Ambiguity, Earnings Surprises and Stock Returns∗

December 17, 2018

Abstract

We study the effect of ambiguity on the return-earnings relations at both firm- and

aggregate-level. We find that individual earnings response coefficient increases with am-

biguity about stock-specific cash flow news. When stocks are aggregated into portfolios,

there is a positive contemporaneous relationship between aggregate returns and earn-

ings growth for portfolios with high firm-level ambiguity. These results are consistent

with the notion that ambiguity impedes diversification of firm-specific news, thereby

yielding a significant cash flow news impact on the aggregate returns. High market-level

ambiguity about discount rate news further amplifies those effects. These findings sug-

gest that ambiguity should be taken into account when examining the incorporation of

information into stock price, particularly for the aggregate level.

Keywords: Aggregate Earnings; Ambiguity; Cash Flow News; Discount Rate News;

Market Returns.

JEL Classification: G12

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Paper #900365

1 Introduction

Earlier literature has documented a positive relationship between firm-level stock returns and

earnings surprises. Ball and Brown (1968) and Beaver (1968) argue that positive earnings

news is informative about future cash flows which in turn increases the stock price. Cready

and Gurun (2010) however argue that the firm-specific information should not be priced in

equilibrium as it is of no use for a holder of a well diversified portfolio. Given that information

contained in earnings surprises is predominantly idiosyncratic, it is diversified away when form-

ing a portfolio. Kothari, Lewellen and Warner (2006) and Cready and Gurun (2010) provide

indirect empirical evidence by documenting a negative contemporaneous relationship between

aggregate stock returns and earnings surprises. High aggregate earnings contains information

about high discount rates which in turn lowers the aggregate stock returns. Investors use

aggregate earnings to form expectations about discount rates.

This diversification argument, however, does not sustain when investors have to process

ambiguous information because ambiguous signals are not diversified away if the degree of

ambiguity is high (see Epstein and Schneider 2008). In this case, the cash flow information

contained in earnings surprises can be informative about the aggregate portfolio return. In

this paper we study the effect of ambiguity on earnings response coefficients at both individual

firm- and aggregate-level.

We build a simple theoretical model to capture the return-earnings relation in a market

with ambiguous information. Realized returns are decomposed into current expected returns,

cash flow news and discount rate news (see Campbell and Shiller 1988a, Campbell 1991).

Investors extract signals about firm-specific cash flow and market-wide discount rate compo-

nents of returns from individual and aggregate earnings surprises respectively. Each of these

components can be ambiguous in the sense of Knight (1921) – investors do not have precise

knowledge about their statistical distributions. Hence, investors face two sources of ambiguity

when forming their expectations about stock returns: ambiguity about stock specific cash-

flow information (firm-level ambiguity) and ambiguity about market wide discount rate news

(market-level ambiguity).

Firm-level ambiguity affects individual earnings response coefficients. Investors use Bayesian

rule to update their beliefs about the two components of unexpected returns. However, they re-

spond to ambiguous information in an asymmetric way (Epstein and Schneider 2008). Specifi-

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Paper #900365

cally, investors overreact to negative ambiguous information and underreact to a positive one.

In total, the overreaction to negative information is stronger which implies that firm-level

return-earnings relation is more pronounced for firms with larger degree of ambiguity in their

cash-flow news. Therefore, individual earnings response coefficient increases with the degree

of firm-level ambiguity.

Market-level ambiguity also affects the individual earnings response coefficient. High de-

gree of market-level ambiguity leads to an increase in the earnings response coefficient of

high-ambiguity stocks and to a decrease in the earnings response coefficient of low-ambiguity

stocks.

More importantly, both levels of ambiguity affect the aggregate response coefficient. The

asymmetric reaction induced by firm-level ambiguity prevents stocks’ idiosyncratic cash flow

components from being completely diversified away. This renders the effect of individual earn-

ings surprises present on the aggregate level. On the other hand, a high degree of market-level

ambiguity amplifies the negative effect of discount rate news on stock market returns. Which

of the two effects dominates depends on the relative degree of the two levels of ambiguity.

In order to test these predictions we have to empirically measure the degree of ambiguity.

Prior empirical literature uses the disagreement of professional forecasters to proxy the degree

of ambiguity in the market (see Andersen, Ghysels and Juergens (2009), Kelsey, Kozhan and

Pang (2011) and Drechsler (2013)). The intuition behind this measure is that investors tend to

condition their beliefs on analysts’ forecasts. If analysts produce very different and conflicting

forecasts about fundamentals of a firm or the market, investors are unable to form beliefs

with regard to the unique probabilistic distribution of stock returns. Thus, high dispersion

among analysts’ opinions regarding the future performance of a stock or the market is likely

to imply a high degree of ambiguity. However, as shown by Barron, Kim, Lim and Stevens

(1998), dispersion of analysts’ forecasts captures only a specific type of uncertainty coming

from the diversity of private information that analysts rely on. Another source of ambiguity

comes from imprecise common information shared by all analysts and investors and hence

measures the ambiguity of public information. We argue that total uncertainty defined as the

sum of those two components captures the degree of ambiguity more comprehensively.

We construct the firm-level ambiguity using analysts’ forecasts of individual firm earnings

from the IBES dataset. These forecasts reflect news about individual firms’ future cash flows.

The higher is the total uncertainty faced by investors, the more ambiguous is the firm’s cash

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Paper #900365

flow news to the investor. We construct a proxy of market-level ambiguity by using analysts’

forecasts of real GDP growth rate that come from the Survey of Professional Forecasters

managed by the Federal Reserve Bank of Philadelphia. Similar to the firm-level ambiguity

measure, we calculate the market-level ambiguity based on the total uncertainty proposed by

Barron, Kim, Lim and Stevens (1998).

We test our predictions using data from the US stock market. Consistent with the model’s

intuition, we find strong empirical evidence that firm-level return-earnings relation mono-

tonically increases with the degree of firm-level ambiguity. High level of market ambiguity

significantly increases the earnings response coefficients of firms with high firm-level ambi-

guity and decreases albeit insignificantly the earnings response coefficients of firms with low

firm-level ambiguity.

When we sort stocks based on the firm-level ambiguity and aggregate them into portfolios,

we find that the aggregate earnings response coefficient is larger for portfolios of high firm-level

ambiguity. The effect, nevertheless, is smaller than in the previous individual case and is only

significant for periods of high market-level ambiguity. In contrast, for the portfolio consisted

of low ambiguity firms, its response coefficient decreases when the market-wide ambiguity is

high, which is suggested by our theoretical prediction.

When we aggregate stocks into the market portfolio, we confirm the finding of existing

literature (see Kothari et al. 2006, Sadka and Sadka 2009) that aggregate response coefficient

is statistically insignificant. However, when we add control of market-level ambiguity, the

aggregate response coefficient turns positive under high market-level ambiguity which is due to

the distortion of diversification effect and negative under low market-level ambiguity because

of relatively complete diversification. These results are consistent with the predictions of our

theoretical model.

Overall, our results suggest that both firm- and market-level ambiguities significantly affect

the response of stock portfolio returns to aggregate earnings surprises. Excluding them from

the analysis may lead to the omitted variable bias.

To provide further evidence that cash flow news drives stocks returns, we perform variance

decomposition in the spirit of Campbell and Shiller (1988a) and Vuolteenaho (2002). We show

that a ratio of cash flow news variance to total unexpected return variance increases with firm-

level ambiguity. This is consistent with our model predictions that idiosyncratic cash flow news

affect aggregate stock returns when the diversification is impeded by information ambiguity.

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This paper contributes to a number of literature. First, it builds on the studies of firm-,

portfolio-, and market-level relationships between stock returns and earnings surprises. Earlier

evidence show that cash-flow news moves stock prices (Ball and Brown 1968, Beaver 1968).

Later studies documented that stocks prices also respond to discount rate news(Campbell and

Shiller 1988b, Fama and French 1989, Fama 1990, Campbell 1991, Cochrane 1992, Vuolteenaho

2002, Hecht and Vuolteenaho 2006, Lettau and Ludvigson 2005, Chen and Zhao 2009). There

is an ongoing debate on which type of news is dominant in moving the stock price. Kothari,

Lewellen and Warner (2006), Cready and Gurun (2010) and Subasi (2011) document a negative

contemporaneous relationship between aggregate stock returns and earnings surprises and

argue that discount rate news is a dominant factor causing this negative relationship. We

contribute to this debate and provide evidence that cash flow news can also have an impact

on the individual and aggregate returns when information available to market participants is

ambiguous.

We contribute to the literature studying the determinants of earnings response coefficient.

Collins and Kothari (1989) show that firm-level earnings response coefficient decreases in firms

systematic risk and risk free rate and increases in the persistence of earnings. Lang (1991)

studies the effect of parameter uncertainty and finds that stock price reaction to earnings

declines over time in magnitude because investors feel less uncertain as they observe more

earnings signals. We show that the earnings response coefficient, whether individual or aggre-

gate, depends on the degree of ambiguity in the cash flow and discount rate news.

Our results add value to the ambiguity literature . Uppal and Wang (2003) and Epstein and

Schneider (2008) argue that ambiguity reduces diversification effect. The empirical evidence on

it is quite scarce. We show in the context of earnings surprises that this under-diversification

has a substantial effect on the way how news is incorporated into the stock market.

The closest to our paper is Subasi (2011). He finds that macroeconomic ambiguity reduces

the magnitude of investors’ reaction to aggregate earnings news. Our study is different from

Subasi (2011)’s in a couple of ways. Firstly, our uncertainty measures are different. Instead of

using the cross-sectional dispersion in realized firm-level earnings surprises which is a ex post

measure, we base our ambiguity measures on actual analysts’ forecasts (i.e. ex ante) that are

directly related to their beliefs. Secondly, we consider two layers of ambiguity at firm- and

market-level. This dual differentiation helps expose the competing effects of cash flow and

discount rate news on the return-earnings relation, particularly for the aggregate level.

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This paper is organized as follows. Section 2 develops our model and presents the model

predictions as our testable hypotheses. Section 3 describes the data and presents our measures

for both firm- and market-level ambiguities. Section 4 presents the empirical results of our

paper. Section 5 conducts the robustness check. Section 6 concludes.

2 The Model

In this section we construct a simple model which captures the main intuition on how am-

biguous information affects the response of returns to earnings surprises. The purpose of the

model is to guide our empirical analysis. The model builds upon the decomposition of re-

turns into the cash flow and discount rate news (see Campbell 1991). There are n firms that

together make up the market portfolio. For simplicity, we assume that all firms are equal in

size. At the end of period t, a representative investor observes earnings announcements eit

of each of the firm i. Firm’s earnings eit consist of two components: eit = cit + mt, where

cit is a firm-specific cash flow component of the earnings and mt is a systematic market-wide

earnings component that is common for all firms (see Kothari et al. 2006). We assume that

cov[cit, cjt] = 0 for i 6= j, cov[cit,mt] = 0 for any i and t. In addition, firms’ earnings contain

useful information about the discount rate dt which subsequently drives stock prices. We

assume that the discount rate is positively correlated with the market-wide component of

earnings news: dt = mt + ηt with cov[cit, ηt] = 0 for any i and t.

At the end of period t−1, the investor observes noisy signals sit about the future earnings

sit = eit + uit,

where uit is idiosyncratic noise with cov[uit, cjt] = 0 and cov[uit, ηjt] = 0 for all i, j and t.

Hence, upon receiving the set of signals st = {s1t, ..., snt} the investor can extract information

about future cash flows of the firms as well as about the future discount rate dt. Denote also

by et = {e1t, ..., ent}, ct = {c1t, ..., cnt}, Σse = cov[s, s] and Σs = var[s].

Firm i’s period t return is given by

Rit = Et−1[Rit] + εit − ωt,

where εit = eit − Et−1 [eit|s] is the revision to expected earnings of firm i conditional on the

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Paper #900365

set of signals st and ωt = dt−Et−1 [dt|s] is a shock to firm i’s return associated with common

for each firm discount rate news (ωt is positive if the discount rates increase). The negative

sign in front of ωt captures the idea that the increase in the expected returns (discount rate)

decreases current prices (see Campbell 1991).

2.1 Non-ambiguous information

In order to establish a benchmark, we start by considering the case with no ambiguity in

signals. This implies that the investor knows exactly the probabilistic distributions of all the

variables in the model. That is, he knows that cit ∼ N(0, σ2c ), mt ∼ N(0, σ2

m), ηt ∼ N(0, σ2η)

and uit ∼ N(0, σ2u) for any i and t.

