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What Drives the Value Effect? Risk versus Mispricing: Evidence from

International Markets*

Denis B. Chaves Jason Hsu

Vitali Kalesnik Yoseop Shim

**

First Draft: June 14, 2011

Current Draft: February 1, 2012

Abstract

Value stocks outperform growth stocks. The academic literature provides two

competing theories on what drives the value premium: exposure to risk factors or

mispricing of the securities. Existing empirical studies have not conclusively rejected one

in support of the other. Using Fama and MacBeth (1973) regressions and extensions of

the portfolio tests based on Daniel and Titman (1997), we provide evidence that the

book-to-market characteristic largely subsumes the loading on the value factor (HML) as

a variable that explains the cross-section of stock returns. We improve the power of

existing tests by using data from 23 developed countries going back more than 30 years.

Given these results, we conclude that mispricing is likely a more significant portion of

the value premium.

*The authors would like to acknowledge helpful comments and suggestions from Rob Arnott, Joseph Chen, David Hirshleifer,

Katy Sherrerd and two anonymous referees.Denis Chaves is a senior researcher at Research Affiliates, LLC, Newport Beach, CA. Email: chaves@rallc.com.

Jason Hsu is chief investment officer at Research Affiliates, LLC, Newport Beach, CA, and an adjunct professor of finance at the

UCLA Anderson Business School, Los Angeles, CA. Email: hsu@rallc.com.Vitali Kalesnik is a vice president at Research Affiliates, LLC, Newport Beach, CA, and an adjunct professor of finance at SDSU,

San Diego, CA. Email: Kalesnik@rallc.com.**

Yoseop Shim is a research associate at Research Affiliates, LLC, Newport Beach, CA. Email: shim@rallc.com.

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1. Introduction

Value strategies have been popular with practitioners since the work of Graham and Dodd (1934).1

There is strong consensus among academics and practitioners, supported by empirical evidence, that

value strategies outperform growth strategies.2The academic literature proposes two competing

theories on the origin of the value premium. The main goal of this paper is to find tests that allow us to

distinguish between these two theories. The tests we propose are extensions of the existing literature

and we increase their power by using a large sample of countries.

The first of the two theories claims that value stocks co-move with some unobserved risk factor.

Potentially, they increase portfolio exposure to distress, liquidity, or some rare and hidden (Black Swan)

risks and, therefore, offer a return premium. Fama and French (1993) construct a proxy for this risk

factorthe HML factorthat can be used to assess a stocks sensitivity to this yet-to-be-identified

source of risk in the economy. Value stocks have high HML loadings and, therefore, are expected to

deliver high average returns as risk compensation.

The alternate theory, initiated by Lakonishok, Shleifer, and Vishny (LSV, 1994), argues that value

stocks are simply undervalued; investors extrapolate poor past performance and push prices too low

relative to fundamentals. According to this theory, value stocks deliver high returns because valuation

ratios, like book-to-market (B/M), mean-revert as investors realize and correct the mispricing.

Moreover, according to Daniel and Titman (1997, pp. 2), LSV do not dispute the possibility that there

may be priced factors associated with value (or growth) stocks, they argue that the return premia

1Value strategies are based on buying stocks with high book-to-market ratio, earnings-to-price ratio, dividend yield, and other

measures of company fundamental to current price. Growth strategies are based on buying stocks with low measures of

company fundamental to current price.2See Fama and French (1992), among others.

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associated with these factor portfolios are simply too large and their covariances with macro factors are

just too low (and in some cases negative) to be considered compensation for systematic risk.

Designing tests to evaluateand ideally distinguishthese two theories is a complicated task,

because HML loadings and B/M characteristics are highly correlated across stocks. In most cases these

tests offer similar predictions or have low power in separating the influence of both theories.

Understanding the source of the value premium has profound implications for the financial

industry. If one believes that the cross-section of expected returns is better explained by the

characteristics of stocks, then some of the current practices adopted in the industry that are based on

factor loadings could be challenged. For example, investors would likely tie their stock selection rules to

reflect the source of the value premium. Strictly speaking, if the risk-based theory is correct, then value

stocks should be selected according to their loadings on the HML factor. On the other hand, if the

mispricing theory is correct, then value stocks should be selected according to B/M or other valuation

ratios.

Perhaps more importantly, investors will view risk differently under the alternative theories. If

the risk-based theory is correct, a value-based strategy will expose the portfolio to added risk. More

specifically, if the interpretation is that value stocks are exposed to unknown and hidden risks, then

value outperformance may come with risks which are unacceptable to some investors. If, on the other

hand, the mispricing theory is true, then investors should benefit from higher allocations to value

strategies with no corresponding increase in systematic risk exposure. Taking this analysis one step

further, when a value stock becomes deep value, the mispricing interpretation would suggest that the

stock has become even cheaper instead of riskier; this would point to an even better buying

opportunity.

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Finally, if the mispricing theory is correct, the HML factor and risk-based adjustments would not

be the most appropriate tools for performance measurement or attribution. Benchmarking strategies

based on B/M and other characteristics, as illustrated by Daniel, Grinblatt, Titman, and Wermers (1997),

would be a better choice for such applications.3

The current view of many academic and practitioners is that the two dominant theories

represent conflicting frameworks. We argue, similarly to LSV, that these two theories can be

complementary, as illustrated, for instance, by the model in Daniel, Hirshleifer, and Subrahmanyam

(2001). To support this claim, we show that the value premium may be generated in part by risk factor

exposure, but mispricing plays a larger and more significant role.

2. Review of Existing Theories and Results

The academic literature features two competing theories on the source of the value premium.

The first theory is risk-based and can nest neatly within the Intertemporal Capital Asset Pricing Model

(ICAPM) framework of Merton (1973), in which the expected return of a stock or portfolio is given by its

loadings, , on a series of risk factors and the risk premiums on these factors, : . (1)

Under the ICAPM framework, investors are sensitive to undiversifiable shocks to their consumption and

their investment opportunity sets. Value stocks (or high fundamental-to-price stocks) are assumed to be

correlated with these shocksmaking them risk-accentuating to investorsand, therefore, carry a risk

premium.

3Factor-based performance attribution might still be useful to test whether a proposed variable has any incremental ability to

explain mispricings in the cross-section of stocks.

