Sources of investor uncertainty and expected stock returns
Chad Larson
Olin School of Business – Washington University in St. Louis
[email protected]
Robert J. Resutek †
Tuck School of Business – Dartmouth
[email protected]
July 2013
Abstract
This study examines the role of investor uncertainty in predicting cross-sectional stock returns. We develop
novel, forward-looking estimates of two sources of investor uncertainty about firm value, future cash flow
uncertainty and uncertainty attributable to information quality. Distinct from prior studies, our forwardlooking estimates of uncertainty represent conditional volatilities surrounding expectations of future cash flows
and accruals. Our tests reveal a strong negative relation between cash flow uncertainty and future returns with
predictive magnitudes similar to those on book-to-market and accruals. In addition, incremental to cash flow
uncertainty, we find a strong positive association between information quality uncertainty and future stock
returns. Collectively, our study offers the first direct empirical evidence that different sources of investor
uncertainty can have countervailing effects on firm value.
JEL Codes: G14, M41
Key Words: Earnings quality, earnings uncertainty, earnings management, information uncertainty
Data Availability: Data is available from public sources as identified in the text.
† Contact author. We thank Kristian Allee, Peter Demerjian, Weili Ge, Cristi Gleason, Bill Mayew, Sarah
McVay, Steve Monahan, Maria Ogneva, Chris Parsons, Cathy Schrand, Gwen Wu, workshop participants at
Dartmouth, Columbia, Penn State, Tillburg, 2012 AAA annual meeting, BYU’s Accounting Research
Symposium, and Washington University in Saint Louis for helpful comments on this study and earlier drafts.
Abstract
This study examines the role of investor uncertainty in predicting cross-sectional stock returns. We develop
novel, forward-looking estimates of two sources of investor uncertainty about firm value, future cash flow
uncertainty and uncertainty attributable to information quality. Distinct from prior studies, our forwardlooking estimates of uncertainty represent conditional volatilities surrounding expectations of future cash flows
and accruals. Our tests reveal a strong negative relation between cash flow uncertainty and future returns with
predictive magnitudes similar to those on book-to-market and accruals. In addition, incremental to cash flow
uncertainty, we find a strong positive association between information quality uncertainty and future stock
returns. Collectively, our study offers the first direct empirical evidence that different sources of investor
uncertainty can have countervailing effects on firm value.
1. Introduction
Over the past fifteen years, an extensive series of theoretical and empirical studies have emerged in the finance
and accounting literatures examining the effect investor uncertainty has on firm value (Hirshleifer 2001; Pastor
and Veronesi 2003; Jiang, Lee, and Zhang 2005; Johnson 2004; Lambert, Leuz, and Verrecchia 2007).
However, how investor uncertainty affects firm value, and the types (or sources) of investor uncertainty that
affect firm value, are still areas of continued debate. The goal of this study is to empirically disentangle the
incremental predictive power of two different sources of investor uncertainty for firm value (as proxied by
future returns), one related to uncertainty in future fundamental performance and the other related to how that
fundamental performance is reported.
Distinct from prior empirical studies, we define investor uncertainty as the conditional volatility surrounding
investors’ expectations of future performance. That is, given an expectation of future performance, such as
expected cash flows, uncertainty represents the distribution surrounding that expectation (i.e., uncertainty is a
measure of precision). We view this interpretation of uncertainty as distinct from theoretical constructs of
information asymmetry and time-series variation in past performance (e.g. past earnings volatility; realized
return volatility) and more in line with the forward-looking uncertainty constructs of Lambert et al. (2007).
Two distinct sets of theories exist describing the relation between investor uncertainty and firm value. One set
emphasizes a negative association between investor uncertainty and firm value (e.g., Merton 1987; Lambert et
al. 2007) while the other set emphasizes a positive association between investor uncertainty and firm value
(Pastor and Veronesi 2003; Johnson 2004). Distinguishing between the two explanations and distilling the
relative economic significance to firm value of these two different sources of investor uncertainty is important
to the accounting literature, both to understand the economic forces of uncertainty on equity valuations and to
better understand how financial reporting and disclosure choices affect firm value. Although prior studies
suggest the existence of different sources of investor uncertainty (Hirshleifer 2001; Jiang et al. 2005), and
theoretical arguments allude to the possibility that different sources of investor uncertainty could have different
effects on expected stock returns (Johnson 2004), prior empirical studies have not explored this possibility.
Consistent with prior studies (Hirshleifer 2001; Zhang 2006), we view investor uncertainty as stemming from
two primary sources: fundamental uncertainty and information quality uncertainty. We interpret fundamental
uncertainty as capturing how precisely, absent estimation error attributable to accrual accounting, a firm’s
future economic performance can be estimated. We use uncertainty in next year’s cash flows as our proxy for
fundamental performance uncertainty.1 We interpret the second source of investor uncertainty, information
quality uncertainty, as capturing how uncertain investors are about a firm’s future performance because of
accrual accounting. That is, because ‘true’ economic performance (Et*) is not observed, investors must make
inferences about it from reported earnings (Et). Thus, this source of investor uncertainty relates to uncertainty
in the mapping of accrual earnings into realized cash flows (i.e., uncertainty in the difference between Et* and
Et). As in prior studies, we use a form of residual accrual volatility to estimate information quality uncertainty
(Francis et al. 2004; Ogneva 2012).
Our central empirical result is that the two components of investor uncertainty, cash flow uncertainty and
information quality uncertainty, have significant, but countervailing, effects on firm value. Consistent with
theories in the parameter uncertainty literature (Johnson 2004), we find a strong negative relation between cash
flow uncertainty and future returns. In predictive regressions of future monthly stock returns over the standard
twelve month horizon (controlling for size, book-to-market, and accruals), slopes on cash flow uncertainty are
consistently negative, with slope precisions ranging between 3.0 to 5.0 standard errors from zero. The strength
and duration of this result is important to note since the predictive power of commonly used proxies for
investor uncertainty, such as forecast dispersion or realized return volatility, is significantly weaker and decays
after one to three months (Diether et al. 2002; Jiang et al. 2005).
With respect to information quality uncertainty, we find a consistently positive relation with future returns
after controlling for cash flow uncertainty (and size, book-to-market, and accruals). In predictive regressions
of future monthly returns, the slopes on information quality uncertainty are consistently positive, with point
estimates between 2.0 and 3.5 standard errors from zero in most samples. Similar in spirit to Ogneva (2012),
1
We acknowledge cash flows are viewed by some as a less complete measure of economic performance, compared
to earnings. However, because cash flows are free from accrual estimation errors and are strongly correlated with
earnings, we believe cash flow uncertainty allows us to make cleaner empirical inferences.
2
we find that a firm’s propensity to realize large future cash flow shocks affects inferences on the predictive
power of information quality for future returns. However, by controlling for a firm’s propensity to realize
significant future cash flow shocks using a variable estimable in the current period (our cash flow uncertainty
variable), we find a similar (and stronger) positive association between information quality and future stock
returns. To the best of our knowledge, we provide the first empirical evidence that variation in a conventional,
accounting-based measure of information quality positively predicts future stock returns.
Our study makes several other contributions to the empirical literatures examining the predictive power of
investor uncertainty for future stock returns.
First, we propose and validate a forward-looking, firm-specific measure of cash flow uncertainty. The premise
of our measure rests upon the notion that the uncertainty construct represents the second moment of a random
variable (expected future cash flows). Accordingly, estimates of uncertainty will only be as good as their first
moment estimates. Building on Barber and Lyon (1996), Blouin, Core, and Guay (2010), and Donelson and
Resutek (2013), we construct a matched firm expectation model to estimate investor expectations of future
cash flows and the uncertainty associated with these expectations. Our uncertainty measures are firm specific,
map neatly into the forward-looking uncertainty constructs discussed in theoretical studies (Lambert et al.
2007), and require a minimal time-series of realizations. Across several specification tests, we show that our
uncertainty proxies are reasonably well specified (more precise and less biased than estimates derived from
time-series models) and are associated with future firm characteristics in a direction consistent with theory.
Second, we provide new evidence on the predictive power of the components of investor uncertainty for firm
value. Prior studies suggest total investor uncertainty is comprised of two correlated, but distinct, types of
uncertainty: fundamental uncertainty and uncertainty attributable to the information environment (Hirshleifer
2001; Zhang 2006). However, prior work has not directly examined the incremental predictive power of these
two sources of investor uncertainty for firm value, suggesting instead that both types of uncertainty affect firm
value similarly. By directly estimating the individual uncertainty sources, we provide the first evidence that
uncertainty in future fundamental performance, and not uncertainty attributable to a firm’s information quality,
3
explains the negative relation with future returns which prior studies attribute to a generically defined
‘uncertainty’ variable (Johnson 2004; Jiang et al. 2005; Zhang 2006; Ang et al. 2006; 2009).
Third, we provide the first empirical evidence on time-series variation in the predictive properties of
information quality for expected stock returns.
We find that while investor uncertainty attributable to
information quality is smaller (in absolute magnitude) compared to fundamental uncertainty, the relation is
surprisingly stable over our full sample period. Further, in contrast to other prominent predictors of future
returns such as accruals, book-to-market, and size, the two components of investor uncertainty are much more
stable predictors of future stock returns over the sample period.
The remainder of our study proceeds as follows. Section 2 discusses prior literature and motivates our
research question. Section 3 describes our measures of uncertainty and discusses summary statistics. Section
4 reports results from specification tests of our measures of uncertainty relative to other measures derived from
time-series variation in earnings and cash flows. Section 5 documents relations between our uncertainty
measures and future stock returns. Section 6 concludes.
2. Prior literature and motivation
The accounting and finance propose several distinct theories on the relation between investor uncertainty and
cost of equity capital. We briefly review the literature, discuss the empirical relations prior studies have noted
with respect to how investor uncertainty explains future stock returns, and use this discussion to motivate our
empirical design and tests.
2.1 The relation between investor uncertainty and expected stock returns
Conventional asset pricing theory suggests a firm’s expected stock return—its cost of equity capital (re)—is a
function of how the firm’s expected cash flows covary with macroeconomic risk factors. Early theory suggests
a firm’s cost of equity capital is simply a function of the firm’s exposure to an aggregate ‘market’ risk factor
(Sharpe 1964; Lintner 1965), theory supported by subsequent empirical studies (Jensen, Black, Scholes 1972;
Fama and Macbeth 1973). In the early 1990’s, overwhelming empirical evidence emerged suggesting the
correlation of a firm’s cash flows to the cash flows of the aggregate market, CAPM beta, was insufficient to
explain cross-sectional variation in expected stock returns (Fama and French 1992; 1996).
4
From this
‘discovery’, a large literature emerged exploring the predictive power of additional risk-related firm
characteristics for expected stock returns: book-to-market and firm size (Fama and French 1992; 1993);
liquidity (Pastor and Stambaugh 2003); investment and profitability (Fama and French 2006; Chen, NovyMarx, and Zhang 2011). While these characteristics (or factors constructed from these characteristics) vary in
terms of their predictive power for future returns, theoretically they share a common bond: their variation is
explained by correlative relations between a firm’s cash flows and macroeconomic risk factors, suggestive that
these characteristics explain future returns because their variation is associated with systematic risk.2
Over the past ten years, a series of alternative theoretical studies have explored conditions in which a firm’s
cost of equity is explained by two other ‘idiosyncratic’ sources of risk, one relating to uncertainty attributable
to a firm’s information quality and the other relating to uncertainty in a firm’s cash flow process. A key
distinction between these studies, and those noted above, is that the sources of risk explored in these two sets
of studies is not due to how a firm’s cash flows covary with a macroeconomic risk factor. Rather, the sources
of risk explored in these studies relate to how precisely investors can estimate a firm’s future cash flows
irrespective of the behavior of the macro risk factors.
