1.
An Evaluation of the Ability of
Logit-based Financial Statement Analysis
to Identify Market Mispricing*
Richard M. Morton
Florida State University
and
Philip B. Shane
University of Colorado
October 7, 1998
(forthcoming in Advances in Quantitative Analysis of Finance and Accounting, 2000,
Volume 8, pages 1-23)
*We appreciate the helpful comments by an anonymous reviewer, Tom Schaefer, Jake Thomas,
and the participants at a Penn State University workshop. Of course, any remaining errors are
our own.
_______________________________
Please address correspondence to:
Professor Richard M. Morton
College of Business
Florida State University
Tallahassee, FL 32306-1110
phone (850) 644-7877; fax (850) 644-8234
email: rmorton@cob.fsu.edu
2.
An Evaluation of the Ability of
Logit-based Financial Statement Analysis
to Identify Market Mispricing
ABSTRACT
This paper develops and demonstrates an approach to distinguishing market mispricing from
risk-based explanations for abnormal returns associated with trading strategies based on financial
statement analysis. Prior studies suggest that financial statement analysis can predict returns via
an ability to predict earnings. This study develops a two-tailed hypothesis to distinguish the
competing explanations of market mispricing and risk for this market anomaly. Beginning with a
logit analysis similar to Ou and Penman (1989a and 1989b), we manipulate the target earnings
variable by controlling for the market's expected earnings. We hypothesize that this manipulation
should increase (decrease) the trading strategy returns if the anomaly is due to market mispricing
(risk). Our results do not support market mispricing. Rather, controlling for expected earnings
appears to control for expected returns. Our approach could be adapted to other financial
statement analysis studies that attempt to identify market mispricing by predicting accounting-
based performance measures.
Keywords: Financial Statement Analysis, Mispricing, Capital Markets, Market Inefficiency
3.
I. INTRODUCTION
Accounting and finance researchers frequently analyze financial statement data in an effort to
identify market mispricing. A common approach is to devise a trading strategy based on
financial statement analysis and evaluate its ability to generate abnormal returns. However, even
if the trading strategy yields positive returns, an alternative explanation for the observed relation
is that those returns are expected by the market. Rather than a symptom of market mispricing,
the observed “abnormal” returns may compensate for an omitted risk factor not captured by the
researcher’s expected return model. Authors typically deal with this issue by performing several
additional tests that either support or fail to support the risk argument. We contribute to this line
of research by developing a two-tailed test to distinguish the mispricing and risk-based
explanations within the context of the Ou and Penman (1989a and 1989b) studies.
The Ou and Penman studies are representative of the research dilemma described above.
They find that comprehensive logit-based financial statement analysis produces a one-period-
ahead earnings predictor (Pr) that is associated with future abnormal returns. After evaluating a
number of risk-based explanations for their results, Ou and Penman suggest a possible market
inefficiency explanation; i.e., that the abnormal returns result from the market's surprise at
earnings information that was discernible from the prior year's financial statements. The two-
tailed hypothesis we develop directly tests the market inefficiency explanation against the
alternative explanation that Pr proxies for risk omitted from the model used to estimate abnormal
returns.
We hypothesize that if the market inefficiency explanation is true, then estimating Pr to
predict a more refined measure of the market's future earnings surprise should increase the
abnormal returns to the Pr-based trading strategy. Alternatively, if the market is efficient with
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respect to the information impounded in the logit-based financial statement analysis, then the
simple earnings change predicted by the Ou and Penman Pr must be expected by the market, and
the returns to the Pr-based trading strategy must reflect a relation between those expected
earnings and expected returns not captured in the model used to estimate abnormal returns. We
hypothesize that if this is the case, then removing market-expected earnings from the Pr target
variable should correspondingly reduce abnormal returns to the Pr-based trading strategy.
Ou and Penman aim their logit-based financial statement analysis at the residual from a
random walk with drift annual earnings forecast model. This target variable measures the
market's unexpected earnings with error, where the measurement error consists of expected
earnings from the market's perspective. Thus, the target of the Ou and Penman analysis has two
components: expected and unexpected earnings from the market's perspective. We develop a
price-based forecasting model that controls for predictable earnings changes impounded in stock
prices. We similarly estimate a logit model aimed at our more accurate measure of the market's
earnings surprise. Relative to the Ou and Penman target variable, our target variable contains less
expected and more unexpected earnings from the market's perspective. Comparing the abnormal
returns to identical trading strategies based on our Pr model and the Ou and Penman Pr model
allows us to test the market inefficiency explanation against the risk proxy explanation for the
observed return relation. If the relation between Pr and future returns is due to market
inefficiency, then our Pr should generate grearter abnormal returns because our target variable
contains relatively more of the market’s unexpected earnings. Alternatively, if the relation
between Pr and future returns is due to the prediction of expected earnings that are associated
with expected returns, then our Pr should generate smaller abnormal returns because our target
variable contains relatively less of the market’s expected earnings.
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We find no evidence to suggest that estimating Pr to more directly predict the market's
unexpected earnings increases abnormal returns to the Pr-based trading strategy. In each of
three firm-size categories, we estimate that the abnormal returns decline when we take trading
positions using our Pr instead of the Ou and Penman Pr, and for one of the three size groups,
medium-sized firms, the decline is statistically significant (two-tailed p-value = 0.09). We
interpret our results as weakly consistent with the Ou and Penman Pr effectively predicting
expected earnings changes that are associated with expected returns not captured in the model
used to estimate abnormal returns. We acknowledge that differences between our sample and
the Ou and Penman sample limit us from making definitive statements about their results. Thus,
our conclusions pertain to the Ou and Penman model as it applies to our sample.
The rest of this paper is organized as follows. The next section discusses our study in
relation to prior research evaluating whether the association between the Ou and Penman Pr and
future returns reflects market inefficiency. The third section describes our price-based model for
forecasting earnings, compares it to the random walk with drift model, and formally presents
hypotheses about differences in abnormal returns to trading strategies based on predictions of the
residuals from these two forecasting models. The fourth section describes the logit-based
financial statement analysis procedure that predicts the residuals from the alternative forecast
models. The fifth section presents the results of tests for whether trading profits to logit-based
financial statement analysis increase or decrease as the target of the analysis conforms more
closely to the market's earnings surprise. The final section contains our conclusion.
II. PRIOR LITERATURE
Prior research provides mixed evidence on the ability of logit-based financial statement analysis
to identify market mispricing. Bernard, Thomas and Wahlen (BTW 1997) hypothesize that if the
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market inefficiency interpretation is correct, then a trading strategy based on Pr should produce
abnormal returns concentrated around subsequent earnings announcements. BTW find some
evidence consistent with this alternative hypothesis, which would appear to confirm the
conjecture that Pr identifies market failure to fully appreciate value-relevant financial statement
information about future earnings. However, based on further analysis of alternative risk-based
explanations, BTW suggest that abnormal returns to the Pr-based trading strategy appear to
reflect a small-firm/low-price effect that does not depend on the predictable earnings changes.
