Death, Taxes, and Reversion to the Mean

LEGG MASON
LEGG MA
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December 14, 2007

Death, Taxes, and Reversion to the Mean
Mich
Mic ael
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J.
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J. M
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ROIC Patterns: Luck, Persistence, and What to Do About It

Hegel was right when he said that we learn from history that man can never learn anything
from history.

George Bernard Shaw



mmauboussin @ lmc
m m.c
m om
>100
80-100
60-80
)

(%
40-60
ACC
W
20-40
–
I
C
0-20
RO
(20)-0
1997 1998 1999 2000 2001 2002 2003 2004 2005 2006
(40)-(20)
<(40)
Time
Frequency

Source: LMCM analysis.


• Analysts modeling future corporate financial performance should use past ROIC
patterns, including a strong tendency toward mean reversion, as an appropriate
reference class but rarely do. Full consideration of the difficulty in sustaining high
returns should temper the optimism inherent in many models.

• Some companies do post persistently high or low returns beyond what chance
dictates. But the ROIC data incorporate much more randomness than most
analysts realize.

• We had little luck in identifying the factors behind sustainably high returns.

• This analysis has concrete implications for modeling. We unveil some of the
common errors in discounted cash flow models and offer some thoughts on how
to improve them.

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The Inside-Outside View

Company financial models are often a cornerstone of the stock selection process for fundamental
investors. The model forecasts are based on crucial value drivers like sales growth rates, operating
profit margins, investment capital needs, and economic returns. When done properly, detailed long-
term models are laborious because they require input from a wide range of areas, including historical
corporate performance, firm-specific issues, competitive positioning, and the broader macroeconomic
backdrop.

Despite earnest and diligent study, analysts often produce company models that are wildly off the
mark, usually erring on the side of optimism. Even analysts who consider ranges of value outcomes
attach probabilities to favorable scenarios that are too high. Some researchers attribute this
inaccuracy to overconfidence, but that is only part of the story. 1

Another way to understand the challenge is based on what renowned psychologist Daniel Kahneman
calls the inside-outside view. 2 An inside view considers a problem by focusing on the specific task
and the information at hand, and predicts based on that unique set of inputs. This is the approach
analysts most often use in their modeling, and indeed is common for all forms of planning.

In contrast, an outside view considers the problem as an instance in a broader reference class.
Rather than seeing the problem as unique, the outside view asks if there are similar situations that
can provide useful calibration for modeling. Kahneman notes this is a very unnatural way to think
precisely because it forces analysts to set aside all of the cherished information they have unearthed
about a company. This is why people use the outside view so rarely.

This report seeks to shed light on an important reference class for company modelers: patterns of
return on invested capital (ROIC). Companies create shareholder value when they generate returns
on investment in excess of the cost of capital. A positive spread between a company’s ROIC and cost
of capital is a fundamental indicator of value creation.

Earnings growth by itself gives no indication about value creation prospects—a company growing
rapidly but earning only its cost of capital will not enjoy a premium valuation. 3 More accurately,
growth amplifies: higher growth makes positive-spread companies more valuable, and, symmetrically,
higher growth makes negative-spread companies less valuable.

Assumptions about future corporate ROICs are embedded in analyst models, although they are rarely
explicit. More often than not, analysts are too optimistic in their assessment of future ROICs, in part
because they are unaware of how hard it is to sustain high returns. The goal of this report is to make
financial modelers aware of a broad reference class—the outside view—that unequivocally shows the
rarity of generating high returns for a long time in a free market system. This awareness should
temper the optimism embedded in many models.

Here are some of the report’s broad conclusions:

• Reversion to the mean is a powerful force. As has been well documented by numerous
studies, ROIC reverts to the cost of capital over time. This finding is consistent with
microeconomic theory, and is evident in all time periods researchers have studied.
However, investors and executives should be careful not to over interpret this result
because reversion to the mean is evident in any system with a great deal of randomness.
We can explain much of the mean reversion series by recognizing the data are noisy.

• Persistence does exist. Academic research shows that some companies do generate
persistently good, or bad, economic returns. The challenge is finding explanations for that
persistence, if they exist.

