1. business and industrial
2. company
3. merger and acquisition

Corporate governance and equity prices:
A temporary component perspective
Joon Chae a, Dong Wook Lee b,*, Shu Feng Wang a
January 10, 2010
Abstract
This paper examines whether a firm’s openness to takeover markets fosters genuine informed
trading or speculative noise trading for its stock. To this end, we conduct the variance ratio analysis,
and find that firms with fewer antitakeover provisions have greater portion of their daily stock
return volatility attributable to a temporary component in stock price than do firms with more
takeover protections. We also find that this pattern is more evident among the stocks with greater
information asymmetries or greater investor interests. We obtain these results using individual
stock returns; at the portfolio level, no such relationship is found between takeover vulnerability
and variance ratio. Taken together, our results suggest that a firm’s openness to takeover markets
motivates investors to acquire and trade on private information on its stock, but it causes
speculative noise trading more than it fosters genuine informed trading.
Keywords: Corporate governance; Antitakeover provisions; Temporary component; Variance ratio
JEL classification: G10; G14; G30; G34
a
b
*
Seoul National University
Korea University Business School
Corresponding author. Tel.: +82 2 3290 2820; fax: +82 2 3290 1307; email: [email protected].
We are grateful to Kee-Hong Bae, Bok Hyeon Baik, Jaeuk Khil, Woojin Kim, and the seminar
participants and discussants at Korea University Business School, Seoul National University,
Hanyang University (Ansan), the 2009 KFA conference, and the 2009 CAFM conference for
comments.
Corporate governance and equity prices:
A temporary component perspective
January 10, 2010
Abstract
This paper examines whether a firm’s openness to takeover markets fosters genuine informed
trading or speculative noise trading for its stock. To this end, we conduct the variance ratio analysis,
and find that firms with fewer antitakeover provisions have greater portion of their daily stock
return volatility attributable to a temporary component in stock price than do firms with more
takeover protections. We also find that this pattern is more evident among the stocks with greater
information asymmetries or greater investor interests. We obtain these results using individual
stock returns; at the portfolio level, no such relationship is found between takeover vulnerability
and variance ratio. Taken together, our results suggest that a firm’s openness to takeover markets
motivates investors to acquire and trade on private information on its stock, but it causes
speculative noise trading more than it fosters genuine informed trading.
Keywords: Corporate governance; Antitakeover provisions; Temporary component; Variance ratio
JEL classification: G10; G14; G30; G34
1. Introduction
The openness to the market for corporate control is unique in a firm’s governance structure, as
it directly affects the behavior of outside investors as well as that of corporate managers. In
addition to disciplining corporate managers to work in the interests of shareholders, an active
takeover market can incentivize outside investors to acquire and trade on private information
because the benefits of knowing a takeover event ahead of other investors can more than offset the
costs associated with the information acquisition (Ferreira and Laux 2007). Consequently, a firm’s
takeover vulnerability can contribute directly to the informativeness of its stock price. A viable
alternative view on the effect of takeover vulnerability on outside investors, however, is that
investors are overly motivated by the takeover vulnerability so they react even to non-information
as if it were information (Black 1986). While the takeover vulnerability is likely to create both
effects, it is important to understand its net effect and the factors affecting the relative importance
between the two. In this paper, we address these questions.
To this end, we conduct the variance ratio analysis. By comparing the variance of stock return
during a given measurement interval with the return variance over a longer interval, the variance
ratio examines whether the variance increases linearly with the length of the return interval. Such a
linear increase should be the case if there is no temporary component in stock price, thereby
making the value of the ratio equal to one. Hence, the deviation of the variance ratio from unity
helps gauge the extent of a temporary component in stock price (e.g., Lo and MacKinlay 1988).
We estimate this ratio using daily stock returns to deal with the typical controversy regarding the
nature of a temporary component in stock price. More precisely, it is unlikely that the expected
returns are serially dependent at daily frequency, so the temporary component detected by the daily
return-based variance ratio is likely to be trading noise (e.g., French and Roll 1986). 1
1
In line with this view, Ahn et al. (2002) is quoted as saying: “… because time variation in expected returns
is not a high-frequency phenomenon; asset pricing models link expected returns with changing investment
opportunities, which, by their nature, are low-frequency events.” (p.656)
1
Using the governance index of Gompers et al. (2003) and the alternative index of Cremers and
Nair (2005) as a measure of takeover vulnerability, we find that the ratio of one-day stock return
variance to k-day stock return variance (scaled by k) is significantly larger for companies with
greater takeover vulnerability, even after controlling for various firm characteristics such as firm
size, bid-ask spread, and industry fixed effects. This result means that a larger portion of daily
stock return volatility is driven by a temporary component when the company is more vulnerable to
takeover. Given that the expected returns are unlikely to vary at daily frequency, our result is
indicative of more speculative noise trading associated with greater vulnerability to takeovers.
What is more interesting is that the above finding is more pronounced among the stocks with
greater information asymmetries or greater investor interests. Specifically, a larger portion of daily
stock return volatility is attributable to a temporary component especially when the stock has small
market capitalization, when the stock is traded within a wide bid-ask spread, or when the stock has
a low book-to-market ratio. This result implies that the observed relationship between takeover
vulnerability and variance ratio is driven by the investor’s incentive to acquire and trade on private
information.
Instead of measuring variance ratios, one could consider a more straightforward approach, such
as directly measuring the amount of private information, or of noise, associated with takeover
vulnerability. Idiosyncratic stock return volatility, typically as a fraction of the total volatility, is
probably the most popular measure of private information flow. As discussed in Section 2,
however, greater stock return volatility does not necessarily indicate greater information:
theoretically, the relationship is indeed ambiguous (e.g., West 1988; Peng and Xiong 2006). While
the variance ratio analysis also utilizes the second moment of stock return, it correctly distinguishes
information-driven price changes from noise trading-induced volatility by examining whether a
given price change reverses itself subsequently. The variance ratio also reveals the relative
importance between the two drivers of volatility without invoking the assumption that only the
2
idiosyncratic volatility, and not the systematic volatility, reflects information in stock price.
