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A conditional characteristics model of stock returns
Malcolm Baker Harvard Business School and NBER
Jeffrey Wurgler NYU Stern School of Business
August 25, 2003
Abstract
Traditional asset pricing models maintain that differences in expected returns across
securities reflect differences in systematic risk. We develop a model in which cross-sectional differences in expected returns reflect the pattern of mispricing created by timevariation in investor sentiment and cross-sectional variation in the difficulty of valuationand arbitrage As predicted we find that when investor sentiment is high stocks whose
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and arbitrage As predicted we find that when investor sentiment is high stocks whose
I. Introduction
Traditional asset pricing models attribute cross-sectional differences in expected returns
to differences in systematic risk. As in Markowitz (1959), investors are assumed to care about
the mean and variance of their portfolio, and think about individual securities in statistical terms,
as how their respective expected returns, variances, and covariances affect the portfolio return.
Sharpe (1964), Merton (1973), Ross (1976), and Breeden (1979) show that in an equilibrium of
diversified or Markowitz-type investors, individual securities are priced so that their expected
returns depend only on their systematic risks, i.e. their covariances with relevant market
aggregates or state variables.
The systematic risk view is elegant, but its empirical relevance remains uncertain. Market
beta does not explain cross-sectional differences in expected returns, while firm characteristics,
such as size and book-to-market, have robust effects (Banz (1981), Basu (1983), and Fama and
French (1992)). Fama and French (1993) suggest that these characteristics proxy for covariances
with systematic risk factors, but Daniel and Titman (1997) find that they have cross-sectional
explanatory power that is separate from the covariance structure of returns. Recent research has
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which they are claims, as bundles of salient investment characteristics, not as variances and
covariances; that investor sentiment varies over time; and that securities vary cross-sectionally in
the difficulty of valuation and arbitrage. These ingredients lead to a conditional characteristics
model in which expected returns reflect predictable corrections of mispricing, not compensation
for systematic risk. In particular, the model predicts that when sentiment is optimistic, stocks
whose salient characteristics can sustain optimistic valuations, especially those that are difficult
to arbitrage, are relatively overpriced and hence have low expected returns. Conditional on low
sentiment, the same stocks are predicted to be relatively underpriced, and have high expected
returns. We motivate the approach and these specific predictions with a discussion of historical
bubbles and crashes, as well as theoretical and psychological considerations.
To test these predictions, we gather a set of investor sentiment proxies to use as time
series conditioning variables. We use the closed-end fund discount, NYSE turnover, the volume
and first-day returns on IPOs, the equity share, the dividend premium, and a composite index
based on the common variation in these variables. To reduce the likelihood that these proxies are
connected to systematic risks, we orthogonalize them to a range of macroeconomic variables.
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higher on young stocks than older stocks, unprofitable stocks than profitable ones, and nonpayers
than dividend payers. When sentiment is high, however, these patterns completely reverse. Thus,
variables that do not have any unconditional explanatory power actually reveal a striking sign-
flip pattern, in the predicted direction, conditional on sentiment.
The sorts also reveal U-shaped conditional patterns involving salient characteristics of
growth opportunities and distress. When sentiment is low, expected returns are high on both
highest- and lowest-sales growth deciles relative to firms in between. These extreme deciles
represent ultra-growth stocks and distressed stocks with contracting sales, respectively. When
sentiment is high, this U-shaped pattern flips upside down, so both ultra-growth and distressed
stocks now expect lower returns relative to those in the middle. There are U-shaped conditional
patterns in external finance and book-to-market as well. These patterns are consistent with the
prediction that hard-to-value firms are particularly prone to underpricing (overpricing) when
investors are pessimistic (optimistic). Again, note that these U-shaped conditional patterns, like
the monotonic conditional patterns involving age, profitability, and dividend payment, are
averaged away in unconditional studies.
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conclusion. We directly test, and reject, the basic systematic risk alternative explanation in which
the conditionally varying expected returns of young, small, unprofitable, nonpaying, etc. firms
are tied to conditionally varying covariances with the stock market or consumption growth. Also,
we find evidence of conditional patterns in returns around earnings announcements that roughly
match those in the sorts, indicating that at least a portion of those results are due to the correction
of too-optimistic or too-pessimistic expectations.
The results have broad implications, which we highlight at the end of the paper. Here we
point out that the conditional characteristics model builds upon and ties together several themes
in the recent literature. Lettau and Ludvigson (2001) study conditional systematic risks, much as
we condition on sentiment. Daniel and Titman (1997) introduce a firm characteristics model for
expected returns. We extend this approach and give it a specific, conditional motivation. Shleifer
(2000) reviews early research on sentiment and limited arbitrage, two key ingredients in the
model. Barberis and Shleifer (2003) and Barberis, Shleifer, and Wurgler (2003) develop and test
models of category-level trading. Conditional shifts in demand for groups of securities with the
same salient characteristics are at the core of the model.
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[ ] 11211 '' ++= it t it it T a R E xbxb (1)
where i indexes firms or securities, t is time, x is a vector of firm or security characteristics, and
T is a time series conditioning variable. Formally, this model adds conditional effects to the
unconditional characteristics model of Daniel and Titman (1997).
In the remainder of this section, we argue that Eq. (1) is appropriate for capturing the
correction of mispricings that result from broad fluctuations in investor sentiment, i.e. optimism
or pessimism, in the presence of cross-sectional differences in the difficulty of valuation and
arbitrage. We motivate more specific aspects of Eq. (1) with historical observations, economic
considerations, and psychological considerations. We summarize the discussion with empirical
predictions regarding appropriate characteristics and conditioning variables.
B. Historical motivation
Descriptions of historical market bubbles and crashes offer a number of useful insights.
Kindleberger (2001) draws general lessons from bubbles that have occurred over the past few
hundred years, while Brown (1991), Dreman (1979), Malkiel (1990, 1999), Shiller (2000), and
Siegel (1998) focus more specifically on recent U.S. stock market episodes. These accounts help
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boom came back to earth in 1962 Growth stocks took the brunt of the decline, falling much
further than the general market (p. 54 - 57). Dreman (1979, p. 70) confirms this account.
The next widely noted episode of speculation occurred in 1967 and 1968. Brown writes
that scores of franchisers, computer firms, and mobile home manufactures seemed to promise
overnight wealth. [while] quality was pretty much forgotten (p. 90). Malkiel and Dreman
also note this pattern a focus on firms with strong earnings growth or potential, while an
avoidance of the major industrial giants, buggywhip companies, as they were sometimes
contemptuously called (Dreman 1979, p. 74-75). Another characteristic viewed as out of favor
was dividends. According to the New York Times , during the speculative market of the late
1960s many brokers told customers that it didnt matter whether a company paid a dividend
just so long as its stock kept going up (9/13/1976). However, after 1968, as it became clear
that capital losses were possible, investors came to value dividends (10/7/1999).
Anecdotal accounts describe the early 1970s as a bear market, with general investor
sentiment at a low level. The only stocks with notably high valuations were a set of old, large,
stable, consistently profitable stocks known as the nifty fifty. Brown, Malkiel, and Siegel
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and 78. Ritter (1984) studies the hot issue market of 1980, finding greater initial returns on
IPOs of natural resource start-ups than on larger, mature, profitable offerings. Of 1983, Malkiel
(p. 74-75) writes that the high-technology new-issue boom of the first half of 1983 was an
almost perfect replica of the 1960s episodes The bubble appears to have burst early in the
second half of 1983 the carnage in the small company and new-issue markets was truly
catastrophic. Brown confirms this account. Of the mid-1980s, Malkiel suggests that What
electronics was to the 1960s, biotechnology became to the 1980s. new issues of biotech
companies were eagerly gobbled up. having positive sales and earnings was actually
considered a drawback (p. 77-79). By 1987 and 1988, however, market sentiment had changed
from an acceptance of an exciting story to a desire to stay closer to earth with low-multiple
stocks that actually pay dividends (p. 79).
The late 1980s and early 1990s are not viewed as remarkable by these sources. The
mid- through late-1990s bubble in Internet and technology stocks will be familiar. By all
accounts, investor sentiment was generally high before the bubble popped in 2000. This episode
is analyzed in detail by Ofek and Richardson (2002). Malkiel draws parallels to episodes in the
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of generally high sentiment appear to have been associated with a tendency for firms with
characteristics such as small size, young age, no dividends, low or negative current profits, and
apparently strong growth potential to be overpriced relative to firms with the opposite
characteristics. Conditions of low sentiment, on the other hand, are associated with the opposite
pattern in relative prices.
