Duke Investment Analytics
Claudio AritomiSam DingMak PitkeMarcus ShawBrian Wachob
Interfractile Migration Tracking
Summary
Identify a “Primary Factor” for Use as a Basis Univariate Sort
Define and Quantify Interfractile Migration (IM) IM Trending IM Volatility
Study Sequential Sorts on Primary Factor, then IM Define Trading Strategies Test Out-of-Sample Conclusions Recommendations For Further Research
Note that this text-intensive version of the slide deck is an extended version intended for independent study. A condensed version is intended for presentation purposes.
Purpose of Study
“Investigate whether interfractile migration tracking can improve performance in a sort-based stock selection strategy.”
A Note To Those Reading This Slide Deck…
The notes that accompany these slides (viewable in PowerPoint edit mode) contain additional information that is not entirely conveyed in the slides themselves. Please examine these notes when considering the research presented here.
Interfractile Migration - Definition
Define 2 metrics to quantify “interfractile migration” (IM) Interfractile Migration Trending (IMT)
over recent periods, measure the trend of each stock’s movements through fractiles of the primary factor
Interfractile Migration Volatility (IMV) over recent periods, measure the volatility of each
stock’s movements through fractiles of the primary factor
Define fractile resolution (with respect to primary factor) We used 10 fractiles (deciles), as segregated by
Factset’s UDECILE() function.
Identify a Basis Univariate Sort
Candidates: Dividend Yield Book-to-Price Historical (Trailing) Earnings Yield Forward Earnings Yield
I/B/E/S Mean Next Twelve Months I/B/E/S Mean FY1 I/B/E/S Median NTM, FY1 I/B/E/S Median FY2
Implied Cost of Capital
Methodology
FactSet quintile sorts Monthly rebalancing, 1-month holding period In-sample period: 1/31/87-11/31/01* Out-of-sample period: 12/31/01-12/31/04 Universe
US-listed NYSE, NASDAQ, AMEX Top 60% by market cap
Convention: Low factor values are always assigned to low-numbered fractiles
When historical data necessary to evaluate the univariate sorting factor for a given stock is unavailable, that stock is excluded from the universe for that backtest date.
* Note that using 31 as the last day of the month when specifying the date range in Factset is necessary—even when there is no 31st day of the specified month. If not used in this way, lagged variables may not work properly in alpha tester.
Results of Univariate Sorts
The following slides present some data evaluating the performance of selected univariate sorts.
A far more detailed array of data sets and analyses evaluating these univariate sorts (and others) are contained in the Excel workbook files accompanying this PowerPoint presentation.
Dividend Yield - Quintile Performance
Annualized Return, % -- Div. Yld VW Univariate Factor Performance
0.0
5.0
10.0
15.0
20.0
25.0
-1- -2- -3- -4- -5-Fractile
Alpha, Monthly % -- Div. Yld VW Univariate Factor Performance
-0.50
-0.30
-0.10
0.10
0.30
0.50
0.70
-1- -2- -3- -4- -5-
Fractile
Annualized Return, % -- Div.Yld. EW Univariate Factor Performance
0.0
5.0
10.0
15.0
20.0
25.0
-1- -2- -3- -4- -5-Fractile
Valu
e-Weig
hted
Eq
ual-W
eigh
ted
Annualized Return Alpha
Alpha, Monthly % -- Div.Yld. EW Univariate Factor Performance
-0.50
-0.30
-0.10
0.10
0.30
0.50
0.70
-1- -2- -3- -4- -5-
Fractile
Returns & Alpha
Dividend Yield - Quintile Performance
Std. Dev. of Monthly Returns -- Div.Yld. VW As Univariate Sort Factor
0.00
1.00
2.00
3.00
4.00
5.00
6.00
7.00
8.00
-1- -2- -3- -4- -5-Fractile
Beta, on Market (S&P 500) -- Div.Yld. VW As Univariate Sort Factor
0.00
0.20
0.40
0.60
0.80
1.00
1.20
1.40
-1- -2- -3- -4- -5-Fractile
Std. Dev. of Monthly Returns -- Div.Yld. EW As Univariate Sort Factor
0.00
1.00
2.00
3.00
4.00
5.00
6.00
7.00
8.00
-1- -2- -3- -4- -5-Fractile
Valu
e-Weig
hted
Eq
ual-W
eigh
ted
Std. Dev. of Monthly Returns Beta on Market (S&P 500)
Volatility & Beta
Beta, on Market (S&P 500) -- Div.Yld. EW As Univariate Sort Factor
0.00
0.20
0.40
0.60
0.80
1.00
1.20
1.40
-1- -2- -3- -4- -5-Fractile
Dividend Yield – F5-F1 Time Series, VWCumulative
Div.Yld. VW -- Time Series, Cumulative Performance
-3
-2
-1
0
1
2
3
4
1/31
/198
7
1/31
/198
8
1/31
/198
9
1/31
/199
0
1/31
/199
1
1/31
/199
2
1/31
/199
3
1/31
/199
4
1/31
/199
5
1/31
/199
6
1/31
/199
7
1/31
/199
8
1/31
/199
9
1/31
/200
0
1/31
/200
1
log
2 C
um
Ret
urn
-3
-2
-1
0
1
2
3
4
log
2 C
um
Retu
rn fo
r FN
-F1
On
ly
F1FNBmarkFN-F1
Dividend Yield – F5-F1 Time Series, EW
Div.Yld. EW -- Time Series, Cumulative Performance
-2.5
-1.5
-0.5
0.5
1.5
2.5
3.5
1/31
/198
7
1/31
/198
8
1/31
/198
9
1/31
/199
0
1/31
/199
1
1/31
/199
2
1/31
/199
3
1/31
/199
4
1/31
/199
5
1/31
/199
6
1/31
/199
7
1/31
/199
8
1/31
/199
9
1/31
/200
0
1/31
/200
1
log
2 C
um
Ret
urn
-2.5
-1.5
-0.5
0.5
1.5
2.5
3.5
log
2 C
um
Retu
rn fo
r FN
-F1
On
ly
F1FNBmarkFN-F1
Cumulative
Dividend Yield – F5-F1 Time Series
Fractiles, Year-By-Year Returns -- Div.Yld. VW
-30%
-20%
-10%
0%
10%
20%
30%
40%
50%
60%
70%
1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001
Co
mp
ute
d b
y M
ult
iplic
ativ
ely
Ag
gre
gat
ing
Mo
nth
ly R
etu
rns
Ove
r 12
-Mo
. Win
do
ws
F1
F2
F3
F4
F5
Fractile Returns, Trailing 12 Mos. -- Div.Yld. VW
-60%
-40%
-20%
0%
20%
40%
60%
80%
100%
1/31/1
988
1/31/1
989
1/31/1
990
1/31/1
991
1/31/1
992
1/31/1
993
1/31/1
994
1/31/1
995
1/31/1
996
1/31/1
997
1/31/1
998
1/31/1
999
1/31/2
000
1/31/2
001
Com
pute
d by
Mul
tiplic
ativ
ely
Agg
rega
ting
Mon
thly
Ret
urns
Ove
r a T
raili
ng 1
2-M
o. W
indo
w
F1-Bmark
F2-Bmark
F3-Bmark
F4-Bmark
F5-Bmark
F5-F1
Fractiles, Year-By-Year Returns -- Div.Yld. EW
-30%
-20%
-10%
0%
10%
20%
30%
40%
50%
60%
70%
1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001
Co
mp
ute
d b
y M
ult
iplic
ati
ve
ly A
gg
reg
ati
ng
Mo
nth
ly R
etu
rns
Ov
er
12
-Mo
. W
ind
ow
s
F1
F2
F3
F4
F5
Valu
e-Weig
hted
Eq
ual-W
eigh
ted
Year-By-Year Trailing Twelve Months
Fractile Returns, Trailing 12 Mos. -- Div.Yld. EW
-60%
-40%
-20%
0%
20%
40%
60%
80%
100%
1/31/1
988
1/31/1
989
1/31/1
990
1/31/1
991
1/31/1
992
1/31/1
993
1/31/1
994
1/31/1
995
1/31/1
996
1/31/1
997
1/31/1
998
1/31/1
999
1/31/2
000
1/31/2
001
Com
pute
d by
Mul
tiplic
ativ
ely
Agg
rega
ting
Mon
thly
Ret
urns
Ove
r a T
raili
ng 1
2-M
o. W
indo
w
F1-Bmark
F2-Bmark
F3-Bmark
F4-Bmark
F5-Bmark
F5-F1
All Fractiles, 12-Month Windows
Dividend Yield – F5-F1 Returns Distributions
Div.Yld. VW -- FN-F1 Portfolio: Monthly Returns Distribution
