Department of Economics
Faculty of Economics and Business Administration
Campus Tweekerken, St.-Pietersplein 5, 9000 Ghent - BELGIUM
STOCK PRICE ANCHORING
Stock Price Anchoring∗
Mustafa Disli †Koen Inghelbrecht Koen Schoors
March 11, 2019
We provide evidence on a new anomaly in the stock market. We show that stock prices
are very robustly correlated to ﬁrm value in a cross-sectional framework. We interpret
this result as evidence that investors’ valuations are biased by a speciﬁc version of the
availability heuristic, by which investors wrongly interpret the easily available infor-
mation about the stock price as a piece of relevant cross-sectional information about
true ﬁrm value. In this way ﬁrm value is “anchored” to the stock price, conﬁrming
the existence of anchoring eﬀects in ﬁnancial markets beyond the boundaries of the
experimental lab. Interestingly, ﬁrms with a high nominal share price at the end of the
year, tend to have lower returns in the subsequent year. After controlling for common
risk factors, this underperformance amounts to 1.77 basis points per day, or 4.56% per
Keywords: Anchoring eﬀect, heuristics, anomaly, ﬁrm value, stock prices
JEL Codes: G02, G11, G14
∗The authors greatly beneﬁted from discussions with Jan Annaert, Lieven Baele, Turan Bali, Geert
Bekaert, John Campbell, John Cochrane, Werner De Bondt, Catherine D’Hondt, Gerdie Everaert, Chris-
tian Gourieroux, Lars Peter Hansen, Tarun Ramodarai and seminar participants of the 2016 International
Finance and Banking Society, the 2016 Behavioral Finance Working Group, the 2016 Society of Financial
Econometrics Summer School and the 2016 Belgian Financial Research Forum.
†All authors are from Ghent University, Department of Economics. Address correspondence to
Hannes Stieperaere, Department of Economics, Sint Pietersplein 5, 9000 Ghent, Belgium or e-mail:
In most economic settings free prices are determined by the intersection of an upward-sloping
supply function, that captures marginal cost, and a downward-sloping demand function, that
captures marginal utility, in this way coordinating an eﬃcient market equilibrium. In the last
decades, however, evidence is accumulating that the valuation of goods by consumers may
not be independent of the price of these goods and thus that the slope of demand curves may
not be continuously negative, giving rise to the possibility of multiple market equilibria. To
understand the relation between the price of a good and the consumers’ valuation of that good
we need to understand how consumers’ beliefs and expectations shape their decision-making
process and post-cognitive satisfaction. One possibility is that consumers, when faced with
valuation uncertainty about the product’s intrinsic characteristics, rely on extrinsic cues of
the product, such as the price or the brand name, to assess the value of the good.
Consumers frequently make judgments based on incomplete information or limited knowl-
edge, relying on heuristics and prior beliefs instead. We focus on the price-quality heuristic,
which refers to the case where consumers interpret a product’s price as a signal of its qual-
ity. The positive relationship between price and perceived quality is well-documented in the
consumer behavior literature (see e.g., Johnson and Kellaris, 1988; Obermiller, 1988; Rao
and Monroe, 1989). This price driven inference about product quality may also inﬂuence
consumers’ individual choice behavior as documented in Cronley et al. (2005). Shiv et al.
(2005) show that the eﬃcacy of energy drinks to produce behavioral eﬀects depends on their
apparent price. The authors ﬁnd that energy drinks improve performance in a puzzle-solving
task if the participants believe these energy drinks are more expensive. This is consistent
with the view that the experienced valuation system is subject to uncertain perturbations
and therefore resorts to external cues (in this case prices) to facilitate inference and subse-
quent decision-making. The neurobiological basis of this anomaly has been documented by
Plassmann et al. (2008), who demonstrate a positive correlation between neural responses
in medial orbitofrontal cortex and experienced pleasantness for wine tasting subjects if they
believe the same wine was more expensive. Of particular interest is their ﬁnding that price
not only moderates consumers’ pleasure claims, but also their actual experiences.1
Since wine prices per bottle (and other commodity prices per ﬁxed quantity) are com-
parable in their levels, one could still argue that consumers interpret a higher stated price
as a signal of revealed higher valuation by other consumers. The observed correlation be-
tween price and experienced valuation in the presence of asymmetric information about the
product’s quality can then be interpreted as rationally taking into account the valuations
of others in one’s individual valuation. Compared to wine (or any other commodity) prices,
however, stock price levels cannot be directly interpreted as a measure of value of the under-
lying ﬁrm in the eyes of other investors, since the number of outstanding shares is subject
to managerial discretion. This essential diﬀerence should render comparisons between stock
price levels as a measure of ﬁrm quality/value meaningless in a cross-sectional universe.
In eﬃcient and frictionless markets, the nominal stock price can be considered as random
and therefore should have no inﬂuence on the valuation of the underlying ﬁrm. Suppose an
investor holds a position of $1 million in a company. Whether she buys 100 thousand shares
at $10 or 10 thousand shares at $100 dollar, her stake in the ﬁrm should be identical since the
total market value of the ﬁrm should be a reﬂection of the underlying ﬁrm fundamentals only.
Since the stock price is irrelevant to ﬁrm value in standard ﬁnance theory, the relationship
between stock price and ﬁrm value has not been subject to empirical scrutiny. Yet, research
in consumer psychology has found that consumer judgment is often inﬂuenced by irrelevant
anchors. In the classical wheel of fortune experiment, Tversky and Kahneman (1974) show
that the numbers obtained by spinning a wheel of fortune inﬂuenced subjects’ predictions
regarding the number of African countries that are member of the United Nations. Ariely
et al. (2003) found that an arbitrary anchor in the form of the last two digits of the subject’
Social Security number strongly aﬀects the willingness to pay for a variety of consumption
1Related to these ﬁndings is that of Mussweiler and Strack (1999) who show that anchoring eﬀects are
mediated by selectively increased accessibility of anchor-consistent knowledge. In other words, they show
that participants generate evidence that is consistent with the notion that an object’s value is equal to the
value of the anchor.
Despite the fact that the level of the stock price should be irrelevant for the valuation of
the underlying ﬁrm, several papers emphasize that nominal stock prices do inﬂuence investor
behavior. Gompers and Metrick (2001) for example show that institutional ownership is
positively related to the stock price, while Kumar and Lee (2006) ﬁnd that retail investors
are more attracted by low-priced stocks. Related to these ﬁndings, Schultz (2000) documents
that a stock split increases the number of small shareholders. Green and Hwang (2009) show
that asset returns have a higher degree of co-movement with low-priced stocks following a
stock split and argue that this is a result of price-based stock categorization. Furthermore,
it has been observed that individual investors exhibit a stronger preference for low-priced
stocks because of their lottery-like distribution of returns, in particular the large upside
potential (Kumar, 2009; Bali et al., 2011; Birru and Wang, 2016). Firms, in turn, appear
to take note of the behavioral eﬀects of nominal prices and often try to manage the level of
their stock price. Theories oﬀered to rationalize stock price management include eﬀorts to
customize the stock price in accordance with the market norm (Weld et al., 2009), matching
time-varying preferences of investors to maximize ﬁrm value (Baker et al., 2009; Dyl and
Elliott, 2006), and stock splits to signal inside information (Brennan and Copeland, 1988;
Ikenberry et al., 1996).
