Meeting, Beating and Bubbles
Paul Fischer
Wharton School of Business
University of Pennsylvania
pef@wharton.upenn.edu
Jared Jennings
Olin School of Business
Washington University
jaredjennings@wustl.edu
Mark T. Soliman
Marshall School of Business
University of Southern California
msoliman@usc.edu
October 2013
This paper is incredibly early, and by most standards, probably does not qualify for the label
“paper.” We would like to thank the participants at Stanford University for their upcoming
insightful, thoughtful, constructive and heartfelt (Mark’s word) comments.
!
Meeting, Beating and Bubbles
Abstract
The literature in economics and finance document that asset bubbles can emerge and remain
sustained for a variety of reasons. In this paper, we start by developing an analytical model to
characterize two types of rational bubbles can arise in an equilibrium, drift bubbles and
sensitivity bubbles. We conjecture that both types of bubbles, if they do arise, are likely to do so
when firms experience streaks of good news. We use our analytical model coupled with our
conjecture to generate a number of hypotheses expected to hold if drift and/or sensitivity bubbles
arise when firms experience streaks of good news, which we proxy for using lengths of meet or
beat streaks. We provide evidence consistent with streaks of favorable performance being
associated with both drift and sensitivity bubbles. We find no consistent evidence, however, that
bubbles end abruptly when a firm fails to continue a meet or beat streak.
Keywords: Earnings Response coefficient; Meet or Beat Analyst Forecasts; Stock market
bubbles; earnings string.
JEL classification: M4
!
1. Introduction
In traditional equity pricing frameworks, price equals the discounted expectation of future cash flows,
or equivalently, equity book value plus discounted expectations of future residual earnings. A significant
stream of literature suggests, however, that equity prices may be driven away fundamental values for
periods of time, where fundamental value is the equity value consistent with a traditional equity pricing
framework. For example, empirical studies initiated by the studies of LeRoy and Porter (1981) and Shiller
(1981), suggests that the stock prices exhibit excessive volatility relative to underlying fundamental cash
flows and discount rates. In the theoretical realm, a significant literature suggests that asset pricing
bubbles can arise that could drive prices away from fundamental values, and lead to more volatile prices
than fundamentals would suggest.1 Finally, studies in the experimental domain, such as Smith et al.
(1988) or Hirota and Sunder (2006), document bubble like behavior in laboratory settings.
While the antecedent literature raises the prospect of equity pricing bubbles, there is somewhat less
discussion as to when equity pricing bubbles arise and what events might lead them to collapse. In this
study, we conjecture that rational pricing bubbles; bubbles that do not involve trade driven by noise or
excessive optimism regarding fundamentals, are likely to arise when firms experience a streak of good
news and that bubbles end when that streak ends. Our conjecture, coupled with analytically derived
pricing patterns that are expected to emerge during rational pricing bubbles, suggests that equity prices for
a firm experiencing a longer good news streak will have a higher equity price, a lower association
between price and book value, and a stronger association between price and expectations of future
earnings after controlling for fundamental determinants of value (i.e., expectations of future earnings and
discount rates). In addition, our analytical model suggests that prices will fall precipitously when the
streak ends after controlling for changes in the fundamental determinants of value. Our (very) preliminary
empirical evidence, and empirical regularities documented in antecedent literature (Kasznik and
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
1!! Papers offering asset pricing models exhibiting bubbles include Tirole (1985), Delong, Shleifer, Summers and
Waldmann (1990A) and (1990B), Allen and Gale (1994), Bhushan, Brown, and Mello (1997), Spiegel (1998),
Abreu and Bunnermeier (2002) and (2003); and Watanabe (2008).!
!
1!
McNichols (2002) and Barth, Elliott and Finn (1999)), is consistent with our story of firm specific equity
pricing bubbles. We find somewhat weaker evidence that such bubbles collapse when firms fail to
sustain a meet or beat string.
In the initial part of our study, we present a simple model to illustrate two types of rational bubbles
that can arise as an equilibrium phenomenon, which we refer to as drift bubbles and sensitivity bubbles. A
drift bubble, which is considered in Tirole (1985), has the property that price drifts upward simply
because investors believe it will drift upward. The sensitivity bubble, which is considered in Fischer,
Heinle, and Verrecchia (2013), has the property that investor valuations become increasingly more
sensitive to beliefs about fundamentals simply because investors believe subsequent valuations will be
increasingly more sensitive to beliefs about fundamentals. Both of these types of rational bubbles arise in
our setting because, like actual equity markets, there is no terminal date to support backward induction.
After documenting how bubbles might arise generally, we conjecture that both types of bubbles are
likely to arise when firms experience a streak of good news because the excitement generated by this
streak causes the equilibrium pricing path exhibiting bubble-like behavior to become focal. That is, each
investor projects that the excitement in the marketplace causes other investors to anticipate continued
upward price movements and to respond more aggressively to news about fundamentals. That projection,
in turn, leads each investor to anticipate upward price movements and respond more aggressively to
fundamentals, which gives rise to the pricing bubble. We further conjecture that a bubble will end when
the streak of good news comes to an end. We test a number of hypotheses that stem from our analytical
framework coupled with our conjectures that bubbles arise when firms experience positive performance
streaks.