0
1
2
3
4
5
6
7
8
9
10
-0.2
7-0
.26
-0.2
5-0
.24
-0.2
3-0
.22
-0.2
1-0
.2-0
.19
-0.1
8-0
.17
-0.1
6-0
.15
-0.1
4-0
.13
-0.1
2-0
.11
-0.1
-0.0
9-0
.08
-0.0
7-0
.06
-0.0
5-0
.04
-0.0
3-0
.02
-0.0
1 00
.01
0.0
20
.03
0.0
40
.05
0.0
60
.07
0.0
80
.09
0.1
0.1
10
.12
0.1
30
.14
0.1
50
.16
0.1
70
.18
0.1
90
.2 Inf
Monthly Return, Bin Upper Limit
Incr
emen
tal S
har
e o
f A
ll R
etu
rns
Per
Un
it X
(D
ensi
ty)
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
Cu
mu
lati
ve
Sh
are
of
All
Re
turn
s
Incremental
Cumulative
Div.Yld. VW -- FN-F1 Portfolio: ln Monthly Returns Distribution
0
1
2
3
4
5
6
7
8
9
10
-0.3
2-0
.31
-0.3
-0.2
9-0
.28
-0.2
7-0
.26
-0.2
5-0
.24
-0.2
3-0
.22
-0.2
1-0
.2-0
.19
-0.1
8-0
.17
-0.1
6-0
.15
-0.1
4-0
.13
-0.1
2-0
.11
-0.1
-0.0
9-0
.08
-0.0
7-0
.06
-0.0
5-0
.04
-0.0
3-0
.02
-0.0
1 00
.01
0.0
20
.03
0.0
40
.05
0.0
60
.07
0.0
80
.09
0.1
0.1
10
.12
0.1
30
.14
0.1
50
.16
0.1
70
.18
Inf
ln Monthly Return, Bin Upper Limit
Incr
emen
tal S
har
e o
f A
ll R
etu
rns
Per
Un
it X
(D
ensi
ty)
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
Cu
mu
lati
ve
Sh
are
of
All
Re
turn
s
Incremental
Cumulative
Div.Yld. EW -- FN-F1 Portfolio: Monthly Returns Distribution
0
2
4
6
8
10
12
14
-0.2
6-0
.25
-0.2
4-0
.23
-0.2
2-0
.21
-0.2
-0.1
9-0
.18
-0.1
7-0
.16
-0.1
5-0
.14
-0.1
3-0
.12
-0.1
1-0
.1-0
.09
-0.0
8-0
.07
-0.0
6-0
.05
-0.0
4-0
.03
-0.0
2-0
.01 0
0.0
10
.02
0.0
30
.04
0.0
50
.06
0.0
70
.08
0.0
90
.10
.11
0.1
20
.13
0.1
40
.15
0.1
60
.17
0.1
80
.19
0.2
0.2
10
.22
Inf
Monthly Return, Bin Upper Limit
Incr
emen
tal S
har
e o
f A
ll R
etu
rns
Per
Un
it X
(D
ensi
ty)
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
Cu
mu
lati
ve
Sh
are
of
All
Re
turn
sIncremental
Cumulative
Valu
e-Weig
hted
Eq
ual-W
eigh
ted
Monthly Returns
Div.Yld. EW -- FN-F1 Portfolio: ln Monthly Returns Distribution
0
2
4
6
8
10
12
14
-0.3
-0.2
9-0
.28
-0.2
7-0
.26
-0.2
5-0
.24
-0.2
3-0
.22
-0.2
1-0
.2-0
.19
-0.1
8-0
.17
-0.1
6-0
.15
-0.1
4-0
.13
-0.1
2-0
.11
-0.1
-0.0
9-0
.08
-0.0
7-0
.06
-0.0
5-0
.04
-0.0
3-0
.02
-0.0
1 00
.01
0.0
20
.03
0.0
40
.05
0.0
60
.07
0.0
80
.09
0.1
0.1
10
.12
0.1
30
.14
0.1
50
.16
0.1
70
.18
0.1
90
.2 Inf
ln Monthly Return, Bin Upper Limit
Incr
emen
tal S
har
e o
f A
ll R
etu
rns
Per
Un
it X
(D
ensi
ty)
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
Cu
mu
lati
ve
Sh
are
of
All
Re
turn
s
Incremental
Cumulative
ln Monthly Returns
Dividend Yield – F5-F1 Returns Distributions
Valu
e-Weig
hted
Eq
ual-W
eigh
ted
Monthly Returns ln Monthly Returns
Summary Statistics
Book to Price - Quintile Performance
Annualized Return, % -- B/P VW Univariate Factor Performance
0.0
5.0
10.0
15.0
20.0
25.0
-1- -2- -3- -4- -5-Fractile
Alpha, Monthly % -- B/P VW Univariate Factor Performance
-0.50
-0.30
-0.10
0.10
0.30
0.50
0.70
-1- -2- -3- -4- -5-
Fractile
Annualized Return, % -- B/P EW Univariate Factor Performance
0.0
5.0
10.0
15.0
20.0
25.0
-1- -2- -3- -4- -5-Fractile
Valu
e-Weig
hted
Eq
ual-W
eigh
ted
Annualized Return Alpha
Alpha, Monthly % -- B/P EW Univariate Factor Performance
-0.50
-0.30
-0.10
0.10
0.30
0.50
0.70
-1- -2- -3- -4- -5-
Fractile
Returns & Alpha
Book to Price - Quintile Performance
Std. Dev. of Monthly Returns -- B/P VW As Univariate Sort Factor
0.00
1.00
2.00
3.00
4.00
5.00
6.00
7.00
8.00
-1- -2- -3- -4- -5-Fractile
Beta, on Market (S&P 500) -- B/P VW As Univariate Sort Factor
0.00
0.20
0.40
0.60
0.80
1.00
1.20
-1- -2- -3- -4- -5-Fractile
Std. Dev. of Monthly Returns -- B/P EW As Univariate Sort Factor
0.00
1.00
2.00
3.00
4.00
5.00
6.00
7.00
8.00
-1- -2- -3- -4- -5-Fractile
Valu
e-Weig
hted
Eq
ual-W
eigh
ted
Std. Dev. of Monthly Returns Beta on Market (S&P 500)
Volatility & Beta
Beta, on Market (S&P 500) -- B/P EW As Univariate Sort Factor
0.00
0.20
0.40
0.60
0.80
1.00
1.20
-1- -2- -3- -4- -5-Fractile
Book to Price - F5-F1 Time Series, VWCumulative
B/P VW -- Time Series, Cumulative Performance
-1.2
-0.6
0
0.6
1.2
1.8
2.4
3
3.6
1/31
/198
7
1/31
/198
8
1/31
/198
9
1/31
/199
0
1/31
/199
1
1/31
/199
2
1/31
/199
3
1/31
/199
4
1/31
/199
5
1/31
/199
6
1/31
/199
7
1/31
/199
8
1/31
/199
9
1/31
/200
0
1/31
/200
1
log
2 C
um
Ret
urn
-1.2
-0.6
0
0.6
1.2
1.8
2.4
3
3.6
log
2 C
um
Retu
rn fo
r FN
-F1
On
ly
F1FNBmarkFN-F1
Book to Price - F5-F1 Time Series, EWCumulative
B/P EW -- Time Series, Cumulative Performance
-2
-1
0
1
2
3
4
1/31
/198
7
1/31
/198
8
1/31
/198
9
1/31
/199
0
1/31
/199
1
1/31
/199
2
1/31
/199
3
1/31
/199
4
1/31
/199
5
1/31
/199
6
1/31
/199
7
1/31
/199
8
1/31
/199
9
1/31
/200
0
1/31
/200
1
log
2 C
um
Ret
urn
-2
-1
0
1
2
3
4
log
2 C
um
Retu
rn fo
r FN
-F1
On
ly
F1FNBmarkFN-F1
Book to Price – F5-F1 Time Series
Fractiles, Year-By-Year Returns -- B/P VW
-35%
-30%
-25%
-20%
-15%
-10%
-5%
0%
5%
10%
15%
20%
25%
30%
35%
40%
45%
50%
55%
60%
1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001
Co
mp
ute
d b
y M
ult
iplic
ati
ve
ly A
gg
reg
ati
ng
Mo
nth
ly R
etu
rns
Ov
er
12
-Mo
. W
ind
ow
s
F1
F2
F3
F4
F5
Fractile Returns, Trailing 12 Mos. -- B/P VW
-75%
-50%
-25%
0%
25%
50%
75%
100%
125%
150%
1/31/1
988
1/31/1
989
1/31/1
990
1/31/1
991
1/31/1
992
1/31/1
993
1/31/1
994
1/31/1
995
1/31/1
996
1/31/1
997
1/31/1
998
1/31/1
999
1/31/2
000
1/31/2
001
Com
pute
d by
Mul
tiplic
ativ
ely
Agg
rega
ting
Mon
thly
Ret
urns
Ove
r a T
raili
ng 1
2-M
o. W
indo
w
F1-Bmark
F2-Bmark
F3-Bmark
F4-Bmark
F5-Bmark
F5-F1
Fractiles, Year-By-Year Returns -- B/P EW
-35%
-30%
-25%
-20%
-15%
-10%
-5%
0%
5%
10%
15%
20%
25%
30%
35%
40%
45%
50%
55%
60%
1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001
Co
mp
ute
d b
y M
ult
iplic
ati
ve
ly A
gg
reg
ati
ng
Mo
nth
ly R
etu
rns
Ov
er
12
-Mo
. W
ind
ow
s
F1
F2
F3
F4
F5
Valu
e-Weig
hted
Eq
ual-W
eigh
ted
Year-By-Year Trailing Twelve Months
All Fractiles, 12-Month Windows
Fractile Returns, Trailing 12 Mos. -- B/P EW
-75%
-50%
-25%
0%
25%
50%
75%
100%
125%
150%
1/31/1
988
1/31/1
989
1/31/1
990
1/31/1
991
1/31/1
992
1/31/1
993
1/31/1
994
1/31/1
995
1/31/1
996
1/31/1
997
1/31/1
998
1/31/1
999
1/31/2
000
1/31/2
001
Com
pute
d by
Mul
tiplic
ativ
ely
Agg
rega
ting
Mon
thly
Ret
urns
Ove
r a T
raili
ng 1
2-M
o. W
indo
w
F1-Bmark
F2-Bmark
F3-Bmark
F4-Bmark
F5-Bmark
F5-F1
Book to Price – F5-F1 Returns Distributions
B/P VW -- FN-F1 Portfolio: Monthly Returns Distribution
0
2
4
6
8
10
12
14
16
-0.1
7-0
.16
-0.1
5-0
.14
-0.1
3-0
.12
-0.1
1-0
.1-0
.09
-0.0
8-0
.07
-0.0
6-0
.05
-0.0
4-0
.03
-0.0
2-0
.01 0
0.0
10
.02
0.0
30
.04
0.0
50
.06
0.0
70
.08
0.0
90
.10
.11
0.1
20
.13
0.1
40
.15
0.1
60
.17
Inf
