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

End User License Agreement

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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