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Empirical asset pricing the cross section of stock returns


Table of Contents
Cover
Title Page
Copyright
Dedication
Preface
References
Part I: Statistical Methodologies
Chapter 1: Preliminaries
1.1 Sample
1.2 Winsorization and Truncation
1.3 Newey and West (1987) Adjustment
1.4 Summary
References
Chapter 2: Summary Statistics
2.1 Implementation
2.2 Presentation and Interpretation
2.3 Summary
Chapter 3: Correlation
3.1 Implementation

3.2 Interpreting Correlations
3.3 Presenting Correlations
3.4 Summary
References
Chapter 4: Persistence Analysis
4.1 Implementation
4.2 Interpreting Persistence
4.3 Presenting Persistence
4.4 Summary
References
Chapter 5: Portfolio Analysis
5.1 Univariate Portfolio Analysis
5.2 Bivariate Independent-Sort Analysis
5.3 Bivariate Dependent-Sort Analysis


5.4 Independent Versus Dependent Sort
5.5 Trivariate-Sort Analysis
5.6 Summary
References
Chapter 6: Fama and Macbeth Regression Analysis
6.1 Implementation
6.2 Interpreting FM Regressions
6.3 Presenting FM Regressions
6.4 Summary
References
Part II: The Cross Section of Stock Returns
Chapter 7: The Crsp Sample and Market Factor
7.1 The U.S. Stock Market
7.2 Stock Returns and Excess Returns
7.3 The Market Factor
7.4 The Capm Risk Model
7.5 Summary
References
Chapter 8: Beta
8.1 Estimating Beta
8.2 Summary Statistics
8.3 Correlations
8.4 Persistence
8.5 Beta and Stock Returns


8.6 Summary
References
Chapter 9: The Size Effect
9.1 Calculating Market Capitalization
9.2 Summary Statistics
9.3 Correlations
9.4 Persistence
9.5 Size and Stock Returns
9.6 The Size Factor
9.7 Summary
References


Chapter 10: The Value Premium
10.1 Calculating Book-to-Market Ratio
10.2 Summary Statistics
10.3 Correlations
10.4 Persistence
10.5 Book-to-Market Ratio and Stock Returns
10.6 The Value Factor
10.7 The Fama and French Three-Factor Model
10.8 Summary
References
Chapter 11: The Momentum Effect
11.1 Measuring Momentum
11.2 Summary Statistics
11.3 Correlations
11.4 Momentum and Stock Returns
11.5 The Momentum Factor
11.6 The Fama, French, and Carhart Four-Factor Model
11.7 Summary
References
Chapter 12: Short-Term Reversal
12.1 Measuring Short-Term Reversal
12.2 Summary Statistics
12.3 Correlations
12.4 Reversal and Stock Returns
12.5 Fama–Macbeth Regressions
12.6 The Reversal Factor
12.7 Summary
References
Chapter 13: Liquidity
13.1 Measuring Liquidity
13.2 Summary Statistics
13.3 Correlations
13.4 Persistence
13.5 Liquidity and Stock Returns
13.6 Liquidity Factors


13.7 Summary
References
Chapter 14: Skewness
14.1 Measuring Skewness
14.2 Summary Statistics
14.3 Correlations
14.4 Persistence
14.5 Skewness and Stock Returns
14.6 Summary
References
Chapter 15: Idiosyncratic Volatility
15.1 Measuring Total Volatility
15.2 Measuring Idiosyncratic Volatility
15.3 Summary Statistics
15.4 Correlations
15.5 Persistence
15.6 Idiosyncratic Volatility and Stock Returns
15.7 Summary
References
Chapter 16: Liquid Samples
16.1 Samples
16.2 Summary Statistics
16.3 Correlations
16.4 Persistence
16.5 Expected Stock Returns
16.6 Summary
References
Chapter 17: Option-Implied Volatility
17.1 Options Sample
17.2 Option-Based Variables
17.3 Summary Statistics
17.4 Correlations
17.5 Persistence
17.6 Stock Returns
17.7 Option Returns


17.8 Summary
References
Chapter 18: Other Stock Return Predictors
18.1 Asset Growth
18.2 Investor Sentiment
18.3 Investor Attention
18.4 Differences of Opinion
18.5 Profitability and Investment
18.6 Lottery Demand
References
Index
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List of Illustrations
Chapter 7: The Crsp Sample and Market Factor
Figure 7.1 Number of Stocks in CRSP Sample by Exchange
Figure 7.2 Value of Stocks in CRSP Sample by Exchange
Figure 7.3 Number of Stocks in CRSP Sample by Industry
Figure 7.4 Value of Stocks in CRSP Sample by Industry
Figure 7.5 Cumulative Excess Returns of
Chapter 9: The Size Effect
Figure 9.1 Percent of Total Market Value Held by Largest Stocks
Figure 9.2 Cumulative Returns of

Portfolio

Chapter 10: The Value Premium
Figure 10.1 Cumulative Returns of HML Portfolio. This Figure plots the
cumulate returns of the
factor for the period from July 1926 through
December 2012. The compounded excess return for month is calculated as 100
times the cumulative product of one plus the monthly return up to and including
the given month. The cumulate log excess return is calculated as the sum of the
monthly log excess returns up to and including the given month
Chapter 11: The Momentum Effect
Figure 11.1 Cumulative Returns of MOM Portfolio.This Figure plots the
cumulate returns of the
factor for the period from January 1927 through
December 2012. The compounded excess return for month is calculated as 100


times the cumulative product of one plus the monthly return up to and including
the given month. The cumulate log excess return is calculated as the sum of the
monthly log excess returns up to and including the given month
Chapter 12: Short-Term Reversal
Figure 12.1 Cumulative Returns of STR Portfolio.This Figure plots the
cumulate returns of the
factor for the period from July 1926 through
December 2012. The compounded excess return for month is calculated as 100
times the cumulative product of one plus the monthly return up to and including
the given month. The cumulate log excess return is calculated as the sum of the
monthly log excess returns up to and including the given month
Chapter 13: Liquidity
Figure 13.1 Time-Series Plot of
. This Figure plots the values of
, a measure of aggregate stock market liquidity, for the period from August
1962 through December 2012
Figure 13.2 Time-Series Plot of Lm. This Figure plots the values of , a measure
of aggregate stock market liquidity, for the period from August 1962 through
December 2012
Figure 13.3 Cumulative Returns of PSL Portfolio. This Figure plots the
cumulate returns of the
factor for the period from January 1968 through
December 2012. The compounded excess return for month is calculated as 100
times the cumulative product of one plus the monthly return up to and including
the given month. The cumulate log excess return is calculated as the sum of the
monthly log excess returns up to and including the given month
Chapter 15: Idiosyncratic Volatility
Figure 15.1 Cumulative Returns of Low–High
Portfolio. This
Figure plots the cumulate returns of the decile one minus decile 10
value-weighted portfolio for the period from July 1963 through December 2012.
The compounded excess return for month is calculated as 100 times the
cumulative product of one plus the monthly return up to and including the given
month. The cumulate log excess return is calculated as the sum of monthly log
excess returns up to and including the given month.