Monthly Return, Bin Upper Limit
Incr
emen
tal S
har
e o
f A
ll R
etu
rns
Per
Un
it X
(D
ensi
ty)
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
Cu
mu
lati
ve
Sh
are
of
All
Re
turn
s
Incremental
Cumulative
B/P VW -- FN-F1 Portfolio: ln Monthly Returns Distribution
0
2
4
6
8
10
12
14
16
-0.1
8
-0.1
7
-0.1
6
-0.1
5
-0.1
4
-0.1
3
-0.1
2
-0.1
1
-0.1
-0.0
9
-0.0
8
-0.0
7
-0.0
6
-0.0
5
-0.0
4
-0.0
3
-0.0
2
-0.0
1 0
0.0
1
0.0
2
0.0
3
0.0
4
0.0
5
0.0
6
0.0
7
0.0
8
0.0
9
0.1
0.1
1
0.1
2
0.1
3
0.1
4
0.1
5
Inf
ln Monthly Return, Bin Upper Limit
Incr
emen
tal S
har
e o
f A
ll R
etu
rns
Per
Un
it X
(D
ensi
ty)
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
Cu
mu
lati
ve
Sh
are
of
All
Re
turn
s
Incremental
Cumulative
B/P EW -- FN-F1 Portfolio: Monthly Returns Distribution
0
2
4
6
8
10
12
14
-0.3
7-0
.36
-0.3
5-0
.34
-0.3
3-0
.32
-0.3
1-0
.3-0
.29
-0.2
8-0
.27
-0.2
6-0
.25
-0.2
4-0
.23
-0.2
2-0
.21
-0.2
-0.1
9-0
.18
-0.1
7-0
.16
-0.1
5-0
.14
-0.1
3-0
.12
-0.1
1-0
.1-0
.09
-0.0
8-0
.07
-0.0
6-0
.05
-0.0
4-0
.03
-0.0
2-0
.01 0
0.0
10
.02
0.0
30
.04
0.0
50
.06
0.0
70
.08
0.0
90
.10
.11
0.1
20
.13
0.1
40
.15
0.1
60
.17
0.1
80
.19
0.2
0.2
10
.22
Inf
Monthly Return, Bin Upper Limit
Incr
emen
tal S
har
e o
f A
ll R
etu
rns
Per
Un
it X
(D
ensi
ty)
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
Cu
mu
lati
ve
Sh
are
of
All
Re
turn
sIncremental
Cumulative
Valu
e-Weig
hted
Eq
ual-W
eigh
ted
Monthly Returns ln Monthly Returns
B/P EW -- FN-F1 Portfolio: ln Monthly Returns Distribution
0
2
4
6
8
10
12
14
-0.4
8-0
.47
-0.4
6-0
.45
-0.4
4-0
.43
-0.4
2-0
.41
-0.4
-0.3
9-0
.38
-0.3
7-0
.36
-0.3
5-0
.34
-0.3
3-0
.32
-0.3
1-0
.3-0
.29
-0.2
8-0
.27
-0.2
6-0
.25
-0.2
4-0
.23
-0.2
2-0
.21
-0.2
-0.1
9-0
.18
-0.1
7-0
.16
-0.1
5-0
.14
-0.1
3-0
.12
-0.1
1-0
.1-0
.09
-0.0
8-0
.07
-0.0
6-0
.05
-0.0
4-0
.03
-0.0
2-0
.01 0
0.0
10
.02
0.0
30
.04
0.0
50
.06
0.0
70
.08
0.0
90
.10
.11
0.1
20
.13
0.1
40
.15
0.1
60
.17
0.1
80
.19
0.2 Inf
ln Monthly Return, Bin Upper Limit
Incr
emen
tal S
har
e o
f A
ll R
etu
rns
Per
Un
it X
(D
ensi
ty)
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
Cu
mu
lati
ve
Sh
are
of
All
Re
turn
s
Incremental
Cumulative
Book to Price – F5-F1 Returns Distributions
Valu
e-Weig
hted
Eq
ual-W
eigh
ted
Monthly Returns ln Monthly Returns
Summary Statistics
Trailing Earnings Yield - Quintile PerformanceTrailing Twelve Months Earnings Yield (TEY)
Annualized Return, % -- TEY VW Univariate Factor Performance
0.0
5.0
10.0
15.0
20.0
25.0
-1- -2- -3- -4- -5-Fractile
Alpha, Monthly % -- TEY VW Univariate Factor Performance
-0.50
-0.30
-0.10
0.10
0.30
0.50
0.70
-1- -2- -3- -4- -5-
Fractile
Annualized Return, % -- TEY EW Univariate Factor Performance
0.0
5.0
10.0
15.0
20.0
25.0
-1- -2- -3- -4- -5-Fractile
Valu
e-Weig
hted
Eq
ual-W
eigh
ted
Annualized Return Alpha
Alpha, Monthly % -- TEY EW Univariate Factor Performance
-0.50
-0.30
-0.10
0.10
0.30
0.50
0.70
-1- -2- -3- -4- -5-
Fractile
Returns & Alpha
Trailing Earnings Yield - Quintile PerformanceTrailing Twelve Months Earnings Yield (TEY)
Std. Dev. of Monthly Returns -- TEY VW As Univariate Sort Factor
0.00
1.00
2.00
3.00
4.00
5.00
6.00
7.00
8.00
-1- -2- -3- -4- -5-Fractile
Beta, on Market (S&P 500) -- TEY VW As Univariate Sort Factor
0.00
0.20
0.40
0.60
0.80
1.00
1.20
-1- -2- -3- -4- -5-Fractile
Std. Dev. of Monthly Returns -- TEY EW As Univariate Sort Factor
0.00
1.00
2.00
3.00
4.00
5.00
6.00
7.00
8.00
-1- -2- -3- -4- -5-Fractile
Volatility & Beta
Valu
e-Weig
hted
Eq
ual-W
eigh
ted
Std. Dev. of Monthly Returns Beta on Market (S&P 500)
Beta, on Market (S&P 500) -- TEY EW As Univariate Sort Factor
0.00
0.20
0.40
0.60
0.80
1.00
1.20
-1- -2- -3- -4- -5-Fractile
Trailing Earnings Yield - F5-F1 Time Series, VW Trailing Twelve Months Earnings Yield (TEY) Cumulative
TEY VW -- Time Series, Cumulative Performance
-1.5
-0.75
0
0.75
1.5
2.25
3
3.75
1/31
/198
7
1/31
/198
8
1/31
/198
9
1/31
/199
0
1/31
/199
1
1/31
/199
2
1/31
/199
3
1/31
/199
4
1/31
/199
5
1/31
/199
6
1/31
/199
7
1/31
/199
8
1/31
/199
9
1/31
/200
0
1/31
/200
1
log
2 C
um
Ret
urn
-1.5
-0.75
0
0.75
1.5
2.25
3
3.75
log
2 C
um
Retu
rn fo
r FN
-F1
On
ly
F1FNBmarkFN-F1
Trailing Earnings Yield - F5-F1 Time Series, EW Trailing Twelve Months Earnings Yield (TEY) Cumulative
TEY EW -- Time Series, Cumulative Performance
-1.5
-0.75
0
0.75
1.5
2.25
3
3.75
1/31
/198
7
1/31
/198
8
1/31
/198
9
1/31
/199
0
1/31
/199
1
1/31
/199
2
1/31
/199
3
1/31
/199
4
1/31
/199
5
1/31
/199
6
1/31
/199
7
1/31
/199
8
1/31
/199
9
1/31
/200
0
1/31
/200
1
log
2 C
um
Ret
urn
-1.5
-0.75
0
0.75
1.5
2.25
3
3.75
log
2 C
um
Retu
rn fo
r FN
-F1
On
ly
F1FNBmarkFN-F1
Trailing Earnings Yield - F5-F1 Time Series
Trailing Twelve Months Earnings Yield (TEY)Fractiles, Year-By-Year Returns -- TEY VW
-40%
-20%
0%
20%
40%
60%
80%
1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001
Co
mp
ute
d b
y M
ult
iplic
ati
ve
ly A
gg
reg
ati
ng
Mo
nth
ly R
etu
rns
Ov
er
12
-Mo
. W
ind
ow
s
F1
F2
F3
F4
F5
Fractile Returns, Trailing 12 Mos. -- TEY VW
-75%
-50%
-25%
0%
25%
50%
75%
100%
125%
150%
175%
200%
1/31/1
988
1/31/1
989
1/31/1
990
1/31/1
991
1/31/1
992
1/31/1
993
1/31/1
994
1/31/1
995
1/31/1
996
1/31/1
997
1/31/1
998
1/31/1
999
1/31/2
000
1/31/2
001
Com
pute
d by
Mul
tiplic
ativ
ely
Agg
rega
ting
Mon
thly
Ret
urns
Ove
r a T
raili
ng 1
2-M
o. W
indo
w
F1-Bmark
F2-Bmark
F3-Bmark
F4-Bmark
F5-Bmark
F5-F1
Fractiles, Year-By-Year Returns -- TEY EW
-40%
-20%
0%
20%
40%
60%
80%
1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001
Co
mp
ute
d b
y M
ult
iplic
ati
ve
ly A
gg
reg
ati
ng
Mo
nth
ly R
etu
rns
Ov
er
12
-Mo
. W
ind
ow
s
F1
F2
F3
F4
F5
Valu
e-Weig
hted
Eq
ual-W
eigh
ted
Year-By-Year Trailing Twelve Months
Fractile Returns, Trailing 12 Mos. -- TEY EW
-75%
-50%
-25%
0%
25%
50%
75%
100%
125%
150%
175%
200%
1/31/1
988
1/31/1
989
1/31/1
990
1/31/1
991
1/31/1
992
1/31/1
993
1/31/1
994
1/31/1
995
1/31/1
996
1/31/1
997
1/31/1
998
1/31/1
999
1/31/2
000
1/31/2
001
Com
pute
d by
Mul
tiplic
ativ
ely
Agg
rega
ting
Mon
thly
Ret
urns
Ove
r a T
raili
ng 1
2-M
o. W
indo
w
F1-Bmark
F2-Bmark
F3-Bmark
F4-Bmark
F5-Bmark
F5-F1
All Fractiles, 12-Month Windows
Trailing Earnings Yield - F5-F1 Returns Distributions
Trailing Twelve Months Earnings Yield (TEY)
TEY VW -- FN-F1 Portfolio: Monthly Returns Distribution
0
2
4
6
8
10
12
14
-0.2
6-0
.25
-0.2
4-0
.23
-0.2
2-0
.21
-0.2
-0.1
9-0
.18
-0.1
7-0
.16
-0.1
5-0
.14
-0.1
3-0
.12
-0.1
1-0
.1-0
.09
-0.0
8-0
.07
-0.0
6-0
.05
-0.0
4-0
.03
-0.0
2-0
.01 0
0.0
10
.02
0.0
30
.04
0.0
