A Comparison of New Factor Models
Kewei Hou1
Chen Xue2
Lu Zhang3
1 The Ohio State University
and CAFR
2 University of Cincinnati
3 The Ohio State University
and NBER
University of Southern California
April 22, 2016
Introduction
Key result
The
q -factor
model outperforms the Fama-French (2015)
ve-factor model on both empirical and conceptual grounds
Introduction
The Hou-Xue-Zhang (2015) q -factor model
i
i
i
i
i
Rit −Rft = αqi +βMKT
MKTt +βME rME,t +βI/A rI/A,t +βROE rROE,t +
MKTt , rME,t , rI/A,t , and
rROE,t
are the market, size,
investment, and ROE factors, respectively
i
i , βi ,
βMKT
, βME
I/A
and
i
βROE
are factor loadings
Introduction
The Fama-French (2015, FF) ve-factor model
Rit −Rft = ai +bi MKTt +si SMBt +hi HMLt +ri RMWt +ci CMAt +eit
MKTt , SMBt , HMLt , RMWt , and CMAt are the market, size,
value, protability, and investment factors, respectively
bi , si , hi , ri ,
and
ci
are factor loadings
Introduction
The q -factor model predates the ve-factor model by 36 years
Neoclassical factors
An equilibrium three-factor model
Production-based factors
A better three-factor model
that explains more anomalies
An alternative three-factor model
Digesting anomalies: An investment approach
Fama and French (2013): A four-factor model for
the size, value, and protability
patterns in stock returns
Fama and French (2014):
A ve-factor asset pricing model
July 2007
January 2009
April 2009
June 2009
April 2010, April 2011
October 2012 , August 2014
June 2013
November 2013 , August 2014
Introduction
Properties of the q -factors, 1/196712/2013
m
rME
rI/A
rROE
rME
rI/A
βMKT
βSMB
βHML
βUMD
0.34
0.00
0.01
0.98
0.18
0.03
(2.51)
(0.06)
(1.50)
(65.19)
(7.27)
(2.02)
0.44
0.29
(5.12)
(4.54)
−0.06
−0.04
0.41
0.05
(−4.40)
(−1.76)
(13.07)
(1.89)
0.57
0.52
−0.03
−0.30
−0.13
0.27
(5.21)
(5.52)
(−1.31)
(−4.17)
(−1.82)
(6.13)
a
b
s
h
r
c
0.04
0.01
0.98
0.03
−0.01
0.04
(1.22)
(0.76)
(65.86)
(1.14)
(−0.17)
(1.17)
0.12
(3.24)
rROE
αC
0.45
(5.44)
0.01
−0.04
0.04
0.08
0.82
(0.85)
(−2.67)
(1.53)
(2.79)
(25.71)
−0.04
−0.11
−0.25
0.76
0.14
(−1.29)
(−2.65)
(−3.59)
(13.21)
(1.39)
Introduction
Properties of the new FF factors, 1/196712/2013
m
SMB
HML
RMW
CMA
αC
βMKT
βSMB
βHML
βUMD
0.28
−0.02
0.01
1.00
0.13
0.00
(2.02)
(−1.26)
(0.99)
(88.07)
(8.12)
(0.11)
0.37
0.00
−0.00
0.00
1.00
0.00
(2.63)
(1.49)
(−0.68)
(0.37)
(1752.68)
(0.97)
0.27
0.34
(2.58)
(3.36)
0.36
0.19
(3.68)
(2.82)
−0.04
−0.27
−0.00
0.04
(−1.38)
(−3.08)
(−0.07)
(0.83)
−0.09
0.04
0.46
0.04
(−4.42)
(0.90)
(13.43)
(1.52)
Introduction
Properties of the new FF factors, 1/196712/2013
αq
SMB
HML
RMW
βMKT
βI / A
βROE
0.05
−0.00
0.94
−0.09
−0.10
(1.58)
(−0.48)
(58.83)
(−4.72)
(−5.61)
0.04
−0.05
0.00
1.03
−0.17
(0.36)
(−1.37)
(0.01)
(11.67)
(−2.19)
0.04
(0.49)
CMA
βME
0.02
(0.45)
Summary: The
−0.03
−0.12
−0.03
0.52
(−1.07)
(−1.70)
(−0.37)
(8.54)
−0.05
0.04
0.93
−0.11
(−3.65)
(1.58)
(33.68)
(−3.90)
q -factor
model can explain FF ve factors, but the
ve-factor model cannot explain the
q -factors
Introduction
The q -factor model outperforms the FF ve-factor model,
testing deciles with NYSE breakpoints and value-weights
Across a set of 36 signicant anomalies:
The average magnitude of high-minus-low alphas:
.20% in
q,
.36% in FF5, .33% in Carhart
The number of signicant high-minus-low alphas:
7 in
q,
19 in FF5, 21 in Carhart
The number of rejections by the GRS test:
25 in
q,
FF5, and Carhart
Introduction
The q -factor model outperforms the FF ve-factor model,
testing deciles with all-but-micro breakpoints and equal-weights
Across a set of 50 signicant anomalies:
The average magnitude of high-minus-low alphas:
.24% in
q,
.41% in FF5, .40% in Carhart
The number of signicant high-minus-low alphas:
16 in
q,
34 in FF5, 37 in Carhart
The number of rejections by the GRS test:
37 in
q,
35 in FF5, 39 in Carhart
Introduction
Related literature
Barillas and Shanken (2015)
Stambaugh and Yu (2015)
Back, Kapadia, and Ostdiek (2016)
Green, Hand, and Zhang (2016)
Huang and Wang (2016)
Kim and Skoulakis (2016)
Introduction
An empirical research program on q -factors
Hou, Xue, and Zhang (2015, RFS): Digesting anomalies: An
investment approach
Hou, Xue, and Zhang (2016a): A comparison of new factor models
Hou, Xue, and Zhang (2016b): Are anomalies stable?
The magnitude of anomalies has been stable in the broad cross section,
without being contaminated by microcaps
Hou, Xue, and Zhang (2016c): Global
The
q -factor
q -factors
premiums are reliable in global equity markets, and help
explain international value and momentum
Hou, Xue, and Zhang (2016d): International anomalies
Anomalies are stronger in developed markets than in emerging markets,
consistent with the investment CAPM
Outline
1
Factors
2
Testing portfolios
3
Factor Regressions
4
Robustness
5
Conceptual Comparison
Outline
1
Factors
2
Testing portfolios
3
Factor Regressions
4
Robustness
5
Conceptual Comparison
Factors
The q -factors
rME , rI/A ,
and
rROE
from a triple 2
×3×3
sort on size,
investment-to-assets, and ROE
Size: Stock price times shares outstanding from CRSP
Investment-to-assets, I/A: Annual changes in total assets
(item AT) divided by one-year-lagged total assets
ROE: Income before extraordinary items (item IBQ) divided by
one-quarter-lagged book equity
Annual sorts on size and I/A, monthly on ROE
Factors
The new FF factors
SMB, HML, RMW, and CMA from double 2
×3
sorts from
interacting size with B/M, OP, and Inv
Size: Stock price times shares outstanding from CRSP
B/M: Per Davis, Fama, and French (2000)
OP: Revenues minus costs of goods sold, SG&A, and interest
expense, all divided by current book equity
Inv: Annual changes in total assets divided by lagged assets
All annual sorts
Outline
1
Factors
2
Testing portfolios
3
Factor Regressions
4
Robustness
5
Conceptual Comparison
Testing Portfolios
Overview