It is crucial to note that we obtain our results using individual stock returns, not portfolio
returns. We intentionally focus on individual stocks, since the variance ratio of a well-diversified
portfolio would only reveal the average cross-autocorrelation within the portfolio. When we repeat
the analysis with the returns on the equally weighted portfolios sorted by the governance index, the
relationship between variance ratio and takeover vulnerability disappears. This result with portfolio
returns indicates that our individual stock results are driven by a firm-specific component in stock
price. According to Vuolteenaho (2002), this firm-specific component is likely to cash flows
shocks, rather than discount rate shocks. Note, however, that the time-varying component that can
be rationalized in an efficient market is the expected return, not the future cash flows.
Consequently, our result with portfolio returns further supports the interpretation that the temporary
component detected by the variance ratio analysis of individual stock returns is more of a trading
noise rather than information.
In a recent study, Ferreira and Laux (2007) show that idiosyncratic stock return volatility is
positively related to takeover vulnerability, and interpret this result as evidence of greater informed
trading in stocks with greater takeover vulnerability. However, the authors also find that the
efficiency of corporate capital budgeting decisions—measured by the marginal q ratio—increases
only with the idiosyncratic volatility that is unrelated to takeover vulnerability. Given that more
information in stock price is likely to help—rather than hurt—corporate decision making, their
finding actually suggests that only the idiosyncratic volatility that is unrelated to takeover
vulnerability is information.
Most other prior studies on takeover vulnerability focus on the first moment of stock return and
attempt to answer the question of whether takeover vulnerability is, on average, associated with a
higher or a lower stock return. This approach is understandable considering the axiomatic corporate
goal of shareholder wealth maximization. While our analysis does not address this issue, it instead
3
focuses on stock return volatility and helps us understand another important topic, namely, how a
firm’s takeover vulnerability affects the way in which new information arrives in the market and
the way in which investors react to it. 2 In other words, our analysis sheds light on the informational
environment in relation to takeover vulnerability. In this vein, our results—especially those based
on sub-samples—beg the question of whether the effects of takeover vulnerability on outside
investors vary from one country to another depending on the quality of its overall information
environment.
Our analysis may appear to resemble that of Campbell, Grossman, and Wang (1993). They
predict that a price concession by liquidity traders in order to induce other investors to trade and
absorb the liquidity shock gives rise to a negative autocorrelation in stock return. Unlike our
hypothesis, however, the prediction of Campbell, Grossman, and Wang (1993) is a conditional
statement: conditional on an abnormally high trading volume, the stock price will revert if (and
only if) the high trading volume is caused by a liquidity trading. Hence, their model does not
answer why a stock has a certain level of trading activities in the first place. Furthermore, given
that the abnormally high trading volume is determined for each stock and not in cross-section,
stocks that are actively traded at all times may disguise the true cross-sectional patterns. For
example, stocks with greater takeover vulnerability may revert more than other stocks most of the
time, but this cross-sectional pattern may not be observable in the context of Campbell et al. (1993)
in which the researcher identifies high trading volume days for each stock and ends up looking at
different days for different stocks.
This paper proceeds as follows. In Section 2, we formally develop our testing hypothesis.
Section 3 details our sample and data, and Section 4 reports the empirical results. Section 5
concludes the paper.
2
It is also worth mentioning that, unlike the first moment of stock return, the second moment is less subject
to estimation error and the joint hypothesis problem, allowing the inferences to be less controversial (e.g.,
Merton 1980).
4
2. Hypothesis development
2.1. An illustrative example 3
Consider a stock. It has three trading periods, 0, 1, and 2 and its per-period expected price
change is zero. 4 Suppose that there is an information shock at 1 that doubles the stock price. With
no other information shock, the average per-period return volatility of this stock is: [(0 + 1002 + 0) /
3]½ = 57.74%. Alternatively, suppose that a group of investors engage in information acquisition
and become aware of the information shock one period ahead (i.e., at 0). They will trade on this
private information and double the stock price immediately. In this alternative scenario, there is
greater acquisition of private information, but the stock’s average return volatility remains the same:
[(1002 + 0 + 0) / 3]½ = 57.74%. Of course, an in-between case is that the informed traders
incorporate only, say, half the information shock into the price, leaving the other half as public
information at 1; in this case, the volatility is 40.82%: [(502 + 502 + 0) / 3]½.
The upshot of the above example is that the relationship between private information
acquisition and average return volatility is theoretically ambiguous. In this particular example, their
relationship can be anything from positive (with the 2nd and 3rd scenarios) or negative (with the 1st
and 3rd scenarios) to indeterminate (with the 1st and 2nd scenarios). This theoretical ambiguity stems
from the implicit assumption in the example that informed trading only affects the timing of new
information being capitalized into stock price. Perhaps, allowing for more information shocks
associated with active informed trading—besides their faster incorporation into stock price—may
lead to an unambiguous relation. However, this opens up another debate on the nature of those
3
A similar example was used by Randall Morck during his discussion at the 2007 Queen’s University
conference. His point is the same as ours: the relationship between private information acquisition and
average return volatility is theoretically ambiguous.
4
We assume that the terminal date is far into the future and, hence, there is no resolution of fundamental
uncertainty during these three periods. We consider the three trading periods for brevity. The example can be
easily modified to suit other lengths of trading periods. The assumption of zero discount rate is also found in,
e.g., Peng and Xiong (2006). See West (1988) for the effect of a positive discount rate.
5
shocks: some of them may be genuine information but they may also contain trading noise.
These problems carry over to the idiosyncratic component of stock return volatility, thereby
casting doubt on its role as a proxy for private information (see also Hou, Peng, and Xiong 2006).