While anchoring eﬀects have been studied comprehensively in individual choice exper-
iments, their applicability to real market settings, including the stock market, has been
largely neglected (Furnham and Boo, 2011). In this paper, we ﬁll this gap by examining
the relationship between a ﬁrm’s stock price and value. For a cross-sectional universe of US
stocks between 1990 and 2014, we consistently show that the valuation of ﬁrms is surpris-
ingly arbitrary. After controlling for persistence and mechanical eﬀects, ﬁrm value appears
to be signiﬁcantly and positively related to the nominal stock price (i.e., the anchor). First,
this study shows that ﬁrms with higher stock prices have higher valuations, as measured by
their market-to-book ratio. These results hold when we control for ﬁrm-speciﬁc characteris-
tics that account for growth opportunities, intangible asset structures, equity risk, corporate
governance and market risk. These results are robust to alternative measures of ﬁrm valua-
tion such as Tobin’s Q, as well as variations in the set of control variables or the estimation
method. Next, we also examine the association between stock prices and ﬁrm valuation by
matching ﬁrms with similar characteristics but diﬀerent price levels using nearest-neighbor
matching ﬁrst proposed by Rubin (1973, 1977). Results show that ﬁrms in the top price
quintile are valued more than 20% higher than otherwise comparable ﬁrms with a more
moderate share price. Although the nominal stock price should be irrelevant for ﬁrm value,
it is the most visible ﬁgure that investors are subjected to. Our results therefore suggest
that for a considerable proportion of investors their mental representation of a stock’s value
is shaped by the stock’s price. These ﬁndings conﬁrm previous observations in experimental
designs where valuation was found to be manipulated by irrelevant cues or ‘anchors’ (e.g.,
Kahneman and Knetsch, 1992; Ariely et al., 2003). We conﬁrm the relevance of these an-
chors even beyond experimental settings. Our ﬁndings are also in line with Plassmann et al.
(2008) as investors attach more value to a company if the company is traded at a higher
Next, we also investigate whether the higher valuation given to high-priced stocks has
consequences for the ﬁrm’s performance on the stock market. Motivated by psychological
evidence on limited investor attention and anchoring, Li and Yu (2012) document reversal
eﬀects for ﬁrms that enjoyed a historically high share price. Lee and Piqueira (2017) show
that this post-peak underperformance is related to short-selling behavior. These price pat-
terns are also in line with Griﬃn and Tversky (1992), who argue that investors overreact
to a long series of good news, and underreact to sporadic news confronting their beliefs.
Using the approach of Liu and Strong (2008), we construct buy-and-hold portfolios based
on the ﬁrm’s nominal share price. After controlling for common risk factors from Carhart
(1997), the results show that high-priced ﬁrms earn up to 4.88% less during the subsequent
year. Hence, we show that price anchoring is an important channel to explain the presence
of reversal eﬀects.
This paper is organized as follows. Section 2 describes the data. In Section 3, we present
our main empirical results analyzing the link between share price and ﬁrm value. Section 4
examines the relation between share prices and stock market performance. Finally, Section
5 provides a discussion and concluding remarks.
2.1 Sample selection
We obtain data from Thomson Reuters on all companies trading at the US stock markets
spanning from 1990 until 2014. We choose 1990 as the starting date for our sample to
accommodate the availability of the control variables at the level of securities. The sample
includes all stocks with available ﬁnancial data from the Thomson Reuters Datastream
database.2To disentangle the anchoring eﬀect from market microstructure eﬀects of small
stocks, unless otherwise stated, we exclude observations with a stock price lower than 5
dollar. Next, the literature shows (see e.g. Grinblatt et al., 1984; Mcnichols and Dravid,
1990) that corporate actions such as stock splits inﬂuence return expectations and ﬁrm value.
Therefore, we disregard ﬁrms in the years with a split ratio3smaller than 0.95 or larger than
1.05. To ensure that our results are not driven by inordinate observations, we winsorize all
potentially unbounded variables at the 1% and 99% level. The ﬁnal sample consists of 36,360
observations from 4,144 unique companies.
2.2 Variable Description
In line with previous studies (e.g., Core et al., 1999; Green and Jame, 2013), we use the
market-to-book value (MTBV) as a measure of ﬁrm valuation, constructed as the market
2As a result, the sample excludes opaque ﬁrms.
3The number of new shares divided by the number of old shares due to corporate actions like stock splits,
stock dividends or rights issuances.
value divided by the balance sheet value of the ﬁrms’ equity at the end of its ﬁscal year. The
market-to-book value approximates the market’s estimation of the ﬁrm’s net present value,
and largely counters subjective accounting judgments. As an alternative, we use the Tobin’s
Q, which is calculated by dividing the ﬁrm’s market value by the ﬁrm’s asset replacement
costs (e.g., Fang et al., 2009; Morck et al., 1988). While Tobin’s Q is commonly used in
ﬁnance research, our preference is tilted towards the market-to-book value ratio because
the valuation of asset replacement costs in Tobin’s Q suﬀers from diﬃculties in valuing
intangible assets. The market-to-book value directly measures shareholder value creation,
i.e., how shareholders perceive and value a ﬁrm, without suﬀering from potential accounting
biases (Hillman and Keim, 2001). We use the end-of-day unadjusted stock price at the
end of the ﬁrm’s ﬁscal year to measure the nominal price level. This corresponds to the
real trading price on that moment, without historical adjustments for stock splits, stock
dividends or other rights issuances. Per year, we divide our sample into ﬁve groups based
on their nominal share price. We use these groups to compare ﬁrms with the highest prices
in the ﬁfth price quintile to the rest of the sample.
For each ﬁrm-year we compute a series of control variables. For details on the construction
of these control variables, we refer to Appendix A. Since growth perspectives are a crucial
factor for a ﬁrm’s valuation we incorporate sales growth, proﬁtability, age, natural logarithm
of size and growth estimates of professional analysts in our analysis. We control for the
asset structure of the company by including the amount spend on research and development
and the asset turnover. Both measures are associated with the intangible assets that are
not taken into account in the book value, and thus lead to higher market-to-book value and
Tobin’s Q values. Because investors typically demand a compensation for risk, we include
the ﬁrm’s current ratio, leverage, stock volatility and market beta as proxies for equity
risk. As the valuation of a company also relies on its corporate governance practices, we
include the payout ratio, analyst coverage and the cash ratio of the ﬁrm. These proxies
reﬂect managerial freedom to spend available cash, and thus control for agency problems.
Moreover, these ratios are correlated with business maturity and cash ﬂow stability. To
account for the market power of the company, we calculate the concentration within each
sector (Herﬁndahl index), the ﬁrm’s the market share, and the interaction of both measures.
In addition, we construct a market power dummy that indicates when a company is active in
a highly concentrated sector (highest quintile Herﬁndahl index) or has a high market share
(highest quintile market share).
It is well established that market conditions diﬀer over time and have an impact on
the ﬁrm valuation and vary over time. For example, illiquidity can cause ﬁrms to trade at
a discount, while momentum captures possible persistence eﬀects in the market valuation.
Therefore, we control for market risk by incorporating the Amihud (2002) measure of illiq-
uidity, share turnover (liquidity) and momentum eﬀects. Because index membership aﬀects
ﬁrm visibility, we also include NYSE and Nasdaq dummies as controls. Finally, we add
sector ﬁxed eﬀects in the form of 41 sector dummies based on the Industry Classiﬁcation
Benchmark (ICB). Unless stated otherwise in Appendix A, the data correspond to the last
day of the ﬁscal year.
3 Share Price and Firm Value
In this section, we investigate whether higher-priced stocks enjoy a higher valuation. Section
3.1 introduces the methodology to compare ﬁrm value across diﬀerent nominal stock price
levels. Section 3.2 reports the descriptive statistics, and Section 3.3 shows our main results.
In Section 3.4, we present the results using a matching procedure.
