Download Information Disclosure in Speculative Markets

Information Disclosure in Speculative Markets
Florin Dorobantu∗
Department of Economics, Duke University
Box 90097, Durham, NC 27708
Email: [email protected]
June 2005
Abstract
When investors hold different opinions about the value of an asset, prices
can diverge from fundamental values and incorporate a speculative component.
This paper analyzes the effect of such a speculative environment on managerial
incentives to voluntarily disclose information about the value of the firm. I show
that differences of opinion, when they induce a speculative premium, increase the
threshold for information disclosure thereby reducing the likelihood that voluntary
disclosure of information occurs. Using data on management earnings forecasts
as a measure of voluntary disclosure, I provide empirical evidence in favor of this
hypothesis.
∗
I would like to thank S. Viswanathan, Itay Goldstein, Pete Kyle, Oksana Loginova, Dhananjay
Nanda and Curtis Taylor for numerous and very valuable comments and suggestions. Any remaining
errors are my responsibility
1
Introduction
As many of the accounting irregularities that came to light in the recent years occurred
during the late 1990s, a period characterized by highly speculative market behavior,
it is natural to ask the question whether this is a mere coincidence or the result of a
causal relationship between the speculative environment and managerial incentives to
disclose information. Are managers less likely to disclose what they know about their
firms when their stock is overpriced? This paper attempts to shed light on this issue in
the context of a model of discretionary disclosure in the presence of speculative premia
induced by heterogeneity of beliefs, à la Miller (1977) and Harrison and Kreps (1979).
While the focus on discretionary, or voluntary, disclosure prevents the discussion of
actual accounting fraud, I believe an understanding of the incentives at work in the
absence of legal constraints sheds light not only on the disclosure of information that
is not subject to disclosure laws, but also on the mechanism that leads to violation of
legal provisions in order to withhold information that could negatively affect the stock
price.
A large literature on voluntary disclosure of information exists, going back to Grossman (1981) and Milgrom (1981) who use an adverse selection argument to show that full
revelation is always optimal if there are no costs of disclosure and the uninformed parties know about the existence of private information. Empirical evidence however points
toward the existence of partial disclosure equilibria, in which good news is disclosed and
bad news is withheld (see, for example, Miller (2002) and Lev and Penman (1990)). Verrecchia (1983) suggests a model that incorporates proprietary costs of disclosure, which
give rise to an equilibrium that exhibits partial disclosure: in order for the information
held by the manager to be released, it has to be good enough to offset the negative effect
on stock price caused by the drop in the value of the firm imposed by the disclosure of
information of a proprietary nature. Dye (1985) derives a partial disclosure equilibrium
when the information is non-proprietary, based on the assumption that investors are
uncertain about the existence of private information.1 Both papers consider a single
dimensional information variable, and show that there exists a threshold above which
the manager prefers disclosing.
In this paper, I consider a manager who sometimes knows the true value of the firm,
as in Dye (1985), and analyze what happens to the disclosure threshold when investors
have heterogeneous beliefs about the fundamental value of the firm. The reason for
considering this scenario is that heterogeneous prior beliefs have been shown to give
rise to speculative motives for trading, and thus to cause prices to include a speculative
premium. This idea, suggested originally by Keynes (1936), was formalized by Miller
(1977), Harrison and Kreps (1979) and Morris (1996). The intuition behind it is very
simple. First, with short sale constraints, the price of the asset at any time equals
1
For a review of the disclosure literature, see Verrecchia (2001), Dye (2001) and Healy and Palepu
(2001).
2
the highest willingness to pay among the different investors – investors who think the
asset is worth less cannot “make their voices heard” by way of short selling the asset,
and thus are effectively crowded out of the market. Second, at any point in time, the
price of the asset typically exceeds the highest fundamental valuation among investors,
because the investor holding the asset anticipates she will be able to sell the asset at
some point in the future to other investors for a price that, at that time, will exceed
her fundamental valuation. Therefore, due to this option to resell the asset to investors
who will be more optimistic in some future states of the world, prices incorporate a
speculative premium equal to the amount by which the price exceeds the most optimistic
fundamental valuation. Morris (1996) derives conditions under which the speculative
premium is always strictly positive, despite the fact that investors’ posterior beliefs
converge as they incorporate more observations from the dividend process driving the
value of the asset.
The main result of this paper is that when investors have heterogeneous prior beliefs
that induce a speculative premium, the threshold above which the manager finds it
optimal to disclose the private information is higher than in the absence of heterogeneity.
The intuition behind this finding is the following. Heterogeneous prior beliefs induce, in
general, different posterior beliefs about the value of the firm, subsequent to observing a
public signal about the process driving firm value. For a speculative premium to exist,
there must exist states of the world when the original investor does not have the highest
valuation after the public signal is observed. If there are two investors (or two types of
investors) and two states, then investor 1 is optimistic in one state, and investor 2 in
the other. From the manager’s perspective, maximizing stock price entails releasing the
information only when it will raise the price above what it would be without disclosure.
But when the price reflects the highest valuation among two investors, it is always
higher than it would be if only one of the two investors was in the market. Therefore,
there are values of the information variable for which disclosure would be optimal with
only one investor in the market, but it is not when both investors participate in the
market. It is not the speculative premium itself that reduces disclosure, but rather
the same combination of belief heterogeneity and short sale constraints that produces a
speculative premium also reduces the incentives for disclosure. We should then expect
to see reduced disclosure during periods of speculative activity in the market, which is
reminiscent of what happened in the late 1990s.