List of Tables
Chapter 2: Summary Statistics
Table 2.1 Annual Summary Statistics for This Table presents summary statistics
for for each year during the sample period. For each year , we calculate the
mean (
), standard deviation (
), skewness (
), excess kurtosis (
),


minimum (
), fifth percentile ( ), 25th percentile (
), median (
),
75th percentile (
), 95th percentile (
), and maximum (
) values of the
distribution of across all stocks in the sample. The sample consists of all U.S.based common stocks in the Center for Research in Security Prices (CRSP)
database as of the end of the given year and covers the years from 1988 through
2012. The column labeled indicates the number of observations for which a
value of is available in the given year
Table 2.2 Average Cross-Sectional Summary Statistics for This Table presents
the time-series averages of the annual cross-sectional summary statistics for .
The Table presents the average mean (
), standard deviation ( ), skewness (
), excess kurtosis (
), minimum (
), fifth percentile ( ), 25th percentile
(
), median (
), 75th percentile (
), 95th percentile (
), and maximum
(
) values of the distribution of , where the average is taken across all years in
the sample. The column labeled indicates the average number of observations
for which a value of is available
Table 2.3 Summary Statistics for ,
, and
This Table presents summary
statistics for our sample. The sample covers the years from 1988 through 2012,
inclusive, and includes all U.S.-based common stocks in the CRSP database. Each
year, the mean (
), standard deviation ( ), skewness (
), excess kurtosis (
), minimum (
), fifth percentile (5%), 25th percentile (25%), median (
), 75th percentile (75%), 95th percentile (95%), and maximum (
) values of the
cross-sectional distribution of each variable are calculated. The Table presents the
time-series means for each cross-sectional value. The column labeled indicates
the average number of stocks for which the given variable is available. is the beta
of a stock calculated from a regression of the excess stock returns on the excess
market returns using all available daily data during year .
is the market
capitalization of the stock calculated on the last trading day of year and recorded
in $millions.
is the natural log of
.
is the ratio of the book value of
equity to the market value of equity.
is the one-year-ahead excess stock return
Chapter 3: Correlation
Table 3.1 Annual Correlations for ,
,
, and
This Table presents the
cross-sectional Pearson product–moment ( ) and Spearman rank ( )
correlations between pairs of ,
,
, and
. Each column presents either the
Pearson or Spearman correlation for one pair of variables, indicated in the column
header. Each row represents results from a different year, indicated in the column
labeled
Table 3.2 Average Correlations for ,
,
, and
This Table presents the
time-series averages of the annual cross-sectional Pearson product–moment ( )
and Spearman rank ( ) correlations between pairs of ,
,
, and
. Each


column presents either the Pearson or Spearman correlation for one pair of
variables, indicated in the column header
Table 3.3 Correlations Between ,
,
, and
This Table presents the timeseries averages of the annual cross-sectional Pearson product–moment and
Spearman rank correlations between pairs of ,
,
, and
. Below-diagonal
entries present the average Pearson product–moment correlations. Above-diagonal
entries present the average Spearman rank correlation
Chapter 4: Persistence Analysis
Table 4.1 Annual Persistence of This Table presents the cross-sectional Pearson
product–moment correlations between measured in year and measured in
year
for
. The first column presents the year . The subsequent
columns present the cross-sectional correlations between measured at time
and measured at time
,
,
,
, and
Table 4.2 Average Persistence of This Table presents the time-series averages of
the cross-sectional Pearson product–moment correlations between measured in
year and measured in year
for
Table 4.3 Persistence of ,
, and
This Table presents the results of
persistence analyses of ,
, and
. For each year , the cross-sectional
correlation between the given variable measured at time and the same variable
measured at time
is calculated. The Table presents the time-series averages of
the annual cross-sectional correlations. The column labeled indicates the lag at
which the persistence is measured
Chapter 5: Portfolio Analysis
Table 5.1 Univariate Breakpoints for -Sorted Portfolios This Table presents
breakpoints for -sorted portfolios. Each year , the first ( ), second ( ), third
( ), fourth ( ), fifth ( ), and sixth ( ) breakpoints for portfolios sorted on
are calculated as the 10th, 20th, 40th, 60th, 80th, and 90th percentiles,
respectively, of the cross-sectional distribution of . Each row in the Table
presents the breakpoints for the year indicated in the first column. The subsequent
columns present the values of the breakpoints indicated in the first row
Table 5.2 Number of Stocks per Portfolio This Table presents the number of stocks
in each of the portfolios formed in each year during the sample period. The column
labeled indicates the year. The subsequent columns, labeled
for
present the number of stocks in the th portfolio
Table 5.3 Univariate Portfolio Equal-Weighted Excess Returns This Table presents
the one-year-ahead excess returns of the equal-weighted portfolios formed by
sorting on . The column labeled indicates the portfolio formation year. The
column labeled
indicates the portfolio holding year. The columns labeled 1