The first group of studies suggests that investor uncertainty attributable to a firm’s information quality can
affect its cost of capital (Easley and O’Hara 2004; Lambert et al. 2007; 2012; Hughes, Liu, and Liu 2007).
While the theoretical mechanisms differ across these studies, a general prediction suggests that the more
uncertain investors are about how precisely GAAP earnings capture ‘true’ economic performance—i.e., the
wider the dispersion around the expected difference between Et and Et*—the higher is the firm’s cost of
capital. The key innovation, or insight, provided by these studies centers on the link between the precision
with which firm-specific cash flows can be estimated and the systematic risk of the firm. By linking investor
uncertainty to information asymmetry (Easley and O’Hara; Hughes et al. 2007) or estimation risk (Lambert et
al. 2007), these asset pricing models provide a theoretical link for why a firm’s ‘idiosyncratic’ uncertainty
could increase the firm’s expected stock returns.
Despite theoretical predictions, conventional asset pricing tests have generally failed to find a significant
positive relation between investor uncertainty associated with information quality and future returns (McInnis
2
Of course, many of the firm characteristics proposed in prior studies as proxies for systematic risk can also be
interpreted as proxies for mispricing (Shleifer 2003).
5
2010).3 In fact, some prior empirical results suggest firms with poor information quality actually realize lower
cost of capital – a relation that directly opposes the theoretical prediction (Core, Guay, and Verdi 2008).
However, some evidence of a positive relation between information quality and cost of equity is noted in tests
of implied costs of equity (Francis et al. 2004; Francis, Nanda, Olsson 2008).4 While debate continues on the
relative costs and benefits of using realized returns or implied cost-of-equity estimates as proxies for the ‘true’
cost of equity (Elton 1999; Gebhardt, Lee, and Swaminathan 2001; Wang 2013), the lack of a significant
relation between realized returns and measures of information quality have created skepticism of the relevance
of information quality to firm value (Lewellen 2010; Zimmerman 2013).
The second set of studies posits that uncertainty about the parameters of a firm’s cash flow process has
implications for valuation and stock returns (Lewellen and Shanken 2002; Pastor and Veronesi 2003; 2006;
Johnson 2004). Unlike conventional asset pricing studies which generally assume investors agree on the cash
flow process of the firm—i.e., a firm’s future cash flows evolve from a cash flow process with a known mean
and constant volatility—studies in this stream explore the implications for firm value of a cash flow process
with an unknown mean that is learned by investors over time (Pastor and Veronesi 2009). For example,
assume a firm’s cash flow process follows a random walk with drift, CFt+1 = CFt + dt+1 + et+1. While
conventional models usually assume that ‘d’ is random variable, distributed normally around a known mean,
parameter uncertainty models assume ‘d’ has an unknown expectation that is learned by investors over time.
In other words, while conventional asset pricing models assume that there is only uncertainty around the mean,
parameter uncertainty studies explore the implications of uncertainty about the mean.
While modeling choices vary across studies, a primary finding is that uncertainty about the parameters of the
cash flow process can have countervailing effects on firm value compared to other sources of investor
uncertainty.
Perhaps most notably, in contrast to the conventional perspective which views investor
uncertainty of future cash flows as either value-decreasing (through a higher cost of capital) or value-neutral (if
3
While realized returns are often criticized as an unreliable estimate of cost of equity (Botosan and Plumlee 2005;
Easton and Monahan 2010), they have the critical advantage of being an unbiased, albeit potentially noisy, estimate
of ‘true’ expected returns (for the simple reason that true expected returns are defined as the expectation of realized
returns, conditional on all information known prior to the period).
4
We note that Ogneva (2012) and Barth et al. (2013) find that if realized returns are ex-post adjusted for cash flow
shocks, a positive relation between realized future returns and earnings quality can be found.
6
the uncertainty is idiosyncratic), studies in this literature suggest uncertain cash flow processes can lead to
higher firm values (Pastor and Veronesi 2003; 2006) and lower expected stock returns (Johnson 2004).
An easy way to appreciate the (counterintuitive) value-increasing effects of this source of uncertainty is to
consider a simple, stylized, two firm example. Let each firm, Firm A and Firm B, have future cash flow, cost
of equity (re), and expected cash flow growth rate of $10, 10%, and 3% respectively. The only difference
between the two firms relates to cash flow growth rates: A’s cash flows will grow at 3% per year with certainty
(gA = 0.03) while B’s cash flows will grow at either 1% or 5% per year with equal probability (E[gB] = 0.03).
Using a simple cash flow capitalization model (Vt = CFt+1/re-g), the value of firm A is $142.86,
while the value of firm B is $155.55,
,
. If equity is viewed as a call option on a
levered firm’s assets, more idiosyncratic uncertainty raises the option value, which lowers the stock’s exposure
to priced risk and lowers expected returns (Johnson 2004).5
Empiricists have found some support for the idea that uncertainty in a firm’s cash flow process can increase
firm value; however, the evidence is from indirect estimates of uncertainty such as firm age, equity duration,
and return volatility (e.g., Pastor and Veronesi 2003; Jiang et al. 2005) or from simulations that calibrate
theoretical models to real-world empirical patterns (Veronesi 1999; 2000; Pastor, Taylor, and Veronesi 2009).
While these studies have advanced the understanding of uncertainty’s effect on firm value, the strength of the
contribution is limited due to a lack of direct, empirical estimates for uncertainty.6 Further, with respect to the
predictive relation of uncertainty for future returns, an additional limiting factor relates to speed in which the
predictive relation decays. The strong decay rate (one to three months) is difficult to reconcile with typical
risk-based explanations as it suggests the risk profile of the firm changes drastically over a short horizon. In
sum, empirical evidence offered by prior studies is consistent with the theories on the effects of parameter
uncertainty in the financial markets (Pastor and Veronesi 2009), but cannot be viewed as robust as the
empirical evidence offered on the value-relevance of other firm characteristics (e.g., accruals, book-to-market).
5
Similar intuition is noted in Lambert et al. (2007, pp. 392): ceteris paribus, the cost of capital for firm j,
, is
decreasing (increasing) in the expected end-of-period cash flow,
, when Cov ,
is positive(negative).
6
For example, in contrast to studies examining the predictive power of accruals, book-to-market, and return
momentum for future stock returns—studies where the theoretical construct of interest maps directly into the
examined empirical construct—asset pricing studies of uncertainty use indirect or simulated empirical measures.
Frequently, these measures have been used in prior studies to capture theoretical constructs unrelated to uncertainty;
thus, making their interpretation ambiguous.
7
2.2 Research motivation
The above discussion gives rise to several interesting questions with empirical implications for how we
examine the effects of investor uncertainty on firm value. First, the empirical inferences on uncertainty offered
by prior studies are often based on indirect proxies of uncertainty that do not map neatly into theoretical
uncertainty constructs.
Uncertainty represents a conditional volatility, or a distribution surrounding the
expectation of a random variable (i.e., earnings growth, cash flows, etc.). While this view is taken in the
theoretical exploration of the effects of uncertainty on firm value (Pastor and Veronesi 2003; Johnson 2004;
Lambert et al. 2007), empirical tests of the theories are based on indirect measures of uncertainty (as noted
above).7 While it’s plausible that the indirect proxies examined in prior studies are precise, unbiased estimates
of investor uncertainty, because these variables often also capture dynamics associated with expected future
performance, it is difficult for prior studies to distill the predictive power associated with expected future
performance from predictive power associated with the uncertainty in expected future performance.8
Second, the predictive power of uncertainty for firm value, as measured by expected stock returns, is
surprisingly short-lived, extending no more than one to three months (Diether, Malloy, and Scherbina 2002;
Johnson 2004; Ang et al. 2006). If uncertainty is associated with firm value, either through its effect on the
cost of equity or through behavioral pricing biases, an unanswered (and unexamined) question relates to what
changes in the information environment occur so quickly as to resolve investor uncertainty over such short
time horizons?
Are the uncertainty shocks really so transitory, and/or the implied learning about the
uncertainty so intense, that the valuation effects disappear over very short horizons? Or, are the indirect
proxies for uncertainty so noisy that they have relatively weak predictive power for firm valuation?
Third, and perhaps most importantly, there is strong consensus in the accounting literature that firms with more
uncertain operating processes tend to have lower information quality (McNichols 2000; Dechow and Dichev
2002). If so, and if uncertainty associated with information quality and fundamentals have differing effects on
7
See Daniel, Hirshleifer, and Subrahmanyam (1998; 2001) for behavioral-based pricing models on uncertainty
Some researchers believe that analyst forecast dispersion is a pure measure of uncertainty in future earnings.
However, as noted in a series of studies, analyst forecast dispersion is, at best, a noisy estimate of uncertainty. More
likely, empirical evidence suggests that forecast dispersion is a biased estimate of uncertainty - see Diether et al
2002.; Clement and Tse 2005; Barron et al. 1998; Brown and LaRoque 2013; Donelson and Resutek 2013 for
discussions on how different analyst forecasts biases can affect forecast dispersion measures.
8
8
firm value, these joint-correlations could explain why prior studies have failed to find significant, or persistent,
associations between information quality uncertainty and expected stock returns.
A simple way to understand how joint-correlations across different types of uncertainty could affect empirical
inferences is to consider the following. Investors perceive two types of uncertainty, one relating to the
fundamental evolution of a firm’s expected cash flows over time and one related to how precisely investors can
estimate ‘true’ economic performance in any given period. The first type of uncertainty jointly captures the
idea that when forming expectations for future cash flow realizations, investors confront uncertainty in the
underlying cash flow process (e.g., will cash flow grow at 1% or 5%) and uncertainty relating to how precisely
next year’s cash flow can be estimated. The second type of investor uncertainty is due the fact that while
earnings offer a more complete picture of a firm’s expected economic performance, measurement error and
other frictions caused by the accrual process can negatively affect investors’ ability to precisely estimate future
economic performance.
Since investors distinguish between the two types of uncertainty, a firm’s return generating process is a jointfunction of both types of uncertainty. However, to date accounting researchers have only considered one type
of investor uncertainty in their empirical specifications. Accordingly, in the regression specifications offered
in prior studies examining the incremental predictive power of information quality for future stock returns, the
slope on information quality will jointly capture the positive predictive relation associated with information
quality (due to estimation risk) and the negative predictive relation associated with parameter uncertainty.