While there is a relatively large literature that investigates the effect of differences of
opinion on asset prices and returns, few papers look at their effect on the incentives facing
managers whose payoffs depend on asset prices. Two exceptions are Bolton, Scheinkman,
and Xiong (2003) and Panageas (2003). The former look at a principal-agent model of
managerial performance when manager’s pay depends positively on the stock price and
investors have heterogeneous beliefs. They show that the manager exerts effort on a
short-term project that does not increase the value of the firm because it increases
uncertainty and thus exaggerates the speculative premium. This in turn drives up the
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equilibrium price and thus the manager’s compensation. The latter paper analyzes the
effect of overpricing on firm’s investment decision and shows that speculative premia
induce over-investment.
The paper is organized as follows. Section 2 presents the benchmark model with
homogeneous beliefs, and derives the equilibrium disclosure policy. Section 3 introduces
heterogeneity in beliefs, and shows that the resulting disclosure policy is less revealing
than the one in the benchmark model, and section 4 extends this result to show that
the informativeness of the disclosure policy depends negatively on ex-ante belief heterogeneity. Section 5 contains an empirical analysis that brings preliminary evidence in
support of the theoretical implication, and section 6 concludes.
2
The Benchmark Model - Homogeneous Beliefs
This section develops the baseline model in which there is only one type of investor.
There is no difference of opinions and thus no speculative premium.
There are three dates in the model, t ∈ {0, 1, 2}, at which a stock is traded. At
t = 0, the stock is issued, and at dates t = 1, 2 it pays dividend δ. The dividend δ can
take only two values, 0 or 1, and is i.i.d. with Pr(δ = 1) = θ. The dividend process
is assumed to be exogenous (i.e. dividends are not affected by any agent’s actions).
Trade occurs at each date after the dividend is paid. There are an infinity of identical
risk-neutral investors, whose prior beliefs about θ ∈ [0, 1] are represented by the density
π 1 (θ), π 1 : [0, 1] → R.2 The assumption of risk-neutrality is not as restrictive as it may
first seem, as it is usually justified by the assumption that the investors can diversify
away any idiosyncratic risk from holding the asset under analysis.
The other player is the manager of the firm, who is also risk neutral and maximizes
the sum of stock prices over the life of the firm. I assume that at t = 1, there is
probability λ that the manager learns θ0 , the true value of the parameter θ. The
probability λ is exogenous and known to all market participants. If she learns θ0 , the
manager decides whether to disclose it to the market or not. The manager knows the
realized dividend when making the decision, so she is in fact deciding between making
a fully informative announcement (dividend plus the value of the firm), or a partially
informative announcement consisting of only the dividend realization. It is assumed
that the investors can costlessly verify the truth of manager’s announcement, but if the
manager does not report any information, investors cannot verify whether he learned
the true θ0 . The model of disclosure closely follows Dye (1985) and Jung and Kwon
(1988). Figure 1 shows the sequence of events as described above.
Notice that in this model, the disclosure of information does not affect the value of
the firm, it only affects the stock price at time 1. The value of the firm is determined
by θ0 , which is independent of the manager’s actions. In particular, disclosure per se
2
The superscript 1 is used for consistency, in view of introducing a second type of investors in the
next section. All superscripts i in the paper indicate a variable that belongs to a type-i investor.
4
stock is issued
and trades at p0
t=0
dividend δ1 is realized
trading at p1 (δ)
dividend δ2 is realized
t=1
t=2
manager may reveal θ0
Figure 1: Time-line of the game
has no effect on θ0 , it only changes investors’s beliefs about it. Dye (1985) refers to this
type of information as nonproprietary, in contrast to proprietary information whose disclosure does affect firm’s value. The latter includes information “whose disclosure could
generate regulatory action, create potential legal liabilities, reduce consumer demand
for [firm’s] products” etc. However, as he points out, the line between proprietary and
nonproprietary information depends on the set of expectations about the value of the
firm shared by the market participants. It is assumed therefore that all agents in the
model agree that the information potentially arriving to the manager is nonproprietary.
The last important assumption is that investors cannot short-sell the stock. This is
not needed when beliefs are homogeneous, but if investors do not share common beliefs,
then allowing short sales would cause investors to take infinite positions in the stock.
Since investors have different expected values of holding the stock, any price would be
either above or below some investor’s valuation, inducing him to buy or short-sell an
infinite amount.
