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
The Rodney L. White Center for Financial Research Conference on
Financial Decisions and Asset Markets, Wharton
March 20, 2015
Introduction
Insight
The
q -factor
model outperforms the Fama and French (2015)
ve-factor model on both conceptual and empirical grounds
Introduction
The
q -factor
model from Hou, Xue, and Zhang (2015)
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
July 2007
An equilibrium three-factor model
January 2009
Production-based factors
April 2009
A better three-factor model
June 2009
that explains more anomalies
An alternative three-factor model
Digesting anomalies: An investment approach
Fama and French (2013): A four-factor model for
April 2010, April 2011
October 2012 , August 2014
June 2013
the size, value, and protability
patterns in stock returns
Fama and French (2014):
A ve-factor asset pricing model
November 2013 , August 2014
Introduction
Properties of the
m
rME
rI/A
rROE
rME
rI/A
βMKT
βSMB
1/196712/2013
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
q -factors,
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
Outline
1
Factors
2
Conceptual Comparison
3
Empirical Comparison
Outline
1
Factors
2
Conceptual Comparison
3
Empirical Comparison
Factors
The
rME , rI/A ,
and
rROE
from a triple 2
×3×3
q -factors
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
Conceptual Comparison
3
Empirical Comparison
Conceptual Comparison
The
q -factor
model motivated from
q -theory
From the rst principle of investment (the NPV rule):
S
Et [rit+
1] =
Et [Πit+1 /Ait+1 ] + 1
,
1 + a(Iit /Ait )
all else equal,
higher investment means lower expected returns
higher expected ROE means higher expected returns
ROE forecasts returns to the extent that it forecasts ROE (works 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 reasoning 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
2
Return
IRR
Di
Return
SMB
0.26
0.06
0.20
[t]
1.89
9.61
1.45
HML
0.23
0.27
−0.04
−0.23
0.17
0.40
0.21
3.34
2.63
×2
2
×2×2×2
IRR
Di
Return
IRR
Di
0.27
0.07
0.20
1.89
10.18
1.43
0.25
0.05
0.20
1.94
9.98
0.19
1.56
−0.02
−0.14
0.17
0.19
1.37
40.11
−0.02
−0.12
0.27
0.23
0.01
3.38
2.78
4.18
2.64
−0.01
−3.46
0.18
[t]
1.38
RMW
0.32
[t]
2.65
CMA
0.28
0.05
0.23
0.20
0.03
0.17
0.17
[t]
2.75
9.22
2.27
2.67
8.83
2.25
2.68
40.30
−0.08
−15.74
1.42
35.93
−0.06
−13.25
Robust to alternative IRR estimates and earnings forecasts
0.22
2.84
Conceptual Comparison
II: HML separate in theory but redundant in the data
HML redundant in FF (2015), inconsistent with their reasoning
Consistent with
q -theory:
S
Et [rit+
1] =
in which the denominator =
Et [Πit+1 /Ait+1 ] + 1
,
1 + a(Iit /Ait )
Pit /Bit
Conceptual Comparison
III: The expected investment-return relation is likely positive
Reformulating valuation theory with
Pit
=
Pit
Bit
=
Pit
Bit
=
Et [rit+1 ]:
Et [Yit+1 − 4Bit+1 ] + Et [Pit+1 ]
,
1 + Et [rit+1 ]
h
i
h
i
h
Pit+1
1
Et YBit+it 1 − Et 4BBit+
+
E
t Bit+1 1 +
it
4Bit+1
Bit
i
+ Et [rit+1 ]
h
h
h
i
i
i
Yit+1
4Bit+1 Pit+1
Pit+1
Et Bit + Et
−
1
+
E
t
Bit
Bit+1
Bit+1
,
1
1
+ Et [rit+1 ]
Recursive substitution: A positive
Et [4Bit+τ /Bit ]-Et [rit+1 ]
.
