Asset Pricing in Imperfect Markets
Christopher S. Armstrong
[email protected]
John E. Core
[email protected]
Daniel J. Taylor
[email protected]
Robert E. Verrecchia
[email protected]
First draft: August 28, 2008
This draft: January 8, 2008
Abstract: This study investigates the relation between risk and returns under imperfect
competition. When the model of expected returns is based on imperfect competition, the level of
market competition and the degree of adverse selection affect asset prices in conjunction with
market risk. Consistent with our predictions, we find a modest effect from the level of market
competition on expected returns. We also find that expected returns are increasing in the degree
of adverse selection when there is a relatively low degree of market competition. Collectively,
our results suggest that while it may be appropriate to characterize capital markets as a whole by
traditional asset-pricing models based on price-taking behavior, there exist sub-markets within
the wider capital market that are better characterized by imperfect competition.
Keywords: expected returns, cost of capital, market, competition, information, adverse selection
We gratefully acknowledge the comments of Sanjeev Bhojraj, Brian Bushee, Wayne Guay, Heather Tookes, and
seminar participants at Cornell University and Yale University. We gratefully acknowledge the financial support of
the Stanford Graduate School of Business and of The Wharton School. Daniel Taylor also gratefully acknowledges
funding from the Deloitte Foundation. We thank Terrance Odean and Itamar Simonson for providing the individual
investor database, and Yuxing Yan for programming assistance.
1. Introduction
There is a growing interest in whether information in general, and accounting information
in particular, affects the cost of capital over and above the factor loading on market risk such as
the beta factor (or more generally factor loadings on expanded proxies for market risk such as the
Fama and French, 1993, factors). Recently a number of theoretical accounting studies (e.g.,
Hughes, Liu, and Liu, 2007; Lambert, Leuz, and Verrecchia, 2007; and Lambert, Leuz, and
Verrecchia, 2008) suggest that, in perfect markets, the answer is negative. When a market is
perfectly competitive, even if there are differences in information among investors, the only role
for information quality is its effect on market risk; it does not affect the cost of capital through
other channels. As discussed in Lambert et al. (2008, page 28), the result that information quality
only affects the cost of capital through market risk is a consequence of perfect competition
among investors (i.e., investors are price takers):
As each investor determines his demand for shares based on a conjecture that his
demand cannot affect price, more informed investors do not reduce their demand
strategically for fear of revealing their information to others. More importantly, no
trading takes place until an equilibrium price is set. Less informed investors can transact
any quantity at this market clearing price. In addition, they are able to use price as a
conditioning variable in setting their expectations and assessing risk when they submit
their demand order. Thus, with perfect competition, information asymmetry does not
result in adverse selection and there is no compensation for being less informed.
As described in Kyle (1989), Lambert and Verrecchia (2008) and others, perfect
competition, or equivalently the situation in which investors are price takers, occurs when the
number of investors in a security is very large (i.e., countably infinite). When the number of
investors is large, any single investor’s demand has a negligible effect on price, and it is
reasonable for each investor to assume that he and every other investor has no effect on price.
Empirically, we observe a wide range in the number of investors in U.S. firms, with some in the
hundreds of thousands (where the number of investors is large enough to make an assumption of
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price-taking reasonable), but others in the hundreds (where price taking and perfect competition
seem less plausible). In situations where the number of investors is small, it is not reasonable to
assume that investors are price takers. Because each investor knows that he trades against a
small number of other investors, it is reasonable for each investor to assume that he and every
other investor has an effect on price.
Models of imperfect competition, such as Kyle (1989) and Lambert and Verrecchia
(2008), describe asset prices in markets characterized by finite numbers of investors. In these
models, the equilibrium concept relies on the notion that an individual investor conjectures that
prices are upwardly sloping in his demand, and this (alternative) conjecture is sustained in
equilibrium. In other words, here an individual investor presumes that his demand affects prices;
when he trades in firms’ shares his demand will have an unfavorable impact on the prices at
which those trades are executed because prices are upwardly sloping in the investor’s demand.1
The upwardly sloping nature of price inhibits an investor’s willingness to trade in firms’ shares.
The number of investors (which we term “market competition”) and adverse selection
(which results from information asymmetry) are the primary determinants of the degree to which
individual demand affects price in these models (and empirically, see Glosten and Harris, 1998,
p. 138). As mentioned above, as the number of shareholders grows large, markets become more
competitive and approach perfect competition where individual demand no longer affects price.
If individual demand does not affect price, there is no potential for adverse selection, and there is
no role for information or information asymmetry to affect asset prices (other than through
market risk). Conversely, as the number of shareholders declines, markets become less
competitive and more imperfect, and individual demand has an increasing effect on price.
1
While upward-sloping demand curves may seem counterintuitive, they manifest in posted bid-ask spreads and
depths for a given stock. A buy order for more shares than are offered at the quoted depth will increase the price
above the quoted ask (i.e., the trade price is higher in expectation, the greater the demand).
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Following Lambert and Verrecchia (2008), we predict two effects resulting from
individual demand affecting price when markets are imperfect. The first we term a (lack of)
“market competition” effect which predicts that expected returns will be higher in imperfectly
competitive settings even in the absence of investors being dissimilarly informed. The reason for
this effect is that the upwardly sloping nature of investors’ demands, and investors’ recognition
of this fact, inhibits investors’ willingness to trade in a firm’s shares. Therefore there is a greater
discount to the firm’s price than implied by its exposure to market risk alone and, consequently,
expected returns are higher.
The second effect occurs when, in addition to an imperfect market, investors have
information of differing quality. Now the upward-sloping nature of investor demand interacts
with information asymmetry, and adverse selection results. Adverse selection is a consequence
of the fact that when markets are not perfectly liquid, differences in the quality of information
across investors affect the price at which trades are executed. In other words, here an individual
investor presumes that when he trades in a firm’s shares, there is an additional upward slope to
his demand because others will presume that he has superior information. Therefore, in addition
to the discounts to price implied by market-risk considerations and imperfect competition, there
is an additional discount due to adverse selection. Prior research (e.g., Amihud and Mendelson,
1986; Brennan and Subrahmanyam, 1996) shows that because investors price-protect against
adverse selection, stocks that manifest greater adverse selection have greater expected returns.
One innovation of our paper is that we predict and find that this effect occurs only in segments of
markets characterized by imperfect competition as measured by small numbers of investors.
An immediate question is why these effects are not diversifiable. In other words, why do
shareholders in firms with few shareholders receive extra compensation for a risk that essentially
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results from having a limited number of shareholders? It is important to recall that notions of
diversification come from models of perfect markets in which the number of investors in each
firm is large. In a perfect market model such as Lambert et al.’s (2007, pp. 396-397)
reformulation of the CAPM, firm-specific risk is eliminated because it is averaged away as the
number of investors grows large.2 As noted above, however, empirically many firms have only a
few investors, and models of imperfect competition predict that undiversifiable, firm-specific
effects will appear when the number of investors in a given firm is small. When the number of
investors in a given firm is small, each investor bears additional, compensated risk.
To summarize, we predict that the degree of market competition and adverse selection
affect expected returns. To test this hypothesis, we first suggest features of an economy that we
believe are associated with liquidity and adverse selection. Then we test empirically whether
differences in these features affect expected returns in the predicted direction. For example, the
degree to which a market is imperfect is related primarily to the extent to which price is
upwardly sloping in an individual investor’s demand.
In Kyle (1989) and Lambert and
Verrecchia (2008), the extent to which price is upwardly sloping in an individual investor’s
demand is a direct result of the number of investors who participate in the economy. This
suggests that the most appropriate proxy for market competition is the number of investors who
hold shares in a firm. Our main proxy is the number of shareholders-of-record, which is reported
annually in a firm’s 10-K (Compustat DATA100). We also use the number of investors who
hold individual investor accounts at a large retail broker (described in Barber and Odean, 2000;
Graham and Kumar, 2006; and Kumar and Lee, 2006) as a complementary measure of the
degree of market competition.
2
Systematic risk remains important because the number of firms is assumed to grow at the same rate as the number
of investors.
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We measure adverse selection in several ways. Following prior literature (e.g., Brennan
and Subrahmanyam, 1996), our primary measure is the adverse selection component of the bidask spread. We also use the raw bid-ask spread and the Probability of Informed Trade (PIN)
developed by Easley, Hvidkjaer and O’Hara (2002) as alterative direct proxies for the degree of
adverse selection. In addition to these three direct measures, we also use a variety of indirect
measures that have been offered in prior literature.
These proxies include institutional
ownership, analyst coverage, and the presence of intangible assets.
Our findings are as follows. When we focus on the degree of market competition in
isolation, we find weak but (marginally) significant evidence that expected returns are decreasing
in the degree of market competition. The fact that this result is marginal is not surprising given
the high overall level of competition that characterizes U.S. capital markets. When we focus on
adverse selection in isolation, we find modest evidence that expected returns are increasing in the
degree of adverse selection. The theory, however, predicts that the price effects of adverse
selection should only arise when markets are imperfect. When we simultaneously condition on
both market competition and adverse selection, we find strong evidence that the relation between
adverse selection and expected returns is decreasing in the level of market competition. This
result is both statistically and economically significant, and holds for both proxies for the level of
market competition, and for a number of both direct and indirect proxies for adverse selection.
For example, when we measure the degree of market competition as the number of shareholders
and the level of adverse selection using the adverse selection component to the bid-ask spread,
we find that when market competition is low, firms with high adverse selection earn on average
1.01% a month (or 12.12% on an annualized basis) more than firms with low adverse selection
(consistent with our predict of high returns to adverse selection when market competition is low).