through 7 show the excess returns of the seven -sorted portfolios. The column
labeled 7-1 presents the difference between the return of portfolio seven and that
of portfolio one
Table 5.4 Univariate Portfolio Value-Weighted Excess Returns This Table presents
the one-year-ahead excess returns of the value-weighted portfolios formed by
sorting on . The column labeled indicates the portfolio formation year. The
column labeled
indicates the portfolio holding year. The columns labeled 1
through 7 show the excess returns of the seven -sorted portfolios. The column
labeled 7-1 presents the difference between the return of portfolio seven and that
of portfolio one
Table 5.5 Univariate Portfolio Equal-Weighted Excess Returns Summary This
Table presents the results of a univariate portfolio analysis of the relation between
beta ( ) and future stock returns ( ). The row labeled Average presents the
equal-weighted average annual return for each of the portfolios. The row labeled
Standard error presents the standard error of the estimated mean portfolio return.
Standard errors are adjusted following Newey and West (1987) using six lags. The
row labeled -statistic presents the -statistic (in parentheses) for the test with null
hypothesis that the average portfolio excess return is equal to zero. The row
labeled -value presents the two-sided -value for the test with null hypothesis
that the average portfolio excess return is equal to zero. The columns labeled 1
through 7 show the excess returns of the seven -sorted portfolios. The column
labeled 7-1 presents the results for the difference between the return of portfolio
seven and that of portfolio one
Table 5.6 -Sorted Portfolio Excess Returns This Table presents the results of a
univariate portfolio analysis of the relation between beta ( ) and future stock
returns ( ). The Table shows that average excess return for each of the seven
portfolios as well as for the long–short zero-cost portfolio, that is, long stocks in
the seventh portfolio and short stocks in the first portfolio. Newey and West (1987)
-statistics, adjusted using six lags, testing the null hypothesis that the average
portfolio excess return is equal to zero, are shown in parentheses
Table 5.7 Univariate Portfolio Average Values of ,
, and
This Table
presents the average values of ,
, and
for each of the -sorted
portfolios. The first column of the Table indicates the variable for which the
average value is being calculated. The columns labeled 1 through 7 present the
time-series average of annual portfolio mean values of the given variable. The
column labeled 7-1 presents the average difference between portfolios 7 and 1. The
column labeled 7-1 presents the -statistic, adjusted following Newey and West
(1987) using six lags, testing the null hypothesis that the average of the difference
portfolio is equal to zero
Table 5.8 Average Returns of Portfolios Sorted on

,

, and

This Table


presents the average excess returns of equal-weighted portfolios formed by sorting
on each of ,
, and
. The first column of the Table indicates the sort
variable. The columns labeled 1 through 7 present the time-series average of
annual one-year-ahead excess portfolio returns. The column labeled 7-1 presents
the average difference in return between portfolios 7 and 1. -statistics testing the
null hypothesis that the average portfolio return is equal to zero, adjusted
following Newey and West (1987) using six lags, are presented in parentheses
Table 5.9 -Sorted Portfolio Risk-Adjusted Results This Table presents the riskadjusted alphas and factor sensitivities for the -sorted portfolios. Each year , all
stocks in the sample are sorted into seven portfolios based on an ascending sort of
with breakpoints set to the 10th, 20th, 40th, 60th, 80th, and 90th percentiles of
in the given year. The equal-weighted average one-year-ahead excess portfolio
returns are then calculated. The Table presents the average excess returns (Model
= Excess return) for each of the seven portfolios as well as for the zero-cost
portfolio that is long the seventh portfolio and short the first portfolio. Also
presented are the alphas (Coefficient = ) and factor sensitivities (Coefficient =
,
,
, and
) for each of the portfolios using the CAPM (Model =
CAPM), Fama and French (1993) three-factor model (Model = FF), and Fama and
French (1993) and Carhart (1997) four-factor model (Model = FFC). -statistics,
adjusted following Newey and West (1987) using six lags, are presented in
parentheses
Table 5.10 Bivariate Independent-Sort Breakpoints This Table presents the
breakpoints for a bivariate independent-sort portfolio analysis The first sort
variable is and the second sort variable is
. The sample is split into three
groups (and thus two breakpoints) based on the 30th and 70th percentiles of ,
and four groups (and thus three breakpoints) based on the 25th, 50th, and 75th
percentiles of
. The column labeled indicates the year for which the
breakpoints are calculated. The columns labeled
and
present the first and
second breakpoints, respectively. The columns labeled
,
, and
present the first, second, and third
breakpoints, respectively
Table 5.11 Bivariate Independent-Sort Number of Stocks per Portfolio This Table
presents the number of stocks in each of the 12 portfolios formed by sorting
independently into three groups and four
groups. The columns labeled
indicate the year of portfolio formation. The columns labeled 1, 2, and 3
indicate the group. The rows labeled
1,
2,
3, and
4
indicate the
groups
Table 5.12 Average Value for the Difference in Difference Portfolio This diagram
describes how the difference in difference portfolio for a bivariate-sort portfolio
analysis is constructed
Table 5.13 Bivariate Independent-Sort Portfolio Excess Returns This Table presents


the equal-weighted excess returns for each of the 12 portfolios formed by sorting
independently into three groups and four
groups, as well as for the
difference and average portfolios. The columns labeled
indicate the year of
portfolio formation ( ) and the portfolio holding period (
). The columns
labeled 1, 2, 3, Diff, and Avg indicate the groups. The rows labeled
1,
2,
3,
4,
Diff, and
Avg indicate the
groups
Table 5.14 Bivariate Independent-Sort Portfolio Excess and Abnormal Returns This
Table presents the average excess returns (rows labeled Excess Return) and FFC
alphas (rows labeled FFC ) for portfolios formed by grouping all stocks into three
groups and four
groups. The numbers in parentheses are -statistics,
adjusted following Newey and West (1987) using six lags, testing the null
hypothesis that the time-series average of the portfolio's excess return or FFC
alpha is equal to zero
Table 5.15 Bivariate Independent-Sort Portfolio Results This Table presents the
average abnormal returns relative to the FFC model for portfolios sorted
independently into three groups and four
. The breakpoints for the
portfolios are the 30th and 70th percentiles. The breakpoints for the
portfolios are the 25th, 50th, and 75th percentiles. Table values indicate the alpha
relative to the FFC model with corresponding -statistics in parentheses
Table 5.16 Bivariate Independent-Sort Portfolio Results—Differences This Table
presents the average abnormal returns relative to the FFC model for long–short
zero-cost portfolios that are long stocks in the highest quartile of
and short
stocks in the lowest quartile of
. The portfolios are formed by sorting all
stocks independently into groups based on and
. The breakpoints used to
form the groups are the 30th and 70th percentiles of . Table values indicate the
alpha relative to the FFC model with the corresponding -statistics in parentheses
Table 5.17 Bivariate Independent-Sort Portfolio Results—Averages This Table
presents the average abnormal returns relative to the FFC model for portfolios
formed by sorting independently on and
. The Table shows the portfolio
FFC alphas and the associated Newey and West (1987) adjusted -statistics
calculated using six lags (in parentheses) for the average group within each
group of
Table 5.18 Bivariate Independent-Sort Portfolio Results—Differences This Table
presents the average excess returns and FFC alphas for portfolios formed by
sorting independently on and a second sort variable, which is either
or
. The Table shows the average excess returns and FFC alphas, along with the
associated Newey and West (1987) adjusted -statistics calculated using six lags (in
parentheses), for the difference between the portfolios with high and low values of