relation
Conceptual Comparison
IV: Past investment does not forecast future investment
Total assets
≥
$5 millions and book equity
Bit+τ −Bit+τ −1 4TAit
TAit−1
Bit+τ −1
τ
γ0
γ1
1
0.09
0.22
2
0.10
0.10
3
0.10
4
R2
≥
$2.5 millions
Bit+τ −Bit+τ −1 4Bit
Bit−1
Bit+τ −1
γ0
γ1
0.05
0.09
0.21
0.01
0.10
0.10
0.07
0.01
0.10
0.10
0.05
0.00
5
0.10
0.05
6
0.10
7
R2
OPit+τ | OPit
R2
γ0
γ1
0.06
0.03
0.80
0.55
0.02
0.06
0.67
0.36
0.06
0.01
0.07
0.59
0.28
0.10
0.06
0.00
0.09
0.53
0.22
0.00
0.10
0.03
0.00
0.10
0.49
0.19
0.05
0.00
0.10
0.03
0.00
0.10
0.46
0.16
0.10
0.05
0.00
0.10
0.03
0.00
0.11
0.43
0.14
8
0.10
0.03
0.00
0.10
0.01
0.00
0.12
0.40
0.12
9
0.10
0.03
0.00
0.10
0.01
0.00
0.12
0.38
0.12
10
0.09
0.04
0.00
0.10
0.02
0.00
0.13
0.37
0.11
Conceptual Comparison
Summary: Four critiques on the FF (2015) reasoning
I: The IRR of RMW is often signicantly negative
II: The expected investment-return relation is likely positive
III: Past investment is a poor proxy for the expected investment
IV: Without the redundant HML, the ve-factor model becomes
(a noisy version of ) the
q -factor
model
Outline
1
Factors
2
Conceptual Comparison
3
Empirical Comparison
Empirical Comparison
Factor regressions with testing deciles formed on 73 anomalies
Panel A: Momentum
SUE-1 , earnings surprise
SUE-6 , earnings surprise
(1-month holding period),
(6-month holding period),
Foster, Olsen, and Shevlin (1984)
Foster, Olsen, and Shevlin (1984)
Abr-1 , cumulative abnormal stock
Abr-6 , cumulative abnormal stock
returns around earnings announcements
returns around earnings announcements
(1-month holding period), Chan,
(6-month holding period), Chan,
Jegadeesh, and Lakonishok (1996)
Jegadeesh, and Lakonishok (1996)
RE-1 , revisions in analysts' earnings
RE-6 , revisions in analysts' earnings
forecasts (1-month holding period),
forecasts (6-month holding period),
Chan, Jegadeesh, and Lakonishok (1996)
Chan, Jegadeesh, and Lakonishok (1996)
R6-1 , price momentum (6-month prior
R6-6 , price momentum (6-month prior
returns, 1-month holding period),
returns, 6-month holding period),
Jegadeesh and Titman (1993)
Jegadeesh and Titman (1993)
R11-1 , price momentum, (11-month
I-Mom , industry momentum,
prior returns, 1-month holding period),
Moskowitz and Grinblatt (1999)
Fama and French (1996)
Empirical Comparison
Testing deciles formed on 73 anomalies across six categories
Panel B: Value-versus-growth
B/M , book-to-market equity,
Rosenberg, Reid, and Lanstein (1985)
Rev , reversal, De Bondt and Thaler (1985)
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)
A/ME , market leverage,
Bhandari (1988)
E/P , earnings-to-price, Basu (1983)
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)
Empirical Comparison
Testing deciles formed on 73 anomalies across six categories
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,