• Explaining persistence. It’s not clear that we can explain much persistence beyond chance.
But we investigated logical explanatory candidates, including growth, industry
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representation, and business models. Business model difference appears to be a promising
explanatory factor.

• Implications for modeling. The vast majority of models—especially discounted cash flow
models—are uninformed by the outside view of ROIC patterns. This outside view
addresses a number of important aspects of modeling, including assumptions about growth
rates, capital needs, and terminal values.

Death, Taxes, and Reversion to the Mean

Researchers have convincingly showed that industries and companies follow an economic life cycle
(see Exhibit 1). 4 Young companies often apply substantial resources to their business without
immediate payoff, hence generating returns below the cost of capital. In mid-life, companies earn
excess returns as their investments bear fruit. Finally, competitive forces and/or shifts in the
marketplace drive returns down to the cost of capital. In situations where returns sink below the cost
of capital, bankruptcy, consolidation, and disinvestment often serve to lift returns back to cost-of-
capital levels. Empirical research shows that manufacturing companies, on average, generate excess
returns for shorter periods than they did in the past. 5

Exhibit 1: Generic Life Cycle

d
a
r
e
Sp
C
AC
-
W
I
C
O
Time
R


Source: LMCM analysis.

Various studies conducted over multiple decades document this reversion-to-the-mean pattern. 6 We
have reproduced the results here, using data from over 1000 non-financial companies from 1997 to
2006. (See Appendix A for details on the sample and methodology.) Exhibit 2 shows this process.
We start by ranking companies into quintiles based on their 1997 ROIC. We then follow the median
ROIC for the five cohorts through 2006. While all of the returns do not settle at the cost of capital
(roughly eight percent) in 2006, they clearly migrate toward that level.

Exhibit 2: Median ROIC Reversion
25
20
)
15
(%
10
CC
A
5
- W
0
I
C
RO
-5
-10
-15
0
1
2
3
4
5
6
7
8
9
Number of years following portfolio formation

Source: LMCM analysis.
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The gap between the median ROICs from the best to the worst quintiles is 30.5 percentage points in
1997. That gap narrows significantly to 8.6 percentage points in 2006. Further, as the reversion
model would predict, the top quintiles saw declines in median ROICs and the bottom quintiles saw
improvement (see Exhibit 3). While nine years may not be a sufficient amount of time for returns of all
quintiles to converge on the cost of capital, it’s clear that the process is well under way.

Exhibit 3: Change in Median ROIC by Quintile
1997 Groups
Q1
Q2
Q3
Q4
Q5
25
‘97
20
)
15
10
CC (%
‘06
A
5
-
W
C
ROI
‘06
-5
‘97
-10
-15

Source: LMCM analysis.

This result, however, requires careful interpretation. Any system that combines skill and luck will
exhibit mean reversion over time. 7 Francis Galton demonstrated this point in his 1889 book, Natural
Inheritance, using the heights of adults. 8 Galton showed, for example, that children of tall parents
have a tendency to be tall, but are often not as tall as their parents. Likewise, children of short parents
tend to be short, but not as short as their parents. Heredity plays a role, but over time adult heights
revert to the mean.

The basic idea is outstanding performance combines strong skill and good luck. Abysmal
performance, in contrast, reflects weak skill and bad luck. Even if skill persists in subsequent periods,
luck evens out across the participants, pushing results closer to average. So it’s not that the standard
deviation of the whole sample is shrinking; rather, luck’s role diminishes over time.

Separating the relative contributions of skill and luck is no easy task. Naturally, sample size is crucial
because skill only surfaces with a large number of observations. For example, statistician Jim Albert
estimates that a baseball player’s batting average over a full season is a fifty-fifty combination
between skill and luck. Batting averages for 100 at-bats, in contrast, are 80 percent luck. 9

To illustrate this skill and luck mix, we analyzed the batting averages of 100 major league baseball
players who had at least 250 at-bats for each of the past five seasons (see Exhibit 4). These results
likely show some survivorship bias, as the average career of a major leaguer is only 5.6 years.