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In addition consistent with our hypothesis that expected returns decrease as market competition
increases, we find that no “abnormal” returns accrue to the adverse selection hedge portfolio
when market competition is high.
The remainder of the paper proceeds as follows.
The next section develops our
hypotheses along with a discussion of the relevant prior literature. Section 3 describes the
measurement of key variables and the research design for our empirical tests. Section 4 describes
our sample. Section 5 presents our findings and Section 6 concludes the paper.
2. Hypothesis Development
In light of the foregoing discussion, we predict that expected returns are a function of
market risk, market competition, and adverse selection.
Expected returns = f(market risk, market competition, adverse selection)
(1)
In the special case of perfect competition, expected returns are a function of only market risk and
there is no role for adverse selection to affect asset prices. When markets are less than perfectly
competitive, however, both market competition and adverse selection can affect asset prices.
2.1. Market competition
Our first hypothesis predicts a negative relation between market competition and
expected returns. Theory points to the number of shareholders as the primary determinant of the
extent to which each investor’s demand affects price.
Perfect competition relies on the
assumption that the number of investors in the economy is countably infinite, thereby ensuring
that each investor behaves as an atomistic price taker who has no influence on price. When the
number of investors is finite and decreases, however, each investor has increasing pricing power.
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Increasing pricing power results in each investor (correctly) perceiving that his or her trades have
an increasing affect on price.
Like us, Merton (1987) also predicts that the number of shareholders is related to
expected returns, although his prediction is ceteris paribus controlling for firm market value and
idiosyncratic risk. Bodnaruk and Ostberg (2008) confirm this and others of Merton’s (1987)
predictions using a sample of Swedish firms. The Merton (1987) model, however, is “unusual”
in that it presupposes perfect competition (i.e., it assumes that the number of investors is
countably infinite), yet still generates a prediction as to how a decrease in the number of
shareholders increases expected returns.3 In addition, unlike us, his model assumes that demand
curves remain flat (i.e., are unaffected) as the number of shareholders becomes small, so there is
no adverse selection in Merton (1987). Our primary interest is in examining the expected return
effects that result from increases in the slope of demand curves as the number of investors
decreases and adverse selection increases.
The fact that the price is upward sloping in demand means the stock is less liquid, and if
this liquidity varies systematically as suggested by Lambert and Verrecchia (2008), then there is
liquidity risk. It is important to note that our concept of liquidity risk is very different from the
one used by most of the prior empirical literature. For example, Acharya and Pedersen (2005)
view liquidity risk as arising in a setting characterized by perfect competition as a result of the
correlation between a firm’s liquidity costs and the overall level of market liquidity. Similarly,
Pastor and Stambaugh (2003) define liquidity risk as the covariation between a stock’s return and
market liquidity. Their predictions are derived in part from Campbell, Grossman, and Wang’s
(1993) model of perfect competition in which time-varying risk aversion by a subset of traders
3
A circumstance in which investors in a perfect competition setting behave as if they are only finite in number is
dubbed the “schizophrenia” problem: see, for example, Hellwig (1980).
-8-
implies that current order flow predicts future return reversals. In contrast to Campbell et al.
(1993), we allow for imperfect competition so that a stock price’s sensitivity to order flow occurs
because of a limited number of investors. In particular, in our model liquidity effects occur as a
consequence of imperfect competition where investors (correctly) conjecture that their demand
affects the price at which they will transact in a firm’s shares, which inhibits an investor’s
willingness to transact.
Our first hypothesis is related to the total effects of market competition (stated in
alternative form):
Hypothesis 1: Expected returns are decreasing in the level of market competition.
2.2. Adverse Selection
A number of prior studies examine the relation between adverse selection and expected
returns (e.g., Amihud and Mendelson, 1986; Brennan and Subrahmanyam, 1996). The intuition
in these studies comes from market-microstructure models in which adverse selection increases
transactions costs, and these increased transactions costs are predicted to increase expected
returns. In contrast, we consider the effects of market competition and predict that the relation
between expected returns and adverse selection will diminish as the degree of market
competition increases. Imperfect competition is a necessary condition for adverse selection risk
to arise. In other words, as markets become more competitive, they become more liquid and,
when perfect competition is achieved in the limit, there is no role for investors’ information
profiles to affect asset prices and, consequently, no adverse selection.
Thus, our second hypothesis focuses on identifying the effects of adverse selection
incremental to the level of market competition.
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Hypothesis 2: When markets are imperfect, stocks with higher adverse selection
have higher expected returns. As market imperfection increases, the positive
relation between expected returns and adverse selection increases.
3. Variable measurement and research design
This section describes how we measure variables and how we structure our empirical
tests.
3.1. Variable measurement
3.1.1. Market Competition
Because the number of market participants captures the level of competition in a given
market, we use the number of shareholders as our primary measure of the competiveness of the
market for the firm’s shares. As the number of shareholders increases and the market approaches
perfect competition, each investor acts as a price taker who has no influence on price (Kyle,
1989; Lambert and Verrecchia, 2008). If the number of shareholders is small, however, each
investor has increasing pricing power and his trades have an increasing affect on price.
We use the number of shareholders of record as of the fiscal year end as reported by
firms in their annual 10-K filings (Compustat Data #100) as our proxy for the number of
shareholders. This annual measure is available for a large number of firms beginning in 1975. A
limitation of this measure is that it is available only once per year, and may be noisy because the
SEC requires firms to “give the approximate number of shareholders of record” and shareholders
of record may not include individual shareholders when shares are held in street name (Dyl and
Elliott, 2006).
Our ranking procedures should mitigate concerns about noise in the number of
shareholders as a measure of market of competition. As an additional way of addressing this
concern we use data on individual shareholdings at a large retail broker.
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Because these
individual holdings are likely to be correlated with the number of shares held in street name, they
should serve as an alternative proxy for the level of market competition. We obtain the number
of individual investors from a proprietary database containing the accounts (and the associated
trading activity) at a large retail broker for the six year period spanning June 1991 though June
1997. This database has been used extensively in prior research and is described in Barber and
Odean (2000), Graham and Kumar (2006), and Kumar and Lee (2006). Barber, Odean and Zhu
(2008a) show that the trading of individuals in our dataset is correlated with those at another
large broker, and argue that the activity in our dataset is representative of individuals in general.
Although this variable is available for only a relatively short time period, one of its advantages is
that we observe it at a monthly frequency.
One might think that the number of shareholders is a noisy proxy for the degree of market
competition because shares can be dispersed evenly among shareholders or concentrated so that
one shareholder holds most of the shares.
These differences in ownership concentration,
however, are differences in potential adverse selection rather than market competition. As
discussed above, the number of shareholders measures market competition. When these
shareholders are concentrated or when there are information differences across these
shareholders, there will also be adverse selection;
we now turn to how we measure this
construct.4
3.1.2. Adverse Selection.
4
In a contemporaneous working paper, Akins, Ng and Verdi (2008) also test for an interaction between proxies for
market competition and proxies for adverse selection. An important difference between our research design and
theirs is that they do not use the number of shareholders as a proxy for market competition, but instead employ
measures such as institutional ownership, number of analysts, and Amihud’s (2002) measure of the price impact of
trades. The theory on which we base our tests points to these variables as measures of adverse selection rather than
market competition, and points to number of shareholders as the sole measure of market competition.
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In contrast to our first hypothesis where the number of shareholders is relatively easy to
measure, it is less straightforward to capture the degree of adverse selection in a firm’s stock.
Following prior literature (e.g., Brennan and Subrahmanyam, 1996), our primary measure of
adverse selection is the adverse selection component of the bid-ask spread.
The market
microstructure literature has not agreed on a preferred method for estimating the adverse
selection component of the bid-ask spread, and the estimation procedure can be noisy (Van Ness,
Van Ness, and Warr, 2001). We take two approaches to address these issues. First, while we
focus on the adverse selection component of the bid-ask spread, we also use the bid-ask spread
itself and the Probability of Informed Trade (PIN) measure developed by Easley, Hvidkjaer and
O’Hara (2002) as alternative measures of the degree of adverse selection in the firm’s shares.
Second, we show in sensitivity tests that our results are also robust to indirect proxies for adverse
selection. We use institutional ownership and analysts as proxies for information intermediation
that prior research suggests are associated with lower adverse selection (e.g., Brennan and
Subramanyam, 1995; Bushee and Noe, 2000; and Fehle, 2004).5 We also use the ratio of R&D
expense to sales as a proxy for the presence of intangible assets, which prior research suggests is
associated with higher adverse selection (e.g. Barth and Kasznik, 1999; Barth, Kasznik, and
McNichols, 2001).
We estimate the adverse selection component of the bid-ask spread, λ, similar to the one
developed by Madhavan, Richardson, Roomans (1997).6 To do so, we first gather trade-by-trade
5
In future versions of this paper, we will refine our classification of institutional ownerships to use only the
“dedicated” and “quasi-indexer” types based on the classification used in Bushee (2001) and Bushee and Noe (2000
JAR). Based on this prior research, we expect these types to be more strongly negatively associated with adverse
selection.
6
The Madhavan, Richardson, Roomans (1997) model is selected for two reasons. First, it is used by prior literature
to estimate the adverse selection component of the bid-ask spread (e.g., Greene and Smart, 1999). Second it does not
assume that price changes are monotonically increasing in signed transaction size (e.g., Glosten and Harris, 1988).
We are reluctant to make this assumption, because prior empirical work generally finds that it is violated (e.g.,
Barclay and Warner, 1993; Chakravarty, 2001).