Having laid out all the assumptions of the model, I proceed to deriving the equilibrium pricing scheme and disclosure policy. Consider the representative investor’s
decision at time t: if the price pt is higher than the investor’s expected payoff from
holding the stock, he demands zero (since he cannot short-sell), while if it exceeds his
valuation, he demands infinity. Neither case can be an equilibrium because the amount
of stock issued by the firm is finite and positive. It follows then that pt must equal the
investor’s expected payoff from buying the stock. After time 2, the stock pays no dividend, so the expected value from holding it is zero. Therefore, p2 = 0. Let Tδ denote the
set of values of θ0 for which in equilibrium the manager finds it optimal not to disclose
his information when the dividend is δ ∈ {0, 1}, and let D and N D stand for disclosure
and non-disclosure respectively. At time 1, the price depends on the realized dividend
and on the equilibrium Tδ , and is given by:
(
θ0
if D
p1 (δ) =
Pr(no inf o|N D, δ)E(θ|δ) + Pr(inf o|N D, δ)E(θ|θ ∈ Tδ , δ) if ND,
5
where the conditional expectations are obtained using Bayes’ Rule:
R 1 δ+1
θ (1 − θ)1−δ π 1 (θ)dθ
0
E(θ|δ) = R 1
θδ (1 − θ)1−δ π 1 (θ)dθ
R 0 δ+1
θ (1 − θ)1−δ π 1 (θ)dθ
θ∈T
.
E(θ|θ ∈ Tδ , δ) = R δ δ
1−δ π 1 (θ)dθ
θ
(1
−
θ)
θ∈Tδ
When no disclosure is observed, the price reflects the fact that with probability
Pr(no inf o|N D, δ) = 1 − Pr(inf o|N D, δ) the manager had no information. Notice that
Pr(inf o|N D, δ) 6= λ, because upon observing non-disclosure, investors update not only
their beliefs about θ, but also their beliefs about the probability that the manager is
informed (Jung and Kwon, 1988). Prior to observing the manager’s disclosure decision,
three events are possible. With probability 1−λ, no information exists. With probability
λ Pr(θ ∈ Tδ ), the manager has information but it belongs to the non-disclosure set Tδ .
Finally, with probability λ(1−Pr(θ ∈ Tδ )), the information exists and is disclosed. Once
no disclosure is observed, the latter event is ruled out, and the posterior probability that
the manager has information, conditional on observing non-disclosure becomes, by using
Bayes’ Rule,
λ Pr(θ ∈ Tδ )
Pr(inf o|N D, δ) =
1 − λ + λ Pr(θ ∈ Tδ )
If the manager learns θ0 , she faces a discrete choice, to disclose θ0 or not, and makes
her decision so as to maximize p1 . At the time of making the decision, the price at time
0 has already been determined, so although p0 enters the manager’s payoff function, it
is beyond her control. As a result, the problem reduces to maximizing p1 . The analysis
would be different if the manager could commit to a disclosure policy before the stock is
issued at time 0. Such a commitment is precluded by the assumption that the investors
cannot verify whether the manager learned θ0 . Thus, provided that she has information,
the manager makes no disclosure if and only if:
θ0 < p1 (δ),
(1)
so that Tδ is the set of θ0 for which inequality (1) holds. The following lemma characterizes Tδ in equilibrium.
Lemma 1. For any λ ∈ (0, 1), and for each δ ∈ {0, 1}, there exists a unique θδ ∈ (0, 1)
such that the manager does not reveal θ0 if θ0 ∈ [0, θδ ). That is, Tδ = [0, θδ ) for some
unique θδ ∈ (0, 1).
Proof. First, notice that the set Tδ is of the form [0, θδ ) for some θδ , since for any θ0 ∈ Tδ
and θ00 < θ0 , if θ0 < p1 (δ), then also θ00 < p1 (δ).
Now, consider the process by which investors update their beliefs at time 1. There
are two pieces of information arriving simultaneously: the dividend realization and the
6
disclosure decision. Both provide information about the underlying parameter θ0 . In
constructing the posterior beliefs, it is convenient to treat the updating process sequentially, i.e. first to incorporate the information contained in the dividend realization, and
then the additional information provided by the disclosure decision of the manager.
Accordingly, let f 1 (θ) and F 1 (θ) denote the posterior pdf and cdf obtained after the
first updating stage. Then, for a given threshold θδ , the first period price following no
disclosure is:
p1 (δ) = Pr(no inf o|N D, δ)E(θ|no inf o) + Pr(inf o|N D, δ)E(θ|inf o)
Z 1
Z θδ
λF 1 (θδ )
θ
1−λ
1
θdF
(θ)
+
dF 1 (θ)
=
1
1
1
1 − λ + λF (θδ ) 0
1 − λ + λF (θδ ) 0 F (θδ )
The threshold value θδ then must satisfy:
1−λ
θδ =
1 − λ + λF (θδ )
Z
0
1
λ
θdF (θ) +
1 − λ + λF (θδ )
θδ
Z
θdF (θ)
(2)
0
The equation can be rewritten as:
θδ 1 − λ + λF 1 (θδ ) = (1 − λ)
"
Z
Z
1
θdF (θ) + λ
0
1
θdF 1 (θ) − θδ
(1 − λ)
= λ θδ F 1 (θδ ) −
0
Z
(1 − λ)
0
Z
1
0
Z
θδ
θδ
θdF 1 (θ)
#
θdF 1 (θ)
0
1
θdF 1 (θ) − θδ
Z
=λ
θδ
F 1 (θ)dθ
0
It is easy to notice now that at θδ = 0, LHS > RHS, while at θδ = 1, LHS < RHS.
Moreover, the expression on the LHS is decreasing in θδ , while the expression on the
RHS is increasing in θδ . Therefore, there exists a unique solution to the equation, and
thus a unique threshold for revealing the information.