Our primary research intent centers on the investigation of two related questions: (i) do different sources of
investor uncertainty affect expected returns differently and, (ii) what is the relative importance of each source
of uncertainty for expected returns? In the subsequent sections, we develop empirical estimates for two
sources of investor uncertainty: cash flow uncertainty (CFU) and information quality uncertainty (IQU). We
view cash flow uncertainty as a component of investor uncertainty associated with future fundamental
performance, not how the performance is measured. In contrast, we interpret information quality uncertainty
as the component of investor uncertainty associated with how well accruals estimate cash flows from adjacent
reporting periods (i.e., investor uncertainty attributable to how the fundamental performance is measured).
9
Given theory and empirical results offered in prior studies, we expect our cash flow uncertainty variable (CFU)
jointly captures dynamics associated with both estimation risk and parameter uncertainty. The fact that cash
flow uncertainty jointly captures both of these types of investor uncertainty does not imply that it is a poor
estimate of how uncertain investors are about next period’s cash flows. Rather, it recognizes that uncertainty
about the parameters of a firm’s entire future cash flow process is likely positively correlated with how
uncertain investors are about next year’s cash flows. Since the parameter uncertainty relating to a firm’s cash
flow process cannot be definitively estimated (Lewellen and Shanken 2002), we simply acknowledge that our
fundamental uncertainty variable will most likely capture both types of uncertainty.
With respect to information quality uncertainty, however, our predictions are more precise. In empirical
specifications that do not control for cash flow uncertainty, we expect the slopes of information quality
uncertainty for predicting future stock returns to be negatively biased due to the fact the explanatory variable is
correlated with both estimation risk caused by poor information quality and parameter uncertainty associated
with fundamental uncertainty. A negative relation between information quality uncertainty and future returns
would not surprise us since the slope on IQU will be jointly affected by parameter uncertainty and estimation
risk. However, controlling for fundamental uncertainty (CFU), we expect the slope on information quality
uncertainty to become more positive and, if our IQU variable captures estimation risk with a reasonable degree
of precision, we should find a significantly positive slope.
Admittedly, we would prefer to derive independent (orthogonal) estimates of uncertainty that sum to total
investor uncertainty. Unfortunately, estimating sources of investor uncertainty is difficult since estimates of
investor expectations and the distribution surrounding these estimates need to be jointly-estimated. Further, as
noted above, sources of investor uncertainty are likely correlated, causing additional complications. Thus, we
focus our empirical tests on the predictive power of two sources of investor uncertainty: uncertainty in future
cash flows (CFU) and uncertainty due to information quality (IQU), as proxied by residual accrual volatility.
While our empirical proxies for the components of investor uncertainty are presumably imperfect, we argue
that they offer the first direct ex-ante empirical proxies for two different sources of investor uncertainty that
can be estimated for a large sample of publicly traded firms over a long horizon (1973-2010).
10
3. Sample, variable measurement, and descriptive statistics
3.1 Forward-looking cash flow uncertainty estimation
Our proxy for cash flow uncertainty is based on the distribution surrounding an expectation of future cash flow
(Blouin et al. 2010; Donelson and Resutek 2013).9 While expected cash flow does not completely capture
expected fundamental performance, it should be largely free of distortions due to manager reporting choices
and accrual errors (thus, a reasonable proxy for uncertainty in future fundamental performance).
To estimate cash flow uncertainty, we begin by estimating an expectation of t+1 cash flow in the spirit of
Barber and Lyon (1996).10
We match each firm i, at time t, to firms in periods t-5 to t-1 on three
characteristics: size, cash flow, and one-year cash flow change. The goal of our matched-firm empirical design
is to produce a firm-specific estimate of future cash flow that is unbiased, precise, parsimonious, and free of
look-ahead bias.
The variables we choose to match on are not chosen at random; rather, the variables stem from an extensive set
of prior studies. Prior studies have firmly established that the level of firm performance is persistent, but in
any given year, firm performance may contain a transitory element to it (Ball and Watts 1972; Brooks and
Buckmaster 1976; Watts and Leftwich 1977; Freeman, Ohlson, Penman 1982). Further, more recent studies
have noted the earnings process of smaller firms is more volatile and left-skewed than larger firms (Fama and
French 2004). Hence, by choosing to match on these three characteristics, we achieve a reasonable level of
precision in our expectation model without imposing so many data and structural restrictions that the model
cannot be used on a broad set of firms.
The first step of our empirical design is to match firms based on NYSE-based total asset deciles. Each year,
each firm is allocated into one of two asset-based portfolios. The first portfolio comprises all firms with total
assets below the 10th NYSE-based asset percentile; all remaining firms fall in the second portfolio. We then
match each firm i to firms from prior years in the same size portfolio with similar cash flow levels and oneyear change in cash flow to firm i in year t. Specifically, for firm i in fiscal year t, we utilize as matches all
9
Our uncertainty estimates can also be interpreted as conditional volatilities: conditional on the information
available at time t, how ‘volatile’ (or uncertain) are the estimates of future cash flows or future earnings.
10
For brevity, we discuss the construction of our conditional cash flow estimate in this section. The construction of
our conditional earnings volatility follows the exact same steps, but we substitute earnings for cash flows.
11
firms within the same size portfolio in years t-5 to t-1 whose t-τ cash flow and t-τ one-year change in cash flow
are no more or less than 0.5 percent of the total assets of firm i's cash flows and one-year cash flow change in
fiscal year t. This matching process yields, for each firm i, a set of firms with comparable fundamental
performance that is observable at t.11
For each of the matched firms, we compute the change in cash flow between t-τ and t-τ+1. To reduce the
mechanical effect that extreme cash flow changes in a matched-firm has on estimates of cash flow uncertainty,
we discard matched-firms with extreme performance, defined as one-year change in cash flow greater in
absolute magnitude than 50% of total assets.12 We use the average change in cash flow across matched-firms
as firm i's expected cash flow change between t and t+1. We use the standard deviation in the realized cash
flow changes of the matched firms as a measure of firm i's cash flow uncertainty around its t+1 cash flow
expectation. We require at least five matches for each firm to compute this characteristic.
For firms without at least five matched firms, we repeat the matching process using slightly different screens.
Unmatched firms tend to be those with more extreme current cash flow or one-year cash flow change. For
these firms, we utilize a percentile-based matching procedure and use all firms within the same t-τ size
portfolio whose t-τ cash flows and t-τ cash flow change are between 80% and 120% of firm i’s cash flow and
one-year cash flow change in fiscal year t.
As a result of our matched-firm expectation model, for each firm i, we have an expectation of t+1 cash flow
and a conditional volatility (or the uncertainty) surrounding each cash flow expectation. Note, these empirical
variables map neatly into the theoretical constructs of ‘signals’ and ‘signal noise’ relating to firm value
(expected cash flow and cash flow uncertainty, respectively). Further, the matched-firm empirical design
should greatly reduce concerns that the expectation and uncertainty estimates are biased due to idiosyncratic
reporting choices of certain managers: the estimates of firm i are derived from averages of many other firms.
Thus, idiosyncratic reporting choices of any single manager will cancel out in the averaging process.
11
For example, MLI (F/Y/E 2001) had cash flows of 0.148, one-year change in cash flows of 0.02, and total assets
above the 10th NYSE total asset percentile. All firms with total assets above the 10 th NYSE total asset percentile in
fiscal years 1996-2000, with cash flows between 0.143 and 0.153 and one-year change in cash flow between 0.015
and 0.025 serve as MLI’s matched-firms. (In our sample, MLI2001 had 37 matched firms).
12
This screen has a minimal effect on the average number of matched firms per firm (less than 1 percent).
12
Finally, we scale each conditional cash flow volatility estimate by the absolute value of expected future cash
flow. This scaling procedure reduces the mechanical relation between uncertainty and the level of cash flow:
the scaling simply produces a unitless measure of uncertainty that captures the amount of uncertainty relative
to the level of expected future cash flows. Prior studies examining the conditional volatilities or uncertainties
of random variables that are not mean zero generally transform the uncertainty variable similarly (Diether et al.
2002; Minton and Schrand 1999; Minton, Schrand, and Walther 2002; Johnson 2004).
A common question of our empirical estimation design is ‘how’ we decided on the matching process we
employ and ‘if’ we had examined the relevance of other matching criteria such as industry- or market-based
variables. In fact, the simplicity of the matching process elicits an almost endless list of alternative matching
criteria. However, while matching firms on increasingly more precise firm characteristics may produce more
precise expectations (and therefore uncertainty estimates), it also excludes more firms. The more firms that are
excluded from the primary sample of firms, the higher the likelihood that our inferences could be biased (by
firm exclusion), thereby decreasing the generalizability of our results. To avoid overfitting the sample data, we
refrain from experimenting with alternative matching characteristics, preferring the general matching
framework used in prior studies (Barber and Lyon 1996; Kothari, Leone, and Wasley 2005). Ultimately, the
relevance of our empirical estimates for uncertainty is an empirical question. We directly test this in section 4.
3.2 Forward-looking information quality uncertainty estimation
Optimally, we would like to estimate our second uncertainty source, information quality uncertainty, in a
manner similar to cash flow uncertainty: a distribution surrounding an expectation. However, forming this
expectation is difficult since the expectation represents the expected difference between reported earnings and
‘true’ economic earnings. Since ‘true’ economic earnings are never observed, forming an unbiased estimate of
this expected difference (and an associated uncertainty estimate) is not reasonable.13
Instead, we estimate information quality uncertainty using a conventional cross-sectional residual accrual
volatility model (Dechow and Dichev 2002; McNichols 2002). Prior studies have derived information quality
We view IQU as the uncertainty associated with the link between ‘true’ economic performance (the so-called
E*) and reported accrual earnings. More formally, we conceptually interpret IQU as the variance of the expected
13
*
difference between reported earnings and economic earnings, Et[Earnt - Earn t]2).
13
uncertainty using similar forms of this model (Francis et al. 2004; Core et al. 2008; Ogneva 2012).
Conceptually, residual accrual volatility captures time-series variation in accruals that do not map into realized
economic performance. While not forward-looking in the spirit of our other uncertainty measure, assuming
this measure is relatively sticky from year-to-year, residual accrual volatility should be a reasonable proxy.
Consistent with prior studies, we require at least 20 firms per industry year and compute information quality
uncertainty at the firm-level based on firm-level volatility in regression residuals over the trailing five-years.
Since the cross-sectional regression model used to derive residual accrual volatility requires cash flows from
t+1, we lag our time-series volatility estimates one year to prevent a look-ahead bias. Similar to our cash flow
uncertainty variable, we scale residual accrual volatility by the absolute value of the expected accruals, where
expected accruals are simply the difference between expected t+1 earnings and expected t+1 cash flow.14
3.3
Sample Selection
Our primary sample is drawn from the population of all firms listed in the Compustat Annual Industrial and
Research files with fiscal year ends between 1973:06 and 2011:05. The sample begins in 1973 because the
first year Compustat reports flow of funds data, which we use to compute cash flow from operations, is 1971
and we need at least three years of data to perform our matching process (two years for firm i, one year to
match against). After the matching process, we further reduce the sample to domestic nonfinancial firms
traded on the NYSE, AMEX, and NASDAQ (CRSP exchange codes 1-3; share codes 10-12) and require a
nonmissing estimate of cash flow uncertainty or earnings uncertainty. Our primary sample is comprised of all
firms that meet the above criteria, yielding 142,813 observations. Current-year summary statistics are annually
winsorized. To prevent summary statistics from being overly influenced by the increase in observations in the
latter years of the sample and to report results that more closely relate to the average time-series regression
slopes examined in later tests, summary statistics are time series means (an average of each annual statistic).