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Exhibit 4: Mean Reversion in Major League Baseball Player Batting Averages
0.340
0.320
e
0.300
r
ag
e
v
0.280
g A
t
t
i
n
a
0.260
B
0.240
0.220
2003
2004
2005
2006
2007
Season

Source: Baseball Prospectus and LMCM analysis.

The 80 basis point gulf between the best and worst quintile (a .320 versus a .240 average) is cut in
half by the final year (.300 versus .260). 10 This does not mean that the skill level of the players mean
reverted, just that luck evened out over time. For a company, skill is the equivalent of sustainable
value creation, including industry effects and managerial capability. Luck captures external factors,
including competition, business cycles, regulatory shifts, and technological change.

Defying Gravity: Persistence in the ROIC Data

The next question is whether any companies buck the reversion-to-the-mean trend and sustain high
(or low) ROICs throughout the sample period. To answer, we need to measure persistence—the
likelihood a company will stay in the same quintile throughout the measured time frame. To state the
obvious, staying in the top quintile is generally desirable, as it means the company is successfully
fending off competition. 11 Conversely, dwelling in the lowest quintile is unwelcome.

Exhibit 5 shows one measure of persistence: the degree of quintile migration. 12 This exhibit shows
where companies starting in one quintile (the vertical axis) ended up after nine years (the horizontal
axis). Most of the percentages in the exhibit are unremarkable, but two stand out. First, a full 41
percent of the companies that started in the top quintile were there nine years later, while 39 percent
of the companies in the cellar-dweller quintile ended up there. Independent studies of this persistence
reveal a similar pattern. So it appears there is persistence with some subset of the best and worst
companies. Academic research confirms that some companies do show persistent results. Studies
also show that companies rarely go from very high to very low performance or vice versa. 13

Exhibit 5: ROIC Persistence
ROIC Quintile in 2006
Q1
Q2
Q3
Q4
Q5
7
9

19
41%
23%
12%
6%
19%
Q1


in
Q2
24
32
22
11
11
t
i
le
Q3
in
13
21
28
25
14
u
Q4
Q
8
13
22
40
17
I
C
Q5
O
15
12
17
18
39
R

Source: LMCM analysis.

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Before going too far with this result, we need to consider two issues. First, this persistence analysis
solely looks at where companies start and finish, without asking what happens in between. As it turns
out, there is a lot of action in the intervening years. For example, less than half of the 41 percent of
the companies that start and end in the first quintile stay in the quintile the whole time. This means
that less than four percent of the total-company sample remains in the highest quintile of ROIC for the
full nine years.

The second issue is serial correlation, the probability a company stays in the same ROIC quintile from
year to year. As Exhibit 5 suggests, the highest serial correlations (over 80 percent) are in Q1 and
Q5. The middle quintile, Q3, has the lowest correlation of roughly 60 percent, while Q2 and Q4 are
similar at about 70 percent.

This result may seem counterintuitive at first, as it suggests results for really good and really bad
companies (Q1 and Q5) are more likely to persist than for average companies (Q2, Q3, and Q4). But
this outcome is a product of the methodology: since each year’s sample is broken into quintiles, and
the sample is roughly normally distributed, the ROIC ranges are much narrower for the middle three
quintiles than for the extreme quintiles. So, for instance, a small change in ROIC level can move a Q3
company into a neighboring quintile, whereas a larger absolute change is necessary to shift a Q1 and
Q5 company. Having some sense of serial correlations by quintile, however, provides useful
perspective for investors building company models.

To summarize, while the results reflect a lot of randomness, some companies appear to demonstrate
persistence of high returns above and beyond what we can attribute solely to chance. 14 But similar to
the challenge in active investing, the question is, can we identify the persistent value-creating
companies ahead of time?

Can We Explain Persistence?

Up to this point our results, while useful and instructive, are reasonably well known in the academic
literature. The real question for an investor is whether we can explain ROIC persistence ex ante. We
explore this question by looking at three variables that appear as good candidates to explain
persistence: corporate growth, the industry in which a company competes, and the company’s
business model. One of the virtues of these variables is they are to a large degree tractable. But
clearly other variables may be relevant, including management quality. As such, the variables we
investigate may be more proximate than causal.

