mispricing and the cross-section of stock returnsponent (e) of the price–dividend ratio that...
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ORI GINAL RESEARCH
Mispricing and the cross-section of stock returns
Carl R. Chen Æ Peter P. Lung Æ F. Albert Wang
Published online: 8 October 2008� Springer Science+Business Media, LLC 2008
Abstract This paper employs the Campbell-Shiller (Rev Financ Stud 1:195–228, 1988)
VAR model to derive a model-based mispricing measure that captures investor overre-
action to growth. Using this mispricing measure, we find that stocks with low levels of
mispricing outperform otherwise similar stocks. The long–short mispricing strategy gen-
erates statistically and economically significant returns over the sample period of July 1981
to June 2006. Moreover, this mispricing strategy outperforms the contrarian strategy using
various accounting-fundamental-to-price ratios. Our results cast doubt on the risk story in
explaining the abnormal returns of the mispricing strategy. Rather, our evidence suggests
that asset prices reflect both covariance risk and mispricing.
Keywords Model-based mispricing � Investor overreaction � Mispricing strategy �Contrarian strategy � Price–dividend ratio � Stock return predictability �Cross-section of stock returns
JEL Classification G11 � G12 � G14
1 Introduction
‘‘Buy low, sell high’’ is perhaps one of the most well-known investment mottos. Imple-
menting this strategy, however, requires a benchmark valuation model to define what the
value should be, and thereby to distinguish ‘‘low’’ from ‘‘high’’ values. Such benchmark
C. R. Chen (&) � F. A. WangUniversity of Dayton, 300 College Park, Dayton,OH 45469-2251, USAe-mail: [email protected]
F. A. Wange-mail: [email protected]
P. P. LungUniversity of Texas, Arlington, USA
123
Rev Quant Finan Acc (2009) 32:317–349DOI 10.1007/s11156-008-0097-4
value may be called the ‘‘fundamental’’ value, in contrast to the observed market price of
the asset in question. In this context, the difference between the market price and the
fundamental value may be understood as ‘‘mispricing’’ if the two measures are to converge
in the future. Given a benchmark valuation model, the buy-low-and-sell-high strategy thus
calls for buying low-mispricing (or undervalued stocks) and selling high-mispricing (or
overvalued stocks) simultaneously.
We adopt the dynamic valuation framework of Campbell and Shiller (1988) as our
benchmark valuation model. In this framework, we follow the approach of Brunnermeier
and Julliard (2008), and Chen et al. (2008) to measure ‘‘mispricing’’ as the difference
between the observed price–dividend ratio and the expected price–dividend ratio (i.e., the
‘‘fundamental’’ value), estimated based on underlying discount rates and dividend growth
rates. In this setup, we find that the observed price–dividend ratio is correlated with future
stock returns. A closer look at return predictability reveals that it is the mispricing com-
ponent (e) of the price–dividend ratio that predicts future returns, not the fundamental
value component. Furthermore, stocks with low-e earn significantly higher future returns
than otherwise similar stocks. As a result, a long–short mispricing strategy yields an
average log return of 6.96% per annum for the period from July 1981 to June 2006.
Extending the model of Campbell and Shiller (1988), we posit that the mispricing
measure (e) captures investors’ subjective growth rates, which are likely to revert to mean
in the future. Such mean-reversion leads to the arbitrage return of the mispricing strategy;
our empirical tests produce evidence in favor of this hypothesis in explaining the mis-
pricing measure. For example, our results show that the mispricing measure is correlated
with the usual proxies for subjective growth rates in the literature, including the book-to-
market (B/M) ratio, the earnings-to-price (E/P) ratio, the cash-flow-to-price (C/P) ratio, the
past 5-year sales growth rank (GS), and the analysts’ 5-year growth forecast (EG). These
results are also consistent with the empirical evidence in Chen et al. (2008) that this
mispricing measure embodies investor speculation about future growth rates.
Our mispricing strategy is similar in spirit to the contrarian strategy of Lakonishok et al.
(1994) (henceforth, LSV), since both strategies exploit investor overreaction to growth.
Nonetheless, our mispricing strategy substantially outperforms the LSV contrarian strat-
egy, which uses accounting variables, including price ratios, to proxy for subjective growth
rates. For example, Fig. 1 shows that from July 1981 to June 2006, the cumulative return of
the mispricing strategy rose steadily, and since 1990 it has surpassed three LSV contrarian
strategies based on book-to-market (B/M) ratio, earnings-to-price (E/P) ratio, and cash-
flow-to-price (C/P) ratio joint with sales growth rank (GS). The mispricing strategy yielded
a total cumulative return of 174% by the end of June 2006. By contrast, the three contrarian
strategies’ total cumulative returns ranged from 96 to 158% for the same time period.
Figure 2 shows that for a longer horizon (i.e., the five-year holding period) the mispricing
strategy was a consistent winner, whereas the three contrarian strategies were more risky,
as they all experienced substantial losses during the same time period.
The superior performance of the mispricing strategy over the contrarian strategy stems
from the competitive advantage of our model-based mispricing measure relative to the
accounting variables, including price ratios, in capturing investor overreaction to growth.
The mispricing measure of a stock is, by construction, separated from its fundamental
value component. By contrast, the accounting variables used in the contrarian strategy are a
noisy measure of mispricing because they bundle a stock’s fundamental value and mis-
pricing together. Furthermore, to the extent that accounting-based mispricing variables
suffer from the interpretation issue raised in Daniel and Titman (1997), our model-based
318 C. R. Chen et al.
123
mispricing approach validates and in fact strengthens the overreaction hypothesis advo-
cated by LSV in explaining return predictability.
Importantly, the superior performance of the mispricing strategy cannot be explained by
the firm characteristics of value, size, and momentum (Fama and French 1992; Jegadeesh
and Titman 1993). Nor can the superior performance of the mispricing strategy be
explained by risk. In fact, the mispricing strategy has a negative exposure to market beta in
the Fama-French three-factor model. The collected evidence casts doubt on both the firm
characteristics and the time-varying risk premium hypotheses in explaining the returns
from the mispricing strategy; however, the evidence favors our mispricing hypothesis,
0%
20%
40%
60%
80%
100%
120%
140%
160%
180%
200%
1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005
Mispricing B/M E/P (C/P,GS)
Fig. 1 Cumulative returns for mispricing and contrarian strategies 1981–2005. This figure plots thecumulative annual log returns from July 1981 to June 2006 for four arbitrage strategies. For each year t(t = 1981,…, 2005), portfolios are formed based upon single sort of mispricing, B/M, and E/P, and doublesort of C/P & GS at the end of year t - 1. B/M is the book-to-market ratio; E/P is the earnings-to-price ratio;C/P is the cash-flow-to-price ratio; GS is the past sales growth rank. All future return periods begin July 1 ofyear t
1989 1990 1991 1992 1993 1994 1995 1996 1997
Mispricing B/M E/P (C/P,GS)
-10%
-5%
0%
5%
10%
15%
20%
1981 1982 1983 1984 1985 1986 1987 1988 1998 1999 2000 2001
Fig. 2 Annualized 5-year holding period returns for mispricing and contrarian strategies 1981–2001. Thisfigure plots the 5-year holding period log returns from July 1981 to June 2006 for four arbitrage strategies.For each year t (t = 1981,…, 2001), portfolios are formed based upon single sort of Mispricing, B/M, and E/P, and double sort of C/P & GS at the end of year t - 1. The portfolios hold for 5 years. B/M is the book-to-market ratio; E/P is the earnings-to-price ratio; C/P is the cash-flow-to-price ratio; GS is the past salesgrowth rank. All future return periods begin July 1 of year t
Mispricing and the cross-section of stock returns 319
123
which emphasizes investor overreaction to growth. As such, our results lend support to the
concept that asset prices reflect both covariance risk and mispricing (Daniel et al. 2001).
This paper proceeds as follows. Section 2 presents the benchmark valuation model and
methodology by which the fundamental value and the mispricing components are estimated.
Section 3 describes the data used in this study. Section 4 evaluates the performance of simple
contrarian strategy. Section 5 compares mispricing and contrarian strategies. Section 6 tests
our mispricing hypothesis versus the risk hypothesis. Section 7 examines the relation
between mispricing and investor overreaction to growth. Section 8 presents our conclusion.
2 A simple decomposition: fundamental value and pricing error
Following Brunnermeier and Julliard (2008), and Chen et al. (2008), we adopt a model-
based approach to estimate a stock’s fundamental value component, and the corresponding
mispricing component.
2.1 The dynamic valuation framework
To capture time-varying discount rates and dividend growth rates, we use the Campbell
and Shiller (1988) log-linear dynamic valuation framework (ignoring a constant term) to
model the log price–dividend ratio, denoted by pt - dt, as follows:
pt � dt ¼X1
s¼1
qs�1ðDdetþs � re
tþsÞ þ limT!1
qTðptþT � dtþTÞ; ð1Þ
where the constants q � 1=ð1þ expð�d � �pÞÞ, �d � �p denote the average log dividend-price
ratio for the sample period, Dd denotes log dividend growth rate, r denotes log stock return,
Dde denotes Dd, less the log risk-free rate for the period, and re denotes r, less the log risk-
free rate.
Equation 1 says that the log price–dividend ratio, pt - dt, can be written as a discounted
value of all future excess dividend growth rates and future excess stock returns, plus a
terminal value. Taking objective expectations at time t, denoted by Et, on both sides of (1),
we obtain:
pt � dt ¼X1
s¼1
qs�1EtðDdetþs � re
tþsÞ þ et;where et ¼ Et limT!1
qTðptþT � dtþTÞ� �
: ð2Þ
By (2), the observed price–dividend ratio, pt - dt, can be decomposed into a fundamental
value component,P1
s¼1
qs�1EtðDdetþs � re
tþsÞ, and a pricing error term, et. We consider two
competing hypotheses for the pricing error term, et. The null hypothesis is that all investors
have objective expectations, and the transversality condition holds, i.e.,
limT!1
qTðptþT � dtþTÞ ¼ 0. In this case, the observed price–dividend ratio, pt - dt, should
equal the fundamental value component. As a result, the pricing error, et, if any, is simply
random noise (or approximation error) unrelated to either discount rates or dividend
growth rates. As such, the null hypothesis implies that the pricing error term, et, is unre-
lated to future stock returns. In other words, the return predictability of the observed price–
dividend ratio, pt - dt, if any, is due to movement in the fundamental value component or
the time-varying risk premium.
320 C. R. Chen et al.
123
The alternative hypothesis is that the transversality condition need not hold and/or that
investors have subjective (and possibly distorted) beliefs about dividend growth rates. Under
this view, the pricing error term, et, may reflect systematic errors in expectations about growth
rates. Both Brunnermeier and Julliard (2008) and Chen et al. (2008) advocate this alternative
hypothesis and find supporting evidence in housing and stock markets, respectively. This
view is also consistent with evidence in LSV and La Porta (1996) that investors use subjective
growth rates as they extrapolate or overreact to past growth performance.
To incorporate such subjective beliefs, denote by EtS investors’ subjective expectations
at time t, and correspondingly by ftS the subjective component of the dividend growth rate
at that time such that
ESt ðDde
tþsÞ ¼ EtðDdetþs þ f S
tþsÞ; for s ¼ 1; 2; . . .: ð3Þ
Since Eq. 1 holds for any realization ex post, it holds in expectations for any probability
measures, be it objective or subjective. Thus, applying subjective expectations to both sides
of (1), we obtain
pt � dt ¼X1
s¼1
qs�1ESt ðDde
tþs � retþsÞ þ ES
t limT!1
qTðptþT � dtþTÞ� �
: ð4Þ
Plugging (3) into (4), we may rewrite (4) as follows:
pt � dt ¼X1
s¼1
qs�1EtðDdetþs � re
tþsÞ þ et;
where et ¼X1
s¼1
qs�1Etðf StþsÞ þ ES
t limT!1
qTðptþT � dtþTÞ� �
:
ð5Þ
Equation 5 says that under the alternative hypothesis, when investors use subjective
expectations for dividend growth rates, the pricing error is driven by (a) the subjective
component of the future dividend growth rates, ft?sS , and (b) the subjective terminal value.
In this setup, a stock is overvalued (i.e., et [ 0) when investors are too ‘‘optimistic’’ about
dividend growth rates. On the other hand, a stock is undervalued (i.e., et \ 0) when
investors are too ‘‘pessimistic’’ about growth rates.
We call this alternative view the ‘‘mispricing’’ hypothesis, which emphasizes the
relation between stock mispricing and investors’ subjective growth rates. This hypothesis
yields a central, testable prediction that low-mispricing (i.e., undervalued) stocks will
outperform the high-mispricing (i.e., overvalued) stocks in the future as mispricing reverts
to mean. In other words, this hypothesis predicts that the mispricing measure, et, is neg-
atively correlated with the cross-section of future stock returns. This leads to our
mispricing strategy, in which one buys a portfolio of the lowest-mispricing stocks and
simultaneously sells a portfolio of the highest-mispricing stocks. The mispricing strategy
should yield positive arbitrage returns.