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Specifically, Fama and French (1993) argue that the value premium arises as a compensation for

financial distress risk. They argue that value stocks would underperform during credit or liquidity crises.

Working backward, Fama and French use value strategies to construct a factor portfolio that supposedly

measures and captures distress risk. They construct a zero-investment (long/short) portfolio of high B/M

stocks (value stocks) minus low B/M stocks (growth stocks). This long/short portfolio is commonly

referred to as high-minus-low, or HML, and is used as a proxy for distress risk. In Fama and Frenchs

setup, stocks that are sensitive to distress risk exhibit high loadings on the HML factor, , thusearning a distress risk premium. In other words, value stocks generally exhibit, by construction, high

loadings on the HML factor and the value outperformance is interpreted as compensation for being

exposed to distress risk.

The empirical literature, however, reports a weakor even reverserelationship between

distress risk and B/M, HML loading or expected return. For instance, in Shumways(1996) abstract one

reads that the book-to-market effect cannot be described as a distress effect. Dichev (1998, p.1131)

claims that bankruptcy risk is not rewarded by higher returns,and Griffin and Lemmon (2002, p.2318)

show that the group of firms with the highest risk of distress includes many firms with high B/M ratios

and low past stock returns, but actually includes more firms with low B/M ratios and high past stock

returns.More recently, Campbell, Hilscher, and Szilagyi (2008, 2011) show that financially distressed

stocksthose with higher probabilities of defaulthave generally delivered anomalously low returns

despite having much higher loadings on the HML factor. All these results question the original Fama and

French (1993) conjecture that value is compensation for distress risk.4

Today, the risk-based literature is significantly less specific about the nature of those risks or

their economic interpretation. Various articles propose different risks that may be correlated with value

4One exception is Avramov, Chordia, Jostova, and Philipov (2010), who claim that the value effect emerges from taking long

positions in high credit risk firms that survive financial distress and subsequently realize high returns, but is significa nt only

during stable or improving credit conditions.

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stock returns. However, the academe has not thrown its support behind a particular risk story. The

current consensus is that value stocks have exposure to some hidden risks that are rare, hard to

measure, and even harder to observe. (Some observers point to the resemblance between those types

of risk and Black Swan events.)

The second theory is based on Lakonishok, Shleifer, and Vishny (1994), who point out that

mispricings might be the source of the value premium. They argue that value stocks are not risky but, in

fact, cheap. The value effect, according to this strand of the literature, can be interpreted as driven

primarily by mean reversion in prices.5 Expected returns for stocks are, therefore, time-varying and

predictable, containing an abnormal return driven by mispricing, which can be predicted by valuation

ratios like B/M or dividend yield.

The mispricing theory also faces challenges. First, critics point out that value strategies tend to

experience occasional and persistent periods of underperformance. Supporters of the mispricing theory

would answer that these periods of underperformance happen as prices deviate further from

fundamentals, adding to the attractiveness of value strategies.6The second criticism relates to the fact

that if mispricings are random, then portfolios of over- or undervalued stocks should display much

higher Sharpe ratios as their idiosyncratic movements cancel each other out. The usual answer to this

argument is that stocks are also exposed to other factors that increase their correlations but do not

carry any risk premium. Industry factors are the most common example, because they explain a

significant fraction of the comovement between stocks in the same industry without generating any

differences in expected returns (Fama and French (1997)).

5See Arnott and Hsu (2008) and Arnott, Hsu, Liu, and Markowitz (2011) for examples. See also Vayanos and Woolley (2011) for

a rational model of flows between investment funds to explain momentum and mean reversion in prices.6Some mispricings, such as the dot-com bubble, tend to persist for long periods of time before prices revert back to normal

levels.

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The empirical literature also seems divided between supporters of both theories. Daniel and

Titman (1997) run the first tests using U.S. data from 1973 to 1993 and find empirical support for the

mispricing theory. They show that the higher expected returns of value stocks cannot be explained by

covariation of these stocks with risk factors after controlling for their characteristics. However, Davis,

Fama, and French (2000) extend the U.S. tests back to 1926 and find an improved performance for risk

factors outside the Daniel and Titmans 20-year sample. Because the U.S. data seem to give conflicting

results, researchers have focused on finding new datasets to run out-of-sample robustness checks.

Daniel, Titman, and Wei (2001),Lajili-Jarjir (2007), and Lee, Liu, and Strong (2007) run similar tests on

Japan, France and the UK, respectively. All three studies finding evidence that expected returns are

correlated with characteristics and not with factor loadings, lending increasing support for the

mispricing theory.

In this paper we contribute to the empirical literature by further developing existing tests in a

way that makes them relatively easier to follow, and by applying them on a large cross-section of

countries, which increases their power significantly. Our tests are meant to measure whether the cross-

section of expected returns is better explained by characteristics or factor loadings, but our

interpretation of the results leaves open the possibility that both the risk-based and mispricing theories

contributewith possibly different levels of importanceto the value effect.

3. Testing the Risk-Based and Mispricing Theories

This section describes how we use portfolios sorted on factor loadings and characteristics to test the

predictions from the risk-based and mispricing theories. As we show below, each theory has different

predictions for the expected returns of portfolios with similar HML loadings but different B/M

http://www.tandfonline.com/action/doSearch?action=runSearch&type=advanced&result=true&prevSearch=%2Bauthorsfield%3A(Lajili%5C-Jarjir%2C+Souad)http://www.tandfonline.com/action/doSearch?action=runSearch&type=advanced&result=true&prevSearch=%2Bauthorsfield%3A(Lajili%5C-Jarjir%2C+Souad)

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characteristics, or similar B/M characteristics but different HML loadings. Exploring the different

predictions allow us to better distinguish between the competing theories.

Daniel and Titman (1997) propose a simple test to identify whether expected returns are a

function of the B/M characteristic or the loading on the HML factor. The main challenge with these

types of tests is that HML loading and B/M are correlated across stocks, so one needs to find a large

group of stocks that show significant variation along one dimension but not the other. We first describe

their methodology and then how we adapt it for our purposes.

