Download An Empirical Assessment of Models of the Value Premium*

An Empirical Assessment of Models of the Value
Premium*
by
Huijun Wang
Jianfeng Yu
November 2011
Abstract
Recent models of the value premium typically endogenously link B/M to firmspecific attributes. The value firms earn higher subsequent returns because these firms
command a higher risk premium due to a higher default probability, lower profitability,
higher operating leverage, shorter cash flow duration, or higher cash flow risk. Using
several moderators, we first sort the entire sample into several groups of firms, across
which the value premium varies significantly. We find that among the groups in which
the value premium is tiny and insignificant, there is indeed a significant desired relation
between B/M and firm-specific attributes. In sharp contrast, among the groups in
which the value premium is the most pronounced, there is no significant desired relation
between B/M and firm-specific attributes. Moreover, in many cases, these relations
are even opposite to the predictions of these theories. Given the above findings, we
further explore potential sources for the value premium.
Keywords: value premium, mispricing, limits to arbitrage, financial distress, default risk,
profitability, duration, cash flow risk, operating leverage
* First draft: April, 2011. We thank Raj Aggarwal, Frederico Belo, Philip Bond, Stavros Panageas,
Hong Yan, Lu Zhang, and seminar participants at the University of Minnesota for helpful comments. All
errors are our own. Author affiliations/contact information:
Wang: Department of Finance at the Carlson School of Management, University of Minnesota, Suite 3-122,
321 19th Ave. South, Phone: 612-626-9702, Email: [email protected].
Yu: Department of Finance at the Carlson School of Management, University of Minnesota, Suite 3-122, 321
19th Ave. South, Phone: 612-625-5498, Email: [email protected].
1
Introduction
There is considerable evidence that stocks with high book-to-market equity ratios (hereafter
B/M) tend to earn higher subsequent returns than stocks with low B/M. However, researchers
disagree on the economic forces behind the value premium. In earlier studies, the
debate focuses on whether this value premium reflects compensation for systematic risk
or mispricing based on cognitive biases.1 More recently, a number of papers have developed
structural models endogenously linking the dynamics of expected returns and risk to firmlevel investment decisions.2 In these structural models, B/M is typically associated with
firm-specific attributes, such as profitability, default risk, and operating leverage. These
explanations usually imply that the value firms should earn higher subsequent returns
because these firms are riskier due to their higher financial distress risk, lower profitability,
and higher operating leverage. Moreover, based on firms’ cash flow dynamics, many recent
studies have developed structural models of the value premium by linking cash flow duration
and cash flow risk to B/M and expected returns. These models can generate the value
premium since value firms have higher cash flow risk and lower cash flow duration.
Most of the model-implied joint relations between B/M, firm-specific attributes and
expected returns are empirically confirmed, apparently supporting many alternative theories
of the value premium. Similar in spirit to Lewellen, Nagel, and Shanken (2009) and Daniel
and Titman (2011), we feel that this evidence is comforting and yet disconcerting because
many seemingly different forces can all account for the value premium. The main purpose
of this paper is to inspect the mechanisms in the alternative theories with a more powerful
conditional test, and in a systematic way. Our approach is very simple. Based on several
carefully chosen moderators, we first sort all the firms into several groups, such that there
is a large variation in the value premium across these groups. We then investigate the joint
relation between B/M, firm-specific attributes, and returns for each group.
We find that among the groups with a small and insignificant value premium, there
is indeed significant desired relation between B/M and default risk, past profitabilities,
operating leverage, cash flow risk, or cash flow duration, as implied by the structural models.
In sharp contrast, among the groups with a large and significant value premium, there is
no significant desired relation between B/M and firm-specific attributes. Moreover, in many
1
In particular, Fama and French (1993, 1997) argue that value firms are more financially distressed and
hence riskier, while Lakonishok, et al. (1994), Daniel and Titman (1997), and La Porta et al. (1997) argue
for a role of mispricing in the value premium.
2
Section 2 reviews this literature, which dates from the seminal work of Berk, Green, and Naik (1999).
1
cases, the relations are even opposite to the predictions implied by these alternative theories.
A striking feature of our findings is the consistency of our results across all six conditional
variables. This evidence thus casts doubt on the leading explanations for the value premium.
The key step of our test is to identify conditional variables (i.e., moderators) such that the
value premium varies significantly across different groups of firms sorted by the conditional
variables. The way we identify our conditional variables is motivated by the limits-toarbitrage literature, which has shown that the value premium is much more pronounced
among firms with high limits to arbitrage. We therefore choose six commonly used proxies
for limits to arbitrage as our moderators: idiosyncratic volatility, firm size, number of
institutional holders, bid-ask spread, analyst coverage, and return volatility. It is worth
noting that the interpretation of our results does not depend on whether or not these
moderators are good proxies for limits to arbitrage. We simply use these variables to generate
large variations in the value premium across different groups of firms with different levels of
limits to arbitrage. This way, we can investigate how the relation between B/M and firmspecific attributes changes as we move from the group of firms with a low value premium to
the group of firms with a high value premium.
Many studies have tested the aforementioned explanations for the value premium. The
overall evidence is somewhat mixed, but supportive in general.3 In particular, previous
studies appear to find low profitability, low cash flow duration, high cash flow risk, and high
operating leverage for value firms. Our empirical approach differs from previous studies in
two key aspects. First, most of the previous empirical tests are unconditional in the sense
that the relation between these firm-specific attributes and B/M is studied over the whole
sample, whereas our tests are conditional in the sense that the relation between these firmspecific attributes and B/M is studied over different groups of firm with different magnitudes
of the value premium. For example, our conditional approach shows that among the group of
firms with a large value premium, the growth firms have actually a much lower profitability
than the value firms, while the growth firms has a much higher profitability among the group
of firms in which the value premium is small and insignificant. Second, while most previous
studies test one single explanation in isolation, we take a systematic approach by examining
many leading explanations simultaneously with the same conditional test.
3
We refer to Section 2 for more details. For example, for the distress risk-based explanation, Fama and
French (1995) show that the value firms have much lower earnings on book equity than the growth firms for
five years before and five years after portfolio formation, suggesting that the value firms are more distressed.
On the other hand, by showing that bankruptcy risk is not related to future returns, Dichev (1998) refutes
the financial distress explanation for the B/M effect.
2
Given that our findings do not appear to support the leading explanations based on
structural models, we then investigate the obvious alternative hypothesis for the value
premium: the mispricing hypothesis. In particular, we follow Griffin and Lemmon (2002) to
identify possible sources for the B/M effect by investigating sales growth, capital investment,
and R&D. Consistent with Griffin and Lemmon (2002), we find that the growth firms
among the high limits-to-arbitrage group tend to have high sales growth and relatively
high R&D and capital spending, yet these firms have little or no current earnings. In spite
of this, investors appear to award these firms with higher market value relative to both
book equity and sales than growth firms in lower limits-to-arbitrage groups. Overall, the
evidence suggests that investors may underestimate the importance of current fundamentals
and overestimate future growth opportunities for growth firms, especially in the group of
firms with a large value premium. Lastly, following La Porta et al. (1997), we examine the
stock price movements around earnings announcement dates to assess whether systematic
expectational errors can indeed explain the observed pattern in the value premium. Our
findings also support the hypothesis that mispricing is more pronounced in high limits-onarbitrage group.
Perhaps the study most closely related to ours is that of Griffin and Lemmon (2002),
who use Ohlson’ (1980) O-score as a conditional variable to distinguish the financial distress
hypothesis from the mispricing hypothesis. They find that among firms with the highest
distress risk, the value premium is more than twice as large as that in other firms, and
the growth firms actually have a high O-score among the most distressed firms. Our study
differs in that we employ many conditional variables to test many leading explanations
simultaneously, especially those based on recent structural models of the value premium.
Other closely related studies are Lewellen, Nagel, and Shanken (2009) and Daniel and Titman
(2011), which forcefully argue that due to the strong factor structure in the size and B/M
portfolios and the correlation between factor loadings and characteristics, asset-pricing tests
are often highly misleading, in the sense that apparently high cross-sectional R2 s provide
quite weak support for a model of size and value premia. They have proposed a number of
important suggestions for improving empirical tests. Our evidence echoes their findings from
a different angle. By examining the model-implied relation between B/M and firm-specific
attributes, our tests are directly linked to the theories. In this sense, our study complements
theirs.
The rest of the paper is organized as follows. We discuss the leading explanations for the
value premium and their main testable implications in Section 2. Section 3 describes the data,
3
the proxies for limits to arbitrage, and the definition of the firm-specific attributes needed
for our conditional tests. Section 4 presents the empirical findings. Section 5 concludes.
2
Alternative Explanations for the Value Premium
The literature related to the value premium is so vast, it is impossible to provide a
comprehensive review here. In this section, we briefly summarize five leading risk-based
explanations for the value premium and their key testable implications. Inevitably, we miss
a lot of important work related to the value premium.4
The first explanation is related to distress risk. Fama and French (1993, 1997) interpret
the return to B/M as compensation for state-dependent risk related to relative financial
distress. They present evidence that industry-specific variation in the value premium
corresponds with periods of industry strength or distress. However, by showing that
bankruptcy risk is not related to future returns, Dichev (1998) refutes the financial distress
explanation for the B/M effect. Moreover, Griffin and Lemmon (2002) and Campbell et
al. (2008) provide further evidence that financially distressed firms earn lower subsequent
returns. On the other hand, Chava and Purnanandam (2010) argue that prior studies use
noisy ex post realized returns to estimate expected returns. By using ex ante estimates
based on the implied cost of capital, they find a positive cross-sectional relationship between
expected stock returns and default probability. Their results suggest that investors expected
higher returns for bearing default risk. Overall, the evidence of distress risk for value firms
is mixed based on previous unconditional tests.
The second explanation relies on firms’ profitability. Starting with the seminar work
of Berk et al. (1999), many recent studies build structural models to relate stock return
dynamics to firms’ real investment decisions, and hence linking B/M to returns endogenously.
Although the exact underlying mechanisms of the models differ, this type of model, including
Zhang (2005) and Cooper (2006), shares the same essential prediction that more profitable
firms are less risky and are usually firms with low B/M. For example, in an influential
paper, Zhang (2005) shows that firms with low profitability are less flexible than firms with
high profitability, and hence the value firms are riskier and have higher expected returns.
Indeed, in Zhang (2005) sorting firm-level profitability is equivalent to sorting on B/M.
4
Among others, important recent contributions to the value premium we do not discuss in this paper
include Ai, Croce, and Kiku (2010) and Kogan and Papanikolaou (2010a, 2010b)
4
Cooper (2006) makes the same link between profitability and B/M. If a firm has been hit
by adverse profitability shocks, this firm’s B/M ratio is high because its market value falls
while its book value remains fairly constant due to irreversibility. Such a firm is sensitive to
aggregate shocks, and hence riskier. Thus, a direct prediction of this type of model is that
the value firms exhibit lower past profitability than the growth firms, and hence the value
firms are riskier.5
The third explanation is closely related to the second one. Several structural models
predict that firms with high operating leverage should earn higher subsequent returns, and
value firms have a higher operating leverage (e.g., Carlson, Fisher, and Giammarino (2004)
and Zhang (2005)). In particular, Carlson et al. (2004) model the optimal investment
behavior of monopolistic firms facing stochastic market demand conditions, operating
leverage, reversible real options, and finite growth opportunities. Asset betas vary over time
with historical investment decisions and the current product market demand. In particular,
beta is linear in the ratio of fixed costs to total firm value (i.e., operating leverage) and the
ratio of growth opportunities to assets in place. Thus, B/M effects emerge and relate to
operating leverage, while size captures the importance of finite growth opportunities relative
to assets in place. Empirically, Novy-Marx (2011) identifies a positive association between
operating leverage and stock returns and between operating leverage and loadings on the
value factor. However, he finds no association between his measure of operating leverage
and B/M. Gulen et al. (2008) find evidence that value firms have higher operating leverage,
higher ratios of fixed assets to total assets, greater frequency of disinvestment, and higher
financial leverage than growth firms. Finally, Garcı́a-Feijóo and Jorgensen (2010) find a
positive association between B/M and operating leverage, between operating leverage and
stock returns, and between operating leverage and systematic risk.
