Means
0.0747
0.1361
Q2
for
0.0764
0.1517
Q3
MedTurn
0.0981
0.9204
Q4 (High)
Groups
0.1006
0.3220
40
VLPred
47.6984
45.0000
28.3023
5.0000
100.0000
2,016
33.3788
40.6672
51.3684
59.7168
62.2476
51.4136
38.9774
26.9558
54.1795
53.6630
45.3531
35.5310
StdEPS
0.9144
0.5500
1.2750
0.0100
22.0300
2,767
0.6920
0.8209
0.9022
1.2416
0.9278
0.9567
0.8688
0.9046
0.7267
0.8385
1.0180
1.0726
Panel B: Unconditional correlations of transformed variables used in the regressions
Control Variables
StdEst
CoefEst
VLPred
StdEst
(p-value)
_
CoefEst
(p-value)
0.6757**
(0.0000)
_
VLPred
(p-value)
-0.4081**
(0.0000)
-0.5739**
(0.0000)
_
StdEPS
LAvgCap
StdRet
LMedTurn
41
StdEPS
(p-value)
0.3784**
(0.0000)
0.1582**
(0.0000)
-0.3612**
(0.0000)
_
LAvgCap
(p-value)
-0.0693**
(0.0003)
-0.3141**
(0.0000)
0.3844**
(0.0000)
0.2117**
(0.0000)
_
StdRet LMedTurn
(p-value)
(p-value)
0.1145**
0.0468*
(0.0000)
(0.0174)
0.4512**
0.1408**
(0.0000)
(0.0000)
-0.4077** -0.2185**
(0.0000)
(0.0000)
-0.0267
0.1339**
(0.2118)
(0.0000)
-0.3738**
0.1752**
(0.0000)
(0.0000)
_
0.4686**
(0.0000)
_
Table 5
Uncertainty about Future Cash Flows Results
This table provides the results of cross-sectional regressions where the permanent price impact measures are the
dependent variables and the proxies for uncertainty about future cash flows (alongside controls) are the independent
variables. We use as proxies for uncertainty about future cash flows two definitions of dispersion of analysts'
earnings forecasts: log of the standard deviation of analysts' forecasts (StdEst) and log of the coefficient of variation
of analysts' forecasts (CoefEst). I/B/E/S provides monthly observations of the standard deviation and mean of the
analysts' forecasts for the current end-of-fiscal-year. StdEst is the simple average of the monthly standard deviation
observations for all months in 1999, and CoefEst is the ratio of the average standard deviation to the absolute value
of the average monthly mean observations. We also use two proxies for uncertainty about future cash flows based
on past earnings: VLPred is an earning predictability measure provided by Value Line Investment Survey that is
derived from the standard deviation of percentage changes in quarterly earnings over an eight-year period, and
StdEPS is log of the standard deviation of annual earnings for the five years prior to 1999. The following set of
control variables is used in each regression: the logarithmic transformation of the average daily market capitalization
(LAvgCap), the standard deviation of daily returns (StdRet), and the logarithmic transformation of the median daily
turnover (LMedTurn). The regressions also include (but they are not shown in the table) a set of two-digit SIC
dummies to control for industry effects, and dummies for the three primary markets (NYSE, AMEX, and Nasdaq) to
control for institutional characteristics of the markets. Panel A presents the results for the MRR measure, the
permanent price impact of the order flow innovation, estimated using the methodology in Madhavan, Richardson,
and Roomans (1997). Panel B presents the results for the HASAB measure, the trade-correlated component of the
efficient price variance (in standard deviation per hour form), estimated using the methodology in Hasbrouck
(1991b). Panel C presents the results for HASR, the ratio of the trade-correlated component to the total efficient
price variance, also from Hasbrouck (1991b). All estimations are done using OLS, and we report p-values in
parenthesis calculated using White’s heteroskedasticity-consistent standard errors. "**" indicates significance at the
1% level and "*" indicates significance at the 5% level.
Panel A: MRR (dependent variable)
Control variables
StdEst
(p-value)
CoefEst
(p-value)
VLPred
(p-value)
StdEPS
(p-value)
LAvgCap
(p-value)
-0.00468**
(0.0001)
-0.0263**
(0.0000)
-0.0260**
(0.0000)
-0.0238**
(0.0000)
-0.0258**
(0.0000)
-0.0240**
(0.0000)
-0.0240**
(0.0000)
-0.0265**
(0.0000)
-0.0261**
(0.0000)
-0.00130
(0.1527)
-0.00011*
(0.0372)
-0.00023
(0.8506)
-0.00405**
(0.0076)
-0.00221
(0.0630)
-0.00506**
(0.0001)
-0.00138
(0.1382)
-0.00015**
(0.0048)
-0.00014**
(0.0067)
0.00143
(0.2848)
0.00008
(0.9470)
42
StdRet
(p-value)
0.6288**
(0.0000)
0.6263**
(0.0000)
0.4969**
(0.0024)
0.5453**
(0.0000)
0.5278**
(0.0012)
0.5668**
(0.0014)
0.5868**
(0.0000)
0.5873**
(0.0000)
LMedTurn
(p-value)
AdjR2
(in %)
Obs.