C. Economic motivation
Economic considerations tend to reinforce the historical impression that mispricings are
more frequent and severe in young, small, unprofitable, nonpaying, and/or high perceived-
growth firms. The first is that the characteristics of no earnings history and apparently unlimited
growth opportunities combine to allow unsophisticated investors to plausibly defend a wide
range of valuations, from (objectively) much too low to much too high. In bubble periods, the
same characteristics allow investment bankers or, worse, swindlers, to plausibly defend the
higher range in selling securities. Thus, stocks with these characteristics are naturally more
sensitive to sentiment swings. By contrast, the valuation of a mature firm, with an earnings
history and high dividends, is less arbitrary.
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D. Psychological motivation
Financial economists have tended to view firm characteristics as merely proxies for
deeper fundamentals, but some psychological principles suggest that investor demands may be
based directly on firm characteristics. To see how, some comments on the cognitive process of
categorization may be useful. 2 Psychologists suggest that an objects category is determined by a
set of essential features, or characteristics, that are shared by the members of the category. As a
result, categorization is useful for making inferences. For example, for the category birds some
of the defining characteristics include can fly, has wings, and has feathers. Knowing that
an object has two of these features allows it to be categorized as a bird; and then one can
reasonably infer the third feature.
In this spirit, and the spirit of Lancaster (1966, 1971), we propose that typical investors
view individual securities as bundles of salient investment characteristics for example no
earnings, young age, or high dividends. We hypothesize that typical investors determine the
merit of investing in a security by processing its salient characteristics. Investors may evaluate
the salient characteristics directly. More interestingly, they may use characteristics to categorize
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suggested above, this will be true even if there is an intervening process of categorization and
even if all trading is done at the category level, so long as psychologists are correct that
categories are defined by a common bundle of characteristics. It is also empirically convenient to
be able to boil categories down to their defining characteristics. This allows us to study such
episodes as the 1968 growth stocks bubble and the late-1990s Internet bubble in terms of a
roughly similar set of characteristics. The meaning of specific category labels, on the other hand,
are often ephemeral casual observation suggests that the connotation of Internet stocks
changed drastically from 1999 to 2001.
E. Predictions
This discussion helps to flesh out a predictive model of the form of Eq. (1). Both
historical and economic considerations imply that in conditions of general investor optimism
(call it high sentiment, a bubble, or a bull market), firms whose salient characteristics suggest an
opportunity for extreme capital gains are more likely to be overpriced relative to firms with the
opposite characteristics. The reverse applies when investors are more pessimistic (low sentiment,
a crash, a bear market). In addition, psychological considerations suggest that investor demand
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III. Data
A. Firm characteristics and returns
The firm-level data is from the merged CRSP-Compustat database. The sample includes
all common stock (share codes 10 and 11) of nonfinancial firms (excluding SIC code 6) between
1962 through 2001. We match accounting data for fiscal year-ends in calendar year t -1 to
(monthly) returns from July t through June t +1.
Table 1 shows summary statistics. Panel A summarizes returns variables. Following
common practice, momentum MOM is defined as the cumulative raw return for the eleven-
month period between 12 and two months prior to the observation return. We will consider
momentum as a control or robustness variable, not as a salient firm characteristic.
The remaining panels summarize the firm and security characteristics that we consider.
The discussion of the previous section points us directly to several variables. To that list, we add
a few more characteristics that, by introspection, seem likely to be salient to investors. Overall,
we roughly group characteristics as most directly pertaining to firm size and age, profitability,
dividends, growth opportunities, and distress.
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items (Item 18) plus income statement deferred taxes (Item 50) minus preferred dividends (Item
19), if earnings are positive; book equity ( BE ) is shareholders equity (Item 60) plus balance sheet
deferred taxes (Item 35). E> 0 is a dummy variable for profitable firms.
Panel D summarizes dividend payment characteristics. Dividends to equity D/BE is
dividends per share at the ex date (Item 26) times Compustat shares outstanding (Item 25)
divided by book equity. D>0 is a dummy for a firm with positive dividends per share by the ex
date. The decline in the percentage of firms paying dividends is noted by Fama and French
(2001) is apparent. As they point out, this is partly explained by the increasing proportion of
unprofitable firms.
Panel E summarizes characteristics that could serve as salient indictors of growth
opportunities, distress, or both. The elements of book-to-market equity BE/ME are defined
above. External finance activity EF/A is defined as the change in assets (Item 6) minus the
change in retained earnings (Item 36) divided by assets. Sales growth ( GS ) is the change in net
sales (Item 12) divided by prior-year net sales. We measure and report sales growth GS/10 as the
decile of the firms sales growth in the prior year relative to NYSE firms decile breakpoints.
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market timing motives are important to external finance, that variable could serve as a generic
misvaluation indicator as well.
In Panels C, D, and E, the accounting data for fiscal years ending in t -1 are matched to
monthly returns from July of year t through June of year t +1. To reduce the influence of outliers
and data errors, all characteristics variables, plus momentum, are Winsorized each year at their
0.5 and 99.5 percentiles.
B. Investor sentiment
Prior research suggests a number of plausible proxies for investor sentiment to use as
time-series conditioning variables. We consider six proxies the average closed-end fund
discount, NYSE share turnover, the number and average first-day returns on IPOs, the equity
share in new issues, and the dividend premium as well as a composite sentiment index that
takes the first principal component of these proxies. Each variable is measured annually from
1962 through 2000.
To isolate the sentiment component of these proxies from any business cycle
components, we orthogonalize each of them with respect to several macroeconomic variables.
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difference between the net asset value of closed-end fund shares and their market prices. Prior
work suggests that the discount is inversely related to investor sentiment. Zweig (1973) uses the
closed-end discount to forecast reversion in Dow Jones stocks, and Lee, Shleifer, and Thaler
(1991) examine several attributes of the discount. We take the value-weighted average discount
on closed-end stock funds for 1962 through 1993 from Neal and Wheatley (1998), for 1994
through 1998 from CDA/Wiesenberger, and for 1999 and 2000 from turn-of-the-year issues of
the Wall Street Journal .
NYSE share turnover is based on the ratio of reported share volume to average shares
listed from the NYSE Fact Book . Baker and Stein (2002) motivate turnover (and more generally
liquidity) as a sentiment index. In a market with short-sales constraints, irrational investors
participate and add liquidity only when they are optimistic, and hence high liquidity
coincides with overvaluation. Consistent with this interpretation, Jones (2001) finds that high
turnover forecasts low market returns. Turnover displays an exponential positive trend over our
period, however, and the May 1975 elimination of fixed commissions have a visible effect. As a
partial solution, the raw turnover ratio TURN is detrended by the five-year moving average
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non-sentiment explanations for why IPO volume and underpricing vary over time, but they do
not imply predictive relationships in the cross-section of stock returns.
The share of equity issues in total equity and debt issues is another measure of financing
activity that may capture an aspect of investor sentiment. Baker and Wurgler (2000) find that
when the equity share is in its bottom (top) historical quartile, the next years equal-weighted
market return averages 27% (-8%). The equity share is defined as gross equity issuance divided
by gross equity plus gross long-term debt issuance using data from the Federal Reserve Bulletin .
The equity share S is adjusted for the apparent regime change in debt issues in the early 1980s,
which coincided with the emergence of junk debt markets and the drop in inflation. 3
While both measures reflect equity issuance, the number of IPOs and the equity share
have some important differences. The equity share includes SEOs, has strong predictive power
for market returns, and scales by total external finance to isolate the composition of finance from
the overall level. On the other hand, the IPO variables may better reflect demand for certain
regions of the cross-section including young firms, small firms, and extreme-growth firms
that Section II suggests may be particularly sensitive to sentiment.
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relationships, which raises the possibility that different variables may reflect sentiment sooner or
later. For instance, Ibbotson and Jaffe (1975) and Lowry and Schwert (2002), and Benveniste,
Wilhelm, Ljungqvist, and Yu (2003) find that IPO volume lags the first-day returns on IPOs. A
natural interpretation is that sentiment is in part behind the high first-day returns, and this in turn
attracts additional IPO volume with some lag. Put more generally, one suspects that sentiment
measures involving firm supply responses ( S or NIPO ) are likely to lag sentiment measures that
are based directly on stock prices or investor behavior ( RIPO, P D-ND , TURN , and CEFD ).
We form a composite sentiment index SENTIMENT in order to capture the common
factor in the sentiment proxies and to help us identify the most effective timing of the individual
proxies. The process is as follows. We start by estimating the first principal component of the six
sentiment proxies and their lags. This gives us a first-stage index with twelve loadings, one for
each of the current and lagged proxies. We then compute the correlation between the first-stage
index and the current and lagged values of each of the proxies. We then construct SENTIMENT
as the first principal component of six terms the lead or lag of each proxy, whichever has the
higher correlation with the first-stage index. This leads to the final, more parsimonious index:
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variables. We will make use of this pattern in the subsequent analysis, i.e. we will condition on
the first predetermined value of CEFD , NIPO , S , and SENTIMENT , and the lag of the first
predetermined value of TURN , RIPO , and P D-ND .