An extensive list of 73 anomalies from Hou, Xue, and Zhang
(2015), scope comparable with:
Green, Hand, and Zhang (2013)
Harvey, Liu, and Zhu (2013)
McLean and Ponti (2013)
Two sets of testing deciles:
NYSE-VW: NYSE breakpoints and value-weighted returns
ABM-EW: All-but-micro breakpoints and equal-weighted
returns to give sucient weights to small stocks
Testing Portfolios
Six categories of anomalies, 73 in total
Panel A: Momentum
SUE-1 , earnings surprise
(1-month holding period),
Foster, Olsen, and Shevlin (1984)
Abr-1 , cumulative abnormal stock
returns around earnings announcements
(1-month holding period), Chan,
Jegadeesh, and Lakonishok (1996)
RE-1 , revisions in analysts' earnings
forecasts (1-month holding period),
Chan, Jegadeesh, and Lakonishok (1996)
R6-1 , price momentum (6-month prior
returns, 1-month holding period),
Jegadeesh and Titman (1993)
R11-1 , price momentum, (11-month
prior returns, 1-month holding period),
Fama and French (1996)
SUE-6 , earnings surprise
(6-month holding period),
Foster, Olsen, and Shevlin (1984)
Abr-6 , cumulative abnormal stock
returns around earnings announcements
(6-month holding period), Chan,
Jegadeesh, and Lakonishok (1996)
RE-6 , revisions in analysts' earnings
forecasts (6-month holding period),
Chan, Jegadeesh, and Lakonishok (1996)
R6-6 , price momentum (6-month prior
returns, 6-month holding period),
Jegadeesh and Titman (1993)
I-Mom , industry momentum,
Moskowitz and Grinblatt (1999)
Testing Portfolios
Six categories of anomalies, 73 in total
Panel B: Value-versus-growth
B/M , book-to-market equity,
Rosenberg, Reid, and Lanstein (1985)
Rev , reversal, De Bondt and Thaler (1985)
A/ME , market leverage,
Bhandari (1988)
E/P , earnings-to-price, Basu (1983)
EF/P , analysts' earnings forecasts-to-price,
Elgers, Lo, and Pfeier (2001)
D/P , dividend yield,
Litzenberger and Ramaswamy (1979)
NO/P , net payout yield, Boudoukh,
Michaely, Richardson, and Roberts (2007)
LTG , long-term growth forecasts
of analysts, La Porta (1996)
CF/P , cash ow-to-price,
Lakonishok, Shleifer, and Vishny (1994)
O/P , payout yield, Boudoukh, Michaely,
Richardson, and Roberts (2007)
SG , sales growth,
Lakonishok, Shleifer, and Vishny (1994)
Dur , equity duration,
Dechow, Sloan, and Soliman (2004)
Testing Portfolios
Six categories of anomalies, 73 in total
Panel C: Investment
ACI , abnormal corporate investment,
Titman, Wei, and Xie (2004)
NOA , net operating assets, Hirshleifer,
Hou, Teoh, and Zhang (2004)
I/A , investment-to-assets,
Cooper, Gulen, and Schill (2008)
4PI/A , changes in PPE
plus changes in inventory scaled by assets,
Lyandres, Sun, and Zhang (2008)
IG , investment growth,
NSI , net stock issues,
Xing (2008)
Ponti and Woodgate (2008)
CEI , composite issuance,
NXF , net external nancing,
Daniel and Titman (2006)
Bradshaw, Richardson, and Sloan (2006)
IvG , inventory growth,
IvC , inventory changes,
Belo and Lin (2011)
Thomas and Zhang (2002)
OA , operating accruals, Sloan (1996)
TA , total accruals, Richardson, Sloan,
Soliman, and Tuna (2005)
POA , percent operating accruals, Hafzalla, PTA , percent total accruals, Hafzalla,
Lundholm, and Van Winkle (2011)
Lundholm, and Van Winkle (2011)
Testing Portfolios
Six categories of anomalies, 73 in total
Panel D: Protability
ROE , return on equity,
Haugen and Baker (1996)
RNA , return on net operating assets,
Soliman (2008)
ATO , asset turnover,
Soliman (2008)
GP/A , gross prots-to-assets,
Novy-Marx (2013)
TES , tax expense surprise,
Thomas and Zhang (2011)
RS , revenue surprise,
Jegadeesh and Livnat (2006)
FP , failure probability,
Campbell, Hilscher, and Szilagyi (2008)
ROA , return on assets,
Balakrishnan, Bartov, and Faurel (2010)
PM , prot margin, Soliman (2008)
CTO , capital turnover,
Haugen and Baker (1996)
F , F -score,
Piotroski (2000)
TI/BI , taxable income-to-book income,
Green, Hand, and Zhang (2013)
NEI , number of consecutive quarters
with earnings increases,
Barth, Elliott, and Finn (1999)
O , O -score, Dichev (1998)
Testing Portfolios
Six categories of anomalies, 73 in total
Panel E: Intangibles
OC/A , organizational capital-to-assets,
Eisfeldt and Papanikolaou (2013)
Ad/M , advertisement expense-to-market,
Chan, Lakonishok, and Sougiannis (2001)
RD/M , R&D-to-market,
Chan, Lakonishok, and Sougiannis (2001)
H/N , hiring rate,
Belo, Lin, and Bazdresch (2014)
G , corporate governance,
Gompers, Ishii, and Metrick (2003)
BC/A , brand capital-to-assets,
Belo, Lin, and Vitorino (2014)
RD/S , R&D-to-sales,
Chan, Lakonishok, and Sougiannis (2001)
RC/A , R&D capital-to-assets, Li (2011)
OL , operating leverage,
Novy-Marx (2011)
AccQ , accrual quality, Francis, Lafond,
Olsson, and Schipper (2005)
Testing Portfolios
Six categories of anomalies, 73 in total
Panel F: Trading frictions
ME , the market equity,
Ivol , idiosyncratic volatility,
Banz (1981)
Ang, Hodrick, Xing, and Zhang (2006)
Tvol , total volatility,
Svol , systematic volatility,
Ang, Hodrick, Xing, and Zhang (2006) Ang, Hodrick, Xing, and Zhang (2006)
MDR , maximum daily return,
β , market beta,
Bali, Cakici, and Whitelaw (2011)
Frazzini and Pedersen (2014)
D-β , Dimson's beta, Dimson (1979)
S-Rev , short-term reversal, Jegadeesh (1990)
Disp , dispersion of analysts'
earnings forecasts,
Diether, Malloy, and Scherbina (2002)
1/P , 1/share price,
Miller and Scholes (1982)
Illiq , Absolute return-to-volume,
Amihud (2002)
Turn , share turnover,
Datar, Naik, and Radclie (1998)
Dvol , dollar trading volume,
Brennan, Chordia, and Subrahmanyam (1998)
Testing Portfolios
37 insignicant anomalies,
NYSE breakpoints and value-weighted returns
SUE-6 R6-1 A/ME EF/P
m
tm
m
tm
0.17
1.68
0.57
1.88
0.41
1.89
D/P O/P
0.45
1.82
0.19
0.75
TES TI/BI
FP
CTO
F
0.27
1.58
0.34
1.21
Ivol
Tvol MDR
0.30
1.85
0.33 −0.24
1.49 −1.29
β
LTG NXF
TA RNA
D-β S-Rev
0.21
0.85
PM ATO
0.07 −0.27 −0.21 0.11 −0.02