Daniel and Titmans first step follows Fama and French (1993) and yields nine (3x3) portfolios

sorted on B/M and size (market capitalization). Then, the stocks in each of these 9 portfolios are further

sorted into five portfolios according to their exposure to HML,, resulting in a total of 45 (9x5)portfolios. The idea behind this two-step sorting process is to control for the characteristics of the stocks

in the first step and then to obtain variation in factor loadings in the second step. Finally, the third and

last step is to look at each portfolioand in particular at the spreads between portfolios with extreme

factor loadingsto investigate whether characteristics or factor loadings display a stronger relationship

with expected returns and alphas.

Our tests are very similar to Daniel and Titmans, but we modify and extend them in different

directions. First, we improve the statistical power of the tests by applying the methodology to a

significantly larger cross-section sourced from a large number of countries. Second, because other

countries have fewer stocks than the United States, and because we are mostly interested in controlling

for B/M and not size, our tests include fiveportfolios sorted on B/M instead of only three.7Third, as

explained next, we provide results for two types of tests: in the first one we sort stocks first on

characteristics and then on factor loadings, whereas in the second we sort them first on factor loadings

7As a result, we have 25 (5x5) portfolios instead of 45 (9x5). The smaller number of portfolios is offset by the finer granularity in

the B/M dimension, the most important for our purposes.

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and then on characteristics. Finally, because of the shorter international sample and to increase the

accuracy of factor sensitivity estimation, we use daily data to estimate in the ex-ante portfolioformation stage (more details below).

Figure 1 illustrates our extended version of Daniel and Titmans approach. We construct 25

capitalization-weighted portfolios by forming conditional sorts along two dimensions: HML loading,

, on the horizontal axis, and B/M on the vertical axis. (Each portfolio is numbered according to itsposition in this 5 5 grid.) Because we use conditional sorts, the order in which we sort the variables

matters. We choose to use two separate sorts to guarantee that we have enough stocks in each of the

25 portfolios and, at the same time, to ensure that B/M orare kept constant in the different tests.On the left graph we sort stocks first on B/M and then within each B/M quintile we sort them on .Each row in the grid represents a group of stocks with relatively constant B/M but varying . On theright graph we sort stocks first on and then within each quintile we sort them on B/M. Eachcolumn now represents the opposite: constant but varying B/M.

The focus in this paper is on the return differences between the two extreme portfolios in each

row (left graph: highest minus lowest for each of the five B/M control groups), and in eachcolumn (right graph: highest B/M minus lowest B/M for each of the five control groups). Note thatthe difference portfolios constructed from each row will produce high returns when high-stocksoutperform low- stocks, but will not be sensitive to the performance of high-B/M stocks versuslow-B/M stocks, because each of the five difference portfolios will contain equal positive and negative

weights in stocks with similar B/M characteristic. By the same token, the difference portfolios for each

column will have sensitivity to the performance of high B/M versus low B/M stocks, but otherwise no

sensitivity to the relative performance between high and lowstocks.

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M1(Mispricing 1): [] and () .The second portfolio is called HML factor loading-balanced portfolio and is defined as

[( ) ( ) ( ) ( ) ( )]

(3)

where ( ) is the return of the difference portfolio for column j. This portfolio holds constant and examines the difference in returns between stocks with high B/M versus stocks with low

B/M.

According to the risk-based theory, after controlling for , expected returns should bear norelationship with portfolio B/M. This is graphically illustrated in the left graph in Figure 3. The Carhart

alpha would also be constant as we vary B/M because both the expected return and the risk

adjustments are assumed constant under the risk-based theory. Thus, for the HML factor loading-

balanced portfolio, the expected return and the Carhart alpha should both be zero, resulting in the

following testable predictions:

R2(Risk-based 2): [] and () .According to the mispricing theory, expected returns are an increasing function of B/M. This is

illustrated in the right graph in Figure 3. When we hold constantand, thus, the Carhart riskadjustment is kept constantthe measured Carhart alpha should also be increasing in B/M. These two

observations suggest that the HML factor loading-balanced portfolio should have positive expected

return and Carhart alpha:

M2(Mispricing 2): [] and () .

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With the theoretical predictions established, we proceed now to test them on a large sample of

countries. We emphasize at this point that the predictions from the two theories are very different and

should, therefore, provide us with a powerful framework to check which one finds better support in the

data.

4. Results

This section conducts two tests of the risk-based and mispricing theories. The first test uses portfolios

sorted on factor loadings and characteristics to test the predictions derived in the previous section. The

second test uses FamaMacBeth regression to address the concern that HML factor loadings and B/M

are correlated across stocks. As a preview of our results, the empirical tests provide strong support for

the mispricing theory and reject the risk-based theory as the explanation for value stock

outperformance.

4.1. Portfolio Tests

As explained earlier, our portfolio tests have two stages: ex ante portfolio formation and ex post

performance evaluation. Both stages require us to run factor regressions: (1) we need ex anteestimates

of in the first stage to form the 25 portfolios sorted on factor loadings and characteristics, and (2)we need average returns and alphas for the characteristic- and factor loading-balanced portfolios in the

second stage to test the hypotheses developed in the previous section. In both stages we use Carharts

(1997) four-factor model,8

8More details regarding factor construction can be found in the Appendix.

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( ) (4)where MKT, HML, SMB and UMD are the market, value, size and momentum factors constructed

separately for each country, but we run the regressions at different frequencies in each stage.

In the first stage, portfolio formation, we use dailystock and factor returns over the past two

months to estimate the regression coefficients. One possible criticism regarding this choice is that daily

returns might suffer from a series microstructure and liquidity effects, such as bid-ask spreads, stale

prices or asynchronous response to market (or another factor) movements. We alleviate such concerns

by imposing two restrictions on the stocks included in our tests: requiring that they been traded for at

least 22 trading days within each two-month rolling window and allowing a lag of five trading days

before the end of the month to ensure that this strategy can be implemented in the real world.9,10

After

imposing these liquidity restrictions, we consider that, in our case, the advantages of using daily data in

the first stage more than offset the possible disadvantages. First, it allows us to use the international

sample more efficiently, given its shorter period. Note that two months of daily returns contain more

observations than three years of monthly returns, which is a common choice in the literature. Second,

Merton (1980) argues that the precision of covariance estimates increases with data frequency. Third, if

we suspect that factor loadings can be time-varying, using more recent data in each regression

decreases the persistence in the factor loadings and increases the likelihood that theirex antevalues are

indeed good proxies for their ex postvalues.