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and quote data from the Institute for the Study of Security Markets (ISSM) and the Trades and
Automated Quotes (TAQ) database provided by the NYSE. We then match trades and quotes
using the Lee and Ready (1991) algorithm with a five second lag to infer the direction of the
trade (i.e., buy or sell). Specifically, the algorithm classifies a trade as buyer (seller) initiated if it
is closer to the ask (bid) of the prevailing quote. If the trade is exactly at the midpoint of the
quote, a “tick test” classifies the trade as buyer (seller) initiated if the price change is positive
(negative).
Once trades are classified as either buyer- or seller-initiated, we estimate the
following firm-specific regression:
Δpt/pt-1 = ψ ΔDt + λ (Dt – ρDt-1) + ut
(2)
,
where pt is the transaction price, Dt is the sign of trade (+1 if buy and -1 if sell), and ρ is the
AR(1) coefficient for Dt. Note that the estimation procedure and equation (2) differ from
Madhavan, Richardson, Roomans (1997) only in so far as we have deflated the dependent
variable by lagged price for cross-sectional comparability.
Absent such scaling, λ would
depend on Δpt, the change in price, and hence the price-level of the firm.7 Because the
Madhavan, Richardson, Roomans (1997) model pertains to the evolution of transaction prices in
a single firm, it was not intended to apply to a cross-sectional setting where the price level
varies across firms.8 Deflating the change in price by beginning price (i.e., using returns) is a
simple adjustment that makes λ invariant to scale and allows it to be used in a cross-sectional
7
As a simple example of this, consider two firms both with unexpected order flow (Dt – ρDt-1) equal c (ignoring for
the moment ΔDt). In the first firm price moves from 10 to 11, in the second from 100 to 110. Despite identical
changes in order flow, λ for the first firm is 1/c and λ for the second firm is 10/c. This example illustrates that,
ceteris paribus, estimates of λ will differ by a factor of 10 because the price-levels of the firms differ by a factor of
ten.
8
This concern about scaling also applies to other microstructure models and measures of λ (e.g., Glosten and Harris
1988). An alternative is to deflate the resulting estimate by the bid-asked spread, which gives the interpretation of
how much of the spread is related to adverse selection. We prefer the interpretation of how much adverse selection
is as a percentage of price.
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setting. Because the algorithm is very time-consuming to run, we measure λ once a year in
June, using all intra-day data for that month to estimate equation (2) for each firm in the sample.
In addition to the adverse selection component of the bid-ask spread, we also use the raw
bid-ask spread and the Probability of Informed Trade (PIN) developed by Easley, Hvidkjaer and
O’Hara (2002) as alterative direct proxies for the degree of adverse selection. Bid-Ask Spread is
the average bid-ask spread scaled by trade price, quoted on TAQ or ISSM and weighted by order
size for the month of June. PIN is the Probability of Informed Trade as described in Easley,
Hvidkjaer and O’Hara (2002) and provided by Soeren Hvidkjaer.
In addition to these three direct measures, we also use a variety of indirect measures that
have been offered in prior literature. These proxies include percentage institutional ownership,
analyst coverage, and the presence of intangible assets. Institutional Ownership is the ratio of
shares held by institution investors to the total shares outstanding. Analyst Coverage is the
number of analysts issuing one-year-ahead earnings per share forecasts for the firm during the
year according to the I/B/E/S Summary file. R&D Expense to Sales is the ratio of annual
Research and Development Expense to total annual Sales.
3.2. Timing of variable measurement.
The timing of our variable measurement is the same as Fama and French (1993), who
rank firms into portfolios based on market value of equity and the book-to-market ratio. Fama
and French (1993) form portfolios once a year at the end of June, and compute returns for the
next 12 months, and then re-form portfolios at the end of the following June. They measure the
market value of equity at the end of June of year t, and compute book value (and all financial
statement variables) as of the last fiscal year end in year t-1.
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Similarly, we form portfolios once a year at the end of June, and compute returns for the
next 12 months. Because the number of shareholders (and the ratio of R&D to sales) derives
from firms’ 10-K filings, we gather this variable as of the last fiscal year end in year t-1. The
market value of equity, the bid-ask spread and its adverse selection component can be observed
from market data and we measure these variables each June of year t. Finally, we obtain the
Probability of Informed Trade from Soren Hvidkjaer’s website. Easley, Hvidkjaer and O’Hara
(2004) measure the variable for each year ending in December of year t-1 and we match this
value to June of year t in our tests. There is no direct analogy for the number of individual
investors, which is not reported in firms’ 10-K filings and cannot be observed from market data.
As with the market value of equity, this variable is available daily to us as researchers (from
brokerage account records). We measure the in June of year t, which gives us the longest
possible time series (72 months) for the variable. Similar to the number of shareholders, it is not
known when the number of individual investors is observed by the market, it can also be argued
that the variable should be measured at the same time as the number of shareholders (in
December of year t-1). When we do this, our results are unaffected except for some diminution
of statistical significance due to the slightly shorter time series.
More generally, we note that the time periods and the firms for which our proxies are
available differ. While we generally use the largest sample of firm-years available for a given
proxy, our main results are robust to examining restricted samples constrained by the availability
of the least available proxy.
3.3. Research design
We test our hypotheses about expected returns by examining whether future excess
returns (as a proxy for expected returns) are consistent with our hypotheses. For example, we
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examine whether future returns to firms with low numbers of shareholders are greater than future
returns to firms with high numbers of shareholders. The main alternative to using future returns
as a proxy for expected returns is to use an implied cost of capital measure, and we acknowledge
that there is an active debate in the literature on the relative merits of future returns versus
implied cost of capital as a proxy for expected returns (e.g., Easton and Monahan, 2005; Guay,
Kothari, and Shu, 2006; McInnis, 2008). A chief interest of our study, however, is firms with
small numbers of shareholders, and because these firms are little followed by analysts, implied
cost of capital estimates (for which analyst forecasts are required) cannot be calculated for most
of these firms (see Panel B of Table 1). In addition, we attempt to mitigate concerns about noise
in future returns by grouping firms into portfolios.
In out tests, we form portfolios sorted based on the variable of interest (e.g., market
competition). Because most of our hypotheses pertain to the interaction between market
competition and adverse selection, we also use two-dimensional sorts. First, we sort on market
competition and then, within each market competition group, we sort on a proxy for adverse
selection. Our hypotheses predict that returns to firms with high relative adverse selection are
largest (smallest) in the lowest (highest) market competition group. Portfolio sorts have been
used by a number of authors to test whether a firm characteristic predicts future returns. In work
closely related to ours, Brennan and Subrahmanyam (1996) use portfolios sorted on the adverse
selection component of the bid-ask spread to examine whether adverse selection is associated
with an increase in expected returns. Similarly, Pastor and Stambaugh (2003) use portfolios
sorted on firms’ exposure to a liquidity factor (i.e., liquidity beta) as evidence to support their
hypothesis that expected returns are higher when liquidity risk is higher.
- 16 -
A second issue is how to weight firms within each portfolio. Following prior literature
(e.g., Brennan and Subrahmanyam (1996)), we use equal weights because our hypotheses are
about the expected returns for a typical or average stock. If we instead used value-weighting, our
return results would reflect expected returns for a large stock, not for a typical or average stock.
Equal-weighted monthly returns are usually calculated by purchasing an equal-weight portfolio,
holding it for one month, and then rebalancing this portfolio so that it has equal weights at the
start of the next month. The potential concern with this equal-weighted returns calculation,
however, is that frequent rebalancing can produced biased estimates of realized returns due to
bid-ask bounces (Blume and Stambaugh, 1983). To see this, consider a stock with monthly
closes of $2, $1, and $2 due to a $1 bid-asked spread. The equal-weighted average monthly
return on this stock is 25% = ([-50% + 100%]/2), but the buy-and-hold return is 0%. If a
portfolio holding this stock is rebalanced to equal weights each month, its returns will be
upwardly biased. To ensure that our results are conservative and not subject to this bias, we
follow Blume and Stambaugh (1983) and compute returns to a buy-and-hold portfolio. The
portfolio is formed on June 30 based on an initial equal weighting, and the monthly “buy-andhold” return is the portfolio’s percentage change in value (with dividends) for the month. This
procedure yields monthly returns to an equal-weighted portfolio that is rebalanced once at the
beginning of each year.9 Note that rebalancing annually also has the advantage of minimizing
the transaction costs necessary to earn the reported abnormal return (i.e., the portfolio manager
only needs to turn the portfolio over once per year).
To test our first hypothesis that expected returns are decreasing in the level of market
competition, we sort firms into five quintiles based on the level of market competition (measured
9
If we use equal-weighted returns instead of buy-and-hold returns in our main test in Panel A of Table 4 below, the
hedge portfolio return is larger by 0.27% per month (1.28% a month versus the 1.01% per month reported).
- 17 -
as either the number of shareholders or the number of individual investors),. We then compute
buy-and-hold returns for each portfolio for the 12 months from July of year t to June of t+1.10
Following a large asset pricing literature (e.g., Pastor and Stambaugh, 2003; Petkova, 2006), our
tests control for market risk using the three Fama and French (1993) factors (i.e., the market risk
premium (RM-RF), size (SMB), and book-to-market (HML)) where these factors are used to
describe the behavior of expected returns under the null hypothesis that market competition and
adverse selection have no effect on expected returns.
We estimate time-series regressions of the portfolio returns on the three Fama and French
(1993) factors as follows:
Rp,t-RF,t = ap + b1,p (RM,t-RF,t) + b2,p SMBt + b3,p HMLt + εp,t ,
(3)
where Rp,t is the monthly portfolio return and RF,t is the risk-free rate. The coefficient of interest
is the estimated intercept (ap). Our first hypothesis predicts that excess returns are lower when
market competition is higher.