Overall, BTW interpret their results as most consistent with the risk proxy explanation for the
observed relation between Pr and future abnormal returns. 1 Greig (1992) and Stober (1992) also
investigate the market inefficiency explanation for abnormal returns to Pr-based trading
strategies. Greig concludes that the Pr-effect is subsumed by the well-known size anomaly.
Greig's conclusion is questionable, however, since he begins with a replication of Ou and
Penman that produces less abnormal returns than he estimates after implementing his additional
controls for firm size. Stober finds greater abnormal returns to the Pr-based trading strategy
when Pr predictions contradict consensus analysts' earnings forecasts. On the other hand, he
also observes that abnormal returns to the Pr-based trading strategy persist for up to six years
following the release of the financial statements from which the probability of a one-year-ahead
earnings increase is derived. Stober interprets the first result as supportive of the market
mispricing explanation for the relation between Pr and future returns, and he interprets the
second result as supportive of the risk proxy explanation.
Rather than attempting to eliminate the Pr effect in the presence of other risk proxies, such
as Greig (1992) and BTW (1995), our research design extends Ou and Penman's analysis in a way
that should enhance the Pr effect if it reflects market mispricing and should detract from the Pr
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effect if it reflects risk omitted from the model used to estimate abnormal returns. Thus, our
primary contribution to this literature is to develop a two-tailed test that distinguishes the
competing explanations for observed abnormal returns to logit-based financial statement analysis.
The market inefficiency explanation suggests that Pr predicts value-relevant future
earnings that are not fully expected by the market. We hypothesize that if this is true, then
estimating Pr to predict a better proxy of the market's future earnings surprise should produce
larger returns to the Pr-based trading strategy. The target variable of the Ou and Penman
financial statement analysis is the sign of the next year's residual from a random walk with drift
time-series model of annual earnings. We redefine the target variable as the residual from a
price-based forecasting model. We provide evidence that forecasts from our price-based
forecasting model are better proxies for market expectations about future earnings than forecasts
from the random walk with drift model. Given this result, if the link between Pr and abnormal
returns is due to market underutilization of financial statement information, then aiming the
financial statement analysis at the residual from the price-based forecasting model should
generate greater abnormal returns than returns obtained from predicting random walk with drift
residuals. On the other hand, if the market is efficient with respect to information available from
logit-based financial statement analysis, then Pr would not be able to predict value-relevant
earnings changes that are unexpected by the market. In this case, a relation between Pr and
future abnormal returns could still exist if Pr predicts expected earnings that are associated with
expected returns omitted from the model used to estimate abnormal returns. If this is the case,
then changing the target of the financial statement analysis to one that contains less expected
earnings from the market's perspective should reduce the observed abnormal returns to Pr-based
trading strategies.
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III. THE PRICE-BASED FORECAST MODEL AND FORMAL HYPOTHESES
Ou and Penman define unexpected earnings as the residual, UERWDi,t+1, from a random walk
with drift time series model of annual earnings as follows,
1 k=t
UERWDi,t+1 = E i,t+1 - E it - ∑
4 k=t -3
( E ik - E i,k -1 ) (1)
where Eit is firm i's earnings per share before extraordinary items for fiscal year t. The Ou and
Penman financial statement analysis procedure is designed to predict the sign of UERWDi,t+1.
Research by Collins, Kothari, and Rayburn (1987) suggests that UERWDi,t+1 is not the best
measure of unexpected earnings for period t+1 from the market's perspective. They estimate the
following price-based forecasting model for each size group, s, and show that the residual, UEi,t+1,
is more correlated with contemporaneous abnormal returns than the residual from a random walk
time-series model, particularly for large firms,
E i,t+1 - E it
= λ 0s + λ 1s CARit + UE i ′,t+1 (2)
E it
where CARit is the cumulative abnormal return from the first to last month of firm i's fiscal year t.
We modify the Collins, Kothari, and Rayburn price-based forecasting model by adding a
variable related to the firm's E/P ratio. Ou and Penman suggest (1989b, p. 131) that the E/P ratio
predicts future earnings changes, because the market, to some degree, identifies transitory
current earnings. For example, if earnings are artificially high due to current-period transitory
price-irrelevant earnings that the market recognizes, then price will not increase with the current
earnings increase. In this case, the E/P ratio will be relatively high, signaling an earnings
decrease in the next period. However, Ou and Penman also speculate that the ability of Pr to
earn abnormal returns is due to its ability to identify transitory current earnings not reflected in
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E/P. We use the variable TEit from model (3) to proxy for the market's identification of
transitory components of current earnings,
n
E it - 1 E jt
TE it = Pia ( AEPit ) = Pia (
Pia n j=1
∑ P ja ) (3)
where Pia is firm i's stock price at time a, the end of the third month after the end of firm i's fiscal
year t; AEPit is firm i's abnormal earnings-price ratio at time t, and n is the number of firms in
firm i's decile defined by market value of equity at the beginning of calendar year t. To the
extent that E/P identifies transitory earnings, TEit should be negatively correlated with future
earnings changes.
We also change the deflator of the dependent variable in the price-based forecasting
model to price instead of earnings.2 In addition, to avoid problems associated with
nonstationarity and missing return data, we estimate CAR on a size-adjusted basis rather than
using market model residuals. Finally, since Collins and Kothari (1989) find that large-firm
returns begin to impound the information in annual earnings at an earlier point in time than small
firms' returns, we allow the return holding period to vary with size in the estimation of the price-
based forecasting model. We estimate the following model cross-sectionally within each of three
size groups (s=1,2,3 for small, medium-sized, and large firms, respectively) and intertemporally
for the estimation period (t=1973 through 1978),
E i,t+1 - E it TE it
= λ 0s + λ 1s CARi,a -ns,a + λ 2s + UE i,t+1 (4)
Pi,a-ns Pi,a-ns
where Pi,a-ns is firm i's stock price at time a-ns, the beginning of the return accumulation period; a
is the end of the third month of fiscal year t+1; ns is the number of months in the return
accumulation period for size group s; CARi,a-ns,a is the size-adjusted abnormal return for firm i
accumulated from time a-ns to time a; TEit (from equation [3]) proxies for the transitory earnings
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component of Eit recognized by the market by time a;3 and UEi,t+1 is our estimate of firm i's
unexpected earnings, scaled by Pi,a-ns, for period t+1 from the market's perspective. Size-adjusted
returns are computed as follows,
a
CARi,a-ns,a = ∑ (R
k=a-ns
ik - R pk ) (5)
where Rik and Rpk are the month k raw returns for, respectively, firm i and portfolio p. Portfolio p
consists of all stocks in the size decile of which firm i is a member. Size deciles are formed at
the beginning of each estimation period calendar year based on the market value of equity for all
sample firms.