0.18 −1.42 −1.57 0.57 −0.08
O BC/A RD/S RC/A H/N
0.18 −0.55 −0.09
1.31 −1.72 −0.46
m −0.49 −0.36 −0.32 −0.16
tm −1.55 −1.01 −1.04 −0.47
SG
0.04
0.15
G AccQ
0.30
1.67
ME
0.34 −0.28 0.03 −0.04 −0.33
1.40 −1.82 0.09 −0.19 −1.32
Disp Turn
1/P Dvol Illiq
0.07 −0.30 −0.27 −0.15
0.31 −1.50 −1.05 −0.57
0.09 −0.32 0.34
0.29 −1.71 1.54
Testing Portfolios
23 insignicant anomalies,
all-but-micro breakpoints and equal-weighted returns
EF/P
m
tm
D/P O/P
0.47 0.18
1.47 0.87
G AccQ
SG
LTG RNA
0.39 −0.27 −0.47
1.94 −1.70 −1.01
ME Ivol Tvol
0.19
1.18
β
PM ATO TI/BI
0.21 0.16
0.88 0.98
D-β Turn
FP BC/A RD/S RC/A
0.19 −0.49
1.82 −1.76
1/P Illiq
m −0.02 −0.06 −0.22 −0.61 −0.65 −0.25 −0.09 −0.44 −0.05
tm −0.08 −0.30 −1.25 −1.87 −1.80 −0.70 −0.41 −1.65 −0.21
0.29
1.92
0.32 −0.04 0.37
1.45 −0.12 1.11
Outline
1
Factors
2
Testing portfolios
3
Factor Regressions
4
Robustness
5
Conceptual Comparison
Factor Regressions
Overview, NYSE-VW
Across a set of 36 signicant anomalies with NYSE-VW:
The average magnitude of high-minus-low alphas:
.20% in
q,
.36% in FF5, .33% in Carhart
The number of signicant high-minus-low alphas:
7 in
q,
19 in FF5, 21 in Carhart
The number of rejections by the GRS test:
25 in
q,
FF5, and Carhart
Factor Regressions
Signicant momentum anomalies with NYSE-VW, alphas
m
αC
αq
a
tm
tC
tq
ta
|αC |
|αq |
|a|
pC
pq
pa
SUE-1
Abr-1
Abr-6
RE-1
RE-6
R6-6
R11-1
I-Mom
|ave|
0.41
0.35
0.15
0.44
3.65
2.95
1.12
3.74
0.10
0.06
0.11
0.00
0.39
0.02
0.73
0.62
0.64
0.85
5.58
4.40
4.21
5.87
0.12
0.13
0.16
0.00
0.00
0.00
0.30
0.18
0.26
0.44
3.10
2.04
2.25
4.23
0.08
0.07
0.08
0.00
0.01
0.00
0.78
0.49
0.06
0.86
3.05
2.38
0.22
3.23
0.10
0.11
0.20
0.05
0.16
0.01
0.52
0.31
−0.02
0.66
2.35
1.83
−0.07
2.86
0.09
0.12
0.17
0.06
0.02
0.01
0.83
0.07
0.22
0.97
3.44
0.70
0.68
3.38
0.09
0.09
0.17
0.00
0.00
0.00
1.20
0.18
0.26
1.25
4.00
1.41
0.65
3.45
0.13
0.15
0.23
0.00
0.00
0.00
0.58
−0.11
0.03
0.61
2.91
−0.72
0.11
2.45
0.05
0.12
0.21
0.41
0.03
0.00
0.67
0.29
0.21
0.76
4
2
8
0.10
0.11
0.17
5
6
8
Factor Regressions
Signicant momentum anomalies with NYSE-VW, betas
βME
βI/A
βROE
tβME
tβI/A
tβROE
s
h
r
c
ts
th
tr
tc
SUE-1
Abr-1
Abr-6
RE-1
RE-6
R6-6
R11-1
I-Mom
0.10
0.03
0.46
1.88
0.32
5.76
−0.03
−0.17
0.14
0.18
−0.45
−1.67
1.75
1.25
0.07
−0.14
0.28
0.70
−1.31
3.18
−0.05
−0.20
−0.11
0.13
−0.63
−1.80
−1.15
0.84
0.08
−0.17
0.18
1.81
−2.27
2.86
0.01
−0.12
−0.12
−0.07
0.16
−1.74
−1.73
−0.60
−0.19
0.09
1.31
−2.11
0.52
9.82
−0.42
−0.16
0.55
−0.02
−3.79
−0.94
3.28
−0.05
−0.18
−0.07
1.10
−1.98
−0.45
9.36
−0.40
−0.27
0.41
0.02
−4.23
−1.76
2.80
0.07
0.22
0.01
1.01
1.25
0.06
5.40
−0.08
−0.54
0.11
0.39
−0.56
−2.44
0.44
1.25
0.33
0.12
1.46
1.53
0.39
5.80
−0.05
−0.71
0.35
0.67
−0.27
−2.47
1.13
1.62
0.25
0.09
0.82
1.55
0.39
4.95
0.01
−0.37
0.12
0.39
0.06
−1.79
0.51
1.24
Factor Regressions
Signicant value anomalies with NYSE-VW, alphas
m
αC
αq
a
tm
tC
tq
ta
|αC |
|αq |
|a|
pC
pq
pa
B/M
Rev
E/P
CF/P
NO/P
Dur
|ave|
0.64
−0.05
0.16
−0.02
2.88
−0.42
0.96
−0.17
0.07
0.09
0.06
0.08
0.13
0.44
−0.46
−0.07
−0.16
0.08
−2.02
−0.39
−0.93
0.45
0.10
0.08
0.05
0.26
0.25
0.42
0.55
−0.02
0.11
0.05
2.67
−0.13
0.53
0.37
0.08
0.12
0.09
0.15
0.04
0.13
0.46
−0.10
0.15
0.01
2.30
−0.76
0.77
0.09
0.07
0.15
0.13
0.11
0.00
0.03
0.65
0.51
0.36
0.22
3.27
3.45
2.45
1.57
0.15
0.12
0.11
0.00
0.00
0.00
−0.46
0.01
−0.18
−0.05
−2.39
0.09
−0.92
−0.34
0.06
0.08
0.05
0.43
0.36
0.72
0.54
0.13
0.19
0.07
1
1
0
0.09
0.11
0.08
1
3
2
Factor Regressions
Signicant value anomalies with NYSE-VW, betas
βME
βI/A
βROE
tβME
tβI/A
tβROE
s
h
r
c
ts
th
tr
tc
B/M
Rev
E/P
CF/P
NO/P
Dur
0.48
1.40
−0.53
5.86
13.01
−6.24
0.52
1.16
−0.27
0.33
10.93
15.84
−3.80
3.06
−0.64
−1.17
0.72
−7.83
−10.49
7.47
−0.67
−0.47
0.39
−0.77
−6.65
−3.70
4.44
−4.57
0.29
1.01
−0.11
2.34
6.27
−0.78
0.32
1.38
0.16
−0.38
5.96
14.16
2.14
−3.00
0.20
1.00
−0.26
1.91
7.31
−2.03
0.25
1.29
0.00
−0.24
4.92
14.05
0.01
−1.93
−0.32
1.03
0.02
−4.31
10.33
0.21
−0.25
0.46
0.51
0.54
−3.96
5.57
6.83
4.33
−0.26
−0.86
0.27
−1.93
−6.36
2.22
−0.32
−1.18
0.02
0.29
−5.04
−11.93
0.25
2.28
Factor Regressions
Signicant investment anomalies with NYSE-VW, alphas
ACI
4PI/A
IG
−0.50 −0.42
−0.34 −0.21
IvG
IvC
PTA
|ave|
−0.72
−0.61
−0.57 −0.38
−0.45 −0.19
−0.46
−0.31
−0.28 −0.43 −0.42
−0.33 −0.24 −0.31
0.45
0.02
−0.31
−0.25 −0.01
−0.28
−0.54 −0.09 −0.15
0.21
−0.31 −0.08
−3.67 −3.33
−2.55 −1.84
−0.32
−4.56
−4.35
−0.25 −0.12
−3.18 −2.72
−3.71 −1.37
−0.38
−3.30
−2.23
−0.52 −0.12 −0.11
−2.24 −3.08 −3.03
−2.46 −2.01 −2.29
0.25
−1.85 −0.09
−1.95 −3.81 −0.68 −1.03
3
I/A
NOA
m
αC
−0.31 −0.46
−0.19 −0.17
−0.39
−0.43
αq
−0.17
0.09
−0.39
−0.23
a
tm
tC
−0.30 0.04
−2.12 −2.86
−1.23 −1.20
−0.44
−2.82
−3.08
tq
−0.96
0.72
−2.10
ta
−1.91
0.34
−2.62
0.11
0.10
0.14
0.11
0.10
0.15
0.14
0.09
0.10
0.11
0.12
0.11
0.12
0.13
0.10
0.10
0.13
0.09
0.11
0.12
0.10
0.07
0.14
0.12
0.08
0.11
0.15
0.11
0.10
0.11
0.06
0.10
0.10
0.10
0.08
0.12
0.12
0.08
0.10
0.00
0.01
0.00
0.01
0.00
0.00
0.00
0.07
0.03
0.00
0.00
0.00
11
0.00
0.00
0.00
0.00
0.02
0.01
0.01
0.08
0.45
0.00
0.00
0.01
10
0.00
0.00
0.02
0.01
0.28
0.01
0.01
0.04
0.20
0.00
0.00
0.02
10
|αC |
|αq |
|a|
pC
pq
pa
−1.81
0.18
NSI
−2.22
−2.61 −0.75 −2.43
CEI
−2.33 −0.99 −2.92
OA
POA
−4.10 −1.03 −0.87
0.39
8
6
Factor Regressions
Signicant investment anomalies with NYSE-VW, betas
βME
ACI
I/A
NOA
−0.29
−0.14
0.10
βI/A
0.13
βROE −0.19
tβ
−4.99
ME
tβ
I/A
1.01
tβ
ROE −2.10
s
−0.26
h
0.16
r
−0.03
−1.37
0.17
0.01
0.16
1.01
−1.63
−16.71
−0.48 −7.70
2.58
0.08
2.02
−0.10
−0.18
0.16
−0.03
0.46
0.01
0.03
0.08
0.25
−0.02
−4.15
tc
−0.10 −10.88
1.58
−0.07 −0.79
−2.35
c
ts
th
tr
−0.33
4PI/A
−0.08
−1.14 −0.52 −0.75
−1.52
2.25
−0.58
−2.56
5.11
0.16
0.34
0.64
−3.58
3.62
−6.88
IG
NSI
CEI
IvG
IvC
OA
POA
−0.15
0.17
0.25
0.08
−0.01
0.29
0.14
−0.76 −0.72
−0.07 −0.30
−2.60
2.41
−1.04
−0.11
−10.41
−1.18
−0.13
−0.08
−0.14
−6.96
3.92
−14.03
−0.94
−0.68 −0.05
−0.94
PTA
0.15