Figure 1 shows that the sentiment proxies line up well with anecdotal accounts of
investor sentiment. Most of the proxies point to low sentiment in the first few years of the sample
(which follow a 1961 crash in growth stocks) the closed-end fund discount and the dividend
premium are relatively high, and turnover and equity issuance-related variables are low. Each
variable identifies a spike in sentiment in 1968 and 1969, matching anecdotal accounts.
Sentiment then tails off until, by the mid-1970s, it is low by most measures, although for the
turnover this pattern is confounded by deregulation. The late 1970s through mid-1980s sees
generally rising sentiment, and according to the composite index, sentiment has not dropped
below a medium level since 1980. In 1999, the peak of the Internet bubble, sentiment peaks
again by most proxies.
This correspondence with anecdotal accounts is encouraging. It confirms, to the extent
possible, that the proxies capture the intended variation. Also noteworthy is that cleaning the
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IV. Empirical tests
A. Sorts
Table 3 gives a simple, nonparametric look at the conditional characteristics model. We
place each monthly returns observation into a bin according to the decile rank that a given
characteristic takes at the beginning of that month, and then according to the level of a sentiment
proxy from the beginning of that year. We then compute the average monthly return for that bin
and look for patterns. We report sorts on CEFD in Table 3a and SENTIMENT in Table 3b. To be
clear, in light of the timing discussion above, we condition returns from calendar year t on the
December of year t -1 values of CEFD and SENTIMENT . Also, to keep the meaning of the
deciles relatively constant over time, we define them based on NYSE firms only. The tradeoff is
that there is not a smooth distribution of firms across bins in any given month.
For brevity, we omit sorts on the five other sentiment proxies. They give similar results,
which are available upon request, and they are broken out separately in all other tables, where
they fit more compactly. But it seems worth showing results for CEFD alongside the overall
index, however, because CEFD is the cleanest general sentiment indicator. It is not
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The first rows of Table 3 show the effect of size conditional on sentiment. They reveal
that the cross-sectional size effect exists in low-sentiment conditions only, i.e. when CEFD is
positive or when SENTIMENT is negative (a final reminder that here, and in all subsequent
tables, the sentiment proxies are net of macroeconomic effects and standardized). Specifically,
Table 3b shows that when SENTIMENT is negative, returns average 2.59 percent per month for
the bottom ME decile and 0.84 for the top decile. This pattern puts some already known results
into a broader perspective, namely that the size effect is largely a January effect (Keim (1983),
Blume and Stambaugh (1983)), and that the January effect is in turn stronger after a period of
low returns (Reinganum (1983)), which is precisely when sentiment is likely to be low.
As an aside, the average returns across the first two rows of Table 3 show that expected
returns tend to be higher across the board when sentiment is low. This is consistent with prior
results that the equity share and turnover, for example, forecast market returns. More generally, it
supports our premise that investor sentiment broadly affects stocks, and so the existence of richer
conditional patterns in the cross-section should not be entirely surprising.
The conditional cross-sectional effect of Age is even more striking. Investors demand
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of favor when SENTIMENT is low they earn huge subsequent returns of 3.04 percent per
month. However, as with ME , the cross-sectional effect of Sigma appears only in low sentiment
conditions. This suggests that the two effects are closely related.
The next rows examine profitability and dividends. The simplest and perhaps most salient
comparison for investors is between profitable and unprofitable ( E< 0) firms and between payers
and nonpayers ( D=0 ). These contrasts are summarized in the extreme right columns of Table 3,
where we average returns across profitable firms and payers and compare them to unprofitable
firms and nonpayers, respectively. They again demonstrate a conditional sign-flip pattern. Table
3b shows that when SENTIMENT is positive, monthly returns are 0.33 percent higher on
profitable firms than unprofitable firms and 0.42 percent higher on payers. When it is negative,
however, returns are 1.08 percent per month lower on profitable firms and 0.95 percent lower for
payers. The leftmost column shows that this pattern is driven mostly by variation in the returns
of unprofitable and nonpaying firms. Since these firms are hard to value and hard to arbitrage, it
is not surprising that they are especially sensitive to swings in sentiment.
The remaining variables book-to-market, external finance, and sales growth also
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sentiment reverses, this actually flips to an upward U shape. As a result, the difference between
high and low sentiment regimes becomes a pronounced inverted U. Similar conditional U
patterns are apparent, but somewhat less striking, in EF/A and BE/ME . Their shape suggests that
investors are more willing to demand both high growth and distressed firms when they are
optimistic, while they avoid these extremes when they are pessimistic. This may reflect the
notion that extremely fast-growing or shrinking firms are hardest to value, and therefore most
sensitive to sentiment.
Overall, the sorts suggest that the cross-section of expected stock returns is highly
sensitive to investor sentiment. The directions are roughly consistent with theoretical predictions
and historical accounts. A highly stylized summary is as follows. When investors are optimistic,
firms with salient characteristics that cause them to be particularly hard to value and same time
hard to arbitrage young age, high volatility, no profits, no dividends, extreme growth or
distress are more likely to be overpriced in relative terms. They therefore have lower expected
returns. Likewise, firms with these characteristics are prone to being relatively underpriced when
investors are pessimistic. They earn higher subsequent returns at such times. The conditional
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As a baseline, we start by estimating the unconditional predictive ability of each
characteristic. Each month, we run cross-sectional univariate predictive regressions:
it it t it X ba R ++= 1 , (3)
where X is a given characteristic. As earnings and dividends characteristics, we simply consider
the profitability and payer dummies, as the sorts suggest that these will capture the main effects.
Figure 2 reports the time series of the coefficients, and Panel A of Table 4 reports the average
monthly coefficient and t-statistics based on the standard deviation of the coefficients. The
results confirm prior evidence that size, book-to-market, profitability, and external finance have
univariate, unconditional predictive power. High volatility and low sales growth are, on average,
also associated with higher returns. These mean effects are apparent in Figure 2.
Panel B runs multivariate cross-sectional regressions to distinguish novel unconditional
effects from the known effects of size, book-to-market, and momentum:
( ) ( ) it it t it t it t it t it MOM m ME BE h ME s X ba R +++++= 1111 loglog , (4)
where X denotes the characteristic of interest. (There is no X variable when we consider size and
book to market themselves ) We find that age is modestly significant while the unconditional
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columns regress coefficients from (3) on each of the sentiment proxies; the last column regresses
coefficients from (4) on the composite index:4
t t t dSENTIMENT cb ++= 1 . (5)
To be clear, the monthly coefficients from cross-sectional regressions in calendar year t are
regressed on the December of year t -1 value of CEFD , NIPO , S , and the overall SENTIMENT
index, and the December of t -2 value of TURN , RIPO , and P D-ND . The sentiment proxies are
standardized. Standard errors are bootstrapped to correct for the bias induced if the
autocorrelated sentiment proxies have innovations that are correlated with innovations in the
coefficients, as in Stambaugh (1999).
The results confirm the sorts. The first rows show that as sentiment increases (lower
CEFD or P D-ND or higher TURN , NIPO , RIPO , S , or SENTIMENT ), expected returns tend to
decrease on small firms, young firms, firms with volatile returns, unprofitable firms, and non-
dividend-paying firms. In all cases the results are in the expected direction, and those using IPO
volume as the sentiment proxy are particularly strong. The last column shows that the connection
between the cross sectional effect of these variables and SENTIMENT can often be distinguished
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Like the sorts, the regressions show that the cross-sectional effects of book-to-market,
external finance, and sales growth do not have a strong linear relationship with sentiment. To
capture their U-shaped conditional effects, we re-run (3) and (4) for these characteristics but
limit the sample to observations within the top or bottom seven deciles of these variables. 5 The
idea is to bite off separate sides of the U. For instance, the GS (1-7) row examines how the cross-
sectional effect of sales growth varies with sentiment among firms in the lower range of sales
growth, where a marginal increase may predominantly reflect a marginal decrease in distress, not
an increase in growth opportunities. The GS (4-10) row examines the cross-sectional effect of
sales growth in a range where the most salient effect of a marginal increase is an increase in
growth opportunities, not a decrease in distress. Effectively, this procedure views GS (1-7) and
GS (4-10) as if they were distinct characteristics. Figure 2 plots the cross-sectional coefficient
from these regressions, which indeed suggests that these characteristics have different cross-
sectional effects in the bottom and top of their ranges.