This establishes the existence of a unique equilibrium disclosure policy, defined implicitly by the solution to equation (2). The equilibrium disclosure policy is composed
of two threshold levels, one for each possible realization of the dividend δ.
3
The Model with Heterogeneous Beliefs
Heterogeneous beliefs are introduced by adding to the setup above a second group of
investors, whose prior beliefs about θ are captured by the distribution π 2 (θ). Each
investor updates his belief in the manner described in section 2. As shown in Morris
(1996), introducing a second investor creates the possibility of observing a speculative
7
premium. Such a premium will arise if the investor with the highest valuation at time
1 when δ = 1 is not the same as the investor with the highest valuation at time 1
when the dividend is δ = 0. Thus, if investor 1 buys the asset at time 0, he faces a
positive probability (determined by the expected value of θ under π 1 ) of being able to
sell the asset at time 1 to investor 2, at a price higher than investor 1’s own valuation
at that time. Therefore, at time 0, investor 1’s expected payoff from buying the stock
incorporates the option to resell, and is thus higher than his fundamental valuation at
time 0. Less formally, investor 1 is willing to pay for the stock more than what he thinks
it is worth, hence the term speculative premium.
Let T̃δ denote the set of θ0 for which in equilibrium the manager, having observed δ,
finds it optimal not to disclose. Then T̃δ contains all θ0 such that:
θ0 < max{µ1 (δ), µ2 (δ)},
(3)
where
µi (δ) = (1 − Pr(inf o|N D, δ))E i (θ|δ) + Pr(inf o|N D, δ)E i (θ|θ ∈ T̃δ , δ)
is player i’s posterior valuation after having observed dividend δ and no disclosure. The
following lemma is the counterpart of Lemma 1 for the case with heterogeneity.
Lemma 2. For any λ ∈ (0, 1) and for each δ ∈ {0, 1}, there exists a unique θ̃δ ∈ (0, 1)
such that the manager does not reveal θ0 if θ0 ∈ [0, θ̃δ ). That is, T̃δ = [0, θ̃δ ) for some
unique θ̃δ ∈ (0, 1).
Proof. The same argument used in the proof of Lemma 1 can be used to show that the
set T̃δ for which the manager does not disclose her information is of the form T̃δ = [0, θ̃δ ).
As before, the threshold value θ̃δ must satisfy:
θ̃δ = p1 (δ)
with the difference that the time 1 prices are now given by the highest of the two
investors’ valuations:
p1 (δ) = max{µ1 (θ < θ̃δ , δ), µ2 (θ < θ̃δ , δ)}
where µi (θ < θ˜δ , δ) is investor i’s posterior mean for θ after observing dividend δ and
no disclosure on the part of the manager:
µi (θ < θ̃δ , δ) = (1 − Pr(inf o|N D, δ))E i (θ|δ) + Pr(inf o|N D, δ)E i (θ|θ < θ̃δ , δ).
From here on, the proof is analogous to that of Lemma 1, and is therefore omitted.
8
Notice that if player i has the highest valuation both in the high state (i.e. when
the dividend is 1) and in the low state (i.e. when the dividend is 0), then equation (3)
reduces to equation (1), because the price at time 1 will equal investor i’s valuation.
There will then be no speculative premium, and the threshold value of θ for disclosure
will be the same as when there is only investor i in the market, since investor j’s opinion
does not get incorporated in p1 (δ). This paper focuses on the case when investor i has
the highest valuation in the high state, and investor j 6= i has the highest valuation in
the low state. This is formalized in the following definition, adapted from Morris (1996)
to the setup of this paper:
Definition 1. For a given probability λ that the manager learns θ0 , we say that investors’
beliefs exhibit switching if the following two conditions hold:
E i (θ|N D, δ = 1) > E j (θ|N D, δ = 1),
E i (θ|N D, δ = 0) < E j (θ|N D, δ = 0),
for i 6= j.
The next step is to show that heterogeneity decreases disclosure, in the sense that
θ̃δ ≥ θδ , with strict inequality for either δ = 1 or δ = 0. Suppose that player 1 holds the
stock at t = 0, and assume without loss of generality that E 1 (θ|N D, 1) > E 2 (θ|N D, 1)
and E 1 (θ|N D, 0) < E 2 (θ|N D, 0). This implies that if the realized dividend is 0, investor
1 will sell the stock to investor 2 at time t = 1, and will keep the stock otherwise. It
follows that the disclosure threshold will be affected only if δ = 0.
Proposition 1. Suppose that player 1 holds the stock at t = 0, and assume without loss
of generality that E 1 (θ|N D, 1) > E 2 (θ|N D, 1) and E 1 (θ|N D, 0) < E 2 (θ|N D, 0). Then,
if δ = 0, the disclosure threshold is higher under heterogeneous beliefs, i.e. θ̃0 > θ0 .
Proof. First, define the following two functions:
Z 1
Z x
λ
1−λ
1
1
θdF (θ) +
θdF 1 (θ)
φ (x) =
1
1
1 − λ + λF (x) 0
1 − λ + λF (x) 0
Z 1
Z x
1−λ
λ
2
2
φ (x) =
θdF (θ) +
θdF 2 (θ)
1 − λ + λF 2 (x) 0
1 − λ + λF 2 (x) 0
With this notation, the threshold value θ0 is the unique fixed point of φ1 (·), and the
threshold value θ̃0 is the unique fixed point of φ2 (·). From the switching condition, it
follows that
φ2 (θ̃0 ) > φ1 (θ̃0 ).