Xing (2008)
CEI , composite issuance,
Daniel and Titman (2006)
IvG , inventory growth,
Belo and Lin (2011)
OA , operating accruals, Sloan (1996)
NSI , net stock issues,
Ponti and Woodgate (2008)
NXF , net external nancing,
Bradshaw, Richardson, and Sloan (2006)
IvC , inventory changes,
Thomas and Zhang (2002)
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)
Empirical Comparison
Testing deciles formed on 73 anomalies across six categories
Panel D: Protability
ROE , return on equity,
Haugen and Baker (1996)
RNA , return on net operating assets,
ROA , return on assets,
Balakrishnan, Bartov, and Faurel (2010)
PM , prot margin, Soliman (2008)
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)
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)
FP , failure probability,
Campbell, Hilscher, and Szilagyi (2008)
O
,
O -score,
Dichev (1998)
Empirical Comparison
Testing deciles formed on 73 anomalies across six categories
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,
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)
Chan, Lakonishok, and Sougiannis (2001)
H/N , hiring rate,
Belo, Lin, and Bazdresch (2014)
G
, corporate governance,
Gompers, Ishii, and Metrick (2003)
OL , operating leverage,
Novy-Marx (2011)
AccQ , accrual quality, Francis, Lafond,
Olsson, and Schipper (2005)
Empirical Comparison
Testing deciles formed on 73 anomalies across six categories
Panel F: Trading frictions
ME , the market equity,
Banz (1981)
Tvol , total volatility,
Ang, Hodrick, Xing, and Zhang (2006)
MDR , maximum daily return,
Bali, Cakici, and Whitelaw (2011)
D-β , Dimson's beta, Dimson (1979)
Disp , dispersion of analysts'
earnings forecasts,
Ivol , idiosyncratic volatility,
Ang, Hodrick, Xing, and Zhang (2006)
Svol , systematic volatility,
Ang, Hodrick, Xing, and Zhang (2006)
β
, market beta,
Frazzini and Pedersen (2014)
S-Rev , short-term reversal, Jegadeesh (1990)
Turn , share turnover,
Datar, Naik, and Radclie (1998)
Diether, Malloy, and Scherbina (2002)
1/P , 1/share price,
Miller and Scholes (1982)
Illiq , Absolute return-to-volume,
Amihud (2002)
Dvol , dollar trading volume,
Brennan, Chordia, and Subrahmanyam (1998)
Empirical Comparison
Across 36 signicant anomaly deciles with NYSE breakpoints
and value-weighted returns
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
The
q,
q -factor
FF5, and Carhart
model outperforms the ve-factor model the most in
the momentum and protability categories
Empirical Comparison
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
0.73
0.30
0.78
0.52
0.83
1.20
0.58
0.67
0.35
0.62
0.18
0.49
0.31
0.07
0.18
−0.11
0.15
0.64
0.26
0.06
−0.02
0.22
0.26
0.03
0.21
0.44
0.85
0.44
0.86
0.66
0.97
1.25
0.61
0.76
3.65
5.58
3.10
3.05
2.35
3.44
4.00
2.91
2.95
1.12
3.74
4.40
2.04
4.21
2.25
5.87
4.23
2.38
1.83
0.70
1.41
−0.72
0.22
−0.07
0.68
0.65
0.11
3.23