−0.86
0.05
0.18
0.27
0.06
0.05
1.80
−0.13
4.85
3.32
2.44
−12.40
−6.09 −0.51 −10.91
−8.76
−3.85
−1.44
0.60
1.98
4.16
1.21
0.12
0.24
0.11
0.07
0.31
0.18
0.11
−0.12
−0.66
−0.41
−0.41
−0.08
0.03
0.01
0.35
0.40
−0.16
−0.04
−0.23
−0.23
−0.60 −0.57
−2.53
2.58
−1.23 −1.89
−1.90 −9.56
−0.60
−5.45
−6.39
−5.36
0.07
−0.74
−0.64
4.82
2.12
1.29
−6.50
−5.71
−0.91
0.72
−7.32
0.01
−0.75
0.62
−0.57
5.90
4.41
1.76
0.39
0.14
3.77
6.18
−2.94
−0.63
−2.36
−2.76
−4.66
0.10
−8.47
−4.67
Factor Regressions
Signicant protability anomalies with NYSE-VW, alphas
m
αC
αq
a
tm
tC
tq
ta
|αC |
|αq |
|a|
pC
pq
pa
ROE
ROA
GP/A
RS
NEI
|ave|
0.68
0.79
−0.03
0.51
2.95
4.15
−0.24
3.57
0.15
0.10
0.11
0.00
0.01
0.01
0.58
0.64
0.06
0.50
2.54
3.46
0.49
3.43
0.13
0.07
0.15
0.05
0.79
0.06
0.40
0.51
0.20
0.21
2.75
3.51
1.39
1.58
0.15
0.12
0.10
0.00
0.19
0.08
0.31
0.49
0.21
0.53
2.15
3.41
1.41
3.73
0.12
0.08
0.15
0.00
0.04
0.00
0.38
0.42
0.18
0.46
3.34
3.92
1.72
4.57
0.13
0.09
0.15
0.00
0.03
0.00
0.47
0.57
0.14
0.44
5
0
4
0.14
0.09
0.13
4
3
3
Factor Regressions
Signicant protability anomalies with NYSE-VW, betas
βME
βI/A
βROE
tβME
tβI/A
tβROE
s
h
r
c
ts
th
tr
tc
ROE
ROA
GP/A
RS
NEI
−0.39
0.08
1.50
−6.44
0.88
21.14
−0.48
−0.27
1.43
0.20
−6.22
−2.57
12.18
1.27
−0.38
−0.09
1.32
−6.50
−1.12
17.12
−0.48
−0.25
1.25
0.03
−6.13
−2.95
10.52
0.18
0.04
−0.31
0.54
0.76
−3.21
7.58
0.11
−0.45
0.89
0.19
2.25
−4.46
9.56
1.46
−0.13
−0.40
0.61
−2.41
−4.56
7.99
−0.25
−0.47
0.28
−0.02
−4.12
−5.53
3.33
−0.17
−0.09
−0.32
0.65
−2.32
−4.36
11.41
−0.17
−0.35
0.45
−0.08
−3.67
−5.45
6.49
−0.77
Factor Regressions
Signicant intangibles-trading frictions anomalies with
NYSE-VW, alphas
m
αC
αq
a
tm
tC
tq
ta
|αC |
|αq |
|a|
pC
pq
pa
OC/A
Ad/M
RD/M
OL
Svol
|ave|
0.58
0.41
0.13
0.33
4.59
3.34
1.03
2.61
0.12
0.11
0.11
0.00
0.01
0.00
0.78
0.31
0.11
−0.06
2.99
1.38
0.40
−0.32
0.19
0.11
0.12
0.08
0.09
0.28
0.64
0.31
0.60
0.38
2.40
1.43
2.46
1.57
0.21
0.27
0.21
0.00
0.00
0.00
0.46
0.39
0.02
0.09
2.65
2.28
0.14
0.56
0.12
0.11
0.09
0.02
0.03
0.06
−0.55
−0.59
−0.34
−0.34
−2.46
−2.51
−1.37
−1.36
0.16
0.11
0.11
0.03
0.13
0.25
0.60
0.40
0.24
0.24
3
1
1
0.16
0.14
0.13
4
3
2
Factor Regressions
Signicant intangibles-trading frictions anomalies with
NYSE-VW, betas
βME
βI/A
βROE
tβME
tβI/A
tβROE
s
h
r
c
ts
th
tr
tc
OC/A
Ad/M
RD/M
OL
Svol
0.24
0.29
0.51
5.66
2.98
6.92
0.21
−0.13
0.55
0.40
4.49
−1.70
5.13
2.92
0.51
1.40
−0.26
2.92
6.01
−1.34
0.65
1.03
0.47
0.14
6.93
7.17
4.41
0.68
0.66
0.20
−0.58
6.84
1.13
−4.08
0.60
0.05
−0.52
0.41
6.96
0.33
−2.86
1.99
0.30
0.11
0.54
3.10
0.95
4.88
0.37
0.04
0.89
0.06
5.75
0.44
10.50
0.45
0.31
−0.21
−0.42
2.32
−1.32
−3.53
0.25
−0.06
−0.56
−0.12
2.35
−0.39
−4.02
−0.57
Factor Regressions
Summary, NYSE-VW
Except for R&D-to-market, the
q -factor
model performs well
relative to the FF ve-factor model:
The
q -factor
model outperforms the ve-factor model in the
momentum and protability categories by a big margin
The
q -factor
model outperforms in the investment category
The models largely comparable in the value-versus-growth
category, but the ve-factor model has a slight edge
Factor Regressions
Overview, ABM-EW
Across a set of 50 signicant anomalies with ABM-EW:
The average magnitude of high-minus-low alphas:
.24% in
q,
.41% in FF5, .40% in Carhart
The number of signicant high-minus-low alphas:
16 in
q,
34 in FF5, 37 in Carhart
The number of rejections by the GRS test:
37 for
q,
35 for FF5, and 39 for Carhart
Factor Regressions
Signicant momentum anomalies with ABM-EW, alphas
SUE-1 SUE-6 Abr-1 Abr-6 RE-1 RE-6 R6-1 R6-6 R11-1 I-Mom |ave|
m
0.72 0.30 0.97 0.46 0.79 0.44 1.08 0.92 1.24 0.68 0.76
αC
0.58 0.21 0.87 0.31 0.47 0.20 0.16 0.03 0.23 −0.01 0.31
αq
0.31 −0.04 0.85 0.31 0.26 −0.06 0.34 0.04 0.37 0.13 0.27
a
0.70 0.31 1.02 0.52 0.86 0.48 1.12 0.90 1.35 0.62 0.79
tm
6.39 3.36 8.74 5.61 4.08 2.65 3.86 3.82 4.27 3.47
tC
5.40 2.60 8.54 3.47 2.78 1.41 0.84 0.19 1.77 −0.08
5
tq
3.06 −0.53 5.55 2.14 1.53 −0.37 0.84 0.11 0.88 0.48
3
ta
6.50 3.41 7.94 4.68 4.62 2.87 3.10 2.68 3.62 2.44
10
|αC | 0.16 0.13 0.19 0.14 0.15 0.12 0.13 0.10 0.09 0.04 0.13
|αq | 0.11 0.10 0.19 0.17 0.13 0.15 0.16 0.14 0.11 0.10 0.14
|a|
0.19 0.08 0.19 0.11 0.23 0.14 0.18 0.16 0.27 0.21 0.18
pC
0.00 0.00 0.00 0.00 0.01 0.16 0.00 0.00 0.03 0.30
8
pq
0.00 0.01 0.00 0.00 0.01 0.01 0.00 0.00 0.00 0.20
9
pa
0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
10
Factor Regressions
Signicant momentum anomalies with ABM-EW, betas
βME
βI/A
βROE
tβME
tβI/A
tβROE
s
h
r
c
ts
th
tr
tc
SUE-1
SUE-6
Abr-1
Abr-6
RE-1
0.01
0.13
0.62
0.26
2.17
8.42
−0.13
−0.21
0.25
0.26
−2.58
−2.32
4.00
2.46
−0.03
0.07
0.56
−0.91
1.35
12.45
−0.15
−0.19
0.23
0.15
−3.43
−2.66
4.25
1.62
0.10
0.00
0.22
1.35
0.01
2.80
0.01
−0.19
−0.07
0.23
0.19
−2.20
−0.72
1.88
0.13
−0.05
0.25
2.07
−0.48
3.12
0.03
−0.14
−0.02
0.04
0.66
−1.93
−0.19
0.26
0.04
−0.15
0.94
0.72
−1.35
8.78
−0.12
−0.08
0.30
−0.23
−1.38
−0.56
2.89
−1.07
RE-6
R6-1
R6-6 R11-1 I-Mom
−0.01
0.53
0.47
−0.09
0.02
0.12
0.87
1.16
1.21
−0.21
1.85
2.30
−1.03
0.04
0.41
11.16
4.07
5.10
−0.16
0.20
0.11
−0.13 −0.67 −0.60
0.32
0.22
0.26
−0.13
0.65
0.57
−2.34
0.91
0.74
−1.10 −1.95 −2.23
3.58
0.47
0.76
−0.70
1.30
1.38
0.52
−0.06
1.36
2.13
−0.17
5.14
0.14
−0.87
0.19
0.65
0.76
−2.83
0.50
1.47
0.33
0.16
0.70
1.88
0.69
4.02
0.11
−0.35
0.10
0.49
0.74
−1.60
0.36
1.55
Factor Regressions
Signicant value anomalies with ABM-EW, alphas
m
αC
αq
a
tm
tC
tq
ta
|αC |
|αq |
|a|
pC
pq
pa
B/M
E/P
CF/P
NO/P
Dur
A/ME
Rev
|ave|
0.77
0.17
0.06
−0.01
3.29
1.35
0.27
−0.12
0.13
0.14
0.04
0.09
0.21
0.75
0.65
0.29
0.25
0.18
3.20
2.48
1.33
1.46
0.15
0.06
0.06
0.11
0.42
0.49
0.73
0.25
0.20
0.13
3.46
1.87
0.96
0.95
0.15
0.06
0.05
0.10
0.23
0.63
0.64
0.42
0.20
0.24
3.46
3.41
1.46
1.94
0.19
0.11
0.06
0.00
0.048
0.03
−0.64
−0.17
−0.01
−0.06
−2.93
−1.15
−0.04
−0.49
0.14
0.11
0.04
0.08
0.06
0.48
0.67
0.02
−0.17
−0.26
2.56