Our study is directly linked to two literatures, an extensive literature regarding asset pricing bubbles
and the literature on performance strings. The Bubble literature in economics and finance defines asset
bubbles as occurring when assets are traded at higher prices that their fundamental value for a period of
time, after which a price crash ensues. Several reasons have been proposed by this literature for the start
of a bubble, but most center around optimistic investors who believe in a bright future due to some
2!
positive information, which leads to an increase in both price and volume (Flood and Garber, 1984).
Morris and Shin (1998) formulate a game theoretic model in which participants benefit most when taking
the same action or not at all. Others have put forth arguments such as sunspots (Cass and Shell, 1983);
irrational speculation (Shiller, 1981); herd behavior (DeLong et al, 1990); variation in stock supply (Hong
et al., 2006) and coordination (Angeletos and Werning, 2006). In addition, not all bubbles are irrational.
Flood and Garber (1980) argue that bubbles can occur in a rational expectation sense. Several papers
argue that self-fulfilling effects can cause these bubbles (Culter et al., 1990; Subrahmanyam and Titman,
2001). It is against this backdrop that our current paper contributes to the literature by showing tangible
accounting based sources of bubble formation and perpetuation.
In the literature regarding performance streaks, the most relevant antecedent studies are Kasznik and
McNichols (2002) and Barth, Elliott and Finn (1999). Kasznik and McNichols (2002) examine whether
firms that meet or beat expectations receive valuation and/or returns premiums. They argue that firms that
meet or beat expectations may be more highly sought after by institutional investors and analysts or
possible viewed as having lower risk and, as a consequence, have higher valuations. Most relevant to our
study, they find evidence consistent with firms that meet or beat expectations over a three-year period
receive a valuation premium after controlling for expectations of future earnings and book value, which is
consistent with our notion of a drift bubble. Barth, Elliott and Finn (1999) consider the relation between
strings of earnings increases and earnings multiples and find that firms exhibiting such strings have higher
a price multiple on earnings than other firms. They also find that the multiple drops dramatically when the
string is broken. Although we have considered bubbles linked to meet or beat streaks, both of these
findings are consistent with our notion of a sensitivity bubble. Our study complements and, at this early
stage, modestly extends these two antecedent studies in that we provided an economic model explaining
why the phenomena previously document can be attributed to rational bubbles, we simultaneously
3!
consider the possibility of a both types of bubbles, and we provide some limited incremental tests linked
to the rational bubble explanation.2
In!the!next!section!we!develop!a!model!and!analytically!derive!and!present!our!hypotheses.!!In!
Section! 3! we! describe! our! research! design,! variables,! methodology! and! results.! ! In! Section! 4! we!
conclude.
2. Model and Hypotheses
2.1 Model
To formally illustrate the ideas motivating our hypotheses, we develop a model to demonstrate how
an equity price can rationally deviate from fundamental value, where fundamental value is defined as a
steady state pricing function in which price is solely determined by discounted expectations of future cash
flows. The model we employ is a simple overlapping generations model in which a continuum of risk
neutral investors can invest in shares of an infinitely-lived firm as well as an alternative investment
yielding an expected net return of r. The alternative investment and associated r captures an opportunity
cost of funds. At the beginning of each period, the firm pays a dividend, information about future
earnings is revealed, and returns attained from the alternative investment are paid. After the interest,
dividend payments and disclosure, the investment market opens and investors form new portfolios.
Investors live for two periods and have wealth w to invest in the first period of life. In the initial
period of life investors liquidate their investments and consume their wealth. An investor in the first
period of life at time t chooses the quantity of shares, q, to maximize the expectation of
q(dt+1 + Pt+1) + (1+r)(w–qPt),
(1)
where dt+1 is the dividend per share paid in t+1, Pt+1 is the price per share of the firm in t+1, and Pt is the
price per share of the firm in t.
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
2!! Finally, we should also note that Kasznik and McNichols (2002) provide somewhat inconsistent evidence that a
return premium is associated with a meet of beat string. We do not consider a return premium in our analysis
because our theory of a rational bubble does not predict the presence of a return premium over the duration of a
bubble.!
4!
The firm’s dividend share in period t equals γet where γ ∈ (0,1) and et is period t earnings per share.
Period t earnings per share is determined by the net assets per share at the beginning of period t, bvt-1, as
follows:
et = re bvt-1 + εt,
(2)
where re is normal return on equity and εt is residual income (also referred to as “abnormal earnings”). We
restrict re < r/(1–γ), which basically states that the average return on equity cannot be too large relative to
the firms cost of capital, to induce a finite and positive equilibrium relations between price and book
value and price and forecasted residual income.
Assume the residual income follows a process of the form:
εt = λεt-1 + θt,
(3)
where λ ∈ (0,1+re) is a persistence (or growth) parameter , θt ~ N(0,s), and the θt’s are independent across
time. Finally, assume that, at time t, information about θt+1, xt, is also revealed, where xt ~ N(0,ρs), ρ ∈
(0,1), the covariance between xt and θt+1 is ρs, and the covariance between xt and any θj≠t+1 is 0.
2.2 Steady State Equilibrium
It is useful to first establish a simple steady state linear equilibrium pricing function that provides a
benchmark as well as a focal pricing path for the subsequent analysis. Denote a conjectured steady state
linear pricing function at time t as
Pt = α + βbvt + κft,
(4)
where ft = λεt + xt is the expectation of t+1 residual earnings at time t. Given Pt, the objective of an
investor who is in their initial period of life at time t can be written as
q[γ(re bvt + ft) + (α + β(bvt +(1–γ)(rebvt + ft))+ κft)] + (1+r)(w–qPt).