In the second stage, ex postportfolio evaluation, we run the same regressions as in Equation (4),

but with monthly stock and factor returns over the entire sample. Notice that the sample size varies

across countries, depending on the availability of data. We prefer monthly regressions in the second

9For instance, at the end of June, we use data from April 26 to June 23 to estimate the factor loadings for the July portfolio.

10To check the robustness of our liquidity screens and of our conclusions, we follow Dimson (1979) and also estimate the factor

loadings in Equation (4) as the sum of coefficients on current and lagged factor returns. The results (not reported in the paper)

remain qualitatively unchanged under this alternative specification.

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stage because they provide a better comparison between our results and previous results in the

literature, which were all executed at the monthly frequency.

For our study we use data from 23 developed countries. Table 1shows the number of stocks

and starting year for each country in our sample. The starting year is selected by identifying the longest

time horizon that contains at least 25 stocks in all months. This guarantees that each of the 25 portfolios

is non-empty. Also, because the characteristic- and factor loading-balanced portfolios are created as a

combination of ten individual portfolios, both contain 40 percent of the total number of stocks at each

point in time, or a minimum of ten stocks. The average number of stocks is 445 and the average starting

year is 1983. Obviously, the number of stocks per country and the time-period of available data vary

substantially. The U.S. sample is an outlier in terms of length and number of socks, as it contains, on

average, 2279 stocks and starts in 1927.

Starting with the predictions from the previous section, Table 2presents the results for the B/M

characteristic-balanced portfolios (Panel A) and the HML factor loading-balanced portfolios (Panel B).

Individual countries provide interesting evidence, but we focus on the aggregated test statistics at the

bottom of the table, because they are more powerful and allow for a more concise discussion around

the results.

The first aggregated test statistic is the averageacross all 23 countriesof alphas and average

returns. This average is simple to calculate, but obtaining its variance (or t-statistic) is relatively more

complicated. Country regressions give us variances for individual alphas, but not the covariances

between them.11

Thus, we follow the procedure described in the Appendix and use Hansens (1982)

Generalized Method of Moments (GMM) to calculate the covariance between country alphas. GMM is a

11More specifically, to calculate the variance of the average alpha, one needs to evaluate

( )

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good choice in this case, because it takes into account the correlation between portfolios and factors of

different countries, addressing the criticism that correlated countries do not add more independent

observationsor more powerto the tests.12

The second aggregated test statistic is the percentage of countries in the sample with positive

(or negative) average returns and alphas. Assuming a binomial distribution for the sign of these

variables, one would need to observe at least 70 percent of the sample with the same sign to reject the

null hypothesis that the mean of the distribution is zero, at the 5 percent significance level.13

Starting with the results for the B/M characteristic-balanced portfolios, we see that the fraction

of positive to negative average returns is 0.57 to 0.43, and only one country shows an average return

that is statistically different from zero. Therefore, we cannot reject the hypothesis that the mean of the

distribution is zero. The average mean return across the 23 countries is 0.79 percent with a t-statistic of

0.84, which is also indistinguishable from zero. Neither test rejects the hypothesis that expected returns

are zero and the tests do not support the alternative claim that [] . In terms of Carhart alpha,we observe that 83 percent of the countries have negative alphas, which is higher than the 70 percent

critical value necessary to reject the hypothesis of zero alpha in favor of the negative alpha hypothesis.

The average mean alpha is 1.74 percent with a t-statistic of 2.09, which again rejects the zero-alpha

hypothesis in favor of the negative-alpha hypothesis.14Our results appear to support (M1) against (R1).

12Because the sample length differs across countries, we are forced to calculate the standard errors for the averages across

countries using only the common sample: 19912010. Notice that the smaller sample decreases the statistical significance of all

our estimates, given the small number of observations, and therefore does not benefit one theory in detriment of the other.

We have calculated averages in the restricted sample (not reported in the tables) and our all conclusions remain unchanged.

13We acknowledge that using the binomial distribution to test the frequency of positive (or negative) values is only an

approximation, but these results are used mainly to confirm the tests for average expected returns and alphas, for which we

have more accurate distributions.14

Alert readers will wonder why the average alpha is statistically different from zero when only one of the alphas is. The answer

is simple: the test portfolios and the factorsand HML in particularare relatively uncorrelated across different countries

(Fama and French, 1998). This property significantly increases the statistical power in cross-country tests. Our interpretation of

this result is that with longer period of available data more countries would show significant alphas. Moreover, the single

significant alpha occurs exactly in the United States, by far our longest sample.

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In our database, we have 84 years of data for the United States, compared with only about 30

years for the majority of the other countries. Because the recent 30-year span may not be deemed

representative of the true underlying riskreturn dynamic, we look to the U.S. results for robustness.

The average return in the United States for the B/M characteristic-balanced portfolio is slightly negative

(0.76 percent), but is not statistically different from zero (t-statistic of 0.74). The alpha is3.17 percent

and is significantly different from zero (t-statistic of 3.18). These results provide additional strong

support for the mispricing theory (M1) versus the risk-based theory (R1). Our results contradict the

evidence presented in Davis, Fama, and French (2000); we attribute this difference in results to our

application of daily data to estimate

, which we believe results in more accurate ex-ante

measurement of HML loading.

Turning our attention to the results for the HML factor loading-balanced portfolios, we note that

the average returns are positive for 100 percent of the countries in our sample. The average mean

return is 7.61 percent with a t-statistic of 4.65, which provides strong support for the mispricing theory

(M2). The results for Carhart alphas also provide strong support for the mispricing theory, with positive

returns in 87 percent of the countries and a statistically significant average alpha of 3.01 percent. These

results strongly support the mispricing theory (M2) against the risk-based theory (R2).

The results for the United States further support the overall conclusion that M2 is more

descriptive of the data than R2. The average return is 7.20 percent with a t-statistic of 3.94. The alpha is

also positive at 1.29 percent with a t-statistic of 1.71, which is significant at the 10 percent level, though

not at the 5 percent level.

The results for portfolios sorted on factor loadings and characteristics strongly favor the

mispricing theory over the risk-based theory. Nonetheless, we acknowledge that skeptics could still

argue that the double-sorting method only partially controls for the high correlation between B/M and

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HML loading for stocks. Given the controversy surrounding the source of the value premium, we believe

additional evidence is needed to strengthen the claim that mispricing is the more credible explanation.

