A P R O F E S S I O N A L D E V E L O P M E N T J O U R N A L f o r t h e C O N S U LT I N G D I S C I P L I N E S
v a l u a tio n
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Unraveling the Supply-Side Equity Risk Premium
•
T
By Magdalena Mroczek
he equity risk premium (ERP) is arguably the most influential component of a company’s cost of capital. So it is no surprise that it attracts
much debate. The two most commonly used ERP models are the historical and the supply-side ERP. The latter has received a lot of attention and
questions in the recent years. Its complicated nature creates a shroud of confusion,
which can lead to a misinterpretation of
the underlying theory and cause practitioners to shy away from using the premium in valuations.
Those who do use the supply-side
ERP choose it over the historical ERP because it incorporates a forward-looking
assumption in its calculation. Also, the
supply-side ERP usually generates a lower
premium than the historical model. But
are those sufficient reasons to use it? This
article will attempt to simplify the complexities of the supply-side model by addressing (a) the meaning of “supply-side,”
(b) the theory underlying the model used
in the Ibbotson SBBI Valuation Yearbooks
and its calculation, and (c) recommendations on how to use this supply-side ERP.
information such as earnings, dividends,
or general economic productivity figures
in determining the expected ERP. The
third is the demand-side, which develops
the ERP using the additional returns demanded by investors for bearing the risk
of equity investments. The final approach
polls professionals through broad surveys
in order to determine an average ERP. The
survey method is the least recommended
of the four approaches because the survey
participants’ behavioral biases are often
reflected in the reported ERP. Given that
surveys have inherent drawbacks and that
the demand side is difficult to measure,
most practitioners focus on the first two
of these four approaches: the historical
and the supply-side.
Four ERP Approaches
Before diving into the components of
the published supply-side ERP, it is important to briefly explain the four broad ERP
approaches. The first and most widely
used approach, the historical ERP, derives
the premium using historical market returns. The Valuation Yearbook calculates
the historical ERP using the simple average of returns since 1926. The second approach, the supply-side, uses fundamental
Theory of Supply-side
The term “supply-side” sparks much
confusion, since it is not referring to
the economic supply and demand equilibrium of the market. In actuality, the
supply-side ERP primarily takes into account the earnings that companies generate (supply). As such, it omits the expected premium or discount embedded
within market price attributed to investor trading. On the other hand, a de-
the value examiner
mand-side model’s methodology would
only consider this price divergence from
fair value, which is investor-demand
driven. While the words “supply” and
“demand” portray images of economic
equilibrium, they are really referring to
a buildup of total return components.
Total Return
Three components comprise annual
total equity returns: income return,
capital appreciation, and reinvestment
return. Income return is the portion of
total return that comes from a periodic
cash flow—usually dividends. The company determines the amount distributed as dividends, thus demonstrating
that equity income returns are company
generated. Capital appreciation returns
make up the portion of total return attributable to change in stock price. It is
important to note that capital appreciation returns incorporate both demand
and supply components, since price is
affected by company earnings as well
as investor expectations. The historical
ERP includes all components of total return in its calculation, while supply-side
ERP attempts to remove this investordriven component.
Capital Appreciation
Since the key to this model lies in
distinguishing between the companysupplied and investor-demanded components of total return, in 2003 Roger
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Ibbotson and Peng Chen evaluated various supply-side ERP theories.1 After analyzing them, they determined that earnings were the driving force behind changes
in equity returns. They used their findings to create a new earnings model, which
is currently used in the Valuation Yearbooks. It assumes that capital appreciation
returns are a function of inflation, the growth of earnings per share, and the growth
of price to earnings. Another way to define capital appreciation is the real growth of
stock price plus inflation, as seen in Equation 1. Essentially, this model splits the real
growth of stock price into the real growth of price to earnings and the real growth
of earnings per share, as shown in Equation 2.