2.2 Empirical methodology
To obtain the empirical counterpart of the mispricing measure, et, one must first estimate
the fundamental value component of the observed price–dividend ratio, pt - dt. Following
Campbell and Shiller (1988); Campbell (1991), and Campbell and Vuolteenaho (2004), we
estimate objective expectations of discount rates and dividend growth rates using a reduced
form vector autoregressive (VAR) model. The VAR model employs four variables
Mispricing and the cross-section of stock returns 321
123
(all de-meaned): (a) the realized log price–dividend ratio pt - dt, (b) the realized excess
log dividend growth rate, Dde, (c) the realized excess log return, re, and (d) the smoothed
moving average of inflation, p.1 Specifically, we define xt as a 4 9 1 vector for the four
variables at time t, i.e.,2
xt ¼ ðpt � dt;Ddet ; r
et ; ptÞ
0: ð6Þ
The VAR model is specified as
xt ¼ Bxt�1 þ nt; ð7Þ
where B is a 4 9 4 matrix of VAR coefficients and nt is a 4 9 1 vector representing shocks
to the VAR model.3 Given (7), the multiperiod forecast is determined as
EtðxtþsÞ ¼ Bsxt: ð8Þ
We further define two vectors, e2 = (0, 1, 0, 0)0 and e3 = (0, 0, 1, 0)0. The discounted
expected future excess log dividend growth rates,P1
s¼1
qs�1EtðDdetþsÞ, are thus given by
X1
s¼1
qs�1EtðDdetþsÞ ¼
X1
s¼1
qs�1e20Bsxt ¼ e20BðI � qBÞ�1xt; ð9Þ
where Et represents the conditional expectations calculated using the estimated VAR
parameters. Likewise, the discounted expected future excess log returns,P1
s¼1
qs�1EtðretþsÞ,
are given by
X1
s¼1
qs�1EtðretþsÞ ¼
X1
s¼1
qs�1e30Bsxt ¼ e30BðI � qBÞ�1xt: ð10Þ
With the estimated VAR parameters, we can decompose the realized log price–dividend
ratio, pt - dt, into three components: (a) discounted expected excess log dividend growth
rates,P1
s¼1
qs�1EtðDdetþsÞ, (b) discounted expected excess log stock returns,
P1
s¼1
qs�1EtðretþsÞ,
and (c) estimated mispricing term, et, as follows:
pt � dt ¼X1
s¼1
qs�1EtðDdetþsÞ �
X1
s¼1
qs�1EtðretþsÞ þ et: ð11Þ
The fundamental value component consists of the first two terms on the right-hand side of
(11),P1
s¼1
qs�1EtðDdetþsÞ �
P1
s¼1
qs�1EtðretþsÞ, whereas the pricing error term, et, is the dif-
ference between the realized price–dividend ratio, pt - dt, and the estimated fundamental
value component.
For each year t (t = 1981,…, 2005), the above VAR model is estimated for each stock
separately based on data spanning a 25-year period from t - 25 to t - 1. In so doing, we
ensure that the VAR model is estimated for each year and for each stock without look-
ahead bias.
1 Inflation is exponentially smoothed using 12 monthly lags. Excess log dividend growth rates are therealized log dividend growth rate minus 3-month log T-bill rates.2 Alternatively, we also incorporate risk measures (i.e., VIX and default yield spread) into the VAR, the testresults are qualitatively similar.3 To be consistent with Campbell and Vuolteenaho (2004), we employ one lag in the VAR model.
322 C. R. Chen et al.
123
3 Data
The sample period covered in this study, for stock return tests, is July 1981 to June 2006.
The portfolios are formed at the end of each year t - 1 (t = 1981,…, 2005). Stock prices
and returns are drawn from the Center for Research in Securities Prices (CRSP), which
includes NYSE, AMEX, and NASDAQ stocks. Accounting measures are taken from
COMPUSTAT. Analyst forecasts of earnings growth rates are obtained from the Institu-
tional-Brokers-Estimates-System (I/B/E/S). To ensure that all accounting variables are
known to the market before they are used to explain stock returns, we match accounting
data for all fiscal years ending in calendar year t - 1 with future stock returns for holding
periods of 1–5 years, all beginning on July 1 of year t.We use a firm’s market equity at the end of December of year t - 1 to compute the
book-to-market (B/M), earnings-to-price (E/P), and cash-flow-to-price (C/P) ratios, and use
its market equity at the end of June of year t to measure size. Book value is calculated as
the sum of common equity, balance sheet deferred taxes, and investment tax credit, minus
the book value of preferred stock. Earnings are the sum of income before extraordinary
items, deferred taxes and investment tax credit, minus the book value of preferred divi-
dends. Cash flow equals earnings plus depreciation. The log price–dividend ratio of year t,pt - dt, is the average log price–dividend ratio over the four quarters in fiscal year t.4 Thus,
to be included in the stock return tests beginning July of year t, a firm must have CRSP
stock prices for the beginning of fiscal year t - 1, for the end of December of year t - 1,
and for the end of June of year t. The firm must also have book value, earnings, and cash
flow data in COMPUSTAT for the fiscal year ending in calendar year t - 1. Moreover, the
firm must have analyst forecasts for five-year (‘‘long-run’’) earnings growth rates in I/B/E/
S. These rules lead to our all-merged-stocks data set as reported in Table 1, Panel A. The
panel shows that the number of merged firms in this data set increases from 1,327 in 1981
to 3,068 in 2005.
Like La Porta (1996), our sample for stock return tests begins in 1981 so that (a) all
eligible stocks have analyst forecasts for 5-year (‘‘long-run’’) earnings growth rates in I/B/
E/S, and (b) the selection bias in COMPUSTAT prior to 1977 is minimized (Banz and
Breen 1986; Kothari et al. 1995). Following LSV and Fama and French (1996), a firm must
have sales growth data for the past 5 years in order to compute 5-year sales growth rank.5
Finally, to ensure the quality of our VAR model, which requires sufficient dividend data
for estimation, we exclude firms that fail to pay dividends more than 30% of the time
during the 25-year period prior to the year of portfolio formation. To sum up, stocks
eligible for our sample must have (a) analyst forecasts of 5-year earnings growth rates, (b)
sales growth rates for the past 5 years, and (c) at least 70% of the dividend data are
available for the past 25 years. These three criteria reduce our sample size further from the
all-merged-stocks to the all-eligible-stocks as reported in the last column of Table 1, Panel
A. The final sample size varies by year, with an average of 405 firms per year over the
sample period. This final sample set of all eligible stocks is used to construct the mispricing
portfolio for each year.
4 The log price–dividend ratio of year t, pt-dt, is computed as pt � dt ¼P4
q¼1
ðpq;t � dq;tÞ=4, where pq,t is thelog stock price at the beginning of quarter q in year t, and dq,t is the annualized log cash dividend paymentfor quarter q in year t.5 A firm’s past 5-year sales growth rank for year t, GSt, is computed as GSt ¼
P5
j¼1
ð6� jÞ � Rankt�j, whereRankt-j is the firm’s sales growth rank in year t-j.
Mispricing and the cross-section of stock returns 323
123
Ta
ble
1S
um
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tics
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elig
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s—Ju
ly1981
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Are
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colu
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(%)
19
81
5,4
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4,6
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1,6
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1,3
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5,9
28
35
9,0
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32
4,4
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1,8
65
84
6,0
25
1,8
31
88
6,8
10
33
72
,365
,85
21
8.4
1
19
83
6,5
09
26
9,9
19
5,2
22
37
1,0
28
2,1
39
67
5,0
66
2,0
61
67
9,3
16
33
32
,099
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41
6.1
6
19
84
6,4
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5,3
70
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1,9
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2,3
16
77
9,0
41
2,2
09
80
8,4
59
33
52
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,86
01
5.1
7
19
85
6,6
13
42
2,8
24
5,4
83
44
0,2
84
2,3
19
99
9,7
23
2,1
97
1,0
48
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29
83
,512
,01
51
3.5
6
19
86
7,1
28
45
2,6
28
5,8
36
47
8,4
04
2,4
22
1,1
27
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2,2
80
1,1
87
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30
64
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,70
41
3.4
2
19
87
7,1
53
39
4,9
82
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51
48
0,8
76
2,7
10
90
9,2
31
2,5
42
95
2,2
76
37
73
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31
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3
19
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53
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56
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97
2,4
37
1,1
03
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2,3
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54
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36
53
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31
5.8
3
19
89
6,9
31
49
5,3
85
6,0
39
65
7,6
64
2,5
61
1,1
59
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2,4
27
1,2
14
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36
84
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31
5.1
6
19
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6,8
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52
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97
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31
63
4,5
01
2,6
67
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66
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2,5
74
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36
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81
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2,5
09
1,4
32
,144
33
74
,727
,65
01
3.4
3
19
92
7,3
71
65
8,9
39
6,7
25
81
6,4
39
2,8
36
1,4
85
,785
2,7
91
1,5
04
,776
36
75
,034
,69
81
3.1
5
19
93
8,1
90
62
1,8
47
7,4
65
88
0,0
35
3,1
64
1,3
67
,951
3,0
96
1,3
96
,610
38
64
,794
,45
11
2.4
7
19
94
8,3
28
73
0,6
47
7,8
53
86
2,2
07
3,5
37
1,5
25
,171
3,4
66
1,5
45
,758
41
85
,900
,21
31
2.0
6
19
95
8,9
16
88
3,9
51
8,0
97
1,0
91
,20
03
,722
1,8
25
,886
3,6
37
1,8
60
,050
41
77
,222
,84
51
1.4
7
19
96
9,1
64
1,0
97
,767
8,5
78
1,2
87
,21
14
,300
2,0
89
,503
4,1
87
2,1
40
,578
44
59
,360
,96
41
0.6
3
19
97
9,2
05
1,4
25
,168
8,5
40
1,6
74
,20
94
,510
2,6
18
,128
4,4
06
2,6
73
,989
61
79
,267
,90
91
4.0
0
19
98
8,5
48
1,8
24
,932
8,2
38
2,2
49
,74
24
,441
3,1
72
,240
4,3
50
3,2
38
,463
57
01
0,6
98
,22
91
3.1
0
19
99
8,4
39
2,2
01
,442
8,0
44
2,7
94
,03
14
,303
3,7
60
,864
4,2
01
3,8
51
,367
54
21
0,3
99
,56
91
2.9
0
20
00
8,0
18
1,8
87
,519
7,9
64
2,6
32
,28
93
,966
3,5
08
,269
3,9
01
3,5
55
,605
49
51
1,7
51
,77
21
2.6
9
324 C. R. Chen et al.
123
Ta
ble
1co
nti
nu
ed
Pan
elA
:B
yy
ear
Yea
rA
llC
RS
Pst
ock
sA
llC
OM
PU
ST
AT
sto
cks
All
I/B
/E/S
sto
cks
All
mer
ged
stock
sA
llel
igib
lest
ock
s
No
.o
ffi
rms
Mea
nsi
zeN
o.
of
firm
sM
ean
size
No
.o
ffi
rms
Mea
nsi
zeN
o.
of
firm
sM
ean
size
No
.o
ffi
rms
Mea
nsi
zeE
lig
ible
(%)
20
01
7,5
37
1,7
04
,808
7,3
98
2,4
76
,35
33
,596
3,2
01
,750
3,5
59
3,2
35
,455
42
71
1,1
56
,86
61
2.0
0
20
02
7,1
11
1,8
16
,142
7,0
15
2,2
14
,94
33
,550
3,2
47
,018
3,5
13
3,2
83
,111
41
71
0,8
77
,05
01
1.8
7
20
03
7,0
84
2,2
29
,809
6,7
07
3,0
32
,73
23
,502
4,0
46
,672
3,4
70
4,0
88
,146
43
91
2,8
71
,23
61
2.6
5
20
04
7,2
66
2,3
68
,930
6,3
42
3,3
98
,99
93
,482
4,3
45
,227
3,4
49
4,3
66
,718
41
61
3,9
28
,92
31
2.0
6
20
05
7,1
37
2,6
67
,799
5,5
48
3,5
59
,97
63
,487
4,6
61
,743
3,0
68
4,8
35
,143
38
81
6,1
31
,70
11
2.6
5
Pan
elB
:B
ysi
zefo
r1
99
2
Siz
ed
ecil
eA
llC
RS
Pst
ock
sA
llC
OM
PU
ST
AT
stock
sA
llI/
B/E
/Sst
ock
sA
llm
erg
edst
ock
sA
llel
igib
lest
ock
s
No
.o
ffi
rms
Mea
nsi
zeN
o.
of
firm
sM
ean
size
No
.o
ffi
rms
Mea
nsi
zeN
o.
of
firm
sM
ean
size
No
.o
ffi
rms
Mea
nsi
zeE
lig
ible
(%)
13
,284
22
,15
22
,97
82
0,4
73
46
93
2,0
89
45
33
2,0
94
11
30
,57
32
.43
28
86
75
,56
27
55
75
,46
62
92
76
,52
22
88
76
,40
89
77
,04
13
.13
37
21
12
7,7
54
64
91
28
,28
23
01
13
0,6
82
29
71
30
,66
31
11
28
,27
63
.70
45
30
20
6,9
50
44
92
05
,36
92
79
20
8,6
93
27
62
09
,09
91
32
02
,46
44
.71
54
60
31
5,6
44
42
13
15
,66
82
79
31
8,2
41
27
23
19
,00
71
23
32
,43
04
.41
63
48
48
9,8
44
30
74
92
,50
92
42
48
8,8
89
23
84
88
,11
22
05
01
,78
18
.40
73
50
78
0,0
71
32
27
93
,49
82
63
78
4,7
44
25
97
83
,62
13
48
26
,46
41
3.1
3
82
95
1,3
62
,369
28
31
,340
,575
25
31
,363
,603
25
11
,36
5,0
95
69
1,3
51
,349
27
.49
92
61
2,7
52
,085
28
72
,836
,878
23
92
,778
,958
23
82
,78
1,7
68
82
2,8
38
,300
34
.45
10
23
61
1,8
92
,66
52
74
12
,64
2,2
27
21
91
2,1
28
,22
42
19
12
,12
8,6
30
10
61
3,9
10
,87
94
8.4
01
Mispricing and the cross-section of stock returns 325
123
The proportion of eligible stocks in the all-merged-stocks data set thus varies from
10.63% in 1996 to 27.51% in 1981. Moreover, the panel shows that the average size of
eligible stocks is substantially larger than that of the all-merged stocks. This fact is
illustrated further by the breakdown based on the NYSE-size decile in 1992 as reported in
Table 1, Panel B. This panel indicates that our eligible stocks comprise mostly large
stocks, and that the proportion of eligible stocks in each decile increases almost mono-
tonically across deciles. For example, the proportion of eligible stocks is 2.43% in the first
decile, and 48.40% in the tenth decile.