50
.06
0.0
70
.08
0.0
90
.10
.11
0.1
20
.13
0.1
40
.15
0.1
60
.17
0.1
80
.19
0.2
0.2
10
.22
0.2
3In
f
Monthly Return, Bin Upper Limit
Incr
emen
tal S
har
e o
f A
ll R
etu
rns
Per
Un
it X
(D
ensi
ty)
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
Cu
mu
lati
ve
Sh
are
of
All
Re
turn
s
Incremental
Cumulative
TEY VW -- FN-F1 Portfolio: ln Monthly Returns Distribution
0
2
4
6
8
10
12
14
-0.3
1-0
.3-0
.29
-0.2
8-0
.27
-0.2
6-0
.25
-0.2
4-0
.23
-0.2
2-0
.21
-0.2
-0.1
9-0
.18
-0.1
7-0
.16
-0.1
5-0
.14
-0.1
3-0
.12
-0.1
1-0
.1-0
.09
-0.0
8-0
.07
-0.0
6-0
.05
-0.0
4-0
.03
-0.0
2-0
.01 0
0.0
10
.02
0.0
30
.04
0.0
50
.06
0.0
70
.08
0.0
90
.10
.11
0.1
20
.13
0.1
40
.15
0.1
60
.17
0.1
80
.19
0.2
0.2
1In
f
ln Monthly Return, Bin Upper Limit
Incr
emen
tal S
har
e o
f A
ll R
etu
rns
Per
Un
it X
(D
ensi
ty)
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
Cu
mu
lati
ve
Sh
are
of
All
Re
turn
s
Incremental
Cumulative
TEY EW -- FN-F1 Portfolio: Monthly Returns Distribution
0
2
4
6
8
10
12
14
16
18
20
-0.4
-0.3
9-0
.38
-0.3
7-0
.36
-0.3
5-0
.34
-0.3
3-0
.32
-0.3
1-0
.3-0
.29
-0.2
8-0
.27
-0.2
6-0
.25
-0.2
4-0
.23
-0.2
2-0
.21
-0.2
-0.1
9-0
.18
-0.1
7-0
.16
-0.1
5-0
.14
-0.1
3-0
.12
-0.1
1-0
.1-0
.09
-0.0
8-0
.07
-0.0
6-0
.05
-0.0
4-0
.03
-0.0
2-0
.01 0
0.0
10
.02
0.0
30
.04
0.0
50
.06
0.0
70
.08
0.0
90
.10
.11
0.1
20
.13
0.1
40
.15
0.1
60
.17
0.1
80
.19
0.2
0.2
10
.22
0.2
30
.24
0.2
5In
f
Monthly Return, Bin Upper Limit
Incr
emen
tal S
har
e o
f A
ll R
etu
rns
Per
Un
it X
(D
ensi
ty)
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
Cu
mu
lati
ve
Sh
are
of
All
Re
turn
sIncremental
Cumulative
Valu
e-Weig
hted
Eq
ual-W
eigh
ted
Monthly Returns ln Monthly Returns
TEY EW -- FN-F1 Portfolio: ln Monthly Returns Distribution
0
2
4
6
8
10
12
14
16
18
20
-0.5
2-0
.51
-0.5
-0.4
9-0
.48
-0.4
7-0
.46
-0.4
5-0
.44
-0.4
3-0
.42
-0.4
1-0
.4-0
.39
-0.3
8-0
.37
-0.3
6-0
.35
-0.3
4-0
.33
-0.3
2-0
.31
-0.3
-0.2
9-0
.28
-0.2
7-0
.26
-0.2
5-0
.24
-0.2
3-0
.22
-0.2
1-0
.2-0
.19
-0.1
8-0
.17
-0.1
6-0
.15
-0.1
4-0
.13
-0.1
2-0
.11
-0.1
-0.0
9-0
.08
-0.0
7-0
.06
-0.0
5-0
.04
-0.0
3-0
.02
-0.0
1 00
.01
0.0
20
.03
0.0
40
.05
0.0
60
.07
0.0
80
.09
0.1
0.1
10
.12
0.1
30
.14
0.1
50
.16
0.1
70
.18
0.1
90
.20
.21
0.2
2In
f
ln Monthly Return, Bin Upper Limit
Incr
emen
tal S
har
e o
f A
ll R
etu
rns
Per
Un
it X
(D
ensi
ty)
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
Cu
mu
lati
ve
Sh
are
of
All
Re
turn
s
Incremental
Cumulative
Trailing Earnings Yield - F5-F1 Returns Distributions
Trailing Twelve Months Earnings Yield (TEY)
Valu
e-Weig
hted
Eq
ual-W
eigh
ted
Monthly Returns ln Monthly Returns
Summary Statistics
Forward Earnings Yield
Four different definitions of forward earningsA. Mean I/B/E/S earnings forecast for “Next Twelve Months”B. Mean I/B/E/S earnings forecast for “Next Twelve Months”.
If this data is unavailable, mean I/B/E/S earnings forecast for the current fiscal year is used instead.
C. Median I/B/E/S earnings forecast for “Next Twelve Months”. If this data is unavailable, median I/B/E/S earnings forecast for the current fiscal year is used instead.
D. Median I/B/E/S earnings forecast for forward fiscal year number 2.
We backtested our univariate screening and sorting methodology using each of these definitions to contribute the numerator to our earnings yield computation.
Forward Earnings Yield
Performance across these four factor definitions is similar. Median analyst earnings estimates appear preferable to
means. Definition C appears to generate the best quintile sorts. Still, closer scrutiny of the results pertaining to these four
definitions is warranted and there still remains ample room for improvement in these factor definitions. We leave this for future research.
We choose to focus our analysis on the backtest results using definition C for Forward Earnings Yield:
Median I/B/E/S earnings forecast for “Next Twelve Months”. If this data is unavailable, median I/B/E/S earnings forecast for the current fiscal year is used instead.
Forward Earnings Yield - Quintile PerformanceForecast Next 12 Mos. Earnings Yield (FEY)
Annualized Return, % -- FEY VW Univariate Factor Performance
0.0
5.0
10.0
15.0
20.0
25.0
-1- -2- -3- -4- -5-Fractile
Alpha, Monthly % -- FEY VW Univariate Factor Performance
-0.50
-0.30
-0.10
0.10
0.30
0.50
0.70
-1- -2- -3- -4- -5-
Fractile
Annualized Return, % -- FEW EW Univariate Factor Performance
0.0
5.0
10.0
15.0
20.0
25.0
-1- -2- -3- -4- -5-Fractile
Valu
e-Weig
hted
Eq
ual-W
eigh
ted
Annualized Return Alpha
Returns & Alpha
Alpha, Monthly % -- FEW EW Univariate Factor Performance
-0.50
-0.30
-0.10
0.10
0.30
0.50
0.70
-1- -2- -3- -4- -5-
Fractile
Forward Earnings Yield - Quintile PerformanceForecast Next 12 Mos. Earnings Yield (FEY)
Std. Dev. of Monthly Returns -- FEY VW As Univariate Sort Factor
0.00
1.00
2.00
3.00
4.00
5.00
6.00
7.00
8.00
9.00
-1- -2- -3- -4- -5-Fractile
Beta, on Market (S&P 500) -- FEY VW As Univariate Sort Factor
0.00
0.20
0.40
0.60
0.80
1.00
1.20
1.40
-1- -2- -3- -4- -5-Fractile
Std. Dev. of Monthly Returns -- FEW EW As Univariate Sort Factor
0.00
1.00
2.00
3.00
4.00
5.00
6.00
7.00
8.00
9.00
-1- -2- -3- -4- -5-Fractile
Volatility & Beta
Valu
e-Weig
hted
Eq
ual-W
eigh
ted
Std. Dev. of Monthly Returns Beta on Market (S&P 500)
Beta, on Market (S&P 500) -- FEW EW As Univariate Sort Factor
0.00
0.20
0.40
0.60
0.80
1.00
1.20
1.40
-1- -2- -3- -4- -5-Fractile
Forward Earnings Yield - F5-F1 Time Series, VW Forecast Next 12 Mos. Earnings Yield (FEY) Cumulative
FEY VW -- Time Series, Cumulative Performance
-3
-2
-1
0
1
2
3
4
1/31
/198
7
1/31
/198
8
1/31
/198
9
1/31
/199
0
1/31
/199
1
1/31
/199
2
1/31
/199
3
1/31
/199
4
1/31
/199
5
1/31
/199
6
1/31
/199
7
1/31
/199
8
1/31
/199
9
1/31
/200
0
1/31
/200
1
log
2 C
um
Ret
urn
-1.5
-1
-0.5
0
0.5
1
1.5
2
log
2 C
um
Retu
rn fo
r FN
-F1
On
ly
F1FNBmarkFN-F1
Forward Earnings Yield - F5-F1 Time Series, EW Forecast Next 12 Mos. Earnings Yield (FEY) Cumulative
FEY EW -- Time Series, Cumulative Performance
-3
-2
-1
0
1
2
3
4
1/31
/198
7
1/31
/198
8
1/31
/198
9
1/31
/199
0
1/31
/199
1
1/31
/199
2
1/31
/199
3
1/31
/199
4
1/31
/199
5
1/31
/199
6
1/31
/199
7
1/31
/199
8
1/31
/199
9
1/31
/200
0
1/31
/200
1
log
2 C
um
Ret
urn
-1.5
-1
-0.5
0
0.5
1
1.5
2
log
2 C
um
Retu
rn fo
r FN
-F1
On
ly
F1FNBmarkFN-F1
Forward Earnings Yield - F5-F1 Time Series
Forecast Next 12 Mos. Earnings Yield (FEY)Fractiles, Year-By-Year Returns -- FEY VW
-36%
-24%
-12%
0%
12%
24%
36%
48%
60%
72%
84%
96%
