Estimating The Equity Risk Premium

Brown Bag PresentationJuly 30, 2010

Paul Daddio

Estimating the Equity Risk Premium

Willamette Management Associates 1

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.


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).


Historical Realized ERP• Even using an 80 year time span results in a relatively high standard

error of 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.

Estimation Period Standard Error of Risk Premium Estimate5 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%


Historical Realized ERP– 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 themost 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.


Historical Realized ERP

• 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.

Arithmetic Geometric Arithmetic Geometric1928-2009 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%

ERP: Stocks minus T-Bills ERP: Stocks minus T-Bonds

Source: "Equity Risk Premiums (ERP): Determinants, Estimation and Implications," Aswath Damodaran, 2/10.


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, whichreports 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 1990-2009U.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, thehistorical 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%.


• 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


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 equityg = expected long-term growth rateke = 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.


Implied ERP: DCF Model-based Premia


Implied ERP: DCF Model-based Premia• 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/SpreadImputed 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 EstimatesApproach 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 thecompany 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

Documents

Transcript of Estimating The Equity Risk Premium