(5)
For the market to clear it must be the case that each investor is indifferent between acquiring and not
acquiring a share or, equivalently, that the first derivative of (5) with respect to q is 0:
[γ(rebvt + ft) + (α + β(bvt +(1–γ)(rebvt + ft))+ κλft)] – (1+r)Pt = 0.
Rearranging yields
5!
(6)
!
!
!
Pt = !!!
α + !!!
[γre + β(1+(1–γ)re)]bvt + !!!
[γ + β(1–γ) + κλ]ft,
(7)
which implies that, in any linear equilibrium,
α=
β=
!!!
!!!
!
!!!
+!
α
(8)
!! !!! !!
!!!
β
(9)
and
κ=
!
!!!
+
!!!
!!!
β+
!
!!!
κ.
(10)
Solving for the α, β, and κ that satisfy (8) to (10) yields Lemma 1.
Lemma 1. There exists a single steady state linear equilibrium of the form Pt = α + βbvt + κft, where ft =
λεt + xt is the investors’ expectation of t+1 residual earnings at time t. The coefficients in the pricing
equation satisfy:
α=0
(11)
!
β = !!!!!
! (!!!)
(12)
κ = (!!!! !!!!!)(!!!!!) .
(13)
and
The steady state pricing function has some standard properties. For example, if there is no excess
expected return to dividend reinvestment, re = r, the price each period is simply equal to book value (i.e.,
!
β = 1) plus a capitalization of expected residual earnings (i.e., κ = !!!!!
), where the capitalization rate is
decreasing in the discount rate r and increasing in the persistence of residual earnings, λ. If, on the other
hand, there is an excess expected return arising from reinvesting dividends, re > r, the coefficient on the
book value is greater than 1, the coefficient on residual income is larger, and both coefficients are
decreasing in the dividend payout rate.
6!
2.3 Introducing a Rational Bubble
To demonstrate the possibility of a pricing path with a rational bubble, which we define as any path in
which price deviates from the steady state price, conjecture an equilibrium pricing path that is initially
characterized at t = 0 by a pricing path of the form:
Pt = αt + βbvt + κtft,
(14)
where α0 ≠ 0 or κ0 ≠ κ. We assume that the pricing function reverts to the steady state pricing function Pt
in any period t > 0 with probability 1–p and continues with the previous period’s pricing path with
probability p. This assumption implies that once the pricing path has reverted from the bubble pricing
path initiated at time 0, it stays along the steady state path. The strict probability of reversion to the steady
state is introduced to ensure that the bubble almost surely ends as time passes.
In the conjectured equilibrium, the objective function of an investor in the initial period of life if the
path has reverted to the steady state is given by (5) and the steady state price clears the market. If the path
has not reverted to the steady state, the objective function of an investor in the initial period of life is
q[γ(re bvt + ft) + p(αt+1 + β(bvt +(1–γ)(rebvt + ft))+ κt+1ft) + (1–p)(β(bvt +(1–γ)(rebvt + ft))+ κft]
+ (1+r)(w–qPt).
(15)
For the market to clear it must be the case that each investor is indifferent between acquiring and not
acquiring a share or, equivalently, that the first derivative of (15) with respect to q is 0:
[γ(re bvt + ft) + p(αt+1 + β(bvt +(1–γ)(rebvt + ft))+ κt+1ft) + (1-p)(β(bvt +(1–γ)(rebvt + ft))+ κft] –
(1+r)Pt = 0.
(16)
Rearranging yields
Pt =
Because, β =
!
!!!
!
!!!
pαt+1 +
!
!!!
[γre + β(1+(1–γ)re)]bvt +
!
!!!
[γ + β(1–γ) + (1–p)κ λ + pκt+1λ]ft.
(17)
[γre + β(1+(1–γ)re)] by construction, the conjectured equilibrium is an equilibrium if
α! =
!
!!!
and
7!
α!!!
(18)
κ! =
!
!!!
+
!!!
!!!
β+
(!!!)!
!!!
κ+
!!
κ .
!!! !!!
(19)
Proposition 1 follows from identifying a solution to the difference equations (18) and (19).
Proposition 1. There exists an equilibrium in which the price at t = 0 is of the form Pt = αt + βbvt + κtft,
and the price at any time j > 0 is Pj with probability p if t – 1 price is Pj-1 and is the steady state price Pj
otherwise. The time varying coefficients in the pricing equation Pt satisfy:
α! =
!!! !
Δ
(20)
!!! !
!
!!
(21)
!
and
κt = κ +
,
where Δ > 0 and δ > 0 are constants.
The set of equilibria characterized in Proposition 1 is sufficient to highlight two types of rational
bubble-like behavior, which we refer to as drift bubbles and sensitivity bubbles. In drift bubbles, which
are considered in Tirole (1985), prices drift upwards simply because investors project that subsequent
investors will price the security higher. The magnitude of the drift bubble is parameterized by the constant
Δ in Proposition 1. In sensitivity bubbles, which are considered in Fischer, Heinle, and Verrecchia (2013),
prices exhibit greater sensitivity to news about fundamentals simply because investors project that
subsequent investors will price the security in a manner that exhibits greater sensitivity to news about
fundamentals. The magnitude of the sensitivity bubble is parameterized by the constant δ. Finally, by
forcing the coefficient on β to be equal to its steady state value, we have ruled out the possibility of
bubbles tied to book value. We have done so because we anticipate that sensitivity bubbles are more
likely to be tied to information about uncertain future flows as opposed to current stocks.