4 Simple mispricing strategy
At the end of each year t - 1 (t = 1981,…, 2005), following the procedure described in
Sect. 2.2., we estimate a four-variable VAR system for each stock and thereby decompose
the observed log price–dividend (P/D) ratio into the expected log price–dividend ratio
(EPD), and the mispricing component (e). Stocks are then sorted into decile portfolios
based on each stock’s P/D, EPD, and e, respectively. We examine the post-formation return
performance of these decile portfolios and of the corresponding arbitrage strategy of
buying the first decile and selling the tenth decile stocks (P1–P10) for holding periods of 1–
5 years, all beginning on July 1 of year t.Arbitrage strategy based on the P/D ratio is similar in spirit to the contrarian strategy
based on accounting-fundamental-to-price ratios, such as B/M, E/P, and C/P. Under the
null (i.e., rational expectations) hypothesis, the mispricing strategy should yield no dis-
cernable return patterns. By contrast, the mispricing hypothesis predicts that the mispricing
strategy should generate positive arbitrage returns. Furthermore, by comparing these three
strategies based on P/D, EPD, and e, respectively, we may distinguish the sources of stock
return predictability of the P/D ratio as among the fundamental value component (EPD)
and the mispricing component (e)—i.e., time-varying risk premium versus mispricing.
4.1 Return performance of arbitrage strategies: P/D, EPD, and mispricing
In Table 2, Panel A, we present return performance of the portfolios sorted by P/D for
years 1 through 5 after portfolio formation. The numbers shown are the average annualized
log returns across all formation periods in the sample. The results indicate that low (high)
P/D stocks tend to have high (low) future returns. For example, for year 1 the first-decile
portfolio (P1) yields a return of 14.49%, whereas the tenth-decile portfolio (P10) yields a
return of 8.39%, resulting in a difference of 6.11% per annum. An arbitrage strategy of
buying first-decile stocks and simultaneously selling tenth-decile stocks (P1–P10) yields
statistically significant positive returns for all 5 years.
In Panel B of Table 2, we present the corresponding return performance of the port-
folios sorted by EPD, for years 1 through 5. In contrast to the results in Panel A above, the
strategy of buying first-decile and simultaneously selling tenth-decile stocks (P1–P10)
yields returns indistinguishable from zero for all 5 years. This result suggests that the
return predictability of the P/D ratio, reported in Panel A above, cannot be attributed to the
fundamental value component (EPD). To the extent that the EPD captures the time-varying
fundamental risk, the results of Panel B do not support the time-varying risk premium
hypothesis for the return predictability of the P/D ratio.
In Panel C of Table 2, we present the return performance of the e-sort portfolios. The
results indicate that future stock returns generally decline with mispricing for all five (years
326 C. R. Chen et al.
123
Ta
ble
2R
etu
rnp
erfo
rman
ceo
fth
ed
ecil
ep
ort
foli
os
sort
edb
yP
/D,
EP
D,
and
e.F
or
each
yea
rt
(t=
19
81
,…,
20
05),
stock
sar
eso
rted
into
dec
ile
po
rtfo
lio
sb
ased
on
P/D
,E
PD
,an
de,
resp
ecti
vel
y,
asat
the
end
of
the
last
fisc
aly
ear.
P/D
isth
ed
e-m
ean
edre
aliz
edp
rice
–div
iden
dra
tio,
EP
Dis
the
esti
mat
edp
rice
–div
iden
dra
tio,
and
eis
the
mis
pri
cin
gm
easu
re.
EP
Dan
de
are
esti
mat
edb
ased
on
Cam
pb
ell
and
Sh
ille
r’s
(19
88)
VA
Rm
od
el.
All
futu
rere
turn
per
iod
sb
egin
July
1o
fy
ear
t.T
he
po
st-f
orm
atio
ns-
yea
rav
erag
ean
nual
ized
log
retu
rn,
R(s
y),
cov
ers
the
per
iod
July
1o
fy
ear
tto
Jun
e3
0o
fy
ear
t?
s(s
=1
,…,
5).
P1
isth
em
ost
un
der
val
ued
po
rtfo
lio
,w
hil
eP
10
isth
em
ost
ov
erv
alu
edp
ort
foli
o.
P1
–P
10
rep
rese
nts
anar
bit
rag
ep
ort
foli
oo
fb
uy
ing
P1
and
sell
ing
P1
0.
t-st
atis
tics
are
pre
sen
ted
inp
aren
thes
es.
*,
**
,an
d*
**
den
ote
sign
ifica
nce
atth
ete
n,
five,
and
one
per
cent
level
s,re
spec
tivel
y
Pan
elA
:R
awre
turn
s:P
/D-s
ort
P/D
t�1
R(1
y)
R(2
y)
R(3
y)
R(4
y)
R(5
y)
P1
0.1
44
90
.142
60
.130
10
.13
07
0.1
25
8
P2
0.1
33
90
.141
20
.137
00
.13
21
0.1
30
7
P3
0.1
38
80
.145
60
.129
70
.12
76
0.1
26
6
P4
0.1
33
90
.132
20
.125
50
.12
30
0.1
21
8
P5
0.1
29
10
.125
80
.119
60
.11
42
0.1
13
0
P6
0.1
25
40
.127
70
.124
40
.12
23
0.1
18
0
P7
0.1
19
10
.119
70
.112
80
.10
81
0.1
08
9
P8
0.1
05
60
.117
20
.109
60
.10
55
0.1
00
4
P9
0.1
06
20
.105
30
.097
70
.09
37
0.0
92
4
P1
00
.083
90
.078
50
.072
50
.07
44
0.0
70
5
P1
–P
10
0.0
61
1(1
.82
)*0
.064
1(2
.95
)**
*0
.057
6(3
.16
)**
*0
.05
63
(3.5
9)*
**
0.0
55
3(3
.86
)**
*
Pan
elB
:R
awre
turn
s:E
PD
-sort
EP
Dt�
1R
(1y)
R(2
y)
R(3
y)
R(4
y)
R(5
y)
P1
0.1
24
50
.115
70
.11
07
0.1
11
50
.109
5
P2
0.1
24
30
.133
30
.12
21
0.1
22
20
.120
9
P3
0.1
33
60
.136
70
.12
91
0.1
22
90
.120
8
P4
0.1
30
70
.136
60
.12
44
0.1
23
20
.126
8
P5
0.1
38
40
.141
60
.12
88
0.1
24
40
.117
7
Mispricing and the cross-section of stock returns 327
123
Ta
ble
2co
nti
nu
ed
P6
0.1
23
60
.12
57
0.1
18
20
.113
00
.10
79
P7
0.1
31
90
.12
08
0.1
14
30
.110
10
.10
82
P8
0.1
04
40
.11
32
0.1
10
50
.106
00
.10
34
P9
0.0
97
60
.10
54
0.1
03
20
.102
30
.10
03
P1
00
.109
30
.10
42
0.0
97
80
.098
30
.09
65
P1
–P
10
0.0
15
1(0
.47
)0
.01
15
(0.5
7)
0.0
12
8(0
.76
)0
.013
2(0
.88
)0
.01
30
(0.9
3)
Pan
elC
:R
awre
turn
s:e-
So
rt
e t-
1R
(1y)
R(2
y)
R(3
y)
R(4
y)
R(5
y)
P1
0.1
45
50
.141
60
.132
20
.13
12
0.1
28
4
P2
0.1
39
80
.136
00
.119
60
.11
79
0.1
15
6
P3
0.1
36
10
.146
00
.136
10
.13
47
0.1
31
6
P4
0.1
28
90
.130
70
.122
40
.11
94
0.1
20
0
P5
0.1
24
50
.125
10
.125
00
.12
12
0.1
17
3
P6
0.1
25
80
.123
40
.118
10
.11
45
0.1
12
2
P7
0.1
19
70
.127
70
.115
30
.10
98
0.1
08
6
P8
0.1
12
30
.113
30
.110
10
.10
69
0.1
04
1
P9
0.1
15
10
.116
00
.107
30
.10
24
0.0
97
5
P1
00
.075
90
.070
30
.065
10
.06
60
0.0
64
7
P1
–P
10
0.0
69
6(2
.04
)*0
.071
2(3
.25
)**
*0
.067
1(3
.61
)**
*0
.06
51
(4.1
9)*
**
0.0
63
7(4
.52
)**
*
328 C. R. Chen et al.
123
1 through 5) holding periods. For example, for year 1 the first-decile (the most undervalued
portfolio) yields a return of 14.55% whereas the tenth-decile (the most overvalued port-
folio) yields a return of 7.59%. Therefore, the mispricing strategy of buying the first-decile
and simultaneously selling the tenth-decile stocks (P1–P10) yields a statistically and
economically significant arbitrage return of 6.96% per annum. This mispricing strategy
continues to generate significant, positive arbitrage returns for years 2 through 5, all at the
one percent significance level. These slowly-decaying arbitrage returns are consistent with
the results of De Bondt and Thaler (1985), LSV, La Porta (1996), and Vuolteenaho (2002).
In addition, the performance of the mispricing strategy is uniformly stronger than that of
the arbitrage strategy, based on the P/D ratio reported in Panel A above.
4.2 The decomposition of the P/D ratio
The superior performance of the mispricing strategy over the arbitrage strategy based on P/
D suggests that the effectiveness of the latter strategy in exploiting mispricing may be
attenuated by the associated fundamental value component (EPD). That is, a high P/D ratio
may be due to a high fundamental value component (EPD), or a high mispricing com-
ponent (e), or both. In other words, the P/D ratio bundles the fundamental value component
and the mispricing component, and hence is a noisy measure of mispricing. By contrast,
the model-based mispricing measure (e) is, by construction, a relatively clean proxy for
mispricing, as the fundamental value component is removed in the estimation process. To
verify this conjecture, for each decile portfolio in Table 2 we evaluate the decomposition
of its P/D ratio into the corresponding fundamental value (EPD), and mispricing compo-
nent (e). The results of this decomposition are reported in Panel A of Table 3. A number of
observations are worth noting.
First, the decomposition of the P/D-sort portfolios reveals that the variation of the P/D
ratio across the decile portfolios is driven primarily by the mispricing component (e), rather
than by the fundamental value component (EPD). This result suggests that the cross-
sectional return predictability of the P/D ratio can be attributed to its mispricing component
(e), but not to its fundamental value component (EPD). This casts doubt on the time-
varying risk premium hypothesis in explaining the return predictability of the P/D ratio;
rather our mispricing hypothesis is favored.
Second, the results of the decomposition indicate that the e-sort portfolios produce a
substantially greater difference in the mispricing measure between the two extreme deciles
(P1–P10) than do both the P/D-sort and the EPD-sort portfolios. Specifically, the difference
in the mispricing measure (e) is -8.86 for the e-sort portfolios and -7.47 for the P/D-sort
portfolios; both are statistically significant at the one percent level. This is consistent with
our conjecture that the mispricing measure embedded in the P/D-sort portfolios is atten-
uated by the fundamental value component (EPD). It also highlights the advantage of our
model-based mispricing measure (e) over the noisy P/D ratio in capturing mispricing
opportunities.
Third, for the EPD-sort portfolios the difference is actually positive at 1.16 between the
two extreme deciles (P1–P10). This suggests that the EPD strategy buys overvalued stocks
and simultaneously sells undervalued stocks. As a result, the performance of this strategy is
worst in comparison with the other two strategies. In this regard, the mispricing strategy
has the largest built-in ‘‘margins of safety’’ with the greatest mispricing differential, -8.86
between the two extreme decile portfolios.