Table 1 panel A displays descriptive statistics by size group for market value of equity,
UEi,t+1, CARi,a-ns,a, and Eit/Pia for the estimation period years 1973 to 1978. Substantial dispersion
in firm-size between size categories is apparent. The median size of large firms is about 6 times
the median of medium-sized firms and about 30 times the median of small firms. The absolute
value and standard deviation of the scaled earnings forecast error from our price-based model,
UEi,t+1 , is decreasing with firm size. For small firms the standard deviation of UEi,t+1 is about 3.2
times that of large firms, and the mean absolute value of small-firm UEi,t+1 is about 4 times that
of large firms. These results are consistent with prior literature finding that small-firm earnings
are more variable and less predictable than large-firm earnings (e.g., Bathke, Lorek, and
Willinger 1989), and that the predictive accuracy of price-based forecast models is inversely
related to firm-size (e.g., Collins, Kothari, and Rayburn 1987). Median earnings-price ratios
range from 10.8% for large firms to 13.6% for small firms, and like UEi,t+1 and CARi,a-ns,a, Eit/Pa is
more variable for small firms than for larger firms.
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A. Estimation of the Price-based Forecasting Model
Table 1 panel B shows the results of estimating equations (2) and (4) for each of three stable size
groups. For each estimation and prediction period year, the sample is restricted to NYSE firms
included in the 1990 data bases of both COMPUSTAT (combined Research and PST Files) and
CRSP (Monthly Master File) that remained in the same size category during the three preceding
years. To identify firms with stable size, we follow the procedure in Bathke, Lorek, and
Willinger (1989). Firms are trichotomized into three size categories based on market value of
outstanding common stock as of the current fiscal year-end of the financial statements from
which Pr is derived and the two preceding fiscal year-ends. Firms that change size strata are
eliminated from the analysis for that Pr year. Sample observations are further reduced, as
described in the appendix, due to missing descriptor variable information needed for the financial
statement analysis procedure.4
Table 1 panel B shows the optimal return accumulation period, ns, for each size group.
For each size group, we allowed the return accumulation period to vary from the fourteen-month
period ending at time a, to the three-month period ending at time a, where time a is the last
trading day of the third month after the firm's fiscal year-end. The ns reported in Table 1 is the
one for each size group that produced the highest adjusted R2 in model (4). Consistent with the
results in Collins and Kothari (1989), the optimal return accumulation period for large firms
begins at an earlier point in time than the optimal return accumulation period for small firms
(ns=13 for large firms and 7 for small firms). The significant positive coefficients relating
abnormal returns to deflated future earnings changes in models (2) and (4) support the
conclusion of Beaver, Lambert, and Morse (1980) who argue that price changes contain
information about permanent earnings changes that will be recorded in the next year's earnings
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reports. The significant negative coefficient relating deflated TEit to deflated future earnings
changes is consistent with the reasoning in Ou and Penman (1989b) that E/P ratios capture the
market's ability to, at least partially, identify transitory components of current earnings. The
significant intercept reflects a positive drift in the deflated earnings change. Thus, across all size
groups, we find that lagged abnormal returns and E/P ratios in our price-based forecast models
explain significant variation in the random walk with drift residual that is the target of the Ou
and Penman analysis.
B. The Price-based Forecasting Model as a Proxy for Market Expectations
The best test of model (4) as a proxy for market expectations is to evaluate, out-of-sample, the
association of residuals from the model with abnormal returns. Panel C of Table 1 shows the
size-adjusted abnormal return an investor with perfect foresight would earn during the period
1978-1983 by balancing a long position in stocks of firms with a positive UEi,t+1 from model (4)
against a short position in stocks of firms with UEi,t+1<0. Also shown are the similar returns to
trading on the sign of the residual from a random walk with drift forecast, UERWDi,t+1. The
abnormal returns range from 10.33% (8.24%) for large firms to 24.95% (21.46%) for small firms
for hedge portfolios formed based on the sign of UEi,t+1 (UERWDi,t+1).5 Thus, while we expect
that both UEi,t+1 and UERWDi,t+1 measure the market's unexpected earnings with error, UEi,t+1
apparently contains less error than UERWDi,t+1 (i.e., UEi,t+1 contains relatively less expected
earnings from the market's perspective). This relation provides the foundation for our testable
hypotheses, which we develop below.
C. Hypotheses
To clarify the relation between the two target variables, we expand UERWDi,t+1 to include the
price-based forecast residual, as follows: UERWDi,t+1=(UERWDi,t+1 - UEi,t+1)+UEi,t+1. The first
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component represents (from the market's perspective) expected earnings that can be purged using
the price-based forecasting model. The second term is the residual from the price-based model
and should consist of a proportionately greater amount of unexpected earnings from the market's
perspective. Whereas Pr(UERWDi,t+1>0) is estimated to predict the combination of both
components, Pr(UEi,t+1>0) isolates the second component. Following the logic that the market is
inefficient and the relation between Pr(UERWDi,t+1>0) and future returns is due to the prediction
of (from the market's perspective) unexpected future earnings, then UEi,t+1 provides a better proxy
of the variable of interest, and the first component of UERWDi,t+1 becomes noise in the analysis.
In this case, estimating Pr to predict only the second component of UERWDi,t+1 removes some of
the noise and should result in a greater association between Pr(UEi,t+1>0) and future returns than
the relation between Pr(UERWDi,t+1>0) and future returns. This leads to the first hypothesis,
stated in the alternative form:
HA1: If the relation between Pr and future returns is due to market inefficiency, then
estimating Pr to predict UEi,t+1 instead of UERWDi,t+1 should produce larger
abnormal returns to a Pr-based trading strategy.
Alternatively, if the market efficiently processes the future earnings implications of
financial statement information, then neither UEi,t+1 nor UERWDi,t+1 should contain value-relevant
unexpected earnings from the market's perspective, and any relation between predictions of these
target variables and abnormal returns must be due to the prediction of (from the market's
perspective) expected earnings that are associated with expected returns not accounted for in the
estimation of abnormal returns. Since UEi,t+1 contains less expected earnings from the market's
perspective than UERWDi,t+1, Pr(UEi,t+1>0) should be less effective than Pr(UERWDi,t+1>0) at
predicting any expected period t+1 returns that are correlated with expected period t+1 earnings.