We therefore expect that ap decreases across the portfolio
quintiles.
As a more direct test of our hypothesis, we also form a hedge portfolio that takes a long
position in the portfolio of firms with the highest level of market competition and a short position
in firms with the lowest level of market competition:
RH,t = aH + b1,p (RM,t-RF,t) + b2,p SMBt + b3,p HMLt + εp,t
.
(4)
The variable of interest is the estimated intercept aH. If aH is significantly less than zero, firms
with high competition earn lower returns (after controlling for existing market risk factors) than
do firms with low competition. This suggests competition affects expected returns as predicted
by our hypothesis. We acknowledge, however, that a significant hedge return in portfolio sorts
10
If a firm delists in one of these months, we compute the return for that month by compounding the return and the
delisting return (if the delisting return for a given month is not missing), and reinvest any remaining proceeds in the
portfolio.
- 18 -
may also be interpreted as evidence of mispricing, as in Sloan (1996) and Daniel, Hirshleifer,
and Subrahmanyam (2001). We try to mitigate this alternative interpretation by using the
comprehensive Fama-French model in our main tests and by showing our results are robust to a
variety of different specifications in sensitivity tests.
Extending the portfolio sort method to test our hypothesis related to the interaction
between market competition and adverse selection (Hypothesis 2) is straightforward. Because
this hypothesis predicts an interactive effect, we perform dependent sorts where we first sort
firm-years into five quintiles based on the number of shareholders (or number of individual
investors) and then we divide each of these quartiles into five equally-sized quintiles by sorting
on the degree of adverse selection. The first sort is motivated by the fact that as a firm’s
shareholder base becomes larger, trading in the stock approaches perfect competition; the second
sort is intended to partition firms according to the relative presence of adverse selection. We
compute buy-and-hold returns to each of the 25 (= 5 x 5) portfolios, reforming the portfolios
annually at the end of every June, and we compute returns to the hedge portfolios that take a long
position in firms with the highest level of either adverse selection (the lowest level of
competition), and a short position in firms with the lowest level of either adverse selection (the
highest level of competition). We then estimate the Fama-French α for each of portfolio. Our
interest here is the five adverse selection hedge portfolios that are long firms with high adverse
selection, and short firms with low adverse selection within a given market competition quintile.
Our prediction is that we will observe higher excess returns to adverse selection when there is
less market competition. We test this prediction by examining whether the Fama-French α for
the low-competition adverse selection hedge portfolio is significantly higher than the FamaFrench α for the high-competition adverse selection hedge portfolio.
- 19 -
4. Sample Selection
We construct our sample using data from Compustat, the individual investor database,
CRSP, and ISSM and TAQ, I/B/E/S, and CDA Spectrum. To be included in the sample, a firm
must have a non-missing return and market value on the CRSP monthly file in June of year t.
We begin the sample, in June 1976 when the number of shareholders becomes available on
Compustat, and conclude the in June 2005. This allows the inclusion of return data from CRSP
from June 1976 to June 2006. The first two columns of Panel A of Table 1 shows the annual
availability of market value from CRSP and Data100 from Compustat.
The remaining columns of Panel A of Table 1 shows the availability of the remaining.
Our alternative, indirect measure of the degree of market competition, the number of individuals
who own the firm’s stock, is available only for the six year period June 1991 to June 1997,
although we do have information for more firms than with the number of shareholders during the
years in which this variable is available. We begin measuring the adverse selection component of
the bid-ask spread, λ, and the bid-ask spread in 1988, which is when intraday data for the NYSE,
AMEX and NASDAQ becomes available from ISSM.11 λ is available for a smaller number of
firms than is the bid-ask spread, which is due to our requirement that there be at least 50
transactions during the month with which to calculate λ. Finally, Panel A shows that PIN is
computed for a relatively small fraction of firms (i.e., only NYSE- and AMEX-listed firms)
compared to our other two direct measures of adverse selection (i.e., λ and the bid-ask spread).
In order to have a sample that covers a reasonable number of years and firms, for a given
test, we only require availability of the test variables. For example, when we test our hypothesis
11
NYSE / AMEX firms are available starting in 1984, but because these firms are typically much larger in terms of
number of shareholders, we could not find a reasonable way to include them in the full time-series.
- 20 -
about market competition and adverse selection using number of shareholders and λ, we use all
available data for which we have estimates of λ (from 1988 to 2005), but when we test the same
hypothesis using number of analysts, we extend to sample to 1976 to 2005.
Panel B of Table 1 presents descriptive statistics for the primary variables according to
the number of shareholders. In particular, each year we sort firms into one of five quintiles
based on the number of shareholders and report the median, standard deviation and number of
observations for each of the primary variables. We also report the median, standard deviation
and number of observations for firms without information on the number of shareholders (i.e.,
Missing) and for the full sample (i.e., All). For the purposes of Panel B (of this table only), we
winsorize variables each year at the bottom and top percentiles to mitigate the influence of
outliers on the computed standard deviations.
Panel C of Table 1 presents a slightly unusual correlation matrix.
It shows only
Spearman correlations because many of our variables are highly skewed and because our
portfolios use ranked values. Above the diagonal, we report Spearman correlations for the full
sample, and below the diagonal, we report Spearman correlations for the sample restricted to
firms in the smallest quintile of shareholders (ranked each year). Because of our interest in crosssectional relations between variables (e.g., market competition and adverse selection), we
compute annual correlations and report the mean of the annual correlations in the table. We
compute standard errors using the time-series standard deviation of the correlations, and denote
significant (at the 5% level, two-sided) correlations in bold. In the full sample (shown above the
diagonal) there is a positive correlation between Number of Shareholders and Individual
Investors, our two proxies for market competition. Also there is a positive correlation between
each of λ, Bid-Ask Spread, and PIN, our three direct proxies for adverse selection. Consistent
- 21 -
with these variables measuring similar constructs, these correlations indicate the variable capture
similar information. Consistent with prior research that Institutional Ownership and Analyst
Coverage are proxies for information intermediation that are associated with lower adverse
selection, there is a negative correlation between λ, Bid-Ask Spread, and PIN and these variables.
The correlations between R&D Expense to Sales are small, and generally not consistent with our
prediction that more R&D is associated with greater adverse selection. Also note the negative
correlation between the Number of Shareholders and λ and the negative correlation between
Individual Investors and λ. This is consistent with Hypothesis 2: As market competition
increases, adverse selection decreases. Also of note is the large (0.54) correlation between
market value and the number of shareholders. While this correlation suggest a potential size
effect, recall that we control for size by including the SMB factor in the factor regressions in all
of our tests. We also describe in sensitivity tests below additional ways in which we control for
firm size.
In the small shareholder subsample below the diagonal, the univariate correlations
between Number of Shareholders and Individual Investors and each of λ, Bid-Ask Spread, and
PIN are smaller than in the full sample. Also noteworthy are that the correlation between market
value and λ becomes less negative than in the full sample, although still large (a reduction from 0.75 to -0.54).
5. Results
5.1. Market competition and expected returns
Table 2 presents the results of our portfolio tests of Hypothesis 1 that expected returns are
decreasing in the level of market competition. In Panel A, we sort firms into five quintiles based
- 22 -
on the firm’s number of shareholders as of the last fiscal year ending on or before December of
year t-1, such that firms in the fifth quartile have the most shareholders and therefore the greatest
degree of market competition. Each portfolio contains an average of 949 firm months over
period 1976 to 2006. The top of row of the Panel shows the monthly buy-and-hold raw returns
that accrue to the various portfolios. Although the returns of the Q1 portfolio exceed those of the
Q5 portfolio, the difference is not statistically significant. The second row of the Panel shows
returns adjusted for risk using the Fama and French (1993) factors. Although the relation is not
monotonic, the intercept, or alpha, is generally decreasing in the degree of market competition as
we move to the right from the first to the fifth quintile. Moreover, the hedge portfolio that takes
a long position in the firms in the first quintile and a short position in the firms in the fifth
quintile earns an abnormal return of -0.24% per month (or -2.88% per year), on average, which is
statistically significant.
Panel B shows similar results over the shorter time period when the number of individual
investors is used as an alternative proxy for market competition. Each portfolio contains an
average of 1,330 firm months over the period 1991 to 1996. When adjusted for the Fama and
French (1993) factors, the hedge portfolio that takes a long position in the firms in the first
quintile and a short position in the firms in the fifth quintile earns an abnormal return of -0.68%
per month or -7.86% per year, on average, which is also statistically significant.
Overall, Table 2 provides modest evidence in support of Hypothesis 1. We note that ex
ante one is concerned with whether there is sufficient cross-sectional variation in the degree of
market competition, given our focus on U.S. equities during a recent time period. Our results are
consistent with the conjecture that the number of shareholders exhibits enough variation to
provide evidence in support of our hypothesis. We also note that our second hypothesis predicts
- 23 -
an interaction between market competition and adverse selection. In our tests of this interaction
below, we find that market competition has a large effect on expected returns when adverse
selection is high, but a small effect when adverse selection is low. This later finding is consistent
with our findings in Table 2 of a small, unconditional effect of market competition when we do
not partition on the degree of adverse selection.
5.2. Adverse selection and expected returns
In Table 3, we examine the unconditional relation between adverse selection and
expected returns. While Hypothesis 2 predicts a relation conditional on the level of market
competition, we provide unconditional results in Table 3 as a benchmark for our later tests, and
also to replicate prior work such as Brennan and Subramanyam (1996) that predicts and finds an
unconditional relation between adverse selection and expected returns.