Equation 1:
Inflation
+ Real Growth of Price per Share
Capital Appreciation
Equation 2:
Real Growth of Price per Share =
Price
Earnings
(1 + Real Growth of
) x (1 + Real Growth of
)-1
Earnings
Shares
Growth of Price to Earnings
Earnings are a function of a company’s profitability, therefore investor expectations and market transactions do not affect it. Price can be defined as the amount
an investor is willing to pay for a slice of equity. There is no denying that price is
affected by a company’s earnings, but the movement in price is due to investors’
future expectations. It is the result of market transactions rather than a component
companies can control. Price to earnings (P/E) is the relationship between the price
an investor demands and the earnings that the company can supply. If the growth
of a company’s P/E is positive, the market is forecasting future growth because
the demanded price (which reflects future expectations) is greater relative to what
companies are currently able to supply. If it is negative, the market is forecasting
a decline, since investors are demanding a lower price relative to what companies
are earning.
Methodology
The supply-side ERP, as published in the Valuation Yearbook, is calculated using
the same equation as the historical ERP with slightly different inputs. The difference lies within the equity returns whereby the supply-side ERP only includes the
returns attributable to economic growth (i.e., inflation) and company earnings.
These returns are termed supplied equity returns. Calculating the supplied equity
returns can be done in two ways: using a bottom-up or a top-down approach.
The bottom-up approach adds up all the supply-side components of equity returns
1 Roger Ibbotson and Peng Chen, “Long-Run Stock Returns: Participating in the Real Economy,” 2003 http://
corporate.morningstar.com/ib/documents/MethodologyDocuments/IBBAssociates/StockMarketReturns.pdf.
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together, while the top-down approach
starts with total return and subtracts
out the demand components.
The Valuation Yearbook mainly focuses on explaining the bottom-up approach, as it is essentially a step-by-step
explanation of the supply-side model.
This approach states that the supplied
equity returns include inflation, the
growth in real S&P 500 earnings per
share, income return, and reinvestment
return; it omits the investor-driven component, the S&P 500’s growth of P/E.
The top-down approach would calculate
the supplied equity returns by beginning
with the S&P 500 total returns and subtracting out the compound P/E growth
for the entire period. As shown before in
equations 1 and 2, the capital appreciation components according to the earnings model (inflation, the growth in real
earnings per share, and the growth of
P/E) should equal the actual capital appreciation return of the S&P 500. Therefore, both approaches in theory should
produce the same supply-side ERP.
Bottom-Up Approach
Even though the final supply-side
ERP published in the back page of
the Valuation Yearbook is calculated
through the top-down approach, as
stated earlier, the theory is best explained using the bottom-up approach.
It begins with calculating the supplied
equity return, as opposed to total return. As mentioned above, the main
difference between the two supply-side
methods is the exclusion of P/E growth.
Price is considered to be investor-driven
as opposed to company-supplied, so it
should not be included. As a result, the
equation for supplied equity return (SR)
is shown in Equation 3.
Since the equation calls for the growth
of earnings per share, the capital appre-
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Components of Returns
Bottom-Up
Total Return
Top-Down
+
Capital Appreciation Return
Inflation
+
P/E Growth
EPS Growth
—
+
Income Return
+
Reinvestment Return
+
(Supplied Equity Return)
Bottom-Up Approach
Equation 3:
SR = [(1 + CPI) x (1 + gREPS) - 1] + Inc + Rinv
Where,
SR = Supplied Equity Returns;
CPI = Consumer Price Index (Inflation);
gREPS = Growth of Earnings per Share;
Inc = Income Return; and,
Rinv = Reinvestment Return.
Equation 4:
SERP
(1 + SR)
= – 1
(1 + CPI) x (1 + RRf )
Where,
SERP= Supply Side Equity Risk Premium;
SR = Supplied Equity Returns;
CPI = Consumer Price Index (Inflation); and,
RRf = Real Risk-Free Rate.
Equation 5:
RA = RG +
σ2
2
Where,
RA = Arithmetic Average;
RG = Geometric Average; and,
σ = Standard Deviation of Equity Returns.
the value examiner
=
=
SER
SER
ciation returns can only be calculated
geometrically, and these inputs must
all be geometric averages with the same
time horizon. Once the supplied equity
returns are calculated, the income returns of the risk-free asset must be geometrically subtracted from the supplied
equity returns to create a premium. This
is illustrated in Equation 4.