The fraction of idiosyncratic volatility in the total volatility is also problematic. This relative
measure postulates that only the idiosyncratic volatility, and not the systematic volatility, reflects
private information. However, it is indeed plausible that private information concerns some
market-wide or aggregate events, as well as firm-specific affairs (see, e.g., Albuquerque et al.
2009). Moreover, private information acquisition activities in these two dimensions are likely to be
positively correlated. 5 In such a case, the fraction of idiosyncratic volatility is misleading as the
idiosyncratic component and the systematic component crowd out each other in the relative
volatility measure (e.g., Chan and Hameed 2006; Fernandes and Ferreira 2008). In the following
sub-sections, we formalize these observations and derive our testing hypotheses in the context of
the variance ratio analysis.
2.2. A formal setup
To formalize our idea, we use the following model for stock price (in logarithm):
*
Pt = Pt + u t ,
(1)
where Pt* follows a random walk process and ut follows a mean-zero stationary process. The
former thus represents a permanent component in stock price (with an innovation, εt, following iid
(0, σε2)), whereas the latter stands for a temporary component (with a variance of σu2). Simple as it
is, this model proves to be fairly general. For example, Beveridge and Nelson (1981) show that
“any time series which exhibits the kind of homogeneous non-stationarity typical of economic time
series can be decomposed into two additive components, a stationary series and a pure random
5
For example, Durnev et al. (2003) recognize it by saying: “... because some business activities are more
subject to economy- and industrywide shocks than others, and firm-specific events in these industries may be
correspondingly more intense though the intensity may intrinsically stem from environmental volatility.”
(p.801)
6
walk.” (p.153) It is also a generalized version of the model in Summers (1986), Fama and French
(1988), and Poterba and Summers (1988). 6
In this setup, the average one-period return variance is:
var(R1 ) = σ e2 + 2(1 − ρ 1 ) σ u2 ,
(2)
where R1 stands for one-period return on the stock and ρ1 is the one-period autocorrelation of the
temporary component. 7 Eq. (2) reveals two sources of stock return volatility. First, greater
innovations in the permanent component (i.e., greater σε2) increase the stock return volatility, which
amounts to saying that more information shocks add to the volatility. Second, greater variance of
the temporary component leads to greater stock return volatility; hence, trading noise also increases
the volatility. More instructively, Eq. (2) shows that the persistence of the temporary component is
inversely related to the volatility, meaning that the volatility rises as investors are quick to respond
to a transient shock and to rectify their mistaken reaction subsequently. In other words, trading
noise is greater when there are more innovations in the temporary component and/or when those
innovations are more quickly incorporated into stock price. The latter condition, in particular,
corresponds to the notion that an investor’s incentive to trade on private information may force him
to respond even to non-information, thereby creating speculative noise trading.
2.3. Hypothesis
We now consider a k-period return. We begin with k that is large enough to make the
temporary component irrelevant. (Later in this sub-section, we consider the case of a relatively
small k.) The variance of k-day return is kσε2 + 2(1–ρk) σu2, in which ρk is the kth-order
6
In a similar attempt to decompose stock return, Campbell (1991) suggests a VAR model with some preselect state variables. We do not employ this alternative, since it requires a set of state variables and, due to
the nature of most candidate state variables, the estimation of a VAR model cannot be conducted with highfrequency data. Utilizing the high-frequency data is crucial for our purposes; otherwise, the nature of a
temporary component would be hard to determine. For the correspondence between Eq. (1) in the text and
this alternative VAR specification, see Cohen et al. (2002; p.415-416).
7
See, e.g., Poterba and Summers (1988) or Campbell, Lo, and MacKinlay (1997).
7
autocorrelation of the temporary component. With a sufficiently large k, the variance ratio
converges to: 8
VRk ≡
→
var(R1 )
var(Rk ) / k
σ e2 + 2(1 − ρ1 ) σ u2
σ e2
= 1+
2(1 − ρ1 ) σ u2
σ e2
(3)
.
Given that more trading noise is associated with a higher value of σu2 and/or a lower value of ρ1, we
have the following hypothesis.
H1: If takeover vulnerability causes speculative noise trading more than genuine informed trading,
then the stock of a firm with greater takeover vulnerability will have a higher variance ratio. If, on
the other hand, takeover vulnerability fosters informed trading more than speculative noise trading,
then the stock of a firm with greater takeover vulnerability will have a lower variance ratio.
Eq. (3) does not allow the variance ratio to be lower than one in the limit. If k is not sufficiently
large, however, the ratio can be smaller than one. We now discuss how our hypothesis is affected
by this consideration. With a relatively small k, we cannot assume the convergence of the variance
ratio. Instead, we need to examine the exact value of the ratio, which is:
VRk =
σ e2 + 2(1 − ρ1 ) σ u2
σ
2
e+
2
(1 − ρ k ) σ u2
k
(4)
.
The variance ratio can be smaller than one if (1–ρ1) < (1–ρk)/k. Although three different variables
affect this inequality, ρ1 is likely to play the largest role because ρk is typically small in magnitude
8
Hence, a one-period is defined as the measurement interval during which a temporary component is present,
whereas a k-period is the one in which the temporary component grows stale.
8
(even with a relatively small k) and k is given in this discussion. This notion is consistent with
Fama and French (1988) who show that a more persistent temporary component makes the stock
returns serially more positively correlated; hence, a larger value of ρ1 and a smaller-than-one
variance ratio. In our context, since speculative noise trading is associated with a smaller value of
ρ1, stocks with more such trading will have a higher variance ratio. Thus, the above hypothesis, H1,
holds.
