Estimating The Equity Risk Premium

Estimating the
Equity Risk Premium

Brown Bag Presentation
July 30, 2010

Paul Daddio

Introduction
• Broadly, there are three approaches to estimating the Equity Risk
Premium (ERP). These employ the use of (1) historical data, (2) surveys,
and (3) market data.
• Estimates of ERP may vary widely, depending upon which approach is
used and which inputs the analyst selects.
• This presentation will cover portions of (1) a recent article by Aswath
Damodaran, “Equity Risk Premium (ERP): Determinants, Estimation and
Implications – The 2010 Edition” and (2) recent articles by Pablo
Fernandez, “The Equity Risk Premium in 150 Textbooks”, “Market Risk
Premium Used in 2010 by Professors: a Survey with 1,500 answers”, and
“Market Risk Premium Used in 2010 by Analysts and Companies: a Survey
with 2,400 Answers.”
• Disclaimer: This presentation communicates the findings and opinions of
the above sources. It is not intended to be definitive. Each analyst should
exercise discretion in determining the appropriate ERP to apply to a given
valuation analysis. Further, this presentation does not address other
inputs critical to deriving present value discount rates (e.g., beta, size
premia, company-specific risk premia, etc.). Careful consideration must
be given to these factors as well.
Willamette Management Associates 1

The ERP
• The ERP is the rate of return investors receive as
compensation for the risk of equities in excess of the rate
of return received on the risk-free security
ERP = E(Rm) – Rf
where:
E(Rm) = Expected return on the market
Rf = Risk-free rate of return
• ERP is a forward-looking concept. It is based on the
expected excess return on the stock market during the
term of the investment and should be reflective of what
the ERP will be in the future. However, the ERP is
unobservable and as a result the ERP must be estimated.


Estimation Approaches
• Historical Realized ERP: The actual past returns earned on
stocks over a long time period is estimated, and compared
to the actual past returns earned on a risk-free investment
(usually a government security). The difference, on an
annual basis, between the two returns is computed and
represents the historical realized ERP.
• Historical Expected ERP: Fundamental information– such as
earnings, dividend, or overall economic productivity– are
used to estimate the expected ERP.
• Survey-based ERP: Individual investors,
institutional/professional investors, CFOs, and/or academics
are asked for their expectations of the ERP.
• Implied ERP: Market prices on assets as of the valuation
date are used to estimate a forward-looking ERP.


Historical Realized ERP
• The historical realized ERP used in practice varies widely
across analysts, from 3% to 12% at the extremes.
• Reasons for divergence
– Time period: Analysts use historical data that ranges from as
long as 1792 to the present to as short as the most recent 10
years.
• Some analysts believe that using data over a shorter historical
time frame is preferable to a longer one because the risk aversion
of investors changes over time. However, using a shorter time
frame results in “noisier” data (i.e., a higher standard error).


• Even using an 80 year time span results in a relatively high standard
error of 2.23%.
Estimation Period Standard Error of Risk Premium Estimate
5 years 20% / √5 = 8.94%
10 years 20% / √10 = 6.32%
25 years 20% / √25 = 4.00%
50 years 20% / √50 = 2.83%
80 years 20% / √80 = 2.23%

– Length of term on risk-free security: Analysts use a broad range of
maturity lengths. Since the yield curve has typically been upward
sloping, the ERP is larger when estimated relative to short-term
government securities and smaller when estimated relative to long-
term government securities.
• Using T-Bills makes sense only if a single period (say, one) year ERP is
being estimated. If the time horizon being estimated for is long-term, T-
Bonds should be used.
• Most analysts and Ibbotson Associates (in their SBBI Valuation Edition
yearbooks) use the 20-year Treasury Bond.


– Averaging approach:
• Arithmetic vs. Geometric
– Arithmetic average: the simple mean of a series of annual returns.
– Geometric average: the compounded average return.
• Arithmetic average results in higher ERP than geometric average.
• The arithmetic average provides a better estimate of the ERP than
does the geometric average if there is no “serial correlation” (or
autocorrelation) between returns.
• SBBI recommends the arithmetic mean based on (1) empirical
evidence which they conclude indicates no serial correlation and
(2) the belief that a full range of outcomes is possible and the
most reasonable expectation is the weighted average of all
outcomes.
• Damodaran states that evidence of serial correlation is
“extensive.” He also states that using the arithmetic average to
obtain discount rates which are then compounded over time
“seems internally inconsistent” and that the argument for using
geometric average premiums as estimates is strong.


ERP: Stocks minus T-Bills ERP: Stocks minus T-Bonds
Arithmetic Geometric Arithmetic Geometric
1928-2009 7.53% 6.03% 5.56% 4.29%
1967-2009 5.48% 3.78% 4.09% 2.74%
1997-2009 -1.59% -5.47% -3.68% -7.22%
Source: "Equity Risk Premiums (ERP): Determinants, Estimation and
Implications," Aswath Damodaran, 2/10.