Table 3 presents the results using our three direct proxies for adverse selection – namely
λ, which is the adverse selection component of the bid-ask spread (Panel A), the raw bid-ask
spread (Panel B) and PIN (Panel C). The top row of Panel A shows that raw buy-and-hold
returns are monotonically increasing in adverse selection as measured by λ (moving to the right
across the Panel), and that the hedge portfolio difference between quintiles five and one is
positive as predicted but is not statistically significant. The lower part of Panel A shows excess
monthly buy-and-hold returns (ap) for the five quintiles of λ after controlling for market risk
using the three Fama and French (1993) factors, and shows that the hedge portfolio difference
between the fifth and first quintiles is positive and significant, as predicted. The coefficient
shows a monthly excess return of 0.52% per month, or about 6.24% annually. This 0.52%
adverse selection hedge portfolio return for our sample of NYSE, AMEX, and Nasdaq stocks
- 24 -
from 1988 to 2006 is very similar to the 0.55% return reported in Brennan and Subramanyam
(Table 4, 1996) for their sample of NYSE stocks from 1984 to 1991.12
We also present results using the bid-ask spread (Panel B) and PIN (Panel C). In both
cases, although the returns are generally increasing in the degree of adverse selection and the
hedge portfolios have the predicted sign, none are statistically significant. This is not surprising
in the case of the bid-ask spread because it is a noisy version of λ. The weak results for PIN are
consistent with prior findings that PIN only generates excess returns for smaller stocks (Easley et
al., 2004; Mohanram and Rajgopal, 2008).
5.3. Relation between Market Competition, Adverse Selection and Expected Returns
Our second hypothesis predicts an interactive effect between market competition and
adverse selection. In particular, we predict that increases in the degree of market competition
decrease the positive relation between expected returns and adverse selection. In Table 4, we
present results of our portfolio tests of Hypothesis 2. To perform these tests, we perform dual
dependent sorts where we first sort firm years into five quintiles based on their degree of market
competition, and then we subdivide each of these quintiles into five equally-sized quintiles by
sorting on one of measures of adverse selection.
As in Table 2, we again use two complementary measures of market competition and, in
both cases, use λ as the measure of adverse selection. Panel A shows results where market
competition is measured using the number of shareholders. This sample contains on average 141
firms per month for each of the 25 equal-sized market competition-adverse selection portfolios
for the period July 1988 to June 2006. The last column of the table presents the results of the
12
Brennan and Subramanyam (1996) estimate a pooled GLS regression (Table 4), in which they include interactions
for the Fama-French factors for each of their portfolios. Therefore, their procedure is in essence the same as ours in
which the intercepts may be interpreted as hedge portfolio alphas. The difference between their low-adverse
selection intercept and high-adverse selection intercept is the adverse selection hedge portfolio return.
- 25 -
adverse selection hedge portfolio (i.e., Q5 – Q1) according to quintile of market competition.
Consistent with Hypothesis 2, the hedge portfolio return for the lowest market competition
quintile is positive and significant, which indicates that higher returns accrue to these lowcompetition firms with a greater degree of adverse selection Except for the highest market
competition quintile, the hedge portfolios are all positive. Higher returns to firms with a greater
degree of adverse selection is consistent with the results presented in Panel A of Table 3. Our
second hypothesis also predicts that the effect of adverse selection on expected returns is
decreasing in the degree of market competition. As a formal test of this hypothesis, we examine
the difference between the returns to adverse selection hedge portfolio in the low market
competition quintile (1.01% per month, significant with p < 0.01) and the high market
competition portfolio (-0.00% per month and not significant). The returns to this two-way hedge
portfolio are presented in the bottom right cell and are economically large, 1.01% per month or
12.12% annually, and highly statistically significant. This provides strong support for our
second hypothesis.
Panel B repeats the analysis where the number of individual investors is the proxy for
market competition. Each cell in this table contains an average of 164 firms for the period July
1991 to June 1997. We again find that the magnitude of the adverse selection hedge portfolios
are generally decreasing in the level of market competition, which is also consistent with the
results presented in Panel A of Table 3.
The two-way hedge portfolio again produces
economically large returns (1.08% monthly or 12.96% annually) that, despite the limited time
period, are statistically significant. Overall, the results in both panels of Table 4 provide strong
evidence in support of Hypothesis 2.
- 26 -
Before concluding our examination of Table 4, let us return for a moment and examine
the hedge portfolio results on the bottom row of Panels A and B. Each hedge portfolio shows the
difference in returns between the low market competition portfolio (i.e., row 1) and the high
market competition portfolio (i.e., row 5) for a given level of adverse selection. Recall that
Hypothesis 1 predicts that expected returns are decreasing in the level of market competition,
which implies a positive coefficient should obtain on the hedge portfolios. Panels A and B both
suggest that this effect occurs when there is a relatively high degree of adverse selection (i.e.,
columns 4 and 5), but not when there is a relatively low degree of adverse selection (i.e.,
columns 1, 2 and 3). In both cases, the effects are economically large with average monthly
(annual) returns of 0.84% (10.08%) and 1.20% (14.40%) accruing to the hedge portfolio with the
highest degree of adverse selection (i.e., Quintile 5) in Panels A and B, respectively. In addition,
average monthly (annual) returns to the hedge portfolios with the second highest degree of
adverse selection (i.e., Quintile 4) are 0.67% (8.04%) and 0.62% (7.44%) in Panels A and B,
respectively. Because market competition has a large effect on expected returns when adverse
selection is high, but a small effect when adverse selection is low, its overall effect is small,
consistent with our findings in Panel A of Table 2 of a small unconditional effect of market
competition (i.e., when we do not partition on the degree of adverse selection).
5.4. Alternative proxies for adverse selection
Table 5 presents results for the adverse selection hedge portfolios when we perform a
dual sort based on the number of shareholders as the measure of market competition, and one of
five alternative proxies for the degree of adverse selection. The proxies are the Probability of
Informed Trade (column 1), the transaction-weighted bid-ask spread (column 2), the ratio of
shares held by institutional investors to the total shares outstanding (column 3), analyst coverage
- 27 -
(column 4), and the ratio of R&D expense to total sales (column 5). The adverse selection hedge
portfolios for these five proxies follow a similar pattern to those in Table 4 in that they generally
decline as the number of shareholders increases. Moreover, the market competition hedge
portfolio is generally highly statistically and economically significant. Similar to Easley et al.
(2004), who find that small firms have a higher compensation for PIN than large firms, we find
that low-competition firms have higher returns to adverse selection as measured by PIN (MC
Hedge of 0.70, t-stat 2.58).13 The bid-ask spread results in Column (2) are very similar to those
for λ in Panel A of Table 4, though slightly weaker with a hedge return of 0.86 versus 1.01 for λ.
Note our second hypothesis predicts a negative hedge portfolio return for Institutional
Ownership and Analyst Coverage because the degree of adverse selection is expected to be
decreasing in these variables. Column (3) shows that we obtain this expected result with
Institutional Ownership as an inverse proxy for adverse selection (MC Hedge of -0.68, t-stat 3.03), and similarly for Analyst Coverage as an inverse proxy for adverse selection (MC Hedge
of -0.48, t-stat -2.98). Note that in Columns (4) and (5), we rank firms into three (rather than
five) adverse selection portfolios. We use terciles with these variables because in many years
close to 50% of the analyst and R&D variables have zero values. The smallest result (in
economic magnitude) obtains when adverse selection is measured as the ratio of R&D expense to
total sales. The hedge portfolio in this case produces an average monthly return of 0.43% (t =
2.93), or 5.16% on average on an annual basis, which is still economically significant. Overall,
Table 5 shows that the results of Table 4 are robust to a variety of alternative direct and indirect
measures for the degree of adverse selection in firms’ shares.
5.5. Sensitivity analyses
13
An unusual feature in Column 1 is that the high-competition adverse selection portfolio has a significant negative
return.
- 28 -
Table 6 presents sensitivity analyses of our primary results where we calculate the returns
to dual sorts, using the number of shareholders as the measure of market competition and λ as the
measure of adverse selection. Again, for the sake of parsimony, we present only the results of
the adverse selection hedge portfolios. The first column replicates the adverse selection hedge
from Panel A of Table 4 for comparability. The second column presents portfolio returns
excluding all stocks with a price of less than $5 from the sample. This is another way (in
addition to our use of buy-and-hold returns) of ensuring that our results are not driven by
microstructure effects of thinly traded firms, and also provides some comfort that our results are
not driven by microcap firms that are not representative of the population of investable shares.
We again find that the market competition hedge portfolio earns average monthly returns of
1.34% (t = 2.97) and average annual returns of 16.08%. The second column presents average
monthly buy-and-hold returns when we restrict the sample to the period after June of 2001 when
the decimalization of share prices was instituted on the NYSE. The results are strong both
economically (1.33% average monthly returns and 15.96% average annual returns) and
statistically (t = 3.16). These results are important because this more recent period (during which
bid-asked spreads fell and trading practices changed greatly), is likely to be more similar to U.S.
capital markets going forward, and shows that our theory does not apply only to past data.