To investigate the impact of the nominal stock price on ﬁrm valuation, we regress our value
measures, market-to-book value and Tobin’s Q, on the stock price and several control vari-
ables. The baseline speciﬁcation is deﬁned as follows:
V alueit =β0+β1Pit +β2V aluei,t−1+β3MPit +β4Xit +εit (1)
where V alueit is the log market-to-book value or the log Tobin’s Q measured at the end of the
ﬁrm i’s ﬁscal year t. The variable of interest Pit represents the nominal share price of a ﬁrm’s
market value of equity. Xit controls for an extensive battery of ﬁrm-speciﬁc characteristics. β
is the the matrix of coeﬃcient estimates, and εit is the model’s error term. All speciﬁcations
incorporate industry ﬁxed eﬀects. To account for non-linear price eﬀects, the Pit variable
enters Eq.(1) as a covariate categorized in quintiles rather than introducing it as a continuous
covariate. We only report the coeﬃcient estimates for top price quintiles, while prices ranked
at or below the third quintile serve as the reference category.4Eq. 1 is devised in such a way
that it captures persistence eﬀects and accounts for the potential mechanical relationship5
from increased prices to a higher valuation metric. A lagged dependent variable is included
to absorb the persistence eﬀects that are not explicitly captured by other control variables.
One of the factors in the deviation of a ﬁrm’s value is the market price of a ﬁrm’s equity.
Ideally, we want to isolate the informational content of the market price from the mechanical
linkage between the price and ﬁrm value. Hence, the inclusion of both the lagged dependent
variable and the price change during the corresponding year helps us to eliminate the part of
the price that gives rise to the mechanical eﬀect on ﬁrm value. By doing so, the coeﬃcient
β1is intended to capture the pure causal impact of the stock price level on ﬁrm value (see
Furﬁne and Rosen (2011) for a similar approach). Rearranging Eq. 1 into the following form
MV alueit =β0+β1Pit +β3MPit +β4Xit +εit makes our estimation strategy more intuitive.
As explained in the introduction, standard ﬁnance theories predict that there should be no
causal eﬀect from the stock price to the valuation of the ﬁrm. If, however, β1is positive, this
4We proceed with this classiﬁcation to maintain consistency with the matching procedure in Section 3.4.
We reach the same conclusions in any other combinations of price quintiles, as well as if Pit is deﬁned as a
continuous variable. These results are available on request.
5Section 4 includes a performance analysis demonstrating the potential beneﬁts for investors, eliminating
possible concerns on a mechanical relation.
would provide support for anchoring eﬀects, as it would suggest that higher nominal share
prices result in higher ﬁrm valuation. The focus of this study is to test for cross-sectional
diﬀerences in ﬁrm valuation. Therefore, we use the Fama and MacBeth (1973) two-step
procedure to estimate our model. In the ﬁrst step, we perform a cross-sectional regression
for each single time period (i.e., each year). In the second step, the ﬁnal coeﬃcient estimates
are obtained by taking the average of the ﬁrst step coeﬃcient estimates. We use the Newey
and West (1987) standard errors with a lag length of 4 years to correct for heteroskedasticity
and serial autocorrelation.
3.2 Descriptive Statistics
Table 1 provides the summary statistics of the valuation metrics, the nominal share price,
and all control variables. The left-hand side of Table 1 reports the statistics for the full
sample, while the right-hand sides focuses on the 20% shares with the highest share price,
i.e., ﬁrms in price quintile 5. For the full sample, the average share price is 28.63 US dollar.
In the group of the 20% highest priced ﬁrms, this amounts to 63.15 US dollar. On average,
higher priced ﬁrms enjoy a higher valuation. Higher-priced ﬁrms also tend to have a higher
sales growth, proﬁtability, age and size, while the average analyst growth estimates tend
to be lower. The average amount spend on R&D and asset turnover is lower for ﬁrms
in the ﬁfth price quintile. We notice that the current ratio, volatility and market beta are
slightly lower for high-priced ﬁrms. Interestingly, the average leverage ratio is lower for these
companies. Highly priced ﬁrms also tend to have more market power, while the payout ratio,
analyst coverage and ﬁrm’s cash position suggest that this coincides with better corporate
governance. Moreover, these ﬁrms enjoy a higher liquidity and momentum.
3.3 Empirical Results
Table 2 reports our main empirical results. The coeﬃcient of the price level variable is
positive and signiﬁcant at the 1% level. When we use the market-to-book value as the
measure for ﬁrm performance, the upper quantile coeﬃcient estimate indicates that shares
in the highest price quantile have a valuation reward of 12.9% compared to stock prices
ranked at or below the third quintile. Our results remain qualitively similar when we consider
the alternative valuation metric, i.e., the Tobin’s Q. The highest-priced stocks are granted
a valuation premium of 11.8%. These results support our main hypothesis that higher
share prices are correlated with higher ﬁrm value, while controlling for a variety of ﬁrm
To strengthen our hypothesis, we conduct a series of robustness tests using alternative
sample selections, model speciﬁcations, and price variables. In the interest of brevity, Table 3
only reports the coeﬃcient estimates of the ﬁfth share price quintile. Model 1 corresponds to
the baseline model from Table 2. To start, rows 2 to 7 show the results using diﬀerent sample
selection procedures. In model 2, we repeat our analysis but exclude all ﬁnancial companies
from our sample. In particular because some ﬁrm characteristics can be very diﬀerent for
these ﬁrms. For example, the levels of leverage that are common in the ﬁnancial industry
would indicate very high levels of stress in other industries. Both coeﬃcient estimates and
standard errors share the magnitude of the baseline model, which demonstrates that the
results are not driven by ﬁnancial ﬁrms. Model 3 includes the ﬁrm-year observations with a
share price below 5 US dollar. The results are very similar to model 1, indicating that the
impact of low priced penny stocks is limited. In model 4 and 5, we split our sample in two
subperiods: from 1990 until 2001 and from 2002 until 2014. Estimates are slightly higher
for the latter period, suggesting that the eﬀect did not mitigate over time. In model 6 and
7, we repeat our analysis using ﬁrms that had respectively negative or positive stock returns
over the past three years. The main motivation for this approach was to check whether
stocks who experienced bad returns, but still have high prices, lose their value reward. The
estimates in model 6 are still positive, indicating that having a negative return over the past
three years does not erase the positive relation between stock prices and ﬁrm value. We refer
to Section 4 for a more elaborate analysis on the share prices and returns.
Next, rows 8 to 13 of Table 3 show the results using diﬀerent model speciﬁcations. For
model 8, we do not winsorize our variables. Again, results are in line with previous ﬁndings.
Model 9 presents the estimates obtained by including quintile dummies of all control vari-
ables. By doing so, we allow for non-linear eﬀects of these control variables on the dependent
variable. The results conﬁrm the ﬁndings of our baseline speciﬁcation. Next, model 10 ad-
dresses the concern that our valuation measures is correlated with the ﬁrm’s size, momentum
and proﬁtability. Therefore, we adjust the ﬁrm’s valuation by subtracting the average value
of similar ﬁrms in a reference group. Each year, we divide all stocks in ﬁve size groups.
Subsequently, within each size group, we sort the ﬁrms based on momentum creating 25
groups. To end, in every one of the 25 groups, we sort the ﬁrms in ﬁve groups based on
proﬁtability. Consequently, we constructed 125 portfolios based on size, momentum and
proﬁtability. Within each portfolio, we calculate the mean market-to-book value and To-
bin’s Q. This mean valuation serves as a benchmark for each company that belongs to that
portfolio. Next, we subtract the mean value of the benchmark portfolio from the value of the
ﬁrm. Finally, we rerun our model with the adjusted valuation serving as dependent variable.
The results of model 8 show that our ﬁndings remain intact. The coeﬃcients and t-statistics
even increase, lending further support to our hypothesis. Model 11 and 12 report the results
using a pooled OLS model respectively without and with standard errors clustered on the
ﬁrm level. T-statistics are considerably higher compared to our baseline results, showing the
importance of using the Fama and MacBeth (1973) two-step procedure to produce reliable
estimates of the cross-sectional variation in our model. Model 13 uses the between-estimator
which can be seen as a cross-section regression on the mean data for each stock. Hence,
the between-estimator mitigates problems because of short-term ﬂuctuations in ﬁrm char-
acteristics, outliers and serial correlation of the error term. The between-estimator results
reveal that coeﬃcient estimates of the upper price quintile for both valuation measures are
lower in magnitude compared to the pooled OLS estimates. This is not surprising as the
between-estimator puts the focus on the cross-sectional heterogeneity, excluding the impact
of intertemporal variation on the estimation results.