2.4 Hypotheses
Because our empirical analysis employees book values and earnings, it is useful to transform the
equilibrium pricing function in Proposition 1 to one that is a function of book value and forecasted
earnings:
8!
Pt = αt + Βtbvt + κtFt,
(22)
where Βt = β – reκt and Ft = rebvt + ft is the time t forecast of t+1 earnings. If the pricing bubble path
characterized in equation (22) is descriptive of actual bubble pricing behavior, that characterization
suggests the following feature, which is integral to three of our testable hypotheses.
Observation 1. Over the time horizon that a pricing bubble of the form in equation (22) is sustained, the
constant term in the linear pricing function is increasing if the bubble is a drift bubble, Δ > 0, the
coefficient on expected earnings is increasing if the bubble is an expected residual income sensitivity
bubble, δ > 0, and the coefficient on book value is decreasing if the bubble is an expected residual income
sensitivity bubble, δ > 0.
While Proposition 1 provides a plausibility argument for how bubbles might be sustained as in
equilibrium, it does not provide any guidance as to when a bubble might arise or what might trigger a
bubble’s end. Hence, assessing whether actual prices exhibit features identified in Observation 1 requires
ex ante identification of the events that are expected to trigger the initiation and termination of a bubble.
Bubbles are often asserted to arise when investors are optimistic, excited or frenzied, and we
conjecture that such behaviors can make a bubble-pricing path focal, thereby inducing bubble pricing as
an equilibrium phenomenon. We further conjecture that such behavior arises when firms experience a
streak of good news and ends when the streak ends. To provide a sports analogy, fan interest and
excitement tends to grow when a team gets on a win streak, and greater fan interest and excitement tends
to feed upon itself, with each fan becoming more interested and excited as other fans become more
interested and excited. Finally, within the context of the model, we identify a streak of good news as
being characterized by a period of time when a firm’s performance repeatedly exceeds prior expectations,
which is commonly referred to as the meet or beat phenomenon.
To introduce the above story into the formal model, assume a bubble begins at date 0 if the firm
experienced a sting of periods prior to date 0 in which the realization of earnings for period t, Ft, exceeds
investors’ prior period expectation, Ft-1. Further, assume that the bubble continues as long as those
9!
expectations continue to be exceeded, which implies that the bubble can continue in any period t > 0 if Ft
> E[Ft|εt-1,xt-1] or, equivalently, θt > E[θt|xt-1]. Because the distribution function for θ conditioned upon xt1
is normal with mean xt-1, the probability that the bubble continues in any period corresponds in the
model to p = .5. In summary, then, we have Conjecture 1.
Conjecture 1. A pricing bubble can begin when a firm has a streak of meeting or beating residual earnings
expectations and, once a bubble begins, it persists as long as the meet or beat streak is sustained.
The traditional valuation perspective suggests that prices should be completely characterized by
discounted expectations of future cash flows, which in our simple model is determined by the parameters
{bvt,Ft,r,re,λ,γ}, and other events or firm characteristics should not be associated with price. Our model
coupled with Conjecture 1, however, suggests that prices can also be associated with the length of a meet
or beat streak even though that steak provides no incremental information to investors about future cash
flows or discount rates. Furthermore, when coupled with Conjecture 1, Observation 1 provides some
motivation for three primary hypotheses.
Consider first the initiation of a bubble exhibiting drift, Δ > 0. Observation 1, when coupled with
Conjecture 1, suggests the following hypothesis:
Hypothesis 1: Price at date t is increasing in the length of a meet or beat streak prior to date t.
Consider next the initiation of a bubble exhibiting sensitivity to forecasted residual income. Again,
Observation 1 coupled with Conjecture 1 suggests the following two hypotheses:
Hypothesis 2. The association between price and forecasted earnings at date t is increasing in the
length of the meet or beat streak prior to date t.
Hypothesis*3.***The association between price and book value at date t is decreasing in the length of
the meet or beat streak prior to date t.
Given our conjecture that either type of pricing bubble begins when news is favorable and persists as
long as expectations are exceeded, we derive some hypotheses concerning the change in price that will
10!
occur in conjunction with the bubble ending. Assume a bubble that began at time 0 ends at time t > 1.
The change in price between t and t–1 can be represented as:
(Pt – Pt-1) = (αt!–!αtG1)!+!Βt!(BVt!–!BVtG1)+!κt!(Ft!–!FtG1)!+!(Βt!–!ΒtG1)BVtG1!+!(κt!–!κtG1)FtG1.!
(23)!
Because!steady!state!pricing!ensues!at!time!t,!it!follows!that!αt!=!0,!Βt!=!Β!=!β!–!reκ,!and!κt!=!κ.!!After!
exploiting!this!observation!and!using!Proposition!1!to!note!that!αtG1!=!
+!
!
!!! !!!
!!
!
!!! !!!
!
Δ,!βtG1!=!β,!and!κtG1!=!κ!
δ,!equation!23!can!be!written!as:!
(Pt – Pt-1) =
!!! !!!
!