In the final three columns, we attempt to address the concern that computing portfolio
returns relative to the Fama-French factors does not adequately control for the size effect. Our
proxies for market competition (i.e., number of shareholders) are strongly positively correlated
with market value, and our proxies for adverse selection (i.e., λ) are strongly negatively
correlated with market value. A potential concern is that sorting firms according to the number
of shareholders is simply picking up a size-effect. As a first approach, we begin with the same
- 29 -
sort of firms on number of shareholders and λ as shown in the first column. Then we sort firms
on market value, and delete the smallest and largest 20% of firms in the sample (i.e., the top and
bottom quintile when ranked on market value). If the market competition hedge portfolio returns
are induced by an implicit sort on size, removing the extreme size portfolios should eliminate the
excess returns between the quintile portfolios with the largest and the smallest number of
shareholders. The fourth column shows the results from this reduced sample. The low
shareholder AS hedge portfolio is still significant, and of comparable magnitude to that of the
full sample in column 1. The high shareholder AS hedge portfolio, however, becomes more
positive, but still insignificant, with the result that the MC hedge falls to 0.78% and is only
marginally significant (p-value = 0.12 two-sided). Although the coefficient is economically
significant, the reduction in statistical significance is likely due to a large increase in the standard
error from the reduced sample size.
A related concern is that our dual sorts on λ may effectively sort firms within a given
market competition quintile by size. To address this concern, in fifth column we take a similar
approach as we did in the fourth column. We again begin with the same sort of firms on number
of shareholders and λ as shown in the first column. Then within each market competition
quintile, we sort firms on market value, and delete the smallest and largest firms in each market
competition quintile. If the adverse-selection hedge portfolios returns are induced by an implicit
sort on size within market competition quintile, removing the extreme size portfolios should
eliminate the excess returns. But Column 5 shows that the results are essentially unchanged (as
compared to Column 1) when we make this change.
In the last column, we calculate abnormal returns as the difference between monthly
portfolio returns and the returns on a portfolio matched on size and book-to-market. We use the
- 30 -
25 Fama-French size and book-to-market portfolios as our benchmark portfolios. Note that in
the previous tests we calculate abnormal returns relative to the three Fama and French (1993)
factors which includes both the SMB and the HML factors. Using the size and book-to-market
matching technique, however, is potentially more robust to nonlinearities in the relation between
size and book-to-market and returns (Daniel, Grinblatt, Titman, and Wermers, 1997). Although
the magnitude of the hedge portfolio abnormal return is smaller than the one reported in Table 4
(Panel A), the results are still significant. The muted statistical and economic significance may
be expected because firm size, the number of shareholders, and λ are highly correlated.
Separating the effects is difficult, and is made more difficult because these effects are expected
under our hypotheses: low competition firms with high adverse selection have high discount
rates and therefore low market values. Overall, the results presented in Tables 5 and 6 show that
the results in Table 4 are robust to alternative proxies for the degree of adverse selection,
alternative samples, restricted time periods, and alternative ways of calculating abnormal returns.
6. Conclusion
This study investigates the relation between risk and returns under imperfect competition.
When markets are less than perfectly competitive, as in Kyle (1989) and Lambert and Verrecchia
(2008), market competition and adverse selection affect asset prices. We test hypotheses related
to these effects and find evidence supporting our predictions. In particular, we find that the effect
of adverse selection on asset prices is decreasing in the level of market competition. We find
that expected returns are increasing in the degree of adverse selection when there is a relatively
low degree of market competition.
Collectively, our results suggest that while it may be
appropriate to characterize capital markets as a whole by traditional asset-pricing models based
- 31 -
on price-taking behavior, there exist sub-markets within the wider capital market that are better
characterized by imperfect competition in combination with information asymmetry, thereby
giving rise to adverse selection.
- 32 -
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- 34 -
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VAN NESS, B.; R. VAN NESS; AND R.WARR. “How Well Do Adverse Selection Components
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- 35 -
Table 1 – Descriptive Statistics
Panel A. Number of Observations by Year
This table presents the annual number of observations available for the primary variables. Year is the year of
portfolio formation. Number of Shareholders (Data #100) is the number of shareholders of record measured as of
the firm’s fiscal year end. Number of Individual Investors is the number of individuals who hold a long position in
the firms shares at the end of June each year. λ is the modified Madhavan, Richardson, Roomans (1997) measure of
the adverse selection component of the bid-ask spread, estimated over the month of June. Bid-Ask Spread is the
average bid-ask spread scaled by trade price, quoted on TAQ or ISSM and weighted by order size for the month of
June. PIN is the Probability of Informed Trade as described in Easley, Hvidkjaer and O’Hara (2002). Institutional
Ownership is the ratio of shares held by institution investors to the total shares outstanding.. Analyst Coverage is the
number of analysts issuing one-year-ahead earnings per share forecasts for the firm during the year according to the
I/B/E/S Summary file. R&D Expense to Sales is the ratio of annual Research and Development Expense to total
annual Sales. Market Value is the market capitalization (in millions of dollars) measured at the end of June.
Year
Number of
Shareholders
Number of
Individual
Investors
1976
3,239
-
1977
4,018
1978
PIN
Institutional
Ownership
Analyst
Coverage
R&D
Expense
to Sales
Market
Value of
Equity
-
.
3,550
4,056
4,103
-
.
4,091
4,120
4,177
-
-
.
4,035
4,046
4,098
-
-
-
.
4,032
4,041
4,106
-
-
-
-
4,038
4,011
4,017
4,105
4,037
-
-
-
-
4,232
4,096
4,236
4,356
4,229
-
-
-
-
4,447
4,312
4,436
4,574
1983
4,364
-
-
-
-
4,701
4,468
4,592
4,822
1984
4,646
-
-
-
1,960
5,139
4,864
4,986
5,337
1985
4,811
-
-
-
1,908
5,235
4,957
5,050
5,418
1986
4,806
-
-
-
1,857
5,379
4,982
5,077
5,568
1987
5,041
-
-
-
1,787
5,783
5,346
5,439
6,060
1988
5,214
-
3,477
4,011
1,823
6,022
5,546
5,485
6,239
1989
5,139
-
3,294
3,973
1,825
5,992
5,512
5,333
6,172
1990
5,080
-
3,275
3,924
1,794
6,001
5,475
5,299
6,190
1991
5,038
5,989
3,308
3,982
1,780
6,017
5,406
5,296
6,202
1992
5,102
6,321
3,256
3,914
1,847
6,335
5,554
5,522
6,507
1993
5,307
6,706
4,112
5,069
1,936
6,736
5,847
5,777
6,928
1994
5,850
7,419
4,723
5,501
2,058
7,588
6,454
7,026
7,785
1995
6,076
7,477
5,089
5,970
2,075
7,792
6,732
7,234
7,936
1996
6,208
7,632
5,280
6,075
2,076
8,171
7,154
7,609
8,352
1997
6,670
-
5,818
6,534
2,101
8,479
7,542
7,924
8,631
1998
6,623
-
5,951
6,584
2,122
8,426
7,509
7,838
8,522
1999
6,177
-
6,134
6,495
2,154
8,047
7,090
7,396
8,111
2000
5,986
-
5,859
6,154
2,016
7,942
6,950
7,411
8,054
2001
5,560
-
5,585
5,887
1,919
7,418
6,325
6,901
7,505
2002
5,092
-
5,274
5,513
1,861
6,926
5,733
6,377
7,023
2003
4,665
-
4,962
4,993
-
6,405
5,358
5,901
6,563
2004
4,528
-
4,728
3,089
-
6,294
5,219
5,719
6,469
2005
4,528
-
4,689
3,358
-
6,003
5,240
5,693
6,511
λ
Bid-Ask
Spread
-
-
-
-
-
3,959
-
-
1979
3,988
-
1980
3,972
1981
1982
- 36 -
Table 1 – Descriptive Statistics (cont’d)
Panel B. Descriptive Statistics by Shareholder Quintile
This table presents the median, standard deviation and number of our primary variables by Number of Shareholders
quintile, based on an annual ranking. Number of Shareholders Quintile is the quintile of the number of shareholders
if this variable is available, missing if unavailable, and all for the pooled sample. Number of Shareholders (Data
#100) is the number of shareholders of record measured as of the firm’s fiscal year end. Number of Individual
Investors is the number of individuals who hold a long position in the firms shares at the end of June each year. λ is
the modified Madhavan, Richardson, Roomans (1997) measure of the adverse selection component of the bid-ask
spread, estimated over the month of June. Bid-Ask Spread is the average bid-ask spread scaled by trade price,
quoted on TAQ or ISSM and weighted by order size for the month of June. PIN is the Probability of Informed
Trade as described in Easley, Hvidkjaer and O’Hara (2002). Institutional Ownership is the ratio of shares held by
institution investors to the total shares outstanding. Analyst Coverage is the number of analysts issuing one-yearahead earnings per share forecasts for the firm during the year according to the I/B/E/S Summary file. R&D
Expense to Sales is the ratio of annual Research and Development Expense to total annual Sales. Market Value is
the market capitalization (in millions of dollars) measured at the end of June.
Number
of
Sharehol
ders
Quintile
1
Statistic
Median
Number of
Shareholders
241
Number of
Individuals
Investors
3.00
Λ
0.0021
BidAsk
Spread
0.0243
PIN
0.25
Institutional
Ownership
0.09
Analyst
Coverage
0.00
R&D
Expense
to Sales
0.00
Market
Value
Equity
28
1
Std. Dev.
237
18.48
0.2926
0.0806
0.08
0.24
3.05
0.98
722
1
Nobs.
30,863
6,340
12,748
13,789
2,949
30,654
30,863
30,268
30,863
2
Median
700
5.00
0.0021
0.0248
0.24
0.10
0.00
0.00
33
2
Std. Dev.
385
14.92
0.6446
0.0780
0.08
0.24
3.53
0.94
1,018
2
Nobs.
30,880
6,494
13,999
15,497
4,573
30,749
30,880
30,374
30,880
3
Median
1,584
6.00
0.0020
0.0241
0.23
0.14
1.00
0.00
53
3
Std. Dev.