Finally, we construct new price quintiles using respectively the average, lowest, and high-
est price during the ﬁscal year in model 14, 15 and 16. Coeﬃcient estimates are lower, but
interestingly, we still ﬁnd a signiﬁcant impact of the nominal stock price on the valuation of
a ﬁrm. The robustness tests above all conﬁrm our main ﬁnding. High share prices coincide
with a higher valuation.
In this section we test the validity of our main hypothesis by comparing the valuations of
otherwise similar ﬁrms with diﬀerent price levels. We follow a matching procedure ﬁrst
introduced by Rubin (1973, 1977) to pair ﬁrms. In line with Section 3.1, the goal is to
compare ﬁrms in the quintile with the 20% highest share prices within one year, the treatment
group, to ﬁrms in share price quintile 1 to 3, the control group. We start by matching each
ﬁrm in the treatment group with one6ﬁrm in the control group that is most similar. To
execute this matching, we need a set of characteristics to determine the similarity between
ﬁrms. To counter industry ﬁxed eﬀects, we impose that ﬁrms are matched within the same
industry. Additionally, ﬁrms are matched based on their size, momentum, proﬁtability,
analyst coverage, sales growth, R&D, market beta and cash ratio.7We use the Nearest-
neighbor matching (NNM) procedure to pair each ﬁrm in the treatment group to the ﬁrm in
the control group that is most similar. This is accomplished by calculating the Mahalanobis
distance.8The matching is done with replacement, meaning that ﬁrms in the control group
can be matched with multiple high-priced ﬁrms. As a result, ﬁrms are always matched with
the most identical pair, which improves the matching accuracy and avoids the concern that
the initial ordering of the treatment observations matters (Smith and Todd, 2005). Because
6Table 5 shows that our results are robust to a changing number of matched ﬁrms.
7We choose these covariates based on the highest correlations with our valuation measures. Alternative
groups of control variables are tested, conﬁrming our results below.
8The Mahalanobis distance is based on a Pythagorean theorem adapted to handle the fact that covariates
may be correlated and measured on diﬀerent scales.
we match ﬁrms based on more than one continuous control variable, we correct for a possible
large-sample bias as suggested by Abadie and Imbens (2006, 2008). This procedure leads to
a ﬁnal sample of 7237 observations with a high price, paired to 3908 ﬁrms from our control
sample. Finally, we compute the average treatment eﬀects on the treated (ATET) by taking
the average of the valuation diﬀerences between the pairs of treated and control ﬁrms.
We start our empirical analysis by comparing the summary statistics of the most impor-
tant control variables. Table 4 presents the group averages of the ﬁrm’s size, momentum,
proﬁtability, analyst coverage, sales growth, R&D, market beta and cash ratio. The left-
hand panel describes the high-priced treatment group. The middle part reports on the full
sample of ﬁrms in price quintiles one to three, while the right-hand side panel describes the
statistics of the control ﬁrms matched with our ﬁrms in the treatment group. To start, we
calculate the percentage standardized diﬀerences of the sample means by dividing the dif-
ference in means between the treatment and control group by the square root of the average
standard deviation in both groups. The column ’Bias full’ refers to the diﬀerence between
the full sample and the treatment group, while column ’Bias matched’ compares the control
group with the treatment group. The column ’% change in bias’ reports how much this bias
changed after the full sample was limited to the matched companies in the control group. It
shows that for seven out of eight control variables, the bias reduces by 72% to 98%. Second,
the t-statistics in Table 4 reveal that the diﬀerences between the control group and the treat-
ment group are smaller and less signiﬁcant after our matching procedure. Figure 1 presents
the decrease in standardized diﬀerences graphically. Although some of the covariates are still
signiﬁcantly diﬀerent, Figure 2 clearly shows that the distribution of the ﬁrm characteristics
of high-priced ﬁrms are very similar to the distribution in our control group.
Table 5 reports the average treatment eﬀect on the treated for both the market-to-book
value and Tobin’s Q. The baseline model in row 1 shows that ﬁrms with a share price in
the top quintile enjoy a signiﬁcantly higher valuation. The average value reward is 24%
for the market-to-book value and 11% for Tobin’s Q. Similar to our analysis in Section 3.3,
model 2 until 9 of Table 5 show that our results are robust to diﬀerent sample selections
and model speciﬁcations. Again, we adjust our sample by excluding ﬁnancials, incorporating
stocks under 5 US dollar, and splitting the sample in two shorter periods. In addition, we
impose in model 6 that ﬁrms are matched within the same year, or allow high-priced ﬁrms
to be paired with more than one control ﬁrm in model 7, 8 and 9. Coeﬃcient estimates and
t-statistics are in line with our baseline model, conﬁrming the previous ﬁndings. Although
there is no initial reason to believe that a 100 dollar share with identical characteristics to a
10 dollar stock should be valued higher, our results indicate that stock prices are associated
with ﬁrm valuation, validating our main hypothesis.
4 Share Price and Future Returns
If our estimation strategy and the battery of robustness checks still do not fully eliminate
concerns about the mechanical eﬀects between the nominal stock price and ﬁrm value, the
reader should bear in mind that, given our ﬁndings, it should not be possible to devise a
trading strategy that systematically outperforms the market. In this section, we investigate
whether having a high share price, and the accompanying higher valuation, has implications
for the ﬁrm’s performance on the stock market. Given the price eﬀects on valuation, high
stock prices will be appealing to investors. Conversely, lower stock prices will be unappealing
to investors. Since high price stocks are overvalued, we examine whether these stocks have,
on average, low subsequent returns as compared to lower price stocks.
In line with Section 3, we compare two portfolios based on the ﬁrm’s share price level.
Using daily return series, we construct buy-and-hold portfolios as suggested by Liu and
Strong (2008). At the end of every year, we sort the ﬁrms based on their share price and
form two portfolios, one with stocks from the highest price quintile and one with stocks from
the ﬁrst three price quintiles. We invest the same dollar amount in every stock in the two
portfolios. Stocks are kept in portfolio for 1 year, reﬂecting a feasible and realistic trading
strategy for investors. By using this approach, we avoid high transaction costs due to the
need of frequent portfolio rebalancing and address the concern that our trading strategy
would suﬀer from statistical inferences (Liu and Strong, 2008). In addition, working with
daily return series but yearly rebalancing is in line with Section 3, where we sorted companies
based on the end-of-year9share prices using yearly data.
Table 6, Panel A, shows the raw portfolio returns. Row 1 of Panel A reports the returns
of the portfolio with ﬁrms from the top price quintile at the end of the previous year. The
second line of the table shows the portfolio returns of the control group with shares from
the lowest three quintiles at the end of the previous year. Most interestingly, the third line
shows the diﬀerence of both portfolios, which mimics a long/short portfolio that is long in
high-priced stocks and short in the control group. On average, high-priced ﬁrms earn 1.61
basis points per day, or 4.14% per annum, less during the subsequent year in an equally
weighted portfolio. For a value-weighted portfolio, this return diﬀerence equals 1.28 basis
points per day, or 3.28% per annum. This suggests that high-priced ﬁrms are overvalued,
causing them to underperform on the stock market. Next, we investigate whether this
return diﬀerence can be explained by common risk factors. Panel B of Table 6 reports the
results of regressing our buy-and-hold portfolios on the risk factors of the Carhart (1997)
four-factor model and the Fama and French (2016) ﬁve-factor model with momentum. The
equally weighted long/short portfolio using the Carhart (1997) model generates a signiﬁcant
negative alpha of 1.77 basis points per day, corresponding to a loss in return of 4.56% per
annum. When using the ﬁve-factor model, our long/short strategy generates an annual
proﬁt of 3.54%. The results for value-weighted portfolios show that the long/short strategy
is slightly less proﬁtable, with an annual return diﬀerence of 3.12%. Both in term of size
and signiﬁcance, the return diﬀerence is lower for value-weighted portfolios. Even after
controlling for a possible size eﬀect in the factor models, the results remain equivalent. This
means that the eﬀect is smaller for ﬁrms with a higher market capitalization, in which
9In Section 3, ﬁscal year-end data are used to be consistent with control variables based on accounting
data. Here, we use share prices of December 31 to have one portfolio rebalancing moment per year.
ownership is typically dominated by institutional investors. Not surprisingly, small stocks
are more prone to the eﬀects of stock price anchoring, as retail investors make a larger part
of their investor base. This ﬁnding is also in line with Baker and Wurgler (2006) showing
that smaller, harder to arbitrage, ﬁrms are more likely to diﬀer more from their true value.