the second sort variable (
or
). The first column indicates the second sort
variable. The remaining columns correspond to different groups, as indicated in
the header
Table 5.19 Bivariate Independent-Sort Portfolio Results—Averages This Table
presents the average excess returns and FFC alphas for portfolios formed by
sorting independently on and a second sort variable, which is either
or
. The Table shows the average excess returns and FFC alphas, along with the
associated Newey and West (1987) adjusted -statistics calculated using six lags (in
parentheses), for the difference between the portfolios with high and low values of
the second sort variable (
or
). The first column indicates the second sort
variable. The remaining columns correspond to different groups, as indicated in
the header
Table 5.20 Bivariate Dependent-Sort Breakpoints This Table presents the
breakpoints for portfolios formed by sorting all stocks in the sample into three
groups based on the 30th and 70th percentiles of , and then, within each group,
into four groups based on the 25th, 50th, and 75th percentiles of
among
only stocks in the given groups. The columns labeled indicates the year of the
breakpoints. The columns labeled
and
present the breakpoints. The
columns labeled
,
, and
indicate the th
breakpoint for
stocks in the first, second, and third group, respectively, where is indicated in
the columns labeled
Table 5.21 Bivariate Dependent-Sort Number of Stocks per Portfolio This Table
presents the number of stocks in each of the 12 portfolios formed by sorting
dependently into three groups and then into four
groups. The columns
labeled indicate the year of portfolio formation. The columns labeled 1, 2,
and 3 indicate the group. The rows labeled
1,
2,
3, and
4 indicate the
groups
Table 5.22 Bivariate Dependent-Sort Mean Values This Table presents the equalweighted excess returns for each of the 12 portfolios formed by sorting all stocks in
the sample into three groups and then, within each of the groups, into four
groups. The columns labeled
indicate the year of portfolio formation (
) and the portfolio holding period (
). The columns labeled 1, 2, 3, and
Avg indicate the groups. The rows labeled
1,
2,
3,
4,
and
Diff indicate the
groups
Table 5.23 Bivariate Dependent-Sort Portfolio Results Risk-Adjusted Summary
This Table presents the results of a bivariate dependent-sort portfolio analysis of
the relation between
and future stock returns after controlling for
Table 5.24 Bivariate Dependent-Sort Portfolio Results This Table presents the
average abnormal returns relative to the FFC model for portfolios sorted


dependently into three groups and then, within each of the groups, into four
groups. The breakpoints for the portfolios are the 30th and 70th
percentiles. The breakpoints for the
portfolios are the 25th, 50th, and 75th
percentiles. Table values indicate the alpha relative to the FFC model with the
corresponding -statistics in parentheses
Table 5.25 Bivariate Dependent-Sort Portfolio Results—Differences This Table
presents the average abnormal returns relative to the FFC model for long–short
zero-cost portfolios that are long stocks in the highest quartile of
and short
stocks in the lowest quartile of
. The portfolios are formed by sorting all
stocks independently into groups based on and
. The breakpoints used to
form the groups are the 30th and 70th percentiles of . Table values indicate the
alpha relative to the FFC model with the corresponding -statistics in parentheses
Table 5.26 Bivariate Dependent-Sort Portfolio Results—Averages This Table
presents the average abnormal returns relative to the FFC model for portfolios
formed by sorting independently on and
. The Table shows the portfolio
FFC alphas and the associated Newey and West (1987)-adjusted -statistics
calculated using six lags (in parentheses) for the average group within each
group of
Table 5.27 Bivariate Dependent-Sort Portfolio Results—Differences This Table
presents the average excess returns and FFC alphas for portfolios formed by
sorting independently on and a second sort variable, which is either
or
. The Table shows the average excess returns and FFC alphas, along with the
associated Newey and West (1987)-adjusted -statistics calculated using six lags (in
parentheses), for the difference between the portfolios with high and low values of
the second sort variable (
or
). The first column indicates the second sort
variable. The remaining columns correspond to different groups, as indicated in
the header
Table 5.28 Bivariate Dependent-Sort Portfolio Results—Averages This Table
presents the average excess returns and FFC alphas for portfolios formed by
sorting independently on and a second sort variable, which is either
or
. The Table shows the average excess returns and FFC alphas, along with the
associated Newey and West (1987)-adjusted -statistics calculated using six lags (in
parentheses), for the difference between the portfolios with high and low values of
the second sort variable (
or
). The first column indicates the second sort
variable. The remaining columns correspond to different groups, as indicated in
the header
Table 5.29 Bivariate Independent-Sort Portfolio Average
This Table presents
the average
for portfolios formed by sorting independently on and
Table 5.30 Bivariate Dependent-Sort Portfolio Average

This Table presents


the average

for portfolios formed by sorting dependently on

and then on

Chapter 6: Fama and Macbeth Regression Analysis
Table 6.1 Periodic FM Regression Results This Table presents the estimated
intercept ( ) and slope ( , , ) coefficients, as well as the values of squared ( ), adjusted -squared (Adj. ), and the number of observations ( )
from annual cross-sectional regressions of one-year-ahead future stock excess
return ( ) on beta ( ), size (
), and book-to-market ratio (
). Panels A, B,
and C present results for univariate specifications using only ,
, and
,
respectively, as the independent variable. Panel D presents results from the
multivariate specification using all three variables as independent variables. All
independent variables are winsorized at the 0.5% level on an annual basis prior to
running the regressions. The column labeled
indicates the year during which
the independent variables were calculated ( ) and the year from which the excess
return, the dependent variable, is taken (
)
Table 6.2 Summarized FM Regression Results This Table presents summarized
results of FM regressions of future stock excess returns ( ) on beta ( ), size (
), and book-to-market ratio (
). The columns labeled (1), (2), and (3) present
results for univariate specifications using only ,
, and
, respectively, as the
independent variable. The column labeled (4) presents results from the
multivariate specification using all three variables as independent variables. is
the intercept coefficient. is the coefficient on . is the coefficient on
. is
the coefficient on
. Standard errors, -statistics, and -values are calculated
using the Newey and West (1987) adjustment with six lags
Table 6.3 FM Regression Results This Table presents the results of FM regressions
of future stock excess returns ( ) on beta ( ), size (
), and book-to-market
ratio (
). The columns labeled (1), (2), and (3) present results for univariate
specifications using only ,
, and
, respectively, as the independent variable.
The column labeled (4) presents results from the multivariate specification using
all three variables as independent variables. -statistics, adjusted following Newey
and West (1987) using six lags, are presented in parentheses
Chapter 7: The Crsp Sample and Market Factor
Table 7.1 SIC Industry Code Divisions This Table lists the industries corresponding
to different SIC industry codes
Table 7.2 Summary Statistics for Returns (1926–2012) This Table presents
summary statistics for return variables calculated using the CRSP sample for the
months from June 1926 through November 2012 or return months
from
July 1926 through December 2012. Each month, the mean (
), standard
deviation ( ), skewness (
), excess kurtosis (
), minimum (
), fifth