We are interested in computing the response of individual firm returns to earnings an-

nouncements as well as the response of market returns to aggregate announcements. We start

with the former one.

Individual firm’s earnings response coefficient. Upon receiving the set of signals s, the

investor updates his priors about eit and dt in a Bayesian fashion. His expectations about the

realizations of variables eit and dt are linear in sit and st = 1n

n∑j=1

sjt:

Et−1[eit|s] = γist =n∑j=1

γji sjt

Et−1[dt|s] = δst,

where

γi = {γ1i , ..., γ

ni } = ΣseΣ

−1s (1)

and

δ =cov[dt, st]

var[st]=

nσ2m

σ2c + nσ2

m + σ2u

(2)

are individual and aggregate signal response coefficients respectively. Hence, the earnings

surprise return components εit and ωt are

εit = eit − Et−1[eit|s] = eit −n∑j=1

γji sjt, (3)

ωt = dt − Et−1[dt|s] = dt − δst. (4)

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Paper #900365

The earnings response coefficient of firm i’s return to its earnings surprise is equal to the

slope coefficient of the regression Rit = αi + βi∆eit + vit of the stock’s returns on the current

earnings changes:

βi =cov[Rit,∆eit]

var[∆eit], (5)

where the variance of the earnings changes var[∆eit] = σ2c + σ2

m and the covariance between

the returns of the stock and the changes in the earnings announcements,

cov[Rit,∆eit] = cov[εit, eit]− cov[ωt, eit].

Given that

cov[εit, eit] = var[eit]−n∑j=1

γji cov[sjt, eit] = (σ2c + σ2

m)(1− γii)− (n− 1)γji σ2m,

cov[ωt, eit] = cov[dt, eit]− δcov[st, eit] = σ2m −

δ

n(σ2

c + nσ2m)

we get

cov[Rit,∆eit] = (σ2c + σ2

m)

(1− γii +

δ

n

)− σ2

m

(1 + (n− 1)γji − δ +

δ

n

).

Aggregate earnings response coefficient. In order to compute the reaction of the market

portfolio returns to the aggregate earnings (aggregate earnings response coefficient), we define

the aggregate market return as

Rmt =1

n

n∑i=1

Rit = Et−1[Rmt] + εt − ωt

where Et−1[Rmt] = 1n

n∑i=1

Et−1[Rit] and εt = 1n

n∑i=1

εit = et − 1n

n∑i=1

n∑j=1

γji sjt with the aggregate

earning being defined as et = 1n

n∑i=1

eit = 1n

n∑i=1

cit +mt.

The aggregate earnings response coefficient of the portfolio returns to the aggregate earn-

ings is given by the slope coefficient of the regression Rmt = αm + βm∆et + vt of the portfolio

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Paper #900365

returns on the current aggregate earnings changes

βm =cov[Rmt,∆et]

var[∆et], (6)

where the variance var[∆et] = σ2c+nσ2

m

nand the covariance between the aggregate returns of

the the changes in aggregate earnings is computed as

cov[Rmt,∆et] = cov[εt, et]− cov[ωt, et]. (7)

Since cov[sjt, et] = σ2m + σ2

c

nwe have

cov[εt, et] = var[et]−1

n

n∑i=1

n∑j=1

γji cov[sjt, et]

= var[et]−1

n

n∑i=1

n∑j=1

γji

(σ2m +

σ2c

n

)=

(σ2c + nσ2

m)

n

(1− γii − (n− 1)γji

). (8)

It is also straightforward to compute

cov[ωt, et] = cov[dt, et]− δcov[st, et] = σ2m −

δ(σ2c + nσ2

m)

n. (9)

Substituting (8) and (9) into (7) implies

cov[Rmt,∆et] =σ2c + nσ2

m

n

(1− γii − (n− 1)γji + δ − nσ2

m

σ2c + nσ2

m

). (10)

2.2 Ambiguous information

Let us consider now an extension of the model where the investor faces ambiguity regarding

the distribution of both earnings components. We consider two levels of ambiguity – firm-

and market-level. Firm-level ambiguity reflects uncertainty regarding the distribution of the

firm-specific earnings’ cash flow component c and is purely idiosyncratic. Market-level ambi-

guity reflects uncertainty about the distribution of the systematic earnings component m and

represents ambiguity about the economy growth.

We model both types of ambiguity using the multiple prior model of Gilboa and Schmeidler

(1989). More specifically, the investor does not observe the variances of cit and mt and know

only their interval ranges: σ2ci ∈ [σ2

c , σ2c ] and σ2

m ∈ [σ2m, σ

2m] respectively. Similar approach is

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Paper #900365

adopted by Epstein and Schneider (2008) and Kelsey, Kozhan and Pang (2011). Investor’s

preferences exhibit ambiguity aversion as described by the multiple prior expected utility

model (see Gilboa and Schmeidler (1989) for the preference specification of the model). We

assume that the investor chooses parameters σ2ci and σ2

m by solving the minimization problem

min

σ2ci ∈ [σ2

c , σ2c ]

σ2m ∈ [σ2

m, σ2m]

E[Rmt(σ

2c1, ..., σ

2cn, σ

2m)|s

], (11)

where

E[Rmt(σ

2c1, ..., σ

2cn, σ

2m)|s

]=

1

n

n∑i=1

n∑j=1

γji(σ2c1, ..., σ

2cn, σ

2m

)sjt + δ

(σ2c1, ..., σ

2cn, σ

2m

)st.

We use here the notations γj ≡ γj (σ2c1, ..., σ

2cn, σ

2m) and δ ≡ δ (σ2

c1, ..., σ2cn, σ

2m) to emphasize

that both individual and aggregate signal response coefficients depends on the specific values

of σ2c1,..., σ2

cn, σ2m that the investor perceives in the specific situation. Since the perceived

variances depends on the realization of the signal st observed in period t − 1, we denote by

γj(s) ≡ γj (σ2∗c1 , ..., σ

2∗cn, σ

2∗m ) and δ(s) ≡ δ (σ2∗

c1 , ..., σ2∗cn, σ

2∗m ), where σ2∗ ≡ (σ2∗

c1 , ..., σ2∗cn, σ

2∗m ) is

the solution of the minimization problem (11). In the following section we compute both

individual and aggregate earnings response coefficients.

Individual firm’s earnings response coefficient. Given the realizations of signals st and the

choice of parameters determined by the representative investor preferences, the return of asset

i is given by

Rit = Et−1[Rit] + εit − ωt = Et−1[Rit] +

(eit −

n∑j=1

γji (s)sit

)− (dt − δ(s)st) .

The individual earnings response coefficient βi is computed as in (5) where the covariance

between the returns of the stock and the current earnings in the case of ambiguous information

is

cov[Rit,∆eit] = cov[εit, eit]− cov[ωt, eit], (12)

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Paper #900365

with

cov[εit, eit] = var[eit]−n∑j=1

cov[γji (s)sjt, eit] = σ2c + σ2

m −n∑j=1

E[γji (s)sjteit]

= σ2c + σ2

m −n∑j=1

E[γji (s)sjtE[eit|s]] = σ2c + σ2

m −n∑j=1

n∑ι=1

γιiE[γji (s) sjtsιt]

and

cov[ωt, eit] = cov[dt, eit]− cov[δ(s)st, eit] = σ2m − E[δ(s)steit]

= σ2m − E[δ(s)stE[eit|s]] = σ2

m −n∑j=1

γjiE[δ(s)stsjt].

Aggregate earnings response coefficient. As before, we compute the aggregate response

coefficient of the market returns to the aggregate change in earnings according to (6). The

covariance between the market return and the aggregate change in earnings is given by

cov[Rmt,∆et] = cov[εt, et]− cov[ωt, et], (13)

where εt = et − 1n

n∑i=1

n∑j=1

γji (s)sjt. Note, that the individual signal response coefficients γi(σ∗)

are not constant across firms and are functions of the variances σ2∗, which, in turn, is the

function of the set of signals st. Thus,

cov[εt, et] = var[et]−1

n

n∑i=1

n∑j=1

cov[γji (s)sjt, et] = var[et]−1

n

n∑i=1

n∑j=1

E[γji (s)sjtet]

= var[et]−1

n

n∑i=1

n∑j=1

E[γji (s)sjtE[et|s]] =σ2c + nσ2

m

n− 1

n2

n∑i=1

n∑j=1

n∑ι=1

n∑k=1

γkι E[γji (s)sjtskt]

and

cov[ωt, et] = cov[dt, et]− cov[δ(s)st, et] = σ2m − E[δ(s)stet] = σ2

m −1

n

n∑i=1

E[δ(s)stE[eit|s]]

= σ2m −

1

n

n∑i=1

n∑j=1

γjiE [δ(s)stsjt] .

In the subsequent section we provide a comparative static analysis of the earnings response

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Paper #900365

coefficients on the degree of firm-level and market-level ambiguity. We also develop a testable

hypothesis for the following empirical study.

2.3 Comparative static analysis and hypotheses development

In order to quantify the effect of ambiguity on earnings response coefficients we perform a

comparative statics analysis. The earnings response coefficients cannot be computed in the

closed form. To circumvent this difficulty we fix the values of σ2η, σ

2u, σ

2c , σ

2m and n and use

Monte Carlo simulations to estimate the earnings response coefficients for different values of

ambiguity parameters ∆c = σ2c − σ2

c and ∆d = σ2m − σ2

m. To do this we simulate 100,000

repetitions of variables c, m, v and u for each of n firms with n = 500.

We assume the actual parameters are as follows: σ2η = 4.0 × 10−4, σ2

u = 5.3 × 10−4,

σ2c = 2.94× 10−4 and σ2

m = 1.22× 10−5. These coefficients are computed using back-envelope

method using actual earnings response coefficients.1 We consider six different degrees of

firm-level ambiguity: ∆c = 0, 0.2σ2c , 0.4σ2

c , 0.6σ2c , 0.8σ2

c , 0.99σ2c and six different degrees of

market-level ambiguity: ∆d = 0, 0.2σ2m, 0.4σ2

m, 0.6σ2m, 0.8σ2

m, 0.99σ2m.

Insert Figure 1 about here

Figure 1 plots the individual earnings response coefficients for different degrees of firm-level

and market-level ambiguity. The individual earnings response coefficient clearly increases with

firm-level ambiguity. This is true for any degree of market-level ambiguity.

The intuition is as follows. Under no ambiguity, the investor extracts the same extent of

cash flows news from both positive and negative news. With ambiguity, the investor overreacts

to bad news by (as if) extracting less cash flow news from signals and underreacts to good news

by (as if) extracting relatively larger cash flow news. Overall, the overreaction is stronger and

the investor extracts less cash flows news from signals, captured by variable γii . Therefore, on

average a firm’s signal response coefficient γii for its cash flow news decreases with firm-level

ambiguity (see Panel A of Figure 2).

Insert Figure 2 about here

The response coefficient of signal j for firm i cash flow news, γij for i 6= j, increases with

firm-level ambiguity during periods of low market-level ambiguity and decreases during periods

1See the following section how we estimate the earnings response coefficients empirically.

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Paper #900365

of high market-level ambiguity (see Panel B of Figure 2). However, its economic magnitude

is very small and is dominated by γii . Finally, the signal response coefficient for discount rate

news, δ, does not change much with firm-level ambiguity (see Panel C of Figure 2). Hence, the

relation between γii and firm-level ambiguity generally determines the fact that the individual

earnings response coefficient increases with firm-level ambiguity as high ambiguity leads to a

larger earnings surprises (see Equation (3)).

Insert Figure 3 about here

Figure 3 contains plots of the aggregate earnings responses coefficients. Similarly to the

individual earnings response coefficients, the aggregate response increases with the degree of

firm-level ambiguity. When forming portfolios, non-ambiguous firm-specific cash flow news

and their effects diversify away so that only market-wide news prevail (see, e.g., Kothari,

Lewellen and Warner (2006)). However, due to asymmetric reaction of the ambiguity averse

investor, ambiguous idiosyncratic news are not diversified away (see Epstein and Schneider

(2008)). Therefore, positive cash flow news effect remains also in the aggregate response

coefficient for portfolios consisting of stocks with high degree of firm-level ambiguity.