1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001
Co
mp
ute
d b
y M
ult
iplic
ati
ve
ly A
gg
reg
ati
ng
Mo
nth
ly R
etu
rns
Ov
er
12
-Mo
. W
ind
ow
s
F1
F2
F3
F4
F5
Fractile Returns, Trailing 12 Mos. -- FEY VW
-75%
-50%
-25%
0%
25%
50%
75%
100%
125%
150%
175%
200%
225%
1/31/1
988
1/31/1
989
1/31/1
990
1/31/1
991
1/31/1
992
1/31/1
993
1/31/1
994
1/31/1
995
1/31/1
996
1/31/1
997
1/31/1
998
1/31/1
999
1/31/2
000
1/31/2
001
Com
pute
d by
Mul
tiplic
ativ
ely
Agg
rega
ting
Mon
thly
Ret
urns
Ove
r a T
raili
ng 1
2-M
o. W
indo
w
F1-Bmark
F2-Bmark
F3-Bmark
F4-Bmark
F5-Bmark
F5-F1
Fractiles, Year-By-Year Returns -- FEY EW
-36%
-24%
-12%
0%
12%
24%
36%
48%
60%
72%
84%
96%
1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001
Co
mp
ute
d b
y M
ult
iplic
ati
ve
ly A
gg
reg
ati
ng
Mo
nth
ly R
etu
rns
Ov
er
12
-Mo
. W
ind
ow
s
F1
F2
F3
F4
F5
Valu
e-Weig
hted
Eq
ual-W
eigh
ted
Year-By-Year Trailing Twelve Months
All Fractiles, 12-Month Windows
Fractile Returns, Trailing 12 Mos. -- FEY EW
-75%
-50%
-25%
0%
25%
50%
75%
100%
125%
150%
175%
200%
225%
1/31/1
988
1/31/1
989
1/31/1
990
1/31/1
991
1/31/1
992
1/31/1
993
1/31/1
994
1/31/1
995
1/31/1
996
1/31/1
997
1/31/1
998
1/31/1
999
1/31/2
000
1/31/2
001
Com
pute
d by
Mul
tiplic
ativ
ely
Agg
rega
ting
Mon
thly
Ret
urns
Ove
r a T
raili
ng 1
2-M
o. W
indo
w
F1-Bmark
F2-Bmark
F3-Bmark
F4-Bmark
F5-Bmark
F5-F1
Forward Earnings Yield - F5-F1 Returns Distributions
Forecast Next 12 Mos. Earnings Yield (FEY)
FEY VW -- FN-F1 Portfolio: Monthly Returns Distribution
0
2
4
6
8
10
12
14
16
-0.2
6-0
.25
-0.2
4-0
.23
-0.2
2-0
.21
-0.2
-0.1
9-0
.18
-0.1
7-0
.16
-0.1
5-0
.14
-0.1
3-0
.12
-0.1
1-0
.1-0
.09
-0.0
8-0
.07
-0.0
6-0
.05
-0.0
4-0
.03
-0.0
2-0
.01 0
0.0
10
.02
0.0
30
.04
0.0
50
.06
0.0
70
.08
0.0
90
.10
.11
0.1
20
.13
0.1
40
.15
0.1
60
.17
0.1
80
.19
0.2
0.2
10
.22
0.2
30
.24
0.2
50
.26
0.2
7In
f
Monthly Return, Bin Upper Limit
Incr
emen
tal S
har
e o
f A
ll R
etu
rns
Per
Un
it X
(D
ensi
ty)
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
Cu
mu
lati
ve
Sh
are
of
All
Re
turn
s
Incremental
Cumulative
FEY VW -- FN-F1 Portfolio: ln Monthly Returns Distribution
0
2
4
6
8
10
12
14
16
-0.3
1-0
.3-0
.29
-0.2
8-0
.27
-0.2
6-0
.25
-0.2
4-0
.23
-0.2
2-0
.21
-0.2
-0.1
9-0
.18
-0.1
7-0
.16
-0.1
5-0
.14
-0.1
3-0
.12
-0.1
1-0
.1-0
.09
-0.0
8-0
.07
-0.0
6-0
.05
-0.0
4-0
.03
-0.0
2-0
.01 0
0.0
10
.02
0.0
30
.04
0.0
50
.06
0.0
70
.08
0.0
90
.10
.11
0.1
20
.13
0.1
40
.15
0.1
60
.17
0.1
80
.19
0.2
0.2
10
.22
0.2
30
.24
Inf
ln Monthly Return, Bin Upper Limit
Incr
emen
tal S
har
e o
f A
ll R
etu
rns
Per
Un
it X
(D
ensi
ty)
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
Cu
mu
lati
ve
Sh
are
of
All
Re
turn
s
Incremental
Cumulative
FEY EW -- FN-F1 Portfolio: Monthly Returns Distribution
0
2
4
6
8
10
12
14
16
-0.4
3-0
.42
-0.4
1-0
.4-0
.39
-0.3
8-0
.37
-0.3
6-0
.35
-0.3
4-0
.33
-0.3
2-0
.31
-0.3
-0.2
9-0
.28
-0.2
7-0
.26
-0.2
5-0
.24
-0.2
3-0
.22
-0.2
1-0
.2-0
.19
-0.1
8-0
.17
-0.1
6-0
.15
-0.1
4-0
.13
-0.1
2-0
.11
-0.1
-0.0
9-0
.08
-0.0
7-0
.06
-0.0
5-0
.04
-0.0
3-0
.02
-0.0
1 00
.01
0.0
20
.03
0.0
40
.05
0.0
60
.07
0.0
80
.09
0.1
0.1
10
.12
0.1
30
.14
0.1
50
.16
0.1
70
.18
0.1
90
.20
.21
0.2
20
.23
0.2
40
.25
0.2
6In
f
Monthly Return, Bin Upper Limit
Incr
emen
tal S
har
e o
f A
ll R
etu
rns
Per
Un
it X
(D
ensi
ty)
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
Cu
mu
lati
ve
Sh
are
of
All
Re
turn
sIncremental
Cumulative
Valu
e-Weig
hted
Eq
ual-W
eigh
ted
Monthly Returns ln Monthly Returns
FEY EW -- FN-F1 Portfolio: ln Monthly Returns Distribution
0
2
4
6
8
10
12
14
16
-0.5
8-0
.57
-0.5
6-0
.55
-0.5
4-0
.53
-0.5
2-0
.51
-0.5
-0.4
9-0
.48
-0.4
7-0
.46
-0.4
5-0
.44
-0.4
3-0
.42
-0.4
1-0
.4-0
.39
-0.3
8-0
.37
-0.3
6-0
.35
-0.3
4-0
.33
-0.3
2-0
.31
-0.3
-0.2
9-0
.28
-0.2
7-0
.26
-0.2
5-0
.24
-0.2
3-0
.22
-0.2
1-0
.2-0
.19
-0.1
8-0
.17
-0.1
6-0
.15
-0.1
4-0
.13
-0.1
2-0
.11
-0.1
-0.0
9-0
.08
-0.0
7-0
.06
-0.0
5-0
.04
-0.0
3-0
.02
-0.0
1 00
.01
0.0
20
.03
0.0
40
.05
0.0
60
.07
0.0
80
.09
0.1
0.1
10
.12
0.1
30
.14
0.1
50
.16
0.1
70
.18
0.1
90
.20
.21
0.2
20
.23
Inf
ln Monthly Return, Bin Upper Limit
Incr
emen
tal S
har
e o
f A
ll R
etu
rns
Per
Un
it X
(D
ensi
ty)
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
Cu
mu
lati
ve
Sh
are
of
All
Re
turn
s
Incremental
Cumulative
Forward Earnings Yield - F5-F1 Returns Distributions
Forecast Next 12 Mos. Earnings Yield (FEY)
Valu
e-Weig
hted
Eq
ual-W
eigh
ted
Monthly Returns ln Monthly Returns
Summary Statistics
Implied Cost of Capital - Idea
Idea: Base a univariate sorting factor on an estimation of implied cost of capital. Implied cost of capital should be a far more
comprehensive relative valuation metric than earnings yield, dividend yield, or book-to-price.
Earnings yield can be viewed as an extremely simplified expression of implied cost of equity. Common valuation models can be simplified to yield
the following relations if extreme over-simplifying assumptions are made (i.e. firms have reached steady-state and will not grow)
er
EP 1
0 0
1
P
Ere
re is the cost of equity, which can be equated to cost of capital if another extreme over-simplifying assumption is made: all firms are 100% equity financed.
Implied Cost of Capital - Implementation
A residual income (i.e. “abnormal earnings”) valuation model can serve as the basis for estimating an implied cost of equity, re, for each firm (based on the market capitalization observed in the market).
Estimates of leverage and cost of debt, rd, for each firm can be integrated with the residual income model to estimate implied cost of capital for each firm.
All firms could be ranked on implied cost of capital. The firms with the highest implied cost of capital might be considered undervalued (long candidates). Those with the lowest implied cost of capital might be considered overvalued (short candidates).
Implied Cost of Capital - Limitations
It is obviously false to assert that the implied cost of capital for all firms should be equivalent in expectation.
However, the assertion is similarly flawed for the other valuation metrics previously examined (earnings yield, dividend yield, book-to-price).
Still, an advantageous informational advantage seems to have been found (for forward earnings yield, for example)
Differing expected future growth rates and patterns, payout ratios, and capital structures are sources of differing expected earnings yield. Implied cost of capital can take all of these firm-specific features into account.