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Thus, if the market is efficient, we expect less abnormal returns to a trading strategy based on
predicting UEi,t+1. This leads to the second hypothesis, stated in the alternative form:
HA2: If the relation between Pr and future returns is due to the ability of Pr to predict
expected earnings that are correlated with expected returns omitted from the model
used to estimate abnormal returns, then estimating Pr to predict UEi,t+1 instead of
UERWDi,t+1 should produce smaller abnormal returns to a Pr-based trading strategy.
IV. ESTIMATION OF LOGIT MODELS TO PREDICT UNEXPECTED EARNINGS
This section applies the Ou and Penman (1989a) financial statement analysis procedure to estimate
logit models of Pr(UEi,t+1>0), the probability of a positive residual from the price-based forecasting
model in (4) above. We estimate separate size-related models for each of the three firm-size
categories.6 To estimate each model, we begin with 64 of the 68 candidate descriptor ratios in Ou
and Penman (1989a).7 We then follow the procedure described in Ou and Penman (1989a) to
systematically reduce the 64-variable set to a parsimonious set of ratios that predict the target
variable of interest. The important difference between our approach and the Ou and Penman
approach to predicting unexpected earnings is in the definition of the target variable. We use the
residual from (4) in our analysis, whereas they use the residual from (1) in their analysis. Other
differences in the way we apply the logit procedure are minor and are described in the appendix.
Table 2 displays the variables and coefficients for the three logit models that result from
the financial statement analysis, along with the global logit model estimated by Ou and Penman
(1989a). The first model displayed is labeled OP and it reproduces the number of observations,
coefficients, and chi-square statistics for the 18-variable Ou and Penman logit model estimated
with 1973 to 1978 data and used to generate their Pr(UERWDi,t+1>0), the probability of a positive
residual from a random walk with drift time series model. The OP model is compared in Table 2
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to our size-related models, UES, UEM, and UEL, which are estimated across stable-sized firms
within each size category and across all estimation-period years 1973-1978. Models UES, UEM,
and UEL produce Pr(UEi,t+1>0), the probability of a positive residual from our price-based
forecasting model (4).
Considerable differences are apparent between the four logit models displayed in Table
2.8 However, all of the models in Table 2 appear to be reasonably well-specified. Model chi-
squares are all highly significant, and the percentage of concordant pairs is at least 62 percent for
each model.9 The larger firms produce a size-related Pr model with the best in-sample prediction
of the sign of UEi,t+1. We are most concerned with any differences between the logit models in
the out-of-sample predictions. We turn to this issue next.
V. RESULTS
A. Prediction of the Sign of UEi,t+1.
Before testing the hypotheses, we assess the ability of our logit models to predict the sign of the
target variables. Primarily, we wish to verify that Pr(UEi,t+1>0) outperforms Pr(UERWDi,t+1>0) in
successfully predicting the sign of UEi,t+1. Even though Pr(UERWDi,t+1>0) was estimated to
predict the sign of UERWDi,t+1, it could outperform Pr(UEi,t+1>0) in the prediction of UEi,t+1,
because: (a) UEi,t+1 and UERWDi,t+1 are highly correlated (prediction period spearman rank
correlation of 0.79); and (b) the parameters of the price-based forecasting model may exhibit
significant instability between the estimation and prediction period as compared to the naive
random walk with drift model.10
Predictive accuracy of the various logit models is summarized for Pr>0.6 and Pr<0.4,
since the Ou and Penman strategy only takes trading positions when Pr is in these ranges. Table
3 shows the predictive accuracy of Pr(UEi,t+1>0) and Pr(UERWDi,t+1>0) with respect to the actual
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signs of all UEi,t+1 in the prediction period, 1978-1983. Table 3 shows that the Pr(UEi,t+1>0) logit
models (UES, UEM, and UEL) outperform the Ou and Penman logit model in the prediction of
UEi,t+1 across the full sample (63.68% accuracy versus 59.26%). Only within the large firm
group does Pr(UERWDi,t+1>0) provide more accurate predictions of the sign of UEi,t+1. For small
and medium-sized firms, Pr(UEi,t+1>0) outperforms Pr(UERWDi,t+1>0) in predicting the sign of
UEi,t+1, which should lead to Pr(UEi,t+1>0) producing greater abnormal returns if the market
underutilizes financial statement information. Furthermore, to the extent that this market
inefficiency exists, we expect that it would be most prevalent for smaller firms. Thus, the small
and medium-sized firms in particular provide an appropriate context for testing the market
inefficiency hypothesis.
B. The Relation of Pr(UERWDi,t+1>0) and Pr(UEi,t+1>0) with Abnormal Returns
For each firm-size category and for 12-, 24-, and 36-month holding periods, Table 4 shows the
average size-adjusted returns to long and short positions following the Ou and Penman trading
strategy. The cumulative abnormal returns to each position are derived by: (1) computing Prit at
the end of each fiscal year t during the prediction period 1978-1983; (2) assigning securities to
long positions (Prit > 0.6) and short positions (Prit < 0.4) as of the end of the third month
following the end of each fiscal year t; (3) obtaining an average abnormal return for each month
of the holding period (in event time) for all stocks assigned to each position and still trading; and
(4) summing the average abnormal returns across all event time months in the holding period.
Table 4 also summarizes the abnormal returns to the long and short positions into a hedge return
by subtracting the returns for the short position from the returns for the long position.11 Table 4
also shows the mean values of Prit on the long and short sides of each hedge portfolio.
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Table 4 shows that basing the trading strategy on Pr(UEi,t+1>0) generates less abnormal
returns than the trading strategy based on Pr(UERWDi,t+1>0) for all three size-categories.
Pr(UEi,t+1>0) underperforms Pr(UERWDi,t+1>0) in predicting abnormal returns in spite of the
evidence that: (a) perfect foresight of UEi,t+1 would produce greater abnormal returns than perfect
foresight of UERWDi,t+1; and (b) at least for small and medium-sized firms (where market
inefficiency, if it exists, should be most prevalent) Pr(UEi,t+1>0) is a better predictor of UEi,t+1
than Pr(UERWDi,t+1>0). Thus, we find no evidence in favor of HA1. The evidence is more
consistent with HA2, although abnormal returns to the trading strategy based on Pr(UEi,t+1>0) are
significantly less (at the 10 percent level) than abnormal returns to the trading strategy based on
Pr(UERWDi,t+1>0) only for medium-sized firms (t-statistic=1.69, two-tailed p-value=0.09). The
direction of our results weakly suggests that the relation between Pr(UERWDi,t+1>0) and
abnormal returns derives from the prediction of expected earnings not included in UEi,t+1.