At the same time, market-level ambiguity may have opposite effects on the aggregate re-

sponse coefficient depending on the degree of the firm-level ambiguity of the portfolio. Specif-

ically, market-level ambiguity increases the aggregate response coefficient for portfolios of

high-ambiguity firms while it decreases the aggregate response coefficient for portfolios of low-

ambiguity firms. Since returns respond to the market-wide discount rate news in the opposite

way than to the cash flow news, market-wide ambiguity amplifies its negative effect. Hence,

for portfolios of stocks with low degree of firm-level ambiguity, cash flow news are diversified

away and the aggregate earnings response coefficient mainly reflects a strong negative effect of

the discount rate news component (as in Kothari, Lewellen and Warner (2006)). However, for

portfolios consisting of highly ambiguous firms, the non-diversified effect of ambiguous cash

flow news dominates the negative effect of the discount rate news and we observe a positive

aggregate response coefficient.

Similar intuition is applied when the market response coefficient is computed. There are

two opposite effects here: negative impact of discount rates news and positive cash flow news

effect coming from high firm-level ambiguity preventing idiosyncratic cash flow news to be

diversified away. Which of those effects dominates depends on the number of stocks with high

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Paper #900365

degree of firm-level ambiguity in the market as well as on the degree of this ambiguity. This

is an empirical question and we shed light on it in Section 4.

Hence, based on the theoretical predictions we formulate the following three empirical

hypotheses.

Hypothesis 1: Individual earnings response coefficient increases with the degree of firm-

level ambiguity.

Hypothesis 2: Aggregate earnings response coefficient increases with the degree of firm-

level ambiguity. Moreover, this increase is more pronounced when the degree of market-level

ambiguity is high.

Hypothesis 3: High degree of market-level ambiguity leads to an increase in the earn-

ings response coefficient of high-ambiguity stocks and to a decrease in the earnings response

coefficient of low-ambiguity stocks.

3 Data and variable definition

Our sample selection starts from all firms with March, June, September, or December fis-

cal year-end from 1986 to 2014, with available accounting data in the Compustat quarterly

database. We use earnings per share (basic) excluding extraordinary items (Compustat item

EPSPXQ) adjusted by stock splits (Compustat item AJEXQ). In case this data is not avail-

able, we use earnings per share (diluted) excluding extraordinary items (Compustat item EPS-

FXQ) adjusted. Following Daniel and Titman (2006), we define book value as book equity to

be shareholders’ equity numbers (Compustat item SEQQ) minus total preferred/preference

stock (Compustat item PSTKQ) plus the deferred taxes and investment tax credit (Compus-

tat item TXDITCQ) and divided by common shares outstanding (Compustat item CSHOQ)

adjusted. If book equity is missing, we use total common/ordinary equity (Compustat CEQQ)

or total assets (Compustat item ATQ) minus total liabilities (Compustat item LTQ).

Following prior literature (e.g., Kothari, Lewellen and Warner (2006), Sadka and Sadka

(2009)), earnings surprise dEPit of firm i in quarter t is defined as

dEPit =Ei,t − Ei,t−4

Pi,t−4

,

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Paper #900365

where Ei,t − Ei,t−4 is seasonally differenced quarterly earnings and Pit is the market price.

For robustness we also perform the analysis with the seasonally differenced quarterly earnings

being scaled by either book equity (Bit), or earnings (Eit). These results are presented in the

Appendix.

For market- and portfolio-level estimates of earnings surprises, we use value-weighted cross-

sectional averages of individual stock earnings surprises where value weights are calculated as

the beginning-of-period market capitalization. Stock returns Rit are calculated using adjusted

prices (Compustat items PRCCQ / AJEXQ). In each period we exclude firms with beginning-

of-quarter price below $1. Also, we exclude the top and bottom 1% ranked on the distribution

of the corresponding measures of earnings surprise each quarter.

We calculate earnings surprises for portfolios as well as the overall market using aggregate

data. The aggregate series is simply the cross-sectional sum of each firm’s earnings change

multiplied by its number of shares outstanding, subsequently scaled by the sum of lagged

market price (we also use lagged book equity and lagged multiplication of earnings in the

Appendix) and the number of shares outstanding for the same group of firms.2

Analysts’ earnings forecasts data are from the Institutional Brokers Estimate System

(IBES) U.S. Detail History dataset via WRDS. The data is available on a monthly basis;

the forecasts are provided on the third Thursday of every month. We only consider fore-

casts that are within the fiscal quarter. Some description on how do we use the individual

forecasts? We use individual forecasts from the IBES U.S. Detail History dataset to miti-

gate earnings forecasts’ problematic rounding procedure in the Summary file (see Payne and

Thomas (2003)). We exclude firms that in the current quarter has less than two analysts’

earnings per share forecasts.

3.1 Measures of the degree of ambiguity

Analysts’ forecasts are widely used in the recent financial and accounting literature to estimate

uncertainty about future earnings. Specifically, the disagreement of professional forecasters

measured as dispersion of analysts’ forecasts can be used as a proxy of the degree of ambiguity

in the market (see Andersen, Ghysels and Juergens (2009), Kelsey, Kozhan and Pang (2011)

2We also use the value-weighted data based on per share numbers, where the per share earnings surprisesdEit/Pi,t−4 are weighted using the number of shares outstanding of quarter t. Results are qualitatively similarand can be available upon request.

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Paper #900365

and Drechsler (2013)). Intuitively, if forecasters produce very different and conflicting forecasts

about the fundamentals (either of a firm or the economy in general), investors are likely to

be unsure about the distribution of stock returns as they tend to condition their beliefs on

the analysts’ forecasts. Thus, when dispersion among analysts’ opinions regarding the future

performance of stock markets is high, ambiguity is also likely to be high since investors cannot

confidently narrow down the set of their beliefs to a single prior.

At the same time, dispersion of analysts’ forecasts might not be the ideal proxy for measur-

ing the degree of ambiguity. Prior literature, e.g., Abarbanell, Lanen and Verrecchia (1995),

Barron, Kim, Lim and Stevens (1998), Johnson (2004) argue that dispersion of analysts’ fore-

casts might not capture uncertainty well. The reason for this is that captures only a specific

type of uncertainty coming from the diversity of private information that analysts rely on.

Another source of ambiguity comes from imprecise common information shared by all analysts

and investors and hence measures the ambiguity of public information. We argue that total

uncertainty defined as the sum of those two components captures the degree of ambiguity more

comprehensively. Following Barron, Kim, Lim and Stevens (1998) define the total uncertainty

measure U as

U =D

1− ρ, (14)

where ρ = H/(H + Z) measures the consensus among the analysts, H = (SE−D/N)(SE−D/N+V )2

mea-

sures the precision of common information and Z = D(SE−D/N+D)2

measures the precision of

idiosyncratic private information. Here, SE is the mean squared error of forecasts scaled by

the absolute value of the actual forecasted variable, D is the variance of forecasts scaled by

the absolute value of the actual forecasted variable, and N is the number of forecasts. Thus,

the variable U measures the uncertainty attributable to both experts’ reliance on imprecise

common as well as idiosyncratic information. We argue that this measure captures the degree

of ambiguity embedded in the dispersion of analysts’ forecasts: that is, the more informa-

tion uncertainty is, the more likely that investors form multiple beliefs about fundamentals of

stocks and the economy as a whole.

We construct firm-level ambiguity by using analysts’ forecasts of individual firm earnings.

They reflect news about individual firms’ future cash flows. The higher is the total uncertainty

backed out from the dispersion of analysts’ earnings forecasts, the more ambiguous are the

signals about firms’ cash flow news. We denote FUi as the total uncertainly for firm i.

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Paper #900365

In order to examine the cross-sectional effect of firm-level ambiguity on earnings response

coefficient we categorize stocks into five different groups based on the degree of their firm-level

ambiguity. Specifically, every quarter we group stocks into quintiles according to firm-level

ambiguity variable FUi. We define dummy variable Djit, j = 1, ..., 5 to be equal to 1 if stock

i falls into firm-level ambiguity quintile j in quarter t. In this way, dummy variable D1

corresponds to the stocks with the least ambiguous cash-flow information and D5 correspond

to the most ambiguous stocks.

We construct market-level ambiguity by using individual analyst’s forecasts for macroe-

conomic variables, e.g. real GDP growth or inflation growth, that comes from the Survey of

Professional Forecasters managed by the Federal Reserve Bank of Philadelphia. Similar to

the firm-level ambiguity measure, we calculate the total uncertainty, denoted as MU , from

the dispersion of analysts’ forecasts for the next period real GDP growth rate.3 In order to

estimate the differential effect of market-level ambiguity on earnings response coefficient, we

define a dummy variable DMt with value equal to 1 if MUt is above its historical mean, and

zero otherwise.4

The choice of realized value, needed for calculating the mean squared forecasts’ error,

depends on the version of data that professional forecasters are trying to predict. Survey

of Professional Forecasters database offers five vintages of the realized value, ranging from

the initial-release numbers to the values that we understand today. The reliability of the

historical values increases in time while the availability decreases in time. We use the latter

four vintages on the ground that they suffer less measurement error yet are close enough to

what the professionals are try to forecast5. The results are similar for each of the four.

3.2 Summary statistics

Table 1 reports summary statistics for quarterly stock returns, earnings surprises and am-

biguity measures. From Panel A, the average number of stocks per quarter is 1,380. The

average quarterly return across firms is around 2.98%, with a standard deviation 19.97%. The

3Other studies, for instance Andersen, Ghysels and Juergens (2009) and Drechsler (2013), have used theraw dispersion of next period GDP growth rate to gauge macroeconomic uncertainty.

4We have also used an alternative definition of the market-level ambiguity dummy variable DMt . It has a

value equal to 1 if MUt is in its historical top quintile, and zero otherwise. Results remain similar and can beavailable upon request.

5The middle three measures of historical numbers are, respectively, the revised values as they appear one,five, and nine quarters after the initial release.

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Paper #900365

mean for earnings surprise measure dEP is 0.2%. The mean for dEB and dEE are 0.46%

and 17.58% respectively. Firm-level uncertainty has a very dispersed and positively skewed

distribution with mean value 0.085 (while its median is 0.008) and standard deviation 0.279.

The average value of market-level ambiguity is about 2.95 with standard deviation 4.586.

Figure 4 plots the time-series of the market-level ambiguity measure for our sample period.

The series has several big spikes, particularly in the third quarter of 1986, end of 1990 -

beginning of 1992 (The Gulf War), 1995 (The US federal government shutdown), 2000-2001

(dot-com bubble burst), 2008-2009 (Lehman’s bankruptcy and the subsequent financial crisis)

and 2011 (European sovereign credit crisis).

Panel B of Table 1 presents the average values and standard deviations of returns and

earnings surprise variables for each of the five portfolios sorted by the firm-level ambiguity

measure. Average quarterly returns are around 2-3% for each of the portfolios except for

the one with the highest degree of firm-level ambiguity (for the highest ambiguity portfolio

the average return is 0.874%). Earnings surprise measures increase monotonically with firm-

level ambiguity except for the most ambiguous portfolio. Specifically, dEP increases from

-0.37% for P1 to 0.35% for P4 and then drops to -28.76% for P5. dEB and dEE exhibit

similar pattern. Finally, firms with lower degree of firm-level ambiguity is on average larger in

terms of market capitalization than the firms with higher degree of ambiguity, however, this

difference is not very big.

Table 2 reports correlations among variables at different levels of aggregation. Panel A

presents firm-level correlations. Returns exhibit positive and statistically significant correla-

tion with earnings surprise measures at 5% level. Firm-level ambiguity is significantly nega-

tively correlated with returns and earnings surprises at 5% level. Panel B reports portfolio-level

correlations. Correlations between returns and aggregate earnings surprises become statisti-

cally insignificant regardless of the direction. However, the aggregated firm-level ambiguity

has a negative and significant at 5% level correlation with earnings surprises. Correlation be-

tween returns and ambiguity measure remains insignificant. Finally, Panel C reports market

level correlation. Market returns are uncorrelated with aggregate earnings surprises as well

as market-level ambiguity. Also, market-level ambiguity has insignificant correlation with ag-

gregate earnings surprises. At all three levels, the three measures of earnings surprises are

significantly correlated with each other at 5%. Their correlation magnitudes increase as the

level of aggregation becomes wide.

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4 Empirical Analysis

Our main tests explore how firm- and market-level ambiguity affect the stocks reaction to

earnings surprises. We start our analysis with individual firms’ responses.