percentile (5%), 25th percentile (25%), median (
), 75th percentile (75%),
95th percentile (95%), and maximum (
) values of the cross-sectional
distribution of each variable are calculated. The Table presents the time-series
means for each cross-sectional value. The column labeled indicates that average
number of stocks for which the given variable is available.
is the excess stock
return, calculated as the stock's month
return, adjusted following Shumway
(1997) for delistings, minus the return on the risk-free security.
is the stock
return in month
, adjusted following Shumway (1997) for delistings.
is the
unadjusted excess stock return in month
.
is the unadjusted stock return
in month
. All returns are calculated in percent
Table 7.3 Summary Statistics for Returns (1963–2012) This Table presents
summary statistics for return variables calculated using the CRSP sample for the
months from June 1963 through November 2012 or return months
from
July 1963 through December 2012. Each month, the mean (
), standard
deviation ( ), skewness (
), excess kurtosis (
), minimum (
), fifth
percentile (5%), 25th percentile (25%), median (
), 75th percentile (75%),
95th percentile (95%), and maximum (
) values of the cross-sectional
distribution of each variable are calculated. The Table presents the time-series
means for each cross-sectional value. The column labeled indicates that average
number of stocks for which the given variable is available.
is the excess stock
return, calculated as the stock's month
return, adjusted following Shumway
(1997) for delistings, minus the return on the risk-free security.
is the stock
return in month
, adjusted following Shumway (1997) for delistings.
is the
unadjusted excess stock return in month
.
is the unadjusted stock return
in month
. All returns are calculated in percent
Chapter 8: Beta
Table 8.1 Summary Statistics This Table presents summary statistics for variables
measuring market beta calculated using the CRSP sample for the months from
June 1963 through November 2012. Each month, the mean (
), standard
deviation ( ), skewness (
), excess kurtosis (
), minimum (
), fifth
percentile (5%), 25th percentile (25%), median (
), 75th percentile (75%),
95th percentile (95%), and maximum (
) values of the cross-sectional
distribution of each variable are calculated. The Table presents the time-series
means for each cross-sectional value. The column labeled indicates that average
number of stocks for which the given variable is available.
,
,
,
, and
are calculated as the slope coefficient from a time-series regression of the
stock's excess return on the excess return of the market portfolio using one, three,
six, 12, and 24 months of daily return data, respectively.
,
,
, and
are
calculated similarly using one, two, three, and five years of monthly return data.
is calculated following Scholes and Williams (1977) using 12 months of daily


return data.
return data

is calculated following Dimson (1979) using 12 months of daily

Table 8.2 Correlations This Table presents the time-series averages of the annual
cross-sectional Pearson product–moment (below-diagonal entries) and Spearman
rank (above-diagonal entries) correlations between pairs of variables measuring
market beta
Table 8.3 Persistence This Table presents the results of persistence analyses of
variables measuring market beta. Each month , the cross-sectional Pearson
product–moment correlation between the month and month
values of the
given variable is calculated. The Table presents the time-series averages of the
monthly cross-sectional correlations. The column labeled indicates the lag at
which the persistence is measured
Table 8.4 Univariate Portfolio Analysis—Equal-Weighted This Table presents the
results of univariate portfolio analyses of the relation between each of measures of
market beta and future stock returns. Monthly portfolios are formed by sorting all
stocks in the CRSP sample into portfolios using decile breakpoints calculated based
on the given sort variable using all stocks in the CRSP sample. The Table shows the
average sort variable value, equal-weighted one-month-ahead excess return (in
percent per month), and the CAPM alpha (in percent per month) for each of the 10
decile portfolios as well as for the long-short zero-cost portfolio that is long the
10th decile portfolio and short the first decile portfolio. Newey and West (1987) statistics, adjusted using six lags, testing the null hypothesis that the average
portfolio excess return or CAPM alpha is equal to zero, are shown in parentheses
Table 8.5 Univariate Portfolio Analysis—Value-Weighted This Table presents the
results of univariate portfolio analyses of the relation between each of measures of
market beta and future stock returns. Monthly portfolios are formed by sorting all
stocks in the CRSP sample into portfolios using decile breakpoints calculated based
on the given sort variable using all stocks in the CRSP sample. The Table shows the
value-weighted one-month-ahead excess return and CAPM alpha (in percent per
month) for each of the 10 decile portfolios as well as for the long–short zero-cost
portfolio that is long the 10th decile portfolio and short the first decile portfolio.
Newey and West (1987) -statistics, adjusted using six lags, testing the null
hypothesis that the average portfolio excess return or CAPM alpha is equal to zero,
are shown in parentheses
Table 8.6 Fama–MacBeth Regression Analysis This Table presents the results of
Fama and MacBeth (1973) regression analyses of the relation between expected
stock returns and market beta. Each column in the Table presents results for a
different cross-sectional regression specification. The dependent variable in all
specifications is the one-month-ahead excess stock return. The independent
variable in each specification is indicated in the column header. The independent
variable is winsorized at the 0.5% level on a monthly basis. The Table presents