0.10
−0.69
−1.85
0.13
0.14
0.08
0.18
0.10
0.25
−0.64
−0.22
−0.30
−0.20
−3.50
−1.31
−1.89
−1.30
0.13
0.08
0.04
0.047
0.12
0.39
0.68
0.22
0.17
0.15
2
0
0
0.15
0.10
0.05
2
1
1
Factor Regressions
Signicant value anomalies with ABM-EW, betas
βME
βI/A
βROE
tβME
tβI/A
tβROE
s
h
r
c
ts
th
tr
tc
B/M
E/P
CF/P
NO/P
Dur
A/ME
Rev
0.11
1.82
−0.10
0.99
8.32
−0.59
0.15
1.29
0.39
0.51
3.66
23.11
3.93
4.32
0.00
1.15
−0.01
0.00
7.92
−0.11
0.03
1.12
0.38
−0.01
0.72
16.35
4.75
−0.06
0.01
1.33
0.04
0.04
7.82
0.26
0.06
1.26
0.53
0.04
1.21
18.64
6.28
0.40
−0.25
1.08
0.27
−5.48
10.01
2.66
−0.25
0.44
0.57
0.54
−4.66
6.55
6.51
4.98
−0.07
−1.18
−0.34
−0.61
−7.43
−1.88
−0.09
−1.11
−0.71
−0.05
−1.55
−12.35
−6.44
−0.30
0.07
1.97
−0.08
0.48
8.40
−0.40
0.13
1.49
0.52
0.42
2.78
20.90
5.35
3.45
−0.36
−1.13
0.44
−5.74
−9.19
4.13
−0.36
−0.45
0.21
−0.65
−4.44
−4.02
1.64
−3.74
Factor Regressions
Signicant investment anomalies with ABM-EW, alphas
m
αC
αq
a
tm
tC
tq
ta
|αC |
|αq |
|a|
pC
pq
pa
ACI
I/A
NOA
4PI/A
IG
NSI
CEI
NXF
−0.32
−0.19
−0.13
−0.26
−3.74
−2.10
−1.32
−2.85
0.17
0.10
0.07
0.00
0.15
0.09
−0.72
−0.47
−0.30
−0.34
−4.84
−3.84
−2.52
−3.21
0.19
0.14
0.08
0.00
0.01
0.01
−0.56
−0.63
−0.71
−0.79
−3.40
−3.94
−3.26
−4.89
0.21
0.17
0.15
0.00
0.00
0.00
−0.64
−0.50
−0.34
−0.45
−5.07
−4.28
−2.72
−4.27
0.21
0.17
0.12
0.00
0.00
0.00
−0.41
−0.22
−0.03
−0.12
−4.30
−2.43
−0.34
−1.45
0.15
0.12
0.04
0.00
0.41
0.89
−0.82
−0.62
−0.26
−0.34
−5.49
−4.73
−2.02
−3.04
0.20
0.14
0.10
0.00
0.00
0.00
−0.65
−0.54
−0.28
−0.43
−3.90
−4.69
−2.12
−3.99
0.20
0.12
0.07
0.00
0.00
0.00
−0.67
−0.54
−0.23
−0.33
−3.80
−4.34
−1.70
−2.55
0.22
0.13
0.09
0.00
0.00
0.00
Factor Regressions
Signicant investment anomalies with ABM-EW, alphas
m
αC
αq
a
tm
tC
tq
ta
|αC |
|αq |
|a|
pC
pq
pa
IvG
IvC
OA
POA
TA
PTA
|ave|
−0.50
−0.34
−0.29
−0.38
−4.32
−3.24
−2.35
−3.55
0.18
0.10
0.08
0.00
0.00
0.00
−0.50
−0.43
−0.42
−0.50
−4.30
−3.80
−3.37
−5.12
0.17
0.11
0.10
0.00
0.00
0.00
−0.30
−0.33
−0.53
−0.51
−2.50
−2.35
−4.05
−4.79
0.18
0.16
0.12
0.00
0.00
0.00
−0.43
−0.24
−0.14
−0.23
−3.88
−2.63
−1.51
−2.74
0.18
0.16
0.13
0.00
0.00
0.00
−0.46
−0.38
−0.45
−0.38
−3.99
−2.89
−4.13
−3.68
0.17
0.13
0.07
0.00
0.00
0.04
−0.51
−0.43
−0.35
−0.33
−5.06
−4.82
−3.88
−3.62
0.19
0.14
0.09
0.00
0.00
0.00
0.53
0.42
0.32
0.39
14
10
13
0.19
0.14
0.09
14
12
12
Factor Regressions
Signicant investment anomalies with ABM-EW, betas
βME
βI/A
βROE
tβME
tβI/A
tβROE
s
h
r
c
ts
th
tr
tc
ACI
I/A
NOA
4PI/A
IG
NSI
CEI
NXF
−0.14
−0.15
−0.15
−3.78
−2.09
−2.19
−0.10
0.11
−0.03
−0.24
−2.67
1.76
−0.41
−2.60
0.02
−1.25
0.15
0.46
−15.01
2.09
0.08
−0.20
0.02
−0.97
1.75
−2.97
0.19
−8.90
−0.03
0.00
0.18
−0.19
−0.01
1.47
0.11
0.61
0.51
−0.65
1.68
5.91
4.32
−5.41
0.01
−0.82
0.02
0.11
−8.50
0.25
0.08
0.06
0.06
−0.82
1.83
0.81
0.89
−8.64
0.01
−0.77
−0.08
0.29
−12.00
−1.30
0.05
−0.09
−0.13
−0.63
1.29
−1.96
−2.01
−6.75
0.07
−0.90
−0.43
1.19
−8.86
−5.10
0.04
−0.21
−0.80
−0.65
0.92
−3.98
−9.90
−7.02
0.29
−0.94
−0.31
6.47
−10.62
−3.64
0.33
−0.41
−0.45
−0.40
5.62
−5.75
−5.67
−4.28
0.23
−0.89
−0.38
5.09
−8.09
−4.26
0.27
−0.14
−0.59
−0.68
5.17
−2.02
−5.96
−6.19
Factor Regressions
Signicant investment anomalies with ABM-EW, betas
βME
βI/A
βROE
tβME
tβI/A
tβROE
s
h
r
c
ts
th
tr
tc
IvG
IvC
OA
POA
TA
PTA
0.08
−0.68
0.05
1.94
−7.46
0.79
0.13
−0.03
0.10
−0.58
3.03
−0.49
1.49
−6.31
0.10
−0.55
0.17
2.38
−6.07
2.85
0.17
0.00
0.32
−0.47
5.27
0.07
5.21
−5.68
0.22
−0.19
0.43
4.07
−1.69
4.84
0.25
0.01
0.62
−0.13
6.22
0.15
8.35
−1.08
0.18
−0.77
−0.01
5.60
−12.18
−0.22
0.23
−0.21
−0.02
−0.47
6.71
−4.71
−0.33
−6.42
0.05
−0.65
0.42
1.16
−7.89
4.90
0.05
−0.12
0.38
−0.48
0.93
−1.32
4.71
−3.26
0.09
−0.58
0.04
2.14
−9.28
0.72
0.06
−0.18
−0.14
−0.35
1.50
−2.99
−2.46
−3.53
Factor Regressions
Signicant protabilities anomalies with ABM-EW, alphas
m
αC
αq
a
tm
tC
tq
ta
|αC |
|αq |
|a|
pC
pq
pa
ROE
ROA GP/A
RS
NEI
CTO
F
TES
O
|ave|
1.00
0.91
0.10
0.56
4.60
4.42
0.71
4.14
0.19
0.12
0.12
0.00
0.00
0.00
0.90
0.65
0.82
0.53
0.12 −0.06
0.51
0.00
4.03
3.67
3.87
3.15
0.89 −0.41
3.52
0.01
0.18
0.16
0.14
0.14
0.14
0.08
0.00
0.00
0.00
0.01
0.00
0.03
0.57
0.67
0.26
0.59
4.49
5.61
2.39
5.07
0.16
0.09
0.12
0.00
0.01
0.00
0.47
0.44
0.05
0.36
4.28
4.25
0.70
4.02
0.21
0.11
0.19
0.00
0.00
0.00
0.36
0.23
−0.15
−0.18
1.98
1.29
−0.79
−1.32
0.15
0.12
0.09
0.00
0.01
0.02
0.58
0.49
0.25
0.48
2.57
2.72
1.28
2.67
0.18
0.12
0.13
0.00
0.08
0.01
0.32
0.27
0.03
0.32
2.52
2.25
0.28
2.65
0.14
0.10
0.09
0.09
0.54
0.19
−0.28
−0.42
−0.23
−0.31
−1.98
−3.23
−1.51
−2.21
0.17
0.13
0.08
0.00
0.02
0.08
0.57
0.53
0.14
0.37
8
1
7
0.17
0.12
0.12
8
7
7
Factor Regressions
Signicant protabilities anomalies with ABM-EW, betas
βME
βI/A
βROE
tβME
tβI/A
tβROE
s
h
r
c
ts
th
tr
tc
ROE
ROA
GP/A
RS
NEI
CTO
F
TES
O
−0.12
0.24
1.50
−1.11
2.24
20.45
−0.15
−0.03
1.59
0.20
−1.98
−0.22
16.11
1.32
−0.12
0.12
1.40
−1.28
1.08
18.27
−0.17
−0.07
1.48
0.14
−2.25
−0.69
14.48
0.90
0.25
0.23
0.84
2.98
1.75
8.00
0.35
−0.19
1.44
0.45
7.73
−2.80
18.02
3.84
−0.11
−0.17
0.76
−2.61
−2.69
13.52
−0.20
−0.35
0.56
0.11
−4.24
−4.90
6.98
1.09
−0.03
−0.08
0.80
−1.13
−2.20
26.12
−0.12
−0.25
0.65
0.10
−2.72
−4.00
10.97
1.01
0.44
−0.18
0.64
4.19
−1.47
6.84
0.59
−0.08
1.16
0.01
13.27
−1.31
16.02
0.06
−0.23
0.38
0.68
−3.03
2.46
5.60
−0.28
0.27
0.68
0.00
−2.93
2.22
5.20
0.01
0.10
−0.32
0.51
2.01
−2.93
6.97
0.02
−0.27
0.22
−0.13
0.34
−3.67
2.32
−1.01
0.16
0.29
−0.54
2.89
2.37
−5.74
0.17
0.27
−0.60
−0.07
3.45
3.17
−4.95
−0.60
Factor Regressions
Signicant intangibles-trading frictions anomalies with
ABM-EW, alphas
OC/A Ad/M RD/M
m
αC
αq
a
tm
tC
tq
ta
|αC |
|αq |
|a|
pC
pq
pa
0.35
0.38
0.39
0.45
3.72
3.67
3.12
4.38
0.15
0.17
0.10
0.00
0.00
0.00
0.64
0.20
−0.25
−0.32
2.15
0.84
−0.84
−1.45
0.23
0.23
0.14
0.10
0.047
0.23
0.94
0.65
0.78
0.69
3.69
2.70
2.66
2.70
0.27
0.36
0.22
0.01
0.00
0.04
H/N
OL
−0.50
−0.28
−0.05
−0.11
−3.62
−2.68
−0.44
−1.19
0.16