We also observe from Table 4 that abnormal returns to trading strategies based on
Pr(UEi,t+1>0) are negative for small and medium-sized firms. This observation taken together
with the results in Table 3 suggests that while logit-based financial statement analysis adds to the
predictive ability of a price-based earnings forecast model, that improvement does not translate
into larger abnormal returns. Thus, the predictive accuracy of Pr(UEi,t+1>0) relates to a portion of
earnings that the market assesses as value-irrelevant and, therefore, like UERWD i,t+1, UE i,t+1 may
contain some earnings that can be predicted using logit-based financial statement analysis but
that are not unexpected to the market. However, unlike the predictable component of
UERWDi,t+1, the predictable component of UE i,t+1 is not related to future returns. Apparently,
adding the price-based variables to the earnings forecasting model effectively purges from the
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target of the logit-based financial statement analysis any expected earnings changes that are
related to expected returns. In any case, it does not appear that Pr(UEi,t+1>0) is able to
successfully predict the portion of unexpected earnings associated with the large perfect-
foresight returns documented in panel C of Table 1. Overall, the results in Tables 3 and 4
suggest that the price-based forecasting model controls for future earnings that are anticipated
and priced by the market.
The market inefficiency explanation for the success of Pr(UERWDi,t+1>0) is that financial
statement analysis can identify unexpected value-relevant earnings. This implies that the ability
of our price-based forecast model to control for the market's expected earnings should have
enhanced the abnormal returns to the Pr-based trading strategy. Instead, we find that the trading
strategy is no longer successful over 12, 24 or 36 month horizons. As described in the third
section of this paper, UERWDi,t+1 may be divided into two components:
UERWDi,t+1=(UERWDi,t+1-UEi,t+1) + UEi,t+1. Our results suggest that the success of Pr in predicting
abnormal returns is likely due largely to the ability of Pr to predict the first of these two
components, which we argue represents value-relevant but (from the market's perspective)
expected earnings. A relation between future returns and expected earnings is most consistent
with the interpretation that these returns are expected and proxy for an omitted risk factor in the
estimation of abnormal returns.
Consistent with results reported by Morton and Shane (1993 and 1998), Table 4 also
shows that small-firm logit-based financial statement analysis does not generate greater
abnormal returns than larger firm logit-based financial statement analysis.12 This result holds
regardless of whether the target of the financial statement analysis is UEi,t+1 or UERWDi,t+1 and
suggests that if the market underutilizes information in financial statements about future
19.
17
earnings, the underutilization does not appear to be inversely related to the richness of the firm's
information environment.13
VI. CONCLUSION
Using logit-based financial statement analysis, Ou and Penman (1989a) obtain an estimate,
Pr(UERWDi,t+1>0), of the probability that the coming year's residual from a random walk time-
series model of annual earnings will have a positive sign. Using this predictor, Ou and Penman
develop a trading strategy that appears to identify mispriced securities. Others have evaluated
this claim with mixed results. This study develops an approach to distinguish between the
market inefficiency and risk proxy explanations for the relation between the Ou and Penman Pr
and future returns.
While a portion of the random walk with drift residual is predictable using logit-based
financial statement analysis, not all of this predictable earnings change is unexpected to the
market. Thus, the target variable of the Ou and Penman analysis contains both expected and
unexpected earnings from the market's perspective. We repeat the Ou and Penman analysis, but
also estimate an alternative Pr model aimed at the residual from a price-based forecasting model
of earnings. The target variable of our alternative Pr contains relatively more unexpected and
relatively less expected earnings from the market's perspective. We hypothesize that if market
inefficiency explains the ability of the Ou and Penman Pr to predict future returns, then our Pr,
aimed at a target that contains relatively more unexpected earnings, should result in greater
abnormal returns to the Pr-based trading strategy. Alternatively, we argue that if the market is
efficient with respect to the information impounded in the logit-based financial statement
analysis, then the Ou and Penman Pr cannot successfully predict value-relevant unexpected
earnings from the market's perspective. In this case, Pr must be predicting earnings that are
20.
18
expected by the market and associated with risk not accounted for in the abnormal return
estimate. If in fact the Ou and Penman Pr proxies for risk, then our Pr, aimed at an earnings
forecast residual that contains relatively less expected earnings, should produce smaller abnormal
returns. Thus, the models are constructed such that a relational test of the resulting abnormal
returns evaluates one hypothesis against the other.
Based on our application of this approach to the Ou and Penman Pr-based trading
strategy, we find no evidence consistent with market inefficiency. In each of three firm-size
categories, we estimate that the abnormal returns decline when we take trading positions using
our Pr instead of the Ou and Penman Pr, and for medium-sized firms the decline is statistically
significant. We interpret our results as weakly consistent with the Ou and Penman Pr effectively
predicting expected earnings changes that are associated with expected returns not fully
accounted for in the model used to estimate abnormal returns.
We view the Ou and Penman analysis as representative of a broader class of research that
uses financial statement data to predict future accounting measures of firm performance, and
then uses those predictions as the basis for a trading strategy. The dilemma in these studies is
attributing the observed abnormal returns to market mispricing, as opposed to an inability to
control for risk. By manipulating the financial statement target variable, our study identifies a
two-tailed approach that simultaneously tests the competing hypotheses of market mispricing
and risk. We suggest that variations of this approach could be insightful for similar applications
of financial statement analysis.
21.
19
APPENDIX
Model Estimation and Return Accumulation Procedures
The following procedures pertain to our estimation of separate size-related logit models,
and the subsequent accumulation of hedge portfolio returns in the holdout period. Modifications
to the Ou and Penman procedures are noted below.
1. Data for model estimation were drawn from the COMPUSTAT Annual Industrial File
(primary/secondary/tertiary, full coverage, and research tapes). The estimation sample
consisted of firm-year observations pooled across the five year estimation period,
1973-1977, which met the following conditions: (1) listed on the NYSE, (2)
COMPUSTAT fiscal year-end month (FYR) had a value of 1-12, (3) COMPUSTAT
earnings per share (#58) for the current, prior and next fiscal years were non-missing, (4)
COMPUSTAT fiscal year-end price (#199) and shares outstanding (#25) were non-
missing. Use of the monthly returns file in the prediction period limited the estimation
sample to NYSE firms only. For each firm-year observation, the 68 financial statement
ratios identified by Ou and Penman (1989) were computed from the COMPUSTAT data,
using data definitions provided by the authors.
2. For each fiscal year in the five year estimation period, the observations were ranked on
year-end market value of equity and assigned to one of three equal-sized groups (small,
medium, and large). This market value ranking and assignment was also performed on
each observation for the two preceding fiscal-year ends. Firm-year observations were
then deleted if they were not assigned to the same size group in each of these three years
(t-2, t-1, and t). This resulted in a sample of firms with relatively stable size ranking.