average slope and intercept coefficients along with -statistics (in parentheses),
adjusted following Newey and West (1987) using six lags, testing the null
hypothesis that the average coefficient is equal to zero. The rows labeled Adj.
and present the average adjusted -squared and number of data points,
respectively, for the cross-sectional regressions
Chapter 9: The Size Effect
Table 9.1 Summary Statistics This Table presents summary statistics for
variables measuring firm size calculated using the CRSP sample for the months
from June 1963 through November 2012. Each month, the mean (
), standard
deviation ( ), skewness (
), excess kurtosis (
), minimum (
), fifth
percentile (5%), 25th percentile (25%), median (
), 75th percentile (75%),
95th percentile (95%), and maximum (
) values of the cross-sectional
distribution of each variable are calculated. The Table presents the time-series
means for each cross-sectional value. The column labeled indicates the average
number of stocks for which the given variable is available.
is calculated as
the share price times the number of shares outstanding as of the end of month ,
measured in millions of dollars.
is the natural log of
.
is
adjusted using the consumer price index to reflect 2012 dollars and
is the
natural log of
.
is the share price times the number of shares
outstanding calculated as of the end of the most recent June, measured in millions
of dollars.
is the natural log of
.
is
adjusted using
the consumer price index to reflect 2012 dollars, and
is the natural log of
Table 9.2 Correlations This Table presents the time-series averages of the annual
cross-sectional Pearson product moment (below-diagonal entries) and Spearman
rank (above-diagonal entries) correlations between pairs of variables measuring
firm size
Table 9.3 Persistence This Table presents the results of persistence analyses of
,
,
, and
values. Each month , the cross-sectional Pearson
product–moment correlation between the month and month
values of the
given variable is calculated. The Table presents the time-series averages of the
monthly cross-sectional correlations. The column labeled indicates the lag at
which the persistence is measured
Table 9.4 Univariate Portfolio Analysis—NYSE Breakpoints This Table
presents the results of univariate portfolio analyses of the relation between each of
measures of market capitalization and future stock returns. Monthly portfolios are
formed by sorting all stocks in the CRSP sample into portfolios using decile
breakpoints calculated based on the given sort variable using the subset of the
stocks in the CRSP sample that are listed on the New York Stock Exchange. Panel A
shows the average market capitalization (in $millions), CPI-adjusted (2012 dollars)


market capitalization, percentage of total market capitalization, percentage of
stocks that are listed on the New York Stock Exchange, number of stocks, and for
stocks in each decile portfolio. Panel B (Panel C) shows the average equal-weighted
(value-weighted) one-month-ahead excess return and CAPM alpha (in percent per
month) for each of the 10 decile portfolios as well as for the long–short zero-cost
portfolio that is long the 10th decile portfolio and short the first decile portfolio.
Newey and West (1987) -statistics, adjusted using six lags, testing the null
hypothesis that the average portfolio excess return or CAPM alpha is equal to zero,
are shown in parentheses
Table 9.5 Univariate Portfolio Analysis—NYSE/AMEX/NASDAQ
Breakpoints This Table presents the results of univariate portfolio analyses of
the relation between each of measures of market capitalization and future stock
returns. Monthly portfolios are formed by sorting all stocks in the CRSP sample
into portfolios using decile breakpoints calculated based on the given sort variable
using all stocks in the CRSP sample. Panel A shows the average market
capitalization (in $millions), CPI-adjusted (2012 dollars) market capitalization,
percentage of total market capitalization, percentage of stocks that are listed on the
New York Stock Exchange, number of stocks, and for stocks in each decile
portfolio. Panel B (Panel C) shows the average equal-weighted (value-weighted)
one-month-ahead excess return and CAPM alpha (in percent per month) for each
of the 10 decile portfolios as well as for the long–short zero-cost portfolio that is
long the 10th decile portfolio and short the first decile portfolio. Newey and West
(1987) -statistics, adjusted using six lags, testing the null hypothesis that the
average portfolio excess return or CAPM alpha is equal to zero, are shown in
parentheses
Table 9.6 Bivariate Dependent-Sort Portfolio Analysis—NYSE
Breakpoints This Table presents the results of bivariate dependent-sort portfolio
analyses of the relation between
and future stock returns after controlling
for the effect of . Each month, all stocks in the CRSP sample are sorted into five
groups based on an ascending sort of . Within each group, all stocks are sorted
into five portfolios based on an ascending sort of
. The quintile breakpoints
used to create the portfolios are calculated using only stocks that are listed on the
New York Stock Exchange. The Table presents the average one-month-ahead
excess return (in percent per month) for each of the 25 portfolios as well as for the
average quintile portfolio within each quintile of
. Also shown are the
average return and CAPM alpha of a long–short zero-cost portfolio that is long the
fifth
quintile portfolio and short the first
quintile portfolio in each
quintile. -statistics (in parentheses), adjusted following Newey and West (1987)
using six lags, testing the null hypothesis that the average return or alpha is equal
to zero, are shown in parentheses. Panel A presents results for equal-weighted
portfolios. Panel B presents results for value-weighted portfolios


Table 9.7 Bivariate Dependent-Sort Portfolio Analysis –
NYSE/AMEX/NASDAQ Breakpoints This Table presents the results of
bivariate dependent-sort portfolio analyses of the relation between
and
future stock returns after controlling for the effect of . Each month, all stocks in
the CRSP sample are sorted into five groups based on an ascending sort of .
Within each group, all stocks are sorted into five portfolios based on an
ascending sort of
. The quintile breakpoints used to create the portfolios are
calculated using all stocks in the CRSP sample. The Table presents the average
one-month-ahead excess return (in percent per month) for each of the 25
portfolios as well as for the average quintile portfolio within each quintile of
. Also shown are the average return and CAPM alpha of a long–short zerocost portfolio that is long the fifth
quintile portfolio and short the first
quintile portfolio in each quintile. -statistics (in parentheses), adjusted
following Newey and West (1987) using six lags, testing the null hypothesis that
the average return or alpha is equal to zero, are shown in parentheses. Panel A
presents results for equal-weighted portfolios. Panel B presents results for valueweighted portfolios
Table 9.8 Bivariate Independent-Sort Portfolio Analysis—NYSE
Breakpoints This Table presents the results of bivariate independent-sort
portfolio analyses of the relation between
and future stock returns after
controlling for the effect of . Each month, all stocks in the CRSP sample are
sorted into five groups based on an ascending sort of . All stocks are
independently sorted into five groups based on an ascending sort of
. The
quintile breakpoints used to create the groups are calculated using only stocks that
are listed on the New York Stock Exchange. The intersections of the and
groups are used to form 25 portfolios. The Table presents the average one-monthahead excess return (in percent per month) for each of the 25 portfolios as well as
for the average quintile portfolio within each quintile of
and the average
quintile within each quintile. Also shown are the average return and
CAPM alpha of a long–short zero-cost portfolio that is long the fifth
( )
quintile portfolio and short the first
( ) quintile portfolio in each (
) quintile. -statistics (in parentheses), adjusted following Newey and West (1987)
using six lags, testing the null hypothesis that the average return or alpha is equal
to zero, are shown in parentheses. Panel A presents results for equal-weighted
portfolios. Panel B presents results for value-weighted portfolios
Table 9.9 Bivariate Independent-Sort Portfolio Analysis –
NYSE/AMEX/NASDAQ Breakpoints This Table presents the results of
bivariate independent-sort portfolio analyses of the relation between
and
future stock returns after controlling for the effect of . Each month, all stocks in
the CRSP sample are sorted into five groups based on an ascending sort of . All