The fourth explanation is based on the cash flow duration. Lettau and Wachter (2007,
2011), Croce, Lettau, and Ludvigson (2007) and Da (2009) propose theoretical models in
which the growth firms have a higher cash flow duration and firms with higher cash flow
duration are less risky. Hence, these models can account for the observed value premium. In
particular, Lettau and Wachter (2007) specify a stochastic discount factor such that shocks
to cash flow are priced, but shocks to the discount rate are not. Their model implies that
growth firms covary more with the discount rate than do value firms, which covary more
with cash flows, and hence a value premium is obtained. Empirically, Cornell (1999a, 1999b),
Dechow, Sloan, and Soliman (2004), Da (2009), and Binsbergen, Brandt, and Koijen (2010)
5
This type of model tends to imply that the value firms face a higher default probability, especially during
recessions. This prediction is also consistent with the argument of Fama and French (1993).
5
find that assets with shorter duration in their cash flows tend to have higher expected returns
and that value firms tend to have a lower cash flow duration. Therefore, these studies suggest
that the shorter cash flow duration of the value firms can potentially account for the higher
subsequent returns for these firms.6
The fifth explanation is based on the cash flow risk. The cash flow risk of an asset has
recently been an active research topic. Bansal and Yaron (2004) model the consumption
cash flow risk and find that it can explain many time-series properties of asset markets.
Furthermore, among others, Campbell and Vuolteenaho (2004), Bansal, Dittmar, and
Lundblad (2005), Kiku (2007), Hansen, Heaton, and Li (2008), and Da (2009) theoretically
show that in cross section, value firms could have a higher cash flow risk than growth firms,
and hence a higher expected return. These studies also empirically document that value
firms have a higher cash flow risk in the data and that cash flow risk, measured by the cash
flow covariance with the aggregate consumption or by the covariance between returns and
market cash flow news, can explain a significant amount of the cross-sectional variation of
expected returns. On the other hand, Chen and Zhao (2009) show that the positive relation
between the cash flow risk and B/M is sensitive to the instrumental variables in estimating
the cash flow news.
In sum, these risk-based explanations imply that the value firms should earn higher
subsequent returns because the value firms have higher financial distress risk, lower
profitability, higher operating leverage, higher cash flow risk, or lower cash flow duration.
Previous studies find supportive evidence for each of the explanations. However, these studies
usually employ unconditional tests. In this paper, we perform more restrictive conditional
tests to further identify which theory is an empirically more plausible explanation for the
value premium. In particular, we use several variables as our moderator to classify the whole
sample of firms into different categories. Among some categories the value premium is much
more pronounced, while among other categories the value premium is tiny and insignificant.
A natural prediction of the previous explanations is that, within the category of firms in
which the value premium is more pronounced, the value firms have a high financial distress
risk, a lower profitability, a higher operating leverage, a higher cash flow risk, and a lower
cash flow duration.
We summarize the testable implications of these explanations in the following table:
6
In a contemporaneous paper, Chen (2011b) argues that after taking care of survivorship and static
biases, value firms have longer durations than growth stocks.
6
Hypothesis
Firm-specific attribute
V-G
H(V-G)-L(V-G)
1
2
3
4
5
default probability
profitability
operating leverage
cash flow duration
cash flow risk
positive
negative
positive
negative
positive
positive
negative
positive
negative
positive
Here, the third column (column V-G) shows the expected sign of the spread between the
firm-specific attribute of value firms and the firm-specific attribute of growth firms. The last
column shows the expected sign of the difference between the spread in the third column
among the group of firms with a high value premium and the spread among the group of
firms with a low value premium.
For completeness, we also quickly review the mispricing-based explanation. Many
researchers attribute the B/M effect to behavioral biases. For example, Lakonishok et al.
(1994) suggest that mispricing arises from investors extrapolating past operating performance
too far into the future. La Porta et al. (1997) and Skinner and Sloan (2002) show that for
high (low) B/M securities, market participants underestimate (overestimate) future earnings,
and that stock price reactions to future earnings announcements of extreme B/M stocks are
consistent with the correction of the systematically biased expectations. Consistent with
the mispricing hypothesis and the limits to arbitrage theory of Shleifer and Vishny (1997),
Griffin and Lemmon (2002), Ali et al. (2003), and Nagel (2005) further show that the B/M
effect is much stronger among firms that are hard to arbitrage.
3
Data and Measurements
The sample data come from eight sources. Data on accounting information are from the
COMPUSTAT Annual Industrial Files. Stock market data are from CRSP. Institutional
holdings records are from Thomson Reuters. Information on analyst forecasts is from
I/B/E/S. The aggregate consumption data are from Sydney Ludvigson’s website and the
Bureau of Economic Analysis (BEA). Price indexes are from the BEA and the Federal
Reserve System. The US business cycle reference dates are from NBER. The sample is from
January 1962 to December 2010. We choose 1962 as the start date because COMPUSTAT
data prior to 1962 have a strong bias toward big, successful firms. Finally, we follow Fama
and French’s (1992) procedure to measure the book equity of a firm.
7
The sample is constructed in a manner similar to Fama and French (1992). NYSE,
NASDAQ, and AMEX ordinary common stocks (excluding firms with shrcd >= 20 in CRSP)
with monthly returns from CRSP and with nonnegative book values of equity available from
COMPUSTAT are examined from July 1962 to December 2010. Further, to reduce the
survival bias inherent in the way COMPUSTAT adds firms to its tapes, we don’t include
firms until they are on COMPUSTAT for two years (see, e.g., Banz and Breen (1986)).
Stocks are ranked each June according to their previous December B/M, and other firm
characteristics in June. Finally, we correct the delisting bias by following Shumway (1997).
3.1
Firm and Portfolio Characteristics
To test the leading explanations for the value premium, we need to measure the
characteristics implied by those theories. In the data appendix, we provide details on our
procedure. Below we briefly describe these measurements.
The first explanation is based on distress risk. Following Ohlson (1980) and Griffin and
Lemmon (2002), we use the probability of financial distress based on the O-score to measure
the financial distress risk and use the portfolio median as the portfolio-level probability
of financial distress. The O-score is calculated using accounting values from the previous
December for the June rankings. The median level of financial distress probability in a
portfolio is our portfolio financial distress probability.
For the second explanation based on firm-level profitability, we use return-on-assets
(ROA) as the profitability measure. The annual ROA is defined as income before
extraordinary items scaled by total assets, and the portfolio ROA is the ratio of the portfolio
aggregate income before extraordinary items to the portfolio aggregate total assets.
The third explanation relies on the firm’s operating leverage. Measuring a firm’s
operating leverage is difficult. Following previous literature (e.g., Mandelker and Rhee
(1984) and Garcı́a-Feijóo and Jorgensen (2010)), we estimate the operating leverage of a
portfolio by the sensitivity of the percentage deviation of earnings from its trend relative to
the percentage deviation of sales from its trend. In particular, we proceed in two steps. To
measure the percentage deviation of portfolio aggregate earnings and sales from its trend, we
run five-year overlapping regressions of the portfolio earnings and sales on time respectively
in the first step. We next regress the residuals of the earnings regression on the residuals of
the sales regression both from the first step. This second-step OLS regression coefficient is
8
our portfolio-level operating leverage.
The fourth explanation is based on cash flow duration. Following Cohen, Polk, and
Vuolteenaho (2009) and Da (2009), we adopt the buy-and-hold procedure to estimate the
cash flow of a portfolio. Whenever a portfolio is formed, we hold its composition constant
and trace out its cash flow over time. Moreover, to overcome the empirical difficulties
associated with dividend data (Campbell (2000)), we use earnings data to estimate cash
flow characteristics as in Da (2009). In particular, for every portfolio formation at date t,
the cash flow duration of a portfolio is measured as the difference between the discounted
sum of all firms’ future dividends within the portfolio and the time t expectation of the
discounted sum of all future log aggregate consumption growth. The discounted sum of
future dividends is derived from accounting earnings based on the accounting clean surplus
identity (Vuolteenaho (1999)), i.e., the difference between the discounted sum of all portfolio
future accounting returns and the log portfolio cash-flow-to-book-equity ratio at the portfolio
formation date, minus a constant term. We also use alternative measures developed by
Dechow et al. (2004) as robustness checks.
Lastly, the fifth explanation is based on cash flow risk. Following Bansal et al. (2005),
we measure the cash flow risk of a portfolio as the covariance between portfolio cash flow
growth rates and the history of consumption growth. In particular, we regress the portfolio
de-meaned real dividend growth rate on a trailing moving average of past 8-quarter demeaned real consumption growth. The OLS coefficient is our portfolio cash flow risk.
3.2
Conditional Variables
In our main analysis, we choose six variables as conditional variables to classify firms into
subgroups such that the value premium varies substantially across these subgroups. Previous
studies find that the value premia are much more pronounced among firms that are difficult
to arbitrage. Therefore, the proxies for limits to arbitrage are our natural choices. Again,
for the purpose our test, one does not have to interpret these variables as proxies for limits
to arbitrage. We simply use them to generate variations in value premium across groups of
firm.
Previous studies have identified many proxies for limits to arbitrage (e.g., Pontiff (1996,
2006), Amihud (2002), Ali et al. (2003), Nagel (2005), Mashruwala et al. (2006), Zhang
(2006), Avramov et al. (2010), Lam and Wei (2011), Duan et al. (2010), and Wang and
9
Yu (2010)). Out of all the proxies used by previous studies, we choose six of them as our
conditional variables. The way we pick these variables is not arbitrary. We choose these
variables because they can produce large variations in the value premium across different
groups of firms classified by these variables. Other proxies for limits to arbitrage do not yield
a significant variation in the value premium, although it is still true that the value premium
is stronger among the high limits-to-arbitrage group. In principle, any variable that can
produce variation in the value premium can be used as a conditional variable in our test. We
want to emphasize again that our tests do not depend on whether the higher value premium
is due to the limits of arbitrage or whether the proxies are appropriate proxies for limits of
arbitrage. We simply use these variables to identify the subgroup of firms among which the
value premium varies.
The first conditional variable is idiosyncratic stock return volatility (IdioVol). We
measure the standard deviation of the residual values from the following time-series market
model:
Ri,t = b0 + b1 RM,t + εi,t ,
where Ri,t is stock i’s monthly return in month t and RM,t is the monthly return of the
S&P 500 index in month t. We estimate the above equation for each stock each month
in the data set using the previous 36 months of returns. Shleifer and Vishny (1997) argue
that professional arbitrage is conducted by a relatively small number of highly specialized
investors using other people’s capital. Such arbitrage is ineffective when prices diverge further
from fundamental values before they converge. Furthermore, arbitrageurs are risk averse and
typically poorly diversified, and hence they are concerned about the idiosyncratic risk of their
portfolios. Thus, Shleifer and Vishny (1997) predict that idiosyncratic volatility will deter
arbitrage activities7 .
The other five conditional variables are the number of institutional investors (N(INST)),
analyst coverage (COVER), the bid-ask spread (BIDASK), firm size, and individual stock
volatility (RETVOL). N(INST) is measured as the number of institutional investors holding
a firm’s shares at the portfolio formation date; COVER is measured as the number of
analysts following the firm at the portfolio formation date; BIDASK is calculated as the
7
Pontiff (2006) argues that the larger the portfolio weight that an arbitrageur assigns to a stock, the
more the stock’s idiosyncratic variance affects the portfolio’s variance. Hence, all else equal, the risk-averse
arbitrageur will take a relatively small position in a high idiosyncratic risk stock (for both short and long
positions). This result does not depend on the arbitrageur’s level of diversification, and hence idiosyncratic
risk will limit arbitrage with equal effectiveness in portfolios containing many and few securities
10
time-series average of 2 ∗ ((Ask − Bid)/(Ask + Bid)) at the end of each month over the 12
months prior to the portfolio formation date, where Ask (Bid) is the asking (bid) price;
firm size is measured as the market capitalization at the portfolio formation date; and
RETVOL is measured as the standard deviation of weekly excess returns over the year
ending at the portfolio formation date. Weekly returns are calculated from Thursday to
Wednesday to mitigate nonsynchronous trading effects in daily prices. As a robustness
check, the percentage of outstanding shares held by institutional investors at the portfolio
formation date (Perc(INST)) and dispersion in analyst forecast (DISPER) are also used
as our conditional variables. Dispersion in analyst forecast is measured as the standard
deviation of analyst one-year earnings forecasts at the portfolio formation date scaled by the
prior year-end stock price to mitigate heteroskedasticity.8
3.3
Summary Statistics
Table 1 reports the summary statistics for double-sorted portfolio returns and firm-specific
attributes. The value premium ranges from 0.1% to 0.3% per month among the firms with
low limits to arbitrage, whereas the value premium ranges from 0.93% to 2.06% per month
among the high limits-to-arbitrage group. Thus, the value premium is much higher among
firms with high idiosyncratic volatility, small firm size, high bid-ask spread, high return
volatility, and a small number of institutional investors. Moveover, the value premia are
very small and insignificant among firms with low limits to arbitrage. These results confirm
the findings in Griffin and Lemmon (2002), Ali et al. (2003), and Nagel (2005). This evidence
on the heterogeneity of the B/M effect is consistent with both the behavioral explanation of
the value premium and the rational explanation of the value premium (e.g., Chen (2011a)
and Garlappi and Yan (2011)). Here, we intend to be agnostic about the interpretation of
this evidence. Instead, in next section, we examine the underlying link between B/M and
firm-specific attributes across different groups of firms to evaluate alternative theories of the
value premium.9
8
These proxies could also be interpreted as proxies for information quality or information uncertainty as
in Veronesi (2000). However, our results do not depend on the interpretation of the conditional variables, as
long as they produce large variations of the value premium across different groups of firms.