3. Models were independently estimated for each of the three size groups. The dependent
variable was defined as a binary variable representing the sign of one-year-ahead
unexpected earnings. The set of independent variables consisted of 64 of the 68 ratios
used by Ou and Penman. Four ratios, relating to advertising and research and
development expenditures, were eliminated due to the high frequency of missing data.
22.
20
None of these ratios were included in the Ou and Penman global model for either of their
estimation periods.
4. The distributions of each of the 64 ratios were analyzed, and any observation that was in
the first percentile or above the ninety-ninth percentile was coded as missing.
5. Separate univariate logit estimations were performed with each of the 64 ratios as the sole
explanatory variable of the binary dependent variable.
6. A multivariate logit estimation was then performed with all the ratios significant at the
0.10 level in step 5. At this point, Ou and Penman simultaneously eliminated all ratios
not significant at the 0.10 level in the multivariate model. We chose to perform
backwards elimination on the model, keeping ratios significant at the 0.10 level.
Coefficient estimates at this point use only those observations that had non-missing
values for all independent variables originally entering the multivariate model.
7. Using the final set of ratios identified in step 6, we re-estimated the logit model with
backwards elimination. This step was performed to allow more observations to be used
in estimating the model. Specifically, the data constraints associated with ratios
eliminated in step 6 did not limit the sample used to estimate the model.
8. Each size related model was then applied to a six year prediction period, 1978-1983. The
prediction sample reflected the data constraints from step 1 and additionally required that
observations have a non-missing return on monthly CRSP for the fourth month after
fiscal year-end.
9. Firm-year observations were assigned to the three size groups, formed at each of the six
fiscal year-ends, as described in step 2. Predicted probabilities for each observation were
computed by multiplying the coefficient estimates from the appropriate size-related
model, estimated in step 7, by the required prediction year ratios. If the predicted
23.
21
probability was greater than 0.6 (less than 0.4), the observation was assigned to a long
(short) position.
10. Size-adjusted returns to the portfolio assignments were obtained by first assigning each
observation to a size decile based on fiscal year-end market value of equity. The mean
return was computed for each month of the holding period for each size decile. An
observation's monthly size-adjusted return was calculated as its monthly raw return less
the monthly mean return of the size decile, to which it was assigned. Note that size
decile assignments were performed once, at the fiscal year-end preceding the holding
period.
11. The monthly size-adjusted returns were then averaged across all observations in each
portfolio position (long and short) of each size group (small, medium, and large). Thus,
firms that stop trading during the holding period will be included up to the point they stop
trading, but will be excluded from portfolio averages thereafter. Finally, the monthly
portfolio returns were summed across the number of months in the holding period (12,
24, or 36).
12. The hedge return for each size group is computed as the long position return less the short
position return. However, the portfolio positions reflect a pooling of firms across years
and different fiscal year-ends, and are not intended to reflect the returns to an
implementable investment strategy.
25.
23
REFERENCES
Bathke, A.W. Jr., K.S. Lorek, and G.L. Willinger. (1989). “Firm-Size and the Predictive Ability of
Quarterly Earnings Data.” The Accounting Review 64 (January): 49-68.
Beaver, W., D. Lambert, and D. Morse. (1980). “The Information Content of Security Prices.”
Journal of Accounting and Economics 2 (March): 3-28.
Bernard, V., and J. Thomas. (1990). “Evidence that Stock Prices Do Not Fully Reflect the
Implications of Current Earnings for Future Earnings.” Journal of Accounting and Economics
13 (December): 305-340.
Bernard, V., J. Thomas and J. Wahlen. (1997). “Accounting-based Stock Price Anomalies: Separating
Market Inefficiencies from Risk.” Contemporary Accounting Research 14 (Summer): 89-136.
Christie, A.A. (1987). “On Cross-sectional Analysis in Accounting Research.” Journal of
Accounting and Economics 9 (December): 231-258.
Collins, D.W., S.P. Kothari, and J.D. Rayburn. (1987). “Firm Size and the Information Content of
Security Prices with Respect to Earnings.” Journal of Accounting and Economics 9, (July):
111-137.
Collins, D., and S.P. Kothari. (1989). “An Analysis of Intertemporal and Cross-Sectional
Determinants of Earnings Response Coefficients.” Journal of Accounting and Economics 11,
(July): 143-181.
Elgers, P., and D. Murray. (1992). “The Relative and Complementary Performance of Analyst and
Security-Price-Based Measures of Expected Earnings.” Journal of Accounting and Economics
15, (June/September): 303-316.
Greig, A.C. (1992). “Fundamental Analysis and Subsequent Stock Returns.” Journal of
Accounting and Economics 15, (June/September): 413-442.
26.
24
Holthausen, R.W., and D.F. Larcker. (1992). “The Prediction of Stock Returns Using Financial
Statement Information.” Journal of Accounting and Economics 15 (June/September): 373-411.
Morton, R.M., and P.B. Shane. (1993). “Firm-Size and the Predictive Ability of Financial
Statement Analysis.” In Earnings Quality, ed. S.A. Butler. The University of Oklahoma Center
for Economic and Management Research, 87-110.
Morton, R.M., and P.B. Shane. (1998). “The Information Environment and the Ability of Logit-
Based Financial Statement Analysis to Predict Abnormal Returns,” Accounting and Finance 38
(July): 71-89.
Ou, J.A., and S.H. Penman. (1989a). “Financial Statement Analysis and the Prediction of Stock
Returns.” Journal of Accounting and Economics 11 (November): 295-329.
Ou, J.A., and S.H. Penman. (1989b). “Accounting Measurement, Price-Earnings Ratio, and the
Information Content of Security Prices.” Journal of Accounting Research (Supplement):
111-144.
Stober, T. (1992). “Summary Financial Statement Measures and Analysts' Forecasts of Earnings.”
Journal of Accounting and Economics 15 (June/September): 347-372.
27.
Table 1. Price-Based Forecasting Model
Panel A: Descriptive statistics.
Market Value ($ millions) UE from model (4) Monthly CAR Earnings-Price Ratios
Size Std. Absolute Value Std. Absolute Value Std. Std.
Category Mean Median Dev. Mean Median Dev. Mean Median Dev. Mean Median Dev.