This procedure brings out the U-shaped conditional effects in book-to-market, external
finance, and sales growth. As in the sorts, expected returns on stocks with characteristics of
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low values. We have just seen that the average payer, for example, earns higher returns than the
average nonpayer when sentiment is high, so sentiment must forecast a long-short portfolio
formed on dividend payment. But it is useful to show explicitly how sentiment affects portfolios
like SMB and HML, for example, because a large literature has used them as proxies for
systematic risks. Also, the portfolio method is less parametric than the regressions for individual
stocks, so to the extent it delivers similar results it indicates that the results are not driven by
changes in the cross-sectional distribution of firm characteristics.
The first several columns of Table 6 use individual sentiment proxies to predict long-
short portfolios: 6
it t t Low X t Hig h X dSENTIMENT c R R it it ++= == 1,, . (6)
So the dependent variable is the monthly return on a long-short portfolio, such as SMB, and these
monthly returns from January through December of t are regressed on the December t -1 value of
SENTIMENT or a sentiment proxy. The last column again separates novel comovement effects
from known ones using a multivariate prediction:
sSMBRMKTdSENTIMENTcRR +++=
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ME stocks that is separate from returns on HML. HML is constructed to isolate the difference
between high- and low- BE/ME portfolios.7
For profitability and dividend payment status, the coefficients from the portfolio
approach are identical to those for the individual stock approach by construction. The other
results are very similar (the sign for predicting SMB is opposite to the earlier ME sign). Both
SMB and HML are significantly related to sentiment in some specifications. But for HML, as
with long-short portfolios formed on external finance and sales growth, the more interesting
story is the U-shaped conditional effect. We separate growth opportunities and distress effects by
constructing High, Medium, and Low portfolios for these characteristics based on the top three,
middle four, and bottom three NYSE decile breakpoints, respectively. Using sentiment to
forecast the High-Medium portfolio for sales growth, for example, is analogous to using it to
predict the cross-sectional effect of GS (4-10).
D. Systematic risk
The conditional characteristics effects are unlikely to be compensation for systematic
risk, for a number of reasons. First, the sentiment variables have been orthogonalized with
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nonpaying firms, and are recognized as such by the marginal investor. This is counterintuitive.
Sixth, the effects seem large. This is clearest in the sorts, which hint that conditional expected
returns on (clearly risky) stocks are around zero or even negative for extreme combinations of
characteristics and sentiment.
Table 7 investigates the systematic risk explanation directly, asking whether sentiment
coincides with time-variation in market betas in a way that would at least qualitatively reconcile
the results with a conditional asset pricing model. Specifically, we predict returns on the
characteristics portfolios:
( ) it t t t t Low X t Hig h X RMRF fSENTIMENT edSENTIMENT c R R it it ++++= == 11,, . (8)
The systematic risk hypothesis predicts that the composite coefficient f , reported in Table 7,
will be of the same sign as the estimates of d in Table 6. A quick comparison of these tables
shows, however, that when the coefficient f is statistically significant, it is usually the wrong
sign. We have repeated this analysis with RMRF replaced by aggregate consumption growth.
Similar results obtain, i.e. when the composite coefficient is significant, it is typically of the
wrong sign for a systematic risk interpretation A table is available upon request
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This methodology has only limited power to detect how expectational errors affect our
results, however, because the essential feature of our results is the correlated correction of
mispricing. A firms announcement event returns, on the other hand, pick up the expectational
corrections that occur only to it alone and within its own announcement window. A quote from
Malkiel (1999) illustrates the problem: The music slowed drastically for the conglomerates on
January 19, 1968. On that day, the granddaddy of the conglomerates, Litton Industries,
announced that earnings for the second quarter of that year would be substantially less than
forecast. the announcement was greeted with disbelief and shock. In the selling wave that
followed, conglomerate stocks declined by roughly 40 percent (p. 67). And so while an
analysis of announcement event returns will capture the idiosyncratic corrective effect of Litton
Industries announcement on its own stock, it will capture none of its broader effects, which are
important to our main results.
This limitation notwithstanding, we gather quarterly earnings announcement dates from
the merged CRSP-Compustat file, which are available beginning in 1971. For each firm-calendar
quarter observation, we compute the cumulative abnormal return over the value-weighted market
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percentage points) in 10 of the 82 corresponding portfolios. The intersection of these strong
results is 6 cells, and the signs agree in all cases. Among the 5 cells that are strong in Table 3b
but insignificant in Table 8, 4 have matching signs. Likewise, among the 6 significant results in
Table 8 that are not associated with especially large conditional differences in Table 3b, 5 are of
the same sign. The clear anomaly is the significantly negative coefficient on the oldest firms;
perhaps one such anomaly is a chance outcome of so many comparisons. Overall, these results
suggest that at least a portion of our results appears to reflect the correction of conditional errors
in earnings expectations.
V. Summary and implications
We develop and test a conditional characteristics model of the cross-section of expected
returns. In a nutshell, it is an empirical framework that captures the corrections of mispricing that
arise in a world in which investors view stocks as bundles of salient investment characteristics,
are prone to time-varying sentiment, and trade stocks that vary cross-sectionally in the difficulty
of valuation and arbitrage. This approach ties together several important strands in the recent
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distinct from well-known cross-sectional patterns. The approach thus helps us to identify several
new conditional patterns in the cross-section that leave no unconditional trace, because their signdepends on sentiment conditions.
Several aspects of the results indicate that they do not reflect compensation for bearing
systematic risk. For instance, we directly consider, and reject, a connection between the
conditional patterns in expected returns and conditional patterns in covariance with market
returns or aggregate consumption growth. In addition, we find some conditional patterns in
earnings announcement returns, which suggests that at least a component of the basic results can
be directly attributed to expectational errors.
If the conditional characteristics model and our interpretation are correct, the implications
for finance are significant. For corporate finance, one implication is the relevance of dividends.
Black and Scholes (1974) view the unstable cross-sectional effect of dividends as evidence that
dividends are irrelevant to market value, as in the efficient markets setup of Miller and
Modigliani (1961). Our results suggest that this conclusion is incorrect. While the cross-sectional
effect of dividends is indeed unstable, its sign is predictable from prevailing sentiment. This
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being orthogonalized to macroeconomic conditions, can predict the factor portfolios of the Fama
and French (1993) three-factor model. The results also suggest that stock returns are difficult to properly interpret without some appreciation of historical stock market bubbles and crashes.
More research will help to determine whether the systematic risk model should, as an empirical
matter, be replaced by the conditional characteristics model.
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Figure 1. Investor Sentiment. The first panel shows the year-end, value-weighted average discount on closed-endmutual funds. The data on prices and net asset values (NAVs) come from Neal and Wheatley (1998) for 1962through 1993; CDA/Wiesenberger for 1994 through 1998; and turn -of-the-year issues of the Wall Street Journal for 1999 and 2000. The second panel shows detrended log turnover. Turnover is the ratio of reported share volume toaverage shares listed from the NYSE Fact Book. We detrend using the past five-year average. The third panel showsthe annual number of initial public offerings. The fourth panel shows the average annual first-day returns of initial
public offerings. Both series come from Jay Ritter, updating data analyzed in Ibbotson, Sindelar, and Ritter (1994).The fifth panel shows gross annual equity issuance divided by gross annual equity plus debt issuance from Baker and Wurgler (2000). We adjust the series for the one-time change in the share from 1983 to 1984. The sixth panelshows the year-end log ratio of the value-weighted average market-to-book ratios of payers and nonpayers fromBaker and Wurgler (2003). The dashed line is raw data. We regress each measure on the growth in industrial
production, the growth in durable, nondurable and services consumption, the growth in employment and a flag for NBER recessions. The solid line is the residuals from this regression. The final panel presents a first principalcomponent index of the six measures. In the index, turnover, the average annual first-day return, and the dividend
premium are lagged one year relative to the other three measures.