3.4 Descriptive Statistics
Table 1 provides descriptive statistics for all firms in our primary sample. Summary statistics are largely in
line with those reported in prior studies, although several characteristics are worth noting. First, conditional
14
An alternative interpretation of this uncertainty estimate is that it represents the reciprocal of an unsigned student
t-statistic, which informs on the precision (instead of the uncertainty) of a point estimate.
14
volatilities based on our matched-firm empirical design capture roughly 15-20% more observations per year
than the respective time-series volatility variables. This is due to the minimal data requirements imposed by
our matched-firm expectation model, allowing us to form expectations and estimate uncertainties for a larger
percentage of firms. Second, our matched-firm expectations (eEarn and eCF) are approximately equal, on
average, to realized earnings and cash flows (Earn and CF) although the average cross-sectional standard
deviations of eEarn and eCF are approximately 30% lower than those of Earn and CF. Finally, table 1 notes
the average number of matched-firms used to generate our expectations of future earnings and cash flows is
significant. Expected earnings are derived from, on average, 62.6 matched firms while expected cash flows
are computed from, on average, 27.3 firm-year observations. These numbers imply that idiosyncratic reporting
choices of individual matched-firms should have, at most, minimal effect on our uncertainty estimates.
Table 2 provides a correlation matrix for key variables and results again are largely in line with prior studies.
Time-series volatility and conditional volatility estimates are positively correlated, but are not highly collinear
(0.40<ρ<0.60). This suggests that the uncertainty variables capture similar economic variation to past earnings
and cash flow volatilities, but are distinct. Second, our uncertainty variables (EU, CFU, IQU) are positively
correlated with their respective unscaled, conditional volatility estimates (cEV, cCFV, tAQ), suggesting the
transformation does not distort the signs of the correlations. Finally, note the uncertainty variables have lower
correlations with current performance measures such as earnings and cash flows than the conditional (and
time-series) volatility variables. A common criticism of conventional time-series volatility and accrual quality
variables is that they are strongly (negatively) correlated with current firm performance (McNichols 2002;
Ogneva 2012). Our scaled uncertainty variables generally have similarly signed correlations, but with much
weaker correlative relations.
4. Specification tests of uncertainty
In this section, we empirically examine our matched-firm conditional volatility measures against the more
conventional time-series volatility measures. Our specification tests are presented in two formats. In our first
set of tests (table 3), we report results from a formal regression analysis. The structure of the regression tests is
based on the well-worn specification tests employed in the finance literature for estimates of future return
15
volatility and serve as a formal test of how well our uncertainty variables proxy for actual uncertainty at time t,
relative time-series based volatility measures. The second set of results are more descriptive in nature and
illustrate how our uncertainty measures vary across different industries, future accounting characteristics (sales
volatility, forecast errors), and market-based variables prior studies have associated with investor uncertainty.
4.1 Specification comparison of the uncertainty measures to the time-series volatility variables
To assess how well our conditional volatility estimates proxy for actual uncertainty at time t, relative to
conventional volatility measures derived from time-series realizations, we annually regress the absolute value
of unexpected t+1 earnings and cash flows against their respective volatilities. Specifically, table 3 reports the
time-series average intercepts (γ0) and slopes (γ1) on our estimates of conditional earnings volatility (cEV),
conditional cash flow volatility (cCFV), time-series earnings volatility (tEV) and time-series cash flow
volatility (tCFV). The general intuition of these regressions stems from the fact that the average absolute
deviation from the expected value of a random variable is roughly equivalent to the standard deviation of the
random variable. If the our matched-firm volatility estimates poorly proxy for uncertainty and, in the extreme,
are random noise, the intercept (γ0) will equal the sample mean of absolute value of unexpected earnings and
the slope (γ1) will equal 0.0.
As our matched-firm volatility estimate more closely approximates actual
uncertainty at time t, (γ0) will decrease towards zero and (γ1) will increase towards 1.0. Similar empirical
specification tests have been used to examine return volatility estimates (e.g., Schwert 1989).15
In addition, because estimates of earnings and cash flow volatility are direct functions of earnings and cash
flow expectations, we also report average cross-sectional intercepts (β0) and slopes (β1) from regressions of
actual earnings and cash flows regressed on expected earnings and cash flows. Results from all specification
regressions are reported across two time horizons: 1973-2010; 1990-2010.
Results in table 3 show the average slopes (γ1) on both conditional volatility measures (cEV and cCFV) are
significantly higher than their time-series volatility equivalents (tEV and tCFV). This pattern holds in the full
sample and is particularly more significant in the post-1990 sample. Further, point estimates of the intercepts
15
If one assumes cash flow is a normally distributed variable, the expected value of the absolute error is less than
the standard deviation from a normal distribution. In untabulated results, we assume cash flow is normally
distributed and correct for this friction by multiplying all absolute errors by (2/π)-1/2 ≈ 1.2533. Average slopes
change minimally and inferences are qualitatively identical.
16
are much closer to zero for the conditional volatility estimates compared to the time-series volatility variables.
With respect to the specification of the cash flow and earnings expectations from our matched firm design,
results in table 3 suggest that the expectation models perform remarkably well. The slopes (β1) on our
expected cash flow and earnings estimates are significantly closer to unity (1.0) in the matched-firm
expectation model than the conventional random walk estimates. Further, intercepts (β0) in the matched firm
sample are almost indistinguishable from zero with small point estimates. In contrast, intercepts from the
random walk are significant, not only statistically, but also economically.
In sum, the evidence in table 3 suggests that our matched-firm empirical design produces reasonable estimates
of earnings and cash flow uncertainty as proxied by conditional volatilities. These estimates are not only more
precise, but also less biased (γ0 ≈ 0.0; γ1≈ 1.0) compared to conventional estimates based on time-series
variation. In table 4, we report descriptive evidence on the validity of our uncertainty measures, cash flow
uncertainty (CFU) and information quality uncertainty (IQU). While the evidence in table 4 does not provide
rigorous econometric proof that our uncertainty measures are reasonable, it does provide qualitative support for
the construct validity of our measures.
Panel A reports the relative proportion of firm-year observations that fall into each uncertainty quintile by
industry. Obviously, there is no ‘right’ or ‘expected’ empirical relation between uncertainty quintiles and
industry classification. However, ex-ante, certain expectations exist with respect to specific industries. For
example, the ‘Utility’ industry is often characterized as an industry with very stable cash flows (hence, the high
leverage found of most utility firms). In contrast, the ‘Business Equipment’ industry, which is comprised of
many high technology, high R&D firms, is generally characterized as having unpredictable cash flows and
poor information quality. The empirical patterns noted in panel A generally comport to our expectations.
Firms in the ‘Utility’, ‘Telecom’ and ‘Energy’ industries tend to have lower cash flow uncertainty and better
information quality, consistent in tenor to the idea that firms in these industries have a relatively stable cash
flow process. In contrast, both types of investor uncertainty for firms in the ‘Business Equipment’ industry are
high. In fact, almost fifty percent of firms in this industry fall into the fourth or fifth uncertainty quintile,
percentages higher than any other industry.
17
In panel B, we report the time-series averages of three market-based characteristics and three accounting-based
characteristics prior studies have associated with investor uncertainty. Note, averages of the characteristics are
based on future realizations (i.e., t+1 realizations); thus, there should be no mechanical relation between our
uncertainty measures and the accounting realizations. Again, while we cannot definitively form expectations
of the expected differences across uncertainty quintiles for each characteristic, if our uncertainty variables
capture actual investor uncertainty at time t regarding t+1 realizations, we expect a monotonically increasing
pattern from low-to-high uncertainty quintiles. Indeed, this is the exact pattern panel B notes. With the
exception of no relation across IQU quintiles for future absolute forecast errors, there is a strong positive
relation across both types of investor uncertainty for all six characteristics (all differences, Q1-Q5, are
significant, p-value ≤ 0.01).
In sum, the evidence presented in tables 3 and 4 suggests that our uncertainty variables are reasonable proxies
for actual investor uncertainty at time t. Are these estimates of uncertainty perfect for each firm? Presumably
not, but they appear to have empirical properties that more closely mirror the conceptual properties of actual
investor uncertainty than the time-series variables used in prior studies. Thus, the uncertainty variables should
provide a more powerful mechanism to test the relative predictive power of investor uncertainty than the timeseries variables used in prior studies.
5. Equity market consequences of uncertainty
In this section, we examine if, and to what extent, the two sources of investor uncertainty affect firm value (as
proxied by future stock returns). Motivation for these tests stems from disparate directional predictions noted
in the theoretical accounting and finance literatures on the effect of investor uncertainty on firm value. Neither
explanation is mutually exclusive; thus, our return tests should not be viewed as providing evidence supporting
one explanation while ruling out the other. Our tests simply show which asset pricing effect is dominant in
explaining the cross-section of expected stock returns.
5.1 Return sample
The sample of firms we examine in our return tests closely mirrors the primary sample we describe in section
3.3 with a few minor differences. First, because we need a future return series to match against current period
18
firm characteristics, our primary return sample spans 1978:05 – 2011:04. The future return period begins in
the fifth month of fiscal year t+1 and extends twelve months (through the end of month 4, t+2). We focus on
monthly returns to avoid making assumptions about firms that drop off CRSP during the future return period.
Our tests simply include a firm up until the month it drops from CRSP, including any delisting return. All
predictor variables are winsorized monthly at the 1st and 99th percentile and are updated once per fiscal year.
To avoid spurious inferences driven by low priced stocks, we exclude firms with share prices below $1 per
share as of the last day of trading before the future return period begins. We report the robustness of our
results to other samples in table 6.
Consistent with prior studies, we report time-series average slopes from monthly cross-sectional regressions of
future returns regressed on our uncertainty variables and conventional firm characteristics known to be
associated with future returns over a twelve month span. Specifically, we include log market value of equity
(MEt), log book-to-market (BMt), and accruals (Acct). These variables respectively control for the size
anomaly (Banz 1981), value/growth anomaly (Rosenberg, Reid, and Lanstein 1985; Fama and French 1992),
and the accrual anomaly (Sloan 1996). We report average slopes for two sets of analyses: models 1-3 are
predictive slopes of future returns on monthly winsorized predictor variables (1st and 99th percentile); models
1r-3r are predictive slopes on the same predictor variables ranked monthly into deciles.
5.2 The predictive relation of uncertainty for future returns
Three key results emerge from table 5. First, cash flow uncertainty (CFU) is strongly negatively associated
with future returns. Controlling for size, book-to-market, and accruals, the economic differential between high
and low cash flow uncertainty firms (model 1r) is very similar to the difference between high and low accrual
firms: future realized monthly returns are approximately 0.47 percent higher in low CFU firms than high CFU
firms. Note CFU has significant predictive strength over twelve month horizons (all CFU slopes are more than
3.0 standard errors from zero). This fact is important as prior studies typically show that less direct uncertainty
proxies, such as analyst forecast dispersion or realized return volatility, have little predictive power for future
returns past three months (Diether et al. 2002; Ang et al. 2006).