If takeover vulnerability affects the degree of informed or speculative noise trading, this
relationship is likely to be more pronounced when information asymmetries are greater and thus
investors have a stronger incentive to acquire and trade on private information. Similarly, the
relationship is expected to be stronger when investors have a greater interest in the stock. This
notion yields our second hypothesis:
H2: The positive or negative relationship between takeover vulnerability and variance ratio will be
more pronounced among stocks with greater information asymmetries or greater investor interests.
2.4. Relationship between variance ratio and relative idiosyncratic volatility measure
The most widely used measure of private information flow in the recent literature is the relative
idiosyncratic volatility, often known as “one minus R2” (e.g., Ferreira and Laux 2007) It is thus
instructive to clarify how this popular measure is related to our workhorse, variance ratio. In the
introduction, we have pointed out that the relative idiosyncratic volatility is problematic because of
its assumption that only the idiosyncratic component reflects information. This assumption can be
relaxed in the context of a temporary vs. a permanent component in stock price by stating that the
variance of the idiosyncratic component in stock return is the sum of its contributions to the
variance of the permanent component (i.e., information) and to the variance of the temporary
component (i.e., trading noise). In other words,
9
var(idiosyncratic component in stock return)
= w1*var(temporary component) + w2*var(permanent component),
where both w1 and w2 are between 0 and 1 (since the systematic component also contributes to the
two variances). The relative idiosyncratic volatility, denoted below by IDIO, can then be written as:
IDIO =
w1 × var(temporary component) + w2 × var(permanent component)
.
var(temporary component) + var(permanent component)
On the other hand, Eq. (3) shows that the variance ratio has the following alternative representation:
VR k =
var(temporary component) + var(permanent component)
.
var(permanent component)
In other words,
IDIO = w1 × (1 − VR −k 1) + w2 × VR −k 1
or
VR k =
( w2 − w1 )
.
( IDIO − w1 )
With the assumption embedded in the relative idiosyncratic measure (i.e., w1=0 and w2=1), VRk
is simply the reciprocal of IDIO. Unlike IDIO, however, the variance ratio can allow for a non-zero
w1 and a less-than-one w2; consequently, it can be viewed as the “adjusted” relative idiosyncratic
volatility measure. In other words, the variance ratio is a more informative measure, since it is
based only on the notion that speculative noise trading cannot continue to affect stock price
because it is not supported by information.
3. Sample and data
We start constructing the sample with the companies in the IRRC database. Following the
convention in the literature, we exclude companies with multiple classes of stock from the sample
(see, e.g., Gompers et al. 2003; footnote 5). We obtain stock return data from CRSP and require
that at least three years’ worth of daily stock return data be available during our sample period from
10
September 1990 to December 2005. These data requirements leave us with 1,722 firms as our
sample for the univariate analysis. For the later multivariate analysis, we employ several other
databases such as the Compustat, and they serve as additional data requirements reducing the
sample size to 1,567 firms.
The IRRC database provides firm-level information about various antitakeover provisions. Its
initial coverage in the 1990 database—out in September of that year—included the companies in
the Standard and Poor’s 500 Index and some other firms that are followed by major news media
(e.g., Fortune). Subsequently, it has expanded into smaller companies, covering approximately
1,500 companies in a given year. Using this database, Gompers, Ishii, and Metrick (2003) construct
an index, namely the governance index, by adding up the incidences of 24 pre-select takeover
protections within a company. We use this index as a measure of a firm’s takeover vulnerability.
One potential problem with this index is that the 24 takeover protections may not have the
same effectiveness. To address this issue, Cremers and Nair (2005) propose an alternative index
focusing on three core protection schemes: the existence of classified (staggered) boards, of blank
check preferred stock (poison pill), and of restrictions on shareholders on calling special meetings
or acting through written consent. We also employ this alternative index to ensure the robustness of
our results.
4. Empirical results
4.1. Summary statistics
Table 1 reports summary statistics of the daily log return at various measurement intervals,
namely, 1 day, 5 days, 10 days, 15 days, and 20 days. Across the 1,722 sample stocks, the average
daily log return is virtually zero with a standard deviation of 3.2%. Both the average and the
standard deviation increase with the length of the interval. Daily log returns range between -28.5%
and 23.1%, which is somewhat wide, but this range does not increase much with the interval length.
11
For example, the 20-day (i.e., monthly) returns are between -43.5% and 37.2%, and it is only less
than twice wide than the daily return case.
In calculating the variance ratio, we treat a certain multi-day window as a missing observation
if there is any missing daily return during that window. We also require at least 30 observations to
estimate the return variance. Consequently, a valid 20-day return variance, for example, needs at
least 30 20-day windows each of which has all 20 daily returns. Using these valid return variances,
we calculate four variance ratios for each stock as defined by Eq. (3) (i.e., VR5, VR10, VR15, and
VR20). As shown by, e.g., Cochrane (2005), there is a bias in a variance ratio estimate when the
sample is small. However, such a bias is likely to be negligible as we require at least three years’
worth of data and use the entire sample period for the ratio estimation. 9
Table 2 shows that the average variance ratio is always greater than one. This result attests to a
non-negligible role of a temporary component in daily stock price changes. Although the result
may also be driven by the bid-ask bounce (e.g., Roll 1984), it seems indisputable that part of the
daily stock return volatility is attributable to a temporary component in stock price.
4.2. Univariate analysis
We now conduct the univariate analysis. To this end, we sort the sample stocks into four
groups by their governance index values. Since the variance ratio of a stock is estimated over the
entire sample period, we also use the governance index averaged across the sample period. 10
Specifically, group 1 contains stocks whose average index value is less than or equal to 5. Group 2
consists of stocks whose average index value is greater than 5 but smaller than 10. Stocks in group
9
⎡
⎢⎣
k
Specifically, E[ρj] = −1/(T−j) and VRk = 1 + 2 ∑ (| k − j | × ρ j ) k
j =1
⎤
⎥⎦
−1
. Consequently, with T equal to 750,
the bias for VR5, for example, is of the order of 0.005.