(4)
Now suppose that θ0 ≥ θ̃0 . Then φ1 (θ0 ) ≥ φ2 (θ̃0 ). Since φ1 (·) has a unique fixed
point and φ1 (0) > 0, it follows that for any x < θ0 , φ1 (x) > x. Therefore, since we
assume θ̃0 ≥ θ0 ,
φ1 (θ̃0 ) ≥ θ̃0 ⇒
φ1 (θ̃0 ) ≥ φ2 (θ̃0 )
9
But this contradicts the inequality (4) implied by the switching condition. Therefore,
we conclude that θ̃0 > θ0 , which completes the proof.
The intuition behind this result is simple. When facing two types of investors with
beliefs that induce switching, the manager’s expected payoff from not reporting is strictly
higher than with only one type of investor in the state in which switching occurs, i.e.
when the asset changes hands at time 1. The price at time 1 is strictly higher when
there are two types of investors, because it is the investor with the highest valuation
among the two types who determines the equilibrium price. Therefore it takes a higher
θ0 to make it rational for the manager to disclose. Heterogeneity raises the price that
prevails in the absence of disclosure, and thus makes disclosure less attractive for some
values of the underlying fundamental variable θ0 . This implies that on average, the
market observes less voluntary disclosure.
It is worth noticing that the same argument can be constructed in the context of a
model of disclosure with proprietary costs such as Verrecchia (1983). In such a model,
disclosure costs play exactly the same role as the uncertainty about the existence of information plays in this paper. Increasing the payoff from non-disclosure makes disclosure
more costly, and therefore less frequent.
4
Comparative Analysis
The result derived in the previous section can be extended to investigate how the difference θ̃δ − θδ changes with the degree of heterogeneity in beliefs. This step requires
defining what it means that a certain setup exhibits more heterogeneity than another.
The switching property, which determines the speculative premium and the decreased
likelihood of information disclosure, is driven by differences in the tightness of agents’
priors. An agent with a tighter prior has a posterior mean that is “closer” to the prior
mean, and thus values the asset relatively higher in the bad state and relatively lower in
the good state. It is important to notice that it is not the difference in prior means that
causes switching, but the difference in the tightness of the priors. Figure 2 illustrates
this graphically.
Analytically, this can be done by fixing a prior distribution π 1 , such as the uniform
in Figure 2, and then considering a sequence of scenarios in which the type 2 investor
has increasingly tighter priors, in the sense that each prior in the sequence has a lower
variance than the previous. Because of the truncation involved in the computation of the
posterior distributions, such a general setting is not amenable to closed form solutions.
Instead, the analysis is conducted numerically using Beta distributions as priors.
Let type 1 investor’s preferences be described by a Beta distribution with arbitrary
parameters a and b:
1
π 1 (θ) =
θa−1 (1 − θ)b−1 ,
B(a, b)
10
Less heterogeneity
More heterogeneity
2
2
1.5
1.5
1
1
0.5
0.5
0
0
0.5
1
0
0
0.5
1
Figure 2: The setup on the right exhibits more heterogeneity than the one on the left.
R1
where B(a, b) = 0 xa−1 (1 − x)b−1 dx is the Beta function. Let type 2 investor’s prior
distribution be Beta(γa, γb), where γ ≥ 1. Notice that for any such γ, the two investors
a
. However, the type 2 investor has a tighter prior because
have the same prior mean, a+b
the variance of his prior distribution is lower:
γaγb
(γa + γb)2 (γa + γb + 1)
ab
=
(a + b)2 (γ(a + b) + 1)
ab
≤
2
(a + b) (a + b + 1)
= σ12
σ22 =
where σi2 is the variance of player i’s prior distribution. The inequality is strict if γ > 1.
Therefore, a type 2 investor has a tighter prior in this setting. The higher γ is, the higher
is the difference between the two investors’ opinions. To see how disclosure varies with
this difference, consider a sequence of values for γ ranging from 1 to 10 in increments of
0.01. Figure 3 illustrates how the disclosure threshold in the low state, θ̃0 , varies with
γ for parameter values λ = 0.5, a = 1 and b = 1, when type 1 investor’s parameters are
held fixed. Different choices of the three parameters yield different numerical values,
but the qualitative relationship remains the same.
Because analytical solutions cannot be derived, for each combination of a, b, λ and γ
the equilibrium disclosure threshold has been determined numerically, using MATLAB.
Before employing the numerical procedure, the expressions for the functions φ1 and φ2
must be derived, since the equilibrium disclosure thresholds are given by the solutions
11
λ=0.5, a=1, b=1
Increase in disclosure threshold
0.18
0.16
0.14
0.12
0.1
0.08
0.06
0.04
0.02
0
1
2
3
4
5
γ
6
7
8
9
10
Figure 3: The difference θ̃0 − θ0 as a function of heterogeneity of beliefs
to φ1 (θ0 ) = θ0 and φ2 (θ̃0 ) = θ̃0 . The expression for φ1 is:
1−λ
B(a + 1, b + 1)
+
1 − λ + λBx (a, b + 1) B(a, b + 1)
λ
B(a + 1, b + 1)
+
Bx (a + 1, b + 1)
1 − λ + λBx (a, b + 1) B(a, b + 1)
φ1 (x) =
R x a−1
1
where B(·, ·) is the Beta function as defined previously, and Bx (a, b) = B(a,b)
ξ (1 −
0
b−1
ξ) dξ is the incomplete Beta function. Both Beta functions are readily implementable
in MATLAB. The expression for φ2 can be derived analogously, using its definition.