2.86
3.38
3.45
2.45
0.29
4
2
8
0.10
0.12
0.08
0.10
0.09
0.09
0.13
0.05
0.10
0.06
0.13
0.07
0.11
0.12
0.09
0.15
0.12
0.11
0.11
0.16
0.08
0.20
0.17
0.17
0.23
0.21
0.17
0.00
0.00
0.00
0.05
0.06
0.00
0.00
0.41
5
0.39
0.00
0.01
0.16
0.02
0.00
0.00
0.03
6
0.02
0.00
0.00
0.01
0.01
0.00
0.00
0.00
8
Empirical Comparison
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
0.07
0.08
−0.19
0.22
0.33
0.25
0.03
−0.14
−0.17
0.09
−0.18
−0.07
0.01
0.12
0.28
0.18
0.46
1.31
1.10
−1.98
−0.45
1.88
0.70
1.81
−2.11
0.32
−1.31
−2.27
0.52
5.76
3.18
2.86
−0.03
−0.17
0.14
−0.05
−0.20
−0.11
0.18
0.13
−0.45
−1.67
1.75
−0.63
−1.80
−1.15
1.25
0.84
0.01
−0.12
−0.12
−0.07
0.16
−1.74
−1.73
−0.60
1.01
1.46
1.25
1.53
0.06
0.39
0.09
0.82
1.55
0.39
9.82
9.36
5.40
5.80
4.95
−0.42
−0.16
−0.40
−0.27
−0.08
−0.54
−0.05
−0.71
−0.37
0.55
0.41
0.01
0.11
0.35
0.12
−0.02
−3.79
−0.94
0.02
0.39
0.67
0.39
−4.23
−1.76
−0.56
−2.44
−0.27
−2.47
−1.79
3.28
2.80
−0.05
0.07
0.06
0.44
1.13
0.51
1.25
1.62
1.24
Empirical Comparison
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
0.58
0.40
0.31
0.38
0.47
0.79
0.64
0.51
0.49
0.42
−0.03
0.06
0.20
0.21
0.18
0.14
0.51
0.50
0.21
0.53
0.46
0.44
2.95
2.54
2.75
2.15
3.34
4.15
3.46
3.51
3.41
3.92
−0.24
0.49
1.39
1.41
1.72
3.57
3.43
1.58
3.73
4.57
0.57
5
0
4
0.15
0.13
0.15
0.12
0.13
0.14
0.10
0.07
0.12
0.08
0.09
0.09
0.11
0.15
0.10
0.15
0.15
0.13
0.00
0.05
0.00
0.00
0.00
4
0.01
0.79
0.19
0.04
0.03
3
0.01
0.06
0.08
0.00
0.00
3
Empirical Comparison
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
−0.38
−0.09
0.04
−0.31
−0.13
−0.40
−0.09
−0.32
1.50
1.32
0.54
−6.44
−6.50
−1.12
−3.21
21.14
17.12
7.58
−0.48
−0.27
−0.48
−0.25
−0.45
1.43
1.25
0.89
0.08
0.88
0.76
0.11
0.20
0.03
0.19
−6.22
−2.57
−6.13
−2.95
−4.46
12.18
10.52
9.56
1.27
0.18
2.25
1.46
0.61
0.65
−2.41
−4.56
−2.32
−4.36
7.99
11.41
−0.25
−0.47
−0.17
−0.35
0.28
0.45
−0.02
−4.12
−5.53
−0.08
−3.67
−5.45
3.33
6.49
−0.17
−0.77
Empirical Comparison
Across 50 signicant anomaly deciles with all-but-micro
breakpoints and equal-weighted returns
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
The
q -factor
q,
35 for FF5, and 39 for Carhart
model continues to outperform the ve-factor model
the most in the momentum and protability categories
Empirical Comparison
Signicant momentum anomalies with ABM-EW, alphas
SUE-1 SUE-6 Abr-1 Abr-6
m
αC
αq
a
tm
tC
tq
ta
|αC |
|αq |
|a|
pC
pq
pa
R6-6 R11-1 I-Mom
|ave|
RE-1
RE-6
R6-1
0.72
0.30
0.97
0.46
0.79
0.44
1.08
0.92
1.24
0.68
0.58
0.21
0.87
0.31
0.47
0.20
0.16
0.03
0.23
−0.01
0.31
−0.04
0.85
0.31
0.26
−0.06
0.34
0.04
0.37
0.13
0.27
0.79
0.70
0.31
1.02
0.52
0.86
0.48
1.12
0.90
1.35
0.62
6.39
3.36
8.74
5.61
4.08
2.65
3.86
3.82
4.27
3.47
5.40
2.60
8.54
3.47
3.06
−0.53
5.55
2.14
6.50
3.41
7.94
4.68
2.78
1.41
0.84
0.19
1.77
−0.08
1.53
−0.37
0.84
0.11
0.88
0.48
4.62
2.87
3.10
2.68
3.62
2.44
0.76
0.31
5
3