Information loss associated with the averaging is likely to be minuscule, since the index value seldom
changes over time. For example, Gompers, Ishii, and Metrick (2003) report that the average absolute change
in the index for an individual company is only 0.60, while the median change is zero.
10
12
3 have the average index value of 10 or higher but less than 14. Finally, group-4 stocks have the
average index value of 14 or higher. In each of the four groups, both the mean and median variance
ratios are calculated, and they are compared between groups 1 and 4.
Table 3 shows that the variance ratio is typically greater for stocks with fewer antitakeover
provisions than for stocks with more such protections. More precisely, the difference in mean or
median variance ratio between groups 1 and 4 is statistically significant. Across the four variance
ratios, the p-values for the mean difference are at most 0.006 and those for the median difference
are also smaller than 0.05 with just one exception, in which case the p-value is 0.051.
We also examine the economic significance of those variance ratios. On average, group 1’s
VR5 is 1.15, meaning that 13 percent (1 – 1/1.15) of daily return variance is caused by the
innovations in a temporary component. (Here the temporary component is defined as the one that
dissipates within a week.) Over a longer horizon, the temporary component becomes more evident.
Specifically, the VR20 of 1.27 indicates that more than 21% of daily return variance is attributable
to the innovations in a temporary component. Group 4 has a much smaller fraction of daily return
variance driven by the innovations in a temporary component, as less than 10% (1 – 1/1.11) of
daily return variance is caused by a temporary component.
4.3. Multivariate analysis
4.3.1. Control variables
We now conduct the multivariate analysis to establish that stocks with fewer antitakeover
provisions have a greater variance ratio even after controlling for other firm or stock characteristics.
Given the finding of French and Roll (1986) that small stock returns are more negatively
autocorrelated at daily frequency, firm size is one of the most natural control variables. A negative
autocorrelation in stock return at daily frequency may also be caused by bid-ask bounce (Roll
1984), so we control for the bid-ask spread. Book-to-market ratio also needs to be controlled for,
13
since it represents the intensity of investor interests. It may also reflect the degree of mispricing, in
which case the relationship between book-to-market ratio and the extent of a temporary component
in stock price may not be linear (e.g., Baker and Wurgler 2006). Additionally, we control for
leverage, since it makes equity value more uncertain and thus creates room for a temporary
component. Alternatively, leverage, often combined with merger-related covenants, can function as
a takeover deterrent (Billet et al. 2007). Controlling for institutional holdings is motivated by the
need to take into account the investor heterogeneity in terms of their sophistication.
We control for industry effects by using the 0/1 industry dummy variables, which are defined
by Fama and French’s 49 industry classifications. This control is crucial, since takeover
vulnerability and stock return volatility are likely to be endogenously determined at the industry
level. For instance, Gaspar and Massa (2006) find that firms in more competitive industries have a
greater idiosyncratic volatility. Gillan, Hartzell, and Starks (2003) also show that industry is an
important factor affecting a firm’s governance including its takeover vulnerability. In particular,
Cremers, Nair, and Peyer (2008) show that, conditional on a certain relationship with stakeholders,
companies in more competitive industries have more antitakeover provisions. We thus need to
ensure that our univariate results are not driven by the cross-industry differences.
Finally, we note that a stock’s fundamental uncertainty and the incentive of outside investors to
collect private information on the stock are likely to be positively correlated (Grossman and Stiglitz
1980). This implies that the numerator and the denominator in the variance ratio can be positively
correlated, reducing the power of the variance ratio test. We thus control for the denominator by
including k-day return variance as one of the control variables. This approach amounts to asking
whether takeover vulnerability fosters informed trading or speculative noise trading more than the
fundamental uncertainty does.
Table 4, Panel A, reports summary statistics of these control variables. Like the governance
and alternative indices, each of the control variables is first averaged across the sample period and
14
the summary statistics in the table are for those averages. Panel A confirms that there are no
extreme values in the control variables.
Panel B then shows the correlation coefficients between them, along with the governance and
alternative indices. The two indices are highly correlated with each other but, at the same time, they
are not identical (ρ = 0.608). It is thus instructive to use them alternatively to ensure the robustness
of our results. The control variables are highly correlated with at least one of the two indices,
validating themselves as a necessary control. However, no control variable seems to pose the
multicollinearity problem as the largest correlation coefficient between one of the two indices and a
control variable is only 0.181 in absolute terms.
The correlation coefficients among the control variables are also significant in most cases and
some of them appear to be too highly correlated with each other, potentially making the inferences
difficult. Specifically, the correlation coefficient between firm size and bid-ask spread is -0.623.
We thus orthogonalize one variable to the other (i.e., regressing one variable on the other and using
the regression residuals) when both variables need to be in one regression.
4.3.2. Regression analysis – test of H1
To formally test H1, we estimate the following equation:
C
VR k ,i = α + β Indexi + ∑ γ c X c ,i + ε i ,
(5)
c =1
where VRk,i is the variance ratio of daily return variance to k-day return variance (scaled by k) for
stock i estimated over the entire sample period, Indexi is either the governance or the alternative
index for stock i averaged over the sample period, and Xc,i represents one of the control variables
for stock i averaged over the sample period. Among the control variables, bid-ask spread is first
orthogonalized to firm size and then included in the regression. Throughout the paper, we use the
White (1980) standard errors to control for heteroscedasticity.
15
Table 5 reports the regression results. Starting with the left-half panel, we find that the
governance index enters the regression with a significant and negative coefficient in the presence
of the control variables. This result demonstrates that a greater variance ratio associated with a
lower governance index value is not attributable to other firm characteristics. That is, two stocks
with similar characteristics except for takeover vulnerability have statistically different variance
ratios; in particular, the one with fewer takeover protections has a higher variance ratio. This result
clearly favors the speculative noise trading hypothesis over the informed trading hypothesis. We
also note that the result remains robust across the four different variance ratios.