0.12
0.08
0.00
0.00
0.01
0.41
0.38
−0.04
−0.01
2.18
2.14
−0.22
−0.08
0.15
0.13
0.07
0.05
0.11
0.18
Svol
MDR S-Rev
−0.45 −0.66
−0.47 −0.73
−0.15 −0.16
−0.18 −0.28
−2.18 −2.14
−2.23 −3.62
−0.76 −0.76
−0.92 −2.02
0.17
0.19
0.16
0.12
0.08
0.09
0.06
0.00
0.04
0.03
0.31
0.04
Disp
−0.57 −0.44
−0.67 −0.63
−0.62 −0.04
−0.43 −0.33
−2.61 −1.98
−2.94 −3.47
−1.74 −0.25
−1.45 −2.32
0.20
0.16
0.19
0.10
0.15
0.07
0.02
0.01
0.00
0.29
0.03
0.07
Dvol
|ave|
−0.37 0.53
−0.15 0.45
0.03 0.25
0.08 0.29
−2.64
−1.32
8
0.20
2
0.73
4
0.08 0.18
0.12 0.17
0.06 0.11
0.02
7
0.00
7
0.15
5
Factor Regressions
Signicant intangibles-trading frictions anomalies with
ABM-EW, betas
OC/A Ad/M RD/M
βME
βI/A
βROE
tβME
tβI/A
tβROE
s
h
r
c
ts
th
tr
tc
0.00
0.04
0.03
0.07
0.34
0.35
−0.02
−0.07
−0.02
0.07
−0.56
−1.06
−0.26
0.59
0.14
1.67
0.27
1.02
8.52
1.38
0.25
0.98
1.01
0.55
3.16
10.27
9.44
3.95
H/N
OL
0.63
0.09 0.26
0.28 −1.14 0.29
−0.37
−0.02 0.47
4.61
2.39 3.82
1.05 −15.65 2.29
−2.02
−0.32 4.51
0.50
0.13 0.30
−0.28 −0.25 −0.07
−0.39 −0.20 0.86
0.76 −0.82 0.41
5.07
2.89 5.45
−2.08 −4.82 −0.88
−1.67 −2.63 8.81
2.73 −7.73 2.98
Svol
MDR S-Rev
Disp
Dvol
0.18
0.67 0.05
0.28 −0.64
−0.16 −1.19 0.16 −0.14 −0.74
−0.52 −0.78 0.19 −1.04
0.02
1.19
4.65 0.20
4.61 −6.85
−0.87 −6.23 0.58 −2.08 −8.45
−4.00 −4.44 0.98 −14.58
0.20
0.15
0.65 −0.06
0.28 −0.69
0.09 −0.64 −0.31
0.02 −0.43
−0.60 −1.24 −0.13 −1.06 −0.33
−0.23 −0.53 0.50 −0.02 −0.32
1.23
10.53 −0.37
5.32 −12.70
0.62 −4.86 −1.31
0.25 −6.24
−3.78 −12.43 −0.42 −16.58 −5.39
−1.23 −3.54 1.86 −0.17 −3.68
Factor Regressions
Summary, ABM-EW
The
q -factor
The
model performs well vis-a-vis the ve-factor model:
q -factor
model outperforms the ve-factor model in the
momentum and protability categories by a big margin
The two models are largely comparable in the
value-versus-growth, investment, intangibles, and trading
frictions categories
Outline
1
Factors
2
Testing portfolios
3
Factor Regressions
4
Robustness
5
Conceptual Comparison
Robustness
Overview
The
q -factor
model outperforms the FF ve-factor model with
alternative factor constructions
Robustness
Properties of alternative q -factors, 1/196712/2013
2×2×2
rME
rI/A
rROE
rME
rI/A
m
βMKT
βSMB
βHML
βUMD
0.33
−0.03
0.05
1.03
0.19
0.02
(2.27)
(−0.79)
(4.82)
(74.66)
(6.66)
(1.24)
0.26
0.18
(3.90)
(3.63)
−0.07
−0.02
0.28
0.03
(−5.38)
(−0.56)
(10.14)
(1.31)
0.40
0.36
−0.01
−0.20
−0.08
0.18
(5.00)
(4.99)
(−0.63)
(−3.53)
(−1.52)
(5.50)
a
b
s
h
r
c
−0.01
0.05
1.03
0.02
0.01
0.08
(−0.39)
(5.32)
(76.52)
(0.88)
(0.24)
(2.19)
0.07
(2.20)
rROE
αC
0.29
(4.80)
−0.02
−0.04
0.01
0.00
0.59
(−2.47)
(−2.94)
(0.61)
(0.21)
(22.79)
−0.01
−0.05
−0.17
0.59
0.10
(−0.51)
(−1.67)
(−3.23)
(12.90)
(1.26)
Robustness
Properties of alternative q -factors, 1/196712/2013
2×3
rME
rI/A
m
rME
rI/A
rROE
βMKT
βSMB
βHML
βUMD
0.30
−0.05
0.04
1.03
0.19
0.01
(2.07)
(−1.49)
(4.54)
(87.41)
(6.85)
(0.53)
0.29
(3.07)
rROE
αC
0.13
−0.08
0.01
0.48
0.02
(1.88)
(−4.57)
(0.45)
(15.75)
(0.76)
0.57
0.52
−0.03
−0.31
−0.10
0.27
(4.44)
(4.40)
(−0.89)
(−3.51)
(−1.06)
(5.04)
a
b
s
h
r
c
−0.02
0.04
1.02
0.05
−0.03
0.02
(−0.79)
(5.29)
(100.22)
(3.31)
(−1.22)
(0.78)
−0.04
0.00
−0.03
0.07
−0.04
0.90
(−1.34)
(0.52)
(−1.89)
(3.07)
(−2.03)
(31.81)
0.37
(4.02)
−0.02
−0.06
−0.24
0.97
0.16
(−0.63)
(−1.22)
(−3.09)
(12.90)
(1.41)
Robustness
Properties of alternative q -factors, 1/196712/2013
2×2
rME
rI/A
rROE
rME
rI/A
rROE
m
αC
βMKT
βSMB
βHML
βUMD
0.29
−0.07
0.06
1.05
0.19
0.00
(1.96)
(−1.91)
(6.34)
(88.91)
(6.57)
(0.15)
0.19
0.10
(2.68)
(1.99)
−0.08
0.01
0.32
0.01
(−5.47)
(0.32)
(13.36)
(0.30)
0.40
0.35
0.00
−0.21
−0.07
0.19
(4.36)
(4.04)
(0.17)
(−3.07)
(−1.06)
(4.61)
a
b
s
h
r
c
−0.04
0.05
1.05
0.04
−0.03
0.03
(−1.61)
(8.20)
(103.46)
(2.83)
(−1.36)
(1.20)
0.00
−0.03
−0.03
0.05
−0.08
0.59
(0.05)
(−3.09)
(−2.95)
(3.00)
(−4.48)
(24.00)
0.23
(3.59)
0.01
−0.02
−0.16
0.72
0.09
(0.55)
(−0.64)
(−2.97)
(12.82)
(1.04)
Robustness
Properties of the new FF factors, alternative constructions,
1/196712/2013
2×2×2×2
SMB
HML
RMW
CMA
m
αC
βMKT
βSMB
βHML
βUMD
0.29
0.03
−0.02
0.94
0.08
0.00
(2.23)
(1.26)
(−3.18)
(66.68)
(5.26)
(0.52)
0.29
0.06
−0.02
−0.06
0.69
0.00
(2.74)
(1.66)
(−1.82)
(−3.73)
(47.39)
(0.10)
0.27
0.25
(3.78)
(3.97)
0.16
0.14
(2.84)
(2.88)
−0.02
−0.16
0.20
0.00
(−1.24)
(−3.35)
(6.09)
(0.00)
−0.08
−0.03
0.15
0.02
(−5.51)
(−1.55)
(6.23)
(0.97)
Robustness
Properties of the new FF factors, alternative constructions,
1/196712/2013
2×2×2×2
SMB
HML
RMW
αq
βME
βI / A
βROE
0.07
−0.03
0.89
−0.11
−0.05
(1.88)
(−1.89)
(48.08)
(−3.89)
(−2.38)
0.09
−0.06
−0.05
0.65
−0.07
(0.89)
(−1.90)
(−0.81)
(8.97)
(−1.05)
0.13
(1.68)
CMA
βMKT
−0.00
(−0.01)
−0.03
−0.10
0.16
0.21
(−1.19)
(−1.82)
(2.84)
(4.33)
−0.04
−0.02
0.44
−0.02
(−3.79)
(−1.09)
(19.61)
(−0.68)
Robustness
Properties of the new FF factors, alternative constructions,
1/196712/2013
2×2
SMB
HML
RMW
CMA
m
αC
βMKT
βSMB
βHML
βUMD
0.28
−0.03
0.02
1.01
0.14
0.00
(2.03)
(−1.45)
(3.20)
(92.98)
(8.18)
(0.05)
0.27
0.03
−0.02
−0.03
0.71
0.00
(2.58)
(1.17)
(−3.37)
(−3.99)
(68.49)
(0.22)
0.19
0.23
(2.56)
(3.27)
0.24
0.14
(3.33)
(2.90)
−0.01
−0.19
−0.02
0.01
(−0.37)
(−2.94)
(−0.32)
(0.44)
−0.08
0.02
0.32
0.02
(−5.38)
(0.69)
(12.31)
(1.08)
Robustness
Properties of the new FF factors, alternative constructions,
1/196712/2013
2×2
SMB
HML
RMW
αq
βME
βI / A
βROE
0.05
0.01
0.95
−0.08
−0.10
(1.40)
(0.71)
(59.89)
(−4.16)
(−5.71)
0.04
−0.06
−0.03
0.76
−0.12
(0.51)
(−2.09)
(−0.58)
(11.78)
(−2.12)
0.03
(0.50)
CMA
βMKT
0.03
(0.93)
0.00
−0.09
−0.05
0.36
(0.07)
(−1.78)
(−0.89)
(7.87)
−0.06
0.03
0.63
−0.09
(−5.34)
(1.28)
(30.82)
(−3.76)
Robustness
Performance across 36 signicant anomalies with NYSE-VW
The average magnitude of high-minus-low alphas:
q:
.20% in 2
.29% in 2
FF5:
× 3 × 3,
.26% in 2
× 2 × 2,
.26% in 2
× 3,
×2
.36% in 2
× 3,
.40% in 2
× 2 × 2 × 2,
.37% in 2
×2
The number of signicant high-minus-low alphas:
q:
7 in 2 × 3 × 3, 10 in 2 × 2 × 2, 11 in 2 × 3, 11 in 2 × 2
FF5:
19 in 2
× 3,
19 in 2
× 2 × 2 × 2,
20 in 2
×2
The number of rejections by the GRS test:
q:
25 in 2 × 3 × 3, 20 in 2 × 2 × 2, 25 in 2 × 3, 23 in 2 × 2
FF5:
25 in 2
× 3,
23 in 2
× 2 × 2 × 2,
25 in 2
×2
Robustness
Performance across 50 signicant anomalies with ABM-EW
The average magnitude of high-minus-low alphas:
q:
.24% in 2
.31% in 2
FF5:
× 3 × 3,
.29% in 2
× 2 × 2,
.29% in 2
× 3,
×2
.41% in 2
× 3,
.46% in 2
× 2 × 2 × 2,
.43% in 2
×2
The number of signicant high-minus-low alphas:
q:
16 in 2 × 3 × 3, 20 in 2 × 2 × 2, 21 in 2 × 3, 22 in 2 × 2
FF5:
34 in 2
× 3,
36 in 2
× 2 × 2 × 2,
35 in 2
×2
The number of rejections by the GRS test:
q:
37 in 2 × 3 × 3, 37 in 2 × 2 × 2, 36 in 2 × 3, 36 in 2 × 2
FF5:
35 in 2
× 3,
34 in 2
× 2 × 2 × 2,
35 in 2
×2
Outline
1
Factors
2
Testing portfolios
3
Factor Regressions
4
Robustness
5
Conceptual Comparison
Conceptual Comparison
The q -factor model inspired from the investment CAPM
Two periods,
t
and
t +1
Heterogenous rms, indexed by
Firm
i 's
productive assets,
Ait
i = 1, . . . , N
and
Ait+1
Ait+1 = Iit + Ait
in which Iit is investment
Firm
i 's
operating prots in dates
constant returns to scale in assets
Mt+1 :
Stochastic discount factor
t
and
t + 1, Πit
and
Πit+1 ,
Conceptual Comparison
The investment CAPM
Firm
i 's
value-maximization problem:
Pit + Dit ≡ max Πit − Iit −
{Iit }
a
2
Iit
Ait
2
Ait + Et [Mt+1 [Πit+1 + Ait+1 ]]
The rst principle for investment:
Πit+1
Iit
1+a
= Et Mt+1
+1
Ait
Ait+1
A more familiar form from capital budgeting:
S
rit+
1 =
Pit+1 + Dit+1
Πit+1 + Ait+1
Πit+1 /Ait+1 + 1
=
=
Pit
Et [Mt+1 (Πit+1 + Ait+1 )]
1 + a(Iit /Ait )
Conceptual Comparison
The investment CAPM
Motivating the investment and ROE factors:
S
Et [rit+
1] =
Et [Πit+1 /Ait+1 ] + 1
1 + a(Iit /Ait )
Higher investment, lower expected returns, all else equal
Higher expected ROE, higher expected returns, all else equal
ROE forecasts returns to the extent that it forecasts ROE (serves
as a proxy for the expected ROE)
Conceptual Comparison
The FF ve-factor model based on valuation theory
The Miller-Modigliani (1961) valuation model:
Pit
=
Bit
P∞
τ =1 E [Yit+τ
− 4Bit+τ ]/(1 + ri )τ
,
Bit
FF (2006, 2015) derive three predictions, all else equal:
A lower
Pit /Bit
means a higher
A higher
E [Yit+τ ]
A higher
E [4Bit+τ ]/Bit
ri
means a higher
ri
means a lower
The FF motivation seems awed
ri
Conceptual Comparison
I: IRR 6= the one-period-ahead expected return
FF (2015, p. 2): Most asset pricing research focuses on
short-horizon returnswe use a one-month horizon in our tests. If
each stock's short-horizon expected return is positively related to its
internal rate of returnif, for example, the expected return is the
same for all horizonsthe valuation equation... (our emphasis).
Assumption clearly contradicting price and earnings momentum
Conceptual Comparison
I: IRR 6= the one-period-ahead expected return
IRR estimates per Gebhardt, Lee, and Swaminathan (2001)
2×3
Return
SMB
[t]
HML
[t]
RMW
[t]
CMA
[t]
0.26
1.89
0.23
1.38
0.32
2.65
0.28
2.75
IRR
2×2
Di
Return
0.06
0.20
9.61
1.45
0.27 −0.04
40.30 −0.23
−0.08
0.40
−15.74
3.34
0.05
0.23
9.22
2.27
0.27
1.89
0.17
1.42
0.21
2.63
0.20
2.67
IRR
2×2×2×2
Di
0.07
0.20
10.18
1.43
0.19 −0.02
35.93 −0.14
−0.06
0.27
−13.25
3.38
0.03
0.17
8.83
2.25
Return
IRR
Di
0.25
0.05
0.20
1.94
9.98
1.56
0.17
0.19 −0.02
1.37 40.11 −0.12
0.23 0.01
0.22
2.78 4.18
2.64
0.17 −0.01
0.18
2.68 −3.46
2.84
Conceptual Comparison
I: IRR 6= the one-period-ahead expected return
IRR estimates per the Easton (2004) MPEG model
2×3
Return
SMB
[t]
HML
[t]
RMW
[t]
CMA
[t]
0.26
1.86
0.25
1.43
0.34
2.54
0.29
2.86
IRR
2×2
2×2×2×2
Di
Return
IRR
Di
Return
IRR
Di
0.18
0.08
29.04
0.59
0.25
0.00
15.46 −0.01
−0.24
0.57
−21.17
4.34
0.19
0.11
17.02
1.07
0.27
1.86
0.19
1.50
0.22
2.45
0.20
2.68
0.18
28.97
0.17
15.38
−0.16
−19.57
0.12
16.37
0.09
0.60
0.02
0.17
0.37
4.24
0.09
1.15
0.27
2.01
0.18
1.40
0.23
2.56
0.16
2.54
0.15
33.10
0.12
12.26
−0.10
−14.28
0.08
12.53
0.11
0.85
0.06
0.46
0.33
3.72
0.09
1.38
Conceptual Comparison
I: IRR 6= the one-period-ahead expected return
IRR estimates per Claus and Thomas (2001)
2×3
SMB
[t]
HML
[t]
RMW
[t]
CMA
[t]
2×2
2×2×2×2
Return
IRR
Di
Return
IRR
Di
Return
IRR
Di
0.27
1.95
0.23
1.36
0.31
2.78
0.27
2.67
0.08
14.78
0.00
0.01
0.04
5.71
0.01
0.97
0.19
1.40
0.23
1.36
0.28
2.47
0.26
2.62
0.27
1.95
0.17
1.42
0.20
2.76
0.19
2.59
0.08
14.64
0.01
1.02
0.03
8.08
−0.01
−1.39
0.20
1.41
0.17
1.36
0.17
2.37
0.20
2.68
0.26
1.99
0.17
1.38
0.23
2.90
0.16
2.61
0.07
14.39
0.02
2.63
0.05
11.74
−0.01
−1.60
0.19
1.45
0.15
1.20
0.18
2.32
0.17
2.69
Conceptual Comparison
I: IRR 6= the one-period-ahead expected return
IRR estimates per Gordon and Gordon (1997)
2×3
Return
SMB
[t]
HML
[t]
RMW
[t]
CMA
[t]
0.27
2.00
0.19
1.16
0.31
3.17
0.23
2.28
IRR
2×2
Di
0.00
0.27
−0.61
2.06
0.25 −0.06
20.81 −0.39
0.08
0.23
12.68
2.37
0.03
0.20
6.03
1.97
Return
IRR
2×2×2×2
Di
Return
0.27
0.00
0.27
1.99 −0.27
2.03
0.15
0.18 −0.03
1.28 19.82 −0.26
0.20 0.05
0.16
3.08 9.83
2.38
0.16
0.02
0.14
2.23
5.67
1.94
0.26
2.03
0.15
1.26
0.23
3.20
0.15
2.35
IRR
Di
−0.01
0.27
−2.27
2.15
0.22 −0.07
23.49 −0.56
0.13
0.10
33.25
1.35
−0.02
0.17
−7.08
2.75
Conceptual Comparison
I: IRR 6= the one-period-ahead expected return
IRR estimates per Ohlson and Juettner-Nauroth (2005)
2×3
SMB
[t]
HML
[t]
RMW
[t]
CMA
[t]
2×2
2×2×2×2
Return
IRR
Di
Return
IRR
Di
Return
IRR
Di
0.27
1.98
0.17
1.04
0.30
3.05
0.25
2.46
0.05
9.39
0.05
7.13
0.00
0.19
0.00
0.59
0.22
1.64
0.12
0.75
0.30
3.05
0.25
2.43
0.27
1.98
0.14
1.18
0.19
2.80
0.17
2.24
0.05
9.41
0.03
6.92
−0.00
−0.05
−0.00
−1.23
0.22
1.63
0.11
0.90
0.19
2.80
0.17
2.32
0.25
1.99
0.15
1.17
0.21
2.80
0.15
2.39
0.04
7.81
0.04
8.77
0.02
4.15
−0.01
−4.21
0.21
1.71
0.11
0.85
0.19
2.55
0.17
2.61
Conceptual Comparison