672
26.32
0.3931
0.0795
0.07
0.25
4.17
0.61
1,340
3
Nobs.
30,881
6,593
15,001
16,115
6,275
30,778
30,881
30,451
30,881
4
Median
3,906
10.00
0.0014
0.0194
0.20
0.23
3.00
0.00
125
4
Std. Dev.
1,659
39.27
0.4297
0.0727
0.06
0.26
5.19
0.64
2,153
4
Nobs.
30,886
6,658
16,310
16,716
8,487
30,732
30,886
30,457
30,886
5
Median
17,873
37.00
0.0005
0.0115
0.16
0.36
9.00
0.00
836
5
Std. Dev.
47,853
115.52
0.2305
0.0648
0.05
0.27
8.57
0.63
6,362
5
Nobs.
30,870
6,683
16,477
16,562
13,198
30,733
30,870
30,634
30,870
Missing
Median
.
2.00
0.0018
0.0193
0.22
0.07
3.00
0.00
78
Missing
Std. Dev.
.
30.44
0.4679
0.0738
0.09
0.18
3.90
0.63
2,013
Missing
Nobs.
-
8,776
10,279
12,347
1,417
33,322
14,193
23,255
38,562
All
Median
1,651
6.00
0.0015
0.0199
0.19
0.14
2.00
0.00
80
All
Std. Dev.
25,786
58.90
0.4257
0.0752
0.08
0.25
6.03
0.76
3,092
All
Nobs.
154,380
41,544
84,814
91,026
36,899
186,968
168,573
175,439
192,942
- 37 -
Table 1 – Descriptive Statistics (cont’d)
Panel C. Comparison of Spearman Correlations
Full Sample (above diagonal) / Bottom Quintile of Shareholders (below diagonal)
This table presents the correlation among the proxies for adverse selection and information asymmetry that are used
in the analysis. Bold indicates statistical significance at the 5% level (or lower). The table presents spearman
correlations for the full sample (above diagonal), and for the bottom quintile of number shareholders (lowest 20%
each year) (below diagonal). Number of Shareholders (Data #100) is the number of shareholders of record measured
as of the firm’s fiscal year end. Number of Individual Investors is the number of individuals who hold a long
position in the firms shares at the end of June each year. λ is the modified Madhavan, Richardson, Roomans (1997)
measure of the adverse selection component of the bid-ask spread, estimated over the month of June. Bid-Ask
Spread is the average bid-ask spread scaled by trade price, quoted on TAQ or ISSM and weighted by order size for
the month of June. PIN is the Probability of Informed Trade as described in Easley, Hvidkjaer and O’Hara (2002).
Institutional Ownership is the ratio of shares held by institution investors to the total shares outstanding.. Analyst
Coverage is the number of analysts issuing one-year-ahead earnings per share forecasts for the firm during the year
according to the I/B/E/S Summary file. R&D Expense to Sales is the ratio of annual Research and Development
Expense to total annual Sales. Market Value is the market capitalization (in millions of dollars) measured at the end
of June.
Number of Shareholders
Individual Investors
λ
Bid-Ask Spread
PIN
Institutional Ownership
Analyst Coverage
R&D Expense to Sales
Market Value of Equity
0.54
0.24
-0.03
-0.46
-0.26
-0.59
-0.52
-0.20
-0.58
0.58
0.67
0.56
-0.30
0.32
Market Value of Equity
0.47
-0.07
0.36
0.45
0.13
0.50
-0.55
-0.69
0.01
-0.75
-0.46
-0.54
-0.02
-0.57
-0.41
-0.61
-0.07
-0.66
0.65
0.03
0.67
0.03
0.75
-0.02
-0.11
0.54
0.00
-0.36
0.45
0.30
0.03
0.31
-0.46
-0.46
-0.28
0.03
0.34
-0.55
-0.51
-0.36
0.57
0.07
0.21
-0.05
-0.04
-0.04
0.01
0.04
0.03
0.36
-0.59
-0.52
-0.43
0.64
0.56
- 38 -
R&D Expense to Sales
Analyst Coverage
Institutional Ownership
PIN
Bid-Ask Spread
λ
Individual Investors
Spearman
Correlations
Quintile of
Shareholders (below
diagonal)
Number of Shareholders
Spearman Correlations for Full Sample (above diagonal)
0.54
0.00
0.03
Table 2 – Market Competition Portfolios
We form five equal-weighted portfolios at the end of June of year t, and compute monthly buy-and-hold returns for
each portfolio. We rank firms into quintiles in June of year t based on market competition measured as either
Number of Shareholders or Number of Individual Investors. Raw Returns is the monthly portfolio return and FamaFrench α is the intercept from a Fama-French 3-factor model. To be included in a portfolio the firm must have a
non-missing return and market value on the CRSP monthly file in June of year t.
Panel A. Measure of Market Competition: Number of Shareholders
The sample in Panel A spans July 1976 – June 2006 and contains on average 949 firms per portfolio per month.
Number of Shareholders (Data #100) is the number of shareholders of record measured as of the firm’s fiscal year
end.
Model
Raw Returns
Fama-French α
Quintiles formed on Number of Shareholders
1
2
3
4
5
1.42
1.43
1.37
1.36
1.20
(4.00)
(4.44)
(4.59)
(4.72)
(5.09)
0.10
0.03
-0.04
-0.07
-0.14
(0.82)
(0.36)
(-0.48)
(-1.05)
(-3.14)
Hedge
Q5-Q1
-0.22
(-1.12)
-0.24
(-2.02)
Panel B. Measure of Market Competition: Number of Individual Investors
The sample in Panel B spans July 1991 – June 1997 and contains on average 1,330 firms per portfolio per month.
Number of Individual Investors is the number of investors at a large retail broker that hold a long position in the
stock of the firm as of the end of June each calendar year.
Model
Raw Returns
Fama-French α
Quintiles formed on Number of Individual Investors
1
2
3
4
5
1.73
1.68
1.58
1.31
1.34
(4.52)
(3.92)
(3.39)
(2.78)
(3.22)
Hedge
Q5-Q1
0.43
(1.80)
-0.68
(-3.29)
0.18
(1.00)
0.05
(0.31)
-0.23
(-1.79)
-0.25
(-2.17)
-0.39
(-1.76)
Table 3 – Adverse Selection Portfolios
We form five equal-weighted portfolios at the end of June of year t, and compute monthly buy-and-hold returns for
each portfolio. We rank firms into quintiles in June of year t based on adverse selection measured as either λ, BidAsk Spread, or PIN. Raw Returns is the monthly portfolio return and Fama-French α is the intercept from a FamaFrench 3-factor model. To be included in a portfolio the firm must have a non-missing return and market value on
the CRSP monthly file in June of year t.
Panel A. Measure of Adverse Selection: λ
λ is the modified Madhavan, Richardson, Roomans (1997) measure of the adverse selection component of the bidask spread and is computed during the month of June of year t. The sample in Panel A spans July 1988 – June 2006
and contains on average 893 firms per portfolio per month.
Model
Raw Returns
Fama-French α
1
1.09
(3.63)
-0.09
(-1.32)
Quintiles formed on λ
2
3
4
1.15
1.24
1.34
(3.10)
(2.89)
(3.14)
-0.10
0.06
0.18
(-1.62)
(0.70)
(1.25)
5
1.53
(3.56)
0.43
(2.00)
Hedge
Q5-Q1
0.44
(1.43)
0.52
(2.29)
Panel B. Measure of Adverse Selection: Bid-Ask Spread
Bid-Ask Spread is the average bid-ask spread scaled by trade price quoted on TAQ or ISSM and weighted by order
size during the month of June of year t. The sample in Panel B spans July 1988 – June 2006 and contains on
average 992 firms per portfolio per month.
Model
Raw Returns
Fama-French α
Quintiles formed on Bid-Ask Spread
1
2
3
4
1.12
1.24
1.32
1.37
(3.32)
(3.67)
(3.45)
(3.30)
-0.09
0.06
0.17
0.27
(-0.85)
(0.88)
(1.79)
(1.75)
- 40 -
5
1.40
(3.15)
0.27
(1.17)
Hedge
Q5-Q1
0.28
(0.85)
0.37
(1.33)
Table 3 – Adverse Selection Portfolios (cont’d)
Panel C. Measure of Adverse Selection: PIN
PIN is the probability of informed trade measured as in Easley, Hvidkjaer, O’Hara (2002) and provided by Soeren
Hvidkjaer. The sample in Panel C spans July 1984 – June 2003 and contains on average 372 firms per portfolio per
month.
Model
Raw Returns
Fama-French α
1
1.13
(3.98)
-0.14
(-1.71)
Quintiles formed on PIN
2
3
4
1.12
1.09
1.00
(3.44)
(3.22)
(2.93)
-0.21
-0.23
-0.25
(-2.29)
(-2.31)
(-2.21)
- 41 -
5
1.07
(3.18)
-0.08
(-0.55)
Hedge
Q5-Q1
-0.06
(-0.26)
0.06
(0.36)
Table 4 – Market Competition Portfolios Partitioned by Adverse Selection
We form twenty five equal-weighted portfolios at the end of June of year t, and compute monthly buy-and-hold
returns for each portfolio. Firms are first ranked into quintiles based on the degree of market competition measured
as either Number of Shareholders or Number of Individual Investors. Then within each quintile firms are ranked
into five portfolios based on λ which is the modified Madhavan, Richardson, Roomans (1997) measure of the
adverse selection component of the bid-ask spread and is computed during the month of June of year t. The FamaFrench α is the intercept from a Fama-French 3-factor model. To be included in a portfolio the firm must have a
non-missing return and market value on the CRSP monthly file in June of year t.