9
In Garlappi and Yan’s (2011) model, for instance, the magnitude of the value premium depends on the
default probability, and hence their model could be consistent with the evidence on the heterogeneity of the
B/M effect. However, the value firms in their model still tend to have higher operating leverage and default
probability. Our tests below focus directly on the underlying relations between B/M and operating leverage
and between B/M and default probability .
11
Unconditionally, the correlations between B/M and the firm-specific attributes are
consistent with the implications of the structural explanations, and these findings are also
consistent with the evidence in the prior literature. In particular, the value firms on average
have a higher default probability, lower past profitability, higher operating leverage, lower
cash flow duration, and higher cash flow risk than the growth firms do. Thus, unconditionally,
we do find support for all the leading explanations for the value premium. Because the
firm-specific attributes are very persistent, we use Newey and West (1987) standard errors
(with lag = 4) to calculate t-statistics. If we change the lag value, the resulting t-statistics
usually change. However, the interpretation of our evidence does not crucially rely on the
t-statistics. We mostly focus on the coefficients and the correlations below. Thus, we do not
report robustness results with different values of the Newey-West lag.
4
Empirical Results
This section presents our main empirical evidence. We first report results on the conditional
tests based on our proxies for limits to arbitrage. We then explore possible sources underlying
the observed value premium.
4.1
Conditional
Relation
Between
B/M
and
Firm-Specific
Attributes
First consider explanation one, which predicts that B/M is positively correlated with default
probability. Following Griffin and Lemmon (2002), Table 2 reports the median O-scores
for the double-sorted portfolios. We find support for this explanation among the group
of firms in which the value premium is the weakest. However, among the high limits-toarbitrage firms, growth firms actually have a higher default probability, which is opposite
to the underlying assumption of the distress risk hypothesis. One striking feature is that
the above pattern is consistent across all of our moderators. For instance, among the group
with low return volatility, the growth firms have a median default probability of 0.459%,
whereas the value firms have a higher default probability of 1.076%. In contrast, among
the group with high return volatility, the growth firms have a median default probability of
32.125%, whereas the value firms have a lower default probability of 7.145%. Moreover, the
difference-in-differences are significant across all the proxies for limits to arbitrage.
12
Table 2 also reports the (conditional) correlation between the portfolio returns and the
corresponding O-scores for each level of limits to arbitrage. In general, for the lowest level
of limits to arbitrage, the correlation is positive, consistent with the financial-distress-based
explanation. However, for the highest level of limits to arbitrage, the correlation is negative.
Overall, the R2 from the cross-sectional regression of the 25 double-sorted portfolio returns
onto the corresponding O-scores is very low. Here, we put a negative sign in front of the R2
to indicate a negative overall correlation. The relation between B/M and O-scores is also
similar with the relation between portfolio returns and the O-scores. Thus, the evidence on
the relation among B/M, returns, and O-scores does not appear to support explanation one.
In Figure 1, we plot O-scores 5 years before and after the formation periods. It is evident
that there is a monotonic relation between O-score and B/M among the firms in which
the value premium is the weakest. By contrast, there is no obvious pattern among the firms
with high arbitrage costs. For example, among the firms with a large number of institutional
holders, there is a clear monotonic pattern that the value firms have a higher O-score than
the growth firms. In contrast, among the firms with a small number of institutional holders,
the relation between B/M and the O-score is not evident. In fact, both the extreme growth
and extreme value firms have high O-scores whereas the rest of the firms have a low O-score.
Since the value premium is strongest among the firms with a small number of institutional
holders, our evidence does not appear to support the financial distress hypothesis.
Previous studies find mixed evidence on the cross-sectional relation between default
probability and expected return, lending limited support for the financial distress risk
hypothesis. For example, Campbell et al. (2008) find the distressed firms tend to have lower
subsequent returns, whereas Chava and Purnanandam (2010)) argue that subsequent realized
returns are not a good measure for expected returns, and they find that the distressed firms
actually have a lower implied cost of capital. Our conditional test focuses on the fundamental
link between B/M and default probability, and our results provide clear evidence against
this explanation. Since our evidence does not rely on where financially distressed firms earn
higher or lower returns, we sidestep the previous debate on whether there is a positive or
negative relation between default probability and expected returns.
Next we consider explanation two, which implies a negative relation between B/M and
profitability. Table 3 reports the portfolio-level ROA of the double-sorted portfolios. It
reveals that among the firms in which the B/M effect is the weakest, there is indeed a
monotonic negative contemporaneous relation between B/M and ROA. That is, as B/M
increases, profitability decreases. In contrast, among the firms in which the B/M effect is
13
the most pronounced, the growth firms tend to have a lower ROA than the value firms.
For instance, among the big firms, the growth portfolio has a large ROA of 0.105, whereas
the value portfolio has a low ROA of only 0.031. In contrast, among the small firms, the
growth portfolio has a negative ROA of -0.118, whereas the value portfolio has an ROA of
-0.032. Again, it is striking that this pattern holds for all the moderators. Moreover, the
difference-in-differences are significant across all the proxies for limits to arbitrage. Since the
theory would suggest that the ROA spread between the value and the growth firms should
be decreasing as the value premium increases, this pattern does not appear to square with
the explanation based on profitability. Another interesting observation is that the firms with
high limits-to-arbitrage tend to have a low ROA on average.
In Figure 2, we plot the ROA dynamics 5 years before and 5 years after the formation
periods. We only plot the ROA dynamics for the firms with the least and the largest limits
to arbitrage. Clearly, there is a monotonic negative relation between ROA and B/M among
the low limits-to-arbitrage group, consistent with the theory. In this category of firms, the
growth firms tend to have a higher ROA 5 years before and 5 years after the portfolio
formation. However, among the group of firms in which the value premium is the strongest,
there is basically no negative relation between ROA and B/M. If anything, the relation seems
reversed, which is opposite to the prediction of the theory. Thus, these plots confirm the
empirical findings in Table 3.
By sorting on the firm’s profitability directly, Chen et al. (2010) and Novy-Marx
(2010) find that firms with high profitability tend to have a higher subsequent return, in
contradiction to the profitability-based explanation as well. Here, we go one step further by
showing that the growth firms actually have a lower profitability than the value firms among
the firms in which the value premium is the most pronounced. Thus, it is even conceivable
that the value premium resulted from the low profitability of the growth firms, rather than
from the high profitability of the growth firms. That is, the value premium could result from
investors’ underreaction to the growth firms’ low past profitability, rather than overreaction
to the growth firms’ good past performance since the profitability of the growth firms are
very low among the group of firms with a large value premium. We will return to this point
later when we examine the mispricing hypothesis of the B/M effect.
We now turn to explanation three, which suggests that the value firms are riskier because
these firms tend to have a higher operating leverage. Similar to the previous results, Table
4 shows that for the low limits to arbitrage group, there is a monotonic positive relation
between B/M and operating leverage. However, as we move to firms with higher limits to
14
arbitrage, the positive relation between B/M and operating leverage is not evident anymore,
and in many cases, the growth firms have a high operating leverage than the value firms do.
For instance, among the low idiosyncratic risk group, the growth firms have a lower
operating leverage than the value firms. However, among the group with the highest
idiosyncratic risk and the highest value premium, the value firms have a lower operating
leverage. Furthermore, the correlation between the operating leverage and the average return
among this group is a negative 78.8%, contrary to the prediction implied by this explanation.
A similar pattern holds when size, the number of institutional holders, and analyst coverage
are used as conditional variables. When the bid-ask spread or return volatility is used as a
conditional variable, the difference in operating leverage between the value and growth firms
is indeed significantly higher among the high limits-to-arbitrage group than among the low
limits-to-arbitrage group, supporting explanation five. However, when volatility is used as a
conditional variable, the overall correlation between the operating leverage and the average
return is actually a negative value of -0.8%. This suggests that a high operating leverage
does not necessarily yield a higher average return.
In sum, out of the six conditional variables, five of them do not appear to support
the operating leverage-based explanation. Only the bid-ask spread lends support to this
explanation. On the other hand, based on unconditional tests, Gulen et al. (2008), Garcı́aFeijóo and Jorgensen (2010), and Novy-Marx (2011) find evidence supporting the role of
operating leverage in the value premium. Our conditional tests again suggest that one needs
to be careful in interpreting previous evidence from unconditional tests, since more powerful
conditional tests tend to yield different conclusions.
We then consider the duration-based explanation of Lettau and Wachter (2006) and
Da (2009), which predicts a negative association between B/M and cash flow duration. In
Table 5, we follow Da (2009) in constructing the cash flow duration for our double-sorted
portfolios. Since this measure is an affine transformation of the true duration, it can be
negative. Table 5 shows that the growth firms in the low limits-to-arbitrage group indeed
have a higher cash flow duration. In sharp contrast, among the high limits-to-arbitrage
group, there is no apparent relation between cash flow duration and B/M. For example,
for the size proxy, the growth portfolio in the low limits-to-arbitrage group has a duration
of 1.375, whereas the value portfolio in the group has a duration of 0.415. On the other
hand, the growth portfolio has a duration of only −0.834 in the high limits-to-arbitrage
group, whereas the value portfolio has a duration of 0.177. Similar results also hold for other
proxies. Moreover, in untabulated analysis, we show that the same pattern remains if we
15
use the duration measure of Dechow et al. (2004). In fact, the correlations between the
25 double-sorted portfolio returns and the duration, and between 25 double-sorted portfolio
B/M and duration, are close to zero for the six conditional variables, lending little support
to the duration-based explanation.
Table 5 also indicates that the difference-in-differences is significantly positive for all the
proxies except the bid-ask spread. That is, the difference in cash flow duration between the
growth portfolio and the value portfolio in the high limits-to-arbitrage group is significantly
smaller than that in the low limits-to-arbitrage group. The value premium is tiny among
the low limits-to-arbitrage group, whereas the value premium is highly significant among
the high limits-to-arbitrage group. This finding is exactly opposite to the prediction by
the duration-based explanation. Thus, the evidence in Table 5 appears not to support the
duration-based structural models.
On the other hand, previous unconditional tests tend to find support for this explanation.
For example, Dechow et al. (2004) and Da (2009) find that the value firms have lower cash
flow duration and firms with higher duration earn lower subsequent returns. Our conditional
test suggests that the unconditional tests do not provide a complete picture on the relation
between B/M and cash flow duration. While it is true that there is a strong overall negative
relation between B/M and duration, the negative relation is not present among the firms in
which the value premium is the biggest. Thus, the more informative conditional tests do not
appear to support the duration-based explanation.
Finally, we consider explanation five, which predicts that value firms tend to have a
higher cash flow sensitivity than the growth firms do. Table 6 presents our findings. We
follow Bansal et al. (2005) in measuring portfolios’ cash flow sensitivity with respect to longrun consumption growth. We regress portfolio-level dividend growth on smooth average
consumption growth to obtain cash flow sensitivities. Table 6 shows that, for the size
moderator, the growth firms have a lower cash flow risk than the value firms among the
firms with low limits to arbitrage. This result is supportive of the cash flow risk-based
explanation. This result is also consistent with earlier studies, since the cash flow risk-based
model can also account for the size anomaly.