• If, based on the aforementioned discussion, an analyst takes the position that a
long-term (1928-2009) geometric average premium over T-Bonds is the most
appropriate measure, 4.29% would be the appropriate ERP. SBBI reports that the
historical realized ERP on a geometric average basis for the period 1926 to 2009 was
4.7%.
• However, this conclusion comes with significant standard error (about 2.4%) and is
reflective of time periods (e.g., the 1920s and 1930s) when the U.S. equity market
(and investors in it) had very different characteristics than they do today.
• Further, the addition or subtraction of just one year will have a large impact on the
conclusion. Because stock market returns were so high in 2009, if instead of 1928-
2009, a period of 1928-2008 were used, the geometric average premium over T-
Bonds would be 3.88% (0.41% lower than the 1928-2009 period). The impact of
using data ended 2008 instead of 2009 would have a large impact on any of the
above approaches to calculating historical realized ERP.


• Sources of the historical realized ERP include:
– The Ibbotson SBBI Valuation Yearbook 2010, which reports an
historical realized ERP for large company stocks of 6.7% over
the period 1926 to 2009.
– The Duff & Phelps, LLC, Risk Premium Report 2010, which
reports an historical realized ERP for large company stocks of
4.25% over the period 1963 to 2009.
– Dimson, Marsh, Staunton and Wilmont (2010) estimated
equity returns for 19 markets from 1900 to 2009. Their results
are summarized as follows:
2000-2009 1960-2009 1990-2009
U.S. -7.4% 2.3% 4.2%
World -6.6% 0.9% 3.7%
World ex-U.S. -5.2% 0.6% 3.8%
Europe -5.7% 1.3% 3.9%


Historical Expected ERP
• Many studies have concluded that the historical realized ERP is higher than
investors have expected. Therefore, the expected ERP should be less than
the historical realized ERP.
• To measure the expected ERP, researchers have created supply-side
models which use fundamental information, such as earnings, dividend, or
overall economic productivity, to estimate the expected ERP.
• In recent years, the SBBI Valuation Edition Yearbook has presented the
the supply-side ERP model developed by Ibbotson and Peng. This earnings
model breaks historical realized equity returns into four pieces: (1)
inflation, (2) income return, (3) growth in real earnings per share, and (4)
growth in P/E ratio.
• The three returns historically supplied by companies (i.e., inflation, income
return, and growth in real earnings per share) are expected to continue in
the future. However, the growth in the P/E ratio, which is based on
investors’ predictions of future earnings growth, is not. As a result, the
historical growth in the P/E ratio is subtracted from the ERP forecast.
• In the Ibbotson SBBI Valuation Yearbook 2010, the supply-side ERP for
large company stocks is reported to be 5.2%.


Survey-based ERP
• The rationale for using surveys to estimate ERP is that, if
the objective of estimating ERP is to conclude what return
investors require on risky assets, then the most logical way
to accomplish this is to ask investors.
• Survey groups
– Investors
• Individual investors: conducted by (1) Robert Shiller; (2)
UBS/Gallup; and (3) The Securities Industry Association (SIA).
– The Shiller and UBS/Gallup surveys are directional in nature and do not
report an ERP. The SIA survey reported an ERP of 8.3% in 2004
• Institutional investors: conducted by (1) Investors Intelligence and
(2) Merrill Lynch.
– Investors Intelligence is a directional survey, which does not report an
ERP. The Merrill Lynch monthly survey of 300 institutional investors
reported an average ERP of 3.8% in 2009.


Survey-based ERP
– Managers and Analysts
• Graham and Harvey annual survey of CFOs:
– 2009 survey reported an average ERP of 4.7% and a median ERP of
4.3% (up from 3.8% and 4.2%, respectively, in 2008). It also reported
significant dispersion, with expected return on the market ranging from
1.3% to 12.4% at the 10th and 90th percentiles.
• Fernandez survey of analysts and companies
– Among analysts, the 2010 survey reported an average ERP of 5.1%
and a median ERP of 5.0%. Among companies, the 2010 survey
reported an average ERP of 5.3% and a median ERP of 5.0% (U.S. and
Canadian survey respondents).


Survey-based ERP
– Academics
• While academics are obviously not big players in equity markets,
practitioners often use their work as support for the ERP estimates they
use.
• Surveys
– Welch (2000) surveyed 226 financial economists on the magnitude of the
ERP and reported interesting results. On average, economists forecast an
average ERP (arithmetic) of about 7% for a ten-year time horizon and 6-7%
for one to five-year time horizons. As with other the other survey estimates,
there is a wide range on the estimates, with premia ranging from 2% to
13%.
– Fernandez (2009) examined 150 widely used textbooks in corporate finance
and valuation and noted that the ERP varied widely across the books and
that the moving average premium has declined from 8.4% in 1990 to 5.7%
in 2008. The average of the ERP of the textbooks he surveyed was 6.5%.
– Fernandez (2010) surveyed finance and economics professors. He found
that the average ERP used by U.S. professors was 6.0%. He also found that
the dispersion of responses was high among U.S. professors (from 2% to
12% with a standard deviation of 1.7%).
• The ERP indicated by surveys of academics (1) are much higher than the
ERP in practice and (2) contradict other academic research that indicates
that even the lower ERP used by practitioners are too high.