I: IRR 6= the one-period-ahead expected return
IRR estimates averaged across the ve estimation models
2×3
SMB
[t]
HML
[t]
RMW
[t]
CMA
[t]
2×2
2×2×2×2
Return
IRR
Di
Return
IRR
Di
Return
IRR
Di
0.25
1.77
0.25
1.45
0.35
2.68
0.28
2.75
0.09
13.05
0.17
20.96
−0.07
−16.56
0.08
14.96
0.16
1.14
0.07
0.43
0.42
3.25
0.20
1.99
0.25
1.76
0.19
1.52
0.23
2.69
0.20
2.66
0.09
13.13
0.12
19.82
−0.05
−14.90
0.05
12.90
0.16
1.13
0.07
0.53
0.28
3.23
0.15
2.06
0.24
1.84
0.18
1.45
0.25
2.91
0.16
2.61
0.08
13.37
0.12
19.72
0.00
1.36
0.02
5.21
0.17
1.27
0.06
0.49
0.25
2.86
0.15
2.34
Conceptual Comparison
I: IRR 6= the one-period-ahead expected return
Robustness with Hou, van Dijk, and Zhang's (2012) cross-sectional
earnings forecasts, IRRs averaged across the ve models
2×3
Return
SMB
[t]
HML
[t]
RMW
[t]
CMA
[t]
0.28
2.00
0.33
2.26
0.28
2.62
0.31
3.48
IRR
2×2
Di
Return
0.23
0.06
13.49
0.41
0.42 −0.10
51.22 −0.67
−0.13
0.41
−21.32
3.81
0.21
0.10
35.32
1.15
0.29
2.00
0.22
2.06
0.20
2.68
0.21
3.15
IRR
2×2×2×2
Di
0.23
0.06
13.38
0.43
0.30 −0.08
52.28 −0.72
−0.10
0.29
−22.16
4.02
0.15
0.06
37.92
0.97
Return
IRR
Di
0.29 0.21
0.09
2.17 13.87
0.64
0.25 0.30 −0.05
2.33 50.53 −0.45
0.25 0.03
0.22
3.62 8.08
3.18
0.15 0.07
0.08
2.86 14.05
1.51
Conceptual Comparison
I: IRR 6= the one-period-ahead expected return
Robustness with Tang, Wu, and Zhang's (2014) cross-sectional
ROE forecasts, IRRs averaged across the ve models
2×3
Return
SMB
[t]
HML
[t]
RMW
[t]
CMA
[t]
0.32
2.39
0.31
2.25
0.23
2.32
0.28
3.21
IRR
2×2
Di
Return
0.00
0.32
0.10
2.39
0.40 −0.09
39.43 −0.63
−0.17
0.40
−33.97
4.06
0.15
0.13
30.53
1.50
0.33
2.41
0.23
2.20
0.15
2.23
0.19
2.97
IRR
2×2×2×2
Di
Return
0.01
0.32
0.82
2.37
0.28 −0.05
39.39 −0.51
−0.12
0.27
−36.15
4.03
0.11
0.08
27.79
1.31
0.30
2.41
0.26
2.45
0.24
3.42
0.14
2.56
IRR
Di
−0.04
0.34
−4.57
2.69
0.26
0.00
40.15 −0.01
−0.02
0.26
−6.49
3.69
0.05
0.09
14.83
1.62
Conceptual Comparison
II: HML is redundant in describing average returns in the data
HML redundant in FF (2015), inconsistent with their reasoning
Consistent with the investment CAPM:
S
Et [rit+
1] =
in which the denominator =
Et [Πit+1 /Ait+1 ] + 1
,
1 + a(Iit /Ait )
Pit /Bit
Consistent with valuation theory too: Investment forecasts returns
via
Pit /Bit ,
not
Et [4Bit+τ /Bit ]
as FF argue
Conceptual Comparison
III: The expected investment-return relation is likely positive
Reformulating valuation theory with
Pit
Pit
Bit
Pit
Bit
=
Et [Yit+1 − 4Bit+1 ] + Et [Pit+1 ]
,
1 + Et [rit+1 ]
h
i
h
i
h
Pit+
Et YBit+it − Et 4BBit+
+
E
1+
t Bit+
it
1
=
1
1
1
4Bit+1
Bit
i
+ Et [rit+1 ]
h
h
i
i
i
4Bit+
Pit+
Pit+
+ Et
−
1
+
E
t
Bit
Bit+
Bit+
,
1
Et
=
Et [rit+1 ]:
h
Yit+1
Bit
1
1
1
1
1
1
+ Et [rit+1 ]
Recursive substitution: A positive
Et [4Bit+τ /Bit ]-Et [rit+1 ]
.
relation
Conceptual Comparison
III: The expected investment-return relation is likely positive
In a dynamic investment model,
S
rit+
1 =
Πit+1
Ait+1
+ (a/2)
Iit+1
Ait+1
1
2
+a
+
Iit
Ait
h
1
+a
Iit+1
Ait+1
i
S
The Iit+1 /Iit -Et [rit+1 ] relation is positive, per Cochrane (1991)
See the aggregate evidence in Lettau and Ludvigson (2002) and
cross-sectional evidence in Liu and Zhang (2008, 2014)
Conceptual Comparison
IV: Past investment is a poor proxy for the expected investment
Et [4Bit+τ /Bit ]-Et [rit+1 ] relation,
to proxy for E [4Bit+τ ]/Bit
After arguing for a negative
(2015) use
4TAit /TAit−1
FF
However, past assets (book equity) growth does not forecast future
book equity growth (while protability forecasts future protability)
See the lumpy investment literature, e.g., Dixit and Pindyck
(1994); Domes and Dunne (1998); Whited (1998)
Conceptual Comparison
IV: Past investment is a poor proxy for the expected investment
Total assets
≥
$5 millions and book equity
Bit+τ −Bit+τ −1 4TAit
TAit−1
Bit+τ −1
τ
1
2
3
4
5
6
7
8
9
10
≥
$2.5 millions
Bit+τ −Bit+τ −1 4Bit
Bit−1
Bit+τ −1
OPit+τ
Bit+τ
OPit
Bit
γ0
γ1
R2
γ0
γ1
R2
γ0
γ1
R2
0.09
0.10
0.10
0.10
0.10
0.10
0.10
0.10
0.10
0.09
0.22
0.10
0.07
0.05
0.05
0.05
0.05
0.03
0.03
0.04
0.05
0.01
0.01
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.09
0.10
0.10
0.10
0.10
0.10
0.10
0.10
0.10
0.10
0.21
0.10
0.06
0.06
0.03
0.03
0.03
0.01
0.01
0.02
0.06
0.02
0.01
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.03
0.06
0.07
0.09
0.10
0.10
0.11
0.12
0.12
0.13
0.80
0.67
0.59
0.53
0.49
0.46
0.43
0.40
0.38
0.37
0.55
0.36
0.28
0.22
0.19
0.16
0.14
0.12
0.12
0.11
Conceptual Comparison
IV: Past investment is a poor proxy for the expected investment
Total assets
≥
$25 millions and book equity
Bit+τ −Bit+τ −1 4Bit
Bit−1
Bit+τ −1
Bit+τ −Bit+τ −1 4TAit
TAit−1
Bit+τ −1
τ
1
2
3
4
5
6
7
8
9
10
≥
$12.5 millions
OPit+τ
Bit+τ
OPit
Bit
γ0
γ1
R2
γ0
γ1
R2
γ0
γ1
R2
0.08
0.09
0.09
0.09
0.09
0.09
0.09
0.09
0.09
0.09
0.23
0.13
0.09
0.07
0.06
0.05
0.05
0.03
0.04
0.05
0.05
0.02
0.01
0.01
0.00
0.00
0.00
0.00
0.00
0.00
0.08
0.09
0.09
0.09
0.09
0.09
0.09
0.09
0.09
0.09
0.25
0.13
0.09
0.07
0.05
0.04
0.04
0.02
0.02
0.03
0.07
0.02
0.01
0.01
0.01
0.00
0.00
0.00
0.00
0.00
0.03
0.06
0.08
0.09
0.10
0.11
0.12
0.13
0.13
0.14
0.82
0.69
0.61
0.56
0.52
0.49
0.45
0.42
0.41
0.40
0.61
0.42
0.32
0.26
0.22
0.19
0.16
0.14
0.13
0.12
Conceptual Comparison
Four concerns on the FF (2015) conceptual framework
The IRR of RMW is often signicantly negative
The expected investment-expected return relation is likely positive
Past investment is a poor proxy for the expected investment
Without the redundant HML, the ve-factor model becomes a
noisy version of the
q -factor
model
Conclusion
A comparison of new factor models
The FF ve-factor model is a noisy version of the
q -factor
model
Conclusion
Ongoing revision
Extending the anomaly variables from nearly 80 to 450
Extending the set of alternative models to include Carhart, FF5,
Carhart
+
Pastor-Stambaugh, Jagannathan-Wang's 4th-quarter
consumption growth, and the leverage factor