Furthermore, equally weighted returns are more reﬂective of the performance of the typical
ﬁrm, hence representing the price response of many stocks rather than the response of a few
Our results show that the underperformance of highly priced ﬁrms can not be fully
attributed to common risk factors, suggesting that the overvaluation of ﬁrms based on their
nominal share price is not fully priced into the market.
This paper shows that higher stock prices coincide with higher valuations, as measured
by the market-to-book value or Tobin’s Q. This result is robust under a very wide set
of model speciﬁcations, control variables, time periods and subsamples. As a result, this
paper provides evidence on a new and surprising anomaly in the stock market, namely the
cross-sectional correlation between the level of the stock price and the ﬁrm value. Two
otherwise identical ﬁrms with only a diﬀerence in their stock price should not be valued any
diﬀerent by the market, as their stock prices can be freely set by choosing the number of
shares. Our results, however, suggest the opposite. We argue that the underlying mechanism
for this anomaly originates from investors suﬀering from a behavioral bias that causes a
positive correlation between stock prices and the perceived value. Speciﬁcally, since investors
may have incomplete information about the value of the ﬁrm or may lack the necessary
competences to process that information, their valuation may be biased by a version of the
availability heuristic, by which investors wrongly interpret the easily available stock price as a
piece of relevant cross-sectional information about true ﬁrm value (Tversky and Kahneman,
1974). In this way the ﬁrm value may become ”anchored” to the stock price.
Interestingly, the results also show that, after enjoying a higher valuation, high-priced
ﬁrms subsequently underperform. Results show that the yearly underperformance of 4.14%
per annum can not be fully attributed to common risk factors, suggesting that the overval-
uation of ﬁrms based on their nominal share price is not fully priced into the market. In
addition, our results show that the eﬀect of stock price anchoring is larger for smaller ﬁrms.
Abadie, Alberto, and Guido W. Imbens, 2006, Large sample properties of matching estima-
tors for average treatment eﬀects, Econometrica 74, 235–267.
Abadie, Alberto, and Guido W. Imbens, 2008, On the Failure of the Bootstrap for Matching
Estimators, Econometrica 76, 1537–1557.
Amihud, Y, 2002, Illiquidity and stock returns: cross-section and time-serieseﬀects., Journal
of Financial Markets 5, 31–56.
Ariely, Dan, George Loewenstein, and Drazen Prelec, 2003, “Coherent arbitrariness”: Stable
demand curves without stable preferences, Quarterly Journal of Economics 118, 73–105.
Baker, Malcolm, Robin Greenwood, and Jeﬀrey Wurgler, 2009, Catering through nominal
share prices, Journal of Finance 64, 2559–2590.
Baker, Malcolm, and Jeﬀrey Wurgler, 2006, Investor sentiment and the cross-section of stock
returns, Journal of Finance 61, 1645–1680.
Bali, Turan G., Nusret Cakici, and Robert F. Whitelaw, 2011, Maxing out: Stocks as lotteries
and the cross-section of expected returns, Journal of Financial Economics 99, 427–446.
Birru, Justin, and Baolian Wang, 2016, Nominal price illusion, Journal of Financial Eco-
nomics 119, 578–598.
Brennan, Michael J., and Thomas E. Copeland, 1988, Stock splits, stock prices, and trans-
action costs, Journal of Financial Economics 22, 83–101.
Carhart, Mark M., 1997, On persistence in mutual fund performance, Journal of Finance
Core, John E., Robert W. Holthausen, and David F. Larcker, 1999, Corporate governance,
chief executive oﬃcer compensation, and ﬁrm performance, Journal of Financial Eco-
nomics 51, 371–406.
Cronley, Maria L, Steven S Posavac, Tracy Meyer, Frank R Kardes, and James J Kellaris,
2005, A Selective Hypothesis Testing Perspective on Price-Quality Inference and Inference-
Based Choice, Journal of Consumer Psychology 15, 159–169.
Dyl, Edward A., and William B. Elliott, 2006, The Share Price Puzzle*, The Journal of
Business 79, 2045–2066.
Fama, Eugene F., and Kenneth R. French, 2016, Dissecting Anomalies with a Five-Factor
Model, Review of Financial Studies 29, 69–103.
Fama, Eugene F., and James D. MacBeth, 1973, Risk, Return, and Equilibrium: Empirical
Tests, Journal of Political Economy 81, 607–636.
Fang, Vivian W., Thomas H. Noe, and Sheri Tice, 2009, Stock market liquidity and ﬁrm
value, Journal of Financial Economics 94, 150–169.
Furﬁne, Craig H., and Richard J. Rosen, 2011, Mergers increase default risk, Journal of
Corporate Finance 17, 832–849.
Furnham, Adrian, and Hua Chu Boo, 2011, A literature review of the anchoring eﬀect,
Journal of Socio-Economics 40, 35–42.
Gompers, Paul A., and Andrew Metrick, 2001, Institutional investors and equity prices,
Quarterly Journal of Economics 116, 229–259.
Green, T. Clifton, and Byoung Hyoun Hwang, 2009, Price-based return comovement, Journal
of Financial Economics 93, 37–50.
Green, T. Clifton, and Russell Jame, 2013, Company name ﬂuency, investor recognition, and
ﬁrm value, Journal of Financial Economics 109, 813–834.
Griﬃn, Dale, and Amos Tversky, 1992, The weighing of evidence and the determinants of
conﬁdence, Cognitive Psychology 24, 411–435.
Grinblatt, Mark S., Ronald W. Masulis, and Sheridan Titman, 1984, The valuation eﬀects
of stock splits and stock dividends, Journal of Financial Economics 13, 461–490.
Hillman, Amy J., and Gerald D. Keim, 2001, Shareholder value, stakeholder management,
and social issues: What’s the bottom line?, Strategic Management Journal 22, 125–139.
Ikenberry, D L, G Rankine, and E K Stice, 1996, What Do Stock Splits Really Signal?, The
Journal of Financial and Quantitative Analysis 31, 357–375.
Johnson, Rose L., and James J. Kellaris, 1988, An Exploratory Study of Price/Perceived-
Quality Relationships Among Consumer Services, Advances in Consumer Research 15,
Kahneman, Daniel, and Jack L. Knetsch, 1992, Valuing Public-Goods - the Purchase of
Moral Satisfaction, Journal of Environmental Economics and Management 22, 57–70.
Kumar, Alok, 2009, Who Gambles in the Stock Market?, Journal of Finance 64, 1889–1933.
Kumar, Alok, and Charles M C Lee, 2006, Retail investor sentiment and return comovements,
Journal of Finance 61, 2451–2486.
Lee, Eunju, and Natalia Piqueira, 2017, Short selling around the 52-week and historical
highs, Journal of Financial Markets 33, 75–101.