Let’s start with growth, where there is good news and bad news. The good news is there appears to
be some correlation between growth and persistence. Companies that start and end in the top two
quintiles enjoy average growth just above the 9.4 percent for the full sample. The four growth rates
closest to the upper-left corner in Exhibit 6 show this.

Similarly, the companies that start and end in the bottom two quintiles—the four rates near the
bottom-right corner of the exhibit—grew at a well-below-average five percent rate. We can say much
less about companies that went from good to bad (upper-right corner) or companies that went from
bad to good (bottom-left corner) because the sample sizes are substantially smaller than the rest of
the exhibit. 15












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Exhibit 6: Earnings Growth by Quintile

EBIT Growth (10-Year CAGR)
ROIC Quintile in 2006
Q1
Q2
Q3
Q4
Q5
Q1
8%
10%
15%
6%
16%
1997
n
Q2
i
11%
9%
14%
10%
19%
t
i
l
e
Q3
i
n
12%
8%
8%
11%
16%
u
Q
Q4
6%
14%
8%
9%
-6%
I
C
O
R
Q5
9%
8%
6%
6%
12%


Source: LMCM analysis.

It is important to emphasize that we cannot infer cause and effect from these results. We don’t know
whether growth allows the company to sustain high returns or whether the growth is a consequence
of the high returns. But it is safe to say that high returns appear difficult to sustain over time without
satisfactory growth. Further, the exhibit shows that growth by itself does little to assure attractive
economic returns; the companies that ended in the fifth quintile generated aggregate growth faster
than the total sample.

The bad news about growth, especially for modelers, is it is extremely difficult to forecast. While there
is some evidence for sales persistence, the evidence for earnings growth persistence is scant. As
some researchers recently summarized, “All in all, the evidence suggests that the odds of an investor
successfully uncovering the next stellar growth stock are about the same as correctly calling coin
tosses.” 16 This observation has important implications for modeling.

Industry effects are another candidate to explain persistent excess returns. One approach is to simply
see which industries are overrepresented in the highest return quintile throughout our measured
period. Industries that satisfy this requirement include pharmaceuticals/biotechnology and software.
This approach is flawed, however, because it fails to consider the full industry populations. For
industries with large-variance ROIC distributions, some companies will look good simply by virtue of
that distribution. Looking solely at the successful companies in these large-variance industries paints
a misleading picture of performance. 17 And, unfortunately, selecting successful companies and
attaching attributes to them is a common practice in research. 18

Let’s go back to our overrepresented industries, pharmaceuticals/biotechnology and software. It turns
out these industries are not only represented in the highest quintile, but are also overrepresented in
the lowest quintile. Further, other industries—utilities and telecom services—have little representation
in the best or worst quintiles. We can explain this by examining the ROIC distribution variance (see
Exhibit 7). Wide-variance industries have high- and low-performing companies, while the narrow-
variance industries are clustered in the middle ROIC quintiles. The main point is to avoid selection
bias when seeking explanations for persistent returns.












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Exhibit 7: Some Industry Success a Result of Industry ROIC Variance
Median annual ROIC, excluding goodwill, 1963-2004 (%)
0
5
10
15
20
25
30
35
40
Pharmaceuticals, biotechnology
Software, services
Telecommunication services
Utilities


Source: Bin Jiang and Timothy M. Koller, “Data Focus: A Long-Term Look at ROIC,” The McKinsey Quarterly, 1, 2006. Used with permission.

Another strand of research considers the regularities in abnormal profits, both good and bad. 19 This
work suggests industry effects are more important than firm-specific effects for high-performing
companies, while the opposite is true for low-performing companies. This descriptive work suggests
positive, sustainable ROICs emerge from a good strategic position within a generally favorable
industry. So industry does matter for explaining persistence, especially for sustainable above-average
returns. More accurately, persistent high ROICs, on average, combine an attractive industry with a
good business model. There is also good strategy research on the threats to sustainable superior
performance. 20

This leads to a closer look at business models. Michael Porter introduced two generic sources of
competitive advantage: differentiation and low-cost production. These are also known as consumer
and production advantages. 21 We can relate these generic strategies to ROIC by breaking ROIC into
its two prime components, net operating profit after tax (NOPAT) margin and invested capital
turnover. NOPAT margin equals NOPAT/sales, and invested capital turnover equals sales/invested
capital. ROIC is the product of NOPAT margin and invested capital turnover.