Implied Cost of Capital -Industry-Normalization? The implied cost of capital for each firm
should theoretically reflect the inherent risk of its underlying assets, ra.
Thus, it probably makes more sense to compare any given firm’s implied cost of capital against that of other firms in the same industry. Of course, by the same logic, industry normalization might improve performance of other valuation metrics such as earnings yield, dividend yield, and book-to-price.
Implied Cost of Capital -Implementation Challenges Estimating even implied cost of equity (let alone
implied cost of capital) for each firm requires numeric methods.
FactSet’s Alpha Testing module does not appear capable of implementing the necessary algorithms.
Time limits did not permit us to write our own code to replicate the functionality of FastSet’s Alpha Testing and implement numeric methods to solve for implied cost of capital.
However, we believe we have determined that the implementation of this backtest is possible with FQL (FactSet Query Language) and even in Excel via Visual Basic and the FastSet Excel Plug-In.
“Implied Cost of Capital” -Ours Is A Weak Approximation Though we present the idea here, we did not implement a
strong evaluation of implied cost of capital as a univariate sorting factor.
We did implement an extreme simplification of the idea using the following relation to grossly approximate implied cost of equity:
Note that we chose 5.5% as the nominal terminal growth rate, g∞, for all firms.
This relation could be implemented in FactSet’s Alpha Testing because it is solvable for re by the quadratic equation.
Note that though we have called this “implied cost of capital,” it is in truth a highly over-simplified implementation of what is typically meant by “implied cost of capital.” This implementation does little more than achieve a reasonable integration of forward earnings yield and book-to-price into one metric.
)1)(())(1(
1000101
ee
e
e
e
rgrBrEg
rBrEBP
“Implied Cost of Capital” ≡ ICCTwo methods of calculation Recognizing that our “implied cost of capital” had become little
more than an integration of forward earnings yield and book-to-price into a single metric, we experimented with two definitions of forward earnings (denoted E1 in the preceding slide):
1. ICC1: Median I/B/E/S earnings forecast for “Next Twelve Months”. If this data is unavailable, median I/B/E/S earnings forecast for the current fiscal year is used instead (as in FEY definition C).
2. ICC2: Median I/B/E/S earnings forecast for forward fiscal year number 2 (as in FEY definition D). (Idea/justification: Use the most forward earnings forecast to extrapolate into perpetuity even though this earnings estimate should be discounted more heavily.)
The following slides focus on the backtest results using ICC1 (definition 1 for E1).
This definition was chosen because backtest results were similar across both definitions for ICC, but definition 1 is more theoretically valid in the highly simplified valuation expression presented in the previous slide.
ICC1 - Quintile Performance
Annualized Return, % -- ICC VW Univariate Factor Performance
0.0
5.0
10.0
15.0
20.0
25.0
-1- -2- -3- -4- -5-Fractile
Alpha, Monthly % -- ICC VW Univariate Factor Performance
-0.50
-0.30
-0.10
0.10
0.30
0.50
0.70
-1- -2- -3- -4- -5-
Fractile
Annualized Return, % -- ICC EW Univariate Factor Performance
0.0
5.0
10.0
15.0
20.0
25.0
-1- -2- -3- -4- -5-Fractile
Valu
e-Weig
hted
Eq
ual-W
eigh
ted
Annualized Return Alpha
Returns & Alpha
Alpha, Monthly % -- ICC EW Univariate Factor Performance
-0.50
-0.30
-0.10
0.10
0.30
0.50
0.70
-1- -2- -3- -4- -5-
Fractile
ICC1 - Quintile Performance
Std. Dev. of Monthly Returns -- ICC VW As Univariate Sort Factor
0.00
1.00
2.00
3.00
4.00
5.00
6.00
7.00
8.00
-1- -2- -3- -4- -5-Fractile
Beta, on Market (S&P 500) -- ICC VW As Univariate Sort Factor
0.00
0.20
0.40
0.60
0.80
1.00
1.20
-1- -2- -3- -4- -5-Fractile
Std. Dev. of Monthly Returns -- ICC EW As Univariate Sort Factor
0.00
1.00
2.00
3.00
4.00
5.00
6.00
7.00
8.00
-1- -2- -3- -4- -5-Fractile
Valu
e-Weig
hted
Eq
ual-W
eigh
ted
Std. Dev. of Monthly Returns Beta on Market (S&P 500)
Volatility & Beta
Beta, on Market (S&P 500) -- ICC EW As Univariate Sort Factor
0.00
0.20
0.40
0.60
0.80
1.00
1.20
-1- -2- -3- -4- -5-Fractile
ICC1 - F5-F1 Time Series, VWCumulative
ICC VW -- Time Series, Cumulative Performance
-1.6
-0.8
0
0.8
1.6
2.4
3.2
4
1/31
/198
7
1/31
/198
8
1/31
/198
9
1/31
/199
0
1/31
/199
1
1/31
/199
2
1/31
/199
3
1/31
/199
4
1/31
/199
5
1/31
/199
6
1/31
/199
7
1/31
/199
8
1/31
/199
9
1/31
/200
0
1/31
/200
1
log
2 C
um
Ret
urn
-0.8
-0.4
0
0.4
0.8
1.2
1.6
2
log
2 C
um
Retu
rn fo
r FN
-F1
On
ly
F1FNBmarkFN-F1
ICC1 - F5-F1 Time Series, EWCumulative
ICC EW -- Time Series, Cumulative Performance
-1.6
-0.8
0
0.8
1.6
2.4
3.2
4
1/31
/198
7
1/31
/198
8
1/31
/198
9
1/31
/199
0
1/31
/199
1
1/31
/199
2
1/31
/199
3
1/31
/199
4
1/31
/199
5
1/31
/199
6
1/31
/199
7
1/31
/199
8
1/31
/199
9
1/31
/200
0
1/31
/200
1
log
2 C
um
Ret
urn
-0.8
-0.4
0
0.4
0.8
1.2
1.6
2
log
2 C
um
Retu
rn fo
r FN
-F1
On
ly
F1FNBmarkFN-F1
ICC1 – F5-F1 Time Series
Fractiles, Year-By-Year Returns -- ICC VW
-40%
-20%
0%
20%
40%
60%
80%
1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001
Co
mp
ute
d b
y M
ult
iplic
ati
ve
ly A
gg
reg
ati
ng
Mo
nth
ly R
etu
rns
Ov
er
12
-Mo
. W
ind
ow
s
F1
F2
F3
F4
F5
Fractile Returns, Trailing 12 Mos. -- ICC VW
-75%
-50%
-25%
0%
25%
50%
75%
100%
125%
150%
175%
1/31/1
988
1/31/1
989
1/31/1
990
1/31/1
991
1/31/1
992
1/31/1
993
1/31/1
994
1/31/1
995
1/31/1
996
1/31/1
997
1/31/1
998
1/31/1
999
1/31/2
000
1/31/2
001
Com
pute
d by
Mul
tiplic
ativ
ely
Agg
rega
ting
Mon
thly
Ret
urns
Ove
r a T
raili
ng 1
2-M
o. W
indo
w
F1-Bmark
F2-Bmark
F3-Bmark
F4-Bmark
F5-Bmark
F5-F1
Fractiles, Year-By-Year Returns -- ICC EW
-40%
-20%
0%
20%
40%
60%
80%
1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001
Co
mp
ute
d b
y M
ult
iplic
ati
ve
ly A
gg
reg
ati
ng
Mo
nth
ly R
etu
rns
Ov
er
12
-Mo
. W
ind
ow
s
F1
F2
F3
F4
F5
Valu
e-Weig
hted
Eq
ual-W
eigh
ted
Year-By-Year Trailing Twelve Months
All Fractiles, 12-Month Windows
Fractile Returns, Trailing 12 Mos. -- ICC EW
-75%
-50%
-25%
0%
25%
50%
75%
100%
125%
150%
175%
1/31/1
988
1/31/1
989
1/31/1
990
1/31/1
991
1/31/1
992
1/31/1
993
1/31/1
994
1/31/1
995
1/31/1
996
1/31/1
997
1/31/1
998
1/31/1
999
1/31/2
000
1/31/2
001
Com
pute
d by
Mul
tiplic
ativ
ely
Agg
rega
ting
Mon
thly
Ret
urns
Ove
r a T
raili
ng 1
2-M
o. W
indo
w
F1-Bmark
F2-Bmark
F3-Bmark
F4-Bmark
F5-Bmark
F5-F1
ICC1 – F5-F1 Returns Distributions
ICC VW -- FN-F1 Portfolio: Monthly Returns Distribution
0
2
4
6
8
10
12
14
16
18
-0.2
1-0
.2-0
.19
-0.1
8-0
.17
-0.1
6-0
.15
-0.1
4-0
.13
-0.1
2-0
.11
-0.1
-0.0
9-0
.08
-0.0
7-0
.06
-0.0
5-0
.04
-0.0
3-0
.02
-0.0
1 00
.01
0.0
20
.03
0.0
40
.05
0.0
60
.07
0.0
80
.09
0.1
0.1
10
.12
0.1
30
.14
0.1
50
.16
0.1
70
.18
0.1
90
.20
.21
0.2
20
.23
Inf
Monthly Return, Bin Upper Limit
Incr
emen
tal S
har
e o
f A
ll R
etu
rns
Per
Un
it X
(D
ensi
ty)
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
Cu
mu
lati
ve
Sh
are
of
All
Re
turn
s
Incremental
Cumulative
ICC VW -- FN-F1 Portfolio: ln Monthly Returns Distribution
0
2
4
6
8
10
12
14
16
18
-0.2
4-0
.23
-0.2
2-0
.21
-0.2
-0.1
9-0
.18
-0.1
7-0
.16
-0.1
5-0
.14
-0.1
3-0
.12
-0.1
1-0
.1-0
.09
-0.0
8-0
.07
-0.0
6-0
.05
-0.0
4-0
.03
-0.0
2-0
.01 0
0.0
10
.02
0.0
30
.04
0.0
50
.06
0.0
70
.08
0.0
90
.10
.11
0.1
20
.13
0.1
40
.15
0.1
60
.17
0.1
80
.19
0.2
0.2
1In
f
ln Monthly Return, Bin Upper Limit
Incr
emen
tal S
har
e o
f A
ll R
etu
rns
Per
Un
it X
(D
ensi
ty)
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