Li, Jun, and Jianfeng Yu, 2012, Investor attention, psychological anchors, and stock return
predictability, Journal of Financial Economics 104, 401–419.
Liu, Weimin, and Norman Strong, 2008, Biases in decomposing holding-period portfolio
returns, Review of Financial Studies 21, 2243–2274.
Mcnichols, Maureen, and Ajay Dravid, 1990, Stock Dividends, Stock Splits, and Signaling,
The Journal of Finance .
Morck, Randall, Andrei Shleifer, and Robert W. Vishny, 1988, Management ownership and
market valuation. An empirical analysis, Journal of Financial Economics 20, 293–315.
Mussweiler, Thomas, and Fritz Strack, 1999, Comparing Is Believing: A Selective Accessibil-
ity Model of Judgmental Anchoring, European Review of Social Psychology 10, 135–167.
Newey, Whitney K., and Kenneth D. West, 1987, A Simple, Positive Semi-Deﬁnite, Het-
eroskedasticity and Autocorrelation Consistent Covariance Matrix, Econometrica 55, 703.
Obermiller, Carl, 1988, When Do Consumers Infer Quality from Price?, Advances in Con-
sumer Research 15, 304–310.
Plassmann, Hilke, John O’Doherty, Baba Shiv, and Antonio Rangel, 2008, Marketing ac-
tions can modulate neural representations of experienced pleasantness., Proceedings of the
National Academy of Sciences of the United States of America 105, 1050–1054.
Rao, Akshay R., and Kent B. Monroe, 1989, The Eﬀect of Price, Brand Name, and Store
Name on Buyers’ Perceptions of Product Quality: An Integrative Review, Journal of
Marketing Research 26, 351–357.
Rubin, D. B., 1977, Assignment to Treatment Group on the Basis of a Covariate, Journal
of Educational and Behavioral Statistics 2, 1–26.
Rubin, Donald B., 1973, Matching to remove bias in observational studies, Biometrics 159–
Schultz, Paul, 2000, Stock Splits, Tick Size, and Sponsorship, Journal of Finance 55, 429–
Shiv, Baba, Ziv Carmon, and Dan Ariely, 2005, Placebo Eﬀects of Marketing Actions: Con-
sumers May Get What They Pay For, Journal of Marketing Research 42, 383–393.
Smith, Jeﬀrey A., and Petra E. Todd, 2005, Does matching overcome LaLonde’s critique of
nonexperimental estimators?, Journal of Econometrics 125, 305–353.
Tversky, Amos, and Daniel Kahneman, 1974, Judgment under uncertainty, Science 185,
Weld, William C, Roni Michaely, Richard H Thaler, and Shlomo Benartzi, 2009, The Nom-
inal Share Price Puzzle, Journal of Economic Perspectives 23, 121–142.
Table 1: Summary statistics
Full sample Price quintile 5
Mean Median Stdev Mean Median Stdev
Nominal share price 28.63 22.61 22.04 63.15 56.99 20.63
MTBV 3.07 2.13 3.32 4.20 3.04 3.90
Tobin ’s Q 3.59 2.59 4.23 4.73 3.46 4.66
Sales growth 12.24 8.49 21.34 13.30 9.54 18.04
Proﬁtability 0.33 0.29 0.48 0.46 0.37 0.46
Age 18.25 16.78 10.37 21.11 20.06 10.61
Size 5.26 0.74 21.22 14.06 3.05 40.83
Analyst growth estimates 5.89 0.00 67.02 -5.48 0.00 23.24
Research & development 7.58 0.00 40.80 4.35 0.22 25.93
Asset turnover 113.03 0.96 83.19 101.18 88.00 72.48
Current ratio 2.64 1.98 2.40 2.18 1.63 2.04
Leverage 28.96 28.01 23.28 31.62 31.74 21.32
Volatility 32.50 30.97 11.83 25.80 23.87 9.07
Market beta 0.94 0.91 0.57 0.92 0.90 0.46
Payout ratio 18.00 0.00 24.92 24.80 20.92 24.12
Analyst coverage 356.92 170.00 467.29 540.62 393.00 574.31
Cash 30.81 24.14 25.78 28.90 22.53 23.55
Herﬁndahl index 14.48 0.10 12.48 15.75 10.44 13.42
Market share 3.99 0.01 9.56 8.76 3.09 14.29
Market power 103.06 0.00 549.64 244.33 33.24 807.73
Illiquidity 4.30 0.00 37.56 0.73 0.01 23.67
Turnover shares 1.92 1.21 7.70 2.40 1.34 16.55
Momentum 3 year 13.07 10.38 25.42 20.43 16.85 21.02
Table 1 reports the summary statistics for the main variables used in our sample period spanning from 1990
until 2014. The sample includes stocks with available ﬁnancial data from the Thomson Reuters Datastream
database. This results in 36,360 observations for 4,144 companies. Per year, we divide our sample into 5
groups based on their nominal share price. The left-hand side of the table shows the summary statistics for
the whole sample, while the right-hand side reports the summary statistics of the ﬁrms with the 20% highest
prices, price quintile 5. All potentially unbounded variables are winsorized at the 1% and 99% level. More
detailed information on the construction of our variables is available in Appendix A. Unless otherwise stated
in Appendix A, data correspond to the ﬁrms’ ﬁscal year.
Table 2: Nominal share price and ﬁrm value
MTBV Tobin’s Q
Nominal share price
Quintile 4 0.079∗∗∗ (5.38) 0.060∗∗∗ (9.53)
Quintile 5 0.129∗∗∗ (5.08) 0.118∗∗∗ (8.88)
Valuationt-1 0.770∗∗∗ (34.65) 0.677∗∗∗ (48.38)
Momentum 1 year 0.351∗∗∗ (7.65) 0.224∗∗∗ (10.17)
Sales growth -0.000∗∗∗ (-2.91) -0.000∗∗ (-2.50)
Proﬁtability 0.042∗∗ (2.73) 0.063∗∗∗ (4.24)
Age -0.000∗∗∗ (-3.01) -0.001∗∗∗ (-3.95)
Size -0.041∗∗∗ (-6.20) -0.048∗∗∗ (-9.32)
Analyst growth estimates -0.075∗∗ (-2.63) -0.053∗∗ (-2.65)
Research & development 0.054∗∗∗ (3.97) 0.111∗∗ (2.20)
Asset turnover 0.035∗∗∗ (9.24) 0.028∗∗∗ (9.14)
Current ratio -0.015∗∗∗ (-6.11) -0.015∗∗∗ (-4.54)
Leverage 0.001∗∗∗ (6.14) 0.005∗∗∗ (14.29)
Volatility -0.001∗(-1.73) -0.002∗∗∗ (-4.70)
Market beta 0.033∗∗∗ (6.16) 0.036∗∗∗ (4.14)
Payout ratio 0.000∗∗∗ (7.29) 0.000∗∗∗ (6.97)
Analyst coverage 0.000∗∗∗ (8.10) 0.000∗∗∗ (6.96)
Cash 0.001∗∗∗ (3.97) 0.000∗∗∗ (4.51)
Herﬁndahl index 0.000 (1.23) 0.000∗∗ (2.37)
Market share 0.002∗∗∗ (2.97) 0.004∗∗∗ (3.58)
Market power -0.004∗∗ (-2.59) -0.005∗∗ (-2.56)
Market power dummy 0.009∗∗∗ (3.05) 0.010∗(1.94)
Illiquidity -0.081∗∗∗ (-5.16) -0.109∗∗∗ (-4.18)
Turnover shares -0.004∗∗ (-2.42) -0.003∗(-1.92)
Momentum 3 year 0.001∗∗∗ (5.38) 0.001∗∗∗ (4.99)
NYSE 0.041∗∗∗ (4.22) 0.043∗∗∗ (5.20)
S&P 500 0.005 (0.68) -0.001 (-0.14)
Constant 0.493∗∗∗ (6.59) 0.687∗∗∗ (9.27)
Industry ﬁxed eﬀects Yes Yes
N 36,360 31,966
Table 2 shows the results of Fama and MacBeth (1973) two-step panel regressions of ﬁrm value on the stock
price and ﬁrm characteristics. Column 2 and 3 show the results using the natural logarithm of the market-
to-book value (MTBV), while column 4 and 5 report on the results using the Tobin’s Q. The price variables
dummies for quintile 4 and quintile 5 compare high-priced stocks to stocks trading at a low to moderate
price. The lag of the natural log of market-to-book value captures persistence eﬀects, and the one-year
momentum accounts for a possible mechanical relation between stock prices and ﬁrm value. Firms with a
stock price lower than 5 US Dollar are excluded to mitigate market microstructure eﬀects of small stocks.