4.1 Firm-level analysis

We test our hypothesis 1 by estimating the following pooled panel regression:

Rit = α0 +

5∑j=2

αjDjit + α6D

Mt + β1dEPit +

5∑j=2

βjdEPit ×Djit (15)

+ γ1dEPit ×DMt +

5∑j=2

γjdEPit ×Djit ×D

Mt +Xit + εit, .

where Rit is the arithmetic return for stock i in quarter t and dEPit is the firm-level earnings

surprise for stock i in quarter t. Djit refer to firm-level ambiguity and is a dummy variable

assigned with value 1 when stock i is in ambiguity group j in quarter t, and value zero

otherwise. Xit is a vector of control variables including log market capitalization, log book-

to-market ratio and the market return. We cluster standard errors by firm and quarter to

account for potential cross-correlations. The estimation results are given in Table 3.

Insert Table 3 about here

The results are consistent with our theoretical predictions. The individual stock prices

react positively to earnings surprises dEP . The earnings response coefficient β1 is 0.950 and

is statistically significant at 1% level when we do not control for ambiguity. When firm-

level ambiguity variables are included in the regression (column (2) of Table 3), the earnings

response coefficient for the least ambiguous firms is 0.389, statistically insignificant at 10%

level. The coefficient increases monotonically with the degree of firm-level ambiguity. The

earnings response coefficient for the most ambiguous firms is significantly (at 1% level) higher

than the one for the least ambiguous firms by 0.806.

Finally, the earnings response coefficient maintains a monotonic relationship with the

degree of firm-level ambiguity when we control for market-level ambiguity (column (3) of

Table 3). The difference between the earnings response coefficients for the most and the

least ambiguous firms is significantly positive (at 1% level) and equals to 0.759. Market-

level ambiguity has no material impact on the relationship. However, note that market-level

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Paper #900365

ambiguity decreases the earnings response coefficient of the least ambiguous firms (by -0.116)

while increases the coefficient of the most ambiguous firms (by 0.091), albeit both insignificant

at 10% level. Overall, the results indicate that investors respond to corporate earnings news

more strongly when the information environment around the firm is highly ambiguous. This

confirms our Hypothesis 1.

In order to ensure that our results are not driven by characteristics like size and book-to-

market, we include them into the specification (see columns (4) - (6) of Table 3). We also

include the market return to control for the market-wide movements of the returns. The

results remain qualitatively similar.

4.2 Portfolio-level analysis

In order to test Hypotheses 2 and 3 and estimate the effect of ambiguity on aggregate response

coefficient, we form portfolio of stocks ranked on the degree of firm-level ambiguity. That

is, each quarter we group stocks into quintiles based on FUi and form five value-weighted

portfolios. For each portfolio we compute the aggregated earnings surprises. To perform our

tests we estimate the following panel regression:

Rpt = α0 +5∑j=2

αjDjpt + α6D

Mt + β1dEPpt +

5∑j=2

βjdEPpt ×Djpt (16)

+ γ1dEPpt ×DMt +

5∑j=2

γjdEPpt ×Djpt ×DM

t +Xpt + εpt,

where p denotes the corresponding quintile portfolio. Rpt is the value-weighted return on

portfolio p. dEPpt is the aggregate earnings surprise of portfolio p in quarter t. Djpt is a

dummy variable with assigned value 1 if portfolio p is in ambiguity group j in quarter t,

and zero otherwise. DMt is a dummy variable with value of 1 when market-level ambiguity

is above its mean, and zero otherwise. Xpt is the vector of control variables including log

market capitalization of portfolio p, log book-market-ratio and the market return. We cluster

standard errors by portfolio. The results are provided in Table 4.

Insert Table 4 about here

Similarly to the firm-level case, the aggregate earnings response coefficient increases with

the degree of firm-level ambiguity. Column (5) of Table 4 shows that with all three control

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variables, the aggregate earnings response coefficient increases monotonically with the degree

of firm-level ambiguity. The difference between the portfolio of most ambiguous firms and the

least one is 5.681 significant at 1% level. When we add in the interaction effect of market-level

ambiguity, the monotonic relationship weakens for the low degree of market-level ambiguity,

but remains for the high degree of market-level ambiguity. These results are consistent with

our theoretical predictions and confirms our Hypothesis 2. Indeed, the pale grey line on Figure

3 is almost flat suggesting that earnings response coefficient increases with firm-level ambiguity

very slowly when the degree of market-level ambiguity is low. At the same time, the black

line is steep suggesting that when the information about discount rates is very ambiguous

the earnings response coefficient increases with firm-level ambiguity at much higher rate. The

results remain qualitatively similar if we do not control for the three Fama-French type factors

( see columns (1) - (3) of Table 4).

The estimation results of Equation (16) also provides a strong support for our Hypothesis

3. Column (3) of Table 4 shows that the coefficient of dEPpt × DMt term is negative (-

3.520) and statistically significant at 5% level. This means that an increase in market-level

ambiguity significantly decreases the earnings response coefficient for the portfolio of lowest

ambiguity firms. On the other end, we observe an significant increase in the earnings response

coefficient for the highest ambiguity portfolio. Comparing to the coefficient at low degree of

market-ambiguity (dEPpt×D5pt), high degree of market-level ambiguity increases the coefficient

by 5.943, statistically significant at 1% level. The coefficient for portfolio of the least firm

ambiguity at high level of market ambiguity is -0.715 (the sum of the coefficients of dEPpt×D5pt

and dEPpt). The coefficient for portfolio of the highest firm ambiguity at high level of market

ambiguity is 5.005 (the sum of the coefficients of dEPpt ×D5pt and dEPpt ×D5

pt ×DMt ).

Overall, the presented results suggest that both firm and market levels of ambiguity signif-

icantly affect stock portfolio response to aggregate earnings surprises and omitting them from

the analysis may lead to the omitted variable bias. Indeed, without looking at ambiguity, one

would conclude there is positive relationship between stock returns and earning surprises, for

instance 3.508 in column 4 of Table 4. Now we know that this positive relationship comes

from high degree of firm-level ambiguity amplified by high degree of market-level ambiguity.

By controlling both, the earnings response coefficient becomes negative (-1.290 in column 6 of

Table 4). The coefficient for lowest ambiguity portfolio at high degree of ambiguity is -2.130

(i.e. β1 + γ1 = −1.290− 0.840). The coefficient for highest ambiguity portfolio at high degree

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Paper #900365

of market-level ambiguity is 5.070 (i.e. β1 + β5 + γ1 + γ5 = −1.290 + 3.636− 0.840 + 3.564).

4.3 Aggregate-level analysis

Our theoretical model implies that the sign of the aggregate earnings response coefficient

depends on the overall level of ambiguity about cash flow news on the market. That is, if

low ambiguity firms prevail in the market we can expect a negative price responses to the

aggregate earnings. On the other hand if the overall level of cash flow ambiguity is high, the

earnings response coefficient is expected to be positive. If the market is populated by firms

with both high and low degrees of firm-level ambiguity then both effects would cancel each

other and we expect to see small and insignificant market reaction. In this section we verify

empirically which of those statements is true. To do this we estimate the following time series

regression:

RMt = β0 + β1dEPt + β2D

Mt + β3dEPt ×DM

t + εt, (17)

where RMt is the market return at time t, dEPt is the aggregate earnings surprises at time t, and

DMt is a dummy variable with value of 1 when market-level ambiguity is above its mean, and

zero otherwise. The standard errors are corrected for heteroscedasticity and autocorrelation.

Table 5 show the estimation results.

Insert Table 5 about here

When market-level ambiguity is not included in the regression, the results are similar to

what is found in the existing literature (see Kothari, Lewellen and Warner (2006), Sadka

and Sadka (2009)): an insignificant aggregate earnings response coefficient (see column (1)

of Table 5). When we control for market-level ambiguity, the coefficient β1 becomes smaller

(2.379) and remain insignificant at 10% level. The coefficient β3 for the interaction term of

aggregate earning responses and market-level ambiguity dummy is positive but statistically

insignificant at 10% level.

Our theoretical model provides an explanation for these results. As stated in our Hypoth-

esis 3, high degree of market-level ambiguity leads to an increase in the earnings response

coefficient of high-ambiguity stocks and a decrease in the earnings responses of low-ambiguity

stocks. When we aggregate stocks into a market portfolio, we mixed up both high and low

ambiguity firms. On the aggregate level, the effect coming from the high ambiguity firms

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Paper #900365

marginally dominates, therefore we observe a positive albeit insignificant earnings response

coefficient in the state of high market-wide ambiguity.

5 Robustness checks

In this section we perform a series of robustness checks to ensure that the above results are

not driven by a particular specification of our variables and methods. So far we have defined

the earnings surprise variable as seasonally differenced earnings scaled by the stock market

price. However, literature also uses book equity or earnings to scale the changes in earnings

(see Kothari, Lewellen and Warner (2006), Sadka and Sadka (2009)). We re-estimate our

main regressions using these alternative definitions of earnings surprises. That is, we define

dESit =Ei,t − Ei,t−4

Si,t−4

,

where Ei,t − Ei,t−4 is seasonally differenced quarterly earnings and Sit is either book equity

(Sit = Bit) or earnings (Sit = Eit).

Insert Tables 6, 7 and 8 about here

The estimation results for firm-level analysis are presented in Table 6, the portfolio-level

results are in Table 7 and the market-level analysis is shown in Table 8. All analyses are

conducted with controls wherever appropriate. Most of our conclusions remain unchanged

with the new definitions of earnings surprise proxies. Specifically, firm-level earnings response

coefficient monotonically increases with the firm-level ambiguity (Table 6). This monotonic

relationship is translated into the portfolio level (Table 7). For the high regime of market-level

ambiguity, portfolio earnings response coefficient is generally higher for more ambiguous firms.

This difference comparing to that of less ambiguous firms is economically large and statistically

significant at at least 5% level. Finally, as in the case of dEPit, the aggregate response

coefficient is positive albeit statistically insignificant during both low and high regimes of

market-level ambiguity (Table 8). Hence, our results are robust to the alternative definitions

of earnings surprise proxy.

Secondly, we conduct robustness checks on our ambiguity measures. The main results

in the paper are based on total uncertainty measure V defined by Barron, Kim, Lim and

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Paper #900365

Stevens (1998). This measure includes both common uncertainty due to imprecise public

information shared by analysts (C) and idiosyncratic uncertainty as a result of differing private

information between analysts (D). In that sense, total uncertainty is a very comprehensive

and safe measure. That being said, some might argue that ambiguity is about uncertainty

induced by imprecise (or lack of) public information rather than information asymmetry.

Also our model setting of ambiguity is based on all investors having access to the same noisy

signals about each firm’s earnings news. Thus, using a proxy of ambiguity that is based on

public information seems to be a natural extension. Following Barron, Kim, Lim and Stevens

(1998)’s definition of consensus, we refer to ρ as public information ambiguity defined as

ρ =C

V(18)

This consensus proxies how much the analysts’ average belief reflects public versus private

information. The higher ρ indicates the more reliance on public information. Using ρ matches

more closely to our theoretical setup of ambiguity. We re-run our main regressions using this

alternative ambiguity measure.

Insert Tables 9, 10 and 11 about here

Tables 9, 10 and 11 present the estimation results for firm, portfolio and market levels of

analysis, respectively. All analyses are conducted with the interactions of firm-specific and

market-wide ambiguities for all three earning surprises measures, with or without character-

istics controls. The results remain very similar to those of our main analyses. Both firm-level

and portfolio-level earnings response coefficients increases with the degree of firm-level ambi-

guity (Tables 9 and 10). Market-level ambiguity decreases the coefficient for portfolio of the

least ambiguous firms while increases the coefficient for portfolio of high ambiguity firms (Ta-

ble 10). The coefficient for the market portfolio is positive albeit insignificant due to mixture

of low and high ambiguous firms (Table 11). Thus, our results are robust to this alternative

public information ambiguity measure.

6 Conclusion

Diversification is one of the key concepts in finance. Idiosyncratic news about stocks’ future

cash flows should not matter if investors hold large well diversified portfolios. This is why the

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Paper #900365

literature agrees that only discount rate news that is common to all stocks should dominate

when considering the return-earnings relation at the aggregate level. Yet, if idiosyncratic

news is ambiguous and investors are ambiguity averse, then negative news tends to dominate

positive news in an asymmetric fashion and the diversification argument fails. In this paper

we show that ambiguity has a pronounced effect on the earnings response coefficients at both

firm- and aggregate-level. Using quarterly data of US stock returns and earnings surprises, we

find that individual earnings response coefficient increases with firm-level ambiguity. When

stocks are aggregated into portfolio based on the degree of firm-level ambiguity, we find that

aggregate earnings response coefficient also increases with the degree of firm-level ambiguity.