stocks are independently sorted into five groups based on an ascending sort of
. The quintile breakpoints used to create the groups are calculated using all
stocks in the CRSP sample. The intersections of the and
groups are used
to form 25 portfolios. The Table presents the average one-month-ahead excess
return (in percent per month) for each of the 25 portfolios as well as for the
average quintile portfolio within each quintile of
and the average
quintile within each quintile. Also shown are the average return and CAPM alpha
of a long–short zero-cost portfolio that is long the fifth
( ) quintile
portfolio and short the first
( ) quintile portfolio in each (
)
quintile. -statistics (in parentheses), adjusted following Newey and West (1987)
using six lags, testing the null hypothesis that the average return or alpha is equal
to zero, are shown in parentheses. Panel A presents results for equal-weighted
portfolios. Panel B presents results for value-weighted portfolios
Table 9.10 Fama–MacBeth Regression Analysis This Table presents the
results of Fama and MacBeth (1973) regression analyses of the relation between
expected stock returns and firm size. Each column in the Table presents results for
a different cross-sectional regression specification. The dependent variable in all
specifications is the one-month-ahead excess stock return. The independent
variables are indicated in the first column. Independent variables are winsorized at
the 0.5% level on a monthly basis. The Table presents average slope and intercept
coefficients along with -statistics (in parentheses), adjusted following Newey and
West (1987) using six lags, testing the null hypothesis that the average coefficient
is equal to zero. The rows labeled Adj. and present the average adjusted squared and the number of data points, respectively, for the cross-sectional
regressions
Chapter 10: The Value Premium
Table 10.1 Summary Statistics This Table presents summary statistics for variables
measuring the ratio of a firm's book value of equity to its market value of equity
calculated using the CRSP sample for the months from June 1963 through
November 2012. Each month, the mean (
), standard deviation ( ), skewness
(
), excess kurtosis (
), minimum (
), fifth percentile (5%), 25th
percentile (25%), median (
), 75th percentile (75%), 95th percentile (95%),
and maximum (
) values of the cross-sectional distribution of each variable are
calculated. The Table presents the time-series means for each cross-sectional
value. The column labeled indicates that average number of stocks for which the
given variable is available.
for months from June of year through May of
year
is calculated as the book value of common equity as of the end of the
fiscal year ending in calendar year
to the market value of common equity as of
the end of December of year
.
is the natural log of
.
and
are the
book value and market value, respectively, used to calculate
, both adjusted to
reflect 2012 dollar using the consumer price index and recorded in millions of


dollars.

is the share price times the number of shares outstanding

Table 10.2 Correlations This Table presents the time-series averages of the annual
cross-sectional Pearson product–moment (below-diagonal entries) and Spearman
rank (above-diagonal entries) correlations between pairs
,
, , and
Table 10.3 Persistence This Table presents the results of persistence analyses of
and
. Each month , the cross-sectional Pearson product–moment
correlation between the month and month
values of the given variable is
calculated. The Table presents the time-series averages of the monthly crosssectional correlations. The column labeled indicates the lag at which the
persistence is measured
Table 10.4 Univariate Portfolio Analysis This Table presents the results of
univariate portfolio analyses of the relation between the book-to-market ratio and
future stock returns. Monthly portfolios are formed by sorting all stocks in the
CRSP sample into portfolios using
decile breakpoints calculated using all
stocks in the CRSP sample (Panel A) or the subset of the stocks in the CRSP
sample that are listed on the New York Stock Exchange (Panel B). The
Characteristics section of each panel shows the average values of
,
,
, and , the percentage of stocks that are listed on the New York Stock Exchange,
and the number of stocks for each decile portfolio. The EW portfolios (VW
portfolios) section in each panel shows the average equal-weighted (valueweighted) one-month-ahead excess return and CAPM alpha (in percent per month)
for each of the 10 decile portfolios as well as for the long–short zero-cost portfolio
that is long the 10th decile portfolio and short the first decile portfolio. Newey and
West (1987) -statistics, adjusted using six lags, testing the null hypothesis that the
average portfolio excess return or CAPM alpha is equal to zero, are shown in
parentheses
Table 10.5 Bivariate Dependent-Sort Portfolio Analysis This Table presents the
results of bivariate dependent-sort portfolio analyses of the relation between
and future stock returns after controlling for the effect of each of and
(control variables). Each month, all stocks in the CRSP sample are sorted into five
groups based on an ascending sort of one of the control variables. Within each
control variable group, all stocks are sorted into five portfolios based on an
ascending sort of
. The quintile breakpoints used to create the portfolios are
calculated using all stocks in the CRSP sample. Panel A presents the average return
and CAPM alpha (in percent per month) of the long–short zero-cost portfolios that
are long the fifth
quintile portfolio and short the first
quintile portfolio in
each quintile, as well as for the average quintile, of the control variable. Panel B
presents the average return and CAPM alpha for the average control variable
quintile portfolio within each
quintile, as well as for the difference between the
fifth and first
quintiles. Results for equal-weighted (Weights = EW) and valueweighted (Weights = VW) portfolios are shown. -statistics (in parentheses),