What Figure 3 reveals is a confirmation of the intuition that it is not only the case
that heterogeneity makes disclosure less likely by raising the disclosure threshold, but
the larger the disagreement among investors, the less information is disclosed in equilibrium. Since the size of the speculative premium is also an increasing function of the
heterogeneity of belief, this analysis supports the conclusion that markets that exhibit
high speculative premia are characterized by little voluntary disclosure of information.
5
5.1
Empirical analysis
Hypothesis
The implication of the theoretical analysis above is that the likelihood of voluntary
disclosure of information held by firm insiders decreases with the magnitude of the
12
difference of opinions among investors when short selling is not possible. The same
qualitative implication holds more generally if investors are risk-averse and short-selling
is possible, but costly. In this case, the beliefs of the pessimistic investors are partially
reflected in the price, but the extent to which they are is inversely related to the costs
associated with short-selling. The latter scenario is more closely related to the actual
stock market trading environment, and it is this more general hypothesis that will be
tested empirically.
The extent of voluntary disclosure has typically been proxied in the literature either
by the Association for Investment Management and Research (AIMR) disclosure scores
or by the prevalence of management earnings forecasts (Healy and Palepu, 2001). I will
use management earnings forecasts in this paper because they are easily available from
the First Call Historical Database, and also because the AIMR scores have not been
updated since the early 1990s. In terms of this measure, the hypothesis to be tested is:
Hypothesis 1. The propensity of a firm to issue a management earnings forecast is
negatively affected by the magnitude of the differences of opinion. This effect increases
with short-selling costs.
5.2
Methodology and data
In order to test the hypothesis, I model the probability that a firm issues a forecast as
follows:
P r(F orecastit ) = F (Dispersionit− , InstOwnit− , LogSizeit− , LogAnalystsit−
N Y SEit , N asdaqit , RegF Dit , P SLRAit , RoAit+
IndustryDummies, Constant)
(5)
where F (·) can be the CDF of either the normal or the logistic distribution. The choice
of the distribution does not significantly alter the results.
The unit of analysis is a pair firm-year, and the sample is the universe of US firms
covered by First Call and traded on NYSE, Nasdaq or AmEx, over the period 1990-2004.
The dependent variable takes the value 1 if firm i issued an earnings forecast in year
t. Dispersionit− is the dispersion of analysts’ forecasts of earnings, averaged over the
period since the beginning of the fiscal year until the date the forecast was issued.3 If a
firm issued multiple forecasts for the same year, I take as a cutoff the date of the first
forecast. This is done in order to avoid possible endogeneity of the dispersion measure:
once a forecast is issued, it affects analysts’ calculation of their forecasts. For the nonforecasting firms, the cutoff date is computed by subtracting from the fiscal year end
date the average number of days prior to the year-end that forecasting firms issued their
forecast (the average forecast horizon). Both management and analyst forecast data are
taken from First Call.
3
Dispersion is computed as standard deviation divided by the absolute value of the mean forecast.
If the mean was zero, the observation was dropped.
13
InstOwnit− is the fraction of shares outstanding held by institutional investors,
obtained from the quarterly 13F filings available from the CDA/Spectrum database.
These data are reported quarterly at end of March, June, October and December of
each year. I use the value from the most recent quarter ending before the forecast date.
This variable serves as an indicator of short selling costs, because stocks with a larger
institutional holding are easier to borrow and therefore arguably less costly to short.
Thus, a high value of InstOwn indicates low short-selling costs.
These two regressors are at the core of the hypothesis put forward in this paper. The
hypothesis suggests a negative effect for the Dispersion variable, and a positive effect for
InstOwn. Furthermore, including an interaction term Dispersion ∗ InstOwn captures
a key aspect of the mechanism, namely that the effect of differences of opinion increases
with short selling costs. Since high values of InstOwn indicate low short-selling costs,
the predicted sign of the interaction effect is positive.
I also include a measure of firm’s earnings performance, in order to account for the
fact that, holding other things constant, the firm is more likely to release information
if it has good news about earnings. An obvious measure is actual annual earnings, but
these need to be scaled by an appropriate variable to allow for meaningful comparison
between firms of different sizes and number of shares outstanding. Scaling by the stock
price at the end of year is one possibility that has been employed in the literature, but
in this context it may be inappropriate if prices deviate from fundamental values. I use
instead annual return on assets, RoA, computed over the year for which the forecast
observation is made. Despite the theoretical concerns about the use of scaled earnings as
a measure of performance, doing so yields very similar results to using return on assets.
The other variables included in the regression control for various factors that theory
or empirical evidence suggests as determinants of the decision to release management
forecasts. LogSize is the log of the market value of the firm at the beginning of the
fiscal year (in $ millions), computed using data from CRSP. It has been suggested as
proxy for the demand of information in the market (see, for example, Brown, Hillegeist,
and Lo (2004)), and is expected to be positively correlated with the propensity to issue
a management forecast. Additionally, large firms are more likely to be sued for failing
to disclose information that would negatively affect prices, and so are likely to provide
more disclosure in order to reduce expected litigation costs (Skinner, 1997).