Generally speaking, differentiated companies with a consumer advantage generate attractive returns
mostly via high margins and modest invested capital turnover. Consider the successful jewelry store
that generates large profits per unit sold (high margins) but doesn’t sell in large volume (low turnover).
In contrast, a low-cost company with a production advantage will generate relatively low margins and
relatively high invested capital turnover. Think of a classic discount retailer, which doesn’t make much
money per unit sold (low margins) but enjoys great inventory velocity (high turnover). Exhibit 8
consolidates these ideas in a simple matrix.

Exhibit 8: Linking Competitive Advantage to ROIC Components

Consumer and
Consumer
Production
Advantage
Advantage
s
n
rgi
a
M
T
A
No
Production
Advantage
Advantage
NOP
Invested Capital Turnover

Source: LMCM analysis.
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We looked at the 42 companies that stayed in the first quintile throughout the measured period to see
whether they leaned more toward a consumer or production advantage (see Exhibit 9). Not
surprisingly, this group outperformed the broader sample on both NOPAT margin and invested capital
turnover, but the impact of margin differential (2.4 times the median) was greater on ROIC than the
capital turnover differential (1.9 times). While equivocal, these results suggest the best companies
may have a tilt toward consumer advantage.

Exhibit 9: ROIC Components for High-Performing Companies

100%
100
)
g

(
l
o
s
i
n
r
g
a
10%
10
M
Sam
Sa pl
p e Me
e
d
Me i
d an
a
PAT
O
N
n
i
a
d
e
M
l
e
p
m
Sa
1%
1
10
1
10
1 0
0
In
I v
n e
v s
e ted
e C
d
api
C
tal
a Tu
T r
u nov
r
er
nov
er (
l
( og
o )
g


Source: LMCM analysis.

A look at the roughly 30 companies that remained in the fifth quintile is also revealing. Symmetrical
with the high-performing companies, they posted NOPAT margins and invested capital turnover
below the full sample’s median. This group was persistently unprofitable, posting negative NOPAT
margins for the measured period. Invested capital turns, while poor, were roughly 60 percent of the
median. The results for both the best and worst companies also reflect the reality that the distribution
of NOPAT margins is much wider than that for invested capital turnover.

Exhibit 10 summarizes the performance composition for the best and worst companies, starting with
the median ROIC for the full sample (bar on the far left), then substituting invested capital turns
(second from the left), then substituting NOPAT margins (third from left), and finally showing the
returns for the whole subgroup (far right).









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Exhibit 10: Decomposition of Persistently Best and Worst Companies

100
90
80
70
)
60
(%
50
IC
O
R
40
30
20
10
0
Sample
Q1
Q1 Margins
Q1 Turnover
Median
Turnover
and Margins


20
Q5 Turnover
10
Q5 Margins
and Margins
0
Sample
-10
Q5
Median
Turnover
-20
)
-30
%
(
-40
IC
O
R
-50
-60
-70
-80
-90
-100


Source: LMCM analysis.

Our search for factors that may help us anticipate persistently superior performance leaves us little to
work with. We do know persistence exists, and that companies that sustain high returns over time
start with high returns. Operating in a good industry with above-average growth prospects and some
consumer advantage also appears correlated with persistence. Strategy experts Anita McGahan and
Michael Porter sum it up: 22

It is impossible to infer the cause of persistence in performance from the fact that persistence
occurs. Persistence may be due to fixed resources, consistent industry structure, financial
anomalies, price controls, or many other factors that endure . . . In sum, reliable inferences
about the cause of persistence cannot be generated from an analysis that only documents
whether or not persistence occurred.

Implications for Modeling

The objective of our brief tour through the world of ROIC patterns is to provide guidance for investors
building company models. More specifically, these empirical findings can help modelers avoid
common errors. Here are the main implications for modeling:

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