-0.0360**
(0.0000)
-0.0365**
(0.0000)
-0.0377**
(0.0000)
-0.0357**
(0.0000)
-0.0375**
(0.0000)
-0.0379**
(0.0000)
-0.0354**
(0.0000)
-0.0357**
(0.0000)
63.21
2788
63.02
2788
65.23
2011
63.18
2758
65.37
2011
65.29
2011
63.39
2758
63.20
2758
Panel B: HASAB (dependent variable)
Control variables
StdEst
(p-value)
CoefEst
(p-value)
VLPred
(p-value)
StdEPS
(p-value)
-0.00047
(0.8380)
0.00957**
(0.0000)
-0.00020
(0.1514)
0.00150
(0.5692)
-0.00673*
(0.0193)
0.01030**
(0.0014)
-0.00028
(0.0604)
-0.00002
(0.8764)
-0.00122
(0.6418)
0.00190
(0.5201)
-0.00068
(0.8104)
0.00953**
(0.0001)
LAvgCap
(p-value)
-0.0256**
(0.0000)
-0.0237**
(0.0000)
-0.0204**
(0.0000)
-0.0254**
(0.0000)
-0.0206**
(0.0000)
-0.0195**
(0.0000)
-0.0256**
(0.0000)
-0.0235**
(0.0000)
StdRet
(p-value)
LMedTurn
(p-value)
AdjR2
(in %)
Obs.
0.0268**
(0.0000)
0.0263**
(0.0000)
0.0307**
(0.0000)
0.0270**
(0.0000)
0.0310**
(0.0000)
0.0318**
(0.0000)
0.0271**
(0.0000)
0.0270**
(0.0000)
67.74
2786
68.04
2786
68.57
2009
67.77
2756
68.63
2009
68.83
2009
67.76
2756
68.05
2756
LMedTurn
(p-value)
AdjR2
(in %)
Obs.
0.0092**
(0.0000)
0.0091**
(0.0000)
0.0118**
(0.0000)
0.0095**
(0.0000)
0.0118**
(0.0000)
0.0117**
(0.0000)
0.0096**
(0.0000)
0.0095**
(0.0000)
75.26
2786
75.26
2786
72.15
2009
75.37
2756
72.14
2009
72.14
2009
75.37
2756
75.38
2756
7.9227**
(0.0000)
7.62220*
(0.0000)
8.4458**
(0.0000)
7.9068**
(0.0000)
8.4970**
(0.0000)
8.1206**
(0.0000)
7.9169**
(0.0000)
7.6174**
(0.0000)
Panel C: HASR (dependent variable)
Control variables
StdEst
(p-value)
CoefEst
(p-value)
VLPred
(p-value)
StdEPS
(p-value)
-0.00093
(0.4650)
-0.00112
(0.2206)
0.00001
(0.8170)
-0.00008
(0.9522)
-0.00054
(0.7636)
-0.00099
(0.4412)
-0.00112
(0.3929)
-0.00127
(0.1683)
0.00001
(0.8986)
-3.33e-06
(0.9587)
0.00029
(0.8296)
0.00021
(0.8724)
LAvgCap
(p-value)
-0.0049**
(0.0001)
-0.0050**
(0.0000)
-0.0040**
(0.0094)
-0.0048**
(0.0001)
-0.0040**
(0.0090)
-0.0041**
(0.0081)
-0.0050**
(0.0000)
-0.0051**
(0.0000)
43
StdRet
(p-value)
-0.6509**
(0.0000)
-0.6248**
(0.0000)
-0.5386**
(0.0002)
-0.6724**
(0.0000)
-0.5345**
(0.0003)
-0.5075**
(0.0008)
-0.6632**
(0.0000)
-0.6338**
(0.0000)
Table 6
Durbin-Wu-Hausman Tests and Cross-sectional 2SLS Estimation
This table provides the results of the Durbin-Wu-Hausman tests as well as cross-sectional two-stage-least-squares
(2SLS) regressions where the permanent price impact measures are the dependent variables and the analyst proxies
for uncertainty about future cash flows (alongside controls) are the independent variables. The following
instruments are used for analysts' earnings forecasts dispersion: (i) the log standard deviation of EPS for the five
years prior to 1999 from COMPUSTAT, (ii) the one-year lagged growth of EPS, (iii) the average absolute value of
quarterly sales growth in 1999 from COMPUSTAT, (iv) the number of days with listing records in CRSP, (v) the
log of the number of SIC codes associated with the firm, and (vi) the dividend payout ratio for 1999 from
COMPUSTAT. We use as proxies for uncertainty about future cash flows two definitions of dispersion of analysts'
earnings forecasts: log of the standard deviation of analysts forecasts (StdEst) and log of the coefficient of variation
of analysts forecasts (CoefEst). I/B/E/S provides monthly observations of the standard deviation and mean of the
analysts' forecasts for the current end-of-fiscal-year. StdEst is the simple average of the monthly standard deviation