This happens because ambiguity prevents idiosyncratic news from being diversified away when

aggregated.

There is an extensive literature arguing that discount rate news is more important than

cash flow news in terms of its effect on market returns (Campbell (1991), Lettau and Ludvigson

(2005), Hecht and Vuolteenaho (2006), Chen and Zhao (2009), Kothari, Lewellen and Warner

(2006), Cready and Gurun (2010), Subasi (2011)). In this paper we provide evidence that

this might not be the case if the degree of ambiguity is high. Because ambiguity impedes

diversification, so individual earnings surprises can affect the aggregate returns. As a result,

the aggregate returns responds positively to aggregated earnings surprises during the periods

of high market uncertainty.

We also show that cash flow news plays a much more important role in price discovery

of stock returns than discount rate news. Specifically, the ratio of cash flow news variance

to total unexpected return variance of stock returns increases monotonically with firm-level

ambiguity. This provides further evidence that ambiguity should be taken into account when

examining the contemporaneous relationship between aggregate earnings surprises and market

returns.

25

Paper #900365

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Figures and Tables

Figure 1: Comparative statics – individual earnings response coefficients

This figure presents the comparative statics on the effect of the degree of firm- and market-level ambiguity on the individualresponse coefficient. In order to compute the individual response coefficient using (5) and (12), we perform Monte Carlo simulationexercise. We set σ2

η = 4.0× 10−4, σ2u = 5.3× 10−4, σ2

c = 2.94× 10−4, σ2m = 1.22× 10−5 and n = 500. The ambiguity parameters

are as follows: firm-level (horizontal axis) ∆c = σ2c − σ2

c with ∆c = 0, 0.2σ2c , 0.4σ2

c , 0.6σ2c , 0.8σ2

c , 0.99σ2c and market-level

∆d = σ2m − σ2

m with ∆d = 0, 0.2σ2m, 0.4σ2

m, 0.6σ2m, 0.8σ2

m, 0.99σ2m. We simulate 100,000 repetitions of variables c, m, η and u

and present the average of the individual response coefficient.

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Paper #900365

Figure 2: Comparative statics: individual signal (γii and γij) and discount ratenews (δ) response coefficients

This figure presents the comparative statics on the effect of the degree of firm- and market-level ambiguity on the reaction tothe cash-flow news coefficients γii (Panel A), γji (Panel B) and the discount rate news coefficient δ (Panel C). We compute γiiand γij according to formula (1) and δ according to formula (2). We use variances and covariances that solves the minimization

problem (11). To perform Monte Carlo simulation we set σ2η = 4.0× 10−4, σ2

u = 5.3× 10−4, σ2c = 2.94× 10−4, σ2

m = 1.22× 10−5

and n = 500. The ambiguity parameters are as follows: firm-level (horizontal axis) ∆c = σ2c − σ2

c with ∆c = 0, 0.2σ2c , 0.4σ2

c ,0.6σ2

c , 0.8σ2c , 0.99σ2

c and market-level ∆d = σ2m − σ2

m with ∆d = 0, 0.2σ2m, 0.4σ2

m, 0.6σ2m, 0.8σ2

m, 0.99σ2m. We simulate 100,000

repetitions of variables c, m, η and u and present the averages of γii , γji and δ.

Panel A: γii

Panel B: γij

Panel C: δ

30

Paper #900365

Figure 3: Comparative statics – aggregate earnings response coefficients

This figure presents the comparative statics on the effect of the degree of firm- and market-level ambiguity on the aggregateresponse coefficient. In order to compute the individual response coefficient using (1) and (13), we perform Monte Carlo simulationexercise. We set σ2

η = 4.0× 10−4, σ2u = 5.3× 10−4, σ2

c = 2.94× 10−4, σ2m = 1.22× 10−5 and n = 500. The ambiguity parameters

are as follows: firm-level (horizontal axis) ∆c = σ2c − σ2

c with ∆c = 0, 0.2σ2c , 0.4σ2

c , 0.6σ2c , 0.8σ2

c , 0.99σ2c and market-level

∆d = σ2m − σ2

m with ∆d = 0, 0.2σ2m, 0.4σ2

m, 0.6σ2m, 0.8σ2

m, 0.99σ2m. We simulate 100,000 repetitions of variables c, m, η and u

and present the average of the aggregate response coefficient.

31

Paper #900365

Figure 4: Time series of the degree of market-level ambiguity

This figure plots the time series of the market-level ambiguity MUt (black line) for the period from Q1 1986 to Q2 2014.MUt is computed using the decomposition of the dispersion of the analysts forecasts of the real GDP growth for the nextquarter. Individual forecasts for real GDP growth are from the Survey of Professional Forecasters at the Federal Reserve Bankof Philadelphia. Grey lines indicate periods when MUt is above its historic mean value.

32

Paper #900365

Table 1: Summary statistics

This table reports the summary statistics of the sample. Panel A describes the mean, standard deviation, and quartiles of thefirm and market level variables. Rit is the quarterly return for firm i at quarter t. dEPit, dEBit, and dEEit are, respectively, theseasonally differenced earnings (dE) scaled by beginning-of-period market price (P), book value (B), or earnings (E) for firm i atquarter t. FUit is the firm-level uncertainty for firm i at quarter t, calculated as the decomposed uncertainty part of the analysts’earnings forecasts dispersion. MUt is the macroeconomic uncertainty for quarter t, calculated as the decomposed uncertainty partof the analysts’ next-period GDP growth forecasts dispersion. Panel B describes the mean and standard deviation (in brackets) ofthe portfolio variables under 5 levels of firm-level uncertainty. SIZEpt is the average of log market value. Earnings are excludingextraordinary items. Earnings, book equity, share price, and shares outstanding data are from Compustat. Analysts’ forecastsare from IBES. Individual forecasts for real GDP growth are from the Survey of Professional Forecasters at the Federal ReserveBank of Philadelphia. The firms are subject to the following screening criteria: 1) data are available for earnings, price, commonshares outstanding, book equity this quarter and four quarters prior; 2) dates are aligned with calendar quarters; 3) price is largerthan $1; 4) at least two analysts’ forecasts for EPS; 5) not in the top and bottom 1 percentile of firms ranked by dEP , dEB, ordEE. Our sample includes all the firms on NYSE, AMEX, and NASDAQ from 1986 Q1 to 2014 Q4.

Panel A: Firm and market level variablesMean Std.Dev. Q1 Median Q3

Rit, % 3.405 18.55 -7.473 3.101 13.72

RMt , % 2.659 8.457 -0.824 3.680 7.594

dEPit, % 0.016 1.850 -0.299 0.141 0.470

dEBit, % 0.390 3.811 -0.673 0.385 1.369

dEEit, % -17.17 151.6 -20.00 10.26 34.43

FUit 0.068 0.678 0.001 0.002 0.014

MUt 5.848 15.30 0.160 0.793 2.294

Obs. 77,237

Panel B: Portfolio level variablesLow 2 3 4 High

Rpt, % 2.771 3.175 2.883 2.263 0.317

[7.810] [8.341] [9.138] [9.065] [10.69]

dEPpt, % 0.171 0.181 0.104 0.142 -0.271

[0.212] [0.236] [0.329] [0.517] [0.973]

dEBpt, % 0.586 0.533 0.342 0.329 -0.638

[0.784] [0.660] [1.018] [1.140] [2.033]

dEEpt, % 11.46 11.22 7.126 7.870 -17.90

[16.95] [15.14] [21.39] [33.01] [55.91]

SIZEpt 9.437 6.887 6.126 5.312 3.945

[4.723] [3.879] [3.645] [2.991] [2.027]

33

Paper #900365

Table 2: Correlations

This table reports the correlations of the sample. Panel A describes the correlations of the firm-level variables. Rit is the quarterlyreturn for firm i at quarter t. dEPit, dEBit, and dEEit are, respectively, the seasonally differenced earnings (dE) scaled bybeginning-of-period market price (P), book value (B), or earnings (E) for firm i at quarter t. FUit is the firm-level uncertaintyfor firm i at quarter t, calculated as the decomposed uncertainty part of the analysts’ earnings forecasts dispersion. Panel B andC describe the correlations of portfolio and market level variables, respectively.MUt is the macroeconomic uncertainty for quartert, calculated as the decomposed uncertainty part of the analysts’ next-period GDP growth forecasts dispersion. Earnings areexcluding extraordinary items. Earnings, book equity, share price, and shares outstanding data are from Compustat. Analysts’forecasts are from IBES. Individual forecasts for real GDP growth are from the Survey of Professional Forecasters at the FederalReserve Bank of Philadelphia. The firms are subject to the following screening criteria: 1) data are available for earnings, price,common shares outstanding, book equity this quarter and four quarters prior; 2) dates are aligned with calendar quarters; 3)price is larger than $1; 4) at least two analysts’ forecasts for EPS; 5) not in the top and bottom 1 percentile of firms ranked bydEP , dEB, or dEE. ∗∗∗, ∗∗, and ∗ indicate significance at the 1%, 5%, and 10% level, respectively. Our sample includes all thefirms on NYSE, AMEX, and NASDAQ from 1986 Q1 to 2014 Q4.

Panel A: firm-level variablesRit dEPit dEBit dEEit FUit

Rit 1 0.094∗∗∗ 0.096∗∗∗ 0.085∗∗∗ -0.025∗∗∗

dEPit 1 0.773∗∗∗ 0.665∗∗∗ -0.093∗∗∗

dEBit 1 0.630∗∗∗ -0.067∗∗∗

dEEit 1 -0.070∗∗∗

FUit 1

Panel B: Portfolio level variablesRpt dEPpt dEBpt dEEpt FUpt

Rpt 1 0.173∗∗∗ 0.203∗∗∗ 0.198∗∗∗ -0.135∗∗∗

dEPpt 1 0.921∗∗∗ 0.958∗∗∗ -0.428∗∗∗

dEBpt 1 0.974∗∗∗ -0.361∗∗∗

dEEpt 1 -0.383∗∗∗

FUpt 1

Panel C: Market level variablesRM

t dEPt dEBt dEEt MUt

RMt 1 0.086 0.142 0.115 0.052

dEPt 1 0.940∗∗∗ 0.963∗∗∗ -0.006

dEBt 1 0.992∗∗∗ -0.032

dEEt 1 -0.030

MUt 1

34

Paper #900365

Table 3: Stock returns and earnings surprises: firm-level regressions

This table reports the coefficient, t-statistic, and adjusted R2 of contemporaneous relations between quarterly returns and earningssurprises, and with the interaction of firm-level and macroeconomic uncertainty:

Rit = α0 +5∑j=2

αjDjit + α6DMt + β1dEPit +

5∑j=2

βjdEPit ×Djit + γ1dEPit ×DMt +5∑j=2

γjdEPit ×Djit ×DMt +Xit + εit,

where dEPit is seasonally differenced earnings scaled by beginning-of-period market price for firm i at time t. Rit is the returnfor firm i at time t. DMt is a dummy variable assigned with 1 if the market-level ambiguity is above its historic mean, and zerootherwise. The market-level ambiguity is defined as the uncertainty part of the dispersion of forecasts for next-period real GDPGrowth. Djit is the uncertainty part of analyst earnings forecast dispersion measuring firm-specific uncertainty for uncertaintyquintile j at time t. D5

it is the quintile with highest uncertainty and so forth. The first quintile is embedded in the no-dummyvariable. Earnings are excluding extraordinary items. Xit is the vector of control variables including log size (LSIZEit), logbook-to-market ratio (LBMit) and the market return (RMt ). Earnings, book equity, share price, and shares outstanding data arefrom Compustat. Analysts’ forecasts are from IBES. Individual forecasts for real GDP growth are from the Survey of ProfessionalForecasters at the Federal Reserve Bank of Philadelphia. The firms are subject to the following screening criteria: 1) data areavailable for earnings, price, common shares outstanding, book equity this quarter and four quarters prior; 2) dates are alignedwith calendar quarters; 3) price is larger than $1; 4) at least two analysts’ forecasts for EPS; 5) not in the top and bottom 1percentile of firms ranked by dEP . Standard errors are given in parentheses and are clustered by firm and quarter. ∗∗∗, ∗∗,and ∗ indicate significance at the 1%, 5%, and 10% level, respectively. Our sample includes all the firms on NYSE, AMEX, andNASDAQ from 1986 Q1 to 2014 Q4.