However, for other moderators, we do not find support for the cash flow risk-based
explanation. For example, for firms with low analyst coverage and a small number of
institutional holders, the growth firms have a higher cash flow risk than the value firms
do. Moreover, for firms with high idiosyncratic volatility and high return volatility, although
16
the value firms appear to have a higher cash flow risk, there is no apparent positive relation
between cash flow risk and portfolio returns. For the moderator of the bid-ask spread, it is
true that the cash flow risk difference between the value portfolio and the growth portfolio
is much larger among the high limits-to-arbitrage group, consistent with hypothesis five.
However, the correlation is only 20.3% among the group with the highest bid-ask spread
and the highest value premium. The overall correlation between portfolio returns and cash
flow risk across the 25 portfolios is only 32%, suggesting an R2 of 10.2% in a cross-sectional
regression, a much smaller magnitude compared with that based on the unconditional test
in prior literature (see, e.g., Bansal et al. (2005)).
We want to mention a caveat to our results, since measuring the cash flow risk of a
portfolio is extremely difficult (see, e.g., Hansen, Heaton, and Li (2008) and Chen and Zhao
(2010)). The results are not very stable if we change the methods of estimating the cash
flow risk. However, the general pattern of a low (or even negative) correlation between B/M
and cash flow risk among the high limits-to-arbitrage group remains. In sum, although the
evidence is not strongly against the cash flow risk-based explanation, our findings do not
appear to support the cash flow risk-based explanation either.
Similar to the previous explanation, existing unconditional tests find support for the
cash flow risk-based explanation. For example, Bansal, Dittmar, and Lundblad (2005)
and Da (2009) find that the growth firms have a lower cash flow sensitivity to aggregate
consumption.10 Previous studies find that the cross-sectional regression of average B/M
portfolio returns on cash flow duration has an R2 typically ranging from 50% to 80%.
However, for our six sets of double-sorted portfolios, the cross-sectional R2 is only about
2% to 20%. Again, our conditional test provides new insights on the relation between cash
flow risk and the B/M. The lack of a positive relation between cash flow sensitivity and B/M
among the firms with the strongest B/M effect suggests that the cash flow risk is unlikely
to account for all the observed value premium.
Overall, with six proxies for limits to arbitrage, our conditional approach provides a
powerful tool for testing the existing leading structural theories of the value premium. Our
evidence indicates that the power of the prior unconditional tests is relatively weak, and
that the apparent support for these explanations based on unconditional tests could be
misleading. In future work, our conditional approach could be used at least as a robustness
10
Instead of focusing on the cash flow sensitivity to the aggregate consumption, Campbell and Vuolteenaho
(2004) show that value firms have a higher exposure to the cash flow news in the aggregate market portfolio.
However, Chen and Zhao (2010) show that the results of Campbell and Vuolteenaho (2004) are very sensitive
to the instruments used to estimate the cash flow news in the market portfolio.
17
check in testing structural models.
4.2
Robustness Checks
As mentioned earlier, we choose idiosyncratic volatility, return volatility, size, the number
of institutional holders, analyst coverage, and the bid-ask spread as our main moderators in
our conditional tests because the magnitude of the value premium varies significantly across
groups of firms partitioned by these variables. Prior studies have used other proxies for limits
to arbitrage, such as firm age, analyst dispersion, percentage of institutional holding, and etc.
It is true that the value premium is stronger among the firms with high limits-to-arbitrage
when other variables are used as proxies. However, these proxies do not offer significant
variations in the value premium across firms with high and low limits to arbitrage. Thus,
for our conditional tests, these variables are not as good as the six proxies we used for our
main analysis.
Nonetheless, as a robustness check, Table 7 reports the results for the tests employing
percentage of institutional holding and analyst dispersion as a proxy for limits to arbitrage.
It shows that the previous pattern largely remains. In particular, among the high analyst
dispersion group, there is no significant desired relation between B/M and firm-specific
attributes, as implied by the structural explanations. For the proxy of analyst dispersion, the
results are opposite of hypotheses 1, 2, and 4. The evidence does not support the explanation
based on operating leverage either, since the cross-sectional regression of the 25 double-sorted
portfolio returns onto the operating leverage has an R2 of only 11.3%. However, our evidence
appears to support the cash flow risk-based explanation. Similar results hold if percentage of
institutional holding is used as a conditional variable. Finally, we want to point out that the
results based on these two conditional variables are not as strong as the previous six proxies
we use in our main analysis. Since percentage of institutional holding and analyst dispersion
does not generate enough variations in the value premium across different limits-to-arbitrage
groups, this slightly weaker evidence does not necessarily lend support for the theories.
Moreover, several models (e.g., Zhang (2005)) imply that the value firms are especially
risky during recessions. Thus, we investigate the default probability of the double-sorted
portfolios during recessions and booms. Table 8 reports the default probability for the
double-sorted portfolio across recessions and booms, separately. It is true that the value
firms have a higher default probability during recessions than during booms, especially in
the high limits-to-arbitrage group. However, it is still true that among the high limits18
to-arbitrage group, the value firms have lower default probabilities even during recessions,
contrary to the theory. Another surprising pattern is that the growth firms in the high
limits-to-arbitrage group actually have a higher default probability during booms than during
recessions, probably because the return-on-assets for the growth firms is actually lower during
booms than during recessions.
Finally, in untabulated analysis, we perform the same analysis using different measures
of cash flow duration, cash flow risk, and operating leverage. For example, we measure cash
flow duration by following Dechow et al. (2004). We also measure the cash flow risk with
adjusted dividend growth by following Bansal et al. (2005). Although different measures of
the firm-specific attributes tend to yield different results, the general pattern remains. That
is, there is a consistent relation between B/M and the firm-specific attributes among the low
limits-to-arbitrage firms, whereas there is no significant desired relation, and the relation is
usually reversed for many conditional variables. In all, our evidence is fairly robust across
different conditional variables and different measures of the firm-specific attributes.
4.3
Potential Source of the B/M Effect
Given that our findings do not appear to support the leading risk-based explanations,
we consider a natural alternative hypothesis, the mispricing hypothesis. The mispricing
hypothesis has a long tradition (see, e.g., Lakonishok et al. (1994)). Although the goal of
this paper is to document the difficulty faced by the leading models, rather than to solve
the value premium puzzle, we attempt to better understand the possible sources behind
the observed value premium. In particular, we explore the reasons why investors award
growth firms with high market values relative to their book values and why these firms
tend to earn lower subsequent returns. One possibility is that investors may overreact to
information about the future growth potential of these firms, as suggested by Griffin and
Lemmon (2002). To investigate this possibility, we follow Griffin and Lemmon (2002) by
examining the sale growth, market value to sales, capital expenditure to book assets, and
R&D to book assets for the firms among the high and low limits-to-arbitrage groups.
Table 9 reports sales growth, the ratio of sales to book assets, the market-to-sales ratio,
the ratio of capital expenditures to book assets, and the ratio of R&D expenditures to book
assets for each portfolio. In general, the sales growth of growth firms is significantly higher
than that of value firms. Table 9 also shows that compared with the value firms in the high
limits-to-arbitrage quintile, the growth firms in the high limits-to-arbitrage quintile (except
19
the analyst coverage proxy) tend to have the lowest ratios of sales to book assets, indicating
that the current level of sales is low relative to the level of assets for these growth firms.
Nevertheless, the market-to-sales ratios, especially the ratios of market-to-sales ratios for
the growth and value portfolios (column L/H under ME/Sales), indicate that relative to the
value firms in the high limits-to-arbitrage group, investors award these growth firms with high
multiples for these low sales levels, suggesting that investors are anticipating improvements
in subsequent sales growth and profitability.
In sharp contrast, compared with the value firms in the low limits-to-arbitrage quintile,
the growth firms in the low limits-to-arbitrage quintile have the highest ratios of sales to
book assets. Despite this, investor only award these growth firms a slightly higher market-tosales ratio than the value firms in the low limits-to-arbitrage group (see column L/H under
ME/Sales). This indicates that in the low limits-to-arbitrage group, the growth firms do have
better fundamentals than the value firms, whereas among the high limits-to-arbitrage group,
the value firms actually have better current fundamentals. It also suggests that relative to
the current fundamentals, the growth firms in the high limits-to-arbitrage group are probably
relatively more overpriced than the growth firms in the low limits-to-arbitrage group.
In addition, Table 9 suggests that the growth firms in the high limits-to-arbitrage group
tend to have large capital expenditures as a fraction of book assets. The R&D expenditures
as a fraction of book assets are also especially high for these firms. These findings indicate
that, despite their poor current earnings, these firms continue to invest heavily in future
growth opportunities. One interpretation of this finding is that despite their poor current
fundamentals for the growth firms in the high limits-to-arbitrage group, investors award
these firms with high market prices relative to both book equity and sales, possibly because
investors perceive good growth opportunities in this category of firms. Subsequently,
however, investors tend to be systematically disappointed and earn low returns. Thus, our
evidence suggests that investors may underestimate the importance of information about
current fundamentals and be overoptimistic about future growth opportunities, confirming
the findings of Griffin and Lemmon (2002) who use the O-score as a conditional variable.
Lastly, following La Porta (1996) and La Porta et al. (1997), we examine the stock price
movements around earnings announcement dates to assess whether systematic expectational
errors can indeed explain the value premium. In particular, if the large value premium
in the group of firms with severe limits on arbitrage is due to mispricing, and if investors
revise their expectations when earnings announcements are made, we would expect value
(growth) firms to earn high (low) returns around earnings announcement days when investors
20
realize their previous expectation errors. This is because value (growth) firms tend to have
positive (negative) earnings surprises on average. Furthermore, the return spread during
announcements should be most pronounced among stocks with severe limits to arbitrage.
To investigate this possibility, we calculate the event returns around earnings
announcements. In particular, at the end of each June, the event return for each stock
is measured quarterly over a three-day window (−1, +1) around the Wall Street Journal
publication dates and then summed up over the next four quarters after portfolio formation.
Equally weighted averages across all stocks within each portfolio are calculated as the annual
event return of this portfolio. Table 10 shows that among stocks with severe limits on
arbitrage, the earnings announcement raw returns are usually negative for growth firms
and positive for value firms. This negative event return for the growth firms among the high
limits on arbitrage group is especially hard to reconcile with any rational theories of the value
premium. Moreover, the return spreads during earnings announcements among this category
of firms are highly significant, whereas the return spreads during earnings announcements
are much weaker and sometimes insignificant for firms with fewer limits on arbitrage. These
findings provide support for the hypothesis that mispricing is more pronounced in high
limits-on-arbitrage group. In terms of magnitude, the value premium is about 8 − 24% per
annum among firms with high arbitrage costs. Table 10 shows that about 30 − 50% of the
value premium is realized during earnings announcements in the subsequent year.
In sum, the above findings, together with the fact that the growth firms earn an abysmally
low subsequent return in the high limits-to-arbitrage group (see Table 1), suggest that the
growth firms in the high limits-to-arbitrage group are more overpriced than those in the low
limits-to-arbitrage group. However, we only view our evidence on mispricing as suggestive
but not conclusive. For example, the R&D of the growth firms in the high limits-to-arbitrage
group is not much significantly higher than the R&D of the growth firms in the low limitsto-arbitrage group. Thus, the force we suggest here may only account for a fraction of the
observed value premium. There might still be a significant portion of the value premium
that we do not fully understand. This requires much more comprehensive analysis, which is
beyond the scope of our study. Overall, the value premium still remains a puzzle to us.
21
5
Conclusion
The leading explanations for the value premium typically imply that the value firms earn
higher subsequent returns because these firms command a higher risk premium due to higher
default probability, lower past profitability, higher operating leverage, higher cash flow risk,
or shorter cash flow duration. Prior supportive evidence for these theories is mostly based
on unconditional tests. Using several conditional variables, we find that within the group
in which the value premium is not significant/existant, there is indeed a significant desired
relation between B/M and the firm-specific attributes. However, within the group in which
the value premium is the most pronounced, there is no significant desired relation. In many
cases, the relation is even opposite to the predictions of the theories. Thus, our evidence
suggests that a high unconditional cross-sectional relation between B/M and firm-specific
attributes is not a sufficiently high hurdle by which to evaluate a model.
Our empirical results suggest that the existing structural models have difficulty explaining
the value premium in isolation. However, it could be possible that, by combining several
mechanisms proposed in the literature, the structural model can explain the value premium
more successfully. On the other hand, our preliminary evidence suggests that investors
may underestimate the importance of information about current fundamentals and be
overoptimistic about future growth opportunities, especially among high limits-to-arbitrage
firms, confirming the findings in Griffin and Lemmon (2002). Indeed, the return patterns
during earnings announcements provide support for the hypothesis that mispricing is
more pronounced among high limits-on-arbitrage firms. Overall, we conclude that our
understanding of the value premium is still very limited.