The R-square corresponds to the average value of the R-squares from the cross-sectional regressions in the
ﬁrst step of the Fama-MacBeth procedure. Newey and West (1987) standard errors with a lag length of 4
years are used to calculate t-statistics, reported in parentheses. *, **, *** indicate the statistical signiﬁcance
at the 10%, 5% and 1% levels.
Table 3: Nominal share price and ﬁrm value: robustness checks
MTBV Tobin’s Q
Quintile 5 R2N Quintile 5 R2N
01 Baseline results 0.129∗∗∗
(5.08) 0.84 36360 0.118∗∗∗
(8.88) 0.78 31966
02 Without ﬁnancials 0.135∗∗∗
(5.08) 0.84 34412 0.127∗∗∗
(8.93) 0.78 30057
03 With penny stocks 0.128∗∗∗
(5.78) 0.81 46026 0.148∗∗∗
(7.89) 0.74 37861
04 Subsample: 1990-2001 0.114∗∗ (2.55) 0.87 12306 0.112∗∗∗
(4.82) 0.79 11022
05 Subsample: 2002-2014 0.145∗∗∗
(12.95) 0.82 24054 0.125∗∗∗
(12.85) 0.78 20944
06 Negative momentum 0.096∗∗∗
(3.07) 0.87 10423 0.054∗(1.71) 0.84 8363
07 Positive momentum 0.120∗∗∗
(5.12) 0.85 25937 0.110∗∗∗
(6.58) 0.79 23603
08 No winsorizing 0.133∗∗∗
(5.23) 0.84 36352 0.123∗∗∗
(8.15) 0.78 33037
09 Quintiles of all controls 0.121∗∗∗
(6.01) 0.78 36360 0.123∗∗∗
(4.57) 0.72 36190
10 SMP adjusted valuation 0.188∗∗∗
(6.92) 0.66 35161 0.169∗∗∗
(6.92) 0.66 35161
11 Pooled OLS 0.193∗∗∗
(17.93) 0.79 36360 0.156∗∗∗
(20.39) 0.74 33044
12 Pooled OLS clustered SE 0.193∗∗∗
(16.43) 0.79 36360 0.156∗∗∗
(16.71) 0.74 33044
13 Between estimator 0.162∗∗∗
(8.34) 0.87 36360 0.144∗∗∗
(6.55) 0.82 33044
14 Year-average 0.077∗∗∗
(6.84) 0.84 36360 0.076∗∗∗
(10.18) 0.78 33044
15 Year-low 0.087∗∗∗
(4.95) 0.84 36360 0.080∗∗∗
(8.65) 0.78 33044
16 Year-high 0.063∗∗∗
(7.78) 0.84 36360 0.070∗∗∗
(8.00) 0.78 33044
Table 3 presents the results of variations in sample selection, model speciﬁcations and price variables com-
pared to the baseline models in table 2. Because the main objective is to test the robustness of the stock
price variable, we only report the coeﬃcient of the ﬁfth price quintile. The ﬁrst row shows the results of
the Fama and MacBeth (1973) two-step panel regressions model that serves as a benchmark model. Rows 2
to 7 show the results using a diﬀerent sample selection procedure. Model 2 excludes ﬁrm from the ﬁnancial
industry and model 3 includes the excluded penny stocks under 5 US Dollar. Row 4 and 5 show the results
based on the subsamples 1990-2001 and 2002-2014. In model 6 and 7, we split our sample based on the ﬁrm’s
returns over the past three years. Model 6 reports the results of ﬁrms with negative momentum, model 7
for ﬁrms with positive momentum. Rows 8 to 13 show the results of alternative model speciﬁcations. Row
8 reports the results without winsorising our variables. To allow for nonlinear eﬀects, model 9 shows the
results when regressing the value measures on quintile dummies of all control variables. Row 10 shows the
results when using 125 portfolios sorted on size, momentum and proﬁtability (SMP), and subsequently adjust
the value measure market-to-book value or Tobin’s Q by subtracting from a ﬁrms’ value the mean value in
the reference group. Row 11, 12 and 13 shows the results using respectively a standard pooled OLS model,
a pooled OLS model with standard erros clustered on the ﬁrm level, and the between estimator to focus
on the cross sectional diﬀerences. Instead of using the price at the end of the ﬁscal year to contruct our
quintile dummies, the year-average, year-low, and year-high are used in model 14, 15 and 16, respectively.
The R-square corresponds to the average value of the R-squares from the cross-sectional regressions in the
ﬁrst step of the Fama-MacBeth procedure. Newey and West (1987) standard errors are used to calculate
t-statistics, reported in parentheses. *, **, *** indicate the statistical signiﬁcance at the 10%, 5% and 1%
Table 4: Nearest-neighbor matching diagnostics
Treatment Full sample Control group
Holding Period N Mean N Mean Diﬀ. t-stat Bias N Mean Diﬀ. t-stat Bias % change t-stat
full matched in bias
Size 7237 14.98 27677 13.00 1.98 −14.73 1.09 3908 14.33 0.65 −7.10 0.11 −90.24 −15.77
Momentum 7237 20.43 27677 8.54 11.89 −14.14 0.49 3908 18.30 2.14 −4.19 0.14 −72.50 −16.29
Cash 7237 28.90 27677 31.96 −3.06 2.09 −0.12 3908 29.67 −0.77 0.89 0.03 −75.78 −2.16
Proﬁtability 7237 0.46 27677 0.28 0.18 −7.58 0.36 3908 0.40 0.06 −4.26 0.11 −68.23 −7.14
Analyst coverage 7237 540.62 27677 273.64 266.99 −11.18 0.55 3908 426.18 114.45 −5.43 0.05 −90.21 −13.66
Sales growth 7237 13.30 27677 12.19 1.11 −1.80 0.05 3908 13.01 0.28 −0.63 0.10 86.52 1.54
R&D 7237 0.04 27677 0.09 −0.05 1.86 −0.13 3908 0.05 0.00 0.55 0.01 −90.92 −1.86
Market beta 7237 0.92 27677 0.92 0.00 −0.04 0.00 3908 0.94 −0.02 1.00 0.00 −97.76 −0.85
Table 4 reports the matching diagnostics for the main variables in the matching procedure. Companies are matched based on the nearest-neighbor
procedure with replacement using the Mahalanobis distance. The left-hand panel shows the summary statistics of the companies in the highest price
quintile. The middle part reports on the full sample of companies in the share price quintiles 1, 2 or 3. The right-hand panel focuses on the companies
that were selected for the control group as nearest-neighbors for companies in the treatment group. The columns ’Bias full’ and ’Bias matched’ show
the standardized percentage bias between the high-priced ﬁrms in the treatment group and respectively the companies in the full sample and control
group. The column ’% change in bias’ shows how much the bias changed after the full sample was limited to the matched companies in the control
Table 5: Nominal share price and ﬁrm value: nearest-neighbor matching
MTBV Tobin’s Q
ATET N ATET N
01 Baseline results 0.241∗∗∗ (20.88) 7237 0.113∗∗∗ (10.97) 7061
02 Without ﬁnancials 0.247∗∗∗ (20.48) 6855 0.120∗∗∗ (11.07) 6681
03 With penny stocks 0.252∗∗∗ (21.06) 7237 0.119∗∗∗ (11.00) 7061
04 Subsample: 1990-2001 0.209∗∗∗ (10.68) 2439 0.102∗∗∗ (5.95) 2359
05 Subsample: 2002-2014 0.259∗∗∗ (18.08) 4798 0.131∗∗∗ (10.25) 4702
06 Match within year 0.256∗∗∗ (24.56) 7237 0.135∗∗∗ (14.28) 7061
07 Multiple matches: 2 0.254∗∗∗ (24.80) 7237 0.125∗∗∗ (13.71) 7061
08 Multiple matches: 3 0.256∗∗∗ (26.81) 7237 0.127∗∗∗ (14.84) 7061
09 Multiple matches: 4 0.260∗∗∗ (28.47) 7237 0.132∗∗∗ (15.90) 7061
Table 5 reports the average treatment eﬀects on the treated (ATET) on market-to-book value and Tobin’s
Q of matched ﬁrms with a high price compared to the control ﬁrms with a low to medium price. Companies
are matched based on the nearest-neighbor procedure with replacement using the Mahalanobis distance.