4.2. Fama-MacBeth Tests

The ordinary least squares (OLS) regression provides a robust way to address the above skepticism. In

the regression

, (5)where the resulting coefficients,and , explain, by construction, the independenteffects of andon . In other words, the relationship between and , given by , is estimated above and beyondany relationship between and . The same observation is also true for

Now consider a joint cross-sectional regression of stocks expected returns on their B/M

characteristics and HML loadings:

. (6)Notice that the loading on the HML factor,, is now the explanatory variable, and the estimatedcoefficientthe risk premiumis given by . Notice also that we model the relationship betweenexpected returns and B/M in logs, a common practice in finance research.15Regression (6) allows us to

do a horse race between the risk-based and the mispricing theories, measuring which one of orB/M has more explanatory power on expected stock returns in the cross-section, above and beyond the

other.

15See, among others, Fama and French (2008).

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The methodology developed by Fama and MacBeth (1973) takes this idea as a starting point and

expands it across multiple time periods. Running the regression in Equation (6) for multiple time

periods,

, (7)we obtain a time-series of the independent relationships between or and stocksreturns. Therefore, we can look at the average values ofand over time and make relevantcomparisons on their signs, magnitudes, and statistical significances. See the Appendix for details.

Table 3 presents results from two specifications of FamaMacBeth regressions on individual stocks.

Similar to Table 2, it also shows aggregated test statistics calculated from the 23 countries.16

The first

regression includes only the factor loadings on the four Carhart factors considered,

, (8)and tells us how differences in loadings on the value factor (HML) explain differences in expected

returns. The second, and more interesting, regression includes all four factor loadings plus the three

characteristics related to value, size, and momentum:

()

(9)

Notice that we also use logs to adjust the size characteristic, and that we invert its sign to obtain a

positive relationship with expected returns. Although we are not interested in the magnitude of

16Similar to the portfolio tests, we are forced to calculate the variance of the average premiums across countries using only the

common years, 19912010, because of the different sample lengths. Notice that the smaller sample decreases the statistical

significance of all our estimates, given the small number of observations, and therefore does not benefit one theory in

detriment of the other. We have calculated averages in the restricted sample (not reported in the tables) and our all

conclusions remain unchanged.

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5. Conclusion

In this study, we use two distinct econometric tests to distinguish between the two competing

theories to explain value premium: the risk-based and the mispricing theories. First, we extend the

method of Daniel and Titman (1997). Second, we apply the Fama and MacBeth (1973) method for

estimating premiums associated with sources of returns. We add more power to these tests by using a

large cross-section of countries. In both cases, we find strong support for the mispricing theory.

Specifically, using both methods we find that after controlling for B/M characteristic, HML loading

explains only a small fraction of the cross-section of expected returns. On the other hand, after

controlling for HML loading, B/M characteristic still remains the most important variable for explaining

the cross-section of expected returns.

While we are careful not to outright reject the claim that value premium is compensation for

risk, we do conclude that mispricing is responsible for a larger component of the value premium. This

conclusion has very important implications for portfolio management and performance attribution. It

suggests a less important role for risk as an explanation of the outperformance of value stocks, and that

investors should therefore benefit from a higher allocation to value strategies. It also suggests that

traditional factor-based benchmarking, like the FamaFrench 3-factor and Carhart 4-factor models, may

be inadequate or limited as means of doing performance measurement or attribution.

significant and becomes indistinguishable from zero only in Panel B, after the characteristics are included in the regression.

Moreover, as stressed by Daniel and Titman (1999), the errors-in-variable problem does not affect our conclusions from the

previous section, because the factor loadings are never used as second stage explanatory variables.

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References

Arnott, Robert D., and Jason C. Hsu. 2008. Noise, CAPM and the Size and Value ffects.Journal of

Investment Management, vol. 6, no. 1 (First Quarter):1-11.

Arnott, Robert D., Jason C. Hsu, Jun Liu, and Harry Markowitz. 2011. Can Noise Create the Size and

Value ffects? Working paper, University of California at San Diego and Research Affiliates.

Avramov, Doron, Tarun Chordia, Gergana Jostova, and Alexander Philipov. 2010. Anomalies and

Financial Distress. Unpublished working paper.

Campbell, John Y., Jens Hilscher, and Jan Szilagyi. 2008. In Search of Distress Risk.Journal of Finance,

vol. 63, no. 6 (December):2899-2939.

Campbell, John Y., Jens Hilscher, and Jan Szilagyi. 2011. Predicting Financial Distress and the

Performance of Distressed Stocks.Journal of Investment Management, vol. 9, no. 2 (Second

Quarter):14-34.

Carhart, Mark M. 1997. On Persistence in Mutual Fund Performance.Journal of Finance, vol. 52, no. 1

(March):5782.

Daniel, Kent, Mark Grinblatt, Russ Wermers, and Sheridan Titman. 1997. Measuring Mutual Fund

Performance with Characteristic-Based Benchmarks.Journal of Finance, vol. 52, no. 3 (July):10351058.

Daniel, Kent, and Sheridan Titman. 1997. vidence on the Characteristics of Cross Sectional Variation in

Stock Returns.Journal of Finance, vol. 52, no. 1 (March):133.

Daniel, Kent, and Sheridan Titman. 1999. Sorting Out Sorting Out Sorts. Unpublished working paper.

Daniel, Kent, Sheridan Titman, and K.C. J. Wei. 2001. xplaining the Cross-Section of Stock Returns in

Japan: Factors or Characteristics?Journal of Finance, vol. 56, no. 2 (April):743766.

Daniel, Kent D., David Hirshleifer, and Avanidhar Subrahmanyam. 2001. Overconfidence, Arbitrage, and

quilibrium Asset Pricing.Journal of Finance, vol. 56, no. 3 (June): 921965.

Davis, James L., ugene F. Fama, and Kenneth R. French. 2000. Characteristics, Covariances, and

Average Returns: 19291997.Journal of Finance, vol. 55, no. 1 (February):389406.

Dimson, Elroy. 1979. Risk Measurement when Shares Are Subject to Infrequent Trading.Journal of

Financial Economics, vol. 7, no2. (June):197226.