Panel A. Closed-end fund discount %
-15
-10
-5
0
5
10
15
20
25
30
1962 1967 1972 1977 1982 1987 1992 1997
-20
-15
-10
-5
0
5
10
15
Panel B. Turnover %
-15
-10
-5
0
5
10
15
20
25
1962 1967 1972 1977 1982 1987 1992 1997
-15
-10
-5
0
5
10
15
Panel C. Number of IPOs
0
200
400
600
800
1000
1200
1962 1967 1972 1977 1982 1987 1992 1997
-600
-400
-200
0
200
400
600
Panel D. Average first-day return
-10
0
1020
30
40
50
60
70
80
1962 1967 1972 1977 1982 1987 1992 1997
-30
-20
-100
10
20
30
40
50
60
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Figure 2. Average Annual Coefficients. Average annual coefficients from monthly univariate regressions of returns on firm characteristics X .
it it t t it e X ba R ++= 1
The firm characteristics are size, age, total risk, indicator variables for profitable firms and dividend payers, book-to-market ratio, external finance over assets,and sales growth decile. Size is the log of market equity. Market equity (ME) is price times shares outstanding from CRSP. Age is the number of years since thefirms first appearance on CRSP. Total risk is the annual standard deviation in monthly returns from CRSP. Earnings (E) is defined as income beforeextraordinary items (Item 18) plus income statement deferred taxes (Item 50) minus preferred dividends (Item 19). The book-to-market ratio is the log of the ratioof book equity to market equity. Book equity (BE) is defined as shareholders equity (Item 60) plus balance sheet deferred taxes (Item 35). External finance (EF)is equal to the change in assets (Item 6) l ess the change in retained earnings (Item 36). When the change in retained earnings is not available we use net income(Item 172) less common dividends (Item 21) instead. Sales growth decile is formed using NYSE breakpoints for sales growth. Sales growth is the percentagechange in net sales (Item 12). For the last three characteristics, we analyze the top (solid) and bottom (dashed) seven deciles separately.
Panel A. log(ME)
-1.5
-1.0
-0.5
0.0
0.5
1.0
1 9 6 3
1 9 6 5
1 9 6 7
1 9 6 9
1 9 7 1
1 9 7 3
1 9 7 5
1 9 7 7
1 9 7 9
1 9 8 1
1 9 8 3
1 9 8 5
1 9 8 7
1 9 8 9
1 9 9 1
1 9 9 3
1 9 9 5
1 9 9 7
1 9 9 9
2 0 0 1
Panel B. Age
-0.10
-0.08
-0.06
-0.04
-0.02
0.00
0.02
0.04
0.06
0.08
1 9 6 3
1 9 6 5
1 9 6 7
1 9 6 9
1 9 7 1
1 9 7 3
1 9 7 5
1 9 7 7
1 9 7 9
1 9 8 1
1 9 8 3
1 9 8 5
1 9 8 7
1 9 8 9
1 9 9 1
1 9 9 3
1 9 9 5
1 9 9 7
1 9 9 9
2 0 0 1
Panel C. Total Risk
-20
-10
0
10
20
30
40
50
1 9 6 3
1 9 6 5
1 9 6 7
1 9 6 9
1 9 7 1
1 9 7 3
1 9 7 5
1 9 7 7
1 9 7 9
1 9 8 1
1 9 8 3
1 9 8 5
1 9 8 7
1 9 8 9
1 9 9 1
1 9 9 3
1 9 9 5
1 9 9 7
1 9 9 9
2 0 0 1
Panel D. E>0
-5.0
-4.0
-3.0
-2.0
-1.0
0.0
1.0
2.0
3.0
1 9 6 3
1 9 6 5
1 9 6 7
1 9 6 9
1 9 7 1
1 9 7 3
1 9 7 5
1 9 7 7
1 9 7 9
1 9 8 1
1 9 8 3
1 9 8 5
1 9 8 7
1 9 8 9
1 9 9 1
1 9 9 3
1 9 9 5
1 9 9 7
1 9 9 9
2 0 0 1
Panel E. D>0
-5.0
-4.0
-3.0
-2.0
-1.0
0.0
1.0
2.0
3.0
1 9 6 3
1 9 6 5
1 9 6 7
1 9 6 9
1 9 7 1
1 9 7 3
1 9 7 5
1 9 7 7
1 9 7 9
1 9 8 1
1 9 8 3
1 9 8 5
1 9 8 7
1 9 8 9
1 9 9 1
1 9 9 3
1 9 9 5
1 9 9 7
1 9 9 9
2 0 0 1
Panel F. log(BE/ME)
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
2.5
1 9 6 3
1 9 6 5
1 9 6 7
1 9 6 9
1 9 7 1
1 9 7 3
1 9 7 5
1 9 7 7
1 9 7 9
1 9 8 1
1 9 8 3
1 9 8 5
1 9 8 7
1 9 8 9
1 9 9 1
1 9 9 3
1 9 9 5
1 9 9 7
1 9 9 9
2 0 0 1
Panel G. EF/A
-20.0
-15.0
-10.0
-5.0
0.0
5.0
10.0
1 9 6 3
1 9 6 5
1 9 6 7
1 9 6 9
1 9 7 1
1 9 7 3
1 9 7 5
1 9 7 7
1 9 7 9
1 9 8 1
1 9 8 3
1 9 8 5
1 9 8 7
1 9 8 9
1 9 9 1
1 9 9 3
1 9 9 5
1 9 9 7
1 9 9 9
2 0 0 1
Panel H. GS/10
-8.0
-6.0
-4.0
-2.0
0.0
2.0
4.0
6.0
1 9 6 3
1 9 6 5
1 9 6 7
1 9 6 9
1 9 7 1
1 9 7 3
1 9 7 5
1 9 7 7
1 9 7 9
1 9 8 1
1 9 8 3
1 9 8 5
1 9 8 7
1 9 8 9
1 9 9 1
1 9 9 3
1 9 9 5
1 9 9 7
1 9 9 9
2 0 0 1
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Table 1. Summary Statistics, 1963-2001. Panel A summarizes the returns variables. Returns are measured monthly. Momentum (MOM) is defined as thecumulative return for the eleven-month period between 12 and two months prior to t . Panel B summarizes the size, age, and risk characteristics. Size is the log of market equity. Market equity (ME) is price times shares outstanding from CRSP in the June prior to t . Age is the number of years between the firms firstappearance on CRSP and t . Total risk ( ) is the annual standard deviation in monthly returns from CRSP for the 12 months ending in the June prior to t . Panel Csummarizes profitability variables. The earnings-price ratio is defined for firms with positive earnings. Earnings (E) is defined as income before extraordinaryitems (Item 18) plus income statement deferred taxes (Item 50) minus preferred dividends (Item 19). Book equity (BE) is defined as shareholders equity (Item60) plus balance sheet deferred taxes (Item 35). Panel D reports dividend variables. Dividends (D) are equal to dividends per share at the ex date (Item 26) timesshares outstanding (Item 25). Panel E reports variables used as proxies for growth opportunities and distress. T he book-to-market ratio is the log of the ratio of
book equity to market equity. External finance (EF) is equal to the change in assets (It em 6) less the change in retained earnings (Item 36). When the change inretained earnings is not available we use net income (Item 172) less common dividends (Item 21) instead. Sales growth decile is formed using NYSE breakpointsfor sales growth. Sales growth is the percentage change in net sales (Item 12). In Panels C through E, accounting data from the fiscal year ending in t -1 arematched to monthly returns from July of year t through June of year t +1. All variables are Winsorized at 99.5 and 0.5 percent.
Full Sample Subsample Means
N Mean SD Min Max 1960 s 1970s 1980s 1990s 2000-1
Panel A. Returns
R t (%) 1,398,432 1.38 18.70 -97.37 2400.00 1.06 1.59 1.24 1.45 1.19MOM t -1 (%) 1,398,432 13.44 60.32 -86.00 359.40 21.45 12.51 14.85 12.11 11.95
Panel B. Size and AgeME t -1 ($M) 1,398,432 576 2,152 1 21,623 392 238 371 805 1,411
Age t (Years) 1,398,432 13.68 13.89 0.03 69.17 15.91 12.97 13.80 13.65 14.06
t- 1 (%) 1,396,198 14.39 9.07 0.00 64.00 9.20 12.62 13.69 15.28 21.53
Panel C. Profitability
E+/BE t -1 (%) 1,398,432 10.62 10.32 0.00 67.48 12.14 12.10 11.29 9.28 9.08
E>0t -1 1,398,432 0.76 0.42 0.00 1.00 0.96 0.91 0.77 0.68 0.63
Panel D. Dividend Policy
D/BE t -1 (%) 1,398,432 1.96 2.96 0.00 17.61 4.42 2.72 1.98 1.36 1.05
D>0t -1 1,398,432 0.45 0.50 0.00 1.00 0.78 0.65 0.48 0.30 0.24Panel E. Growth Opportunities and Distress
BE/ME t -1 1,398,432 0.93 0.86 0.02 5.78 0.70 1.35 0.92 0.72 0.81
EF/A t -1 (%) 1,365,115 11.70 24.99 -69.00 131.18 7.09 6.34 10.72 14.77 19.16
GS t -1 (Decile) 1,349,463 5.94 3.19 1.00 10.00 5.66 5.66 5.97 6.12 5.91
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Table 2. Investor Sentiment. Means, standard deviations, and correlations for measures of investor sentiment. The first measure (CEFD) is the year-end, value-weighted average discount on closed-end mutual funds. The data on prices and net asset values (NAVs) come from Neal and Wheatley (1998) for 1962 through1993; CDA/Wiesenberger for 1994 through 1998; and turn-of-the-year issues of the Wall Street Journal for 1999 and 2000. The second measure (TURN) isdetrended log turnover. Turnover is the ratio of reported share volume to average shares listed from the NYSE Fact Book. We detrend using the past five-year average. The third measure (NIPO) is the annual number of initial public offerings. The fourth measure (RIPO) is the average annual first-day returns of initial
public offerings. Both IPO series come from Jay Ritter, updating data analyzed in Ibbotson, Sindelar, and Ritter (1994). The fifth measure (S) is gross annualequity issuance divided by gross annual equity plus debt issuance from Baker and Wurgler (2000). We adjust the series for the one-time change in the share from1983 to 1984. The sixth measure (P D-ND ) is the year-end log ratio of the value-weighted average market-to-book ratios of payers and nonpayers from Baker andWurgler (2003). Turnover, the average annual first-day return, and the dividend premium are lagged one year relative to the other three measures. The index isthe first principal component of the six measures. In the first panel, we present raw data. In the second panel, we regress each measure on the growth in industrial
production, the growth in durable, nondurable and services consumpt ion, the growth in employment and a flag for NBER recessions. The adjusted measures arethe residuals from these regressions. The sentiment index is the first principal component of the six measures. a, b, and c denote statistical significance at 1%,5%, and 10%.