Finally, this paper shows that the insights from the limits-to-arbitrage literature can be
used to test structural models. In future work, the conditional approach could be applied
to test competing explanations for other anomalies, such as the momentum effect and the
asset growth anomaly, among others. For example, Johnson (2002), Bansal et al. (2005),
Sagi and Seasholes (2007), and Zurek (2008) propose different structural models that can
generate the momentum effect by linking past returns to firm-specific attributes, such as
dividend growth, cash flow risk, and exposure to investment-specific shock. On the other
hand, previous studies suggest that the momentum effect is much stronger among firms with
low analyst coverage (e.g., Hong, Lim, and Stein (2000), high information uncertainty (e.g.,
Zhang (2006)), and high trading volume (e.g., Hou, Peng, and Xiong (2009)). Therefore,
one could use these variables as moderators to perform the same conditional tests as we have
22
done for the value premium. We leave this for future research.
23
Data Appendix
O-score and Financial Distress Probability
Following Ohlson (1980), the O-score of any individual firm is defined as follows:
total assets(Compustat annual item AT)
)
GNP price-level index(GNP price-level index from Fed)
total liabilities(Compustat annual item LT)
+ 6.03(
)
total assets
working capital(Compustat annual item ACT-Compustat annual item LCT)
− 1.43(
)
total assets
current liabilities(Compustat annual item LCT)
+ 0.076(
)
current assets(Compustat annual item ACT)
net income
)
− 1.72(1 if total liabilities¿total assets, 0 otherwise) − 2.37(
total assets
funds from operations(Compustat annual item PI)
)
− 1.83(
total liabilities
+ 0.285(1 if net loss for the last two years, 0 otherwise)
net incomet − net incomet−1
− 0.521(
)
|net incomet | + net incomet−1
Oscore = −1.32 − 0.407log(
The corresponding probability of financial distress is
P rob =
1
.
1 + exp(−Oscore)
The median-level financial distress probability of a portfolio is our portfolio financial
distress probability. We include all common stocks traded on NYSE, AMEX, and NASDAQ
with nonnegative book values of equity, except financial firms (firms with SICCD in
[6000,6999]) and firms with missing or nonpositive total assets, total liabilities, and current
assets in this sample.
Profitability
Following Novy-Marx (2010), annual ROA is defined as income before extraordinary items
(Compustat annual item IB) scaled by total assets (Compustat annual item AT). The
24
portfolio ROA is calculated as portfolio aggregate income before extraordinary items divided
by portfolio aggregate total assets.
We include all common stocks (excluding stocks with shrcd >= 20 in CRSP) traded on
NYSE, AMEX, and NASDAQ with nonnegative book values of equity, except financial firms
in this sample (firms with SICCD in [6000,6999]).
Operating Leverage
The operating leverage of the individual firm is estimated by two steps. First, we run the
following two five-year overlapping regressions of EBIT (Compustat annual item EBIT) and
Sale (Compustat annual item Sale) onto time t, respectively:
LnEBITt = LnEBIT0 + gebit t + µt,ebit LnSalest = LnSales0 + gsales t + µt,sales
where EBIT0 and Sales0 are the beginning levels of EBIT and Sales, respectively. To
deal with the negative earnings, we follow a transformation common in accounting research,
ln(1 + EBIT ) if EBIT ≥ 0, and −ln(1 − EBIT ) if EBIT < 0.
Second, we take the residual series µt,ebit and µt,sales from the first step and estimate the
following equation:
µt,ebit = OLµt,sales + et
Since negative OL is economically irrational, we delete firms with negative OL before
portfolio formation. We include all common stocks (excluding stocks with shrcd >= 20 in
CRSP) traded on NYSE, AMEX, and NASDAQ with nonnegative book values of equity, sale
and OL, except financial and utilities firms (firms with SICCD in [6000,6999] and [4900,4999])
in this sample.
To get portfolio OL, we repeat the same two steps as before, but on the portfolio level.
In particular, we sum the EBITs and Sales for all individual firms in a portfolio, and rerun
the above three regressions. New OLS coefficients from the second step are our portfolio
OLs.
25
Cash Flow Duration
Following Da (2009), for each year t after portfolio formation, we construct the ex post cash
flow duration of portfolio i using the formula
Durti =
X
t
ei −
X
κ
− ξti − Et [
∆c].
1−ρ
t
• ρ and κ are chosen to be 0.95 and 0.1985, respectively, which are backed out from the
relationship between accounting earnings and cash flow characteristics implied by the
accounting clean surplus identity.
• The discounted sum of all future accounting earnings
X
ei =
t
∞
X
ρn ei (t, n + 1) is
n=0
calculated by breaking it into a finite summation term (we choose N = 7 as Da (2009))
and the terminal value term:
X
t
ei =
N
−1
X
ρn ei (t, n + 1) +
n=0
∞
X
ρn Et [ei (t, n + 1)],
n=N
Earningsit+1
), and Earnings (Compustat annual item NI)
Book Equityit
and Book Equity of the portfolio i at time t are the aggregate portfolio net income and
book equity, respectively.
where ei (t, n + 1) = log(1 +
i
• ξti = log( Cash Flowt i ). Portfolio i’s cash flow is defined as aggregate portfolio
Book Equityt
common dividend (Compustat annual item DVC) plus common share repurchases.
Following Grullon and Michaely (2002), common share repurchases is defined as the
expenditure on the purchase of common and preferred stocks (Compustat annual item
PRSTKC) minus any reduction in the book value of preferred stock (Compustat annual
item PSTKRV). BookEquityti is the aggregate portfolio book equity at time t defined
as before. All accounting cash flow data are converted to the real terms using the
personal consumption expenditure (PCE) deflator.
X
• The discounted sum of all future log aggregate consumption growth
∆c =
∞
X
t
ρn ∆c( t + n + 1). Its time t expectation is calculated by assuming an ARMA(1,1)
n=0
26
process:
∆ct+1 = µc (1 − ρ1 ) + ρ1 ∆ct + ωt+1 − ρ2 ωt
ωt ∼ N (0, σω2 ).
To match it with the cash flow data series, we measure ∆ct annually (fourth quarter
to fourth quarter) using quarterly log aggregate consumption data taken from Sydney
Ludvigson’s website (http://www.econ.nyu.edu/user/ludvigsons). The sample is from
1951Q2 to 2010Q2.
We include all common stocks (excluding stocks with shrcd >= 20 in CRSP) traded
on NYSE, AMEX and NASDAQ with nonnegative book equity values, except financial and
utilities firms (SICCD in [4900,4999] and [6000,6999])) in this sample. We also delete firms
with missing values of data item NI, missing or negative DVC and PSTKRV. We set missing
values of PRSTKC to be 0 given it commonly exists. Further, since the portfolio cash flow is
essentially the dividend payout to investors, we delete firms with a negative cash flow value
based on the definition above. Finally, to avoid potential data errors and extreme outliers,
we exclude firms whose NI exceeds the 99th percentile or falls below the 1st percentile.
Cash Flow Sensitivity
Following Bansal et al (2005), the Cash Flow sensitivity gamma of the Portfolio i is estimated
from the following regression:
gi,t
K
1 X
gc,t−k ) + ui,t ,
= γi (
K k=1
where gi,t is the de-meaned log dividend growth rate and gi,t is the de-meaned log aggregate
consumption growth rate, both on the quarterly frequency and in real terms. We use the
quarterly seasonally adjusted real per capita consumption of nondurables plus services taken
from the NIPA tables available from the Bureau of Economic Analysis to measure aggregate
consumption. To construct the quarterly levels of dividends, we proceed in two steps.
First, we construct the monthly dividend series of portfolio i as below. The dividend yield
i
yt+1
of portfolio i from time t to time t + 1 is the difference between the value weighted total
i
return Rt+1
(CRSP data item RET) and the value weighted capital gain hit+1 (CRSP data
i
i
item RETX), i.e., yt+1
= Rt+1
− hit+1 .
27
To take account of the effect of repurchase activity, we also consider an adjusted measure
of capital gain series. Denote the number of shares (after adjusting for splits, stock dividends,
etc. using the CRSP share adjustment factor (CRSP data item FACSHR)) of a given firm
as nt :
h∗t+1 = [
nt+1
Pt+1
] × min[(
), 1].
Pt
nt
Let Vti be the value of portfolio i at time t. Then the level of the cash dividends of this
i
i
i
= hit+1 Vti with
− Vti , where Vt+1
= yt+1
portfolio from time t to time t + 1 will be Dt+1
V0i = 1. Following this procedure, we get the nominal levels of cash dividends Dit for each
portfolio on a monthly basis. Further, we convert these nominal series to real by the PCE
deflator taken from the NIPA tables.
Second, we sum the monthly real dividends within the same quarter to get quarterly
levels of dividends. To deal with the strong seasonalities at the quarterly frequency, we
also employ a trailing four-quarter average of these quarterly dividends to construct the
deseasonalized quarterly dividend series.
We include all common stocks (excluding stocks with shrcd >= 20 in CRSP) traded on
NYSE, AMEX, and NASDAQ with nonnegative book equity values in this sample. Further,
to avoid potential problems from extreme outliers when computing log dividend growth, we
exclude stocks whose R, h, and h∗ exceed the 99th percentile or fall below the 1st percentile.
28
Table 1: Summary Statistics
Panel A reports the time-series averages of the monthly excess returns for our 25 double-sorted portfolios
first sorted by our proxies and then by B/M, the difference in the excess returns between the high and low
B/M portfolio, and the t statistics of the differences if available. At the end of June every year, we first
sort NYSE, AMEX, and NASDAQ ordinary common stocks (exclude stocks with shrcd >= 20 in CRSP)
with nonnegative book value of equity into five groups based on the quintile of the ranked values of each
proxy in June, and then sort stocks within each group into five groups based on the quintile of the ranked
values of B/M. The portfolio is rebalanced at the end of June every year. B/M is the book value of equity
divided by market value at the end of last fiscal year. We consider six proxies: idiosyncratic stock return
volatility (IdioVol) is the standard deviation of the previous 36-month residual values from the time-series
market model (Ri,t = b0 + b1 RM,t + εi,t , where Ri,t is the monthly return on stock i and RM is the monthly
return on S&P 500 index). Size (SIZE) is the market value of equity at the end of June. Analyst coverage
(COVER) is the number of analysts following the firm at the end of June. Number of institutional holders
(N(INST)) is the number of institutional investors holding a firm’s shares at the end of June. Bid-ask spreads
(BIDASK) is the time-series average of 2∗((Ask −Bid)/(Ask +Bid)) from June back to the past year. Stock
volatility (RETVOL) is the standard deviation of weekly excess returns from June back to the past year.
Panel B reports the various portfolio-level firm attributes of 5 portfolios single sorted by B/M, the difference
in each attribute between the high and low B/M portfolio, and the t statistics of the differences. At the
end of June every year, we sort stocks in the sample into five groups based on the quintile of the ranked
values of B/M. (The sample varies slightly for different firm attributes; see more in the data appendix.) The
portfolio is rebalanced at the end of June every year. We consider five firm characteristics: The O-score is
the portfolio financial distress probability implied by Ohlson’s (1980) O-score. Portfolio financial distress
probability is the median financial distress probability within a portfolio. ROA is the ratio of the portfolio
aggregate income before extraordinary items to the portfolio aggregate total assets. Portfolio Operating
Leverage (OL) is estimated by two steps: the first step, we run five-year overlapping regressions of the
portfolio earnings and sales on time, respectively. Next we regress the residuals of the earnings regression on
the residuals of the sales regression both from the first step and record this OLS regression coefficient as our
portfolio OL. Cash Flow Duration (CF Dur) is the difference between the discounted sum of all firms’ future
dividends within the portfolio and the time t expectation of the discounted sum of all future log aggregate
consumption growth. Cash Flow Sensitivity (CF Gamma) is OLS coefficients of regressing the portfolio
de-meaned dividend growth rate on a trailing moving average of de-meaned consumption growth in the past
8 quarters. We only report the results of the L (Low), 3, H (High), and High-minus-Low (H-L) proxy groups
and the L (Low), 3, H (High), and High-minus-Low (H-L) B/M portfolios within these groups in Panel A,
and High-minus-Low (H-L) B/M portfolios in Panel B to save space. Sample period is from July 1962 to
December 2010 for IdioVol, SIZE, BIDASK and RetVol; from July 1976 to December 2010 for COVER; and
from August 1983 to December 2010 for N(INST). The excess returns and financial distress probability are
in percentages. The t-statistics are calculated based on Newey-West (1987) adjusted standard errors with
lag =4.