Dichev, Ilia D. 1998. Is the Risk of Bankruptcy a Systematic Risk?Journal of Finance, vol. 53, no. 3

(June):11311147.

Fama, ugene F., and Kenneth R. French. 1992. The Cross-Section of xpected Stock Returns.Journal

of Finance, vol. 47, no. 2 (June):427465.

8/12/2019 SSRN-id1940504

22/31

22

Fama, Eugene F., and Kenneth R. French. 1993. Common Risk Factors in the Returns on Stocks and

Bonds.Journal of Financial Economics, vol. 33, no. 1 (February):356.

Fama, Eugene F., and Kenneth R. French. 1997. Industry Costs of Equity.Journal of Financial

Economics, vol. 43, no. 2 (February):153193.

Fama, Eugene F., and Kenneth R. French. 1998. Value Versus Growth: The International Evidence.

Journal of Finance, vol. 53, no. 6 (December):19751999.

Fama, Eugene F., and Kenneth R. French. 2008. Dissecting Anomalies.Journal of Finance, vol. 63, no.4

(August):16531678.

Fama, ugene F., and James D. MacBeth. 1973. Risk, Return, and quilibrium: mpirical Tests.Journal

of Political Economy, vol. 81, no. 3 (May/June):607636.

Graham, Benjamin, and David Dodd. 1934. Security Analysis. New York: McGraw-Hill.

Griffin, John M., and Michael L. Lemmon. 2002. Book-to-Market Equity, Distress Risk, and Stock

Returns.Journal of Finance, vol. 57, no. 5 (October):23172336.

Hansen, Lars Peter. 1982. Large Sample Properties of Generalized Method of Moment Estimators.

Econometrica, vol. 50, no. 4 (July):10291054.

Lajili-Jarjir,Souad. 2007. xplaining the Cross-section of Stock Returns in France: Characteristics or Risk

Factors? European Journal of Finance, vol. 13, no. 2:145158.

Lakonishok, Josef, Andrei Shleifer, and Robert W. Vishny. 1994. Contrarian Investment, xtrapolation,

and Risk.Journal of Finance, vol. 49, no. 5 (December):15411578

Lee, dward, Weimin Liu, and Norman Strong. 2007. UK vidence on the Characteristics versus

Covariance Debate. European Financial Management, vol. 13, no. 4 (September):742756.

Merton, Robert C. 1973. An Intertemporal Capital Asset Pricing Model. Econometrica, vol. 41, no. 5

(September):867887.

Merton, Robert C. 1980. On stimating the xpected Return on the Market: An xploratory

Investigation.Journal of Financial Economics, vol. 8, no. 4 (December):323361.

Miller, Merton H., and Myron Scholes. 1972. Rate of Return in Relation to Risk: A Re-Examination of

Some Recent Findings. in Michael C. Jenesen, ed.:Studies in the Theory of Capital Markets: 47-48(Praeger Publishers: New York).

Shumway, Tyler. 1996. Size, Overreaction, and Book-to-Market ffect as Default Premia. Working

paper, University of Michigan.

Vayanos, Dimitri, and Paul Woolley. 2011. An Institutional Theory ofMomentum and Reversal.

Unpublished working paper.

http://www.tandfonline.com/action/doSearch?action=runSearch&type=advanced&result=true&prevSearch=%2Bauthorsfield%3A(Lajili%5C-Jarjir%2C+Souad)http://www.tandfonline.com/action/doSearch?action=runSearch&type=advanced&result=true&prevSearch=%2Bauthorsfield%3A(Lajili%5C-Jarjir%2C+Souad)

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Appendix I. Data Description and Factor Construction

For the United States, we use daily and monthly stock returns and annual financial data from the Center

for Research in Security Prices (CRSP) and Compustat. The sample period is January 1926 to December

2010, and only ordinary common shares (as classified by CRSP) are included in our tests. The book equity

data is supplemented by the historical Moodys Manuals values from Kenneth R. Frenchs data library as

in Davis, Fama, and French (2000) whenever it is not available in Compustat. We use the one-month U.S.

Treasury bill rate from Ibbotson Associates as the risk-free rate.

The source for return and accounting data for the other 22 developed countries is Datastream

and Worldscope. The sample period starts in January 1980 to November 1994, depending on individual

countries, and ends in December 2010. All ADRs (as classified by Worldscope) are excluded. Returns are

in U.S. dollars and the risk-free rate is the one-month U.S. Treasury bill rate. One caveat is that

Datastream posts daily returns for non-trading days as well. They use the annualized dividend yield and

the adjusted price (padded), hence there is usually a value given for holidays such as January 1. Thus, we

remove records for a certain day if daily returns are zero for most of the securities within each country.

The construction of the factor portfolios primarily follows Fama and French (1993) and Carhart

(1997). We sort stocks on size (market capitalization) and the ratio of book equity to market equity

(B/M), and form six portfolios (Small Value, Small Neutral, Small Growth, Big Value, Big Neutral, and Big

Growth.) B/M is calculated as book equity for the fiscal year ending in calendar year t1, divided by

market equity at the end of December of year t1. The B/M is used to annually construct the portfolios

at the end of June of year t. We exclude negative book equity firms, and leave out companies until they

have appeared on Compustat or Worldscope for two years to avoid the survivorship bias in the way

those vendors add firms to the data.

For the United States we use NYSE median values (size) and 70thand 30thpercentiles (B/M) from

Ken Frenchs data library as breakpoints. For international stocks, the breakpoints are the 80th

percentile

for size, and 70th

and 30th

percentiles for B/M. We calculate the SMB and HML factors as follows:

SMB = 1/3 (Small Value + Small Neutral + Small Growth) - 1/3 (Big Value + Big Neutral + Big

Growth)

HML = 1/2 (Small Value + Big Value) - 1/2 (Small Growth + Big Growth)

The excess return on the market (MktRf) is the value-weighted return on all stocks including negative

BE firms minus the risk-free rate.

We also form six value-weighted portfolios based on size and cumulative return over prior 12

months excluding the most recent month (Small Up, Small Medium, Small Down, Big Up, Big Medium,

and Big Down). We use the breakpoints from Ken Frenchs data library for the United States, and the

80th(size) and 70th/30th(prior return) percentiles for the other countries. To be included in a portfolio

for month t(formed at the end of the month t1), a stock must have a return for month t12 and t2.