Correlations
Mean SD Min Max Index CEFD TURN NIPO RIPO S PD-ND
Panel A. Raw data
CEFD t 8.87 8.12 -10.41 23.70 -0.51a 1.00
TURN t -1 5.21 7.94 -11.60 18.66 0.62a -0.30 c 1.00
NIPOt 358.41 262.76 9.00 953.00 0.74a -0.57 a 0.38 b 1.00
RIPO t -1 16.94 14.93 -1.67 69.53 0.73a -0.42 a 0.50 a 0.35 b 1.00
St 28.97 10.08 11.15 50.03 0.78a -0.31 c 0.31 c 0.77 a 0.33 b 1.00
Pt -1D-ND 0.20 18.67 -33.17 36.06 -0.85 a 0.53 a -0.50 a -0.56 a -0.58 a -0.67 a 1.00
Panel B. Controlling for macroeconomic conditions
CEFD t 0.00 6.14 -18.31 9.27 -0.51a 1.00
TURN t -1 0.00 6.73 -11.31 11.45 0.65a -0.28 c 1.00
NIPOt 0.00 226.30 -435.98 484.15 0.82a -0.46 a 0.39 b 1.00
RIPO t -1 0.00 14.31 -23.55 46.54 0.76a -0.46 a 0.53 a 0.44 a 1.00
St 0.00 9.47 -22.17 18.78 0.80a -0.18 0.35 b 0.77 a 0.37 b 1.00
Pt -1D-ND 0.00 16.89 -43.20 35.96 -0.85 a 0.28 c -0.60 a -0.46 a -0.68 a -0.61 a 1.00
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Table 3a. Two-way Sorts: Closed-End Fund Discount and Firm Characteristics. For each month, we form ten portfolios according to the NYSE breakpointsof firm size (ME), age, total risk, earnings-book ratio for profitable firms (E/BE), dividend-book ratio for dividend payers (D/BE), book-to-market ratio(BE/ME), external finance over assets (EF/A), and sales growth (GS). We also calculate portfolio returns for unprofitable firms and nonpayers. We then reportaverage portfolio returns over months where the closed-end fund discount is positive, negative, and the difference between the two averages.
Closed- End Fund Discount Decile Overall
0 1 2 3 4 5 6 7 8 9 10 10-1 10-5 5-1>0- 0
ME Positive 2.40 1.93 1.81 1.79 1.83 1.63 1.62 1.49 1.38 1.31 -1.08
Negative 0.46 0.21 0.36 0.24 0.53 0.33 0.45 0.55 0.46 0.38 -0.08
Difference 1.94 1.73 1.46 1.56 1.29 1.30 1.17 0.94 0.92 0.93 -1.00
Age Positive 1.97 1.99 2.05 1.94 2.02 2.01 1.57 1.67 1.63 1.48 -0.49
Negative -0.23 0.50 0.67 0.47 0.62 0.64 0.66 0.65 0.58 0.72 0.95
Difference 2.20 1.49 1.38 1.46 1.40 1.37 0.91 1.01 1.05 0.76 -1.44
Positive 1.20 1.39 1.43 1.52 1.55 1.68 1.72 1.80 1.98 2.86 1.66
Negative 0.57 0.50 0.54 0.50 0.50 0.48 0.48 0.26 0.13 0.60 0.03Difference 0.64 0.89 0.90 1.02 1.05 1.20 1.24 1.54 1.85 2.26 1.62
E/BE Positive 2.48 2.21 2.08 2.11 1.92 1.79 1.95 1.90 1.88 1.77 1.87 -0.34 -0.61
Negative 0.25 0.53 0.65 0.89 0.53 0.46 0.49 0.38 0.50 0.48 0.36 -0.17 0.23
Difference 2.23 1.68 1.43 1.22 1.38 1.32 1.46 1.52 1.38 1.29 1.51 -0.18 -0.84
D/BE Positive 2.35 2.08 1.90 1.92 1.77 1.71 1.59 1.53 1.47 1.44 1.38 -0.70 -0.63
Negative 0.12 0.60 0.51 0.73 0.47 0.58 0.68 0.76 0.70 0.70 0.81 0.21 0.52
Difference 2.23 1.48 1.39 1.19 1.30 1.13 0.91 0.77 0.77 0.74 0.56 -0.91 -1.16
BE/ME Positive 1.47 1.72 1.78 1.86 1.87 1.93 2.12 2.12 2.33 2.58 1.11 0.71 0.40
Negative -0.27 0.09 0.35 0.38 0.56 0.67 0.67 0.77 0.89 0.94 1.21 0.38 0.83Difference 1.74 1.63 1.43 1.48 1.31 1.26 1.45 1.35 1.45 1.64 -0.10 0.33 -0.43
EF/A Positive 2.52 2.18 2.08 1.98 1.82 1.89 1.88 1.80 1.92 1.66 -0.87 -0.17 -0.70
Negative 0.76 0.75 0.84 0.77 0.75 0.63 0.38 0.38 0.24 -0.46 -1.23 -1.21 -0.02
Difference 1.76 1.43 1.25 1.22 1.08 1.27 1.50 1.42 1.67 2.12 0.36 1.05 -0.68
GS Positive 2.37 2.04 1.97 1.79 1.82 1.88 1.98 2.08 1.90 1.81 -0.56 -0.01 -0.54
Negative 0.66 0.61 0.58 0.65 0.62 0.67 0.68 0.56 0.34 -0.41 -1.07 -1.03 -0.04
Difference 1.71 1.43 1.39 1.15 1.20 1.21 1.31 1.52 1.57 2.22 0.51 1.02 -0.51
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Table 3b. Two-way Sorts: Sentiment Index and Firm Characteristics. For each month, we form ten portfolios according to the NYSE breakpoints of firmsize (ME), age, total risk, earnings-book ratio for profitable firms (E/BE), dividend-book ratio for dividend payers (D/BE), book-to-market ratio (BE/ME),external finance over assets (EF/A), and sales growth (GS). We also calculate portfolio returns for unprofitable firms and nonpayers. We then report average
portfolio returns over months where the sentiment index is posit ive, negative, and the difference be tween the two averages.