Finally, for the e-sort portfolios, the first decile has the highest EPD while the tenth
decile has the lowest EPD. This suggests that the lowest mispricing stocks are actually
Mispricing and the cross-section of stock returns 329
123
Tab
le3
Th
ean
ato
my
of
the
mis
pri
cin
gst
rate
gy
:P
/Dd
eco
mp
osi
tio
n,
firm
char
acte
rist
ics,
and
abn
orm
alre
turn
s.P
anel
Ad
isp
lays
the
dec
om
po
siti
on
of
the
P/D
rati
oin
toE
PD
and
efo
rth
ree
sets
of
dec
ile
po
rtfo
lio
s.F
or
each
yea
rt,
sto
cks
are
sort
edin
tod
ecil
ep
ort
foli
os
bas
edo
nP
/D,
EP
D,
and
e,re
spec
tiv
ely
,at
the
end
of
the
last
fisc
aly
ear
t-
1(t
=1
98
1,…
,2
00
5).
P/D
isth
ed
e-m
eaned
real
ized
pri
ce–
div
iden
dra
tio
,E
PD
isth
ees
tim
ated
pri
ce–
div
iden
dra
tio,
and
eis
the
mis
pri
cin
gm
easu
re.
EP
Dan
de
are
esti
mat
edb
ased
on
Cam
pb
ell
and
Sh
ille
r’s
(19
88)
VA
Rm
od
el.
P1
isth
em
ost
un
der
val
ued
po
rtfo
lio
,w
hil
eP
10
isth
em
ost
ov
erv
alu
edp
ort
foli
o.
P1
–P
10
repre
sen
tsan
arbit
rag
ep
ort
foli
oo
fb
uy
ing
P1
and
sell
ing
P1
0.t-
stat
isti
csar
ep
rese
nte
din
par
enth
eses
.*
,*
*,an
d*
**
den
ote
sig
nifi
can
ceat
the
ten
,fi
ve,
and
on
ep
erce
nt
lev
els,
resp
ecti
vel
y.
Pan
elB
dis
pla
ys
the
char
acte
rist
ics
of
the
e-so
rtd
ecil
ep
ort
foli
os.
B/M
isth
eb
oo
k-t
o-m
ark
etra
tio;
E/P
isth
eea
rnin
gs-
to-p
rice
rati
o;
C/P
isth
eca
sh-fl
ow
-to
-pri
cera
tio
;G
Sis
the
pas
tsa
les
gro
wth
ran
k;
EG
isan
alyst
5-y
ear
earn
ing
sg
row
thfo
reca
sts;
Siz
eis
the
firm
’sm
ark
etca
pit
aliz
atio
nin
tho
usa
nds;
bis
the
mar
ket
bet
a;r
isth
est
andar
dd
evia
tio
no
fre
turn
.P
anel
Cre
po
rts
the
e-so
rtp
ort
foli
os’
raw
,R
(1y),
and
abn
orm
al,
Ab
n-R
(1y
),lo
gan
nu
alre
turn
s.T
he
abn
orm
alre
turn
isth
era
wre
turn
,m
inu
sth
eex
pec
ted
retu
rn.
Fo
llow
ing
Fam
aan
dM
acB
eth
(19
73),
thre
eex
pec
ted
retu
rnm
odel
sbas
edon
var
ious
firm
char
acte
rist
ics
are
esti
mat
ed.M
odel
1in
cludes
the
foll
ow
ing
firm
char
acte
rist
ics:
B/
M,C
/P?
,E
/P?
,S
ize,
and
R(-
1y),
wh
ere
C/P
?an
dE
/P?
are
C/P
and
E/P
ifth
eyar
eposi
tive;
oth
erw
ise
zero
.S
ize
isfi
rm’s
log
mar
ket
capit
aliz
atio
n.R
(-1y)
isth
est
ock
’spas
t11-m
onth
retu
rn,
lagged
one
month
.M
odel
2in
cludes
all
firm
char
acte
rist
ics
from
Model
1,
exce
pt
E/P
?.
Model
3in
cludes
all
firm
char
acte
rist
ics
from
Model
1,
exce
pt
C/
P?
.*
,**,
and
***
den
ote
signifi
cance
atth
ete
n,
five,
and
one
per
cent
level
s,re
spec
tivel
y
Pan
elA
:T
he
dec
om
po
siti
on
of
the
P/D
rati
o
P/D
-So
rtE
PD
-So
rte-
So
rt
P/D
t-1
EP
Dt-
1e t
-1
P/D
t-1
EP
Dt-
1e t
-1
P/D
t-1
EP
Dt-
1e t
-1
P1
-3
.517
10
.366
9-
3.8
84
0-
1.1
70
8-
1.4
87
50
.316
7-
3.2
69
01
.38
03
-4
.649
3
P2
-0
.936
2-
0.2
80
8-
0.6
55
5-
0.2
59
8-
0.2
27
9-
0.0
32
0-
0.8
71
7-
0.0
43
6-
0.8
28
1
P3
-0
.462
10
.106
6-
0.5
68
7-
0.1
16
3-
0.1
13
0-
0.0
03
3-
0.4
81
9-
0.0
42
3-
0.4
39
6
P4
-0
.164
40
.047
0-
0.2
11
30
.019
0-
0.0
44
60
.063
6-
0.1
56
3-
0.0
09
4-
0.1
47
0
P5
0.1
31
70
.153
1-
0.0
21
40
.226
20
.013
30
.212
80
.14
37
0.0
25
10
.118
5
P6
0.4
75
20
.090
10
.385
10
.340
80
.071
80
.269
00
.47
13
0.0
67
00
.404
3
P7
0.8
33
70
.128
60
.705
10
.628
10
.148
00
.480
10
.84
14
0.1
25
50
.715
9
P8
1.2
44
60
.173
11
.071
50
.985
80
.236
10
.749
71
.23
02
0.1
63
71
.066
4
P9
1.8
57
60
.204
91
.652
71
.406
30
.373
01
.033
31
.84
37
0.1
95
61
.648
1
P1
03
.953
50
.369
63
.583
91
.504
72
.350
9-
0.8
46
23
.71
44
-0
.49
29
4.2
07
3
P1
–P
10
-7
.470
6(-
43
.5)*
**
-0
.002
7(-
0.0
2)
-7
.467
9(-
41
.0)*
**
-2
.675
5(-
16
.0)*
**
-3
.838
4(-
14
.4)*
**
1.1
62
9(4
.30
)**
*-
6.9
83
4(-
39
.3)*
**
1.8
73
2(7
.34
)**
*-
8.8
56
6(-
31
.78
)**
*
330 C. R. Chen et al.
123
Tab
le3
con
tin
ued
Pan
elB
:F
irm
char
acte
rist
ics
of
the
mis
pri
cin
gp
ort
foli
os
e t-
1B
/Mt-
1E
/Pt-
1C
/Pt-
1G
St-
1E
Gt-
1S
ize t
-1
bt
r t
P1
0.7
79
40
.096
30
.192
82
30
.95
01
10
.50
67
66
83
54
50
.821
10
.267
4
P2
0.7
62
40
.092
10
.172
02
24
.65
63
10
.38
21
61
58
38
70
.776
10
.277
5
P3
0.7
16
00
.094
40
.166
02
27
.73
09
10
.54
89
47
52
53
60
.782
40
.274
6
P4
0.7
23
10
.091
80
.162
32
38
.20
81
10
.18
29
45
54
41
70
.750
40
.266
8
P5
0.7
02
20
.089
70
.159
12
43
.67
05
9.5
11
45
50
66
37
0.6
99
60
.250
5
P6
0.7
49
10
.093
60
.166
32
47
.90
28
9.0
49
56
05
52
03
0.6
78
00
.268
2
P7
0.7
11
40
.093
50
.165
42
45
.94
64
9.1
33
76
71
21
49
0.7
06
80
.252
1
P8
0.6
64
40
.088
00
.158
52
53
.29
28
10
.16
97
82
62
39
70
.755
30
.281
6
P9
0.6
10
40
.087
00
.151
52
54
.46
42
11
.32
52
78
32
34
40
.816
90
.279
6
P1
00
.641
00
.088
70
.156
12
56
.88
01
12
.02
06
83
01
67
20
.864
60
.311
8
P1
–P
10
0.1
38
3(2
.33
)**
0.0
07
6(1
.20
)0
.036
8(3
.78
)**
*-
25
.93
00
(2.6
7)*
*-
1.5
13
9(-
5.4
0)*
**
-1
61
81
27
(-1
.26)
-0
.043
4(-
1.1
2)
-0
.044
4(-
1.0
1)
Pan
elC
:R
awan
dab
no
rmal
retu
rns
of
the
e-so
rtp
ort
foli
os
e t-
1R
awre
turn
Mo
del
1M
odel
2M
odel
3R
(1y)
Ab
n-R
(1y
)A
bn
-R(1
y)
Ab
n-R
(1y
)
P1
0.1
45
50
.02
82
0.0
30
40
.029
3
P2
0.1
39
80
.02
47
0.0
25
80
.025
8
P3
0.1
36
10
.02
20
0.0
23
40
.023
1
P4
0.1
28
90
.01
45
0.0
15
90
.015
6
P5
0.1
24
50
.01
03
0.0
12
10
.011
4
P6
0.1
25
80
.01
16
0.0
14
10
.012
7
P7
0.1
19
70
.00
63
0.0
08
50
.007
4
P8
0.1
12
3-
0.0
00
80
.00
15
0.0
00
3
Mispricing and the cross-section of stock returns 331
123
Ta
ble
3co
nti
nu
ed
Pan
elC
:R
awan
dab
no
rmal
retu
rns
of
the
e-so
rtp
ort
foli
os
e t-
1R
awre
turn
Mo
del
1M
odel
2M
odel
3R
(1y)
Ab
n-R
(1y
)A
bn
-R(1
y)
Ab
n-R
(1y
)
P9
0.1
15
10
.00
50
0.0
07
00
.006
1
P1
00
.075
9-
0.0
34
9-
0.0
33
0-
0.0
33
8
P1
–P
10
0.0
69
6(2
.04
)*0
.06
31
(21
.45)*
**
0.0
63
4(2
7.8
8)*
**
0.0
63
1(2
1.7
1)*
**
332 C. R. Chen et al.
123
undervalued firms with the best fundamental (EPD), or the ‘‘hidden treasure’’ stocks,
whereas the highest mispricing stocks are overvalued firms with the worst fundamental
(EPD), or the ‘‘overbid fantasy’’ stocks. Thus, our mispricing strategy capitalizes on
mispricing opportunities between as yet priced future success and hotly overbid futurefailure. As such, our mispricing strategy captures the original investment wisdom of
Graham and Dodd (1934) that good investment selects undervalued but good companies.
4.3 Firm characteristics of the mispricing strategy
While both LSV contrarian strategy and the simple mispricing strategy exploit stock
mispricing attributable to investors’ subjective growth rates, the two strategies differ
significantly in terms of the measures used in capturing the subjective growth rates. LSV
uses three accounting-fundamental-to-price ratios (B/M, E/P, and C/P) and the 5-year sales
growth rank (GS), while La Porta (1996) uses analyst forecasts of 5-year earnings growth
rates (EG) as potential proxies for subjective growth rates. By contrast, as discussed in
Sect. 2 above, we use the model-based mispricing measure (e) to capture subjective growth
rates.
To the extent that our mispricing measure (e) and both LSV and La Porta’s accounting
variables capture similar subjective growth rates, the mispricing measure is likely to
exhibit characteristics similar to these accounting variables. Table 3, Panel B reports firm
characteristics of the mispricing portfolios in this regard. The results show that the mis-
pricing measure (e) tends to fall with all three LSV price ratios (B/M, E/P, and C/P), and to
rise with the two growth proxies (GS and EG). This result confirms our conjecture that the
mispricing measure (e) does indeed share similar firm characteristics with these accounting
variables, and hence is likely to capture similar subjective growth rates. Nonetheless, as
shown in Sect. 5 below, the model-based mispricing measure is more effective than these
accounting variables in exploiting mispricing opportunities arising from subjective growth
rates.
In addition, Table 3, Panel B shows that the mispricing measure does not have a distinct
relation with firm size. This suggests that the success of the mispricing strategy cannot be
explained by size. Interestingly, the market beta of mispricing portfolios displays a
U-shape pattern across the corresponding mispricing portfolios. In particular, the most
undervalued stocks (P1) and the most overvalued stocks (P10) have similar levels of
market beta. This suggests that the success of the mispricing strategy (P1–P10) is not due
to a compensation for bearing higher market risk. Finally, the mispricing measure does not
have a distinct relation with either beta or standard deviation of returns. This strengthens
the view that the mispricing strategy (P1–P10) is not a risk story, be it market risk or total
risk. In addition to these traditional risk measures, we will revisit the issue of risk and
investigate it more fully in later sections.