Implied ERP: DCF Model-based Premia
• The rationale for using an implied ERP is that it provides an
indication of the forward-looking ERP based on market prices as of
the valuation date.
• DCF Model-based ERP
– The implied ERP can be derived using the following formula:

Where:
E(FCFE) = expected free cash flow to equity
g = expected long-term growth rate
ke = cost of equity

The price of the selected market index (e.g., the S&P 500) as of the
valuation date is input for the “Value of Equity”, projected dividends
and share buybacks can be input for E(FCFE), and the yield on the risk-
free security can be used for the long-term growth rate “g”. Then “ke”
can is solved for. Subtracting the yield on the selected risk-free asset
results in the estimate of the implied ERP.


• As of January 1, 2010, the implied ERP was 4.36%,
calculated as follows:


Implied ERP: Default Spread-based
Premia
• It can be argued that assets across all classes of risky
assets (equities, corporate bonds, etc.) should be priced
consistently.
• If this is the case, ERP can be estimated in terms of the
default spread on corporate bonds.
– For instance, assume that (1) the default spread on Baa-rated
corporate bonds, relative to the ten-year treasury bond, is
2.2% and (2) that the ERP is routinely twice as high as the
default spread on Baa bonds. Then, the ERP would be 4.4%.

• The average and median ratio of the ERP to the Baa
default spread from 1960 to 2008 is 2.38 and 2.02,
respectively.


Default Spreads and DCF Model-based ERP:
1960-2008


Implied ERP: Default Spread-based
Premia
• As of January 1, 2010, the default spread on a Baa-rated bond
was 2.41%. Applying the median ratio of 2.02 (estimated from
1960-2009) to the Baa default spread of 2.41% on January 1,
2010 results in the following estimate of the imputed ERP:
Default Spread on Baa bonds (over treasury) on 9/30/09 = 2.41%
Imputed ERP = Default Spread * Median ratio or ERP/Spread
Imputed ERP = 2.41%* 2.02 = 4.87%

This is higher than the implied DCF model-based ERP of 4.36% in
January 2010, but there is significant variation in the ratio (of ERP
to default spreads) over time.
– The ratio dropped below 1.0 at the peak of the dot.com boom (when
ERP dropped to 2%) and rose to as high as 2.63 at the end of
2006. The standard error in the estimate is 0.20.

• However, whenever the ratio has deviated significantly from the
median there has been reversion back to the median over time.


Summary of ERP Estimates
Approach Used ERP Additional Information
SBBI Long-Horizon ERP (Arithmetic Mean) 6.70% Ibbotson SBBI 2010 Valuation Yearbook (1926-2009)

Duff & Phelps historical ERP for large company stocks 4.25% Duff & Phelps, LLC Risk Premium Report 2010 (1963-2009)

Historical Realized ERP - U.S. (Geometric) 4.70% Geometric Average - Stocks over T-Bonds: 1926-2009

Historical Realized ERP - Multiple Equity Markets 3.70% Average Premium Across 17 Markets: Dimson, Marsh and
Staunton (2010)
SBBI Long-Horizon ERP (Supply Side) 5.20% Ibbotson SBBI 2010 Valuation Yearbook (1926-2009)

Survey: CFOs 4.30% Graham and Harvey survey of CFOs (2009)

Survey: Global Fund Managers 3.80% Merrill Lynch (September 2009) survey of global managers

Survey: Individual Investors 8.30% Securities Industry Association (SIA) survey (2004)

Survey: Analyst and Companies 5.00% Fernandez survey of analysts and companies (2010)

Survey: Academics 7.00% Welch (2000)
Survey: Academics 6.00% Fernandez (2010)
Survey: Textbooks 6.50% Fernandez (2009)
Current Implied DCF-based Premium 4.56% From S&P 500 - February 1, 2010
Average Implied Premium 3.92% Average of Implied ERP: 1960-2009
Default Spread Based Premium 4.87% Default Spread * (ERP / Default Spread average)


ERP used by Damodaran
• Prior to September 2008, Damodaran used 4.0% as the mature
market ERP. This was based on his estimate of the average
implied ERP over time (1960-2007).
• However, the banking and financial crisis of 2008 was unlike other
market downturns and exposed weaknesses in developed capital
markets.
• After the crisis, in the first half of 2009, Damodaran used an ERP
of 5.0 to 6.0% in his valuations.
• Having observed the reversion to historical averages in 2009,
Damodaran will use an ERP of 4.5% to 5.0% in his 2010
valuations.
• “While some may view this shifting equity risk premium as a sign
of weakness, I would frame it differently. When valuing individual
companies, I want my valuations to reflect my assessments of the
company and not assessments of the overall equity market. Using
equity risk premiums that are very different from the implied
premium will introduce a market view into individual company
valuations.” – Aswath Damodaran


Estimating The Equity Risk Premium

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