29
Book-to-Market Equity
Panel A: Double-Sorted Portfolio Excess Returns
L
3
H
H-L
t-stat
L
0.41
0.43 0.68
0.27
1.78
3
0.34
0.67 0.91
0.56
2.13
IdioVol
H
-0.32 0.42 0.95
1.27
4.65
H-L
1.00
3.82
L
0.34
0.38 0.58
0.24
1.28
3
0.32
0.64
0.97
0.65
2.96
1
SIZE
H
0.28
0.93 1.21
0.93
4.27
H-L
0.70
3.47
L
0.42
0.57
0.6
0.19
0.88
3
0.50
0.74 0.91
0.41
1.74
1
COVER
H
0.43
0.82 1.12
0.69
2.32
H-L
0.50
2.00
L
0.46
0.50 0.77
0.30
1.30
3
-0.12
0.71
0.84
0.96
3.37
1
N(INST)
H
-0.85 0.37 1.21
2.06
6.32
H-L
1.76
4.77
L
0.46
0.51 0.60
0.14
0.96
3
0.46
0.71 1.20
0.75
2.89
BIDASK
H
0.22
0.61 1.20
0.98
2.74
H-L
0.84
2.33
L
0.60
0.45 0.61
0.10
0.64
3
0.42
0.64 0.71
0.36
1.22
RetVol
H
-0.60 0.53 0.69
1.72
4.93
H-L
1.62
5.42
Panel B: 5 B/M Portfolio Characteristics
L
3
H
H-L
O-score
0.018 0.010 0.022 0.004
ROA
0.088 0.048 0.021 -0.067
OL
1.920 2.481 3.157 1.234
CF Dur
1.099 0.561 0.401 -0.699
CF Gamma
-2.497 3.790 9.755 12.252
30
t-stat
2.21
-21.92
3.11
-6.20
NA
Table 2: Financial Distress Probability of Double-Sorted Portfolios
This table reports the time-series averages of the default probability implied by Ohlson’s (1980) O-score for
the 25 double-sorted portfolios first sorted by our proxies and then by B/M, the difference of the probability
between the high and low B/M portfolio, and the t statistics of the differences. We use the median level
financial distress probability of a portfolio as our portfolio financial distress probability. At the end of June
every year, we first sort stocks into five groups based on the quintile of the ranked values of each proxy, and
then sort stocks within each group into five groups based on the quintile of the ranked values of B/M. The
portfolio is rebalanced at the end of June every year. B/M is the book value of equity divided by market
value at the end of last fiscal year. We consider six proxies: idiosyncratic stock return volatility (IdioVol), size
(SIZE), analyst coverage (COVER), number of institutional holders (N(INST)), bid-ask spreads (BIDASK),
and stock volatility (RETVOL). The corresponding sample period for each proxy is the same as in Table
1. The column Cond. Corr reports the correlation between the 5 portfolio returns and the corresponding
O-score. The column CS-R2 reports R2 from the cross-sectional regression of the 25 double-sorted portfolio
returns onto the corresponding O-score. A negative sign in front of the R2 indicates a negative overall
correlation. The default probabilities are in percentages.
L
3
IdioVol
H
H-L
L
3
1
SIZE
H
H-L
L
3
1
COVER
H
H-L
L
3
1
N(INST)
H
H-L
L
3
BIDASK
H
H-L
L
3
RetVol
H
H-L
Book-to-Market Equity
L
3
H
H-L
t-stat
0.396 0.922 1.017 0.621
5.02
0.600 0.946 1.862 1.262
5.07
22.759 4.182 5.967 -16.791 -3.35
-17.412 3.42
0.253 0.482 0.781 0.528
5.25
4.234 1.020 1.481 -2.753 -2.58
29.072 4.417 5.269 23.803 -4.04
-24.331 4.08
0.242 0.421 0.915 0.673
5.2
0.709 0.692 1.377 0.669
3.06
2.686 1.049 2.174 -0.511 -0.99
-1.184
2.19
0.281 0.456 1.022 0.741
7.09
2.308 1.081 1.912 -0.396 -0.74
30.562 3.803 4.822 -25.740 -6.89
-26.481 7.01
0.492 1.018 1.061 0.569
4.11
0.671 0.880 1.683 1.012
5.47
27.732 5.794 6.832 -20.900 -3.14
-21.469 3.18
0.459 0.973 1.076 0.617
3.65
0.680 0.941 1.748 1.069
5.22
32.125 6.685 7.145 -24.980 -3.40
-25.597 -3.44
31
Cond. Corr
0.787
0.900
-0.891
CS-R2
-0.274
0.711
-0.856
-0.760
0.013
0.293
0.925
-0.438
0.064
0.858
-0.546
-0.893
-0.471
0.663
0.929
-0.647
-0.015
-0.264
0.835
-0.881
-0.331
Table 3: ROA of Double-Sorted Portfolios
This table reports the time-series averages of the annual portfolio ROA for our 25 double-sorted portfolios
first sorted by our proxies and then by B/M, the difference in the ROA between the high and low B/M
portfolio, and the t statistics of the differences. The portfolio ROA is calculated as portfolio aggregate
income before extraordinary items divided by portfolio aggregate total assets. At the end of June every year,
we first sort stocks into five groups based on the quintile of the ranked values of each proxy, and then sort
stocks within each group into five groups based on the quintile of the ranked values of B/M. The portfolio
is rebalanced at the end of June every year. B/M is the book value of equity divided by market value at the
end of last fiscal year. We consider six proxies: idiosyncratic stock return volatility (IdioVol), size (SIZE),
analyst coverage (COVER), number of institutional holders (N(INST)), bid-ask spreads (BIDASK), and
stock volatility (RETVOL). ROA is defined as income before extraordinary items divided by total assets.
The corresponding sample period for each proxy is the same as in Table 1. The column Cond. Corr reports
the correlation between the 5 portfolio returns and the corresponding ROA. The column CS-R2 reports R2
from the cross-sectional regression of the 25 double-sorted portfolio returns onto the corresponding ROA. A
negative sign in front of the R2 indicates a negative overall correlation.
L
3
IdioVol
H
H-L
L
3
1
SIZE
H
H-L
L
3
1
COVER
H
H-L
L
3
1
N(INST)
H
H-L
L
3
BIDASK
H
H-L
L
3
RetVol
H
H-L
Book-to-Market Equity
L
3
H
H-L
0.093 0.049 0.034 -0.059
0.068 0.031 0.008 -0.061
-0.035 -0.008 -0.029 0.007
0.066
0.105 0.057 0.031 -0.073
-0.014 0.027 0.006 0.021
-0.118 -0.031 -0.032 0.086
0.159
0.111 0.057 0.024 -0.086
0.057 0.046 0.020 -0.037
0.030 0.035 0.005 -0.025
0.061
0.100 0.055 0.023 -0.077
-0.006 0.026 0.002 0.008
-0.046 0.003 -0.014 0.033
0.110
0.090 0.048 0.035 -0.055
0.081 0.039 0.017 -0.064
-0.012 -0.020 -0.031 -0.019
0.037
0.093 0.048 0.035 -0.059
0.077 0.037 0.0140 -0.064
-0.063 -0.024 -0.035 0.028
0.087
32
t-stat Cond. Corr
-19.49
-0.760
-18.70
-0.827
0.52
0.083
5.14
-34.89
-0.838
0.95
0.649
2.85
0.854
4.99
-17.12
-0.650
-4.10
-0.996
-2.27
-0.514
4.97
-19.02
-0.882
0.44
0.518
2.95
0.686
9.05
-16.36
-0.745
-13.47
-0.850
-1.41
-0.982
2.67
-19.75
-0.321
-19.61
-0.826
2.00
0.448
4.69
CS-R2
-0.030
-0.153
-0.375
0.106
-0.281
0.006
Table 4: Operating Leverage of Double-Sorted Portfolios
This table reports the time-series averages of the annual portfolio Operating Leverage (OL) for our 25
double-sorted portfolios first sorted by our proxies and then by B/M, the difference in the OL between the
high and low B/M portfolio, and the t statistics of the differences. The portfolio ROA is calculated as
portfolio aggregate income before extraordinary items divided by portfolio aggregate total assets. At the
end of June every year, we first sort stocks into five groups based on the quintile of the ranked values of
each proxy, and then sort stocks within each group into five groups based on the quintile of the ranked
values of B/M. The portfolio is rebalanced at the end of June every year. B/M is the book value of equity
divided by market value at the end of last fiscal year. We consider six proxies: idiosyncratic stock return
volatility (IdioVol), size (SIZE), analyst coverage (COVER), number of institutional holders (N(INST)),
bid-ask spreads (BIDASK), and stock volatility (RETVOL). We follow Garcı́a-Feijóo and Jorgensen (2010)
in estimating operating leverage. The corresponding sample period for each proxy is the same as in Table 1.
The column Cond. Corr reports the correlation between the 5 portfolio returns and the corresponding OL.
The column CS-R2 reports R2 from the cross-sectional regression of the 25 double-sorted portfolio returns
onto the corresponding OL. A negative sign in front of the R2 indicates a negative overall correlation.
L
3
IdioVol
H
H-L
L
3
1
SIZE
H
H-L
L
3
1
COVER
H
H-L
L
3
1
N(INST)
H
H-L
L
3
BIDASK
H
H-L
L
3
RetVol
H
H-L
Book-to-Market Equity
L
3
H
H-L t-stat
1.412 1.943 1.930 0.518 2.06
3.162 3.587 6.085 2.923 1.48
15.315 11.164 6.183 -9.132 -2.39
-9.649 -2.47
1.506 2.484 2.601 1.095 3.64
6.787 2.337 3.221 -3.566 -1.81
13.115 8.716 11.491 -1.624 -0.43
-2.719 0.72
1.034 2.597 2.474 1.440 2.51
1.608 1.924 2.413 0.805 1.65
4.564 2.353 3.249 -1.315 -0.90
-2.755 1.88
1.533 2.622 2.737 1.204
3
3.828 2.029 3.989 0.162 0.16
9.668 5.447 4.116 -5.552 -1.32
-6.756 1.98
1.348 2.543 1.725 0.377 1.27
2.318 3.387 8.039 5.721
3.8
6.056 9.277 14.411 8.355 1.98
7.978 1.85
1.267 2.100 1.915 0.648 3.74
2.363 2.713 6.679 4.316 3.76
7.319 6.434 13.930 6.612 2.03
5.963 2.21
33
Cond. Corr
0.462
0.657
-0.788
CS-R2
0.038
0.942
-0.981
-0.149
0.242
0.486
0.865
-0.493
0.003
0.685
0.014
-0.770
-0.043
-0.118
0.8346
0.660
0.582
0.342
0.539
0.276
-0.008
Table 5: Cash Flow Duration of Double-sorted Portfolios
This table reports the time-series averages of the annual portfolio Cash Flow Duration for our 25 doublesorted portfolios first sorted by our proxies and then by B/M, the difference in the duration between the
high and low B/M portfolio, and the t statistics of the differences. At the end of June every year, we
first sort stocks into five groups based on the quintile of the ranked values of each proxy, and then sort
stocks within each group into five groups based on the quintile of the ranked values of B/M. The portfolio
is rebalanced at the end of June every year. B/M is the book value of equity divided by market value
at the end of last fiscal year. We consider six proxies: idiosyncratic stock return volatility (IdioVol), size
(SIZE), analyst coverage (COVER), number of institutional holders (N(INST)), bid-ask spreads (BIDASK),
and stock volatility (RETVOL). We follow Da (2009) in measuring the cash flow duration of a portfolio as
the difference between the discounted sum of all firms’ future dividends within the portfolio derived from
accounting earnings and the time t expectation of the discounted sum of all future log aggregate consumption
growth. The corresponding sample period for each proxy is the same as in Table 1. The column Cond. Corr
reports the correlation between the 5 portfolio returns and the corresponding duration. The column CS-R2
reports R2 from the cross-sectional regression of the 25 double-sorted portfolio returns onto the corresponding
duration. A negative sign in front of the R2 indicates a negative overall correlation.