It is widely agreed that an arithmetic
ERP should be used in business valuations. A typical valuation uses projected cash flows and the ERP is expected
to be realized over future periods. An
arithmetic average is more accurate to
use with forward-looking data. A geometric average is more appropriate in
reporting past performance, as it is a
compound average return. This is also
why past growth should be measured
geometrically. So, the geometric supplyside ERP is converted into an equivalent
arithmetic ERP using Equation 5. This is
only one method of converting between
geometric and arithmetic averages, and
it assumes that the returns are independently and lognormally distributed over
time. The output from this equation becomes the arithmetic supply-side ERP
that a practitioner would use when calculating the cost of equity.
Top-Down Approach
When attempting to strip away the
various components of any type of return, we are rarely able to determine
the source for each component. Usually,
therefore, these components do not exactly add up to the return. The bottomup approach is no exception. While it
provides a more detailed explanation
about the relationship between P/E
growth and the market, there is a small
difference between the added components and the actual return. The topdown approach uses the same theory
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TOP-DOWN Approach
Equation 6:
Geo Suppy Side ERP =
(1 + Geo Historical ERP) - 1
(1 + P/E Growth)
Equation 7:
RA = RG +
σ2
2
Where,
RA = Arithmetic Average;
RG = Geometric Average; and,
σ = Standard Deviation of Equity Returns.
as the bottom-up, although it does not
require adding up the various components and, therefore, is more practical.
The calculation begins with the same inputs as the historical ERP—the market’s
total returns and the 20-year Treasury
bond income returns. The top-down
approach allows the practitioner to
remove the portion of returns already
known to be demand-driven (i.e., P/E
growth) from the total return rather
than add up all the company-generated
returns. Although the difference between the bottom-up approach and the
top-down approach is fairly negligible,
the top-down approach is thought to
reach a more accurate supply-side ERP.
The first step in calculating the supply-side ERP using the top-down approach is calculating the historical ERP
geometrically. The top-down approach
shows the supply-side as an adjusted
historical ERP, as it excludes all investor-driven components. As shown in
Equation 6, the geometric supply-side
ERP is calculated by geometrically subtracting (through the use of division)
the compound growth of P/E from the
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1940s and 1950s. In 1949, the difference
between the two peaked when supplyside ERP was 1.52 percent greater than
the historical ERP. In fact, it is expected
that the historical and supply-side ERP
will converge over time, because the P/E
growth of the 1980s is expected to return to historic levels.
geometric historical ERP, both using
data beginning in 1926. Once the geometric supply-side ERP is calculated, it
must be converted to an arithmetic average using the same equation as in the
bottom-up approach, Equation 7. This is
the supply-side ERP that is published in
the back page of the Valuation Yearbook
as well as in Table 5–6.
Supply-Side vs. Historical ERP
After discussing the methodology, it
is easier to understand that the supplyside ERP is very similar to the historical except that it uses supplied equity
returns as opposed to total market returns. The ERP, in general, assumes that
the historic data included within the
calculation is representative of the future. Between 1980 and 2001, company
prices saw an unsustainable growth.
Considering most companies’ earnings
would be unable to catch up to those inflated prices, the supply-side ERP was
created to remove this unsustainable
growth from the historical ERP.
Since the supply-side ERP is currently less than the historical, it implies that investors expect high growth
in future earnings and are pricing the
market accordingly. As a practitioner, if
you choose to use the supply-side ERP,
beware that this model does not always
have an ERP lower than the historical
model. If investors foresaw a future decline in earnings, price would drop in
anticipation with no current change in
earnings. To put this in market terms,
the supply-side ERP will be greater than
the historical if investors foresee enough
negative growth to push down the current market P/E below the 1926 P/E of
10.65. For instance, the supply-side ERP
was consistently greater than the historical between 1977 and 1982. This also was
the case throughout almost half of the
3-Year Average Earnings
It was quickly realized, when Ibbotson’s version of the supply-side model
was first published in 2003, that the annual S&P 500 earnings were quite volatile and, if used, would create equally
volatile and unpractical supply-side
ERPs. On page 65, Graph 5–9, from the
2011 Valuation Yearbook, shows how
unstable earnings data has proved to be.