Among the control variables, firm size is negatively related to the variance ratio, which is
consistent with French and Roll (1986) who find that smaller firms have a more negatively
autocorrelated daily stock returns. Bid-ask spread, orthogonalized to firm size, is positively related
to the variance ratio, indicating that the bid-ask bounce is one reason for a negative serial
correlation in daily stock returns (Roll 1984). Book-to-market ratio is significantly and negatively
related to the variance ratio, suggesting that greater investor attention to a stock leads to a higher
variance ratio for the stock. Institutional holdings are also negatively—albeit only weakly
significantly—related to the variance ratio, which indicates that stocks held by more sophisticated
investors have a lower variance ratio. Note that the coefficients for the latter two variables support
our interpretation that a higher variance ratio indicates greater speculative noise trading of the stock.
Finally, leverage and the k-day return variance are both negatively related to the variance ratio.
Moving on to the right-half panel, we note that the alternative index is not reliably associated
with the variance ratio. The weaker results with the alternative index could be due to several
reasons, including the smaller dispersion in the index value (which ranges from zero to three).
However, a more instructive way of examining the hypothesized relationship between takeover
vulnerability and variance ratio is to test our second hypothesis, since it reveals the sources of the
explanatory power—if any—of the governance or alternative index.
16
.
4.3.3. Sub-sample analysis – test of H2
Our second hypothesis is based on the notion that a certain relationship between takeover
vulnerability and variance ratio—be it positive or negative—will be more pronounced among the
stocks with greater information asymmetries or greater investor interests, provided that the
relationship is driven by the investor’s incentive to acquire and trade on private information. Hence,
we test whether the observed negative relationship between the number of takeover protections and
the variance ratio is more pronounced for a subset of stocks with greater information asymmetries
or investor interests. To this end, we estimate Eq. (5) for each of the sub-samples sorted by a proxy
for information asymmetries or investor interests. Specifically, we use the sample median value of
firm size, bid-ask spread, or book-to-market ratio to split the sample into two groups. We also
obtain the residual bid-ask spread for each of the sub-samples to include it the regression along
with firm size.
Table 6 reports the results. To save space, we only report the coefficient for the governance or
alternative index (along with the White t-statistic). Consistent with the speculative noise trading
hypothesis, the relationship between the governance index and the variance ratio is more evident in
the small-stock group, in the large-bid-ask spread group, and in the low-book-to-market ratio group.
This result is robust to using two alternative indices and also to measuring the variance ratio for
different multi-day horizons.
We also test the difference in the coefficient for the governance (alternative) index between the
two sub-samples by estimating the original full-sample regression with a dummy for one subsample with greater information asymmetries or investor interests, and its interactive term with the
index. Specifically, we estimate the following equation:
C
VR k ,i = α + β 1 Indexi + β 2 Dumi + β 3 ( Indexi × Dumi ) + ∑ γ c X c ,i + ε i ,
c =1
17
(6)
where VRk,i is the variance ratio of daily return variance to k-day return variance (scaled by k) for
stock i estimated over the entire sample period, Indexi is either the governance or the alternative
index for stock i averaged over the sample period, Dumi is a 0/1 dummy variable for stocks with
greater information asymmetries or investor interests, and Xc,i represents one of the control
variables for stock i averaged over the sample period. Again, we use the White (1980) standard
errors to control for heteroscedasticity. When a variable is used to create Dumi, that variable is not
included in the control variable set. As shown in the third row in each panel of Table 6, the
regression coefficients are in general statistically significantly different between the two subsamples with the notable exception that the sample is split by the market capitalization and the
governance index is used. However, the coefficient for the index is larger in absolute magnitude in
the sub-sample with greater information asymmetries or greater investor interests, supporting the
speculative noise trading hypothesis.
4.4. Portfolio analysis
Thus far, we have analyzed individual stock returns. One would ask whether our results carry
over to portfolios. If this were the case, then the temporary component that we have detected via
variance ratio must be due to some common factors such as the discount rate. In other words, such
a finding would make it possible that the temporary component we found is a time-variation in the
expected return. To address this issue, we examine the variance ratio of the takeover vulnerabilitysorted portfolios. While such test portfolios can be constructed using several different weighting
schemes, we choose to use equal weighting. We do so in order not to underweight small stocks that
are the main driver of our earlier results (recall the results in Table 6). That is, we bias ourselves
towards finding something at this portfolio level.
Table 7 shows that there is no particular relationship between the governance-sorted equally
weighted portfolios and their variance ratios. Also, the hedged portfolio (long the group-1 portfolio
18
and short the group-4 portfolio) virtually shows the random-walk pattern, as its variance ratio is
close to one. This result with the equally weighted portfolio verifies that our earlier results with
individual stocks are driven by a firm-specific component in stock return. Again, we stress that we
utilize daily-frequency data and thus such a firm-specific component is unlikely to be due to timevariation in the expected return.
As an aside, we note that all the variance ratios for the equally weighted portfolios are below
one, meaning that their daily returns are positively correlated in time-series. This is in stark contrast
with the greater-than-one average variance ratios with individual stock returns (Table 3). It appears
that stocks in the same takeover vulnerability-sorted group respond to some common shocks at
varying speeds. For example, it could be that those stocks are subject to the common market-wide
merger waves—which themselves are likely to be a low-frequency event—with different
sensitivities (see Cremers, Nair, and John 2009). That would cause a positive cross-autocorrelation
among the stocks in the same group and make the variance ratio of the portfolio return smaller than
one.