Δ!+!Β!(BVt!–!BVtG1)+!κ!(Ft!–!FtG1)!+!re
!!! !!!
!!
δ!BVtG1!–!
!!! !!!
!!
δ!FtG1.! (24)!
Equation (24) yields Observation 2.
Observation 2: If a drift bubble with magnitude Δ ends at time, the change in price from t–1 to t is
decreasing in the length of the bubble. If a residual income sensitivity bubble ends at time t, the
association between the period t–1 forecast of period t earnings and the change in price is decreasing in
the length of the bubble, and the association between the period t–1 book value and the change in price is
increasing in the length of the bubble.
Observation 2 coupled with Conjecture 1 yields the following hypotheses.
Hypothesis 4. The change in price over the period in which a meet or beat streak ends is decreasing in
the length of that meet or beat streak.
Hypothesis 5. The association between the change in price over the period in which a meet or beat
streak ends and the prior period earnings forecast for that period is decreasing in the length of the
meet or beat streak.
Hypothesis 6. The association between the change in price over the period in which a meet or beat
streak ends and the prior period book value is increasing in the length of the meet or beat streak. *
11!
3. Results
3.1 Sample
Our sample consists of 85,187 firm/quarter observations with sufficient information to calculate the
variables detailed in Table 1. We note that financial statement data is obtained from Compustat, price data
is obtained from CRSP, analyst data is obtained from IBES, and the risk free interest rate data is obtained
from the U.S. Department of The Treasury website. Descriptive statistics are presented in Table 2 and
correlations are in Table 3.
3.2 Price Level Regressions
To test the first three hypotheses, we run the following regression, which is empirically
operationalizes the theoretical pricing equation (22):
Pricei,t = γ1 CNTMBEi,t + γ2 CNTMBEi,t*BVi,t + γ3 CNTMBEi,t*Fi,t +
α0 + α1 BVi,t + α2Fi,t + α3COCi,t + α4 BVi,t *COCi,t + α5 Fi,t *COCi,t + α6EGi,t +
α7 BVi,t * EGi,t + α8 Fi,t* EGi,t + Controls,
where CNTMBEi,t is the number of consecutive quarters firm i has met or beaten the quarterly earnings
up to but not including quarter t, BVi,t is the book value of firm i at the end of quarter t, Fi,t is the
consensus analyst forecast for quarter t+1 for analysts revising their forecast within the 21 days after the
quarter t earnings announcement, COCi,t is a cost of capital measure for firm i as of the end of quarter t
and is computed in a manner consistent with Easton (2004) and Botosan et al. (2011), EGi,t is the
consensus analyst three to five year ahead earnings growth rate for analysts revising their firm i period
t+1 forecasts within 21 days of the date t earnings release. The CNTMBEi,t variable is our proxy for the
presence of a bubble in pricing as well as the length of any bubble that has arisen. Hypothesis 1 implies γ1
> 0, Hypothesis 2 implies γ3 > 0, and Hypothesis 2 implies γ2 < 0.
Table 4 includes results for four different model specifications. In Column 1, we cluster the standard
errors by firm and calendar quarter correct for serial and cross-sectional correlation in the standard errors.
In Column 2, we cluster the standard errors by firm and include indicator variables for each calendar
12!
quarter. In Column 3, we cluster the standard errors by calendar quarters and include indicator variables
for each firm. In Column 4, we include indicator variables for each firm and each calendar quarter.
For each specification presented in Columns 1 through 4, we find a positive and significant
coefficient on the CNTMBEi,t variable, which is consistent with Hypothesis 1. The coefficient ranges
between 0.076 and 0.125, suggesting that price increases approximately 7 to 13 cents in each consecutive
quarter the firm meets or beats expectations. In addition, we find a positive and significant coefficient on
the interaction between the CNTMBEi,t and Fi,t variables, which is consistent with Hypothesis 2. We note
that the coefficient ranges between 0.253 and 0.3461, suggesting that price is 4% to 6% more sensitive to
the future expectations of earnings when the firm meets or beats the average number (3.6) of consecutive
quarters in the sample. Finally, the coefficient on the interaction between CNTMBEi,t and BVi,t is
negative, which is consistent with Hypothesis 3.
In addition to the results above, we have conducted additional analyses to ascertain the robustness of
our findings. First, we have run the following regression by CNTMBEi,t terciles:
Pricei,t = α0 + α1 BVi,t + α2Fi,t + α3COCi,t + α4 BVi,t *COCi,t + α5 Fi,t *COCi,t + α6EGi,t +
α7 BVi,t * EGi,t + α8 Fi,t* EGi,t + Controls.
Results are reported in Table 4, and consistent with the results in Table 3, α0 is increasing, α2 is
increasing, and α1 is decreasing across the terciles.
Second, because analyst forecasts are known to be biased and that bias might exhibits some relation
to meet or beat streak length, using the analyst forecasts as a proxy for investor expectations might drive
some of the results. Hence, we construct an alternative proxy by first fitting a model of the form:
EARNi,t = α0 + α1Fi,t-1 + α3CNTMBEi,t + α4 CNTMBEi,t,
where EARNi,t is the realized earnings for quarter t. We employ the fitted model to form new proxies for
forecasted earnings and obtain similar results to those in Table 3.
Finally, we have considered alternative cost of capital measures and considered a number of different
control variables. In general, the results in Table 4 continue to hold under these alternative specifications.