Sentiment Index Decile Overall
0 1 2 3 4 5 6 7 8 9 10 10-1 10-5 5-1>0- 0
ME Positive 0.89 0.74 0.80 0.75 0.96 0.86 1.05 1.00 1.01 1.01 0.12
Negative 2.59 1.91 1.80 1.73 1.76 1.45 1.29 1.25 1.02 0.84 -1.75
Difference -1.70 -1.17 -0.99 -0.98 -0.80 -0.59 -0.24 -0.25 -0.01 0.17 1.87
Age Positive 0.34 0.89 1.03 0.97 1.23 1.32 1.04 1.13 1.05 1.07 0.73
Negative 2.01 2.06 2.11 1.82 1.75 1.64 1.41 1.43 1.43 1.32 -0.69
Difference -1.67 -1.16 -1.08 -0.85 -0.52 -0.32 -0.37 -0.30 -0.38 -0.26 1.42
Positive 0.97 0.99 0.95 0.88 0.85 0.88 0.82 0.63 0.59 1.13 0.17
Negative 0.92 1.09 1.23 1.42 1.49 1.61 1.75 1.91 2.09 3.04 2.12
Difference 0.04 -0.10 -0.28 -0.55 -0.63 -0.73 -0.93 -1.28 -1.50 -1.91 -1.95
E/BE Positive 0.60 0.78 0.99 0.92 0.94 0.94 0.94 0.92 1.04 1.03 0.89 0.12 0.33
Negative 2.89 2.54 2.18 2.54 1.92 1.68 1.93 1.78 1.70 1.54 1.76 -0.78 -1.08
Difference -2.29 -1.77 -1.19 -1.62 -0.99 -0.74 -0.98 -0.86 -0.66 -0.51 -0.87 0.90 1.42
D/BE Positive 0.63 1.02 0.98 1.15 0.92 1.06 1.02 1.09 1.09 1.11 1.01 -0.01 0.42
Negative 2.55 2.11 1.83 1.82 1.68 1.53 1.49 1.39 1.26 1.20 1.34 -0.77 -0.95
Difference -1.92 -1.09 -0.85 -0.66 -0.76 -0.47 -0.46 -0.30 -0.17 -0.09 -0.32 0.77 1.36
BE/ME Positive 0.13 0.69 0.88 1.00 1.11 1.15 1.18 1.19 1.33 1.46 1.33 0.34 0.99
Negative 1.63 1.56 1.63 1.62 1.65 1.78 2.02 2.08 2.32 2.53 0.90 0.89 0.02
Difference -1.51 -0.88 -0.75 -0.62 -0.54 -0.63 -0.84 -0.89 -1.00 -1.08 0.43 -0.54 0.97
EF/A Positive 1.29 1.19 1.37 1.28 1.21 1.19 1.07 0.89 0.77 0.06 -1.23 -1.15 -0.08
Negative 2.51 2.15 1.86 1.78 1.62 1.64 1.56 1.67 1.88 1.79 -0.72 0.17 -0.89
Difference -1.22 -0.96 -0.49 -0.50 -0.41 -0.45 -0.49 -0.78 -1.11 -1.73 -0.51 -1.32 0.80
GS Positive 1.00 1.21 1.20 1.13 1.20 1.18 1.19 1.09 0.89 0.18 -0.81 -1.02 0.20
Negative 2.59 1.79 1.69 1.60 1.53 1.67 1.82 1.98 1.78 1.89 -0.70 0.37 -1.06
Difference -1.59 -0.58 -0.49 -0.48 -0.33 -0.49 -0.63 -0.89 -0.88 -1.71 -0.12 -1.38 1.26
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Table 4. Baseline Regressions, Monthly Returns. Average coefficients and t-statistics from monthly regressions of returns on firm characteristics (X), size(log(ME)), book-to-market (log(BE/ME)), and momentum (MOM).
( ) ( ) it it t it t it t it t t it e MOM m ME BE h ME s X ba R +++++= 1111 loglog We only report the average of b t . The firm characteristics are firm size (log(ME)), age (log(Age)), total risk ( ), an indicator variable for profitable firms (E>0)and dividend payers (D>0), book-to-market ratio (log(BE/ME)), external finance over assets (EF/A), and sales growth decile (GS). The first panel showsunivariate results. The second panel includes book-to-market, size, and momentum as control variables. Standard errors are equal to the time series standarddeviation of b t divided by the number of months.
ME Age E >0 D>0 BE/ME EF/A GS/ 10
s t(s) b t(b) b t(b) b t(b) b t(b) h t(h) b t(b) b t(b)
Panel A. Univariate
-0.17 [-3.3] 0.03 [0.4] 8.28 [4.5] -0.26 [-1.3] -0.17 [-0.8] 0.47 [6.5] -1.63 [-6.8] -0.59 [-4.6]
Panel B. Controlling for Book-to-Market, Size, and Momentum
-0.18 [-3.3] 0.08 [2.3] 0.32 [4.5]
0.02 [0.4] 9.24 [5.3] 0.51 [8.8]
-0.16 [-3.3] -0.05 [-0.4] 0.35 [4.9]
-0.16 [-3.5] 0.05 [0.4] 0.34 [5.1]-0.14 [-2.4] 0.51 [6.7]
-0.16 [-3.0] 0.26 [3.9] -1.16 [-6.8]
-0.15 [-2.8] 0.32 [4.4] -0.26 [-2.7]
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Table 5. Time Series Regressions, Monthly Returns Coefficients. Two-stage regression. In the first stage, we compute coefficients from monthly regressionsof returns on firm characteristi cs (X), size (log(ME)), book-to-market (log(BE/ME)), and momentum (MOM).
( ) ( ) it it t it t it t it t t it e MOM m ME BE h ME s X ba R +++++= 1111 loglog The firm characteristics are firm size (log(ME)), age (log(Age)), total risk ( ), an indicator variable for profitable firms (E>0) and dividend payers (D>0), book-to-market ratio (log(BE/ME)), external finance over assets (EF/A), and sales growth decile (GS). When we analyze growth opportunities, we exclude the top(bottom) three deciles for book-to-market ratio (external finance, sales growth). When we analyze distress, we exclude the bottom (top) three deciles for book-to-market ratio (external finance, sales growth). In the second stage, we regress the monthly coefficients b t on measures of investor sentiment, each standardized tohave unit variance.
t t t udSENTIMENT cb ++= 1
Coefficients are matched to the closed-end fund discount (CEFD), the number of IPOs (NIPO), and the equity share (S) for the calendar year one year before t .Coefficeints are matched to detrended log turnover (TURN), the average annual first-day return (RIPO), and the dividend premium (P D-ND ) for the calendar year two years before t . The first seven columns show univariate results. The last column includes size, book-to-market, and momentum as control variables in thefirst-stage regression and uses the sentiment index in the second stage. Bootstrap p -values are in braces.
CEFD t -1 TURN t -2 NIPO t -1 RIPO t -2 S t -1 P t -2 D-ND
Sentiment Index
Controlling for Size, B/M, and
MOM
d p(d) d p(d) d p(d) d p(d) d p(d) d p(d) d p(d) d p(d)ME -0.2 [.00] 0.1 [.06] 0.2 [.00] 0.2 [.01] 0.1 [.03] -0.1 [.13] 0.2 [.01] 0.2 [.00]
Age -0.2 [.02] 0.1 [.11] 0.3 [.00] 0.2 [.01] 0.2 [.00] -0.1 [.21] 0.2 [.00] 0.1 [.15] 6.4 [.00] -3.9 [.06] -7.2 [.00] -5.2 [.01] -5.3 [.03] 4.0 [.09] -7.0 [.00] -3.9 [.04]
E>0 0.7 [.01] -0.5 [.03] -0.9 [.00] -0.7 [.00] -0.7 [.01] 0.6 [.03] -0.9 [.00] -0.5 [.00]
D>0 -0.8 [.00] 0.5 [.03] 1.0 [.00] 0.7 [.00] 0.8 [.00] -0.5 [.09] 0.9 [.00] 0.5 [.00]
BE/ME -0.0 [.68] 0.1 [.48] 0.1 [.19] 0.1 [.55] 0.1 [.13] -0.0 [.89] 0.1 [.28] 0.2 [.02]
EF/A 0.6 [.02] -0.2 [.52] -0.6 [.02] -0.5 [.06] -0.7 [.02] 0.2 [.52] -0.6 [.05] -0.4 [.08]
GS 0.2 [.16] -0.1 [.40] -0.3 [.06] -0.3 [.04] -0.4 [.03] 0.2 [.34] -0.3 [.05] -0.2 [.22]
BE/ME (1-7) -0.1 [.31] 0.1 [.15] 0.2 [.01] 0.1 [.12] 0.3 [.02] -0.1 [.27] 0.2 [.03] 0.3 [.01]EF/A (4-10) 1.8 [.00] -0.8 [.11] -1.9 [.00] -1.6 [.01] -1.5 [.01] 1.0 [.11] -1.8 [.01] -0.9 [.01]
GS (4-10) 0.1 [.00] -0.1 [.01] -0.1 [.00] -0.1 [.00] -0.1 [.00] 0.1 [.04] -0.1 [.00] -0.1 [.00]
BE/ME (4-10) 0.1 [.30] -0.1 [.17] -0.1 [.21] -0.1 [.31] -0.1 [.24] 0.2 [.07] -0.2 [.10] 0.0 [.64]
EF/A (1-7) -2.1 [.00] 1.1 [.11] 2.4 [.00] 1.9 [.01] 1.7 [.03] -1.6 [.04] 2.4 [.00] 1.1 [.01]
GS (1-7) -0.1 [.02] 0.1 [.03] 0.1 [.01] 0.1 [.05] 0.1 [.09] -0.1 [.09] 0.1 [.01] 0.0 [.09]
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Table 6. Time Series Regressions, Portfolios. Regressions of long-short portfolio returns on measures of sentiment (S), each standardized to have unit variance,the market risk premium (RMRF), the Fama-French factors (HML and SMB), and a momentum factor (UMD).
t t t t t t t low X t high X umUMDhHML sSMB RMRF dSENTIMENT c R R it it ++++++= == 1,,
The long-short portfolios are formed based on firm characteristics (X): firm size (ME), age, total risk ( ), profitability (E), dividends (D), book-to-market ratio(BE/ME), external finance over assets (EF/A), and sales growth decile (GS). High is defined as a firm in the top three NYSE deciles; low is defined as a firm inthe bottom three NYSE deciles; medium is defined as a firm in the middle four NYSE deciles. Monthly returns are matched to the closed-end fund discount(CEFD), the number of IPOs (NIPO), and the equity share (S) for the calendar year one year before t . Monthly returns are matched to detrended log turnover
(TURN), the average annual first-day return (RIPO), and the dividend premium (PD-ND
) for the calendar year two years before t . The first seven columns showunivariate results. The last column includes RMRF, SMB, HML, and UMD as control variables. Bootstrap p-values are in braces.