The momentum factor is constructed monthly as follows:

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UMD = 1/2 (Small Up + Big Up) - 1/2(Small Down + Big Down)

Appendix II. Fama and MacBeth (1973) Regressions

We estimate the premia of the four factors and stock characteristics by using FamaMacbeth two-stage

regressions. First, we find estimates of the factor loadings of each stock from time series regressions

with the Carhart four-factor model as in the portfolio tests. Second, we run monthly cross-sectional

regression of returns on risk exposures and/or characteristics. Finally, we estimate the premium, of

each factor or characteristic as the time series average of the cross-sectional regression estimates:

where Tis the number of months in the period.

The t-statistic of the premium is calculated as follows:

( ) where is the standard deviation of the monthly estimates.Appendix III. GMM Standard Errors

For each country

we run the following factor regression:

, (A1)where and umd .Following Cochrane (2005), we can write each country regression as a set of GMM moment conditions,

[ ] . (A2)Solving this equation yields the same result as traditional OLS,

[ ][ ], (A3)showing that GMM and OLS give us the same coefficients in this case.

Because we want to find the covariances between the coefficients of different countries, we

stack their regressions (or moments) together. The tests in this article involve only the alphas, so we are

interested only in the columns and rows related to them.

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The notation with multiple countries becomes cumbersome quickly. For this reason, here we

solve an example with two countries only. The general case is exactly the same with multiple columns

and rows. The stacked moment conditions for countries 1 and 2 are

, (A4)

where .Hansen (1982) shows that the covariance matrix of is given by

. (A5)In this case is equal to

(A6)

and is block-diagonal: . (A7)

We use no leads or lags in the calculation of because, in our case, the residuals come frommonthly returns, which show very little serial correlation. In other words, the formulas above correct

only for the more important cross-sectional correlation between residuals (and factors) of different

countries.

To confirm that the variance formula (A5) is a generalization of the OLS formula, consider again

the case of one country. Using the usual OLS assumptions that a) the residuals are homoscedastic and

uncorrelated over time, and b) the factors and residuals are independent as well as uncorrelated we

obtain

[ ] [ ] [ ] [ ] [ ] () (A8)which is the traditional OLS formula for the variance of the coefficients.

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Table 1Number of Stocks and Starting Year 23 Developed Countries Sample Summary

CountryMinimum

number of stocks

Average

number of stocks

Maximum

number of stocks

Starting

Year

Australia 66 525 1727 1982

Austria 25 76 107 1987

Belgium 25 109 148 1987

Canada 122 699 2207 1982

Denmark 26 145 217 1986

Finland 32 97 141 1990

France 83 487 842 1982

Germany 83 489 891 1982

Greece 30 182 298 1989

Hong Kong 25 383 977 1991

Ireland 27 57 74 1985

Italy 29 178 286 1982

Japan 321 2156 3849 1982

Netherlands 39 139 221 1982

New Zealand 26 70 144 1990Norway 28 124 209 1987

Portugal 25 58 99 1989

Singapore 28 238 601 1988

Spain 33 120 155 1988

Sweden 29 202 424 1985

Switzerland 26 168 277 1982

United Kingdom 261 1247 2036 1982

United States 425 2279 5645 1927

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Table 2Expected Returns and Alphas for Characteristic-Balanced and Factor Loading-Balanced Portfolios

Country

Panel A: Characteristic-Balanced Portfolios Panel B: Factor Loading-Balanced Portfolios

Ann. Mean

(%) t-stat

Ann. Alpha

(%) t-stat

Ann. Mean

(%) t-stat

Ann. Alpha

(%) t-stat

Australia 3.89 1.47 -2.60 -0.97 4.23 1.65 -2.40 -1.13

Austria 4.52 1.28 1.03 0.29 11.11 3.01 5.02 1.59

Belgium -2.47 -0.74 -5.84 -1.79 3.38 1.33 0.63 0.28

Canada -2.98 -0.90 -5.80 -1.83 9.73 3.45 2.84 1.37

Denmark -3.33 -1.13 -5.37 -1.77 7.12 2.32 5.85 2.29

Finland 2.51 0.54 -0.64 -0.15 7.30 1.36 2.24 0.55

France -1.73 -0.70 -1.79 -0.80 10.21 3.82 3.35 1.72

Germany 3.78 1.54 -0.35 -0.15 7.96 3.09 4.73 2.50

Greece 5.16 1.27 1.48 0.39 6.44 1.46 -0.68 -0.21

Hong Kong 9.66 2.31 4.71 1.30 8.80 2.21 2.25 0.92

Ireland -1.38 -0.27 -3.08 -0.61 9.31 1.92 6.52 1.51Italy -3.25 -1.26 -3.41 -1.36 4.04 1.59 1.49 0.75

Japan 2.65 1.08 -2.10 -0.99 8.56 3.26 1.59 1.18

Netherlands 0.16 0.05 -0.34 -0.12 3.50 1.35 1.85 0.81

New Zealand 1.00 0.23 -0.14 -0.03 0.68 0.16 2.60 0.63

Norway 1.93 0.44 0.12 0.03 4.40 1.04 -2.70 -0.77

Portugal -0.55 -0.13 -2.74 -0.65 23.81 2.02 13.26 1.31

Singapore 0.49 0.16 -2.07 -0.74 7.39 2.31 1.04 0.50

Spain -1.60 -0.56 -2.39 -0.86 9.41 3.08 7.83 2.92

Sweden 1.80 0.53 -0.02 -0.01 3.60 0.99 0.87 0.32

Switzerland -1.60 -0.68 -3.57 -1.50 9.99 4.72 9.27 4.91

United Kingdom 0.31 0.16 -1.97 -1.03 6.87 3.26 0.40 0.28

United States -0.76 -0.74 -3.17 -3.18 7.20 3.94 1.29 1.71

% Positive 57 17 100 87

% Pos. Significant 4 0 57 17

% Negative 43 83 0 13

% Neg. Significant 0 4 0 0

Average 0.79 -1.74 7.61 3.01

(t-stat) (0.84) (-2.09) (4.65) (4.02)

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Panel B: Factor Loadings + Characteristics

Factor Loadings Characteristics

CountryIntercept

(%)