10
0.16
0.13
0.19
0.14
0.15
0.12
0.13
0.10
0.09
0.04
0.13
0.11
0.10
0.19
0.17
0.13
0.15
0.16
0.14
0.11
0.10
0.14
0.19
0.08
0.19
0.11
0.23
0.14
0.18
0.16
0.27
0.21
0.18
0.00
0.00
0.00
0.00
0.01
0.16
0.00
0.00
0.03
0.30
8
0.00
0.01
0.00
0.00
0.01
0.01
0.00
0.00
0.00
0.20
9
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
10
Empirical Comparison
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
RE-6
R6-1
R6-6
R11-1
I-Mom
0.01
−0.03
0.10
0.13
0.04
0.53
0.47
0.52
0.33
0.13
0.07
0.00
−0.01
−0.09
0.02
0.12
−0.06
0.62
0.56
0.22
0.26
−0.91
1.35
2.17
1.35
0.01
8.42
−0.13
−0.21
0.25
0.26
−2.58
−2.32
4.00
2.46
12.45
2.80
−0.05 −0.15
0.25
2.07
0.94
0.72
−0.48 −1.35
3.12
8.78
−0.15
0.01
0.03 −0.12
−0.19 −0.19 −0.14 −0.08
0.23
−0.07 −0.02 0.30
0.15
0.23
0.04 −0.23
−3.43
0.19
0.66 −1.38
−2.66 −2.20 −1.93 −0.56
4.25
−0.72 −0.19 2.89
1.62
1.88
0.26 −1.07
0.87
−0.21
−1.03
11.16
1.16
1.21
1.36
1.85
2.30
2.13
0.04
0.41
−0.17
4.07
5.10
5.14
−0.16
0.20
0.11
0.14
−0.13 −0.67 −0.60 −0.87
0.32
0.22
0.26
0.16
0.70
1.88
0.69
4.02
0.11
−0.35
0.19
0.10
−0.13
0.65
0.57
0.65
−2.34
0.91
0.74
0.76
−1.10 −1.95 −2.23 −2.83
0.49
0.74
−1.60
3.58
0.47
0.76
0.50
0.36
−0.70
1.30
1.38
1.47
1.55
Empirical Comparison
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
0.90
0.65
0.57
0.47
0.36
0.58
0.32
0.57
0.91
0.82
0.53
0.67
0.44
0.23
0.49
0.27
0.10
0.12
−0.06
0.26
0.05
0.25
0.03
0.56
0.51
0.00
0.59
0.36
−0.15
−0.18
0.48
0.32
4.60
4.03
3.67
4.49
4.28
1.98
2.57
2.52
4.42
3.87
3.15
5.61
4.25
1.29
2.72
2.25
0.71
0.89
−0.41
2.39
0.70
1.28
0.28
0.01
5.07
−0.79
−1.32
−0.28
−0.42
−0.23
−0.31
−1.98
−3.23
−1.51
−2.21
4.14
3.52
4.02
2.67
2.65
0.53
0.14
0.37
8
1
7
0.19
0.18
0.16
0.16
0.21
0.15
0.18
0.14
0.17
0.17
0.12
0.14
0.14
0.09
0.11
0.12
0.12
0.10
0.13
0.12
0.12
0.14
0.08
0.12
0.19
0.09
0.13
0.09
0.08
0.12
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.09
0.00
8
0.00
0.00
0.01
0.01
0.00
0.01
0.08
0.54
0.02
7
0.00
0.00
0.03
0.00
0.00
0.02
0.01
0.19
0.08
7
Empirical Comparison
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
−0.12
0.25
−0.11
−0.17
−0.03
−0.08
0.44
−0.23
0.10
0.16
−0.18
0.38
−0.32
0.76
0.80
0.64
−2.61
−2.69
−1.13
−2.20
4.19
−3.03
2.01
−1.47
2.46
−2.93
13.52
26.12
6.84
0.24
0.12
0.23
1.50
1.40
0.84
−1.11
−1.28
2.98
2.24
1.08
1.75
0.68
20.45
18.27
8.00
−0.15
−0.03
−0.17
−0.07
−0.20
−0.35
−0.12
−0.25
0.59
−0.28
0.02
−0.19
−0.08
0.27
−0.27
1.59
1.48
1.44
0.56
0.65
1.16
0.35
5.60
0.51
6.97
0.29
−0.54
2.89
2.37
−5.74
0.17
0.27
0.20
0.14
0.45
0.11
0.10
0.01
0.00
−0.13
−0.60
−0.07
−1.98
−0.22
−2.25
−0.69
7.73
−2.72
−4.00
13.27
−2.93
0.34
3.45
−2.80
−4.24
−4.90
−1.31
2.22
−3.67
16.11
14.48
18.02
6.98
10.97
16.02
1.32
0.90
3.84
1.09
1.01
0.06
0.68
5.20
0.01
0.22
2.32
−1.01
3.17
−4.95
−0.60
Conclusion
A comparison of new factor models
The FF ve-factor model is a noisy version of the
q -factor
model