35

Paper #900365

Table 3 continued.

(1) (2) (3) (4) (5) (6)

dEPit0.950∗∗∗

(0.179)0.389(0.295)

0.463∗∗

(0.187)0.875∗∗∗

(0.104)0.230(0.198)

0.295∗

(0.153)

dEPit ×D2it

0.272(0.228)

0.377(0.294)

0.366∗

(0.205)0.378(0.247)

dEPit ×D3it

0.355∗

(0.215)0.400∗

(0.235)0.271(0.165)

0.342∗

(0.193)

dEPit ×D4it

0.336(0.274)

0.426∗

(0.224)0.414∗

(0.239)0.512∗∗

(0.207)

dEPit ×D5it

0.806∗∗∗

(0.249)0.759∗∗∗

(0.228)0.954∗∗∗

(0.204)0.900∗∗∗

(0.202)

DMt0.010(0.019)

0.016∗∗∗

(0.006)

dEPit ×DMt-0.116(0.558)

-0.082(0.381)

dEPit ×D2it ×DMt

-0.177(0.461)

-0.016(0.409)

dEPit ×D3it ×DMt

-0.064(0.447)

-0.111(0.359)

dEPit ×D4it ×DMt

-0.160(0.547)

-0.179(0.470)

dEPit ×D5it ×DMt

0.091(0.499)

0.100(0.406)

D2it

0.001(0.002)

0.001(0.002)

-0.002(0.002)

-0.002(0.002)

D3it

0.004(0.003)

0.004(0.003)

-0.000(0.003)

-0.000(0.003)

D4it

0.001(0.004)

0.001(0.004)

-0.004(0.004)

-0.004(0.004)

D5it

-0.020∗∗∗

(0.005)-0.020∗∗∗

(0.005)-0.029∗∗∗

(0.005)-0.029∗∗∗

(0.005)

RMt0.118∗∗∗

(0.051)1.117∗∗∗

(0.050)1.120∗∗∗

(0.048)

LSIZEit-0.003∗∗

(0.002)-0.004∗∗

(0.002)-0.004∗∗

(0.002)

LBMit0.009∗∗

(0.004)0.011∗∗∗

(0.004)0.011∗∗∗

(0.004)

Const0.036∗∗∗

(0.010)0.040∗∗∗

(0.009)0.034∗∗∗

(0.012)0.041∗∗∗

(0.016)0.057∗∗∗

(0.016)0.048∗∗∗

(0.015)

Obs. 77,237 77,237 77,237 75,823 75,823 75,823

R2 0.9% 1.2% 1.2% 19.5% 19.9% 20.0%

36

Paper #900365

Table 4: Aggregate returns and earnings surprises: portfolio-level regressions

This table reports the coefficient, t-statistic, and adjusted R2 of contemporaneous relations between quarterly portfolio returnsand earnings surprises, and with the interaction of firm-level and macroeconomic uncertainty:

Rpt = α0 +5∑j=2

αjDjpt + α6DMt + β1dEPpt +

5∑j=2

βjdEPpt ×Djpt + γ1dEPpt ×DMt +5∑j=2

γjdEPpt ×Djpt ×DMt +Xpt + εpt,

where dEPpt is aggregate seasonally differenced earnings scaled by beginning-of-period market price for portfolio p at time t.Rpt is the return for portfolio p at time t. DMt is a dummy variable assigned with 1 if the macroeconomic uncertainty is aboveits mean, and zero otherwise. The macroeconomic uncertainty is defined as the uncertainty part of the dispersion of forecastsfor next-period real GDP Growth. Djpt is the uncertainty part of analyst earnings forecast dispersion measuring firm-specific

uncertainty for uncertainty quintile j at time t. D5pt is the quintile with highest uncertainty and so forth. The first quintile is

embedded in the no-dummy variable. Earnings are excluding extraordinary items. Xpt is the vector of control variables includinglog size (LSIZEpt), log book-to-market ratio (LBMpt) and the market return (RMt ). Earnings, book equity, share price, andshares outstanding data are from Compustat. Analysts’ forecasts are from IBES. Individual forecasts for real GDP growth arefrom the Survey of Professional Forecasters at the Federal Reserve Bank of Philadelphia. The firms are subject to the followingscreening criteria: 1) data are available for earnings, price, common shares outstanding, book equity this quarter and four quartersprior; 2) dates are aligned with calendar quarters; 3) price is larger than $1; 4) at least two analysts’ forecasts for EPS; 5) notin the top and bottom 1 percentile of firms ranked by dES. Standard errors are given in parentheses and are clustered by firmand quarter. ∗∗∗, ∗∗, and ∗ indicate significance at the 1%, 5%, and 10% level, respectively. Our sample includes all the firms onNYSE, AMEX, and NASDAQ from 1986 Q1 to 2014 Q4.

37

Paper #900365

Table 4 continued.

(1) (2) (3) (4) (5) (6)

dEPpt3.060∗∗∗

(0.384)1.029∗∗∗

(0.100)2.805∗∗∗

(0.565)3.508∗∗∗

(0.550)-1.820∗∗

(0.406)-1.290∗∗

(0.836)

dEPpt ×D2pt

-0.634∗∗∗

(0.063)-1.873∗∗∗

(0.206)1.536∗∗∗

(0.098)-0.097(0.239)

dEPpt ×D3pt

2.099∗∗∗

(0.252)3.471∗∗∗

(0.193)3.155∗∗∗

(0.481)5.232∗∗∗

(0.614)

dEPpt ×D4pt

0.956∗∗∗

(0.250)-1.298∗∗

(0.348)4.359∗∗∗

(0.420)2.775∗∗

(0.649)

dEPpt ×D5pt

2.185∗∗∗

(0.331)-0.938(0.539)

5.681∗∗∗

(0.423)3.636(0.841)

DMt0.005(0.004)

0.005(0.005)

dEPpt ×DMt-3.520∗∗

(1.020)-0.840(1.134)

dEPpt ×D2pt ×DMt

2.837∗∗∗

(0.010)2.558∗∗∗

(0.162)

dEPpt ×D3pt ×DMt

-1.910∗∗

(0.584)-3.599∗∗∗

(0.697)

dEPpt ×D4pt ×DMt

5.145∗∗∗

(0.759)3.988∗∗

(0.891)

dEPpt ×D5pt ×DMt

5.943∗∗∗

(1.108)3.564∗

(1.287)

D2pt

0.005∗∗∗

(0.000)0.005∗∗∗

(0.001)-0.011∗∗∗

(0.002)-0.010∗∗∗

(0.002)

D3pt

-0.001∗∗∗

(0.000)-0.002∗∗∗

(0.000)-0.023∗∗∗

(0.003)-0.025∗∗∗

(0.003)

D4pt

-0.004∗∗∗

(0.001)-0.003∗∗∗

(0.001)-0.037∗∗∗

(0.004)-0.037∗∗∗

(0.004)

D5pt

-0.013∗∗∗

(0.001)-0.009∗∗∗

(0.001)-0.061∗∗∗

(0.005)-0.058∗∗∗

(0.005)

RMt0.924∗∗∗

(0.021)0.908∗∗∗

(0.026)0.906∗∗∗

(0.025)

LSIZEpt0.004(0.007)

-0.015(0.008)

-0.014(0.008)

LBMpt0.063∗∗∗

(0.010)0.083∗∗∗

(0.008)0.087∗∗∗

(0.010)

Const0.026∗∗∗

(0.003)0.031∗∗∗

(0.003)0.028∗∗∗

(0.002)0.043(0.059)

0.232∗∗

(0.054)0.228∗∗

(0.056)

Obs. 600 600 600 600 600 600

R2 3.4% 3.8% 4.4% 22.3% 25.3% 26.0%

38

Paper #900365

Table 5: Aggregate returns and earnings surprises: market level regressions

This table reports the coefficient, t-statistic, and adjusted R2 of contemporaneous relations between quarterly returns and earningssurprises, and with the interaction of macroeconomic forecasts dispersion measure:

RMt = β0 + β1dEPt + β2DMt + β3dEPt ×DMt + εt,

where dEPt is aggregate seasonally differenced earnings (dE) scaled by beginning-of-period market price at time t. RMt is themarket return at time t. DMt is a dummy variable assigned with 1 if the macroeconomic uncertainty is above its mean, andzero otherwise. The macroeconomic uncertainty is defined as the uncertainty part of the dispersion of forecasts for next-periodreal GDP Growth. Earnings are excluding extraordinary items. Earnings, book equity, share price, and shares outstandingdata are from Compustat. Analysts’ forecasts are from IBES. Individual forecasts for real GDP growth are from the Survey ofProfessional Forecasters at the Federal Reserve Bank of Philadelphia. The firms are subject to the following screening criteria:1) data are available for earnings, price, common shares outstanding, book equity this quarter and four quarters prior; 2) datesare aligned with calendar quarters; 3) price is larger than $1; 4) at least two analysts’ forecasts for EPS; 5) not in the top andbottom 1 percentile of firms ranked by dES. Standard errors are given in parentheses and are corrected for heteroscedasticityand autocorrelation. ∗∗∗, ∗∗, and ∗ indicate significance at the 1%, 5%, and 10% level, respectively. Our sample includes all thefirms on NYSE, AMEX, and NASDAQ from 1986 Q1 to 2014 Q4.

(1) (2) (3)

dEPt3.083(3.136)

3.159(3.310)

2.379(3.293)

DMt0.002(0.015)

-0.000(0.016)

dEPt ×DMt1.548(6.554)

Const0.020∗∗

(0.008)0.020∗

(0.011)0.021∗

(0.011)

Obs. 120 120 120

R2 1.3% 1.3% 1.4%

39

Paper #900365

7 Appendix

Table 6: Firm-level regressions: alternative measures of earnings surprises

This table reports the coefficient, t-statistic, and adjusted R2 of contemporaneous relations between quarterly returns and earningssurprises, and with the interaction of firm-level and macroeconomic uncertainty:

Rit = α0 +5∑j=2

αjDjit + α6DMt + β1dESit +

5∑j=2

βjdESit ×Djit + γ1dESit ×DMt +5∑j=2

γjdESit ×Djit ×DMt +Xit + εit,

where dESit is seasonally differenced earnings scaled by book value (S = B) or earnings (S = E) for firm i at time t. Rit is thereturn for firm i at time t. DMt is a dummy variable assigned with 1 if the market-level ambiguity is above its historic mean,and zero otherwise. The market-level ambiguity is defined as the uncertainty part of the dispersion of forecasts for next-periodreal GDP Growth. Djit is the uncertainty part of analyst earnings forecast dispersion measuring firm-specific uncertainty foruncertainty quintile j at time t. D5

it is the quintile with highest uncertainty and so forth. The first quintile is embedded inthe no-dummy variable. Earnings are excluding extraordinary items. Xit is the vector of control variables including log size(LSIZEit), log book-to-market ratio (LBMit) and the market return (RMt ). Earnings, book equity, share price, and sharesoutstanding data are from Compustat. Analysts’ forecasts are from IBES. Individual forecasts for real GDP growth are from theSurvey of Professional Forecasters at the Federal Reserve Bank of Philadelphia. The firms are subject to the following screeningcriteria: 1) data are available for earnings, price, common shares outstanding, book equity this quarter and four quarters prior;2) dates are aligned with calendar quarters; 3) price is larger than $1; 4) at least two analysts’ forecasts for EPS; 5) not in thetop and bottom 1 percentile of firms ranked by dES. Standard errors are given in parentheses and are clustered by firm andquarter. ∗∗∗, ∗∗, and ∗ indicate significance at the 1%, 5%, and 10% level, respectively. Our sample includes all the firms onNYSE, AMEX, and NASDAQ from 1986 Q1 to 2014 Q4.

40

Paper #900365

Table 6 continued.