4.4 The abnormal returns of the mispricing strategy
The results in Subsect. 4.3 above indicate that the mispricing decile portfolios display
patterns with regard to various firm characteristics. Daniel and Titman (1997) argue that
firm characteristics may explain cross-sectional variation in stock returns. One question
naturally arises: To what extent can the returns of these decile portfolios be explained by
firm characteristics? More importantly, can the mispricing strategy (P1–P10) still generate
substantial returns after accounting for the expected returns based on firm characteristics?
To address these questions, we consider the ‘‘abnormal’’ returns for the mispricing
Mispricing and the cross-section of stock returns 333
123
portfolios whereby the firm—characteristics-based expected returns are subtracted from
raw returns.
Following Fama-MacBeth (1973), the expected return model is empirically estimated
based on the cross-sectional regression of individual stock returns on a set of firm char-
acteristics, including book-to-market ratio (B/M), adjusted cash-flow-to-price ratio (C/P?),
adjusted earnings-to-price ratio (E/P?), size, and past 11-month return lagged 1 month
(R(-1y)), where C/P? and E/P? are C/P and E/P when they are positive, and zero
otherwise. These firm characteristics—value, size, and momentum–have been shown to
predict stock returns in the literature (FF (1992), LSV, and Jegadeesh and Titman (1993)).
We run a separate cross-sectional regression each year for the 25 portfolio formation years
(1981–2005). The coefficients for these 25 cross-sectional regressions are averaged to be
the loadings of corresponding firm characteristics in the expected return model.
Given the expected return model, the abnormal return for each individual stock is
simply that stock’s raw return, minus its expected return. A decile portfolio’s abnormal
return is the equally weighted average of the abnormal returns of all component stocks in
that decile. In addition to the base model (Model 1) discussed above, for robustness, we
consider two variations of the expected return model. Model 2 includes all firm charac-
teristics listed above except E/P?, while Model 3 includes all except C/P?. Table 3, Panel
C reports both raw and abnormal returns of the mispricing decile portfolios with one-year
holding period. The numbers shown are the average raw and abnormal returns across the
25 formation years in the sample for all three models. Several observations are in order.
First, the abnormal return is large and positive for decile 1, while it is large and negative
for decile 10, regardless of which model is used. For example, for Model 1 abnormal
returns of the first and tenth decile portfolios are 2.82 and -3.49%, respectively. This
suggests that substantial return performance (whether good or bad) of the two extreme
deciles cannot be explained by these firm characteristics. By contrast, these results are
consistent with our mispricing hypothesis that stocks in decile 1 are the most undervalued,
while stocks in decile 10 are the most overvalued.
Second, the abnormal return of the mispricing strategy (P1–P10) is on par with its raw
return and is statistically significant at the one percent level, regardless of which model is
used. Specifically, the abnormal returns of the mispricing strategy (P1–P10) are 6.31, 6.34,
and 6.31% for Models 1, 2, and 3, respectively, compared with the raw return of 6.96%.
This result suggests that the marginal contribution of the mispricing strategy to return
performance is statistically and economically significant, even after controlling for the firm
characteristics of value, size, and momentum. This also lends evidence that the mispricing
strategy is a distinct strategy whose performance cannot be replicated by the value, size,
and momentum strategies.
In summary, the results presented in this section demonstrate that the return predict-
ability of the P/D ratio is driven primarily by its mispricing component, rather than its
fundamental value component. This finding favors our mispricing hypothesis in explaining
return predictability against the time-varying risk premium hypothesis. Furthermore, the
superior performance of the mispricing strategy over the P/D strategy suggests that the
model-based mispricing measure is more effective than the accounting-based P/D ratio in
capturing mispricing opportunities. These results also show that the mispricing measure
shares similar firm characteristics with various accounting variables as a potential proxy
for subjective growth rates. Nonetheless, the abnormal return of the mispricing strategy is
on par with its raw return and cannot be explained by the firm characteristics of value, size,
and momentum. As such, for simplicity, we focus on raw return performance for the
remainder of this paper.
334 C. R. Chen et al.
123
5 Contrarian versus mispricing strategies
5.1 Simple contrarian strategy
Give that both the mispricing strategy and the contrarian strategy exploit investor over-
reaction to growth, it is important to compare the return performance of these two
strategies over identical sample periods. The competitive advantage between the two
strategies depends essentially on the relative effectiveness of the respective measures used
to capture investor overreaction to growth. In this section, we therefore evaluate the
performance of simple LSV contrarian strategy based on each of the three price ratios (B/
M, E/P, and C/P), the 5-year sales growth rank (GS), and La Porta’s contrarian strategy
based on analyst 5-year earnings growth forecasts (EG), respectively.
Table 4, Panel A, shows the results based on the B/M ratio. Unlike the earlier findings
in Fama and French (1992) and LSV for the sample period 1963–1990, the B/M strategy
(P10–P1) produces returns indistinguishable from zero for all 5 years in our sample period
from 1981 to 2005. Nonetheless, our result is consistent with the finding in La Porta (1996)
that the effect of the B/M strategy declines later in the sample period, especially for the
large stocks at the center of this study.
Table 4, Panel B, shows results based on the E/P ratio. Under LSV overreaction
hypothesis, high E/P stocks are identified with value stocks, while low E/P stocks are
glamour stocks. These results indicate that the E/P strategy (P10–P1) produces positive
returns for all 5 years. However, this contrarian strategy underperforms the mispricing
strategy by a large margin, especially for years 2 through 5. For example, for year 5 this
strategy produces an annual return of 3.22% while the mispricing strategy generates an
annual return of 6.37%, a difference of 3.15% per annum.
Table 4, Panel C, presents results based on the C/P ratio. These results are similar to
those shown in Panel B above. For example, the C/P strategy (P10–P1) produces a positive
annual return of 2.88% for year 5. The results of the E/P and C/P strategies in Table 4,
Panels B and C, are similar to the P/D strategy shown in Table 2, Panel A. The similarity is
consistent with the view that E/P, C/P, and D/P (i.e., the inverse of P/D) are closely related
accounting-fundamental-to-price ratios that capture investor overreaction to growth. In this
sense, the superior performance of our mispricing strategy over the contrarian strategy,
based on these price ratios, is testimony that our mispricing measure is more effective in
capturing investor overreaction to growth.
Table 4, Panel D, shows the results based on past sales growth rank (GS). These results
show that the GS strategy produces returns indistinguishable from zero for all 5 years.
Table 4, Panel E shows the results based on analysts’ 5-year (‘‘long-run’’) earnings growth
forecasts (EG). Under the LSV overreaction hypothesis, low EG stocks are identified with
value stocks, while high EG stocks are glamour stocks. The results show that the EG
strategy generates positive returns for years 2 through 5. However, this contrarian strategy
again underperforms the mispricing strategy by a large margin for all 5 years.
To sum up, consistent with previous findings (LSV (1994) and La Porta (1996)), the
contrarian strategy is useful in capturing mispricing opportunities arising from investor
overreaction to growth. Nonetheless, the results also indicate that the contrarian strategy,
based on these accounting-fundamental-to-price ratios and growth proxies, underperforms
the mispricing strategy by a large margin. This renders further evidence that the model-
based mispricing measure is more effective than these accounting variables in capturing
investor overreaction to growth.
Mispricing and the cross-section of stock returns 335
123
Table 4 Return performance of simple contrarian strategy. For each year t (t = 1981,…, 2005), stocks aresorted into decile portfolios based on B/M, E/P, C/P, GS, and EG, respectively, at the end of the last fiscalyear. B/M is the book-to-market ratio; E/P is the earnings-to-price ratio; C/P is the cash-flow-to-price ratio;GS is the past sales growth rank; EG is the analysts’ 5-year earnings growth forecast. All future returnperiods begin July 1 of year t. The postformation s-year average annualized log return, R(sy), covers theperiod from July 1 of year t to June 30 of year t?s (s = 1,…, 5). t-statistics are presented in parentheses. *,**, and *** denote significance at the ten, five, and one percent levels, respectively
Panel A: Raw returns: B/M-sort
B/Mt–1 R(1y) R(2y) R(3y) R(4y) R(5y)
P1 0.1127 0.1166 0.1140 0.1161 0.1167
P2 0.1179 0.1191 0.1091 0.1070 0.1066
P3 0.0941 0.0975 0.0954 0.0900 0.0890
P4 0.0957 0.1033 0.1013 0.0968 0.0937
P5 0.1192 0.1160 0.1098 0.1099 0.1081
P6 0.1063 0.1116 0.1076 0.1105 0.1048
P7 0.1287 0.1247 0.1221 0.1184 0.1147
P8 0.1414 0.1343 0.1211 0.1143 0.1135
P9 0.1403 0.1399 0.1291 0.1241 0.1187
P10 0.1514 0.1442 0.1370 0.1338 0.1303
P10–P1 0.0387(1.13)
0.0276(1.37)
0.0230(1.42)
0.0177(1.19)
0.0135(0.97)
Panel B: Raw returns: E/P-sort
E/Pt-1 R(1y) R(2y) R(3y) R(4y) R(5y)
P1 0.0873 0.0910 0.0779 0.0835 0.0842
P2 0.1025 0.1047 0.1007 0.1011 0.1002
P3 0.1245 0.1210 0.1118 0.1111 0.1089
P4 0.1018 0.1120 0.1147 0.1135 0.1127
P5 0.1194 0.1178 0.1212 0.1153 0.1121
P6 0.1256 0.1343 0.1270 0.1210 0.1180
P7 0.1274 0.1254 0.1198 0.1177 0.1150
P8 0.1258 0.1269 0.1199 0.1139 0.1114
P9 0.1353 0.1340 0.1237 0.1173 0.1126
P10 0.1508 0.1352 0.1224 0.1212 0.1164
P10–P1 0.0635(1.87)*
0.0442(2.21)**
0.0445(2.74)**
0.0377(2.55)**
0.0322(2.28)**
Panel C: Raw returns: C/P-sort
C/Pt-1 R(1y) R(2y) R(3y) R(4y) R(5y)
P1 0.0934 0.0968 0.0880 0.0923 0.0951
P2 0.1024 0.1106 0.1116 0.1068 0.1057
P3 0.1145 0.1095 0.1104 0.1146 0.1100
P4 0.1089 0.1140 0.1045 0.0994 0.1016
P5 0.1249 0.1245 0.1162 0.1127 0.1097
P6 0.1197 0.1220 0.1195 0.1139 0.1075
P7 0.1203 0.1235 0.1181 0.1180 0.1131
336 C. R. Chen et al.
123
5.2 Conditional mispricing and contrarian strategies
In Subsect. 5.1 above, we compare mispricing and contrarian strategies based on single-
sort portfolios. In this subsection, we extend that comparison by considering the marginal
effect of one strategy conditional on the other strategy. Specifically, we examine the
Table 4 continued
Panel C: Raw returns: C/P-sort
B/Mt–1 R(1y) R(2y) R(3y) R(4y) R(5y)
P8 0.1226 0.1239 0.1183 0.1149 0.1129
P9 0.1417 0.1374 0.1284 0.1206 0.1176
P10 0.1571 0.1428 0.1306 0.1266 0.1239
P10–P1 0.0638(1.80)*
0.0460(2.29)**
0.0426(2.59)**
0.0343(2.25)**
0.0288(2.05)*
Panel D: raw returns: GS-sort
GSt-1 R(1y) R(2y) R(3y) R(4y) R(5y)
P1 0.1246 0.1173 0.1122 0.1077 0.1061
P2 0.1321 0.1294 0.1240 0.1218 0.1209
P3 0.1249 0.1249 0.1145 0.1159 0.1138
P4 0.1134 0.1132 0.1121 0.1104 0.1071
P5 0.1185 0.1254 0.1175 0.1119 0.1097
P6 0.1230 0.1196 0.1113 0.1115 0.1101
P7 0.1256 0.1181 0.1101 0.1116 0.1086
P8 0.1094 0.1154 0.1065 0.1037 0.1015
P9 0.1299 0.1225 0.1157 0.1119 0.1096
P10 0.0861 0.0860 0.0848 0.0824 0.0829
P1–P10 0.0385(1.22)
0.0313(1.50)
0.0274(1.58)
0.0253(1.62)
0.0232(1.68)
Panel E: Raw returns: EG-sort
EGt-1 R(1y) R(2y) R(3y) R(4y) R(5y)
P1 0.1306 0.1238 0.1193 0.1139 0.1090
P2 0.1343 0.1281 0.1249 0.1165 0.1086
P3 0.1293 0.1219 0.1209 0.1177 0.1164
P4 0.1445 0.1233 0.1197 0.1164 0.1112
P5 0.1390 0.1237 0.1179 0.1120 0.1082
P6 0.1365 0.1256 0.1213 0.1182 0.1150
P7 0.1320 0.1138 0.1126 0.1130 0.1087
P8 0.1177 0.1169 0.1111 0.1030 0.1010
P9 0.1207 0.0997 0.1017 0.1017 0.0994
P10 0.0991 0.0855 0.0862 0.0826 0.0775
P1–P10 0.0315(0.99)
0.0383(1.87)*
0.0331(2.11)**
0.0314(2.43)**
0.0315(2.72)**
Mispricing and the cross-section of stock returns 337
123
relative performance of various double-sort portfolios based on a pair of two control
variables: mispricing (e), and one of the accounting variables (B/M, E/P, C/P, GS, and EG)
used in the contrarian strategy.
