Problems with Using Four Quarter Trailing
Numbers in Investment Models
August 2010
Marcus C. Bogue III, Ph.D.
President, Charter Oak Investment Systems, Inc.
Overview
• Four Quarter Trailing Numbers help
Remove Seasonal Effects
• But when there are Restatements Four
Quarter Trailing Numbers Mix Data from
Different Accounting Regimes
Toys R Us EPS
(source: Reuters Fundamentals Point in Time)
2.5
2
1.5
1
0.5
Ja
n0
5
Ja
n0
4
Ja
n0
3
Ja
n0
2
Ja
n0
1
Ja
n0
0
Ja
n9
9
Ja
n9
8
Ja
n9
7
Ja
n9
6
Ja
n9
5
Ja
n9
4
Ja
n9
3
Ja
n9
2
-0.5
Ja
n9
1
Ja
n9
0
0
-1
-1.5
EPS 4Q Sum
EPS Annual
-2
-2.5
EPS Quarterly
Four Quarter Trailing thru 1st Quarter Spinoff
Report Date (Point Date) for Period
Q(1,t-1)
FQT(1,t-1)
Q(1,t-1) Q(2,t-1)
100
400
Q(2,t-1)
FQT(2,t-1)
Q(3,t-1)
Q(4,t-1)
Q(1,t)
Q(2,t)
Q(3,t)
Q(4,t)
½ Company Spun off
100
400
As originally Reported
Restated
Reporting Period
Q(3,t-1)
FQT(3,t-1)
100
400
Q(4,t-1)
FQT(4,t-1)
100
400
Y(t-1)
400
Q(1,t)
FQT(1,t)
Q(2,t)
FQT(2,t)
Q(3,t)
FQT(3,t)
Q(4,t)
FQT(4,t)
Y(t)
50
Q(i,t) - Value for ith quarter year t
50
350
50
FQT(i,t) - Four Quarter trailing for
ith quarter year t
50
300
50
50
250
50
50
200
200
200
Four Quarter Trailing thru 2nd Quarter Spinoff
Report Date (Point Date) for Period
Q(1,t-1)
FQT(1,t-1)
Q(1,t-1) Q(2,t-1)
100
400
Q(2,t-1)
FQT(2,t-1)
Q(4,t-1)
Y(t-1)
400
Q(1,t)
FQT(1,t)
Q(4,t)
FQT(4,t)
Y(t)
Q(3,t)
Q(4,t)
½ Company Spun off
100
400
100
400
Q(3,t)
FQT(3,t)
Q(2,t)
As originally Reported
Q(4,t-1)
FQT(4,t-1)
Q(2,t)
FQT(2,t)
Q(1,t)
100
400
Q(3,t-1)
FQT(3,t-1)
Reporting Period
Q(3,t-1)
Restated
Q(i,t) - Value for ith quarter year t
100
400
50
50
50
50
FQT(i,t) - Four Quarter trailing for
ith quarter year t
50
300
50
250
50
50
200
200
200
Four Quarter Trailing thru Spinoff (Acquisition)
• Four Quarter Trailing Numbers, calculated as a sum of
the last four quarters, through a Spinoff (Acquisition)
do not decline (increase) as fast as they should due to
delay in reporting of restated quarters
• The problem is worse the earlier in the year the Spinoff
(Acquisition) occurs
• Ratios of Four Quarter Trailing numbers (Income
statement and Cash Flow statement numbers) to
Balance sheet numbers can be misleading.
Companies with Restated Compustat Net Income or Component
Data
(based on July 29, 2005 Point in Time database)
80%
70%
60%
50%
40%
30%
S&P 500
20%
Next 1000 Largest by Market Capitalization*
Restatements have yet to occur
Second 1000 Largest by Market Capitalization*
10%
All Traded Companies*
*Excludes ADRs, REITs, Mutual Funds and Limited Partnerships
ar
-0
4
M
ar
-0
3
M
ar
-0
2
M
ar
-0
1
M
ar
-0
0
M
ar
-9
9
M
ar
-9
8
M
ar
-9
7
M
ar
-9
6
M
ar
-9
5
M
ar
-9
4
M
ar
-9
3
M
ar
-9
2
M
ar
-9
1
M
ar
-9
0
M
ar
-8
9
M
ar
-8
8
M
M
ar
-8
7
0%
Restatements to Net Income or Component Data from Q1Y87 to Q4Y02
(Based on August 12, 2004 Unrestated Quarterly database)
60%
S&P 500
Next 1000 Largest by Market Capitalization*
50%
Second 1000 Largest by Market Capitalization*
* Excludes ADRs, REITs, Mutual Funds and Limited Partnrships
40%
30%
20%
10%
0%
Some
Difference
> 5%
Difference
> 10%
Difference
> 15%
Difference
> 20%
Difference
> 25%
Difference
11/1/04
% Interim Period Restatements U.S.