(1) (2) (3) (4) (5) (6)

EB EE

dEPit0.395∗∗∗

(0.040)0.143∗∗

(0.059)0.145∗∗

(0.061)0.905∗∗∗

(0.085)0.358∗∗

(0.179)0.537∗∗∗

(0.195)

dEPit ×D2it

0.113(0.082)

0.178∗∗

(0.087)0.195(0.211)

0.159(0.219)

dEPit ×D3it

0.107∗

(0.058)0.122∗

(0.073)0.142(0.180)

0.078(0.208)

dEPit ×D4it

0.173∗∗

(0.074)0.200∗∗

(0.081)0.466∗∗∗

(0.177)0.302∗

(0.160)

dEPit ×D5it

0.445∗∗∗

(0.077)0.397∗∗∗

(0.085)0.849∗∗∗

(0.182)0.522∗∗∗

(0.196)

DMt0.016∗∗

(0.007)0.016∗∗

(0.007)

dEPit ×DMt0.009(0.127)

-0.325(0.354)

dEPit ×D2it ×DMt

-0.115(0.163)

0.103(0.421)

dEPit ×D3it ×DMt

-0.029(0.130)

0.161(0.363)

dEPit ×D4it ×DMt

-0.051(0.158)

0.332(0.351)

dEPit ×D5it ×DMt

0.094(0.161)

0.633∗

(0.360)

D2it

-0.003(0.002)

-0.003(0.002)

-0.002(0.002)

-0.002(0.002)

D3it

-0.001(0.003)

-0.001(0.003)

-0.001(0.003)

-0.001(0.003)

D4it

-0.006(0.004)

-0.006(0.004)

-0.004(0.004)

-0.004(0.004)

D5it

-0.034∗∗∗

(0.005)-0.033∗∗∗

(0.005)-0.030∗∗∗

(0.006)-0.029∗∗∗

(0.006)

RMt1.130∗∗∗

(0.053)1.128∗∗∗

(0.053)1.131∗∗∗

(0.050)1.140∗∗∗

(0.053)1.138∗∗∗

(0.053)1.142∗∗∗

(0.050)

LSIZEit-0.003∗

(0.002)-0.004∗∗

(0.002)-0.004∗∗

(0.002)-0.004∗∗

(0.002)-0.005∗∗∗

(0.002)-0.005∗∗∗

(0.002)

LBMit0.014∗∗∗

(0.005)0.016∗∗∗

(0.005)0.016∗∗∗

(0.005)0.010∗∗∗

(0.004)0.012∗∗∗

(0.004)0.012∗∗∗

(0.004)

Const0.042∗∗

(0.017)0.060∗∗∗

(0.016)0.051∗∗∗

(0.015)0.045∗∗∗

(0.017)0.061∗∗∗

(0.017)0.052∗∗∗

(0.016)

Obs. 76,039 76,039 76,039 75,367 75,367 75,367

R2 19.9% 20.3% 20.4% 19.6% 20.0% 20.1%

41

Paper #900365

Table 7: Portfolio-level regressions: Alternative measures of earnings surprises

This table reports the coefficient, t-statistic, and adjusted R2 of contemporaneous relations between quarterly portfolio returnsand earnings surprises, and with the interaction of firm-level and macroeconomic uncertainty:

Rpt = α0 +5∑j=2

αjDjpt + α6DMt + β1dESpt +

5∑j=2

βjdESpt ×Djpt + γ1dESpt ×DMt +5∑j=2

γjdESpt ×Djpt ×DMt +Xpt + εpt,,

where dESpt is aggregate seasonally differenced earnings (dE) scaled by book value (S = B), or earnings (S = E) for portfolio pat time t. Rpt is the return for portfolio p at time t. DMt is a dummy variable assigned with 1 if the macroeconomic uncertaintyis above its mean, and zero otherwise. The macroeconomic uncertainty is defined as the uncertainty part of the dispersionof forecasts for next-period real GDP Growth. Djpt is the uncertainty part of analyst earnings forecast dispersion measuring

firm-specific uncertainty for uncertainty quintile j at time t. D5pt is the quintile with highest uncertainty and so forth. The

first quintile is embedded in the no-dummy variable. Xpt is the vector of control variables including log size (LSIZEpt), logbook-to-market ratio (LBMpt) and the market return (RMt ). Earnings are excluding extraordinary items. Earnings, book equity,share price, and shares outstanding data are from Compustat. Analysts’ forecasts are from IBES. Individual forecasts for realGDP growth are from the Survey of Professional Forecasters at the Federal Reserve Bank of Philadelphia. The firms are subjectto the following screening criteria: 1) data are available for earnings, price, common shares outstanding, book equity this quarterand four quarters prior; 2) dates are aligned with calendar quarters; 3) price is larger than $1; 4) at least two analysts’ forecastsfor EPS; 5) not in the top and bottom 1 percentile of firms ranked by dES. Standard errors are given in parentheses and areclustered by portfolio. ∗∗∗, ∗∗, and ∗ indicate significance at the 1%, 5%, and 10% level, respectively. Our sample includes allthe firms on NYSE, AMEX, and NASDAQ from 1986 Q1 to 2014 Q4.

42

Paper #900365

Table 7 continued.

(1) (2) (3) (4) (5) (6)

EB EE

dEPpt1.877∗∗

(0.439)-0.222∗

(0.100)0.126(0.231)

6.951∗∗∗

(1.450)-4.587∗∗∗

(0.416)-1.075(1.106)

dEPpt ×D2pt

0.639∗∗∗

(0.024)0.161(0.158)

7.536∗∗∗

(0.157)4.769∗∗∗

(0.426)

dEPpt ×D3pt

1.039∗∗∗

(0.074)1.312∗∗∗

(0.091)6.165∗∗∗

(0.432)7.613∗∗∗

(0.712)

dEPpt ×D4pt

1.769∗∗∗

(0.096)1.030∗∗∗

(0.110)10.46∗∗∗

(0.438)6.049∗∗∗

(0.923)

dEPpt ×D5pt

2.506∗∗∗

(0.093)1.304∗∗∗

(0.249)12.75∗∗∗

(0.420)4.776∗∗∗

(1.169)

DMt0.007(0.005)

0.008(0.005)

dEPpt ×DMt-0.687∗

(0.315)-5.684∗∗

(1.344)

dEPpt ×D2pt ×DMt

1.007∗∗∗

(0.140)5.031∗∗∗

(0.404)

dEPpt ×D3pt ×DMt

-0.473∗∗

(0.152)-2.373∗∗

(0.747)

dEPpt ×D4pt ×DMt

1.743∗∗∗

(0.163)9.049∗∗∗

(1.167)

dEPpt ×D5pt ×DMt

2.029∗∗∗

(0.390)12.44∗∗∗

(1.635)

D2pt

-0.011∗∗∗

(0.002)-0.011∗∗∗

(0.002)-0.016∗∗∗

(0.002)-0.015∗∗∗

(0.002)

D3pt

-0.024∗∗∗

(0.003)-0.024∗∗∗

(0.003)-0.025∗∗∗

(0.003)-0.025∗∗∗

(0.003)

D4pt

-0.037∗∗∗

(0.003)-0.035∗∗∗

(0.003)-0.040∗∗∗

(0.004)-0.038∗∗∗

(0.004)

D5pt

-0.057∗∗∗

(0.004)-0.053∗∗∗

(0.005)-0.058∗∗∗

(0.005)-0.052∗∗∗

(0.005)

RMt0.887∗∗∗

(0.015)0.884∗∗∗

(0.023)0.882∗∗∗

(0.024)0.896∗∗∗

(0.012)0.887∗∗∗

(0.022)0.883∗∗∗

(0.020)

LSIZEpt0.006(0.007)

-0.012(0.008)

-0.010(0.009)

0.003(0.007)

-0.015(0.008)

-0.013(0.008)

LBMpt0.069∗∗∗

(0.011)0.084∗∗∗

(0.009)0.086∗∗∗

(0.009)0.060∗∗∗

(0.011)0.075∗∗∗

(0.011)0.078∗∗∗

(0.012)

Const0.034(0.054)

0.209∗∗

(0.053)0.195∗∗

(0.062)0.049(0.049)

0.230∗∗∗

(0.053)0.216∗∗∗

(0.058)

Obs. 600 600 600 600 600 600

R2 24.1% 27.2% 27.9% 24.0% 27.2% 28.3%

43

Paper #900365

Table 8: Market level regressions: Alternative measures of earnings surprises

This table reports the coefficient, t-statistic, and adjusted R2 of contemporaneous relations between quarterly returns and earningssurprises, and with the interaction of macroeconomic forecasts dispersion measure:

RMt = β0 + β1dESt + β2DMt + β3dESt ×DMt + εt,

where dESt is aggregate seasonally differenced earnings (dE) scaled by book value (S = B), or earnings (S = E) at time t. RMtis the market return at time t. DMt is a dummy variable assigned with 1 if the macroeconomic uncertainty is above its mean, andzero otherwise. The macroeconomic uncertainty is defined as the uncertainty part of the dispersion of forecasts for next-periodreal GDP Growth. Earnings are excluding extraordinary items. Earnings, book equity, share price, and shares outstandingdata are from Compustat. Analysts’ forecasts are from IBES. Individual forecasts for real GDP growth are from the Survey ofProfessional Forecasters at the Federal Reserve Bank of Philadelphia. The firms are subject to the following screening criteria:1) data are available for earnings, price, common shares outstanding, book equity this quarter and four quarters prior; 2) datesare aligned with calendar quarters; 3) price is larger than $1; 4) at least two analysts’ forecasts for EPS; 5) not in the top andbottom 1 percentile of firms ranked by dES. Standard errors are given in parentheses and are corrected for heteroscedasticityand autocorrelation. ∗∗∗, ∗∗, and ∗ indicate significance at the 1%, 5%, and 10% level, respectively. Our sample includes all thefirms on NYSE, AMEX, and NASDAQ from 1986 Q1 to 2014 Q4.

(1) (2) (3) (4) (5) (6)

EB EE

dEPt1.795(1.143)

1.891(1.213)

1.715(1.266)

7.703∗

(4.640)8.070(4.927)

7.714(5.157)

DMt0.006(0.015)

0.005(0.016)

0.005(0.015)

0.005(0.016)

dEPt ×DMt0.296(2.227)

0.616(9.213)

Const0.019∗∗

(0.008)0.016(0.011)

0.017(0.012)

0.020∗∗

(0.008)0.017(0.011)

0.017(0.011)

Obs. 120 120 120 120 120 120

R2 3.8% 3.9% 3.9% 3.7% 3.8% 3.8%

44

Paper #900365

Table 9: Firm-level regressions: Public information ambiguity

This table reports estimation results of the following panel regression of quarterly returns on earnings surprises, and with theinteraction of firm-level and market-level ambiguity:

Rit = α0 +5∑j=2

αjDjit + α6DMt + β1dESit +

5∑j=2

βjdESit ×Djit + γ1dESit ×DMt +5∑j=2

γjdESit ×Djit ×DMt +Xit + εit,

where dESit is seasonally differenced earnings scaled by by price (S = P ), book value (S = B) or earnings (S = E) for firmi at time t. Rit is the return for firm i at time t. Both firm-level and market level ambiguity are based on public informationcomponents only. DMt is a dummy variable assigned with 1 if the market-level ambiguity is above its historic mean, and zerootherwise. The macroeconomic uncertainty is based on the Barron, Kim, Lim and Stevens (1998)’s consensus measure defined asthe ratio of common uncertainty based on public information to total uncertainty based on both public and private information,calculated using individual forecasts for next-period real GDP Growth. Djit is the dummy variable that is equal to 1 if firm i fallsinto js quintile of firms-specific ambiguity based on public information. D5

it is the quintile with highest uncertainty and so forth.The first quintile is embedded in the no-dummy variable. Xit is the vector of control variables including log size (LSIZEit),log book-to-market ratio (LBMit) and the market return (RMt ). Earnings are excluding extraordinary items. Earnings, bookequity, share price, and shares outstanding data are from Compustat. Analysts’ forecasts are from IBES. Individual forecasts forreal GDP growth are from the Survey of Professional Forecasters at the Federal Reserve Bank of Philadelphia. The firms aresubject to the following screening criteria: 1) data are available for earnings, price, common shares outstanding, book equity thisquarter and four quarters prior; 2) dates are aligned with calendar quarters; 3) price is larger than $1; 4) at least two analysts’forecasts for EPS; 5) not in the top and bottom 1 percentile of firms ranked by dES. Standard errors are given in parenthesesand are clustered by firm and quarter. ∗∗∗, ∗∗, and ∗ indicate significance at the 1%, 5%, and 10% level, respectively. Our sampleincludes all the firms on NYSE, AMEX, and NASDAQ from 1986 Q1 to 2014 Q4.