Second, model 2 notes information quality uncertainty (IQU) is positively associated with future returns,
19
although the relation is modest (at best) after controlling for size, book-to-market, and accruals. This result is
consistent with prior studies (Core et al. 2008; Ogneva 2012) and clearly highlights that if investor uncertainty
is negatively associated with future returns (Jiang et al. 2005; Johnson 2004), it is fundamental performance
uncertainty that is responsible for the relation, not information quality uncertainty.
Third, and perhaps most interesting, model 3 shows that after controlling for cash flow uncertainty,
information quality uncertainty is positively associated with future returns. Across both unranked and ranked
specifications, slope estimates on information quality uncertainty are strongly associated with future returns
(slope estimates are 2.6 and 3.6 standard errors from zero in models 3 and 3r respectively). Slope estimates on
cash flow uncertainty are still strongly negative after controlling for information quality uncertainty (in fact,
slopes on CFU increase in both specifications and are each more than 4.0 standard errors from zero). Further,
consistent with prior studies that suggest characteristics associated with underlying economic performance are
more relevant to firm value than characteristics associated with information quality (Zimmerman 2013), the
slopes on CFU are larger (in absolute magnitude) than the slopes on information quality uncertainty.16
Focusing on model 3r, the slope on CFU (-0.056) is nearly 2.0 times larger (in absolute magnitude) compared
to the slope on IQU (0.032). On an annualized basis, this absolute difference between extreme deciles of IQU
suggests a cost of equity capital difference of approximately 3.0 percent, incremental to size, book-to-market,
and accruals.
Taken collectively, the slopes on the two uncertainty variables in table 5 provide compelling new empirical
evidence that is relevant to literatures in both accounting and finance on the effect of investor uncertainty on
expected stock returns. With respect to the literatures examining the valuation effects parameter uncertainty
(Pastor and Veronesi 2009), we offer the first direct empirical evidence showing a strong negative predictive
relation between a direct estimate of uncertainty in future cash flows and future returns. As noted above, the
empirical evidence offered in prior studies is based on indirect estimates of uncertainty and the predictive
power is relatively short-lived. Our results show a direct negative association between uncertainty in future
cash flows and future returns over a twelve month period—a link that is strikingly stronger in both an
16
The difference in the absolute values of the CFU and IQU slopes in model 3 is 0.110 (t-statistic 2.48) and the
difference in the absolute values of the slopes in model 3r is 0.024 (t-statistic 1.40)
20
economic and statistical sense than that reported in prior studies (e.g., Johnson 2004).
Second, prior work has not examined the incremental predictive relevance of fundamental uncertainty and
information quality uncertainty to firm value. Instead, prior studies view both types of uncertainty as having
the same directional effect on firm value (Jiang et al. 2005; Zhang 2006). Our results suggest the opposite,
finding that fundamental uncertainty, as proxied by cash flow uncertainty, is strongly negatively predictive of
future returns while information quality uncertainty has a more modest positive relation with future returns.
With respect to the debate in the accounting literature on the relevance of information quality to firm value, our
results offer a novel link between a series of recent studies. Specifically, Ogneva (2012) suggests firms with
poor accrual quality (high information quality uncertainty) tend to realize extreme future cash flow shocks.17
She stresses that future cash flow shocks attenuate predictive slopes on accounting quality variables, leading
prior studies to find accrual quality is unrelated to cost of equity capital proxied for by realized returns.
Ogneva shows that when realized future returns are stripped of variation attributable to future cash flow
shocks, accrual quality positively explains variation in the future return residual. Our results confirm her
inferences, but do so using a conventional empirical design that does not impose a look-ahead bias. Rather, we
simply control for a firm’s propensity to realize future cash flow shocks via our cash flow uncertainty variable
in the spirit of conventional asset pricing tests.
5.3 Alternative samples
Table 6 reports the predictive slopes of our uncertainty variables for future returns across alternative samples.
The purpose of these alternative samples is simply to examine the robustness of our results in table 5 to sets of
firms of differing size, share prices, exchange listings, and over longer predictive periods. Consistent with
table 5, models 1-5 report predictive slopes on winsorized predictor variables while models 1r-5r report slopes
on monthly decile ranks of the predictor variables. Model 1 reports regression results on the full sample,
inclusive of any firm with the requisite predictor variables and at least one future monthly return realization
regardless of firm size, share price, or exchange listing. Model 2 reports results for firms with share prices
above $5/share as of the last day of trading before the future return period begins. This screen excludes stocks
17
Similar observations on the relation between residual accrual volatility and future cash flow shocks have been
made by Dechow and Dichev (2002); Liu and Wysocki (2007).
21
that may face short-sale constraints or other institutional frictions (institutional ownership restrictions, bid/ask
bounce) that may distort inferences. In the spirit of Ogneva (2012), model 3 trims firms that realize significant
cash flow shocks, which we define as realized monthly returns in excess of 150%.18 Model 4 excludes socalled micro-cap firms, or those with market capitalizations below the 20th NYSE percentile. Prior studies
show that micro-cap firms constitute approximately sixty percent of the publicly traded firms in any given
year, but generally account for only three percent of total market capitalization (Fama and French 2004).
Finally, to test the persistence of our uncertainty variables, model 5 examines the predictive strength of our
uncertainty variables for future returns lagged one year (the future return period begins in month 5 of t+2).
Results in table 5 are qualitatively similar to those reported in table 4, both in terms of relative economic
significance and statistical predictive strength. Cash flow uncertainty strongly predicts future returns across all
five models. For example, in models 1r-3r the difference in expected returns for firms in the high cash flow
uncertainty decile are between 50-60 basis points lower per month than firms in the low decile.
Model 4
suggests that fundamental uncertainty affects the expected returns of larger firms. Again, examining the
ranked specification, model 4r suggests that high fundamental uncertainty firms realize future returns that are
lower by approximately 30 basis points per month (or almost 4.0 percent annualized) than low fundamental
uncertainty firms. Model 5 suggests the predictive power of fundamental uncertainty for future returns is
persistent, extending at least 2 years. In contrast to accruals, which strongly predict future returns over a oneyear period, but have little predictive power beyond the one-year horizon, cash flow uncertainty significantly
explains future return variation beyond the conventional one-year horizon. While not definitive, the longer
horizon predictive power of cash flow uncertainty for future returns is consistent with the idea that the
explanatory power stems from an association with investor risk and not investor mispricing.
With respect to information quality uncertainty, results in table 6 are largely consistent with those reported in
table 5; however, several characteristics are worth noting. First, the economic significance of information
quality uncertainty is relatively consistent across different samples of firms that include microcaps (models 1-
18
Average monthly returns in our sample are approximately 1.2 percent with a standard deviation of 18%; thus, this
screen defines extreme cash flow shocks as monthly return realizations more than 8 standard deviations from the
population mean, or approximately one firm observation per monthly cross-section.
22
3; 5). While the absolute magnitude of the slopes on information quality uncertainty are less than those on
cash flow uncertainty, IQU slope estimates tend to be more stable as noted by smaller standard errors. Again,
this suggests a persistent predictive quality associated with IQU. Finally, in contrast to cash flow uncertainty,
IQU does not have significant predictive power for future returns in samples that exclude microcap stocks
(model 4). However, note this ‘insignificant’ relation is driven by a smaller slope, not a less precisely
estimated slope. This finding does not reduce the relevance of information quality to firm valuation; rather, it
simply emphasizes that variation in information quality is economically more important across smaller firms.
5.4 Alternative information quality uncertainty specification
Table 7 examines the robustness of our information quality uncertainty results to an alternative, forwardlooking specification. If the economic construct of information quality uncertainty is positively associated
with estimation risk, as the theoretical accounting literature suggests, an alternative forward-looking empirical
specification should find similar empirical patterns to those documented in tables 5 and 6.
Our alternative measure of information quality uncertainty, IQU*, is defined as the absolute difference between
the conditional earnings and cash flow volatilities (|cCV – cEV|), scaled by the absolute difference between
expected earnings and cash flows (|eCF – eEarn|). Consistent with our other uncertainty variables, IQU* is a
natural log transform which reduces the statistical influence of explanatory variable skewness on the regression
slopes. Our information quality measure captures the incremental investor uncertainty attributable to the
accrual process. For example, if cash flow uncertainty equals earnings uncertainty – i.e., the accrual process
contributes no incremental uncertainty to investors – then IQU* equals zero. However, if the accrual process
causes earnings uncertainty to be lower than cash flow uncertainty (due to expected cash flow smoothing) or
higher than cash flow uncertainty (due to uncertain future economic performance captured by accruals and not
realized in cash flows), then IQU* will be greater than zero. In fact, the larger the absolute difference between
earnings and cash flow uncertainty, the bigger the role the accrual process is expected to play in investor
uncertainty – exactly the dynamic that should characterize information quality uncertainty.19
19
Jayaraman (2008) finds firms with earnings that are much smoother or more volatile than cash flows tend to have
higher bid-ask spreads and informed trading, consistent with the idea that the larger the role of the accrual process in
reported earnings, the lower the firm’s information quality.
23
Results reported in table 7 are based on the same sample of firms examined in table 5, but because IQU* does
not require a lengthy time-series to compute, our future return period begins earlier: 1974:05 – 2011:04.
Results are quantitatively very similar to those reported in table 5. Cash flow uncertainty strongly predicts
future stock returns: in ranked regressions, the slopes on cash flow uncertainty suggest expected stock returns
for high cash flow uncertainty firms are between 43 and 56 basis points lower per month than low cash flow
uncertainty firms (each more than 3.0 standard errors from zero). Perhaps more interesting, the slopes on
information quality uncertainty are positive in specifications that do not control for fundamental uncertainty
(models 2, 2r), but are significantly more positive in specifications that do control for fundamental uncertainty
(models 3, 3r). The symmetry of these results, compared to those in table 5, confirm our conjecture that both
sources of investor uncertainty affect expected stock returns, albeit in countervailing directions.
5.5 Time-series predictive stability
Accounting and finance researchers tend to focus on the sign and statistical significance from a time-series
average of cross-sectional regressions to confirm whether a firm characteristic is associated with future returns.
Since Fama-Macbeth slopes and t-statistics are functions of equal-weighted averages computed over the
sample period, they are sensitive to extreme realizations over the period examined. Further, as conventionally
reported, the FM slopes and t-statistics tell us very little about whether a relation is getting stronger or weaker.
Figure 1
10-year rolling slope estimates
1988:04-2011:04
The figure plots ten-year rolling average (120 months) of Fama-Macbeth slopes from regressing future returns (in %) on
than decile ranks of scaled cash flow uncertainty (CFU), information quality uncertainty (IQU), market equity (ME),
book-to-market (BM), and accruals (model 3r, table 4). The y-axis represents the incremental difference in average
realized returns between firms in the top and bottom deciles for each respective characteristic.
0.15
0.1
BM
0.05
IQU
0
Apr-88
CFU
Apr-93
Apr-98
Apr-03
-0.05
Apr-08
ME
Acc
-0.1
-0.15
24
As a final robustness test on the predictive relation of our uncertainty variables and future returns, figure 1
plots time-series variation in the 10-year rolling average FM slopes on explanatory variables. The primary
purpose of this analysis is to examine the stability of the average slopes on uncertainty over time and to see if
our primary inferences are sensitive to certain subperiods of the full sample. Specifically, we examine plots of
the 10-year rolling average of the monthly slopes from model 3r of table 5. Since slopes from this model are
associated with decile ranks, the slopes can be interpreted as the trailing 120 month average expected return
differential between firms in the high and low characteristic-based deciles.