Small 26.2 23.5 14.6 0.117 0.061 0.190 0.032 0.024 0.042 0.116 0.136 0.175
(N = 1673)
Medium 129.4 117.3 58.3 0.047 0.025 0.091 0.017 0.013 0.024 0.134 0.127 0.094
(N = 1492)
Large 1498.6 705.9 3094.1 0.029 0.015 0.059 0.014 0.011 0.018 0.114 0.108 0.078
(N = 1897)
Panel B: Estimation of price-based forecasting models
E i,t+1 - E it TE it
= λ 0s + λ 1s CARi,a-ns,a + λ 2s + UE i,t+1 (4)
Pi,a -ns Pi,a-ns
Size Adjusted
Group n ns λ0 λ1 λ2 R-square
Small 1673 7 0.0311 0.1270 3.66%
(6.64) (8.03)
Small 1673 7 0.0335 0.1288 -0.0840 5.64%
(7.19) (8.23) (-6.01)
Medium 1492 11 0.0205 0.0832 5.31%
(8.69) (9.19)
Medium 1492 11 0.0200 0.0840 -0.0997 6.42%
(8.52) (9.33) (-3.99)
Large 1897 13 0.0130 0.0501 4.15%
(9.48) (8.78)
Large 1897 13 0.0126 0.0505 -0.1021 5.41%
(9.23) (8.92) (-5.67)
28.
Table 1. Price-Based Forecasting Model (continued)
Panel C: Perfect foresight abnormal size-adjusted returns in prediction period.
Size Price-based Forecast Random Walk With Drift
Category Long Short Hedge Long Short Hedge
Small 15.25% -9.70% 24.95% 10.43% -11.03% 21.46%
Medium 11.54% -6.38% 17.92% 8.35% -6.86% 15.21%
Large 6.17% -4.16% 10.33% 4.61% -3.63% 8.24%
Pi,a-ns is firm i's stock price at time a-ns, the beginning of the return accumulation period; a is the
end of the third month after fiscal year-end; ns is the number of months in the return
accumulation period for size group s; CARi,a-ns,a is the size-adjusted abnormal return for firm i
accumulated from time a-ns to time a; TEit (from equation [4]) proxies for the price-irrelevant
transitory earnings component of Eit recognized by the market by time a; and UEi,t+1 is our
estimate of firm i's unexpected earnings for period t+1 from the market's perspective. Panel C
shows the size-adjusted abnormal return an investor with perfect foresight would earn during the
period 1978-1983 by balancing a long position in stocks of firms with a positive UEi,t+1 from
model (4) against a short position in stocks of firms with UEi,t+1≤0. Also shown are the similar
returns to trading on the sign of the residual from a random walk with drift forecast model,
UERWDi,t+1.
29.
Table 2. Logit Models to Predict the Sign of UERWDi,t+1, and UEi,t+1
Estimation Period Data, 1973-1978
Model
OP UES UEM UEL
Number of Observations 11,776 776 872 1,055
Chi-Square Statistic 855.97* 61.27* 42.89* 126.28*
% Concordant Pairs 66.4% 62.6% 69.4%
1 Current Ratio
2 % Chg. in 1 -1.2105
(69.14)*
3 Quick Ratio
4 % Chg. in 3 0.8185 1.0488
(53.13)* (8.40)*
5 Days Sales in A/R
6 % Chg. in 5 2.5577
(11.53)*
7 Inventory Turnover
8 % Chg. in 7 1.9530
(9.98)*
9 Inventory/Total Assets -1.0777
(35.21)*
10 % Chg. in 9 -0.7526 -3.4002
(36.30)* (22.94)*
11 % Chg. in Inventory 0.2945
(18.65)*
12 % Chg. in Sales 0.4846
(21.77)*
14 Chg. in Dividend/Shr. -1.5189 -6.0333
(72.14)* (5.23)@
15 Depreciation/Plant Assets 5.8246
(9.95)*
16 % Chg. in 15 1.3634
(3.50)#
17 Return on Opening Equity -1.9197
(44.84)*
18 % Chg. in 17 0.4124
(10.13)*
19 % Chg. in (Capital Exp./
Total Assets)
20 One Year Lag in 19 -0.0288
(4.32)@
21 Debt to Equity Ratio -0.0334
(6.84)*
30.
Table 2. Logit Models to Predict the Sign of UERWDI,t+1, and UEI,t+1
Estimation Period Data, 1973-1978 (continued)
------------------Model--------------
OP UES UEM UEL
-------------------------------------
31 Return on Total Assets -11.3727 -22.3875
(90.95)* (24.90)*
32 Return on Closing Equity -6.4916
(12.80)*
33 Gross Margin Ratio -1.6768
(6.07)@
37 Pretax Income to Sales 7.6530
(3.96)@
38 % Chg. In 37 0.0141
(2.87)#
39 Net Profit Margin -14.6775
(5.12)@
40 % Chg. In 39 -1.1503
(10.48)*
41 Sales to Total Cash -0.0003
(3.81)#
43 Sales to Inventory
44 % Chg. In 43 2.5556
(25.26)*
48 % Chg. In Production 2.0927 -2.5754
(8.90)* (22.34)*
53 % Chg. In Total Assets -0.9628 -2.0908
(37.19)* (3.99)@
54 Cash Flow to Debt 2.8620
(10.84)*
55 Working Cap./Total Assets 0.9571
(28.39)*
57 Oper. Income/Total Assets 3.5859
(43.76)*
58 % Chg. In 57 1.7597
(11.37)*
61 Repayment of LT Debt as % 0.0576 -0.6429
of Total LT Debt (3.87)@ (4.94)@
Intercept 0.7416 -0.1025 0.6685 0.8900
(104.28)* (0.13) (9.75)* (19.93)*
OP reproduces the Ou and Penman model of 18 ratios and coefficients. UES, UEM, and UEL are estimated following the Ou
and Penman procedure for estimating OP, except the dependent variable is redefined as the sign of the residual from our
price-based forecasting model, and the models are estimated separately within small, medium-sized, and large-firm groups,
respectively.
# : Chi-Square significant at .10 level.
@ : Chi-Square significant at .05 level.
* : Chi-Square significant at .01 level.
31.
Table 3. Accuracy of Earnings Predictors in
the Prediction Period, 1978-1983
All Firms Small Firms Medium Firms Large Firms
UE>0 UE<0 % Correct UE>0 UE<0 % Correct UE>0 UE<0 % Correct UE>0 UE<0 % Correct
Pr(UERWD)>.6 794 644 55.22% 396 368 51.83% 182 165 52.45% 216 111 66.06%
Pr(UERWD)<.4 170 390 69.64% 39 89 69.53% 46 126 73.26% 85 175 67.31%
Total 964 1034 59.26% 435 457 54.37% 228 291 59.34% 301 286 66.61%
Pr(UE)>.6 675 493 57.79% 300 208 59.06% 120 108 52.63% 255 177 59.03%
Pr(UE)<.4 532 1122 67.84% 212 462 68.55% 143 289 66.90% 177 371 67.70%
Total 1207 1615 63.68% 512 670 64.47% 263 397 61.97% 432 548 63.88%
The overall percentage correct for each subsample is the sum of the numbers on the diagonal divided by the total of all predictions.