Row 1 shows the results of the benchmark model, in which high-priced companies are matched based on the
ﬁrms’ size, momentum, proﬁtability, analyst coverage, sales growth, R&D, market beta and cash position
with a company in the control group within the same industry. Row 2 until 10 report the results of using
variations of the sample selection and model speciﬁcation. Model 2 excludes ﬁrm from the ﬁnancial industry
and model 3 allows penny stocks under 5 US Dollar to be in the control group. Row 4 and 5 show the results
based on the subsamples 1990-2001 and 2002-2014. Row 6 shows the results when ﬁrms are matched within
the same year instead of the same level 3 ICB sector. Instead of matching with 1 nearest neighbor, model
7, 8 and 9 match the high-priced ﬁrms with respectively 2, 3 and 4 control ﬁrms. The results are corrected
for a possible large-sample bias that exists when matching on more than one continuous covariates using the
method suggested by Abadie and Imbens (2006, 2008). Newey and West (1987) standard errors are used to
calculate t-statistics, reported in parentheses. N refers to the number of high-priced ﬁrms that are matched.
Coeﬃcients marked with ***, **, and * indicate signiﬁcance at the 1, 5, and 10 percent level, respectively.
Table 6: Nominal share price and ﬁrm returns
Equally weighted Value-weighted
Alpha t-stat Alpha t-stat
Panel A: raw returns
High price 5.49∗∗∗ (3.82) 4.30∗∗∗ (2.86)
Control group 7.10∗∗∗ (4.84) 5.58∗∗∗ (3.15)
Diﬀerence -1.61∗∗∗ (-2.68) -1.28 (-1.51)
Panel B: long/short portfolio
Raw returns -1.61∗∗∗ (-2.68) -1.28 (-1.51)
Carhart model -1.77∗∗∗ (-3.95) -1.22∗(-1.69)
FF5-momentum model -1.38∗∗∗ (-3.14) -1.22∗(-1.71)
Table 6 reports the daily buy-and-hold returns of equally and value-weighted portfolios. Panel A reports
the raw returns of the portfolio of high-priced ﬁrms, a portfolio of the ﬁrms in the lower three price quintiles
(control group), and the diﬀerence between these two. Panel B shows the result of the raw diﬀerence
portfolio returns, and this long/short portfolio returns regressed on the Carhart (1997) four-factor model
and the Fama and French (2016) ﬁve-factor model with momentum. The sample includes all ﬁrms with
available price and return data in Thomson Reuters Datastream, using 6484 unique ﬁrms. We have 6300
daily times series observations from 1990 until 2014, resulting in 16.868.432 ﬁrm-day observations. Portfolios
are rebalanced yearly based on the end-of-December share price. Coeﬃcients marked with ***, **, and *
indicate signiﬁcance at the 1, 5, and 10 percent level, respectively. t-statistics reported in parentheses.
Figure 1: Matching diagnostics: standardized diﬀerences
0 50 100
Standardized % bias across covariates
05 Analyst Coverage
Balance after Matching
Figure 1 displays the percentage standardized diﬀerences of the sample means before and after matching for
the eight control variables used in the baseline model 1 of Table 5. The percentage standardized diﬀerences
are calculate by dividing the diﬀerence in mean between the treatment and control group by the square root
of the average standard deviation in both groups.
Appendix A Variable Deﬁnitions
MTBV Market value of the ordinary (common) equity at the end
of the ﬁscal year divided by the balance sheet value of the
ordinary (common) equity in the company.
Tobin’s Q Enterprise value (market capitalization + preferred stock +
minority interest + total debt minus cash) divided by the book
value of the proportioned common equity in the company.
End-of-year Price Unadjusted price: the real price a stock was trading at. Not
adjusted for corporate actions.
Year-average Average unadjusted closing prices over the ﬁscal year.
Year-high Highest unadjusted closing price over the ﬁscal year.
Year-low Lowest unadjusted closing price over the ﬁscal year.
Sales growth Current year’s net sales or revenues divided by the net sales
or revenues four years ago. Reduced to a compound annual
Proﬁtability Earnings Before Interest, Taxes and Depreciation (EBITDA)
divided by the book value.
Age Number of years since Datastream holds information about
Size Natural logarithm of net sales or revenues: represent gross
sales and other operating revenue less discounts, returns and
allowances (billion USD).
Analyst growth estimates Average of 12 month price target by analysts, divided by the
current stock price (%). Data starting from March 1999. If
no target prices are available, we set this variable to zero.
Research & Development Research and Development expenditures divided by the net
sales or revenues (%). We set missing values to zero.
Asset Turnover Net sales or revenues divided by the total assets (%).
Current Ratio Liquidity ratio: Current Assets-Total / Current Liabilities-
Leverage Total debt as a percentage of the total capital.
Volatility A measure of a stock’s average annual price movement to a
high and low from a mean price for each ﬁscal year. For exam-
ple, a stock’s price volatility of 20% indicates that the stock’s
annual high and low price has shown a historical variation of
+20% to -20% from its annual average price.
Market beta The beta factor of the CAPM model. It expresses the relative
movement of the price against the market, showing the likely
relative change for a given market movement and whether the
stock is prone to under- or overreact.
Payout Ratio Dividends per share over earnings per share, multiplied by
Analyst Coverage The total number of estimators covering the company for the
ﬁscal period. We set missing values to zero.
Cash Represents money available for use in the normal operations
of the company. Cash and equivalents as a percentage of total
Herﬁndahl Index Measure of sector concentration(%): sum of the squares of
the market shares (sales) of the ﬁrms within the level 3 ICB
Market Share Share (%) in total sales within the level 3 ICB industry.
Market Power Interaction term of sector concentration (Herﬁndahl index)
and the company’s market share.
Market Power Dummy Dummy variable that indicates companies that are both in a
highly concentrated sector (highest quintile Herﬁndahl index)
and have a high market share (highest quintile).
Illiquidity Amihud (2002) illiquidity ratio: the absolute (percentage)
price change per dollar of daily trading volume, averaged per
Turnover Shares Turnover by volume scaled by shares outstanding.
Momentum 3 Year Multiplied annual (3 years) total investment return reduced
to a compound annual rate.
S&P500 Dummy variable equal to one if the ﬁrm is a constituent of
NYSE Dummy variable equal to one if the ﬁrm trades on the NYSE.
Industry Dummy variables based on the level 3 ICB sectors (41 sectors).
Table A describes the construction of the dependent variables and the controls used in the regression anal-
ysis. All company-level variables are computed each year from 1990 to 2014, using the Thomson Reuters