observations for all months in 1999, and CoefEst is the ratio of the average standard deviation to the absolute value
of the average monthly mean observations. The following set of control variables constructed over the sample
period is used in each regression: the logarithmic transformation of the average daily market capitalization
(LAvgCap), the standard deviation of daily returns (StdRet), and the logarithmic transformation of the median daily
turnover (LMedTurn). The regressions also include (but they are not shown in the table) a set of two-digit SIC
dummies to control for industry effects, and dummies for the three primary markets (NYSE, AMEX, and Nasdaq) to
control for institutional characteristics of the markets. The table presents the regression results for the MRR
measure, the permanent price impact of the order flow innovation, estimated using the methodology in Madhavan,
Richardson, and Roomans (1997), the HASAB measure, the trade-correlated component of the efficient price
variance (in standard deviation per hour form), estimated using the methodology in Hasbrouck (1991b), and HASR,
the ratio of the trade-correlated component to the total efficient price variance, also from Hasbrouck (1991b). "**"
indicates significance at the 1% level and "*" indicates significance at the 5% level.
Control variables
Dependent
variables
MRR
HASAB
StdEst
(p-value)
CoefEst
(p-value)
LAvgCap
(p-value)
StdRet
(p-value)
LMedTurn
(p-value)
Durbin-WuHausman
statistic
(p-value)
0.6052**
(0.0000)
0.5990**
(0.0030)
-0.0332**
(0.0000)
-0.0339**
(0.0000)
0.17725
(0.6737)
0.00106
(0.9740)
2387
-0.00148
(0.7646)
-0.0266**
(0.0000)
-0.0262**
(0.0000)
7.7102**
(0.0000)
7.4620**
(0.0000)
0.0289**
(0.0000)
0.0284**
(0.0000)
0.06131
(0.8044)
0.07384
(0.7858)
2387
0.00715
(0.4295)
-0.0262**
(0.0000)
-0.0245**
(0.0000)
-0.5204**
(0.0000)
-0.4872**
(0.0072)
0.0091**
(0.0000)
0.0088**
(0.0000)
0.15898
(0.6901)
0.01534
(0.9014)
2387
-0.00171
(0.7207)
-0.0057**
(0.0001)
-0.0057**
(0.0010)
-0.00628
(0.1073)
-0.00244
(0.7616)
-0.00251
(0.5405)
HASR
44
Obs.
2387
2387
2387
Table 7
Price Informativeness Analysis
This table provides estimates of correlations between the permanent price impact measures and two measures of
price informativeness about future earnings, FERC and FINC. To construct these measures, we run the following
two regressions:
2
2
τ =1
τ =1
rt = a + b0 ∆E t + ∑ bτ ∆E t +τ + ∑ cτ rt +τ + u t
rt = a + b0 ∆E t + v t
where rt is the quarterly return at time t, rt+τ is the return τ quarters ahead, ∆Et is the change in EPS at time t, and
∆Et+τ is the change in EPS t quarters ahead. All earnings changes are scaled by the price at time t-1. We construct
the returns for four quarters in 1999 using CRSP, and take EPS data from COMPUSTAT for 1999 and the first two
quarters of 2000 (we set τ = 2). The definitions of the price informativeness measures are:
FERC ∫ ∑ bτ
τ
FINC ∫
R 2 r =a +b0 ∆Et + ∑ bτ ∆Et +τ +∑ cτ rt +τ + u t − R 2 rt = a +b0∆Et + vt
2
2
τ =1
τ =1
Since each firm has only four observations, we group stocks with similar permanent price impact measures and
estimate for each group a common price informativeness measure. The permanent price impact measure for the
group is the average of the measures of the stocks in the group. For the MRR measure, we sort the sample firms
according to MRR, form 279 groups of 10 stocks each, estimate the two equations above for each group separately,
and calculate FERC and FINC for the group. A similar procedure is applied to the HASAB and HASR measures.