Pr values are derived from application of the models in table 2 to financial statement data for each year t of the prediction period.
Pr(UERWDi,t+1>0) is derived from the Ou and Penman model, OP, and Pr(UEi,t+1>0) is derived from the relevant size-related
model UES, UEM, or UEL displayed in Table 2.
32.
30
Table 4. Abnormal (size-adjusted) Returns to Hedge Portfolios
by Size Category in the Prediction Period, 1978-1983
Small Medium Large
Long Short Hedge Long Short Hedge Long Short Hedge
Ou and Penman model to predict
sign of random walk with drift
forecast error:
Mean Pr 0.72 0.29 0.69 0.32 0.69 0.33
Holding period CAR:
12-months -1.38% 0.64% -2.02% 2.05% -3.89% 5.95% 2.59% -1.84% 4.43%
24-months -0.15% 2.61% -2.76% 2.32% -10.50% 12.83% 1.05% -4.78% 5.83%
36-months -0.37% 1.82% -2.19% 3.98% -7.52% 11.51% 0.11% -8.56% 8.67%
Size-related logit models to
predict sign of residual from
price-based forecasting model (4):
Mean Pr 0.80 0.26 0.73 0.27 0.74 0.28
Holding period CAR:
12-months -2.80% 0.85% -3.65% -1.62% -0.63% -1.00% 3.29% 0.04% 3.25%
24-months -0.97% 1.30% -2.27% -1.18% -1.45% 0.28% 1.10% -0.48% 1.58%
36-months -3.19% 1.64% -4.83% -3.07% -2.54% -0.53% -0.62% -2.67% 2.06%
Differences in abnormal returns
to trading strategies based on
Pr(UERWDi,t+1>0) versus
Pr(UEi,t+1>0) over the 12-month
holding period:
Difference 1.63% 6.95% 1.18%
t-statistic 0.38 1.69 0.42
Returns to long and short positions are average size-adjusted abnormal returns for 12-, 24-, and 36-month holding periods for
situations where Prit is greater than 0.6 (long positions) and where Prit is less than 0.4 (short positions). The cumulative abnormal
returns to each position are derived by: (1) computing Prit at the end of each fiscal year t during the prediction period 1978-1983; (2)
assigning securities to long positions (Prit > 0.6) and short positions (Prit < 0.4) as of the end of the third month following the end of
each fiscal year t; (3) obtaining an average abnormal return for each month of the holding period (in event time) for all stocks assigned
to each position and still trading; and (4) summing the average abnormal returns across all event time months in the holding period.
Abnormal returns to the hedge portfolio are computed by subtracting the returns for the short position from the returns for the long
position.
33.
1
BTW also use a second procedure to appraise the market inefficiency explanation for the relation
between Pr and future returns. BTW assess the consistency of the profits to a Pr-based trading strategy
over time, and they find that the trading strategy appears risky. That is, while the mean return to the
strategy over time is positive, significant losses occur in some periods.
2
Christie (1987), Collins and Kothari (1989), and others identify price as a more appropriate deflator than
the prior period's earnings when relating unexpected earnings to abnormal returns.
3
Elgers and Murray (1992) include P/E as a variable in their price-based forecasting model. Our model
differs from theirs in that our E/P variable is mean-adjusted and multiplied by price after release of year t
financial statements to obtain a proxy for the market's perception of the transitory earnings component of
year t earnings, our CAR variable is measured over the optimal return accumulation period for each size
category, our dependent variable is deflated by price instead of earnings, and our transitory earnings proxy
is deflated by price.
4
In addition to the restriction to stable-sized firms, our data base is smaller than the one in Ou and Penman
(1989a) due to the inclusion of some AMEX firms in their prediction periods and some OTC and AMEX
firms in their estimation periods.
5
A paired t-test across the three groups finds that the abnormal returns to perfect foresight of UEi,t+1 are
significantly greater than the abnormal returns to perfect foresight of UERWDi,t+1 (t-statistic = 6.823; p-
value = 0.0104).
6
Morton and Shane (1993) find that the Ou and Penman global model outperforms size-related models
estimated to predict the sign of UERWDi,t+1. In tests not reported here, we estimate and compare global
models to predict the sign of UEi,t+1 with the size-related models described in Table 2. We find that the size-
related models marginally outperform the global models.
7
Following Holthausen and Larcker (1992) four ratios, relating to advertising and research and
development expenditures, were eliminated due to the high frequency of missing data. None of these
ratios were included in the Ou and Penman global model for either of their estimation periods.
8
The identifying numbers assigned to the ratios in Table 2 correspond to those in Ou and Penman (1989,
Table 2). The reader is referred to the Ou and Penman paper for the full list.
34.
9
The percentage of concordant pairs, C, is derived by delineating all pairs of observations where for one
observation UEt+1 is greater than zero and for the other UEt+1 is less than or equal to zero. Then C equals
the percentage of pairs where the Pr produced from the model for the positive UEt+1 observation exceeds
the Pr for the negative UEt+1 observation. Somner's D, an index of rank correlation for the logit model, is
equal to 2C-1.
10
In addition, Ou and Penman estimated their Pr on a sample of 11,776 observations, and our sample for
estimating Pr(UEi,t+1>0) consisted of 2333 observations. The difference is due, mainly, to the restriction of
our sample to stable-sized firms.
11
The procedure follows the one described in Ou and Penman (1989a, p. 309), and is not an
implementable hedge. The analysis in this paper focuses on pooled data, without regard to the
implementability of the hedge or to transactions costs. Given the results of the Ou and Penman sensitivity
analysis, this should not have much bearing on the results, particularly since the concern of this paper is
with whether the association between Pr and future returns depends on the definition of the earnings
variable that is the target of the financial statement analysis. As long as the inclusion of any trading profits
that would not be available to an implementable trading strategy after transactions costs does not depend
on the definition of the target earnings variable, our conclusions should not be affected by using pooled
data rather than devising an implementable trading strategy and accounting for transactions costs.
12
Morton and Shane (1993) find that abnormal returns to trading strategies based on logit model
predictions of the Ou and Penman target variable are not greater for smaller firms; and Morton and Shane
(1998) find that abnormal returns to trading strategies based on logit model predictions of the Holhausen
and Larcker (1992) target variable (abnormal returns) are not greater for smaller firms.
13
This evidence is not consistent with evidence regarding market underutilization of information in
quarterly earnings about future earnings. Bernard and Thomas (1990) find that post-earnings-
announcement drift is inversely related to firm-size.
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