5. Conclusions
In this paper, we examine whether the openness to takeover markets indeed fosters informed
trading or ends up causing speculative noise trading. To this end, we conduct the variance ratio
analysis. Our idea is that a price change caused by noise—as opposed to information—cannot be
permanent and will thus be reversed; consequently, the stock return over a longer interval will be
less volatile than the return over a shorter one. Using a sample of stocks in the IRRC database, we
find that stocks with fewer antitakeover provisions have greater portion of their daily return
volatility attributable to a temporary component in stock price than do stocks with more takeover
protections. We also find that this pattern is more pronounced among the stocks with greater
information asymmetries or greater investor interests. Our results suggest that a stock’s takeover
19
vulnerability indeed motivates investors to acquire and trade on private information. On net,
however, it causes speculative noise trading more than it fosters genuine informed trading.
20
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23
Table 1. Summary statistics of log return for various measurement intervals
This table reports summary statistics of log return of the sample stocks for various
horizons. This sample includes stocks that are covered by the IRRC and the CRSP
databases. Stocks of the companies with multiple classes of stock are excluded from the
sample. We also require at least three years’ worth of daily stock return data to be
available during our sample period from September 1990 to December 2005. If there is
any missing daily return during a k-day window, we treat the k-day return for this
window as missing.
Log return
Measurement interval
1 day
5 days
10 days
15 days
20 days
# firms
mean
stdev
min
max
1,722
1,722
1,722
1,722
1,722
0.000
0.001
0.001
0.002
0.003
0.032
0.068
0.095
0.116
0.132
-0.285
-0.342
-0.386
-0.416
-0.435
0.231
0.298
0.333
0.362
0.372
24
Table 2. Summary statistics of variance ratio of one-day variance to k-day variance (VRk)
This table reports summary statistics of variance ratio of one-day return variance to k-day return
variance (VRk). This sample includes stocks that are covered by the IRRC and the CRSP
databases. Stocks of the companies with multiple classes of stock are excluded from the sample.
We also require at least three years’ worth of daily stock return data to be available during our
sample period from September 1990 to December 2005. If there is any missing daily return during
a k-day window, we treat the k-day return for this window as missing.
Variance ratio
# firms
mean
stdev
min
median
max
VR5
1,722
1.1035
0.2078
0.5558
1.0706
3.4560
VR10
1,722
1.1490
0.2824
0.5918
1.1009
4.5625
VR15
1,722
1.1733
0.3404
0.5203
1.1050
5.1594
VR20
1,722
1.1980
0.3494
0.5595
1.1388
4.7048
25
Table 3. Variance ratio by governance index-sorted groups
This table reports the mean and median variance ratio by each governance index (G)-sorted group. The average
governance index averaged over the sample period is used for grouping. Specifically, Specifically, group 1 contains
stocks whose average index value is less than or equal to 5. Group 2 consists of stocks whose average index value is
greater than 5 but smaller than 10. Stocks in group 3 have the average index value of 10 or higher but less than 14.
Finally, group-4 stocks have the average index value of 14 or higher.
Governance index
(G)-sorted group
1 (G ≤ 5)
2 (5 < G < 10)
3 (10 ≤ G < 14)
4 (14 ≤ G)
p-value for
difference: 1 vs. 4
# firms
109
971
591
51
mean
median
VR5
VR10
VR15
VR20
VR5
VR10
VR15
VR20
1.15
1.11
1.09
1.04
1.21
1.16
1.13
1.06
1.26
1.17
1.16
1.08
1.27
1.20
1.18
1.11
1.07
1.07
1.07
1.02
1.10
1.11
1.10
1.02
1.11
1.10
1.11
1.03
1.15
1.15
1.14
1.06
0.002
0.003
0.005
0.006
0.046
0.031
0.023
0.051
26
Table 4. Summary statistics and correlation coefficients of control variables
This table reports summary statistics of control variables, as well as the governance or alternative index, used
for the regression analysis. We first average these variables for each company across the sample period, and
then calculate the summary statistics across sample companies.
Panel A. Summary statistics
Variable
# firms
mean
stdev
min
median
max
Governance index
1,722
8.9970
2.5325
2.0000
9.0000
17.7143
Alternative index
1,722
1.9990
0.8680
0.0000
2.0000
3.0000
ln(market-cap)
1,722
20.5004
1.4465
16.3806
20.3569
25.9283
Bid-ask spread
1,721
0.0172
0.0138
0.0005
0.0138
0.1768
ln(book-to-market)
1,619
-0.8462
0.6210
-6.6935
-0.7937
1.8469
Leverage ratio
1,621
0.2133
0.1429
0.0000
0.2026
0.7710
Institutional holdings
1,575
0.5709
0.1780
0.0186
0.5874
0.9874
27
Table 4. cont.
Panel B. Correlation coefficients
Variable
(1): Alternative index
Governance
index
(1)
(2)
(3)
(4)
(5)
0.608
(0.000)
(2): ln(market-cap)
(3): Bid-ask spread
(4): ln(book-to-market)
(5): Leverage ratio
(6): Institutional holdings
0.168
0.151
(0.000)
(0.000)
-0.098
-0.174
-0.623
(0.000)
(0.000)
(0.000)
0.077
-0.038
-0.414
0.349
(0.002)
(0.131)
(0.000)
(0.000)
0.140
0.028
0.037
0.197
0.140
(0.000)
(0.252)
(0.135)
(0.000)
(0.000)
0.181
0.147
0.325
-0.438
-0.078
0.027
(0.000)
(0.000)
(0.000)
(0.000)
(0.002)
(0.287)
28
Table 5. Regression of variance ratio on governance index and control variables
This table reports the regression results of variance ratio on governance or alternative index and control
variables. All variables are the average across the sample period. Bid-ask spread below is the residual from the
regression of the original bid-ask spread on ln(market-cap); hence, “Bid-ask spreadR.” Numbers in brackets are
the heteroscedasticity-consistent t-statistics.