Cu
mu
lati
ve
Sh
are
of
All
Re
turn
s
Incremental
Cumulative
ICC EW -- FN-F1 Portfolio: Monthly Returns Distribution
0
2
4
6
8
10
12
14
16
18
-0.3
7-0
.36
-0.3
5-0
.34
-0.3
3-0
.32
-0.3
1-0
.3-0
.29
-0.2
8-0
.27
-0.2
6-0
.25
-0.2
4-0
.23
-0.2
2-0
.21
-0.2
-0.1
9-0
.18
-0.1
7-0
.16
-0.1
5-0
.14
-0.1
3-0
.12
-0.1
1-0
.1-0
.09
-0.0
8-0
.07
-0.0
6-0
.05
-0.0
4-0
.03
-0.0
2-0
.01 0
0.0
10
.02
0.0
30
.04
0.0
50
.06
0.0
70
.08
0.0
90
.10
.11
0.1
20
.13
0.1
40
.15
0.1
60
.17
0.1
80
.19
0.2
0.2
10
.22
Inf
Monthly Return, Bin Upper Limit
Incr
emen
tal S
har
e o
f A
ll R
etu
rns
Per
Un
it X
(D
ensi
ty)
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
Cu
mu
lati
ve
Sh
are
of
All
Re
turn
sIncremental
Cumulative
Valu
e-Weig
hted
Eq
ual-W
eigh
ted
Monthly Returns ln Monthly Returns
ICC EW -- FN-F1 Portfolio: ln Monthly Returns Distribution
0
2
4
6
8
10
12
14
16
18
-0.4
6-0
.45
-0.4
4-0
.43
-0.4
2-0
.41
-0.4
-0.3
9-0
.38
-0.3
7-0
.36
-0.3
5-0
.34
-0.3
3-0
.32
-0.3
1-0
.3-0
.29
-0.2
8-0
.27
-0.2
6-0
.25
-0.2
4-0
.23
-0.2
2-0
.21
-0.2
-0.1
9-0
.18
-0.1
7-0
.16
-0.1
5-0
.14
-0.1
3-0
.12
-0.1
1-0
.1-0
.09
-0.0
8-0
.07
-0.0
6-0
.05
-0.0
4-0
.03
-0.0
2-0
.01 0
0.0
10
.02
0.0
30
.04
0.0
50
.06
0.0
70
.08
0.0
90
.10
.11
0.1
20
.13
0.1
40
.15
0.1
60
.17
0.1
80
.19
0.2 Inf
ln Monthly Return, Bin Upper Limit
Incr
emen
tal S
har
e o
f A
ll R
etu
rns
Per
Un
it X
(D
ensi
ty)
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
Cu
mu
lati
ve
Sh
are
of
All
Re
turn
s
Incremental
Cumulative
ICC1 – F5-F1 Returns Distributions
Valu
e-Weig
hted
Eq
ual-W
eigh
ted
Monthly Returns ln Monthly Returns
Summary Statistics
Univariate Sorts - Summary
FEY_C
ICC2
ICC1
FEY_D
FEY_B
TEY
FEY_A
B/P
Div.Yld.
Selected Primary Factor
Forward Earnings Yield Definition C was chosen Even though our backtesting results slightly
favor ICC as a univariate sort factor (especially in value-weighted portfolios), we selected FEY as the primary (basis) factor upon which to experiment with interfractile migration tracking.
FEY was selected because its performance was similar to that of ICC, but its interpretation is more intuitive and its use in financial analyses more widespread.
Interfractile Migration - Definition
Define 2 metrics to quantify “interfractile migration” (IM) Interfractile Migration Trending (IMT)
over recent periods, measure the trend of each stock’s movements through fractiles of the primary factor
Interfractile Migration Volatility (IMV) over recent periods, measure the volatility of each
stock’s movements through fractiles of the primary factor
Define fractile resolution (with respect to primary factor) We used 10 fractiles (deciles), as segregated by
Factset’s UDECILE() function.
Interfractile Migration - Definition
IM Trending, IMT = 0IM Volatility, IMV = 0
0
1
2
3
4
5
6
7
8
9
10
-11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0
Lagged Months
Pri
mar
y F
acto
rD
ecile
s
Red Dot Stock
Interfractile Migration - Definition
IMT is highly positiveIMV is moderate
Green Circle Stock
0
1
2
3
4
5
6
7
8
9
10
-11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0
Lagged Months
Pri
mar
y F
acto
rD
ecile
s
Interfractile Migration - Definition
IMT is only slightly positiveIMV is moderate
Black X Stock
0
1
2
3
4
5
6
7
8
9
10
-11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0
Lagged Months
Pri
mar
y F
acto
rD
ecile
s
Interfractile Migration - Definition
IMT is negligibleIMV is very high
Blue Square Stock
0
1
2
3
4
5
6
7
8
9
10
-11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0
Lagged Months
Pri
mar
y F
acto
rD
ecile
s
Interfractile Migration - Quantification
We implemented two variants of each metric IMT
SMA3(PFD)-SMA12(PFD) Trailing triangular-weighted average of previous
11 ΔPFD’s IMV
Mean of previous 11 |ΔPFD|’s Trailing triangular-weighted average of previous
11 |ΔPFD|’s
PFDi,t – “Primary Factor Decile”; the decile into which a stock is binned when sorted on the primary factor
0
101,, )(
121
)11(2(n
nnini PFDPFD
n
Note that we used some special techniques to estimate IMT and IMV for stocks that were missing primary factor (forward earnings yield) data in some periods within the last 12 months. Refer to our report for more details.
Interfractile Migration - Illustration
To illustrate, let’s focus on these two particular variants of our IM metrics:
IMT: SMA3(PFD)-SMA12(PFD)
IMV: Mean of previous 11 |ΔPFD|’s
Note that we also applied our alternate definitions of IMT and IMV, but at least upon a first look at charts illustrating performance across the 15 sub-fractiles, there does not appear to be significant additional information contributed by these alternate definitions.
Interfractile Migration - Illustration
0.0
5.0
10.0
15.0
20.0
25.0
-1- -2- -3- -4- -5- -6- -7- -8- -9- -10- -11- -12- -13- -14- -15-
Fractile
An
nu
aliz
ed R
etu
rn
0.0
5.0
10.0
15.0
20.0
25.0
-1- -2- -3- -4- -5- -6- -7- -8- -9- -10- -11- -12- -13- -14- -15-
Fractile
An
nu
al R
etu
rn
0.0
5.0
10.0
15.0
20.0
25.0
-1- -2- -3- -4- -5- -6- -7- -8- -9- -10- -11- -12- -13- -14- -15-
Fractile
An
nu
aliz
ed R
etu
rn
IMT Equal-Weighted IMT Value-Weighted
IMV Equal-Weighted IMV Value-Weighted
0.0
5.0
10.0
15.0
20.0
25.0
-1- -2- -3- -4- -5- -6- -7- -8- -9- -10- -11- -12- -13- -14- -15-
Fractiles
An
nu
aliz
ed R
etu
rn
We studied both equal-weighted and value-weighted portfolios.
Findings are roughly similar across both intra-fractile weighting schemes. Thus, in these slides we focus on value-weighted portfolios.
Liquidity issues tend to make these more easily implementable.Refer directly to Excel source files for details of performance in equal-weighted portfolios.
Interfractile Migration - Implementation
We analyze IM factor performance within each Forward Earnings Yield (FEY) quintile:
Two-step sequential sort 1st Sort: Quintiles on primary factor (FEY) 2nd Sort: Sub-Trintiles on IMT or IMV
Interfractile Migration Trending
0.0
5.0
10.0
15.0
20.0
25.0
-1- -2- -3- -4- -5- -6- -7- -8- -9- -10- -11- -12- -13- -14- -15-
Fractile
An
nu
aliz
ed R
etu
rn
Raw Mean Geometric Annualized Return
-0.80
-0.60
-0.40
-0.20
0.00
0.20
0.40
0.60
-1- -2- -3- -4- -5- -6- -7- -8- -9- -10- -11- -12- -13- -14- -15-
Fractile
Alp
ha
Interfractile Migration Trending
Market Risk-Adjusted Monthly Alpha
Interfractile Migration Trending
Standard Deviation of Monthly Returns (Sigma)
0.00
1.00
2.00
3.00
4.00
5.00
6.00
7.00
8.00
-1- -2- -3- -4- -5- -6- -7- -8- -9- -10- -11- -12- -13- -14- -15-
Fractile
Std
. Dev
. of
Mo
nth
ly R
etu
rns
(Sig
ma)
Interfractile Migration Trending
High correlations between high and low IMT fractiles (1 vs. 3; 4 vs. 6) suggest low variance spread trade strategy.
Lower correlations between high and low FEY fractiles (1,2,3 vs. 13,14,15) suggest higher variance spread trade strategy.
Interfractile Correlation
IMT – Trading Strategies
Control Portfolio Long the 3 high FEY fractiles (13,14,15) Short the 3 low FEY fractiles (1,2,3)
IMT Isolation for Low FEY Portfolio Long the low IMT fractiles in low FEY quintiles (1,4) Short the high IMT fractiles in low FEY quintiles (3,6)
Hybrid Portfolio Long fractiles 13,14,15,1 Short fractiles 2,3,6
When building simulated portfolios that combine fractiles, value-weighting was used within fractiles. However, within a multi-fractile long (or short) portfolio, each fractile was equally weighted with monthly rebalancing. This methodology was implemented solely for computational convenience and could be reconsidered in an alternate analysis.
IMT – Hybrid Portfolio Composition
Various combinations of the 15 sub-fractile portfolios were considered and examined as candidate “hybrid portfolios.”