45

Paper #900365

Table 9 continued.

(1) (2) (3) (4) (5) (6)

EP EB EE

dEPit0.258(0.514)

0.226(0.346)

0.133(0.156)

0.124(0.107)

0.613∗

(0.333)0.608∗∗∗

(0.230)

dEPit ×D2it

0.269(0.296)

0.329(0.297)

0.139(0.127)

0.177(0.115)

-0.199(0.292)

-0.091(0.246)

dEPit ×D3it

0.192(0.220)

0.216(0.167)

0.138(0.119)

0.164(0.100)

-0.097(0.230)

-0.081(0.208)

dEPit ×D4it

0.462(0.377)

0.546∗

(0.301)0.160(0.126)

0.182∗

(0.102)0.263(0.289)

0.249(0.228)

dEPit ×D5it

0.775∗∗

(0.377)0.848∗∗∗

(0.294)0.415∗∗∗

(0.153)0.435∗∗∗

(0.127)0.535∗

(0.315)0.460∗∗

(0.234)

DMt-0.000(0.019)

0.013∗∗

(0.006)-0.002(0.020)

0.012∗

(0.007)-0.002(0.020)

0.012∗

(0.007)

dEPit ×DMt0.422(0.626)

0.244(0.438)

0.080(0.196)

0.077(0.140)

0.000(0.476)

-0.106(0.339)

dEPit ×D2it ×DMt

-0.004(0.473)

-0.015(0.441)

-0.146(0.176)

-0.170(0.163)

0.208(0.446)

0.026(0.428)

dEPit ×D3it ×DMt

0.146(0.388)

-0.091(0.307)

-0.027(0.148)

-0.070(0.128)

0.092(0.348)

0.188(0.292)

dEPit ×D4it ×DMt

-0.464(0.495)

-0.458(0.427)

-0.065(0.170)

-0.082(0.152)

-0.034(0.379)

0.012(0.321)

dEPit ×D5it ×DMt

-0.114(0.490)

-0.030(0.410)

0.023(0.192)

-0.005(0.168)

0.339(0.414)

0.388(0.324)

D2it

0.005∗∗

(0.002)0.004∗

(0.002)0.004∗∗

(0.002)0.003(0.002)

0.005∗∗

(0.002)0.004∗

(0.002)

D3it

0.007∗∗

(0.003)0.005(0.003)

0.006∗∗

(0.003)0.004(0.003)

0.007∗∗

(0.003)0.005(0.003)

D4it

0.009∗∗∗

(0.003)0.005(0.004)

0.009∗∗

(0.004)0.004(0.004)

0.009∗∗

(0.004)0.005(0.004)

D5it

-0.014∗∗∗

(0.005)-0.022∗∗∗

(0.005)-0.017∗∗∗

(0.005)-0.026∗∗∗

(0.005)-0.014∗∗

(0.005)-0.022∗∗∗

(0.005)

RMt1.122∗∗∗

(0.049)1.133∗∗∗

(0.051)1.144∗∗∗

(0.052)

LSIZEit-0.004∗∗

(0.002)-0.004∗∗

(0.002)-0.004∗∗

(0.002)

LBMit0.011∗∗∗

(0.004)0.015∗∗∗

(0.005)0.011∗∗

(0.004)

Const0.036∗∗∗

(0.013)0.043∗∗∗

(0.016)0.037∗∗∗

(0.014)0.046∗∗∗

(0.017)0.038∗∗∗

(0.013)0.048∗∗∗

(0.017)

Obs. 77,237 75,823 77,063 76,039 76,811 75,367

R2 1.2% 20.0% 1.3% 20.3% 1.1% 20.0%

46

Paper #900365

Table 10: Portfolio-level regressions: Public information ambiguity

This table reports the coefficient, t-statistic, and adjusted R2 of contemporaneous relations between quarterly portfolio returnsand earnings surprises, and with the interaction of firm-level and macroeconomic uncertainty:

Rpt = α0 +5∑j=2

αjDjpt + α6DMt + β1dESpt +

5∑j=2

βjdESpt ×Djpt + γ1dESpt ×DMt +5∑j=2

γjdESpt ×Djpt ×DMt +Xpt + εpt,,

where dESpt is aggregate seasonally differenced earnings (dE) scaled by by price (S = P ), book value (S = B), or earnings(S = E) for portfolio p at time t. Rpt is the return for portfolio p at time t. DMt is a dummy variable assigned with 1 ifthe macroeconomic uncertainty is above its mean, and zero otherwise. The macroeconomic uncertainty is based on the Barron,Kim, Lim and Stevens (1998)’s consensus measure defined as the ratio of common uncertainty based on public information tototal uncertainty based on both public and private information, calculated using individual forecasts for next-period real GDPGrowth. Djpt is the dummy variable that is equal to 1 if portfolio p falls into js quintile of firms-specific ambiguity based on

public information. D5pt is the quintile with highest uncertainty and so forth. The first quintile is embedded in the no-dummy

variable. Xpt is the vector of control variables including log size (LSIZEpt), log book-to-market ratio (LBMpt) and the marketreturn (RMt ). Earnings are excluding extraordinary items. Earnings, book equity, share price, and shares outstanding data arefrom Compustat. Analysts’ forecasts are from IBES. Individual forecasts for real GDP growth are from the Survey of ProfessionalForecasters at the Federal Reserve Bank of Philadelphia. The firms are subject to the following screening criteria: 1) data areavailable for earnings, price, common shares outstanding, book equity this quarter and four quarters prior; 2) dates are alignedwith calendar quarters; 3) price is larger than $1; 4) at least two analysts’ forecasts for EPS; 5) not in the top and bottom 1percentile of firms ranked by dES. Standard errors are given in parentheses and are clustered by portfolio. ∗∗∗, ∗∗, and ∗ indicatesignificance at the 1%, 5%, and 10% level, respectively. Our sample includes all the firms on NYSE, AMEX, and NASDAQ from1986 Q1 to 2014 Q4.

47

Paper #900365

Table 10 continued.

(1) (2) (3) (4) (5) (6)

EP EB EE

dEPpt-0.068(0.649)

-3.809∗∗∗

(0.713)0.466∗

(0.205)-0.535∗

(0.242)0.880(0.815)

-3.137∗∗

(1.031)

dEPpt ×D2pt

0.248∗∗∗

(0.020)1.672∗∗∗

(0.131)-0.828∗∗∗

(0.011)0.217∗∗∗

(0.040)-1.966∗∗∗

(0.066)1.663∗∗∗

(0.103)

dEPpt ×D3pt

4.683∗∗∗

(0.242)5.608∗∗∗

(0.416)1.182∗∗∗

(0.069)1.439∗∗∗

(0.089)7.645∗∗∗

(0.269)7.562∗∗∗

(0.687)

dEPpt ×D4pt

0.043(0.399)

4.012∗∗∗

(0.502)0.021(0.066)

0.884∗∗∗

(0.133)5.031∗∗∗

(0.528)6.389∗∗∗

(0.848)

dEPpt ×D5pt

1.430∗

(0.631)5.627∗∗∗

(0.696)0.877∗∗

(0.201)2.020∗∗∗

(0.251)3.644∗∗∗

(0.791)7.765∗∗∗

(1.057)

DMt-0.005(0.005)

-0.003(0.006)

-0.002(0.006)

-0.002(0.005)

-0.002(0.004)

-0.001(0.005)

dEPpt ×DMt-2.722∗

(1.014)1.177(1.066)

-1.166∗∗

(0.307)0.180(0.318)

-7.229∗∗∗

(1.102)-3.438∗∗

(1.214)

dEPpt ×D2pt ×DMt

6.657∗∗∗

(0.001)4.114∗∗∗

(0.152)2.426∗∗∗

(0.028)1.178∗∗∗

(0.053)12.55∗∗∗

(0.102)9.522∗∗∗

(0.455)

dEPpt ×D3pt ×DMt

4.577∗∗∗

(0.367)2.488∗∗∗

(0.430)1.379∗∗∗

(0.078)1.075∗∗∗

(0.091)5.084∗∗∗

(0.250)4.485∗∗∗

(0.614)

dEPpt ×D4pt ×DMt

8.414∗∗∗

(0.659)5.593∗∗∗

(0.715)2.690∗∗∗

(0.146)1.890∗∗∗

(0.173)12.80∗∗∗

(0.694)13.28∗∗∗

(0.978)

dEPpt ×D5pt ×DMt

6.278∗∗∗

(1.124)2.727∗

(1.222)2.572∗∗∗

(0.361)1.062∗

(0.384)12.18∗∗∗

(1.246)8.532∗∗∗

(1.462)

D2pt

0.002∗∗∗

(0.000)-0.002∗∗∗

(0.000)0.006∗∗∗

(0.000)-0.000(0.000)

0.004∗∗∗

(0.000)-0.002∗∗∗

(0.000)

D3pt

-0.005∗∗∗

(0.000)-0.017∗∗∗

(0.002)-0.004∗∗∗

(0.000)-0.017∗∗∗

(0.002)-0.005∗∗∗

(0.000)-0.016∗∗∗

(0.002)

D4pt

-0.002∗∗∗

(0.000)-0.027∗∗∗

(0.003)-0.001∗∗∗

(0.000)-0.024∗∗∗

(0.003)-0.007∗∗∗

(0.000)-0.028∗∗∗

(0.003)

D5pt

-0.007∗∗∗

(0.001)-0.046∗∗∗

(0.005)-0.001∗

(0.001)-0.044∗∗∗

(0.004)-0.003∗∗∗

(0.001)-0.042∗∗∗

(0.005)

RMt0.901∗∗∗

(0.030)0.880∗∗∗

(0.031)0.889∗∗∗

(0.029)

LSIZEpt-0.009(0.009)

-0.007(0.010)

-0.009(0.009)

LBMpt0.092∗∗∗

(0.008)0.091∗∗∗

(0.009)0.085∗∗∗

(0.009)

Const0.034∗∗∗

(0.003)0.198∗∗

(0.065)0.031∗∗∗

(0.003)0.175∗

(0.067)0.032∗∗∗

(0.003)0.186∗

(0.067)

Obs. 600 600 600 600 600 600

R2 5.7% 26.9% 7.7% 27.8% 8.4% 28.4%

48

Paper #900365

Table 11: Market level regressions: Public information ambiguity

This table reports the coefficient, t-statistic, and adjusted R2 of contemporaneous relations between quarterly returns and earningssurprises, and with the interaction of macroeconomic forecasts dispersion measure:

RMt = β0 + β1dESt + β2DMt + β3dESt ×DMt + εt,

where dESt is aggregate seasonally differenced earnings (dE) scaled by price (S = P ), book value (S = B), or earnings (S = E)at time t. RMt is the market return at time t. DMt is a dummy variable assigned with 1 if the macroeconomic uncertainty isabove its mean, and zero otherwise. The macroeconomic uncertainty is based on the Barron, Kim, Lim and Stevens (1998)’sconsensus measure defined as the ratio of common uncertainty based on public information to total uncertainty based on bothpublic and private information, calculated using individual forecasts for next-period real GDP Growth. Earnings are excludingextraordinary items. Earnings, book equity, share price, and shares outstanding data are from Compustat. Analysts’ forecastsare from IBES. Individual forecasts for real GDP growth are from the Survey of Professional Forecasters at the Federal ReserveBank of Philadelphia. The firms are subject to the following screening criteria: 1) data are available for earnings, price, commonshares outstanding, book equity this quarter and four quarters prior; 2) dates are aligned with calendar quarters; 3) price is largerthan $1; 4) at least two analysts’ forecasts for EPS; 5) not in the top and bottom 1 percentile of firms ranked by dES. Standarderrors are given in parentheses and are corrected for heteroscedasticity and autocorrelation. ∗∗∗, ∗∗, and ∗ indicate significanceat the 1%, 5%, and 10% level, respectively. Our sample includes all the firms on NYSE, AMEX, and NASDAQ from 1986 Q1 to2014 Q4.

(1) (2) (3)

EP EB EE

dEPt0.536(3.324)

1.715(1.266)

7.714(5.157)

DMt-0.009(0.016)

0.005(0.016)

0.005(0.016)

dEPt ×DMt5.444(6.617)

0.296(2.227)

0.616(9.213)

Const0.027∗∗

(0.012)0.017(0.012)

0.017(0.011)

Obs. 120 120 120

R2 2.3% 3.9% 3.8%

49

Paper #900365