Variable
Using Governance index
Using Alternative index
VR5
VR10
VR15
VR20
VR5
VR10
VR15
VR20
intercept
1.948
[19.33]
2.190
[17.19]
2.528
[15.39]
2.442
[15.40]
1.935
[19.52]
2.171
[17.22]
2.514
[15.18]
2.421
[15.29]
G- or A-index
-0.006
[-2.56]
-0.009
[-2.84]
-0.010
[-2.65]
-0.010
[-2.87]
-0.007
[-1.21]
-0.012
[-1.57]
-0.005
[-0.56]
-0.015
[-1.66]
ln(market-cap)
-0.034
[-7.16]
-0.043
[-7.29]
-0.059
[-8.07]
-0.056
[-7.40]
-0.034
[-7.34]
-0.044
[-7.41]
-0.060
[-8.31]
-0.056
[-7.45]
Bid-ask spreadR
6.539
[7.79]
9.522
[6.15]
11.981
[7.31]
12.880
[8.45]
6.456
[7.70]
9.397
[6.09]
11.929
[7.28]
12.739
[8.29]
ln(book-to-market)
-0.022
[-2.48]
-0.035
[-2.65]
-0.059
[-3.77]
-0.062
[-3.85]
-0.024
[-2.72]
-0.038
[-2.91]
-0.063
[-4.05]
-0.066
[-4.05]
Leverage ratio
-0.165
[-3.96]
-0.270
[-5.15]
-0.279
[-4.38]
-0.318
[-5.12]
-0.173
[-4.11]
-0.281
[-5.41]
-0.295
[-4.64]
-0.330
[-5.32]
Institutional holdings
-0.053
[-1.68]
-0.096
[-2.16]
-0.068
[-1.38]
-0.108
[-2.15]
-0.061
[-1.91]
-0.108
[-2.37]
-0.084
[-1.68]
-0.120
[-2.36]
k-day return variance
-8.258
[-5.64]
-7.469
[-7.19]
-6.762
[-8.45]
-5.642
[-9.01]
-7.756
[-5.54]
-7.086
[-7.20]
-6.515
[-8.51]
-5.429
[-8.99]
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
17.9%
21.3%
23.3%
25.6%
17.6%
20.8%
22.9%
25.3%
1,567
1,567
1,567
1,567
1,567
1,567
1,567
1,567
Industry FEs
R-squared
# of observations
29
Table 6. Regression of variance ratio on governance index and control variables – by sub-sample
This table reports the regression results of variance ratio on governance or alternative index and control
variables. We estimate the regression for each sub-sample sorted either by the sample median ln(market-cap) or
bid-ask spread. All variables are the average across the sample period. Bid-ask spread below is the residual from
the regression of the original bid-ask spread on ln(market-cap) within each sub-sample; hence, “Bid-ask
spreadR.” Numbers in brackets are the heteroscedasticity-consistent t-statistics. * t-stat. for difference is the Eq.
(6) regression t-statistic of the coefficient for the interaction term between the dummy for the sub-sample with
greater information asymmetries or investor interests and the governance (alternative) index.
Sub-sample
Small market-cap
Large market-cap
Coeff. for Governance index
Coeff. for Alternative index
VR5
VR10
VR15
VR20
VR5
VR10
VR15
VR20
-0.008
-0.012
-0.013
-0.012
-0.020
-0.025
-0.021
-0.029
[-2.19]
[-2.34]
[-2.06]
[-2.28]
[-2.14]
[-2.01]
[-1.39]
[-1.97]
-0.004
-0.008
-0.008
-0.009
0.003
-0.003
0.005
-0.006
[-2.17]
[-2.96]
[-2.71]
[-2.65]
[0.42]
[-0.37]
[0.59]
[-0.54]
t-stat. for difference*
[-1.24]
[-1.33]
[-1.04]
[-0.98]
[-2.21]
[-1.88]
[-2.05]
[-1.72]
Large bid-ask spread
-0.009
-0.012
-0.015
-0.015
-0.024
-0.032
-0.035
-0.047
[-2.54]
[-2.55]
[-2.65]
[-2.98]
[-2.52]
[-2.61]
[-2.45]
[-3.19]
-0.002
-0.005
-0.003
-0.003
0.005
0.000
0.012
0.004
[-1.11]
[-1.91]
[-1.09]
[-0.93]
[0.73]
[0.00]
[1.33]
[0.42]
t-stat. for difference*
[-2.02]
[-1.79]
[-1.93]
[-2.22]
[-3.03]
[-3.04]
[-3.61]
[-3.68]
Low book-to-market
-0.008
-0.014
-0.015
-0.015
-0.019
-0.027
-0.022
-0.037
[-2.52]
[-2.97]
[-2.65]
[-3.00]
[-2.17]
[-2.34]
[-1.66]
[-2.70]
Small bid-ask spread
High book-to-market
t-stat. for difference*
-0.002
-0.001
-0.001
-0.001
0.004
0.002
0.010
0.005
[-0.89]
[-0.34]
[-0.28]
[-0.36]
[0.65]
[0.29]
[0.98]
[0.45]
[-2.13]
[-3.21]
[-2.44]
[-2.47]
[-2.64]
[-2.87]
[-2.59]
[-2.97]
30
Table 7. Variance ratio of equally weighted portfolios sorted by governance index
This table reports the variance ratio of the equally weighted portfolios sorted by the
governance index. Each day, stocks are sorted into one of the four portfolios based on
their governance index on that day. Specifically, group-1 portfolio has stocks whose
governance index is up to 5; group-2 between 6 and 9; group-3 between 10 and 13; and
group-4 equal to or greater than 14. The hedged portfolio is the group-1 portfolio minus
group-4 portfolio.
Governance index
-sorted portfolio
VR5
VR10
VR15
VR20
1
0.88
0.79
0.75
0.76
2
0.91
0.82
0.80
0.78
3
0.90
0.78
0.78
0.75
4
0.88
0.75
0.71
0.73
Hedged portfolio
0.93
1.00
0.93
0.99
31