Consider first a set of double-sort portfolios whereby the stocks are sorted by one of the
accounting variables (bottom 30%, middle 40%, or top 30%) and then by the mispricing
measure (bottom 30%, middle 40%, or top 30%). In these portfolios, we may examine the
marginal effect of the mispricing strategy, controlling for the respective contrarian strat-
egy. Likewise, consider next a set of double-sort portfolios whereby the stocks are first
sorted by the mispricing measure, and then by one of the accounting variables. In these
portfolios, we may examine the marginal effect of the respective contrarian strategy,
controlling for the mispricing strategy.
Given that the mispricing measure exhibits characteristics similar to these accounting
variables, we expect that the effects of both conditional strategies are likely to be weak-
ened, compared with their unconditional strategies. Nonetheless, it is still interesting to
observe which strategy remains effective, after controlling for the other strategy. To
conserve space, we show the results of three representative pairs: (E/P, e), (C/P, e), and
(GS, e), since the results are qualitatively similar for the two other pairs: (B/M, e) and
(EG, e).Table 5, Panel A presents the results for portfolios sorted by E/P and e. The left side of
the panel shows the marginal effect of the mispricing strategy after controlling for E/P, as
the portfolios are first sorted by E/P, and then by e. By contrast, the right side of the panel
shows the marginal effect of the E/P strategy after controlling for e, as the portfolios are
first sorted by e, and then by E/P. Our focus is on the return of each strategy after
controlling for the other strategy. The left side of the panel indicates that within the set of
low E/P stocks, the conditional mispricing strategy (P(1,1)–P(1,3)) yields significant
annual returns of over four percent for all 5 years. Thus, the conditional mispricing
strategy remains effective among the glamour (i.e., low E/P) stocks. On the other hand, the
right side of the panel shows that within the set of high e stocks, the conditional E/P
strategy (P(3,3)–P(3,1)) yields significant annual returns of over two percent for years 2
through 4. Thus, the conditional E/P strategy is also effective among the glamour (i.e., high
e) stocks, albeit with a smaller magnitude of returns.
Table 5, Panel B presents the results for portfolios sorted by C/P and e. The results are
qualitatively the same as in Panel A above. Specifically, within the set of low C/P stocks,
the conditional mispricing strategy (P(1,1)–P(1,3)) yields significant annual returns of over
four percent for all 5 years. On the other hand, the conditional C/P strategy is also effective
among the glamour (i.e., high e) stocks for years 2 through 5, albeit with a smaller
magnitude of arbitrage returns.
Table 5, Panel C presents the results for portfolios sorted by GS and e. The left side of
the panel indicates that, except for low GS stocks, the conditional mispricing strategy
remains effective and produces significant, positive returns. For example, within the set of
glamour (i.e., high GS) stocks, the mispricing strategy (P(3,1)–P(3,3)) generates significant
annual returns of over three percent for years 2 through 5. By contrast, the right side of the
panel shows that the GS contrarian strategy remains ineffective once the mispricing
measure (e) is controlled for.
338 C. R. Chen et al.
123
Ta
ble
5R
etu
rnp
erfo
rman
ceo
fco
nd
itio
nal
mis
pri
cin
gan
dco
ntr
aria
nst
rate
gie
s.F
or
each
yea
rt
(t=
19
81
,…,
20
05),
sto
cks
are
sort
edo
nth
eb
asis
of
ean
dfi
rmch
arac
teri
stic
s,in
cludin
gE
/P,
C/P
,an
dG
S,
atth
een
dof
pri
or
fisc
alyea
r.T
he
left
-han
dsi
de
of
the
table
sre
port
retu
rnre
sult
sbas
edupon
port
foli
os
sort
edfi
rst
by
afi
rmch
arac
teri
stic
,th
enby
e(c
on
dit
ion
alm
isp
rici
ng
stra
teg
y).
Th
eri
gh
t-h
and
side
of
the
tab
les
rep
ort
sre
turn
resu
lts
bas
edu
po
np
ort
foli
os
sort
edfi
rst
by
e,th
enb
ya
firm
char
acte
rist
ic(c
ondit
ional
contr
aria
nst
rate
gy).
E/P
isth
eea
rnin
gs-
to-p
rice
rati
o;
C/P
isth
eca
sh-fl
ow
-to-p
rice
rati
o;
GS
isth
epas
tsa
les
gro
wth
ran
k;e
isth
em
isp
rici
ng
mea
sure
.A
llfu
ture
retu
rnper
iods
beg
inJu
ly1
of
yea
rt.
Th
ep
ost
form
atio
ns-
yea
rav
erag
ean
nual
ized
log
retu
rn,
R(s
y),
cov
ers
the
per
iod
from
July
1o
fy
ear
tto
Jun
e3
0o
fy
ear
t?
s(s
=1
,…,5
).t-
stat
isti
csar
ein
par
enth
eses
.*
,*
*,
and
**
*d
eno
tesi
gn
ifica
nce
atth
ete
n,
fiv
e,an
do
ne
per
cen
tle
vel
s,re
spec
tiv
ely
Pan
elA
:D
ou
ble
sort
—E
/Pan
de
Co
nd
itio
nal
mis
pri
cin
gst
rate
gy
:E
/Pt-
1,e t
-1
Con
dit
ion
alco
ntr
aria
nst
rate
gy
:e t
-1,
E/P
t-1
R(1
y)
R(2
y)
R(3
y)
R(4
y)
R(5
y)
R(1
y)
R(2
y)
R(3
y)
R(4
y)
R(5
y)
P(1
,1)
0.1
26
60
.13
09
0.1
22
80
.123
10
.121
0P
(1,1
)0
.133
90
.136
30
.127
90
.129
50
.124
6
P(1
,2)
0.1
10
30
.10
62
0.0
97
70
.099
20
.098
1P
(1,2
)0
.128
60
.134
60
.131
10
.125
60
.125
1
P(1
,3)
0.0
78
90
.08
21
0.0
74
90
.078
30
.078
5P
(1,3
)0
.148
50
.132
20
.120
80
.124
00
.122
0
P(1
,1)–
P(1
,3)
0.0
47
7(1
.75
)*0
.04
88
(2.6
2)*
*0
.04
79
(3.0
0)*
**
0.0
44
9(3
.31
)***
0.0
42
5(3
.33
)**
*P
(1,3
)–P
(1,1
)0
.014
6(0
.46
)-
0.0
04
1(-
0.2
0)
-0
.007
1(-
0.4
4)
-0
.005
5(-
0.3
6)
-0
.002
6(-
0.1
8)
P(2
,1)
0.1
22
30
.12
91
0.1
27
60
.120
40
.120
9P
(2,1
)0
.102
40
.107
40
.100
10
.099
10
.098
6
P(2
,2)
0.1
27
40
.12
78
0.1
26
30
.123
80
.121
2P
(2,2
)0
.132
20
.126
90
.124
80
.122
80
.120
9
P(2
,3)
0.1
05
60
.10
73
0.1
04
80
.101
50
.098
7P
(2,3
)0
.129
30
.134
30
.127
20
.120
00
.116
3
P(2
,1)–
P(2
,3)
0.0
16
8(0
.56
)0
.02
19
(1.1
0)
0.0
22
7(1
.47
)0
.018
9(1
.36
)0
.022
1(1
.91
)P
(2,3
)–P
(2,1
)0
.026
9(0
.90
)0
.026
9(1
.51
)0
.027
1(1
.87
)*0
.020
9(1
.52
)0
.017
7(1
.35
)
P(3
,1)
0.1
53
10
.13
52
0.1
21
10
.125
20
.124
2P
(3,1
)0
.078
60
.076
10
.072
70
.077
80
.079
1
P(3
,2)
0.1
27
40
.13
50
0.1
30
00
.123
00
.117
0P
(3,2
)0
.100
30
.104
10
.100
30
.095
70
.091
4
P(3
,3)
0.1
33
60
.12
22
0.1
11
40
.102
80
.098
5P
(3,3
)0
.124
10
.118
60
.108
80
.102
30
.097
3
P(3
,1)–
P(3
,3)
0.0
19
5(0
.61
)0
.01
31
(0.6
1)
0.0
09
7(0
.57
)0
.022
3(1
.44
)0
.025
7(1
.71
)P
(3,3
)–P
(3,1
)0
.045
5(1
.33
)0
.042
6(2
.19
)**
0.0
36
2(2
.38
)**
0.0
24
5(1
.86
)*0
.018
2(1
.46
)
Mispricing and the cross-section of stock returns 339
123
Ta
ble
5co
nti
nu
ed
Pan
elB
:D
ou
ble
sort
—C
/Pan
de
Con
dit
ion
alm
isp
rici
ng
stra
teg
y:
C/P
t-1,e t
-1
Co
nd
itio
nal
con
trar
ian
stra
teg
y:e t
-1,
C/P
t-1
R(1
y)
R(2
y)
R(3
y)
R(4
y)
R(5
y)
R(1
y)
R(2
y)
R(3
y)
R(4
y)
R(5
y)
P(1
,1)
0.1
26
30
.13
16
0.1
26
60
.127
80
.12
88
P(1
,1)
0.1
27
10
.138
70
.134
50
.13
61
0.1
34
8
P(1
,2)
0.1
07
30
.11
05
0.1
08
70
.111
10
.10
90
P(1
,2)
0.1
31
10
.124
50
.122
60
.11
74
0.1
13
9
P(1
,3)
0.0
78
10
.07
79
0.0
76
40
.076
00
.07
54
P(1
,3)
0.1
50
90
.141
30
.123
70
.12
66
0.1
24
6
P(1
,1)–
P(1
,3)
0.0
48
2(1
.91
)*0
.05
37
(2.7
8)*
**
0.0
50
2(3
.22
)**
*0
.051
7(3
.81
)**
*0
.05
34
(4.2
5)*
**
P(1
,3)–
P(1
,1)
0.0
23
8(0
.73
)0
.002
6(0
.13
)-
0.0
10
8(-
0.6
6)
-0
.00
95
(-0
.65)
-0
.010
2(-
0.7
0)
P(2
,1)
0.1
30
90
.13
09
0.1
24
90
.121
60
.11
91
P(2
,1)
0.1
12
50
.110
90
.107
40
.10
66
0.1
04
6
P(2
,2)
0.1
16
50
.12
20
0.1
19
50
.115
00
.11
22
P(2
,2)
0.1
21
50
.124
20
.119
90
.11
52
0.1
12
9
P(2
,3)
0.1
09
30
.10
89
0.0
97
40
.094
90
.09
10
P(2
,3)
0.1
34
10
.134
50
.127
10
.12
30
0.1
21
5
P(2
,1)–
P(2
,3)
0.0
21
5(0
.79
)0
.02
20
(1.1
7)
0.0
27
6(1
.75
)*0
.026
6(1
.82
)*0
.02
81
(2.1
8)*
*P
(2,3
)–P
(2,1
)0
.02
16
(0.7
4)
0.0
23
6(1
.34
)0
.019
7(1
.40
)0
.01
64
(1.2
0)
0.0
16
9(1
.31
)
P(3
,1)
0.1
49
80
.13
68
0.1
25
90
.125
60
.12
15
P(3
,1)
0.0
79
10
.074
10
.073
10
.07
45
0.0
77
9
P(3
,2)
0.1
34
20
.13
59
0.1
29
80
.124
90
.12
29
P(3
,2)
0.0
96
40
.102
20
.096
90
.09
53
0.0
89
4
P(3
,3)
0.1
37
90
.12
65
0.1
15
20
.108
30
.10
63
P(3
,3)
0.1
30
60
.124
30
.114
00
.10
61
0.1
01
5
P(3
,1)–
P(3
,3)
0.0
11
9(0
.36
)0
.01
03
(0.4
8)
0.0
10
7(0
.61
)0
.017
2(1
.11
)0
.01
52
(1.0
5)
P(3
,3)–
P(3
,1)
0.0
51
4(1
.50
)0
.050
2(2
.57
)**
0.0
40
9(2
.72
)**
0.0
31
7(2
.45
)**
0.0
23
6(1
.91
)*
Pan
elC
:D
ou
ble
sort
—G
San
de
Con
dit
ion
alm
isp
rici
ng
stra
teg
y:
GS
t-1,e t
-1
Condit
ional
contr
aria
nst
rate
gy:e t
-1,
GS
t-1
R(1
y)
R(2
y)
R(3
y)
R(4
y)
R(5
y)
R(1
y)
R(2
y)
R(3
y)
R(4
y)
R(5
y)
P(1
,1)
0.1
31
50
.12
78
0.1
23
60
.122
00
.12
50
P(1
,1)
0.1
34
00
.131
40
.12
37
0.1
20
20
.12
50
P(1
,2)
0.1
35
10
.13
50
0.1
24
90
.118
50
.11
51
P(1
,2)