Figure 1 shows that both cash flow uncertainty and information quality uncertainty are relatively stable
predictors of future returns over the sample period. With the exception of a brief reversal of the predictive
slopes on cash flow uncertainty at the end of 1999, over the past 25 years the difference in expected returns
between high and low CFU firms is approximately 0.60 percent per month. The economic significance of
information quality uncertainty, on the other hand, is significantly smaller (in absolute magnitude) than cash
flow uncertainty. Nonetheless, the predictive power of IQU for future returns is remarkably stable over the
sample period, especially relative to the stability of the predictive slopes on size, book-to-market and accruals.
6. Conclusion
This study examines how different sources of investor uncertainty explain cross-sectional variation in future
stock returns. We connect two sets of uncertainty literature, one that focuses on how information uncertainty
affects firm valuation, and one that examines how uncertainty in the future fundamental performance of the
firm affects firm value. Distinct from prior studies, we define our uncertainty variables as conditional
volatilities. That is, given an expectation of future cash flows or future accruals, our uncertainty estimates
represent a direct estimate of the expectation’s expected precision.
Consistent with inferences from the finance literature on parameter uncertainty (Pastor and Veronesi 2009), we
find a strong negative relation between fundamental performance uncertainty (as proxied by cash flow
uncertainty) and future returns that is incremental to conventional firm characteristics known to predict returns.
In Fama-Macbeth regressions, slopes on cash flow uncertainty are between 2.0 and 5.0 standard errors from
25
zero even when we drop the microcap stocks from the regressions. Perhaps more interesting, the predictive
power of cash flow uncertainty extends over at least a two year horizon and is remarkably stable over the
sample period.
With respect to information quality uncertainty, we find little predictive power for future returns incremental to
size, book-to-market, and current accruals. However, controlling for cash flow uncertainty, we find a modest,
but statistically significant positive relation between information quality uncertainty and future returns. In
Fama-Macbeth regressions, slopes on information quality uncertainty range from 2.0 to 3.5 standard errors
from zero (with the exception of samples excluding microcap stocks). In terms of economic significance,
firms in the high information quality uncertainty decile (poor accounting quality) realize future returns that are,
on average, 25-50 basis points higher than those in the low information quality uncertainty decile (high
accounting quality). On an annualized basis, this difference equates to approximately three percent per year
difference in cost of equity capital, incremental to size, book-to-market, accruals and cash flow uncertainty.
Our study jointly contributes to two existing literatures. First, the strong negative relation we find between
cash flow uncertainty and future returns suggests the strong negative relation prior behavioral studies attribute
to information uncertainty is driven fundamental performance uncertainty, not uncertainty attributable the
information environment (Jiang et al. 2005). Prior studies offer little direct empirical evidence of a negative
relation between investor uncertainty and future stock returns. Rather, evidence supportive of a negative
relation comes from indirect proxies of uncertainty (firm age; forecast dispersion) or simulated data. While
our proxy for cash flow uncertainty is presumably imperfect, the strong negative relation we find on cash flow
uncertainty is consistent with the finance literature on investor learning and parameter uncertainty. Further, the
longer-horizon predictive power of cash flow uncertainty for future stock returns suggests that this effect is
more consistent with some sort of risk-based effect (Johnson 2004) than investor mispricing (Jiang et al. 2005).
Second, prior studies have not attempted to distinguish the incremental predictive strength for future returns of
different sources of investor uncertainty; rather, prior studies often assume both sources of investor uncertainty
affect firm value in the same way (Jiang et al. 2005; Zhang 2006). We offer direct empirical evidence that
challenges this conjecture. We show that while both constructs are positively correlated, they predict future
26
stock returns differently.
Finally, we contribute to the growing literature examining the link between information quality and cost of
capital. Prior empirical studies have generally failed to find a significant positive relation between future
returns and firm-specific earnings quality characteristics (e.g., Core et al. 2008; McInnis 2010), leading
skeptics to doubt its significance in explaining cross-sectional variation in cost of capital. Our empirical
evidence suggests that prior inferences on information quality may be confounded by fundamental
performance uncertainty, an uncertainty component that appears to contain significant parameter uncertainty.
Once fundamental uncertainty (cash flow uncertainty) is controlled, a small, but remarkably stable positive
predictive relation exists.
27
References:
Ang, A., R.J. Hodrick, Y. Xing, and X. Zhang. 2006. The cross-section of volatility and expected returns. The
Journal of Finance LXI(1): 259–299.
Ang, A., R.J. Hodrick, Y. Xing, and X. Zhang. 2009. High idiosyncratic volatility and low returns:
International and further U.S. evidence. Journal of Financial Economics 91: 1-23.
Ball, R., & Watts, R. 1972. Some time series properties of accounting income. The Journal of Finance, 27(3),
663-681.
Banz, R.W. 1981. The relationship between return and market value of common stocks, Journal of Financial
Economics 9: 3-18.
Barber, B.M. and J.D. Lyon. 1996. Detecting abnormal operating performance: The empirical power and
specification of test statistics. Journal of Financial Economics 41: 359-399.
Barron, O.E., O. Kim, S.C. Lim, and D.E. Stevens. 1998. Using Analysts’ Forecasts to Measure Properties of
Analysts' Information Environment. Accounting Review 73(4): 421–433.
Barth, M.E., Y. Konchitchki, and W.R. Landsman. 2013. Cost Of Capital and Earnings Transparency. Journal
of Accounting and Economics 55(78): 206–224.
Blouin, J.L, J. Core and W. Guay. 2010. Have the Benefits of Debt Been Overstated? Journal of Financial
Economics 98: 195-213.
Brooks, L. D., & Buckmaster, D. A. 1976. Further evidence of the time series properties of accounting
income. The Journal of Finance, 31(5), 1359-1373.
Brown, L. and S. Laroque. 2013. I/B/E/S Reported Actual EPS and Analysts’ Inferred Actual EPS. The
Accounting Review 88(3): 853-880.
Chen, L., R. Novy-Marx and L. Zhang. 2011. An alternative three-factor model. Working Paper.
Clement, M.B., and S.Y. Tse. 2005. Financial Analyst Characteristics and Herding Behavior in Forecasting.
The Journal of Finance LX (1).
Core, J.E., W.R. Guay and R.V. Verdi. 2008. Is accruals quality a priced risk factor? Journal of Accounting
and Economics 46(1): 2-22.
Daniel, K., D. Hirshleifer and A. Subrahmanyam. 2001. Overconfidence, Arbitrage, and Equilibrium Asset
Pricing. The Journal of Finance 56(3): 921–965.
Daniel, K., D. Hirshleifer and A. Subrahmanyam. 1998. Investor Psychology and Security Market Under- and
Overreactions. The Journal of Finance 53(6): 1839–1885.
Dechow, P.M. and I.D. Dichev. 2002. The quality of accruals and earnings: The role of accrual estimation
errors. The Accounting Review 77: 35-59.
Diether, K., C. Malloy and A. Scherbina. 2002. Difference of opinion and the cross section of stock returns.
The Journal of Finance 57: 2113-41.
28
Donelson, D. and R. Resutek. 2013. The predictive qualities of earnings volatility and earnings uncertainty.
Tuck School of Business at Dartmouth working paper.
Easley, D. and M. O’Hara. 2004. Information and the cost of capital. The Journal of Finance 59: 1553-1583.
Elton, E.J. 1999. Expected Return, Realized Return, and Asset Pricing Tests. The Journal of Finance LIV(4):
1199–1220.
Elton, E. J. 1999. Presidential address: expected return, realized return, and asset pricing tests. The Journal of
Finance, 54(4), 1199-1220.
Fama, E.F. and K.R. French. 2006. Profitability, investment and average returns. Journal of Financial
Economics, 82(3), 491-518.
Fama, E.F. and K.R. French. 2004. New lists: Fundamentals and survival rates. Journal of Financial
Economics 73: 229-269.
Fama, E.F. and K.R. French. 1996. The CAPM is Wanted, Dead or Alive. The Journal of Finance 51(5): 1947–
1958.
Fama, E.F. and K.R. French. 1993. Common Risk Factors in the Returns on Stocks and Bonds. Journal of
Financial Economics 33: 3–56.
Fama, E.F. and K.R. French. 1992. The cross-section of expected stock returns. The Journal of Finance 47:
427-465.
Fama, E.F. and J.D. MacBeth. 1973. Risk, Return and Equilibrium: Empirical Tests. Journal of Political
Economy 81(3): 607-636.
Francis, J., R. Lafond, P.M. Olsson and K. Schipper. 2004. Costs of Equity Earnings Attributes. The
Accounting Review 79(4): 967-1010.
Freeman, R. N., Ohlson, J. A., & Penman, S. H. (1982). Book rate-of-return and prediction of earnings
changes: An empirical investigation. Journal of Accounting Research, 20(2), 639-653.
Gebhardt, W.R., C.M.C. Lee, and B. Swaminathan. 2001. Toward an Implied Cost of Capital. Journal of
Accounting Research 39 (1): 135–176.
Hirshleifer, D. 2001. Investor Psychology and Asset Pricing. The Journal of Finance LVI (4): 493–494.
Hughes, J.S., K. Liu, and J. Liu. 2007. Information Asymmetry, Diversification, and Cost of Capital. The
Accounting Review 82 (3): 705–729.
Jayaraman, S. 2008. Earnings volatility, cash flow volatility, and informed trading. Journal of Accounting
Research, 46(4), 809-851.
Jensen, M., F. Black and M. Scholes.1972. The capital asset pricing model: Some empirical tests.
Jiang, G., C.M.C. Lee and Y. Zhang. 2005. Information uncertainty and expected returns. Review of
Accounting Studies 10(2): 185–221.
Johnson, T.C. 2004. Forecast dispersion and the cross section of expected returns. The Journal of Finance 59:
1957-1978.
29
Kothari, S. P., A.J. Leone and C.E. Wasley. 2005. Performance matched discretionary accrual measures.
Journal of Accounting and Economics, 39(1): 163–197.
Lambert, R.A., C. Leuz and R.E. Verrecchia. 2011. Information Asymmetry, Information Precision, and the
Cost of Capital. Review of Finance, 16(1): 1–29.
Lambert, R., C. Leuz, and R.E. Verrecchia. 2007. Accounting information, disclosure, and the cost of capital.
Journal of Accounting Research 45: 385-420.
Lewellen, J. 2010. Accounting anomalies and fundamental analysis: An alternative view. Journal of
Accounting and Economics 50: 455-466.
Lewellen, J. and J. Shanken. 2002. Learning, Asset-Pricing Tests, and Market Efficiency. The Journal of
Finance 57: 1113-1145.
Lintner, J. 1965. Security Prices, Risk and Maximal Gains from Diversification. The Journal of Finance,
XX(4): 587–615.
McInnis, J. 2010. Earnings smoothness, average returns, and implied cost of equity capital. The Accounting
Review 85: 315-341.