adjusted following Newey and West (1987) using six lags, testing the null
hypothesis that the average return or alpha is equal to zero, are shown in
parentheses
Table 10.6 Bivariate Independent-Sort Portfolio Analysis—Control for This Table
presents the results of bivariate independent-sort portfolio analyses of the relation
between
and future stock returns after controlling for the effect of . Each
month, all stocks in the CRSP sample are sorted into five groups based on an
ascending sort of . All stocks are independently sorted into five groups based on
an ascending sort of
. The quintile breakpoints used to create the groups are
calculated using all stocks in the CRSP sample. The intersections of the and
groups are used to form 25 portfolios. The Table presents the average one-monthahead excess return (in percent per month) for each of the 25 portfolios as well as
for the average quintile portfolio within each quintile of
and the average
quintile within each quintile. Also shown are the average return and CAPM
alpha of a long–short zero-cost portfolio that is long the fifth
( ) quintile
portfolio and short the first
( ) quintile portfolio in each (
) quintile. statistics (in parentheses), adjusted following Newey and West (1987) using six
lags, testing the null hypothesis that the average return or alpha is equal to zero,
are shown in parentheses. Panel A presents results for equal-weighted portfolios.
Panel B presents results for value-weighted portfolios
Table 10.7 Bivariate Independent-Sort Portfolio Analysis—Control for
This
Table presents the results of bivariate independent-sort portfolio analyses of the
relation between
and future stock returns after controlling for the effect of
. Each month, all stocks in the CRSP sample are sorted into five groups
based on an ascending sort of
. All stocks are independently sorted into five
groups based on an ascending sort of
. The quintile breakpoints used to create
the groups are calculated using all stocks in the CRSP sample. The intersections of
the
and
groups are used to form 25 portfolios. The Table presents the
average one-month-ahead excess return (in percent per month) for each of the 25
portfolios as well as for the average
quintile portfolio within each quintile
of
and the average
quintile within each
quintile. Also shown are the
average return and CAPM alpha of a long–short zero-cost portfolio that is long the
fifth
(
) quintile portfolio and short the first
(
) quintile
portfolio in each
(
) quintile. -statistics (in parentheses), adjusted
following Newey and West (1987) using six lags, testing the null hypothesis that
the average return or alpha is equal to zero, are shown in parentheses. Panel A
presents results for equal-weighted portfolios. Panel B presents results for valueweighted portfolios
Table 10.8 Fama–MacBeth Regression Analysis This Table presents the results of
Fama and MacBeth (1973) regression analyses of the relation between expected


stock returns and book-to-market ratio. Each column in the Table presents results
for a different cross-sectional regression specification. The dependent variable in
all specifications is the one-month-ahead excess stock return. The independent
variables are indicated in the first column. Independent variables are winsorized at
the 0.5% level on a monthly basis. The Table presents average slope and intercept
coefficients along with -statistics (in parentheses), adjusted following Newey and
West (1987) using six lags, testing the null hypothesis that the average coefficient
is equal to zero. The rows labeled Adj. and present the average adjusted squared and the number of data points, respectively, for the cross-sectional
regressions
Chapter 11: The Momentum Effect
Table 11.1 Summary Statistics This Table presents summary statistics for variables
measuring momentum using the CRSP sample for the months from June 1963
through November 2012. Each month, the mean (
), standard deviation ( ),
skewness (
), excess kurtosis (
), minimum (
), fifth percentile (5%),
25th percentile (25%), median (
), 75th percentile (75%), 95th percentile
(95%), and maximum (
) values of the cross-sectional distribution of each
variable are calculated. The Table presents the time-series means for each crosssectional value. The column labeled indicates the average number of stocks for
which the given variable is available.
in month is the return of the stock
during the 11-month period including months
through
.
is the
return of the stock during months
through
.
is the return of the
stock during months
through
.
is the return of the stock during
months
through month .
is the return of the stock during months
through month .
is the return of the stock during months
through month
.
is the return of the stock during months
through month
Table 11.2 Correlations This Table presents the time-series averages of the annual
cross-sectional Pearson product–moment (Panel A) and Spearman rank (Panel B)
correlations between different measures of momentum and each of ,
, and
Table 11.3 Univariate Portfolio Analysis This Table presents the results of
univariate portfolio analyses of the relation between each of the measures of
momentum and future stock returns. Monthly portfolios are formed by sorting all
stocks in the CRSP sample into portfolios using decile breakpoints calculated based
on the given sort variable using all stocks in the CRSP sample. Panel A shows the
average values of
, ,
, and
for stocks in each decile portfolio. Panel
B (Panel C) shows the average value-weighted (equal-weighted) one-month-ahead
excess return (in percent per month) for each of the 10 decile portfolios. The Table
also shows the average return of the portfolio that is long the 10th decile portfolio
and short the first decile portfolio, as well as the CAPM and FF alpha for this


portfolio. Newey and West (1987) -statistics, adjusted using six lags, testing the
null hypothesis that the average 10-1 portfolio return or alpha is equal to zero, are
shown in parentheses
Table 11.4 Univariate Portfolio Analysis— -Month-Ahead Returns This Table
presents the results of univariate portfolio analyses of the relation between each of
measures of momentum and future stock returns. Monthly portfolios are formed
by sorting all stocks in the CRSP sample into portfolios using decile breakpoints
calculated based on the given sort variable using all stocks in the CRSP sample.
Each panel in the Table shows that average -month-ahead return (as indicated in
the column header), in percent per month, along with the associated FF alpha, of
the portfolio, that is, long the 10th decile portfolio and short the first decile
portfolio. Panel A (Panel B) shows results for value-weighted (equal-weighted)
portfolios. Newey and West (1987) -statistics, adjusted using six lags, testing the
null hypothesis that the average portfolio return or alpha is equal to zero are
shown in parentheses
Table 11.5 Bivariate Dependent-Sort Portfolio Analysis—Control for
This
Table presents the results of bivariate dependent-sort portfolio analyses of the
relation between
and future stock returns after controlling for the effect of
. Each month, all stocks in the CRSP sample are sorted into five groups
based on an ascending sort of
. Within each
group, all stocks are
sorted into five portfolios based on an ascending sort of
. The quintile
breakpoints used to create the portfolios are calculated using all stocks in the CRSP
sample. The Table presents the average one-month-ahead excess return (in percent
per month) for each of the 25 portfolios as well as for the average
quintile
portfolio within each quintile of
. Also shown are the average return, CAPM
alpha, and FF alpha of a long–short zero-cost portfolio, that is, long the fifth
quintile portfolio and short the first
quintile portfolio in each
quintile.
-statistics (in parentheses), adjusted following Newey and West (1987) using six
lags, testing the null hypothesis that the average return or alpha is equal to zero,
are shown in parentheses. Panel A presents results for value-weighted portfolios.
Panel B presents results for equal-weighted portfolios
Table 11.6 Bivariate Dependent-Sort Portfolio Analysis—Small Stocks This Table
presents the results of bivariate dependent-sort portfolio analyses of the relation
between
and future stock returns after controlling for the effect of
using only small stocks. Each month, all stocks with values below the 20th
percentile value of
in the CRSP sample are sorted into four groups based on
an ascending sort of
. Within each
group, all stocks are sorted into
five portfolios based on an ascending sort of
. The Table presents the average
one-month-ahead excess return (in percent per month) for each of the 20
portfolios as well as for the average
portfolio within each
group. Also
shown are the average return, CAPM alpha, and FF alpha of a long–short zero-cost


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