0.1
54
40
.147
00
.13
77
0.1
33
70
.12
99
340 C. R. Chen et al.
123
Ta
ble
5co
nti
nu
ed
Pan
elC
:D
ou
ble
sort
—G
San
de
Con
dit
ion
alm
isp
rici
ng
stra
teg
y:
GS
t-1,e t
-1
Con
dit
ion
alco
ntr
aria
nst
rate
gy
:e t
-1,
GS
t-1
R(1
y)
R(2
y)
R(3
y)
R(4
y)
R(5
y)
R(1
y)
R(2
y)
R(3
y)
R(4
y)
R(5
y)
P(1
,3)
0.1
10
60
.10
27
0.0
97
00
.100
90
.098
9P
(1,3
)0
.129
70
.129
10
.124
10
.123
30
.118
8
P(1
,1)–
P(1
,3)
0.0
20
9(0
.70
)0
.02
51
(1.3
0)
0.0
26
5(1
.61
)0
.021
0(1
.22
)0
.026
2(1
.72
)*P
(1,1
)–P
(1,3
)0
.004
4(0
.15
)0
.002
3(0
.11
)-
0.0
00
3(-
0.0
2)
-0
.003
1(-
0.1
8)
0.0
06
2(0
.40
)
P(2
,1)
0.1
46
30
.14
25
0.1
34
50
.129
50
.127
0P
(2,1
)0
.134
90
.135
40
.125
60
.119
40
.117
5
P(2
,2)
0.1
20
60
.12
01
0.1
14
80
.115
80
.112
6P
(2,2
)0
.121
70
.120
70
.117
40
.118
20
.117
3
P(2
,3)
0.0
97
30
.09
89
0.0
92
30
.090
50
.088
1P
(2,3
)0
.114
10
.116
80
.109
70
.104
10
.102
6
P(2
,1)–
P(2
,3)
0.0
49
0(1
.80
)*0
.04
37
(2.2
9)*
*0
.042
2(2
.58
)**
0.0
39
0(2
.72
)**
0.0
38
9(2
.93
)***
P(2
,1)–
P(2
,3)
0.0
20
8(0
.70
)0
.018
6(0
.97
)0
.015
9(1
.05
)0
.015
3(1
.10
)0
.014
9(1
.17
)
P(3
,1)
0.1
33
40
.12
75
0.1
18
80
.115
10
.112
7P
(3,1
)0
.101
80
.092
20
.093
70
.095
90
.091
1
P(3
,2)
0.1
04
30
.11
11
0.1
07
80
.105
20
.104
6P
(3,2
)0
.091
00
.096
50
.083
80
.080
50
.076
7
P(3
,3)
0.0
88
50
.08
51
0.0
79
90
.077
10
.076
1P
(3,3
)0
.085
90
.082
30
.080
20
.079
90
.078
1
P(3
,1)–
P(3
,3)
0.0
44
9(1
.70
)0
.04
24
(2.0
0)*
0.0
39
0(2
.17
)**
0.0
37
9(2
.53
)**
0.0
36
6(2
.69
)**
P(3
,1)–
P(3
,3)
0.0
15
9(0
.48
)0
.009
8(0
.45
)0
.013
5(0
.76
)0
.016
1(1
.09
)0
.013
0(0
.95
)
Mispricing and the cross-section of stock returns 341
123
The return performance of the conditional strategies shown in Table 5 strengthens our
finding, based on the unconditional strategies shown in Tables 2 and 4—that the mis-
pricing strategy unequivocally outperforms the contrarian strategy. The superior
performance of the mispricing strategy suggests that the mispricing measure is more
effective than the accounting variables used in the contrarian strategy in capturing investor
overreaction to growth. Finally, Table 5 shows that both conditional strategies work most
effectively among glamour stocks. This finding is consistent with the previous literature,
which shows that the abnormal returns of contrarian strategies tend to concentrate more on
the short side (i.e., the glamour stocks) than on the long side (i.e., the value stocks). This
asymmetry is also reflected in the simple mispricing strategy shown in Table 3C, and the
simple contrarian strategy shown in Table 4.
6 Mispricing hypothesis versus risk hypothesis
In this section, we examine the risk hypothesis further with two additional tests.
6.1 Multifactor time-series tests
Fama and French (1993, 1996) argue that much of the return predictability in the
literature, including the LSV contrarian strategy, is consistent with a rational explana-
tion about time-varying risk factors. In particular, they propose the FF 3-factor model
(Rm - Rf, SMB, and HML) in the spirit of the intertemporal capital asset pricing model
of Merton (1973). In this model, Rm - Rf is the monthly excess return on a proxy for
the market portfolio; SMB is the difference between the monthly return on small stocks
(bottom 30%) and the return on large stocks (top 30%); and HML is the difference
between the monthly return on high book-to-market stocks (top 30%) and the return on
low book-to-market stocks (bottom 30%). In this setup, the Rm - Rf factor captures the
market risk premium, the SMB factor captures the size premium, and the HML factor
captures the value premium. If the factor model can fully explain the cross-sectional
variation in average stock returns, then the intercept should be indistinguishable from
zero. Moreover, when applied to multiple portfolios simultaneously, the main testable
implication is that the intercepts of all portfolios are jointly zero using the test of
Gibbons et al. (1989).
We thus test whether the FF 3-factor model can explain the cross-sectional variation
in monthly average stock returns across our mispricing decile portfolios. The test results
are reported in Table 6. These results show that the extremely low (high) mispricing
portfolio tends to load less (more) on the market factor, Rm - Rf, but more (less) on
the value factor, HML. This suggests that the mispricing strategy (P1–P10) has a
negative exposure to market risk and a positive exposure to value premium. The results
also show that all decile portfolios, except decile 10, leave unexplained, large, and
significant positive returns in intercepts. This means that the FF 3-factor model fails to
fully explain the expected returns of nine out of 10 decile portfolios. Finally, the GRS
test rejects the risk hypothesis that the FF 3-factor model explains the cross-sectional
342 C. R. Chen et al.
123
variation in average returns of the mispricing portfolios jointly at the one percent
significance level.6
6.2 Year-by-year performance
We have focused our analysis thus far on the average return performance of several
strategies. This can disguise one important aspect of risk when implementing such strat-
egies in the real-world market; this concerns the reliability and consistency of performance
over time. A high average-return strategy is still considered risky if it depends on relatively
few super-performance years, while producing minuscule returns or even negative ones in
many other years. To assess this kind of risk, one should examine the year-by-year per-
formance of each strategy over the entire sample period.
Table 6 Tests of fama-french 3-factor model for the mispricing portfolios. GRS test statistic for a‘s = 0:4.8192 (P \ 0.001). This table reports the results of time-series tests of the Fama-French 3-factor model fore-sort decile portfolios. For each year t (t = 1981,…, 2005), stocks are sorted into decile portfolios based one at the end of year t-1. Rm-Rf is the monthly excess return for the market portfolio; SMB is the differencebetween the monthly returns of small stocks (bottom 30%) and large stocks (top 30%); HML is thedifference between the monthly returns of high book-to-market stocks (top 30%) and low book-to-marketstocks (bottom 30%); PR1YR is the difference between the monthly returns of recent winner stocks (top30%) and recent loser stocks (bottom 30%). GRS statistics tests a hypothesis that all intercepts are jointlyzero. t-statistics are in parentheses. *, **, and *** denote significance at the ten, five, and one percent levels,respectively
et-1 a Rm - Rf SMB HML Adj. R2
P1 0.0031 (3.51)*** 0.8467 (39.86)*** 0.4255 (9.73)*** 0.2950 (7.03)*** 0.7609
P2 0.0044 (4.29)*** 0.7735 (31.45)*** 0.3631 (7.17)*** 0.2384 (4.91)*** 0.6653
P3 0.0039 (4.16)*** 0.8135 (36.46)*** 0.3372 (7.22)*** 0.2843 (6.31)*** 0.7369
P4 0.0031 (3.41)*** 0.7333 (33.58)*** 0.3493 (7.66)*** 0.2481 (5.64)*** 0.6970
P5 0.0023 (2.71)** 0.7463 (37.18)*** 0.2937 (7.11)*** 0.2743 (6.91)*** 0.7289
P6 0.0026 (3.16)*** 0.7286 (36.52)*** 0.2781 (6.77)*** 0.3462 (8.78)*** 0.7159
P7 0.0031 (3.75)*** 0.7428 (36.92)*** 0.1980 (4.78)*** 0.3321 (8.35)*** 0.7175
P8 0.0021 (2.31)** 0.7871 (36.89)*** 0.2643 (6.02)*** 0.3010 (7.14)*** 0.7228
P9 0.0021 (2.25)** 0.7988 (35.92)*** 0.2334 (5.10)*** 0.1465 (3.33)*** 0.7231
P10 -0.0001 (-0.07) 0.9184 (37.84)*** 0.3633 (7.27)*** 0.1819 (3.79)*** 0.7460
P1–P10 0.0032 (3.34)*** -0.0717 (-3.14)*** 0.0621 (1.32) 0.1130 (2.50)**
6 In Table 6, portfolios are sorted into ten deciles according to the e values. In a similar spirit but basedupon different assumptions and procedures, we also run quantile regressions to test the FF 3-factor model forthe 10 decile portfolios. As opposed to the OLS regression result, which reflects the impact of three factorson the mean of the conditional distribution of mispricing, the quantile regression allows for the impact tovary across the mispricing distribution. Therefore, in a quantile regression, multiple slope parameters thatdescribe the relation between mispricing and three factors are allowed. Applying quantile regression to ourdata, we produce 10 decile portfolios that resemble the 10 e-sort decile portfolios presented in Table 6. Wealso conduct t-test for each individual parameters as well as the F-test for the joint test that all intercepts arezero. Not reported here to save space, the results are consistent with the findings in Table 6 that high returnportfolios tend to have positive alphas, lower loadings on Rm-Rf, and higher loadings on both SMB andHML. Most importantly, results of the quantile regressions also indicate that the FF 3-factor model fails tofully explain the expect returns of the 10 decile portfolios. The authors thank the editor for suggesting thisalternative analysis. Quantile regression results are available upon request.
Mispricing and the cross-section of stock returns 343
123
Specifically, we evaluate the year-by-year performance of our mispricing strategy rel-
ative to three representative contrarian strategies, the simple B/M-sort, the simple E/P-sort,
and the joint (C/P, GS) double-sort. All strategies are evaluated based on 1-year and 5-year
holding periods, respectively, for the entire sample period from July 1981 to June 2006.
For the joint (C/P, GS) double-sort portfolios, like LSV, we evaluate the specific value-
glamour strategy: (P(3,1)–P(1,3)).
Table 7 reports the year-by-year performance of these strategies. Considering first the 1-
year holding period return, the results show that the mispricing strategy substantially
Table 7 Year-by-year returns of mispricing and contrarian strategies July 1981 to June 2006. For each yeart (t = 1981,…, 2005), stocks are single-sorted by e, B/M, and E/P, and double-sorted by C/P&GS,respectively, at the end of year t-1. The table reports for each strategy the post-formation long–shortannualized log returns based on one-year (R(1y)) and 5-year (R(5y)) holding periods, respectively. Allfuture return periods begin July 1 of year t. AR is the average returns, and CAR is the cumulative returns. B/M is the book-to-market ratio; E/P is the earnings-to-price ratio; C/P is the cash-flow-to-price ratio; GS is thepast sales growth rank; e is the mispricing measure. t-statistics are presented in parentheses. *, **, and ***denote significance at the ten, five, and one percent levels, respectively
Year et-1 P(1)–P(10) B/Mt-1 P(10)–P(1) E/Pt-1 P(10)–P(1) ðC=Pt�1;GSt�1Þ P(3,1)–P(1,3)
R(1y) R(5y) R(1y) R(5y) R(1y) R(5y) R(1y) R(5y)
1981 0.4220 0.1805 0.1335 0.0776 0.1159 0.0788 0.3154 0.1213
1982 -0.0510 0.0733 0.0913 0.0394 -0.0395 0.0384 0.1877 0.0896
1983 0.0483 0.0265 0.1491 0.0416 0.1629 0.0175 0.1646 0.0318
1984 0.1060 0.0208 0.1907 0.0397 0.3686 0.0527 0.0905 0.0173
1985 -0.0892 0.0405 -0.2159 -0.0248 0.0590 -0.0080 -0.1396 0.0281
1986 0.0719 0.0665 -0.0150 0.0065 -0.1490 0.0608 0.1335 0.0751
1987 -0.0294 0.0578 0.1865 -0.0034 -0.0359 0.0200 -0.0064 -0.0144
1988 0.0708 0.0724 0.0702 0.0168 0.0616 0.0500 -0.0142 -0.0606
1989 0.0552 0.0269 -0.0832 -0.0375 -0.0472 0.0199 -0.1705 -0.0211
1990 0.0978 0.0358 -0.0536 -0.0080 0.1270 0.0312 -0.0766 0.0036
1991 0.1393 0.0751 0.0905 0.0283 0.1643 0.0503 0.0554 0.0453
1992 0.0219 0.0324 0.2169 -0.0094 0.1367 -0.0512 0.3654 0.0286
1993 0.0984 0.0718 -0.1177 -0.0713 -0.0670 -0.0176 -0.0004 -0.0105
1994 0.0729 0.0112 -0.0075 -0.0386 -0.0887 -0.0176 0.0581 0.0153
1995 0.0118 0.0839 -0.1758 -0.0768 0.0977 0.0640 -0.0130 0.0570
1996 0.0465 0.0683 -0.2294 0.0027 0.0054 0.0287 -0.1127 0.0431
1997 0.0168 0.0681 0.0972 0.0213 0.1288 0.0487 0.1732 0.0401
1998 -0.0002 0.0553 0.0315 0.0342 -0.1354 -0.0317 -0.0738 -0.0381
1999 -0.0306 0.0736 0.0068 0.0991 0.0259 0.0794 0.0373 0.0768
2000 0.1894 0.1373 0.1897 0.0854 0.3869 0.0968 0.2107 0.1376
2001 0.2950 0.0600 0.0573 0.0616 0.1898 0.0650 0.2302 0.0797
2002 -0.0311 -0.0200 0.0348 -0.0935
2003 0.1207 0.1049 -0.0751 0.0235
2004 -0.0411 0.1830 0.2380 0.0202
2005 0.1291 0.0860 -0.0786 0.0459
AR 0.0696(3.05)***
0.0637(2.34)**
0.0387(1.47)
0.0135(1.27)