Liu, M., and P. Wysocki. 2007. Cross-sectional Determinants of Information Quality Proxies and Cost of
Capital Measures. Working Paper.
McNichols, M.F. 2002. The Quality of Accruals and Earnings: The Role of Accrual Estimation Errors:
Discussion. The Accounting Review 77 (2002): 61–69.
Merton, RC. 1987. A Simple Model of Capital Market Equilibrium with Incomplete Information. The Journal
of Finance.
Minton, B.A., C.M. Schrand and B.R. Walther. 2002. The role of volatility in forecasting. Review of
Accounting Studies 7: 195-215.
Ogneva, M. 2012. Accrual Quality, Realized Returns, and Expected Returns: The Importance of Controlling
for Cash Flow Shocks. The Accounting Review 87 (4) (July): 1415–1444.
Pastor, L. and R.F. Stambaugh. 2003. Liquidity risk and expected stock returns. Journal of Political Economy,
111:642-685.
Pastor, L., L. Taylor and P. Veronesi. 2009. Entrepreneurial Learning, the IPO Decision, and the Post-IPO
Drop in Firm Profitability. Review of Financial Studies, 22(8): 3005–3046.
Pastor, L. and P. Veronesi. 2009. Learning in financial markets. Annual Review of Financial Economics 1:
361-381.
Pastor, L. and P. Veronesi. 2006. Was there a Nasdaq bubble in the late 1990s? Journal of Financial
Economics, 81: 61–100.
Pastor, L. and P. Veronesi. 2003. Stock valuation and learning about profitability. Journal of Finance 58: 17491789.
Rosenberg, B., R. Kenneth, and R. Lanstein. 1985. Persuasive evidence of market inefficiency. The Journal of
Portfolio Management 11(3): 9-16.
30
Schwert. W.G. 1989. Margin requirements and stock volatility. Journal of Financial Services Research 3: 153164.
Sharpe, W., 1964. Capital asset prices: A theory of market equilibrium under conditions of risk. The Journal of
Finance, XIX(3): 425–442.
Shleifer, A. 2003. Inefficient markets: An introduction to behavioral finance. Oxford University Press.
Sloan, R.G. 1996. Do stock prices fully reflect information in accruals and cash flows about future earnings?
The Accounting Review 71: 289-315.
Veronesi, P. 2000. How does information quality affect stock returns? The Journal of Finance, 55(2): 807–837.
Veronesi, P. 1999. Stock market overreactions to bad news in good times: a rational expectations equilibrium
model. Review of Financial Studies, 12(5): 975–1007.
Wang, C.C.Y. 2013. Measurement Errors of Expected Returns Proxies and the Implied Cost of Capital.
Working Paper.
Watts, R. L., and Leftwich, R. W. 1977. The time series of annual accounting earnings. Journal of Accounting
Research, 15(2), 253-271.
Zhang, F.X. 2006. Information Uncertainty and Stock Returns. The Journal of Finance 61: 105-137.
Zimmerman, J. 2013. Myth: External Financial Reporting Quality Has a 1st Order Effect on Firm Value.
Working Paper (December).
31
Table 1
Descriptive Statistics
This table reports cross-sectional summary statistics. Specifically, we report the time-series average of the annual
cross-sectional mean (Avg.), standard deviation (Std.), 1st percentile (Min.), 50th percentile (Med.), 99th percentile (Max.),
and number of observations (Obs.). The sample spans firms with fiscal year ends between 1973:06 and 2011:05. All
variables are annually winsorized at the 1st and 99th percentile with the exception of Size.
Variable
cEV
cCFV
tEV
tCFV
tAQ
Earn
CF
eEarn
eCF
EU
CFU
IQU
BM
Size
MatchesCF
MatchesEarn
cEV
cCFV
tEV
tCFV
tAQ
Earn
CF
eEarn
eCF
EU
CFU
IQU
BM
Description
Conditional earnings volatility
Conditional cash flow volatility
Time-series earnings volatility
Time-series cash flow volatility
Time-series residual accrual volatility
Earnings before X-ordinary items
Cash flow
Expected t+1 earnings
Expected t+1 cash flows
Earnings uncertainty
Cash flow uncertainty
Information quality uncertainty
Natural log book-to-market
NYSE-based total asset decile
Number of firm matches, Cash Flow
Number of firm matches, Earnings
Avg.
0.075
0.097
0.066
0.087
0.043
-0.001
0.055
0.002
0.059
0.143
0.140
-0.448
-0.433
2.760
27.3
62.6
Std.
0.051
0.046
0.079
0.075
0.035
0.155
0.150
0.116
0.101
1.094
0.960
1.216
0.812
2.569
27.6
99.6
Min.
Med.
Max.
Obs.
0.016
0.030
0.003
0.009
0.005
-0.668
-0.517
-0.482
-0.374
-1.749
-1.476
-2.744
-2.882
1.000
5.0
5.0
0.058
0.088
0.038
0.065
0.033
0.038
0.077
0.031
0.077
-0.048
-0.034
-0.605
-0.353
1.053
17.0
32.3
0.232
0.237
0.450
0.425
0.194
0.252
0.385
0.182
0.235
3.868
3.585
3.525
1.364
10.000
137.5
412.5
3549.8
3433.4
3035.6
2789.1
2148.3
3758.4
3681.6
3549.8
3432.5
3549.8
3432.5
1969.1
3622.1
3758.4
3433.4
3549.8
Conditional earnings volatility computed as described in section 3.1; where earnings is earnings before
extraordinary items (IB)
Conditional cash flow volatility computed as described in section 3.1; where cash flow is equal to earnings
before extraordinary items (IB) + non-working capital accruals (DPC + XIDOC + TXDC + ESUBC + SPPIV
+ FOPO) – change in non-cash working capital
Time-series earnings volatility computed as the standard deviation of earnings before extraordinary items
(IB) scaled by average total assets (AT) between t-4 and t.
Time-series cash flow volatility computed as the standard deviation of cash flow scaled by average total
assets (AT) between t-4 and t.
Time-series residual accrual volatility from annual industry regressions. Volatility is computed at time t from
residuals from t-6 to t-1 from the following regression:
dWCt = b0 + b1 CFOt+1 + b2 CFOt + b3 CFOt-1 + b4 dSalest + b5 PPEt + e;
where dWC equals change in non-cash working capital; dSales is change in Sales, and PPE is net Property,
Plant & Equipment. Regressions are run at industry level (Fama and French 12 Industry) and all regression
variables are scaled by average assets.
Earnings before extraordinary items (IB) scaled by average total assets
Cash flow, defined as earnings before extraordinary items, plus non-working capital accruals, minus change
in non-cash working capital, scaled by average total assets
Expected t+1 earnings computed as described in section 3.1
Expected t+1 cash flow computed as described in section 3.1
Earnings uncertainty, defined as the natural log (cEV/ | eEarn | )
Cash flow uncertainty, defined as the natural log (cCFV / | eCF | )
Scaled accrual quality uncertainty, defined as the natural log (tAQ / | eEarn - eCF | )
Natural log of book equity (shareholders equity minus preferred equity) minus natural log of market equity
32
Table 2
Correlations, 1973–2010
This table reports the time-series average of the annual cross-sectional correlations among the variables listed, winsorized
annually at their 1st and 99th percentiles. The variables and sample are the same as defined in Table 1. Pearson productmoment correlations are reported above the diagonal; Spearman rank correlations are reported below the diagonal. Bold
indicates correlations greater than 0.30 in absolute value.
cEV
cCFV
tEV
tCFV
tAQ
EU
CFU
IQU
Earn
CF
cEV
cCFV
tEV
tCFV
tAQ
EU
CFU
IQU
Earn
CF
0.48
0.60
0.42
0.40
0.37
0.34
0.01
-0.43
-0.29
0.49
0.42
0.52
0.41
0.07
0.58
0.20
-0.22
-0.24
0.56
0.40
0.58
0.56
0.14
0.27
0.17
-0.31
-0.19
0.39
0.49
0.60
0.66
0.08
0.33
0.36
-0.17
-0.18
0.39
0.40
0.58
0.64
0.11
0.30
0.58
-0.18
-0.19
0.19
0.03
0.04
0.05
0.07
0.32
-0.06
-0.42
-0.17
0.26
0.45
0.19
0.22
0.24
0.25
0.32
-0.28
-0.46
-0.05
0.17
0.13
0.28
0.46
-0.06
0.27
0.23
-0.16
-0.63
-0.37
-0.44
-0.27
-0.27
-0.12
-0.16
0.18
0.53
-0.40
-0.41
-0.28
-0.26
-0.24
-0.06
-0.29
-0.13
0.60
-
33
Table 3
Annual cross-sectional specification regressions, 1973-2010
This table reports the time-series average intercepts and slopes from the following annual cross-sectional regressions:
Panel A: Earnings
Panel B: Cash flows
|eEarn – Earnt+1| = γ0 + γ1 cEVt + e
|eCF – CFt+1| = γ0 + γ1 cCFVt + e
Earnt+1 = β0 + β1 eEarnt + e
CFt+1 = β0 + β1 eCFt + e
|Earnt – Earnt+1| = γ0 + γ1 tEVt + e
|CFt – CFt+1| = γ0 + γ1 tCFVt + e
Earnt+1 = β0 + β1 Earnt + e
CFt+1 = β0 + β1 CFt + e
In panel A, the dependent variable in the volatility regressions is defined as the absolute value of unexpected earnings. In
the ‘Match-Firm’ row, expected earnings are from matched-firm expectation model; in the ‘Time-series’ row, expected
earnings equal realized earnings (Earnt). In panel B, the dependent variable in the volatility regressions is defined as the
absolute value of unexpected cash flow. In the ‘Match-Firm’ row, expected cash flow is from the matched-firm
expectation model; in the ‘Time-series’ row, expected cash flow equals realized cash flow (CFt). All independent variables
are winsorized at the 1st and 99th percentile. To minimize a look-ahead bias, future earnings and cash flow values are
winsorized between -1.0 and 1.0. All variables are defined in table 1.
Full Sample 1973-2010
Sample
FM slopes
γ0
γ1
β0
β1
Late Sample 1990-2010
Obs.
γ0
γ1
β0
β1
Obs.
Panel A: Earnings
Match-Firm Avg.
FM t-stat
Time-series Avg.
FM t-stat
-0.001
(-0.300)
0.025
(5.49)
0.875
(18.97)
0.632
(13.66)
-0.006
(-2.73)
-0.005
(-1.67)
0.966 3550
(52.88)
0.764 3035
(45.04)
-0.004
(-1.82)
0.034
(10.20)
0.952
(29.82)
0.567
(10.21)
-0.006
(-1.72)
-0.010
(-4.00)
0.944 3848
(91.21)
0.760 3289
(61.51)
Panel B: Cash Flow
Match-Firm Avg.
FM t-stat
Time-series Avg.