(based on Thomson Reuters Fundamentals Point in Time Database)
70%
60%
50%
40%
30%
20%
10%
INC Rstmt
BAL Rstmt
CAS Rstmt
Any Rstmt
Q1Y09
Q1Y08
Q1Y07
Q1Y06
Q1Y05
Q1Y04
Q1Y03
Q1Y02
Q1Y01
Q1Y00
Q1Y99
Q1Y98
0%
% Interim Period Restatements N. Europe
(based on Thomson Reuters Fundamentals Point in Time Database)
70%
60%
50%
40%
30%
20%
10%
INC Rstmt
BAL Rstmt
CAS Rstmt
Any Rstmt
Q1Y09
Q1Y08
Q1Y07
Q1Y06
Q1Y05
Q1Y04
Q1Y03
Q1Y02
Q1Y01
Q1Y00
Q1Y99
Q1Y98
0%
% Interim Period Restatements All Companies
(based on Thomson Reuters Fundamentals Point in Time Database)
70%
60%
50%
40%
30%
20%
10%
INC Rstmt
BAL Rstmt
CAS Rstmt
Any Rstmt
Q1Y09
Q1Y08
Q1Y07
Q1Y06
Q1Y05
Q1Y04
Q1Y03
Q1Y02
Q1Y01
Q1Y00
Q1Y99
Q1Y98
0%
% Annual Period Restatements U.S.
(based on Thomson Reuters Fundamentals Point in Time Database)
70%
60%
50%
40%
30%
20%
10%
0%
Y98
Y99
Y00
Y01
Any Rstmt
Y02
Y03
INC Rstmt
Y04
Y05
BAL Rstmt
Y06
Y07
CAS Rstmt
Y08
Y09
Restatements by Fiscal Period
Percentage of All U.S. Restatements by Fiscal Period Since Q1Y98
(based on Reuters Fundamentals Point-in-Tme Database)
40%
35%
30%
25%
20%
15%
10%
5%
0%
Fiscal Period 1
Fiscal Period 2
Fiscal Period 3
Fiscal Period 4
Alternative Four Quarter Trailing
• FQT = sum of last four quarters
• Alt FQT(i,t) = YTD(i,t) + Y(t-1) – YTD(i,t-1)
• When there are no restatements, FQT and Alt FQT are
the same.
• When there are restatements, Alt FQT makes the
“jump” occur in the 4th quarter
– Alt FQT(i,t) = Y(t-1) + (YTD(i,t) – YTD(i,t-1))
unrestated
restated
Alternative Four Quarter Trailing
Company Name
MONTH Fiscal Qtr0
Loews Corporation Apr08
1
Loews Corporation Jul08
2
Loews Corporation Oct08
3
Loews Corporation Feb09
4
0
4543
3922
2970
2743
Quarters Back
1
2
3
4430
4604
4637
3612
4430
4604
3767
3612
4430
2970
3767
3612
4
4613
3517
3525
3592
4Q Sum 4Q Sum Alternate
18214
18310
16568
18729
14779
17944
13092
13247
Annual + (YTD(q,y) - YTD(q,y-1))
Loews Four Quarter Sum
20000
18000
16000
14000
12000
4Q Sum
10000
8000
4Q Sum Alternate
6000
4000
2000
0
Apr08
May08
Jun08
Jul08
Aug08
Sep08
Oct08
Nov08
Dec08
Jan09
Feb09
Mar09
Cumulative Returns to SP500 “Value Factor” With Different FQT
Cumulative Returns SP500 "Value Factor" Monthly Rebalancing
(using Compustat Point in Time Data)
10
Cumulative Returns SP500 "Value Factor" Monthly Rebalancing
(using Compustat Point in Time Data)
5
9
4.5
Using FQT EPS
2
1
1
0.5
0
0
Ja
n1
0
1.5
Ja
n0
9
3
Ja
n0
8
2
Ja
n0
7
4
Ja
n0
6
2.5
Ja
n0
5
5
Ja
n0
4
3
Ja
n0
3
6
Ja
n0
0
3.5
Ja
n9
Ja 0
n9
Ja 1
n9
Ja 2
n9
Ja 3
n9
Ja 4
n9
Ja 5
n9
Ja 6
n9
Ja 7
n9
Ja 8
n9
Ja 9
n0
Ja 0
n0
Ja 1
n0
Ja 2
n0
Ja 3
n0
Ja 4
n0
Ja 5
n0
Ja 6
n0
Ja 7
n0
Ja 8
n0
Ja 9
n1
0
7
Using Alt FQT EPS
Ja
n0
2
Using Alt FQT EPS
Using FQT EPS
4
Ja
n0
1
8
Summary
• FQT and Alt FQT are different even at the
portfolio level
– Not clear which is better
• Mixing any Four Quarter Trailing numbers
(however calculated) when there are
restatements with balance sheet numbers is
dangerous
Portfolio Value
Backtesting is an Art, Not a Science!