13!
3.3 Price Change Regressions
To test hypotheses 4, 5 and 6, we identify all firms who fail to meet or beat expectations in quarter t
and run a price change regression of the form:
DPricei,t = γ1 CNTMBEi,t-1 + γ2 BVi,t-1 + γ3 CNTMBEi,t-1*BVt-1 + γ4 Fi,t-1 + γ5 CNTMBEi,t-1*Ft-1 +
α0 + α1 DBVi,t + α2DFi,t + α3DCOCi,t + α4 D(BVi,t *COCi,t) + α5 D(Fi,t *COCi,t) +
α6DEGi,t + α7 D(BVi,t * EGi,t) + α8 D(Fi,t* EGi,t) + Controls,
where DPricei,t = Pricet – Pricet-1, DBVi,t = BVi,t – BVt-1, DFit = Fi,t – Fi,t-1, DCOCi,t = COCi,t – COCi,t-1,
D(BVi,t *COCi,t) = BVi,t *COCi,t – BVi,t-1 *COCi,t-1, D(Fi,t *COCi,t) = Fi,t *COCi,t – Fi,t-1 *COCi,t-1, DEGi,t =
EGi,t – EGi,t-1, D(BVi,t * EGi,t) = BVi,t * EGi,t – BVi,t-1 * EGi,t-1, and D(Fi,t* EGi,t) = Fi,t* EGi,t – Fi,t-1* EGi,t-1.
If Hypothesis 4 is true, we expect γ1 < 0, if Hypothesis 5 is true, we expect γ4 < 0 and γ5 < 0, and if
Hypothesis 6 is true, we expect γ2 > 0, and γ3 > 0. Results for this regression are in Table 5 and are
somewhat consistent with these hypotheses.
4. Conclusion
This paper is expected to contribute to the literature on asset pricing bubbles by assessing whether
accounting disclosures are linked with asset pricing bubbles. We develop an analytical model in which an
asset pricing bubble is linked with accounting constructs and then empirically test for patterns predicted
by that model. Our empirical analysis is consistent with both drift and sensitivity bubbles arising when
firms experience a string of favorable accounting news, which is proxied for by the number consecutive
quarters a firm meets or beats earnings forecasts.
We provide less persuasive evidence, however,
consistent with a bubble collapsing when a firm fails to meet or beat earnings forecasts.
14!
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Earnings Surprise. The Accounting Review 70, 113-134.
Kasznik, R. and M. McNichols. 2002. Does Meeting Earnings Expectations Matter? Evidence from
Analyst Forecast Revisions and Share Prices. The Journal of Accounting Research 40, 727-759
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Finance 56(6), 2389-2413.
15!
Table 1: Primary Regression Variable Definitions
Variable
Definition
Pricei,t
Stock price 21 days after the quarter t earnings release.
CNTMBEi,t
The number of consecutive quarters firm i has meet or beat quarterly earnings up to
but not including quarter t. A firm is defined as meeting or beating if the realized
earnings for period t exceeds the forecast for period t computed IBES actual earnings
are greater or equal to the median consensus forecast on the date of the earnings
announcement
BVt
Equity book value for firm i at the end of quarter t.
Fit
The consensus analyst forecast for quarter t+1 for analysts revising their forecast
within the 21 days after the quarter t earnings announcement.
COCi,t
Firm i’s cost of capital at the end of quarter t. Cost of capital is computed using the
price to short horizon earnings growth ratio, following Easton (2004) and Botosan et
al. (2011). We difference the annual median forecasted earnings per share for year
t+2 and year t+1 immediately prior to the quarter end, divide by the price on the
earnings announcement date, and take the square root of the ratio to obtain the cost of
capital proxy.
EGi,t
The consensus analyst three to five year ahead earnings growth rate for analysts
revising their firm i period t+1 forecasts within 21 days of the date t earnings release.
DPricei,t
Pricet – Pricet-1
DBVi,t
BVi,t – BVt-1
DFit
Fi,t – Fi,t-1
DCOCi,t
COCi,t – COCi,t-1
D(BVi,t *COCi,t)
BVi,t *COCi,t – BVi,t-1 *COCi,t-1
D(Fi,t *COCi,t)
Fi,t *COCi,t – Fi,t-1 *COCi,t-1
DEGi,t
EGi,t – EGi,t-1
D(BVi,t * EGi,t)
BVi,t * EGi,t – BVi,t-1 * EGi,t-1
D(Fi,t* EGi,t)
Fi,t* EGi,t – Fi,t-1* EGi,t-1
16!
Table 1
Descriptive statistics.