More normalized price to three-year average earnings ratios (P/3E), which are
implemented in the supply-side ERP
model, are also shown in the graph.
P/E Ratio
140
1-year P/E
3-year P/E
120
80
60
40
20
0
1925
1935
1945
1955
1965
1975
1985
1995
2005
2010
05
Year-end
For stability and usability, it was
decided that an average would be
more appropriate, since it allows us to
smooth out the volatility of extraordinary events. This also allows earnings
to reflect a normalized trend. However, a simple historical three-year rolling average places too large an empha-
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sis on past earnings and skews the P/E growth adjustment. In order to keep
the timing of the average earnings consistent with the current year’s S&P 500’s
market price, the current year’s earnings must be in the middle of the threeyear average, rather than the last year. Therefore, the earnings must include an
average of the prior year (t -1), the current year (t 0), and the future year (t +1).
This keeps the focal point on the current year for both the denominator and
the numerator.
As such, when the supply-side ERP was calculated as of December 2010 for the
2011 Valuation Yearbook, the earnings for 2011 were estimates. In fact, the 2010
earnings also had not actualized yet. This means that the 2010 supply-side ERP
will permanently stabilize in the 2013 Valuation Yearbook when actual earnings
will be available for both 2010 (t0) and 2011 (t+1). In any version of the Valuation
Yearbooks, the most recent supply-side ERP contains two earnings estimates,
published by Standard & Poor’s, in the P/E adjustment. It takes two years of publications for all inputs to actualize. Therefore, the supply-side ERP should change
every year for two years and remain constant afterward.
Earnings
Year
2011 Yearbook
Data as of 12/10
2012 Yearbook
Data as of 12/11
2013
2013 Yearbook
Data as of 12/12
Estimate
2012
Estimate
Estimate
2011
Estimate
Estimate
Actual
2010
Estimate
Actual
Actual
2009
Actual
Actual
Actual
Using Past Years’ Supply-side ERP
Critics have been sounding the horn when they see revisions to the supplyside ERP. However, does a future change in a forward-looking premium mean
that it is inaccurate or unusable? No. Cost of equity is forward-looking, so it is appropriate to use forward-looking estimates within the calculation. The historical
ERP is a measure of future expectations, because the arithmetic mean of market
returns is assumed to be representative of the future. Earnings estimates are a
measure of expectations, just like the other inputs are used with the expectation
that past trends may continue into the future.
For consistency, beginning in the 2011 Valuation Yearbook and onward,
Table 5–6, which contains historical supply-side ERP, reflects the most up-todate data available. These updated historical premia may not be appropriate for
valuations. The current and next year’s earnings estimates reflect expectations
known as of the publication date, although it is important to realize that these
will change as the earnings data is realized in subsequent years. These revisions incorporate information that was not available as of the publication date.
Therefore, in a valuation engagement, I suggest using the original supply-side
ERP found in historical editions of the Valuation Yearbook, which contains the
earnings estimates.
the value examiner
Conclusion
At Morningstar, we aim to provide
our customers with the most relevant
and reliable data while detailing the various methodologies behind our models.
However, this is in vain if practitioners
do not understand these methodologies. The supply-side ERP model is especially confusing because the name
refers to company-generated returns
rather than economic supply and demand. Also, its calculation and theory
are commonly misunderstood, as is the
reason behind using three-year average
earnings and the annual changes that
are attributed to it.
