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Abstract and Figures

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 information 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 annum.
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Department of Economics
Faculty of Economics and Business Administration
Campus Tweekerken, St.-Pietersplein 5, 9000 Ghent - BELGIUM
Mustafa Disli
Koen Inghelbrecht
Koen Schoors
Hannes Stieperaere
March 2019
Stock Price Anchoring
Mustafa Disli Koen Inghelbrecht Koen Schoors
Hannes Stieperaere
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:
1 Introduction
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
stock price.
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 Data
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.
3.1 Methodology
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,t1+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.
3.4 Matching
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
large stocks.
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.
5 Conclusions
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.
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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
Growth perspectives
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
(In)Tangible assets
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
Equity risk
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
Corporate governance
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
Market risk
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)
Control variables
Valuationt-1 0.770∗∗∗ (34.65) 0.677∗∗∗ (48.38)
Momentum 1 year 0.351∗∗∗ (7.65) 0.224∗∗∗ (10.17)
Growth perspectives
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)
(In)Tangible assets
Research & development 0.054∗∗∗ (3.97) 0.111∗∗ (2.20)
Asset turnover 0.035∗∗∗ (9.24) 0.028∗∗∗ (9.14)
Equity risk
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)
Corporate governance
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)
Market risk
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
R284.2 78.4
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
Sample selection
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
Model specifications
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
Price variable
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
01 Baseline results 0.241∗∗∗ (20.88) 7237 0.113∗∗∗ (10.97) 7061
Sample selection
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
Model specifications
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
(bp/day) (bp/day)
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
08 Beta
07 R&D
06 Salesgrowth
05 Analyst Coverage
04 Profitability
03 Cash
02 Momentum
01 Size
Balance after Matching
Unmatched Matched
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.
Figure 2: Matching diagnostics: balance after matching
Figure 2 reports the distribution of the control variables described in Table 4 for both the full control sample
before the matching procedure (raw), as well as for the control group after matching (matched).
Appendix A Variable Definitions
Variable Definition
Value Metric
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.
Price Variable
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.
Growth Perspectives
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
the issue.
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.
(In)tangible Assets
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 (%).
Equity Risk
Current Ratio Liquidity ratio: Current Assets-Total / Current Liabilities-
Leverage Total debt as a percentage of the total capital.
Variable Definition
Equity Risk
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.
Corporate Governance
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
current assets.
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).
Market Risk
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.
Index Inclusion
S&P500 Dummy variable equal to one if the firm is a constituent of
the S&P500.
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
Datastream database.
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We explore the psychology of stock price levels and provide evidence that investors suffer from a nominal price illusion in which they overestimate the room to grow for low-priced stocks relative to high-priced stocks. While it has become increasingly clear that nominal price levels influence investor behavior, why prices matter to investors is a question that as of yet has gone unanswered. We find widespread evidence that investors systematically overestimate the skewness of low-priced stocks. In the broad cross-section of stocks, we find that investors substantially overweight the importance of price when forming skewness expectations. Asset pricing implications of our findings are borne out in the options market. A zero-cost option portfolio strategy that exploits investor overestimation of skewness for low-priced stocks generates significant abnormal returns. Finally, investor expectations of future skewness increase drastically on days that a stock undergoes a split to a lower nominal price. Empirically, however, future physical skewness decreases following splits.
Although the distance of a stock price to its past price high does not provide fundamental-related information, it plays an important role of anchoring investors' expectations about the performance of stocks. Using a stock's 52-week and historical highs, we examine the impact of the nearness to these price highs on short sellers’ trading behavior in the U.S. equity market from 1988 to 2012. We find that short selling is negatively associated with the nearness of the price to the 52-week high, while it is positively associated with the nearness to the historical high. This suggests that short sellers exploit other investors’ behavioral biases.
A five-factor model that adds profitability (RMW) and investment (CMA) factors to the three-factor model of Fama and French (1993) suggests a shared story for several average-return anomalies. Specifically, positive exposures to RMW and CMA (stock returns that behave like those of profitable firms that invest conservatively) capture the high average returns associated with low market β β, share repurchases, and low stock return volatility. Conversely, negative RMW and CMA slopes (like those of relatively unprofitable firms that invest aggressively) help explain the low average stock returns associated with high β β, large share issues, and highly volatile returns. Received November 11, 2014; accepted April 27, 2015 by Editor Andrew Karolyi.
We develop a model of stock-split behavior in which the split serves as a costly signal of managers' private information because stock trading costs depend on stock prices. We present empirical evidence confirming the relation between stock trading costs and stock prices. The signaling model is estimated using a large sample of splits and explains a substantial fraction of the split-announcement returns.
We test the relationship between shareholder value, stakeholder management, and social issue participation. Building better relations with primary stakeholders like employees, customers, suppliers, and communities could lead to increased shareholder wealth by helping firms develop intangible, valuable assets which can be sources of competitive advantage. On the other hand, using corporate resources for social issues not related to primary stakeholders may not create value for shareholders. We test these propositions with data from S&P 500 firms and find evidence that stakeholder management leads to improved shareholder value, while social issue participation is negatively associated with shareholder value. Copyright ? 2001 John Wiley & Sons, Ltd.
Several matching methods that match all of one sample from another larger sample on a continuous matching variable are compared with respect to their ability to remove the bias of the matching variable. One method is a simple mean-matching method and three are nearest available pair-matching methods. The methods' abilities to remove bias are also compared with the theoretical maximum given fixed distributions and fixed sample sizes. A summary of advice to an investigator is included.
When assignment to treatment group is made solely on the basis of the value of a covariate, X, effort should be concentrated on estimating the conditional expectations of the dependent variable Y given X in the treatment and control groups. One then averages the difference between these conditional expectations over the distribution of X in the relevant population. There is no need for concern about "other" sources of bias, e.g., unreliability of X, unmeasured background variables. If the conditional expectations are parallel and linear, the proper regression adjustment is the simple covariance adjustment. However, since the quality of the resulting estimates may be sensitive to the adequacy of the underlying model, it is wise to search for nonparallelism and nonlinearity in these conditional expectations. Blocking on the values of X is also appropriate, although the quality of the resulting estimates may be sensitive to the coarseness of the blocking employed. In order for these techniques to be useful in practice, there must be either substantial overlap in the distribution of X in the treatment groups or strong prior information.