Panel A: Price level sample
Variable
N
Mean
Std Dev
1st Pctl
25th Pctl
50th Pctl
75th Pctl
99th Pctl
Pricei,t
84,980
31.772
22.623
2.280
15.250
26.830
42.625
120.180
CNT MBEi,t
84,980
4.056
5.640
0.000
0.000
2.000
5.000
29.000
Fi,t
84,980
0.404
0.444
-0.630
0.130
0.330
0.600
2.050
COCi,t
84,980
12.313
6.641
3.074
8.396
10.549
14.069
42.426
EGi,t
84,980
16.007
9.258
1.000
10.000
14.500
20.000
51.000
BVi,t
84,980
13.002
10.480
-1.786
5.719
10.312
17.292
54.938
17#
Panel B: Price change sample
Variable
N
Mean
Std Dev
1st Pctl
25th Pctl
50th Pctl
75th Pctl
99th Pctl
DPricei,t
16,440
-1.539
6.798
-33.440
-3.563
-0.690
1.625
15.813
CNT MBEi,t
16,440
2.381
3.953
0.000
0.000
1.000
3.000
22.000
BVi,t-1
16,440
13.898
11.606
-2.530
5.837
11.014
18.582
62.750
Fi,t-1
16,440
0.416
0.487
-0.710
0.120
0.340
0.630
2.245
DBVi,t
16,440
-0.047
1.394
-7.471
-0.247
0.082
0.398
4.437
DFi,t
16,440
-0.078
0.145
-0.820
-0.100
-0.040
-0.010
0.195
DCOCi,t
16,440
0.661
5.153
-15.392
-1.543
0.307
2.481
21.202
D(BVi,t * COCi,t )
16,440
0.044
0.737
-2.713
-0.180
0.025
0.253
3.058
D(Fi,t * COCi,t )
16,440
-0.012
0.037
-0.217
-0.017
-0.005
0.002
0.080
DEGi,t
16,440
-0.424
3.685
-19.000
-0.500
0.000
0.000
13.600
D(BVi,t * EGi,t )
16,440
-4.636
53.141
-260.953
-12.371
-0.048
7.776
206.920
D(Fi,t * EGi,t )
16,440
-1.263
2.871
-15.875
-1.751
-0.600
-0.010
6.257
18#
Table 2
Correlations.
Pricei,t
CNT MBE i,t
1.000
BVi,t
EGi,t
Fi,t
COC
i,t
MBE
CNT
Price
i,t
i,t
Panel A: Price level sample
0.209
0.696
-0.377
-0.074
0.532
<.0001
1.000
<.0001
0.175
<.0001
-0.175
<.0001
0.026
<.0001
-0.001
<.0001
1.000
<.0001
-0.380
<.0001
-0.289
0.694
0.599
<.0001
1.000
<.0001
0.169
<.0001
-0.157
<.0001
1.000
<.0001
-0.341
Fi,t
COCi,t
EG i,t
<.0001
0.643
BV i,t
19#
DPricei,t
CNT MBE i,t
BV i,t-1
Fi,t-1
DBV i,t
DF i,t
1.000
D(Fi,
t
* EG
i,t
i,t
* EG
i,t
D(BV
i,t
DEG
t
D(Fi,
)
)
Ci,t )
* CO
* CO
i,t
D(BV
Ci,t
DFi,t
DCO
i,t
DBV
Fi,t-1
BVi,t1
MBE
CNT
BVi,t
DPri
cei,t
i,t
Ci,t )
Panel B: Price change sample
-0.079
-0.063
-0.135
0.100
0.327
-0.181
-0.154
0.094
0.029
0.086
0.290
<.0001
1.000
<.0001
0.002
<.0001
0.158
<.0001
0.070
<.0001
0.026
<.0001
-0.015
<.0001
0.018
<.0001
0.066
0.000
0.005
<.0001
0.028
<.0001
-0.001
0.810
1.000
<.0001
0.587
<.0001
-0.011
0.001
-0.240
0.055
-0.020
0.018
0.047
<.0001
-0.116
0.543
0.034
0.000
-0.045
0.902
-0.114
<.0001
1.000
0.155
0.164
<.0001
-0.183
0.011
-0.052
<.0001
0.067
<.0001
0.035
<.0001
0.031
<.0001
0.031
<.0001
-0.129
<.0001
1.000
<.0001
0.199
<.0001
-0.066
<.0001
0.258
<.0001
0.198
<.0001
0.021
<.0001
0.417
<.0001
0.116
<.0001
1.000
<.0001
-0.169
<.0001
-0.111
<.0001
0.642
0.006
0.039
<.0001
0.138
<.0001
0.697
<.0001
1.000
<.0001
0.682
<.0001
-0.082
<.0001
-0.002
<.0001
-0.019
<.0001
-0.138
<.0001
1.000
<.0001
0.181
0.833
0.013
0.017
0.123
<.0001
-0.089
<.0001
1.000
0.093
0.036
<.0001
0.122
<.0001
0.451
<.0001
1.000
<.0001
0.700
<.0001
0.288
<.0001
<.0001
DCOCi,t
D(BV i,t * COCi,t )
D(F i,t * COCi,t )
DEGi,t
D(BV i,t * EGi,t )
1.000
0.381
<.0001
1.000
D(F i,t * EGi,t )
20#
Table 3
Price level regression results
[1]
[2]
[3]
[4]
Pricei,t
Pricei,t
Pricei,t
Pricei,t
0.2630***
0.2706***
0.1484***
0.1500***
5.8930
6.6739
7.7473
10.5880
-0.0258***
-0.0262***
-0.0070***
-0.0087***
-6.2893
-6.5353
-4.2924
-8.9714
0.6479***
0.6726***
0.2934***
0.3392***