Panel A. Market Competition Measured as Number of Shareholders
Quintile of Number of
Shareholders
Number of Shareholders (Data #100) is the number of shareholders of record measured as of the firm’s fiscal year
end. The sample in Panel A spans July 1988 – June 2006 and contains on average 141 firms per portfolio per
month.
1
2
3
4
5
MC Hedge
Q1-Q5
1
-0.22
(-1.55)
0.04
(0.28)
-0.16
(-1.45)
0.00
(0.03)
-0.04
(-0.61)
-0.17
(-1.29)
Quintile of λ (Fama-French α)
2
3
4
-0.22
-0.05
0.45
(-1.52)
(-0.23)
(2.06)
-0.09
-0.03
0.36
(-0.66)
(-0.17)
(1.78)
-0.17
0.21
0.25
(-1.58)
(1.43)
(1.33)
-0.09
0.04
0.19
(-0.87)
(0.33)
(1.35)
-0.08
-0.14
-0.22
(-1.00)
(-1.84)
(-2.18)
-0.15
0.09
0.67
(-0.84)
(0.42)
(2.72)
5
0.79
(2.27)
0.37
(1.54)
0.44
(1.63)
0.28
(1.06)
-0.05
(-0.23)
0.84
(2.96)
AS Hedge
Q5-Q1
1.01
(2.76)
0.34
(1.29)
0.60
(2.23)
0.27
(0.90)
-0.00
(-0.02)
1.01
(3.52)
Panel B. Market Competition Measured as Number of Individual Investors
Quintile of Number of
Individual Investors
Number of Individual Investors is the number of investors at a large retail broker that hold a long position in the
stock of the firm as of the end of June each calendar year. The sample in Panel B spans July 1991 – June 1997 and
contains on average 164 firms per portfolio per month.
1
2
3
4
5
MC Hedge
Q1-Q5
1
0.10
(0.65)
0.09
(0.70)
-0.13
(-1.00)
0.03
(0.28)
-0.02
(-0.21)
0.12
(0.66)
Quintile of λ (Fama-French α)
2
3
4
0.00
0.09
0.04
(-0.01)
(0.39)
(0.16)
-0.06
-0.11
-0.18
(-0.36)
(-0.66)
(-0.71)
-0.37
-0.29
-0.34
(-2.45)
(-1.54)
(-1.57)
-0.22
-0.60
-0.16
(-1.46)
(-3.34)
(-0.59)
-0.12
-0.29
-0.57
(-1.07)
(-2.12)
(-2.72)
0.11
0.38
0.62
(0.50)
(1.42)
(1.95)
- 42 -
5
0.81
(1.99)
0.27
(0.82)
0.25
(0.61)
-0.30
(-0.72)
-0.39
(-0.85)
1.20
(2.62)
AS Hedge
Q5-Q1
0.71
(1.96)
0.18
(0.53)
0.38
(0.98)
-0.33
(-0.74)
-0.38
(-0.83)
1.08
(2.31)
Table 5 – Alternative Proxies for Adverse Selection
We form twenty five equal-weighted portfolios at the end of June of year t, and compute monthly buy-and-hold
returns for each portfolio. Firms are first ranked into quintiles based on Number of Shareholders (Data #100) which
is the number of shareholders of record measured as of the firm’s fiscal year end. Then within each quintile firms
are ranked into five portfolios based on the following five proxies for adverse selection. PIN is the probability of
informed trade measured as in Easley, Hvidkjaer, O’Hara (2002) and provided by Soeren Hvidkjaer. Bid-Ask
Spread is the average bid-ask spread scaled by trade price quoted on TAQ or ISSM and weighted by order size
during the month of June of year t. Institutional Ownership is the ratio of shares held by institutional investors to
total shares outstanding. Number of Analysts is the number of analysts issuing one-year ahead annual earnings per
share forecasts during the fiscal year as reported on the I/B/E/S Summary File. R&D Expense to Sales is the ratio of
annual R&D expense to total annual sales as of the firm’s fiscal year end. Monthly equal-weighted portfolio returns
are calculated assuming annual rebalancing. To be included in a portfolio the firm must have a non-missing return
and market value on the CRSP monthly file in June of year t. The Fama-French α is the intercept from a FamaFrench 3-factor model. Only the adverse selection hedge portfolio α and t-statistics are reported. The sample in the
first column (PIN) spans July 1984 – June 2003 and contains on average 72 firms per portfolio month. The sample
in the second column (Bid-Ask Spread) spans July 1988 – June 2006 and contains on average 171 firms per portfolio
month. The sample in the third column (Institutional Ownership) spans July 1980 – June 2006 and contains on
average 196 firms per portfolio month. The sample in the fourth column (Number of Analysts) spans July 1976 –
June 2006 and contains on average 336 firms per portfolio month. The sample in the fifth column (R&D Expense to
Sales) spans July 1976 to June 2006 and contains an average of 332 firms per portfolio month.
Proxy for Adverse Selection
Quintile of Market
Competition
1
2
3
4
5
MC Hedge
Q1-Q5
(1)
(2)
PIN
AS Hedge
Q5-Q1
0.34
(1.36)
0.50
(1.99)
0.04
(0.19)
0.01
(0.03)
-0.37
(-3.18)
0.70
(2.58)
Bid-Ask Spread
AS Hedge
Q5-Q1
0.74
(1.89)
0.25
(0.84)
0.40
(1.34)
-0.01
(-0.03)
-0.12
(-0.50)
0.86
(2.86)
(3)
Institutional
Ownership
AS Hedge
Q5-Q1a
-0.59
(-1.94)
-0.18
(-0.71)
+0.13
(+0.55)
+0.14
(+0.48)
+0.09
(+0.41)
-0.68
(-3.03)
(4)
Number of
Analysts
AS Hedge
Q3-Q1a
-0.38
(-1.94)
-0.17
(-1.09)
-0.03
(-0.17)
0.05
(0.25)
0.09
(0.84)
-0.48
(-2.98)
(5)
R&D Expense
to Sales
AS Hedge
Q3-Q1
0.51
(2.93)
0.32
(1.74)
0.24
(1.75)
0.35
(2.72)
0.08
(0.60)
0.43
(2.93)
_______________________________
a
Note that our second hypothesis predicts a negative hedge portfolio return for Institutional Ownership and Analyst
Coverage because the degree of adverse selection is expected to be decreasing in these variables.
- 43 -
Table 6 – Sensitivity Analyses
This table reports sensitivity analyses of the results presented in Panel A of Table 4. We form twenty five equalweighted portfolios at the end of June of year t, and compute monthly buy-and-hold returns for each portfolio.
Firms are first ranked into quintiles based on Number of Shareholders (Data #100) which is the number of
shareholders of record measured as of the firm’s fiscal year end. Then within each quintile firms are ranked into
five portfolios based on λ which is the modified Madhavan, Richardson, Roomans (1997) measure of the adverse
selection component of the bid-ask spread and is computed during the month of June of year t. The Fama-French α
is the intercept from a Fama-French 3-factor model. We present the results of the adverse selection hedge portfolios
in the columns. The first column replicates the adverse selection hedge alpha presented in Table 4, Panel A. The
second column presents alphas excluding those stocks with price less than $5 per share at the end of June of year t.
The third column presents alphas for the period following the decimalization of stock prices by the NYSE (i.e., after
June of 2001). In the fifth column, we begin with the same sort shown in the first column, delete the smallest and
largest 20% of firms in the sample (i.e., the top and bottom quintile when ranked on market value). In the fifth
column, we again begin with the same sort of firms shown in the first column, and then within each market
competition quintile, we delete the smallest and largest firms in that market competition quintile. The fifth column
presents monthly abnormal returns calculated by subtracting the monthly return of the respective size and book-tomarket portfolio to which the firm belongs. The sample in the first, fourth, fifth, and sixth columns span July 1988 –
June 2006 and contains on average 157, 95, 95, and 157 firms per portfolio per month, respectively. The sample in
the second column spans July 1988 – June 2006 and contains on average 119 firms per portfolio per month. The
sample in the third column spans July 2001 – June 2006 and contains on average 160 firms per portfolio per month.
λ Hedge Portfolios
Quintile of Number of
Shareholders
(1)
1
2
3
4
5
MC
Hedge
Q1-Q5
Table 4
Panel A
Adverse
Selection
Hedge
1.01
(2.76)
0.34
(1.29)
0.60
(2.23)
0.27
(0.90)
-0.00
(-0.02)
1.01
(3.52)
(2)
(3)
Excluding
Poststocks with decimalization
price < $5
(6/2001)
0.98
1.39
(2.33)
(2.51)
0.32
0.82
(1.32)
(1.88)
0.27
0.62
(1.22)
(1.08)
0.34
0.10
(1.39)
(0.19)
-0.36
0.05
(-2.85)
(0.12)
1.34
1.34
(2.97)
(2.97)
- 44 -
(4)
Excluding
Q1 and Q5
MV
1.06
(2.42)
0.18
(0.64)
0.36
(1.31)
0.41
(1.29)
0.28
(0.55)
0.78
(5)
Excluding
Q1 and Q5
MV by
Num. of
Sh.
Quintile
1.16
(2.61)
0.32
(1.12)
0.29
(1.06)
0.41
(1.26)
-0.30
(-1.60)
1.46
(6)
Size and
Book-toMarket
Portfolio
Adjusted
Returns
0.44
(1.53)
-0.06
(0.24)
0.13
(0.60)
-0.11
(0.46)
-0.14
(0.66)
0.58
(1.56)
(3.24)
(2.02)