L
3
IdioVol
H
H-L
L
3
1
SIZE
H
H-L
L
3
1
COVER
H
H-L
L
3
1
N(INST)
H
H-L
L
3
BIDASK
H
H-L
L
3
RetVol
H
H-L
Book-to-Market Equity
L
3
H
H-L
t-stat
1.173 0.500 0.348 -0.825 -7.68
1.242 0.846 0.381 -0.861 -4.75
1.073 1.223 1.220 0.147
0.44
0.972
2.87
1.375 0.664 0.415 -0.961 -7.27
-0.121 0.415 0.298 0.418
1.07
-0.834 0.201 0.177 1.011
2.23
1.971
4.95
1.334 0.582 0.328 -1.006 -4.27
0.851 0.484 0.283 -0.568 -3.47
0.247 0.212 0.184 -0.063 -0.21
0.943
2.88
1.242 0.442 0.275 -0.968 -4.75
-0.129 0.192 0.187 0.315
0.98
0.090 0.455 0.251 0.161
0.58
1.128
3.25
1.109 0.460 0.394 -0.763 -7.91
1.242 0.752 0.489 -0.752 -5.01
1.674 0.815 0.910 -0.715 -2.70
0.049
0.19
1.233 0.535 0.417 -0.815 -15.15
1.531 0.803 0.467 -1.064 -9.53
-0.026 0.569 0.544 0.571
1.46
1.386
3.43
34
Cond. Corr
-0.763
-0.964
0.229
CS-R2
-0.035
-0.867
0.822
0.780
-0.062
-0.640
-0.941
-0.702
-0.339
-0.990
0.930
0.702
0.063
-0.742
-0.798
-0.720
-0.218
-0.493
-0.826
0.331
-0.044
Table 6: Cash Flow Sensitivity of Double-Sorted Portfolios
This table reports the portfolio Cash Flow Sensitivity for our 25 double-sorted portfolios first sorted by
our proxies and then by B/M, the difference in the sensitivity between the high and low B/M portfolio,
the correlation between portfolio sensitivity and portfolio excess returns within each proxy group and the
whole sample, respectively. At the end of June every year, we first sort stocks into five groups based on
the quintile of the ranked values of each proxy, and then sort stocks within each group into five groups
based on the quintile of the ranked values of B/M. The portfolio is rebalanced at the end of June every
year. B/M is the book value of equity divided by market value at the end of last fiscal year. We consider
six proxies: idiosyncratic stock return volatility (IdioVol), size (SIZE), analyst coverage (COVER), number
of institutional holders (N(INST)), bid-ask spreads (BIDASK), and stock volatility (RETVOL). We follow
Bansal et al. (2005) in measuring the portfolio cash flow sensitivity as the OLS coefficients from regressing
the portfolio de-meaned real dividend growth rate on a trailing moving average of past 8-quarter de-meaned
real consumption growth. The corresponding sample period for each proxy is the same as in Table 1. The
column Cond. Corr reports the correlation between the 5 portfolio returns and the corresponding cash flow
risk. The column CS-R2 reports R2 from the cross-sectional regression of the 25 double-sorted portfolio
returns onto the corresponding cash flow risk. A negative sign in front of the R2 indicates a negative overall
correlation.
L
3
IdioVol
H
H-L
L
3
1
SIZE
H
H-L
L
3
1
COVER
H
H-L
L
3
1
N(INST)
H
H-L
L
3
BIDASK
H
H-L
L
3
RetVol
H
H-L
Book-to-Market Equity
L
3
H
H-L
Cond. Corr
-1.616 2.245 2.995
4.611
0.708
-4.415 4.851 4.007
8.422
0.628
-2.271 -1.307 1.835
4.106
-0.166
-0.505
-2.270 0.560 6.573
8.843
0.859
-1.545 0.504 9.120 10.667
0.818
-1.428 2.486 18.866 20.294
0.581
11.451
-2.529 0.346 10.710 13.238
0.804
-4.009 -1.680 4.682
8.690
0.951
9.939
1.052 3.522 -6.416
-0.439
-19.655
-6.435 1.725 12.459 18.894
0.766
-15.522 8.274 8.947 24.469
0.928
1.905
0.395 -4.461 -6.366
0.374
-25.260
-1.504 1.998 4.575
6.079
0.524
-3.866 7.048 3.510
7.377
0.631
-16.059 4.908 5.615 21.675
0.203
15.595
-1.719 4.970 8.812 10.531
0.478
8.544 -9.017 -8.419 -16.964
-0.757
-1.361 24.653 0.940
2.301
0.359
-8.230
35
CS-R2
0.194
0.203
0.207
0.124
0.102
0.020
Table 7: Robustness Tests
This table reports two robustness tests using two additional proxies: analyst forecast dispersion (Panel
A) and percentage of outstanding shares held by institutional investors (Panel B). Each panel reports the
various portfolio-level firm attributes of 25 double-sorted portfolios first sorted by the proxy, and then by
B/M, the difference in each attribute between the high and low B/M portfolio, and the t statistics of the
differences if available. At the end of June every year, we first sort stocks in the sample into five groups based
on the quintile of the ranked values of the proxy, and then sort stocks within each group into five groups
based on the quintile of the ranked values of B/M. (The sample varies slightly for different firm attributes;
see more in the data appendix) The portfolio is rebalanced at the end of June every year. B/M is the
book value of equity divided by market value at the end of last fiscal year. Analyst forecast dispersion is the
standard deviation of analyst forecasts scaled by the prior year-end stock price to mitigate heteroskedasticity.
Percentage of outstanding shares held by institutional investors is the percentage of outstanding shares held
by institutional investors each month. We consider five firm characteristics: O-score is the portfolio financial
distress probability implied by Ohlson’s (1980) O-score. Portfolio financial distress probability is the median
financial distress probability within a portfolio. ROA is the ratio of the portfolio aggregate income before
extraordinary items to the portfolio aggregate total assets. Portfolio Operating Leverage (OL) is estimated
by two steps: the first step, we get the residuals from the OLS regression of portfolio earnings on time to
measure the percentage deviation of portfolio aggregate earnings from its trend, and the residuals from the
OLS regression of portfolio sales on time to measure the percentage deviations of portfolio aggregate sales
from its trend. In the second step, we regress the residuals from earnings regression in the first step on the
residuals from sales regression in the first step, and this OLS regression coefficient is our portfolio OL. Cash
Flow Duration (CF Dur) is the difference between the discounted sum of all firms’ future dividends within the
portfolio and the time t expectation of the discounted sum of all future log aggregate consumption growth.
Cash Flow Sensitivity (CF Gamma) is OLS coefficients of regressing the portfolio de-meaned dividend growth
rate on a trailing moving average of de-meaned consumption growth in the past 8 quarters. We only report
the results of the L (Low), H (High), and High-minus-Low (H-L) proxy groups and the L (Low), 3, H
(High), and High-minus-Low (H-L) B/M portfolios within these groups to save space. Sample period is
from July 1962 to December 2010 for IdioVol, SIZE, BIDASK and RetVol; from July 1976 to December
2010 for COVER; and from August 1983 to December 2010 for N(INST). The financial distress probability
are in percentages. The column Cond. Corr reports the correlation between the 5 portfolio returns and
the corresponding attributes. The column CS-R2 reports R2 from the cross-sectional regression of the 25
double-sorted portfolio returns onto the corresponding attributes. A negative sign in front of CS-R2 indicates
a negative overall correlation.
36
Book-to-Market Equity
Panel A: Analyst Forecast Dispersion
L
3
H
H-L
t-stat Cond. Corr
L
0.208 0.300 0.875
0.667
6.04
0.538
OSCORE
H 11.804 1.665 2.487 -9.316 -2.61
-0.818
H-L
-9.983
2.81
L
0.134 0.074 0.045 -0.089 -22.05
-0.075
ROA
H
-0.020 0.025 0.001
0.021
1.33
0.398
H-L
0.109
6.07
L
1.043 1.051 1.378
0.336
2.30
0.401
OL
H
8.614 5.804 12.489 3.875
0.65
0.279
H-L
3.540
0.59
L
1.617 0.957 0.691 -0.927 -5.20
-0.747
CF Dur
H
-0.204 0.459 0.457
0.661
2.73
0.765
H-L
1.588
5.48
L
0.553 3.008 3.596
3.043
NA
0.066
CF Gamma H
-5.835 16.159 16.567 22.402
NA
0.904
H-L
19.359
NA
Panel B: Inverse of the Percentage of Institutional Holdings
L
3
H
H-L
t-stat Cond. Corr
L
0.393 0.570 1.078
0.685
5.66
0.695
OSCORE
H 37.927 3.603 4.870 -33.056 -9.30
-0.651
H-L
-33.742 9.32
L
0.087 0.047 0.020 -0.068 -10.39
-0.793
ROA
H
0.014 0.026 -0.007 -0.021 -1.35
-0.698
H-L
0.047
2.57
L
2.116 2.510 4.713
2.597
2.12
0.700
OL
H
5.626 2.841 4.616 -1.011 -0.48
-0.293
H-L
-3.608
1.38
L
1.084 0.420 0.123 -0.961 -6.77
-0.800
CF Dur
H
0.791 0.502 0.431 -0.360 -1.29
-0.926
H-L
0.601
2.22
L
1.727 1.219 11.666 9.939
NA
0.514
CF Gamma H
-0.477 1.634 2.623
3.100
NA
0.434
H-L
-6.839
NA
37
CS-R2
0.001
-0.244
0.113
-0.056
0.297
CS-R2
-0.302
-0.020
0.001
-0.188
0.234
Table 8: O-score of Double-Sorted Portfolios and Macroeconomic Condition
This table reports the time-series averages of the annual portfolio financial distress probability implied by
Ohlson’s (1980) O-score for our 25 double-sorted portfolios first sorted by our proxies and then by B/M, the
difference in the probability between the high and low B/M portfolio, and the t statistics of the differences,
conditional on different macroeconomic conditions. Panel A refers to the recession and Panel B refers to
the expansion. We use the median level financial distress probability of a portfolio as our portfolio financial
distress probability. At the end of June every year, we first sort stocks into five groups based on the quintile of
the ranked values of each proxy, and then sort stocks within each group into five groups based on the quintile
of the ranked values of B/M. The portfolio is rebalanced at the end of June every year. B/M is the book
value of equity divided by market value at the end of last fiscal year. We consider six proxies: idiosyncratic
stock return volatility (IdioVol), size (SIZE), analyst coverage (COVER), number of institutional holders
(N(INST)), bid-ask spreads (BIDASK), and stock volatility (RETVOL). We only report the results of the
L (Low), 3, H (High), and High-minus-Low (H-L) proxy groups and the L (Low), 3, H (High), and Highminus-Low (H-L) B/M portfolios within these groups to save space. Sample period is from July 1962 to
December 2010 for IdioVol, SIZE, BIDASK and RetVol; from July 1976 to December 2010 for COVER; and
from August 1983 to December 2010 for N(INST). The default probabilities are in percentages.