Qualitative justification of long{13, 14, 15, 1} / short{2, 3, 6} Fractiles 2, 3, and 6 showed the lowest raw mean returns
and alphas in-sample. Fractile 1 is highly correlated with fractiles 2, 3, and 6, but
with a higher mean return. It is more highly correlated with the aggregated short fractiles than fractile 4 (and less correlated with its fellow long fractiles 13, 14, and 15).
Of course, low correlations among all-long or all-short portfolio positions result in desirable lower overall volatility. The same is true for high correlations between hedge portfolio positions.
Refer to source spreadsheets for more detail pertaining to assorted experimental candidate hybrid portfolios.
Note that we experimented with portfolio optimization techniques in search of an optimal hybrid portfolio definition, paying special attention to the non-normal nature of monthly fractile return distributions. More focus could be given to these methods in future studies.
IMT – Trading Strategies
-0.75
-0.5
-0.25
0
0.25
0.5
0.75
1
1.25
1.5
1.75
Dec-87 Dec-88 Dec-89 Dec-90 Dec-91 Dec-92 Dec-93 Dec-94 Dec-95 Dec-96 Dec-97 Dec-98 Dec-99 Dec-00 Dec-01
log
2 C
um
Ret
urn
s
-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5
3
3.5
log
2 Cu
m R
eturn
s for S
P500 O
nly
13,14,15 - 1,2,3; Control: FEY Long/Short
1,13,14,15 - 2,3,6; Hybrid
1,4 - 3,6; IMT Isolation
SP500
0.0
5.0
10.0
15.0
20.0
25.0
-1- -2- -3- -4- -5- -6- -7- -8- -9- -10- -11- -12- -13- -14- -15-
Fractile
An
nu
aliz
ed R
etu
rn
Interfractile Migration Volatility
Raw Mean Geometric Annualized Return
-1.00
-0.80
-0.60
-0.40
-0.20
0.00
0.20
0.40
0.60
-1- -2- -3- -4- -5- -6- -7- -8- -9- -10- -11- -12- -13- -14- -15-
Fractile
Alp
ha
Interfractile Migration Volatility
Market Risk-Adjusted Monthly Alpha
Interfractile Migration Volatility
Standard Deviation of Monthly Returns (Sigma)
0.00
1.00
2.00
3.00
4.00
5.00
6.00
7.00
8.00
-1- -2- -3- -4- -5- -6- -7- -8- -9- -10- -11- -12- -13- -14- -15-
Fractile
Std
. D
ev.
of
Mo
nth
ly R
etu
rns
(Sig
ma)
Interfractile Migration Volatility
High correlations between high and low IMT fractiles (1 vs. 3; 4 vs. 6) suggest low variance spread trade strategy.
Lower correlations between high and low FEY fractiles (1,2,3 vs. 13,14,15) suggest higher variance spread trade strategy.
Interfractile Correlation
IMV – Trading Strategies
Control Portfolio Long the 3 high FEY fractiles (13,14,15) Short the 3 low FEY fractiles (1,2,3)
IMV Isolation for Low FEY Portfolio Long the high IMV fractiles in low FEY quintiles (3,6) Short the low IMV fractiles in low FEY quintiles (1,4)
Hybrid Portfolio Long fractiles 3,13,14,15 Short fractiles 1,2,4
When building simulated portfolios that combine fractiles, value-weighting was used within fractiles. However, within a multi-fractile long (or short) portfolio, each fractile was equally weighted with monthly rebalancing.
IMV – Hybrid Portfolio Composition
Various combinations of the 15 sub-fractile portfolios were considered and examined as candidate “hybrid portfolios.”
Qualitative justification of long{3, 13, 14, 15} / short{1, 2, 4} Fractiles 1, 2, and 4 showed the lowest raw mean returns
and alphas in-sample. Fractile 3 is highly correlated with fractiles 1, 2, and 4, but
with a higher mean return. It is more highly correlated with each of these short fractiles than fractile 6 (and less correlated with its fellow long fractiles 13, 14, and 15).
Of course, low correlations among all-long or all-short portfolio positions result in desirable lower overall volatility. The same is true for high correlations between hedge portfolio positions.
Refer to source spreadsheets for more detail pertaining to assorted experimental candidate hybrid portfolios.
Note that we experimented with portfolio optimization techniques in search of an optimal hybrid portfolio definition, paying special attention to the non-normal nature of monthly fractile return distributions. More focus could be given to these methods in future studies.
IMV – Trading Strategies
-0.75
-0.5
-0.25
0
0.25
0.5
0.75
1
1.25
1.5
1.75
Dec-8
7
Dec-8
8
Dec-8
9
Dec-9
0
Dec-9
1
Dec-9
2
Dec-9
3
Dec-9
4
Dec-9
5
Dec-9
6
Dec-9
7
Dec-9
8
Dec-9
9
Dec-0
0
Dec-0
1
log
2 C
um
Ret
urn
s
-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5
3
3.5
log
2 Cu
m R
eturn
s or S
P500
On
ly
13,14,15 - 1,2,3; Control: FEY Long/Short
3,13,14,15 - 1,2,4; Hybrid
3,6 - 1,4; IMV Isolation
SP500
In-Sample Summary
IM Trading Strategies
-8.0
-4.0
0.0
4.0
8.0
12.0
16.0
20.0
24.0
-1- -2- -3- -4- -5- -6- -7- -8- -9- -10- -11- -12- -13- -14- -15-
Fractile
An
nu
aliz
ed R
etu
rnOut of Sample – IMT
Raw Mean Geometric Annualized Return
-0.80
-0.40
0.00
0.40
0.80
1.20
1.60
-1- -2- -3- -4- -5- -6- -7- -8- -9- -10- -11- -12- -13- -14- -15-
Fractile
Alp
ha
Out of Sample – IMT
Market Risk-Adjusted Monthly Alpha
Out of Sample – IMT
-2.00
-1.50
-1.00
-0.50
0.00
0.50
Dec-87
Dec-88
Dec-89
Dec-90
Dec-91
Dec-92
Dec-93
Dec-94
Dec-95
Dec-96
Dec-97
Dec-98
Dec-99
Dec-00
Dec-01
Dec-02
Dec-03
Dec-04
log
2 C
um
Ret
urn
s
-4.00
-3.00
-2.00
-1.00
0.00
1.00
log
2 Cu
m R
eturn
s SP
500 On
ly
13,14,15 - 1,2,3; Control: FEY Long/Short
1,13,14,15 - 2,3,6; Hybrid
1,4 - 3,6; IMT Isolation
SP500
OUT OF SAMPLE
-8.0
-4.0
0.0
4.0
8.0
12.0
16.0
20.0
24.0
-1- -2- -3- -4- -5- -6- -7- -8- -9- -10- -11- -12- -13- -14- -15-
Fractile
An
nu
aliz
ed R
etu
rn
Out of Sample – IMV
Raw Mean Geometric Annualized Return
-0.80
-0.40
0.00
0.40
0.80
1.20
1.60
-1- -2- -3- -4- -5- -6- -7- -8- -9- -10- -11- -12- -13- -14- -15-
Fractile
Alp
ha
Out of Sample – IMV
Market Risk-Adjusted Monthly Alpha
Out of Sample – IMV
-2.00
-1.75
-1.50
-1.25
-1.00
-0.75
-0.50
-0.25
0.00
0.25
0.50
0.75
Dec-87
Dec-88
Dec-89
Dec-90
Dec-91
Dec-92
Dec-93
Dec-94
Dec-95
Dec-96
Dec-97
Dec-98
Dec-99
Dec-00
Dec-01
Dec-02
Dec-03
Dec-04
log
2 C
um
Ret
urn
s
-3.00
-2.50
-2.00
-1.50
-1.00
-0.50
0.00
0.50
1.00
log
2 Cu
m R
eturn
s SP
500 On
ly
13,14,15 - 1,2,3; Control: FEY Long/Short
3,13,14,15 - 1,2,4; Hybrid
3,6 - 1,4; IMV Isolation
SP500
OUT OF SAMPLE
Conclusions
Among the valuation-based univariate screens examined, Forward Earnings Yield and ICC were the best. For unrebalanced FEY long F5 - short F1, monthly alpha = .87%.
A secondary sequential sort on IM trending (or volatility) appeared to add information (in-sample) regarding returns in low FEY quintiles.
IM-based enhanced trading strategies looked promising in-sample. Improved variance and total returns over the control strategy looked possible.
Conclusions
Out of sample, these trading strategies underperformed.
Perhaps the patterns observed in-sample were mere data artifacts.
Alternately, perhaps the 2002-2004 period happens to be a poor period for these IM-based strategies within FEY sorts. Perhaps the pattern observed in-sample will re-emerge in future months.
Recommendations For Future Research
Monitor continuing out-of-sample IMT and IMV performance for Forward Earnings Yield
Examine IM-based sorts in other Primary Factors (besides FEY– perhaps on an improved implied cost of capital factor, or an industry-normalized factor, or a non-valuation-based factor)
Examine sensitivity to IM metric definitions (i.e. lengths of trailing periods, weightings, and fractile resolution). Study a combination of trending and volatility elements
of IM into a single sorting factor. Study a third IM metric definition: IM Permanence–
weighted (?) trailing average of differences with current fractile membership. Maybe:
Incorporate transaction costs into analysis
0
101,0, )(
121
)11(2(n
nnii PFDPFD
n
Recommendations For Future Research
Rigorously implement backtesting of implied cost of capital as a univariate factor sort.
Introduce industry-normalization to definitions of basis univariate sorting factors (seems especially pertinent for these valuation-ratio-grounded metrics).
Study more closely any rebalancing effects on these long/short portfolios. Apparent rebalancing effects observed in this study suggest
that there may exist “factor momentum” where factor portfolio performance in a given month is predictive of factor portfolio performance in the subsequent month.
Implementation of these analyses in a regression-based framework rather than fractile sorts would enable better integration into multivariate stock selection models as well as additional factor performance diagnostics.
Also, refer to slide notes for specific suggested improvements to our screening and sorting methodologies as executed in this analysis.