6.3567
6.7519
6.4598
16.8686
0.3035***
0.3280***
0.8334***
0.8944***
4.4016
4.8726
22.8859
53.0232
35.1526***
34.0351***
17.1554***
16.5210***
20.0392
21.5365
21.8207
50.0728
-0.6245***
-0.5638***
-0.3788***
-0.2493***
-11.8530
-20.4702
-8.8617
-22.6757
0.0151***
0.0134***
-0.0024
-0.0028***
4.3083
4.6923
-1.0985
-3.6121
-1.2494***
-1.2260***
-0.6390***
-0.6008***
-19.1987
-21.4215
-14.6439
-37.3530
0.3410***
0.2704***
0.3863***
0.2867***
7.4883
9.8305
9.5184
30.9942
0.0115***
0.0118***
-0.0006
0.0002
4.1021
4.2514
-0.3245
0.2950
0.3119***
0.3595***
0.5360***
0.5400***
3.6911
5.3656
18.2425
35.9469
13.6968***
14.0156***
11.7225***
8.4312***
17.6065
20.1694
20.9235
10.4547
Observations
84,980
84,980
84,980
84,980
R-squared
0.5950
0.6120
0.7940
0.8110
Firm Dummies
N
N
Y
Y
Year/Quarter Dummies
N
Y
N
Y
Cluster Firm
Y
Y
N
N
Cluster Year/Quarter
Y
N
Y
N
CNT MBEi,t
CNT MBEi,t*BVi,t
CNT MBEi,t*Fi,t
BVi,t
Fi,t
COCi,t
BVi,t*COCi,t
Fi,t*COCi,t
EGi,t
BVi,t*EGi,t
Fi,t*EGi,t
Constant
21#
Table 4
Price level regression results by CNT MBEi,q-1 terciles
[1]
[2]
[3]
Tercile 1 - CNT
MBEi,q-1
Tercile 2 - CNT
MBEi,q-1
Tercile 3 - CNT
MBEi,q-1
Pricei,t
Pricei,t
Pricei,t
0.3857***
0.2393***
-0.2189*
6.0212
3.2456
-1.7346
32.0969***
36.9454***
48.7499***
18.6543
19.9813
17.4282
-0.4970***
-0.5926***
-0.9567***
-11.8797
-11.2181
-11.1617
0.0062**
0.0156***
0.0429***
2.1089
3.9926
6.2472
-0.9665***
-1.1743***
-1.9098***
-15.3253
-14.8807
-13.5341
0.2425***
0.2990***
0.4760***
6.6842
7.0807
6.5110
0.0159***
0.0116***
0.0088*
5.4029
3.5212
1.7319
0.1329
0.2082**
0.4657***
1.4744
2.0424
3.5343
13.8327***
14.5480***
16.6571***
17.2921
17.7324
14.0928
24,292
30,603
30,085
0.59
0.58
0.59
Firm Dummies
N
N
N
Year/Quarter Dummies
N
N
N
Cluster Firm
Y
Y
Y
Cluster Year/Quarter
Y
Y
Y
BVi,t
Fi,t
COCi,q
BVi,t*COCi,t
Fi,t*COCi,t
EGi,t
BVi,t*EGi,t
Fi,t*EGi,t
Constant
Observations
R-squared
22#
Table 5
Price change regression results
CNT MBEi,t
BVi,t-1
CNT MBEi,t * BVi,t-1
Fi,t-1
CNT MBEi,t * Fi,t-1
DBVi,t
DFi,t
DCOCi,t
D(BVi,t * COCi,t )
D(Fi,t * COCi,t )
DEGi,t
D(BVi,t * EGi,t )
D(Fi,t * EGi,t )
Constant
Observations
R-squared
Firm Dummies
Year/Quarter Dummies
Cluster Firm
Cluster Year/Quarter
[1]
DPricei,t
-0.1166***
-3.4600
0.0372***
2.8608
0.0011
0.4662
-1.3702***
-4.4470
-0.0226
-0.4899
0.3456***
3.1528
14.8731***
9.2846
-0.1534***
-8.0542
-0.1185
-0.7417
-30.8931***
-6.4690
-0.0329
-1.0958
0.0012
0.4780
0.2742***
4.6016
0.0354
0.1984
16,440
0.1670
[2]
DPricei,t
-0.1144***
-4.3604
0.0306***
4.2379
0.0015
0.7746
-1.2011***
-6.6974
-0.0373
-0.8655
0.3169***
4.3790
13.9015***
15.3036
-0.0830***
-5.3477
-0.1469
-1.0049
-27.6565***
-10.9153
-0.0328
-1.1128
0.0022
0.8377
0.2533***
6.2909
-0.0503
-0.5210
16,440
0.2880
[3]
DPricei,t
-0.1119***
-2.7128
0.0334
1.2116
0.0022
0.7663
-2.1189***
-4.3904
-0.0324
-0.5154
0.3769***
2.9720
16.2064***
7.7344
-0.1403***
-6.4503
-0.1230
-0.6582
-29.8642***
-5.6713
-0.0418
-1.2335
0.0014
0.4859
0.2548***
4.1141
0.4468
1.2310
16,440
0.3370
[4]
DPricei,t
-0.1098***
-4.3645
0.0163
1.3400
0.0024
1.4912
-1.7719***
-8.4664
-0.0535
-1.4278
0.3593***
7.0499
14.7782***
21.9968
-0.0699***
-4.4047
-0.1693
-1.4562
-25.7216***
-12.1011
-0.0299
-1.3573
0.0019
1.0843
0.2389***
8.0177
1.7253
1.4215
16,440
0.4430
N
N
Y
Y
N
Y
Y
N
Y
N
N
Y
Y
Y
N
N
23#