Market(%) Size(%) Value(%) Mom(%) Size-log(Size) (%) Valuelog(B/M) (%) MomUMD (%)Australia

2.49 0.09 -0.07 0.08 0.14 0.28 0.36 1.10(4.87) (0.42) (-0.58) (0.86) (1.01) (3.87) (2.83) (4.88)

Austria0.58 -0.59 0.21 -0.28 0.29 -0.09 0.52 1.25

(0.98) (-1.34) (0.64) (-0.93) (1.09) (-0.96) (3.32) (1.11)

Belgium1.65 0.08 -0.22 -0.19 -0.57 0.19 0.28 2.25

(2.47) (0.28) (-1.18) (-0.85) (-2.27) (1.55) (0.93) (4.36)

Canada3.55 0.03 -0.09 0.02 0.37 0.51 0.06 0.83

(6.15) (0.14) (-0.53) (0.07) (1.63) (6.53) (0.42) (4.30)

Denmark1.47 0.41 0.39 0.40 0.11 0.24 0.31 1.10

(2.40) (1.14) (1.62) (1.62) (0.41) (2.23) (1.23) (2.85)

Finland1.67 -0.48 -0.30 0.08 0.33 0.17 0.37 0.50

(2.68) (-1.04) (-1.19) (0.25) (0.78) (1.70) (2.82) (1.10)

France2.08 0.18 -0.26 -0.01 -0.15 0.19 0.47 0.82

(4.80) (0.97) (-2.34) (-0.07) (-1.07) (3.36) (5.51) (3.72)

Germany1.14 -0.22 -0.01 0.13 -0.09 0.07 0.17 1.39

(3.65) (-1.31) (-0.17) (1.45) (-0.71) (2.04) (3.05) (5.79)

Greece

3.06 0.03 -0.49 0.02 0.14 0.41 0.20 0.57

(2.92) (0.08) (-1.96) (0.08) (0.44) (2.54) (0.77) (1.11)

Hong Kong3.78 0.34 -0.36 0.19 -0.07 0.50 0.33 0.66

(4.91) (1.02) (-1.90) (0.94) (-0.32) (4.08) (2.67) (2.03)

Ireland1.67 0.23 -0.56 -0.04 -0.58 0.19 0.09 1.02

(2.02) (0.54) (-1.67) (-0.12) (-1.09) (1.39) (0.50) (1.60)

Italy0.80 0.18 -0.15 -0.09 0.01 0.06 0.15 1.12

(1.82) (0.72) (-1.33) (-0.72) (0.07) (1.01) (1.30) (3.85)

Japan1.76 0.30 -0.12 0.09 -0.01 0.17 0.36 -0.19

(3.05) (1.73) (-1.85) (1.19) (-0.07) (2.61) (4.98) (-0.80)

Netherlands1.33 -0.14 -0.25 -0.07 -0.51 0.06 0.18 1.92

(3.03) (-0.67) (-2.07) (-0.45) (-2.61) (1.10) (2.00) (6.23)

New Zealand1.65 0.12 -0.01 0.45 0.24 0.26 -0.18 1.49

(2.48) (0.24) (-0.04) (1.35) (0.57) (2.14) (-0.80) (2.69)

Norway 2.01 0.20 -0.19 -0.30 -0.49 0.22 0.43 1.54(3.16) (0.54) (-0.59) (-0.92) (-1.35) (1.86) (2.20) (4.38)

Portugal2.17 0.48 -1.07 -0.56 -0.80 0.23 1.46 -0.61

(2.70) (0.72) (-2.12) (-0.91) (-1.14) (1.19) (1.79) (-0.71)

Singapore1.12 0.62 -0.08 -0.19 -0.06 0.20 0.52 0.37

(1.78) (2.43) (-0.61) (-1.10) (-0.36) (1.99) (2.86) (0.74)

Spain0.70 -0.28 0.07 0.09 -0.01 0.01 0.09 1.19

(1.37) (-0.96) (0.42) (0.56) (-0.05) (0.08) (0.87) (2.91)

Sweden1.92 -0.33 0.03 -0.07 -0.46 0.18 0.14 1.30

(3.32) (-1.12) (0.15) (-0.34) (-1.75) (1.93) (1.18) (3.34)

Switzerland0.93 -0.07 -0.11 -0.20 -0.19 0.03 0.21 1.27

(2.41) (-0.29) (-0.85) (-1.73) (-1.27) (0.56) (3.53) (4.17)

United Kingdom1.26 0.35 -0.19 0.06 -0.09 0.16 0.23 0.91

(3.56) (2.74) (-2.49) (1.25) (-1.02) (3.54) (4.10) (4.60)United States

3.07 -0.07 -0.03 -0.02 -0.02 0.21 0.23 0.58

(6.23) (-1.15) (-1.45) (-0.64) (-0.49) (5.54) (4.90) (3.33)

% Positive 48 96

% Pos. Significant 0 57

% Negative 52 4

% Neg. Significant 0 0Average 1.79 0.10 -0.18 -0.04 -0.12 0.20 0.33 0.97(t-stat) (5.95) (0.49) (-2.66) (-0.27) (-1.00) (5.29) (5.24) (4.78)

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Figure 1 - Portfolios

(1,1) (1,2) (1,3) (1,4) (1,5)

(2,1) (2,2) (2,3) (2,4) (2,5)

(3,1) (3,2) (3,3) (3,4) (3,5)

(4,1) (4,2) (4,3) (4,4) (4,5)

(5,1) (5,2) (5,3) (5,4) (5,5)

B/M B/M

(5,1) (5,2) (5,3) (5,4) (5,5)

(4,1) (4,2) (4,3) (4,4) (4,5)

(3,1) (3,2) (3,3) (3,4) (3,5)

(2,1) (2,2) (2,3) (2,4) (2,5)

(1,1) (1,2) (1,3) (1,4) (1,5)

Sorting first on B/M then on Sorting first on then on B/M

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Figure 2Predictions from Risk-Based and Mispricing Theories for the Experiment of Holding B/M Constant and

Varying .

Figure 3Predictions from Risk-Based and Mispricing Theories for the Experiment of Holding Constant andVarying B/M.

Predictions from the Risk Exposure Theory Predictions from the Mispricing Theory

B/M

Predictions from the Risk Exposure Theory Predictions from the Mispricing Theory

B/M