An important theoretical determinant of firms’ voluntary disclosure policies is the
amount of asymmetric information in the market. Theory predicts that firms whose
stock is the object of large informational asymmetries among investors are more likely
to release information, because of the resulting increase in liquidity, which reduces the
firm’s cost of capital (Diamond and Verrecchia, 1991). It is difficult to obtain a reliable
measure of the extent of private information in the market. The most refined methods
rely on decomposing the bid-ask spread into three components, one of which measures
the magnitude of the asymmetric information between market makers and informed
investors, as proposed by Huang and Stoll (1997). This method however makes use
14
of intra-day trading data, and is computationally infeasible for the number of stocks
analyzed here. Instead, I will use the log of the number of analysts following the stock,
Analysts, as is also done by Baginski and Hassell (1997) in their study of the determinants of management earnings forecast precision. It is worth noting at this point that
dispersion of analysts’ forecasts of earnings appears to be only weakly correlated with
more precise measures of asymmetric information such as the bid-ask spread and its
adverse selection component, as argued by Van Ness, Van Ness, and Warr (2001). This
lends support to the choice of dispersion of analysts’ forecasts as a proxy of differences of
opinion that are not based on asymmetric information. Furthermore, to the extent that
the dispersion of analysts’ forecasts is correlated with the amount of asymmetric information, this correlation should be positive. Therefore, omitting asymmetric information
should bias the effect of dispersion downward, i.e. against the proposed hypothesis.
N Y SE and N asdaq are dummy variables indicating the exchange on which the
firm’s stock is primarily traded. The predicted sign for these variables’ coefficients is
ambiguous. It can be argued that the NYSE has more stringent listing requirements, including appropriate disclosure levels, and thus NYSE-listed firms feel it is less necessary
to provide voluntary earnings guidance. Conversely, it can be argued that such firms
are subject to more scrutiny and increased expectations of timely disclosures, arguing
in favor of a positive relationship.
The RegF D dummy variable equals 1 if the observation occurs after October 2000,
the time when Regulation Fair Disclosure became effective. This provision, known in
short as RegFD, prohibits firms from selectively disclosing information to analysts or
institutional investors, in effect reducing the communication channels of the firms to
public news releases. Its effect on management forecasts should be positive, since they
are now the only way firms can convey to the market their earnings expectations.
Similarly, P SLRA is a dummy variable indicating a date after the adoption in December 1995 of the Private Securities Litigation Reform Act, a piece of legislation designed to reduce firms’ exposure to lawsuits triggered by failure to meet earnings forecasts, and thus encourage more voluntary disclosure. The expected sign of its coefficient
is positive.
Finally, I use industry dummies based on the first two digits of the NAICS codes in
order to capture some of the effects not directly modelled, such as the likelihood that
the manager is informed about future earnings, which is not directly observed, and proprietary disclosure costs that derive from the intensity of competition that characterizes
the industry. There are a total of 15 such indicator variables variables, corresponding
to 16 industrial sectors. The sample composition by industry is presented in Table 4 in
the Appendix.
Tables 1, 2 and 3 in the Appendix contain descriptive statistics of all regressors, as
well as the dependent variable. Table 5 contains the number of observations broken
down by year.
15
5.3
Regression results
Table 6 in the Appendix contains the results of estimating the model specified in equation (5), using a probit specification.4 Inference about coefficient significance is made
on the basis of Huber-White robust standard errors. As hypothesized, Dispersion has
a negative effect on the probability of forecast, although the significance level is less
than 5%. However, because of the non-linearity inherent in the probit specification, and
the presence of the interaction term, the p-value of this coefficient is not indicative of
the significance of the marginal effect. Figure 4 plots the marginal effect of disclosure
against the predicted probability, together with the corresponding z-statistics and confidence bands. The standard errors of the marginal effects were computed using the
Delta method. As the two graphs show, Dispersion has a negative marginal effect on
disclosure, which is statistically significant for most of the observations. This result is
aligned with the hypothesis that larger differences of opinion reduce the likelihood of
disclosure.
0
0
−2
−0.05
−4
Z−score
Marginal effect
−6
−0.1
−8
−10
−0.15
−12
−14
−0.2
−16
−18
−0.25
0
0.1
0.2
0.3
Predicted probability
0.4
0.5
0.6
0
0.1
0.2
0.3
Predicted probability
0.4
0.5
0.6
Figure 4: Marginal effect of Dispersion as a function of predicted probabilities (left),
with z-scores and 5% significance bands (right).
The fraction of institutional ownership has a positive effect on disclosure, as can be
seen from Figure 5, which plots the marginal effect of InstOwn on disclosure and the
associated z-statistics. However, the relevant effect for the hypothesis is the interaction
effect between Dispersion and InstOwn, plotted in Figure 6. For the most part, the
interaction effect is not statistically significantly different from zero, but it does show
to be mostly negative, which is not in accordance with the mechanism suggested by
theory. This is possibly a result of the fact that institutional ownership, while it should
be correlated with short-selling costs, it may not be a very accurate measure of that.