L
3
IdioVol
H
H-L
L
3
1
SIZE
H
H-L
L
3
1
COVER
H
H-L
L
3
1
N(INST)
H
H-L
L
3
BIDASK
H
H-L
L
3
RetVol
H
H-L
Book-to-Market Equity
Panel A: Recession
Panel B:
L
H
H-L
t-stat
L
H
0.302 0.949 0.648
6.74
0.414 1.030
0.632 2.062 1.428
6.48
0.593 1.824
18.149 7.033 -11.116 -2.97
23.658 5.760
-11.764 3.14
0.289 0.773 0.484
6.70
0.246 0.782
2.556 1.772 -0.784 -2.06
4.561 1.424
24.191 6.277 -17.914 -4.59
30.024 5.072
-18.398 4.67
0.324 0.972 0.648
4.72
0.230 0.907
0.907 1.624 0.717
5.31
0.680 1.340
2.537 3.483 0.946
1.99
2.707 1.985
0.30
0.53
0.330 1.010 0.678
5.47
0.272 1.024
2.006 2.097 0.091
0.31
2.358 1.880
22.023 5.546 -16.477 -5.14
31.995 4.700
-17.155 5.25
0.306 0.989 0.682
7.01
0.529 1.075
0.732 1.640 0.908
4.70
0.659 1.691
22.780 7.426 -15.353 -2.72
28.698 6.716
-16.036 2.83
0.296 1.065 0.769
5.17
0.488 1.078
0.606 2.027 1.421
6.53
0.693 1.699
26.888 8.005 -18.883 -3.31
33.064 6.991
-19.652 3.40
38
Expansion
H-L
t-stat
0.616
12.44
1.230
13.28
-17.898 -9.93
-18.514 10.14
0.536
15.41
-3.136 -7.15
-24.952 -12.06
-25.488 12.18
0.677
14.32
0.662
7.89
-0.722 -2.19
-1.399
4.14
0.752
19.34
-0.478 -1.94
-27.295 -17.39
-28.046 17.75
0.547
10.44
1.032
15.15
-21.982 -9.2
-22.529 9.32
0.590
10.01
1.078
13.07
-26.073 -10.06
-26.663 -10.16
39
L
IdioVol 3
H
L
1
3
SIZE
H
L
1
3
COVER
H
L
1
3
N(INST)
H
L
BIDASK 3
H
L
RetVol
3
H
Sales Growth
L
H
10.87 5.75
18.69 2.72
18.06 2.76
14.24 6.45
22.10 4.90
7.08
0.12
13.56 6.99
18.06 6.14
15.11 4.06
13.40 5.06
18.84 3.95
15.59 4.45
10.23 5.72
17.14 3.95
24.94 3.92
10.78 5.65
20.14 5.16
23.09 2.03
Sales/Book
L
3
1.18 0.87
1.19 1.09
1.05 1.18
1.17 1.04
1.20 1.35
1.39 1.50
1.11 1.01
1.23 1.32
1.25 1.21
1.13 1.01
1.10 1.09
1.08 1.15
1.14 0.79
1.14 1.12
1.06 1.10
1.17 0.83
1.19 1.10
1.03 1.10
Assets
H
0.78
1.05
1.12
0.77
1.25
1.49
0.70
0.92
1.06
0.74
1.08
1.14
0.80
1.06
1.14
0.84
1.08
1.09
Book-to-Market Equity
ME/Sales
Cap Exp/Book Assets
L
H
L/H
L
H
L/H
1.71 0.47 3.64
0.077 0.069 1.116
1.86 0.24 7.83
0.091 0.062 1.468
2.97 0.19 15.90
0.096 0.060 1.600
2.63 0.54 4.89
0.097 0.074 1.311
1.75 0.21 8.26
0.090 0.063 1.429
0.92 0.12 7.59
0.071 0.052 1.365
2.52 0.55 4.56
0.083 0.071 1.169
1.80 0.37 4.86
0.081 0.073 1.110
1.55 0.27 5.69
0.076 0.062 1.226
2.48 0.55 4.54
0.079 0.070 1.129
1.85 0.26 7.06
0.087 0.067 1.299
1.84 0.13 14.01
0.078 0.061 1.279
1.67 0.45 3.73
0.078 0.068 1.147
2.14 0.25 8.43
0.088 0.065 1.354
3.45 0.18 18.73
0.102 0.063 1.619
1.72 0.46 3.73
0.081 0.067 1.209
2.25 0.26 8.50
0.091 0.067 1.358
3.51 0.19 18.74
0.107 0.060 1.783
R & D/Book Assets
L
H
0.029
0.007
0.034
0.009
0.052
0.011
0.038
0.008
0.047
0.008
0.048
0.007
0.047
0.010
0.030
0.010
0.034
0.009
0.042
0.009
0.044
0.006
0.041
0.012
0.029
0.007
0.036
0.010
0.052
0.009
0.029
0.007
0.039
0.010
0.056
0.009
This table reports the time-series averages of various annual portfolio attributes (calculated using accounting data over the year prior to ranking)
for our 25 double-sorted portfolios first sorted by our proxies and then by B/M. At the end of June every year, we first sort stocks into five groups
based on the quintile of the ranked values of each proxy, and then sort stocks within each group into five groups based on the quintile of the ranked
values of B/M. The portfolio is rebalanced at the end of June every year. B/M is the book value of equity divided by market value at the end of last
fiscal year. We consider six proxies: idiosyncratic stock return volatility (IdioVol), size (SIZE), analyst coverage (COVER), number of institutional
holders (N(INST)), bid-ask spreads (BIDASK), and stock volatility (RETVOL). ROA is defined as income before extraordinary items divided by
total assets. We include all common stocks traded on NYSE, AMEX, and NASDAQ with nonnegative book values of equity, except financial firms
and firms with missing value of sales and capital expenditures. Missing values of R&D expenses are set as zero. We only report the results of the L
(Low), 3, H (High), and Low-over-High (L/H) B/M portfolios within these groups to save space. Sample period is from July 1962 to December 2010
for IdioVol, SIZE, BIDASK, and RetVol; from July 1976 to December 2010 for COVER; and from August 1983 to December 2010 for N(INST).
Table 9: Sales and Investments of Double-Sorted Portfolios
Table 10: Event Days Returns of Double-Sorting B/M Portfolios
At the end of June every year, we first sort stocks into five groups based on the quintile of the ranked
values of each proxy, and then sort stocks within each group into five groups based on the quintile of the
ranked values of B/M. At the end of each June, the event return for each stock is measured quarterly over
a three-day window (−1, +1) around the Wall Street Journal publication dates and then summed up over
the next four quarters after portfolio formation. Equally weighted averages across all stocks within each
portfolio are calculated as the annual event return of this portfolio. We consider six proxies: idiosyncratic
stock return volatility (IdioVol), size (SIZE), analyst coverage (COVER), number of institutional holders
(N(INST)), bid-ask spreads (BIDASK), and stock volatility (RETVOL). We include all common stocks
traded on NYSE, AMEX, and NASDAQ with nonnegative book values of equity, except financial firms and
firms with missing value of sales and capital expenditures. We only report the results of the L (Low), 3, H
(High), and High-minus-Low (H-L) B/M portfolios within these groups to save space. The t-statistics are
adjusted for heteroskedasticity and autocorrelation in error terms by a Newey-West standard error. Sample
period is from July 1972 to December 2010 for IdioVol, SIZE, BIDASK, and RetVol; from July 1976 to
December 2010 for COVER; and from August 1983 to December 2010 for N(INST). The 12-day (4 times 3
days) cumulative returns are in percentages.
L
3
IdioVol
H
H-L
L
3
1
SIZE
H
H-L
L
3
1
COVER
H
H-L
L
3
1
N(INST)
H
H-L
L
3
BIDASK
H
H-L
L
3
RetVol
H
H-L
B/M
L
3
H
0.35 0.58 1.67
0.64 1.94 2.30
-2.01 0.92 4.56
0.35 0.42 0.72
0.12 0.85 1.17
-1.33 1.66 3.82
0.76 0.63 0.72
-0.34 0.56 1.02
-1.41 0.42 1.45
1.07 0.52 0.74
-1.07 1.30 1.40
-1.00 2.59 5.54
0.75 1.02 1.88
0.16 2.01 2.85
-1.27 0.96 5.02
0.62 0.65 1.74
0.40 1.49 2.78
-1.67 0.46 4.47
40
H-L t-stat
1.32 2.94
1.66 2.99
6.57 6.02
5.25 4.18
0.37 1.32
1.05 1.47
5.16 8.47
4.78 7.87
-0.04 -0.09
1.35 2.20
2.85 4.48
2.89 3.51
-0.33 -1.13
3.47 5.51
6.54 8.63
6.87 10.29
1.13 2.68
2.69 4.08
6.28 4.23
5.15 3.10
1.12 2.79
2.38 3.74
6.14 5.44
5.02 3.77
Figure 1: Event-time O-score
This figure plots the evnt-time time-series averages of the annually portfolio financial distress probability
(Fail Prob) implied by Ohlson’s (1980) O-score for the 5 B/M portfolios within the lowest and highest
proxy group of our double-sorted portfolios for each of our six proxies. At the end of June every
year, we first sort stocks into five groups based on the quintile of the ranked values of each proxy,
and then sort stocks within each group into five groups based on the quintile of the ranked values of
B/M. The portfolio is rebalanced at the end of June every year. We use the median level financial
distress probability of a portfolio as our portfolio financial distress probability. For each portfolio
formation year t, we calculate the annual portfolio O-score for t + y, y = −5, ..., 5. The O-score for t + y are
then averaged across all the portfolio formation years t. The financial distress probabilities are in percentages.
Lowest Idio Vol Group
Highest Idio Vol Group
1.3
24
Fail Prob
0.3
-5
Fail Prob
-4
-3
-2
-1
0
1
2
Event Year
Biggest Size Group
3
4
2
-5
5
0.9
-4
-3
-2
-1
0
1
2
3
4
Event Year
Most Analyst Coverage Group
2
-5
5
1.1
3
Fail Prob
-4
-3
-2
-1
0
1
2
3
Event Year
Most Inst Holding Group
4
0.8
-5
5
1.2
-4
-3
-2
-1
0
1
2
3
Event Year
Lowest BidAsk Spread Group
4
1
-5
5
1.3
4
5
-3
-2
-1
0
1
2
3
4
Event Year
Least Analyst Coverage Group
5
-4
-3
-2
-1
0
1
2
3
Event Year
Least Inst Holding Group
4
5
-4
-3
-2
-1
0
1
2
3
4
Event Year
Highest BidAsk Spread Group
5
-4
-3
-2
4
5
-4
-3
4
5
30
Fail Prob
-4
-3
-2
-1
0
1
2
3
Event Year
Lowest Ret Vol Group
4
2
-5
5
1.3
-1
0
1
2
3
Event Year
Highest Ret Vol Group
34
Fail Prob
0.3
-5
-4
3
Fail Prob
Fail Prob
0.3
-5
-1
0
1
2
Event Year
Smallest Size Group
31
Fail Prob
0.2
-5
-2
Fail Prob
Fail Prob
0.2
-5
-3
30
Fail Prob
0.2
-5
-4
Fail Prob
-4
-3
-2
-1
0
1
Event Year
2
3
4
2
-5
5
-2
-1
0
1
Event Year
2
3
Growth
B/M2
B/M3
B/M4
Value
41
Figure 2: Event-time ROA
This figure plots the event-time time-series averages of the annual portfolio ROA for the 5 B/M
portfolios within the lowest and highest proxy groups of our double-sorted portfolios for each of our
six proxies. At the end of June every year, we first sort stocks into five groups based on the quintile
of the ranked values of each proxy, and then sort stocks within each group into five groups based
on quintile of the ranked values of B/M. The portfolio is rebalanced at the end of June every year.
The portfolio ROA is calculated as portfolio aggregate income before extraordinary items divided by
portfolio aggregate total assets. For each portfolio formation year t, we calculate the annually portfolio ROAs for t + y, y = −5, ..., 5. The ROA for t + y are then averaged across all the portfolio formation years.
Lowest Idio Vol Group
Highest Idio Vol Group
0.095
0.02
ROA
0.025
-5
ROA
-4
-3
-2
-1
0
1
2
Event Year
Biggest Size Group
3
4
-0.07
-5
5
0.11
-4
-3
-2
-1
0
1
2
3
4
Event Year
Most Analyst Coverage Group
-0.12
-5
5
0.11
-4
-3
-2
-1
0
1
2
3
Event Year
Most Inst Holding Group
4
-0.005
-5
5
4
5
-3
-2
-1
0
1
2
3
4
Event Year
Least Analyst Coverage Group
5
-4
-3
-2
-1
0
1
2
3
Event Year
Least Inst Holding Group
4
5
-4
-3
-2
-1
0
1
2
3
4
Event Year
Highest BidAsk Spread Group
5
-4
-3
-2
4
5
-4
-3
4
5
0.03
ROA
-4
-3
-2
-1
0
1
2
3
Event Year
Lowest BidAsk Spread Group
4
-0.07
-5
5
0.095
0.03
ROA
ROA
-4
-3
-2
-1
0
1
2
3
Event Year
Lowest Ret Vol Group
4
-0.05
-5
5
0.095
-1
0
1
2
3
Event Year
Highest Ret Vol Group
0.02
ROA
0.025
-5
-4
3
0.05
0.115
0.03
-5
-1
0
1
2
Event Year
Smallest Size Group
ROA
ROA
0.015
-5
-2
ROA
ROA
0.02
-5
-3
0.03
ROA
0.02
-5
-4
ROA
-4
-3
-2
-1
0
1
Event Year
2
3
4
-0.07
-5
5
-2
-1
0
1
Event Year
2
3
Growth
B/M2
B/M3
B/M4
Value
42
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