0.0635(2.19)**
0.0322(3.66)***
0.0564(1.99)*
0.0355(3.15)***
CAR 1.7412 0.9670 1.5869 1.4107
344 C. R. Chen et al.
123
outperforms all three contrarian strategies, both on return and on risk dimensions. For
example, the mispricing strategy generates an average annual return of 6.96%, and a 25-
year cumulative return of 174.12%. By contrast, the three contrarian strategies generate
annual returns of at most 6.35%, and a 25-year cumulative return of 158.69% under the E/P
strategy. In addition, the mispricing strategy produces positive returns for all but 7 years,
compared with 9–10 years of negative returns under the three contrarian strategies.
Moreover, the worst one-year performance of the mispricing strategy is -8.92%, com-
pared with -14.90 to -22.94% for the three contrarian strategies.
Consider next the 5-year holding period. In this longer horizon, the mispricing strategy
also dominates the three contrarian strategies, both on return and on risk dimensions. For
example, the annualized return over the 5-year holding period is 6.37% under the mis-
pricing strategy. By contrast, the three contrarian strategies generate annualized returns of
up to 3.55% under the joint (C/P, GS) strategy. On the risk dimension, our simple mis-
pricing strategy is superior, showing positive returns for all 21 years, whereas the three
contrarian strategies have negative returns for 5 to 8 of 21 years.
In sum, these results show that the mispricing strategy consistently and substantially
outperforms the three representative contrarian strategies. Furthermore, the superior per-
formance of the mispricing strategy cannot be attributed to risk by traditional risk
measures, by intertemporal risk factors, or by the risk of performance consistency. The
evidence uniformly casts doubt on risk-based explanations of return predictability of our
mispricing measure (e); rather, the evidence favors the alternative mispricing hypothesis.
7 Mispricing and investor overreaction to growth
We have presented extensive evidence of the superior performance of the mispricing
strategy. We argue that mispricing strategy is successful because it effectively exploits
mispricing opportunities arising from investors’ subjective beliefs about future growth
rates. In particular, the superior performance of the mispricing strategy over the contrarian
strategy is due to the competitive advantage of the more precise, model-based mispricing
measure (e) over the more noisy accounting variables in capturing investor overreaction to
growth.
In Table 3, Panel B, we present preliminary evidence that the mispricing measure (e) is
related to investors’ subjective beliefs about growth at the portfolio level. For example,
these results indicate that the mispricing measure is negatively related to all three
accounting price ratios (B/M, E/P, and C/P), and positively related to both growth proxies
(GS and EG). LSV (1994) and La Porta (1996) use these variables as proxies for subjective
growth rates.
In this section, we investigate this issue further and ask whether the mispricing measure
(e) indeed captures investors’ subjective expectations on growth rates at the level of
individual stocks. By doing so, we further scrutinize the main premise of our mispricing
hypothesis that the mispricing measure (e) is not a random measurement error under the
rational expectations hypothesis, but rather it captures investors’ systematic error in growth
rate expectations. Specifically, we run panel data regressions of the mispricing measure (e)on a host of explanatory variables for 394 firms over 25 years, controlling for both time
and firm fixed effects. The explanatory variables include the prior 12-month return (R
(-12 m)), market beta (Beta), book-to-market ratio (B/M), adjusted earnings-to-price ratio
(E/P?), adjusted cash flow-to-price ratio (C/P?), past 5-year sales growth rank (GS),
analyst forecasts of 5-year earnings growth (EG), and size. Note that in accordance with FF
Mispricing and the cross-section of stock returns 345
123
(1992) and LSV, we define the adjusted price ratios E/P? and C/P? to be E/P and C/P,
respectively, when they are positive, and zero otherwise, in our regressions.
Table 8 reports test results for univariate as well as multivariate regressions. First, the
univariate tests show that the mispricing measure is significantly and negatively related to
all three accounting price ratios (B/M, E/P?, and C/P?), and is significantly and positively
related to both growth proxies (GS and EG). These univariate results are consistent with
our mispricing hypothesis that the mispricing measure is not a random noise, but rather
captures investors’ systematic errors in growth rate expectations.
Furthermore, there is a significant and positive relation between the mispricing measure
(e) in year t and the past 12-month return (R(-12 m)) in year t - 1. This indicates that
high (low) e stocks tend to be recent winners (losers) prior to the formation of mispricing in
year t. In other words, return performance in year t - 1 does contribute to the formation of
mispricing in these stocks in year t. However, the significant mean-reversion in all future
return periods beginning on July 1 of year t ? 1 shown in this study suggests that the
momentum effect is short-lived and does not last beyond the formation period of mis-
pricing in year t.In addition, after controlling for the momentum effect, the multivariate regression
results strengthen the univariate results that the mispricing measure is again significantly
and negatively related to all three accounting price ratios (B/M, E/P?, and C/P?) and is
significantly and positively related to both growth proxies (GS and EG).
Finally, both the univariate and multivariate results show that the mispricing measure is
unrelated to either market beta or size. These results reinforce our findings, discussed
above, that the mispricing measure is not a proxy for risk or size.
In summary, the regression analysis in Table 8 corroborates the evidence of firm
characteristics reported in Table 3, Panel B and lends support to our mispricing hypothesis
that the mispricing measure is not a random measurement error, but rather it captures
investors’ systematic error with respect to growth rate expectations. These results are
consistent with the evidence in Chen et al. (2008) that the mispricing measure incorporates
investor speculation about future growth rates.
8 Conclusion
Following Brunnermeier and Julliard (2008), and Chen et al. (2008), we adopt the dynamic
valuation model of Campbell and Shiller (1988) to estimate stock mispricing. In this
framework, we find evidence that stocks with low mispricing substantially outperform
stocks with high mispricing. The long–short mispricing strategy generates statistically and
economically significant returns over the period July 1981 to June 2006. We find that the
mispricing measure is correlated with the usual accounting variables for subjective growth
rates in the literature, including accounting-fundamental-to-price ratios (B/M, E/P, and C/
P) and growth rate proxies (GS and EG). This suggests that the mispricing measure
captures a similar underlying economic phenomenon—investor overreaction to growth—
as do these accounting variables.
Although our model-based mispricing measure shares similar characteristics with the
accounting variables for subjective growth rates, the long–short mispricing strategy sub-
stantially outperforms the contrarian strategy based on these accounting variables. This
result suggests that the model-based mispricing measure is more effective than noisy
accounting variables in capturing the mispricing opportunities that arise from investor
overreaction to growth. Furthermore, the superior performance of the mispricing strategy
346 C. R. Chen et al.
123
Tab
le8
Reg
ress
ions
of
mis
pri
cing
on
firm
char
acte
rist
ics.
This
table
show
sre
sult
sfo
rre
gre
ssio
ns
of
mis
pri
cing
on
firm
char
acte
rist
ics
bas
edon
pan
eldat
ase
tw
ith
39
4cr
oss
-sec
tio
nal
and
25
tim
e-se
ries
ob
serv
atio
ns.
Inea
chre
gre
ssio
n,
we
con
tro
lfo
rp
ote
nti
alst
ruct
ure
chan
ges
by
add
ing
ati
me
var
iab
le.
We
also
con
tro
lfo
rh
eter
ogen
eou
sfi
rmfi
xed
effe
ctb
yad
din
gb
inar
yv
aria
ble
s.O
ther
ind
epen
den
tv
aria
ble
sar
e:R
(-12
m),
pri
or
12-m
onth
retu
rns;
Bet
a;B
/M,book-t
o-m
arket
rati
o;
E/P
?,ad
just
edea
rnin
gs-
to-
pri
cera
tio
;C
/P?
,ad
just
edca
sh-fl
ow
-to
-pri
cera
tio;
GS
,5
-yea
rsa
les
gro
wth
ran
k;
EG
,an
alyst
s’5
-yea
rea
rnin
gs
fore
cast
,an
dS
IZE
,m
ark
etca
pit
aliz
atio
n.
t-st
atis
tics
are
pre
sen
ted
inp
aren
thes
es.
*,
**
,an
d*
**
den
ote
sign
ifica
nce
atth
ete
n,
fiv
e,an
do
ne
per
cen
tle
vel
s,re
spec
tiv
ely
R(-
12
m)
Bet
aB
/ME
/P?
C/P
?G
SE
GS
IZE
R2
(%)
11
.536
1(7
.05
)**
*4
4.2
2-
0.1
45
8(-
0.7
6)
43
.7
3-
0.5
49
9(-
3.1
4)*
**
43
.8
4-
2.6
34
5(-
2.3
8)*
*4
3.8
5-
4.3
03
4(-
5.5
4)*
**
44
.0
60
.002
0(2
.93
)**
*4
3.8
70
.06
28
(3.6
2)*
**
43
.8
80
.253
9(0
.92
)4
3.7
91
.535
2(7
.05
)**
*-
0.1
38
4(-
0.7
3)
44
.2
10
1.4
55
8(6
.53
)**
*-
0.2
96
3(-
1.6
6)*
44
.2
11
1.5
21
8(6
.99
)**
*-
2.4
03
5(-
2.1
8)*
*4
4.2
12
1.3
73
2(6
.23
)**
*-
3.4
89
1(-
4.4
4)*
*4
4.4
13
1.4
85
3(6
.79
)**
*0
.001
5(2
.21
)**
44
.2
14
1.4
55
6(6
.63
)**
*0
.04
71
(2.7
0)*
**
44
.3
15
1.5
29
8(7
.02
)**
*0
.156
3(0
.57
)4
4.2
16
1.1
84
8(5
.11
)**
*-
0.0
86
6(-
0.4
0)
-0
.388
3(-
1.8
4)*
0.0
00
8(1
.71
)*0
.04
06
(2.0
6)*
*0
.270
8(1
.52
)4
4.7
17
1.2
64
8(5
.59
)**
*-
0.0
68
8(-
0.3
1)
-3
.098
(-2
.69)*
**
0.0
01
2(1
.84
)*0
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4.9
Mispricing and the cross-section of stock returns 347
123
cannot be explained by such firm characteristics as value, size, and momentum. Nor can
the superior performance be explained by risk, be it market risk or total risk.
The significant return predictability of our mispricing measure established in this paper
has important implications for asset pricing. First, to the extent that accounting-based
mispricing variables suffer from the interpretation issue raised in Daniel and Titman
(1997), our model-based mispricing approach validates, and in fact strengthens, the
overreaction hypothesis advocated in LSV in explaining return predictability. For example,
our results indicate that the return predictability of the price–dividend (P/D) ratio is due to
mispricing, rather than time-varying fundamental risk. Second, the superior performance of
our mispricing strategy is testimony to the competitive advantage of the model-based
mispricing measure over the accounting variables. Third, it is remarkable to find that the
superior performance of the mispricing strategy exists within the subset of the largest
dividend paying stocks in the market. In other words, investor overreaction and market
inefficiency are present even in the supposedly most efficient set of the largest stocks.
Finally, consistent with Daniel et al. (2001), our results lend supportive evidence that asset
prices reflect both covariance risk and mispricing.
For future research, it would be interesting to apply the model-based mispricing
approach to the study of return predictability in housing or international equity markets,
where mispricing may abound. In addition, we conjecture that the mispricing phenomenon
could exist among stocks that do not pay dividends consistently. It would be useful to
formulate an alternative valuation model to extract mispricing for these stocks.
Acknowledgments We thank John Campbell, Werner De Bondt, David Hirshleifer, Pete Kyle, BobShiller, Wei Xiong, seminar participants at the 2007 DePaul University Symposium on Topics in BehavioralFinance, and the 2007 Financial Management Association Meetings for helpful comments. The authors aregrateful to the comments from the editor (Cheng-few Lee) and a reviewer.
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