CEFD t -1 TURN t -2 NIPO t -1 RIPO t -2 S t -1 P t -2 D-ND
Sentiment Index
Controlling for RMRF,SMB, HML,and UMD
d p(d) d p(d) d p(d) d p(d) d p(d) d p(d) d p(d) d p(d)
ME SMB 0.4 [.02] -0.2 [.26] -0.6 [.00] -0.4 [.05] -0.4 [.05] 0.2 [.21] -0.5 [.01] -0.4 [.02]
Age High-Low -0.6 [.01] 0.4 [.09] 0.9 [.00] 0.6 [.00] 0.7 [.00] -0.3 [.20] 0.8 [.00] 0.3 [.01]
High-Low 0.8 [.00] -0.6 [.04] -1.0 [.00] -0.6 [.02] -0.8 [.01] 0.6 [.08] -1.0 [.00] -0.3 [.09]E >0 0 =0 -0.8 [.00] 0.5 [.03] 1.0 [.00] 0.7 [.00] 0.8 [.00] -0.5 [.09] 0.9 [.00] 0.4 [.00]
BE/ME HML -0.2 [.41] 0.1 [.58] 0.2 [.18] 0.2 [.15] 0.2 [.22] 0.1 [.60] 0.2 [.38] 0.1 [.75]
EF/A High-Low 0.2 [.12] -0.1 [.43] -0.3 [.01] -0.2 [.06] -0.4 [.00] 0.2 [.15] -0.3 [.02] -0.2 [.06]
GS High-Low 0.1 [.27] -0.1 [.59] -0.2 [.09] -0.2 [.05] -0.2 [.05] 0.1 [.39] -0.2 [.10] -0.2 [.16]
BE/ME Low-Medium -0.1 [.23] 0.2 [.20] 0.3 [.01] 0.2 [.17] 0.3 [.01] -0.1 [.34] 0.3 [.06] 0.2 [.14]
EF/A High-Medium 0.4 [.01] -0.3 [.03] -0.5 [.00] -0.4 [.00] -0.5 [.00] 0.4 [.01] -0.5 [.00] -0.3 [.00]
GS High-Medium 0.4 [.00] -0.3 [.02] -0.5 [.00] -0.4 [.00] -0.4 [.00] 0.3 [.03] -0.5 [.00] -0.3 [.00]
BE/ME High-Medium 0.1 [.41] -0.1 [.43] -0.1 [.26] -0.1 [.43] -0.1 [.36] 0.1 [.09] -0.1 [.18] -0.1 [.45]EF/A Low-Medium -0.2 [.00] 0.2 [.01] 0.2 [.00] 0.2 [.02] 0.2 [.07] -0.2 [.02] 0.3 [.01] 0.2 [.00]
GS Low-Medium -0.3 [.01] 0.2 [.03] 0.3 [.00] 0.2 [.05] 0.2 [.09] -0.2 [.08] 0.3 [.01] 0.1 [.17]
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Table 7. Conditional Market Betas. Regressions of long-short portfolio returns on the market risk premium (RMRF) and the market risk premium interactedwith measures of sentiment (S) , each standardized to have unit variance.
( ) t t t t t low X t high X u RMRF fSENTIMENT edSENTIMENT c R R it it ++++= == 11,,
The long-short portfolios are formed based on firm characteristics (X): firm size (ME), age, total risk ( ), profitability (E), dividends (D), book-to-market ratio(BE/ME), external finance over assets (EF/A), and sales growth decile (GS). High is defined as a firm in the top three NYSE deciles; low is defined as a firm inthe bottom three NYSE deciles; medium is defined as a firm in the middle four NYSE deciles. Monthly returns are matched to the closed-end fund discount(CEFD), the number of IPOs (NIPO), and the equity share (S) for the calendar year one year before t . Monthly returns are matched to detrended log turnover
(TURN), the average annual first-day return (RIPO), and the dividend premium (PD-ND
) for the calendar year two years before t . T-statistics are heteroskedasticityrobust.
CEFD t -1 TURN t -2 NIPO t -1 RIPO t -2 S t -1 P t -2 D-ND Sentiment Index
f t( f) f t( f) f t( f) f t( f) f t( f) f t( f) f t( f)
ME SMB -0.01 [-0.2] -0.02 [-0.6] -0.03 [-0.8] 0.02 [0.5] -0.10 a [-2.6] 0.05 [1.4] -0.04 [-1.1]
Age High-Low -0.02 [-0.5] -0.13 b [-2.9] 0.01 [0.3] -0.13 b [-2.7] -0.01 [-0.3] 0.15 b [3.0] -0.10 b [-2.1]
High-Low 0.01 [0.2] 0.08 [1.6] -0.03 [-0.7] 0.11 b [2.1] -0.03 [-0.7] -0.07 [-1.4] 0.05 [0.9]
E >0-0-
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Table 8. Announcement Effects. For each calendar quarter, we form ten portfolios according to the NYSE breakpoints of firm size (ME), age, total risk,earnings-book ratio for profitable firms (E/BE), dividend-book ratio for dividend payers (D/BE), book-to-market ratio (BE/ME), external finance over assets(EF/A), and sales growth (GS). We also calculate average announcement effects for unprofitable firms and nonpayers. We then regress the average quarterlyearnings announcement effects for each portfolio on lagged values of the sentiment index.
t t t ubSENTIMENT a R ++= 1
We report b . Quarterly average announcement effects are matched to the sentiment index for the calendar year one year before t . T-statistics areheteroskedasticity robust.
Decile
0 1 2 3 4 5 6 7 8 9 10
ME -0.20 -0.06 -0.03 -0.08 -0.06 -0.05 -0.01 -0.05 0.00 -0.02
[-2.21] [-0.97] [-0.42] [-0.92] [-0.95] [-0.72] [-0.13] [-0.79] [0.08] [-0.41]
Age -0.06 -0.02 -0.09 -0.12 -0.17 0.01 0.03 -0.06 -0.03 -0.16
[-0.49] [-0.14] [-1.22] [-1.43] [-2.12] [0.09] [0.56] [-0.90] [-0.48] [-3.10]
-0.04 -0.04 -0.03 0.00 -0.03 -0.01 -0.04 -0.01 -0.08 -0.27
[-0.71] [-0.88] [-0.58] [0.06] [-0.59] [-0.18] [-0.56] [-0.20] [-0.91] [-2.49]
E/BE -0.38 -0.24 0.06 0.14 -0.17 -0.17 -0.06 -0.03 0.02 -0.02 0.13[-3.26] [-2.22] [0.66] [1.16] [-1.73] [-1.88] [-0.66] [-0.35] [0.33] [-0.31] [1.99]
D/BE -0.18 -0.02 -0.10 -0.06 0.00 -0.10 0.00 -0.09 -0.12 0.03 -0.05
[-2.11] [-0.30] [-1.36] [-0.77] [0.04] [-1.59] [0.05] [-1.53] [-2.11] [0.45] [-0.65]
BE/ME -0.08 0.01 0.04 -0.03 -0.03 0.02 -0.13 -0.01 -0.14 -0.21
[-1.21] [0.19] [0.61] [-0.50] [-0.43] [0.28] [-1.74] [-0.07] [-1.64] [-1.77]
EF/A -0.08 -0.06 0.00 -0.06 0.01 -0.07 -0.13 -0.03 -0.14 -0.04
[-0.75] [-0.73] [-0.05] [-0.84] [0.15] [-1.02] [-1.96] [-0.39] [-1.99] [-0.48]
GS -0.29 -0.06 -0.12 -0.02 -0.02 0.04 -0.05 0.01 -0.04 -0.04
[-2.68] [-0.66] [-1.51] [-0.27] [-0.39] [0.58] [-0.79] [0.14] [-0.65] [-0.46]