Panel A presents the Pearson correlations between the groups' permanent price impact measures (where a group
measure is the mean of the measures of the individual stocks in the group) and both FERC and FINC. Panels B, C,
and D present the correlations and p-values of the three information asymmetry measures with FERC and FINC
controlling for the amount of public information and liquidity trading by dividing the stocks into four categories. For
the MRR measure, we sort the stocks according to AvgCap, and separate into two categories (Low and High) with
equal number of stocks. Each category is sorted according to MedTurn and divided into two equal categories. We
then sort the stocks within each category according to MRR, and form groups of 10 stocks each. We estimate FERC
and FINC for each group and compute the correlations separately for each category. The process is repeated with
control variables StdRet and MedTurn. A similar procedure is applied to the HASAB and HASR measures. In all
panels, the two-sided p-values for the asymptotic test of zero correlations are shown in parentheses. "**" indicates
significance at the 1% level and "*" indicates significance at the 5% level.
Panel A: Unconditional correlations
MRR
HASAB
HASR
FERC
(p-value)
-0.0549
(0.2467)
-0.0501
(0.2638)
-0.0035
(0.9624)
FINC
(p-value)
0.0223
(0.7134)
-0.1316*
(0.0147)
-0.0899
(0.1349)
45
Obs.
279
279
279
Panel B: MRR Conditional Correlations
Control
Categories
Low AvgCap
Low MedTurn
Low AvgCap
High MedTurn
High AvgCap
Low MedTurn
High AvgCap
High MedTurn
FERC
(p-value)
-0.0929
(0.3433)
-0.0857
(0.2996)
-0.1495
(0.1854)
-0.1236
(0.2312)
FINC
(p-value)
-0.1398
(0.2744)
0.1344
(0.2932)
0.1847
(0.2527)
-0.1016
(0.3208)
Obs.
70
70
70
70
Control
Categories
Low StdRet
Low MedTurn
Low StdRet
High MedTurn
High StdRet
Low MedTurn
High StdRet
High MedTurn
FERC
(p-value)
0.0249
(0.8508)
-0.0491
(0.6863)
-0.1875
(0.2489)
0.0097
(0.8959)
FINC
(p-value)
0.2437
(0.1179)
0.0226
(0.8679)
-0.0220
(0.8057)
0.1247
(0.5390)
Obs.
Control
Categories
Low StdRet
Low MedTurn
Low StdRet
High MedTurn
High StdRet
Low MedTurn
High StdRet
High MedTurn
FERC
(p-value)
0.0659
(0.5086)
-0.0452
(0.6672)
-0.1749
(0.0654)
-0.2213
(0.0967)
FINC
(p-value)
-0.0233
(0.8443)
-0.0063
(0.9398)
0.0770
(0.4581)
-0.3831**
(0.0006)
Obs.
Control
Categories
Low StdRet
Low MedTurn
Low StdRet
High MedTurn
High StdRet
Low MedTurn
High StdRet
High MedTurn
FERC
(p-value)
-0.0370
(0.7668)
0.1021
(0.2980)
0.0229
(0.8188)
0.0713
(0.3200)
FINC
(p-value)
0.1489
(0.2492)
-0.0462
(0.6388)
-0.0727
(0.4296)
0.0877
(0.2855)
Obs.
70
70
70
70
Panel C: HASAB Conditional correlations
Control
Categories
Low AvgCap
Low MedTurn
Low AvgCap
High MedTurn
High AvgCap
Low MedTurn
High AvgCap
High MedTurn
FERC
(p-value)
-0.0459
(0.6619)
-0.0655
(0.3895)
0.0592
(0.4164)
-0.0246
(0.8636)
FINC
(p-value)
0.0133
(0.8977)
-0.1653
(0.1301)
-0.0397
(0.6814)
-0.0778
(0.5078)
Obs.
70
70
70
70
70
70
70
70
Panel D: HASR Conditional correlations
Control
Categories
Low AvgCap
Low MedTurn
Low AvgCap
High MedTurn
High AvgCap
Low MedTurn
High AvgCap
High MedTurn
FERC
(p-value)
-0.0839
(0.4768)
-0.0011
(0.9886)
-0.0164
(0.8863)
-0.0682
(0.6454)
FINC
(p-value)
-0.3826**
(0.0005)
0.0286
(0.7630)
-0.0170
(0.8948)
0.0751
(0.5108)
Obs.
70
70
70
70
46
70
70
70
70