The control variables used are for the most part significant, and their sign is in
accordance with initial predictions. This finding lends support to the validity of the
4
The results that follow are essentially identical for the logit specification, and are not reported here.
16
10
0.2
8
0.15
6
4
0.05
Z−score
Marginal effect
0.1
0
2
−0.05
0
−0.1
−2
−0.15
0
0.1
0.2
0.3
0.4
Predicted probability
0.5
0.6
−4
0.7
0
0.1
0.2
0.3
0.4
Predicted probability
0.5
0.6
0.7
Figure 5: Marginal effect of InstOwn as a function of predicted probabilities (left), with
z-scores and 5% significance bands (right).
2
0.05
1
0
−1
−0.05
Z−statistic
Interaction effect
0
−2
−0.1
−3
−4
−0.15
−5
−0.2
0
0.1
0.2
0.3
Predicted probability
0.4
0.5
0.6
0
0.1
0.2
0.3
Predicted probability
0.4
0.5
0.6
Figure 6: Interaction effect between Dispersion and InstOwn, as a function of predicted
probabilities (left), with z-scores and 5% significance bands (right).
analysis, because it confirms the results of previous studies investigating the propensity
to issue management earnings forecasts. The exchange indicator variables are both
positive, and the coefficient on N Y SE is significantly larger than the one on N asdaq,
suggesting that firms that list on NYSE are most likely to issue forecasts, followed by
Nasdaq firms and AmEx firms.
6
Conclusion and future research
In this paper I have attempted to show that speculative markets have a negative effect
on voluntary disclosure of information. Speculative premia driven by differences of
opinion make it costlier to release private information and result in a lower likelihood of
17
disclosure. The implication of the theoretical model is supported by empirical evidence
described in section 5 above. In future work, I plan to extend the empirical analysis to
quarterly data, and exploit the panel structure of the data by allowing for firm fixed
effects. Such a specification would better capture the unobserved probability that the
firm is informed about its future earnings. In addition, there is a valid concern that firm’s
decisions with respect to disclosure are not independent over time. It is possible that
having issued forecasts in the past would make it more likely to issue forecasts now, if
for example past disclosure raises the current probability that the firm is informed about
its future earnings. This suggests using a dynamic model specification that allows the
current disclosure decision to depend on the disclosure decision in the previous period.
18
Appendix
Table 1: Descriptive statistics of the dependent variable.
Variable Percentage 1s
Forecast
16.3
Mean horizon (days)
243
Table 2: Descriptive statistics of continuous regressors.
Variable
Mean
Dispersion 0.25
InstOwn
0.53
LSize
6.54
Analysts
1.81
RoA
0.002
Std. dev
0.75
0.22
1.71
0.61
0.24
Median
0.07
0.55
6.42
1.79
0.05
5th pctl.
0.01
0.15
3.93
1.10
-0.31
95th pctl.
1.04
0.86
9.57
2.94
0.17
Table 3: Stock exchange and regulation indicator variables.
Variable
NYSE
Nasdaq
RegFD
PSLRA
Percentage of 1s
53.6
44.5
28.16
75.5
19
Table 4: Sample composition by industry.
Industry
Manufacturing
Information
Retail trade
Professional services
Mining
Wholesale trade
Transportation
Accommodation and food
Administrative, support
Health care
Construction
Real estate
Arts and entertainment
Education
Agriculture
PublicAdministration
Percentage of observations
51.36
12.45
8.13
5.05
4.97
3.97
3.52
2.43
2.11
1.91
1.30
1.02
0.69
0.40
0.37
0.32
Table 5: Sample composition by year.
Year No. obs.
1990
9
1991
323
1992
510
1993
675
1994
809
Year No. obs.
1995
899
1996
1134
1997
1339
1998
1433
1999
1421
20
Year No. obs.
2000
1487
2001
1426
2002
1336
2003
1281
2004
338
Table 6: Probit estimation results. Boldface values are significant at 5 percent.
Variable
Constant
Dispersion
InstOwn
InstOwn ∗ Disp
RoA
LogSize
LogAnalysts
N Y SE
N asdaq
RegF D
P SLRA
Agriculture
M ining
Construction
M anuf acturing
W holesaleT rade
RetailT rade
T ransportationW arehousing
Inf ormation
RealEstate
P rof essionalServices
AdministrativeServices
EducationalServices
HealthCare
Entertainment
AccomodationF ood
N
Pseudo-R2
Coefficient
-2.328
-0.178
0.456
-0.332
0.327
0.024
-0.010
0.326
0.177
0.344
0.811
0.263
-0.461
0.330
-0.055
0.069
0.197
-0.609
0.038
0.031
0.020
0.118
0.155
-0.100
0.217
-0.204
14,420
9.94
21
Robust std. error
0.261
0.116
0.080
0.276
0.118
0.013
0.032
0.124
0.124
0.031
0.043
0.304
0.233
0.242
0.221
0.228
0.224
0.239
0.224
0.252
0.227
0.235
0.291
0.241
0.264
0.237
P-value
0.000
0.063
0.000
0.115
0.003
0.035
0.373
0.004
0.078
0.000
0.000
0.193
0.024
0.086
0.402
0.381
0.189
0.005
0.433
0.451
0.465
0.308
0.298
0.339
0.205
0.195
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