In the end, the most important question practitioners want answered is:
Which model should you use? The historical and supply-side ERP methodologies use the same fundamental factors,
so we believe that these two models are
not in conflict and are both suitable for
use. However, when determining which
to choose, a practitioner should take
into account the assumptions that the
supply-side ERP is making. Some practitioners use the supply-side ERP without recognizing these assumptions, and
others choose not to use the supplyside ERP because they exaggerate the
pitfalls. The main aspects of the supplyside ERP that all practitioners should be
aware of include:
1. Inflation, real growth of P/E, and the
real growth of earnings per share
add up to the capital appreciation
return,
2. The investor-driven aspect of price
change should be removed from total returns,
3. The P/3E in 1926 of $10.65 per share
is a fitting starting point for measuring compound growth to the present
year’s P/3E value,
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4. Using a three-year average earnings
with two estimates (t0 and t+1) is appropriate, and
5. The market will be neither overvalued nor undervalued in the future.
If you agree with these assumptions,
then the supply-side ERP is an appropriate model to use. If you do not feel comfortable with these assumptions, then
use the historical ERP. Either way, it is
important for ERP users to understand
both ERP models and be able to defend
their choice appropriately.
VE
Magdalena Mroczek is
the senior editor of the
Ibbotson SBBI Valuation Yearbook and the
Ibbotson SBBI Classic
Yearbook at Morningstar.
She has written and spoken on the common misconceptions about Morningstar premia,
cost-of-capital analy­sis, company distress
models, and international cost-of-capital
approaches, among other topics. She also
headed various custom cost-of-capital
projects and research studies.
Sidebar
•
2007—An Example of Change in Supply-Side ERP
Let’s recalculate the supply-side ERP
using a top-down approach for 2007,
the year which saw the greatest change
in earnings. Imagine that we are back in
December 2007, the official start of the
last recession. The National Bureau of
Economic Research did not announce
this until December 2008, so no one
knew it at the time. Therefore, while the
economic outlook was uncertain in the
end of 2007, it was not as grim as the
future realized to be.
We begin with the geometrically
calculated historical ERP for December
2007: 4.93 percent. At this time, the S&P
500 earnings for 2006 were realized at
$81.51 per share, and the 2007 and 2008
earnings were estimated to be at $74.15
and $83.70 per share, respectively.
These three earnings averaged to $79.79
per share and the S&P 500 Index in 2007
was 1,468.36, creating a price to threeyear average earnings (P/3E) multiple of
18.40. P/3E grew 0.67 percent since the
1926 P/3E level of 10.65. This 0.67 percent was geometrically subtracted from
the 4.93 percent geometric historical
ERP to create a 4.24 percent geometric supply-side ERP. Using Equation 7
from the methodology section, the supply-side ERP was converted to be 6.23
percent arithmetically. Looking back at
the 2008 Valuation Yearbook, this is the
same premium that is published on the
back page, the Key Variables in Estimating the Cost of Capital page.
Now, let’s fast-forward to December 2009, when both the 2007 and the
2008 earnings are realized. In hindsight,
it is not surprising that both estimates
were higher than the actual earnings.
The S&P 500’s 2007 earnings realized
at $66.18 per share, lower than the expected $74.15. Even more drastically,
the 2008 earnings dropped to $14.88 per
share from the expected $83.70. The realized growth of P/3E from 1926 to 2008
increased to 1.15 percent and changed
the arithmetic supply-side ERP from the
expected 6.23 percent to a much smaller
5.74 percent.
2007 Supply Side ERP: An Example of Change
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Earnings per Share
2006
2007
2008
3-Yr Avg
Earnings
Price to 3-Yr Avg
Earnings (P/3E)
Growth of P/3E
since 1926 to 2007
2007 Geometric
Supply Side ERP
As of
Dec.
2007
$81.51
$79.79
($1,468.36/$79.79)
= 18.40
(18.40/10.65)(1/82)-1
= 0.67%
[(1+4.93%)/(1+0.67%)]-1 4.24%+((19.97%)2/2) 7.05%
= 4.24%
= 6.23%
As of
Dec.
2009
$81.51
($1,468.36/$54.19)
= 27.10
(27.10/10.65)(1/82)-1 [(1+4.93%)/(1+1.15%)]-1 3.75%+((19.97%)2/2) 7.05%
= 1.15%
= 3.75%
= 5.74%
$74.15
$83.70
per share
$66.18
$14.88
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$54.19
per share
2007 Arithmetic
Supply Side ERP
2007 Arithmetic
Historical ERP
the value examiner