FM t-stat
0.012
(2.42)
0.037
(20.99)
0.740
(12.67)
0.633
(20.69)
0.011
(2.21)
0.032
(4.07)
0.834 3414
(16.17)
0.529 2930
(6.93)
0.002
(0.821)
0.040
(24.19)
0.845
(31.56)
0.576
(22.92)
0.001
(0.070)
0.015
(6.29)
0.949 3836
(75.44)
0.693 3157
(18.84)
34
Table 4
Investor uncertainty and future firm characteristics
This table reports descriptive relations between the two types of investor uncertainty, cash flow uncertainty (CFU) and
information quality uncertainty (IQU), and firm characteristics. In panel A, firms are sorted into quintiles each year based
on CFU and IQU. The percentage of the total industry firm-year observations in each uncertainty quintile are reported
along with the total number of firm-year observations. In panel B, we report the average of annual future firm economic
and accounting characteristics sorted into uncertainty quintiles. Monthly return volatility, Illiquidity (Amihud 2002), and
Bid-Ask spread is the average monthly value over months (5/t+1 – 4/t+2); Forecast error is the difference between the
consensus analyst EPS forecast and realized EPS, per I/B/E/S summary file; Sales volatility is the absolute value of Salest
(scaled by average assets t) minus Salest+1 (scaled by average assets t+1).
Panel A: Distribution of 12 Fama-French industries across uncertainty quintiles
Industry
Classification
Uncertainty
Measure
Uncertainty Quintiles
(percent of total firm-year observations)
Total
Observations
1
2
3
4
5
Business Equipment
CFU
IQU
15.0
12.9
17.0
17.3
19.5
20.5
23.0
23.3
25.5
26.0
24,948
13,705
Chemicals
CFU
IQU
26.6
17.2
22.7
21.6
20.0
19.8
16.3
21.8
14.4
19.6
3,853
2,744
Durables
CFU
IQU
18.8
12.2
18.6
19.2
20.3
22.4
20.9
23.1
21.4
23.1
4,550
2,837
Energy
CFU
IQU
27.9
36.0
22.7
22.8
18.1
17.0
15.8
13.3
15.5
10.9
7,349
3,985
HealthCare
CFU
IQU
21.7
12.5
20.5
16.3
18.8
20.2
18.6
23.3
20.4
27.7
12,294
6,352
Manufacturing
CFU
IQU
18.3
15.5
19.6
20.2
21.1
22.1
21.2
21.6
19.8
20.6
20,508
12,472
Non-Durables
CFU
IQU
21.4
14.4
19.2
19.9
20.2
22.2
20.0
21.6
19.2
21.9
9,973
5,434
Other
CFU
IQU
19.8
22.6
19.6
21.3
20.2
19.9
20.5
18.8
19.9
17.4
20,268
10,395
Retail
CFU
IQU
18.8
18.6
19.1
20.4
20.6
20.4
20.5
20.8
21.0
19.8
17,158
10,513
Telecom
CFU
IQU
26.5
43.9
21.0
20.1
18.4
14.2
17.2
11.7
16.9
10.1
3,564
1,792
Utilities
CFU
IQU
28.1
50.6
33.6
26.1
21.1
12.9
11.5
6.3
5.7
4.1
5,969
4,595
35
Table 4 (continued)
Investor uncertainty and future firm characteristics
Panel B: Future economic and accounting firm characteristics across uncertainty quintiles
Firm
Characteristic
Uncertainty
Measure
Uncertainty Quintiles
(time-series averages)
Avg. Firms
1
2
3
4
5
Monthly Return Volatilityt+1
CFU
IQU
0.123
0.131
0.138
0.140
0.154
0.145
0.175
0.150
0.195
0.152
685
440
Illiquidtyt+1
CFU
IQU
2.291
5.757
4.552
7.050
7.067
7.036
11.651
6.993
15.996
7.237
685
440
Bid-ask spreadt+1
CFU
IQU
0.022
0.032
0.030
0.035
0.038
0.036
0.046
0.037
0.053
0.038
685
440
|Forecast Error+1|
CFU
IQU
0.052
0.062
0.059
0.064
0.073
0.063
0.080
0.061
0.091
0.060
685
440
Sales Volatilityt+1
CFU
IQU
0.127
0.118
0.148
0.142
0.167
0.157
0.189
0.166
0.202
0.178
685
440
|dWCt+1|
CFU
IQU
0.059
0.061
0.073
0.073
0.085
0.078
0.099
0.085
0.115
0.089
685
440
36
Table 5
Cross-sectional regressions of future monthly returns on uncertainty components
1978:05-2011:04
This table reports average slopes from 396 cross-sectional regressions of future monthly stock returns (in %) on cash flow
uncertainty (CFU), accrual quality uncertainty (IQU), and other firm characteristics. Our t-statistics are based on the timeseries variability of the slope estimates. Predictor variables in models 1-3 are winsorized monthly at their 1st and 99th
percentiles; predictor variables in models 1r-3rare ranked into deciles at the beginning of each month. Predictor variables
are updated once per year, four months after the end of the firm’s prior fiscal year. CFUt equals the natural log of cash
flow uncertainty scaled by the absolute value of expected cash flows for year t+1. IQUt equals the natural log of the
residual accrual volatility from t-6 to t-1, scaled by the absolute value of expected accruals. MEt is the natural log of
market value of equity per CRSP on the last day of trading in month 4 of t+1. BMt is the natural log of book value minus
the natural log of market value at fiscal year end. Acct is equal to the change in non-cash, non-debt working capital,
minus non-working capital accruals, scaled by average assets. The sample includes all nonfinancial firms on CRSP and
Compustat with nonmissing data for future returns.
Unranked
Intercept
t
CFU t
t
Ranked
(1)
(2)
(3)
(1r)
(2r)
(3r)
1.789
(4.63)
1.671
(4.34)
1.870
(5.21)
1.542
(3.51)
1.396
(3.27)
1.640
(4.25)
-0.160
(-4.26)
-0.047
(-3.20)
-0.141
(-3.86)
IQU t
t
0.028
(1.38)
0.050
(2.61)
-0.056
(-4.11)
0.022
(2.26)
0.032
(3.61)
MEt
t
-0.076
(-1.65)
-0.052
(-1.20)
-0.085
(-2.11)
-0.050
(-1.57)
-0.030
(-1.00)
-0.056
(-2.00)
BMt
t
0.310
(3.47)
0.243
(2.98)
0.250
(3.05)
0.089
(3.11)
0.071
(2.98)
0.075
(3.07)
Acct
t
-0.903
(-2.89)
-1.524
(-5.06)
-1.233
(-3.81)
-0.045
(-3.48)
-0.071
(-6.21)
-0.059
(-4.62)
Obs.
3328
2101
2101
3328
2101
2101
37
Table 6
Cross-sectional regressions of future monthly returns on uncertainty components, alternate samples
This table reports average slopes from cross-sectional regressions of future monthly stock returns (in %) on cash flow
uncertainty (CFU), information quality uncertainty (IQU), and other firm characteristics. Our t-statistics are based on the
time-series variability of the slope estimates. All predictor variables are as defined in prior tables. Predictor variables in
models 1-5 are winsorized monthly at their 1st and 99th percentiles; predictor variables in models 1r-5r are ranked into
deciles at the beginning of each month. Model 1reports results for the full sample (all firms with predictor variables and
future returns); Model 2 reports results for firms with share prices above $5 as of the last day of trading in month 4 of year
t+2; Model 3 reports results for the full sample excluding monthly observations with realized future return greater than
150%; Model 4 reports results for the ‘all-but-tiny’ sample (all firms with market capitalizations above the NYSE 20 th
percentile); Model 5 reports results of predictive regressions for t+2 (predictive slopes relate to monthly regressions
spanning between month 4 of year t+2 and month 3 of year t+3).
(1)
Intercept
t
CFUt
t
IQUt
t
MEt
t
BMt
t
Acct
t
Avg. Obs.
2.116
(5.72)
-0.167
(-4.56)
0.052
(2.68)
-0.125
(-2.92)
0.255
(3.14)
-1.334
(-3.83)
2174
Unranked
(2)
(3)
1.651
(5.02)
-0.168
(-4.08)
0.054
(2.74)
-0.056
(-1.71)
0.203
(2.43)
-1.297
(-3.87)
1713
1.579
(4.62)
-0.175
(-4.87)
0.060
(3.06)
-0.038
(-1.01)
0.292
(3.81)
-0.871
(-2.87)
2100
(4)
(5)
(1r)
1.781
(3.88)
-0.125
(-2.21)
0.024
(0.93)
-0.081
(-1.83)
0.131
(1.45)
-1.484
(-3.15)
1025
1.761
(4.85)
-0.111
(-3.14)
0.048
(2.41)
-0.070
(-1.78)
0.200
(2.67)
-0.278
(-0.90)
1960
1.907
(4.65)
-0.060
(-4.44)
0.033
(3.65)
-0.089
(-2.84)
0.077
(3.13)
-0.065
(-4.68)
2174
38
Ranked
(2r)
(3r)
1.490
(4.60)
-0.054
(-4.16)
0.030
(3.40)
-0.032
(-1.59)
0.058
(2.47)
-0.051
(-4.50)
1713
1.281
(3.56)
-0.061
(-4.67)
0.037
(4.13)
-0.023
(-0.89)
0.087
(3.85)
-0.048
(-3.99)
2100
(4r)
(5r)
1.524
(4.38)
-0.032
(-2.37)
0.014
(1.19)
-0.032
(-1.62)
0.040
(1.65)
-0.045
(-3.19)
1025
1.474
(3.99)
-0.043
(-3.51)
0.022
(2.41)
-0.052
(-1.82)
0.051
(2.52)
-0.013
(-1.05)
1960
Table 7
Cross-sectional regressions of future monthly returns on uncertainty components
1974:05-2011:04
This table reports average slopes from 444 cross-sectional regressions of future monthly stock returns (in %) on cash flow
uncertainty (CFU), an alternate measure of information quality uncertainty (IQU*) and other control variables. IQU* is
natural log of the absolute difference between the conditional cash flow and earnings volatilities (cCFV – cEV) scaled by
absolute value of expected difference between future earnings and cash flows (eEarn - eCF). All other predictor variables
are as defined in prior tables. t-statistics are based on the time-series variability of the slope estimates. Predictor variables
in models 1-3 are winsorized monthly at their 1st and 99th percentiles; predictor variables in models 1r-3r are ranked into
deciles at the beginning of each month.
Unranked
Intercept
t
CFU t
t
Ranked
(1)
(2)
(3)
(1r)
(2r)
(3r)
1.901
(5.13)
1.758
(4.51)
1.937
(5.39)
1.671
(4.05)
1.440
(3.10)
1.696
(4.12)
-0.148
(-3.94)
-0.043
(-3.21)
-0.131
(-3.89)
IQU* t
t
0.023
(1.79)
0.046
(2.82)
-0.056
(-3.67)
0.021
(3.11)
0.037
(3.90)
MEt
t
-0.096
(-2.22)
-0.070
(-1.53)
-0.102
(-2.41)
-0.062
(-2.09)
-0.043
(-1.36)
-0.069
(-2.45)
BMt
t
0.316
(3.81)
0.310
(3.72)
0.307
(3.70)
0.090
(3.44)
0.088
(3.45)
0.088
(3.44)
Acct
t
-1.051
(-3.58)
-1.676
(-6.49)
-1.425
(-5.23)
-0.047
(3.96)
-0.073
(-7.86)
-0.063
(-6.22)
Obs.
3206
3045
3045
3206
3045
3045
39