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The real-time equity risk premium:

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Contents

1 Introduction 2 Overview

3 Introduction to equity risk premiums

4 Ex-post equity risk premiums 8 Ex-ante equity risk premiums 9 The real-time equity risk premium 13 Conclusion

14 References 16 About the authors

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The real-time equity risk premium (RTERP) model is a defi ned process for estimating a customized ex-ante equity risk premium (ERP) in real time or as of any user-specifi ed historical date within the past fi ve years. The RTERP is an integrated, software-based model with a related database that processes certain market data from third-party data services and employs a proprietary algorithm to determine the ex-ante ERP estimate.

The RTERP also provides size and industry risk premium estimates, along with descriptive statistical information such as graphs and charts.

Introduction

Risk premiums change over time as 1) the risk inherent in both the overall economy and the equity market changes, and 2) investors respond to equity market conditions by requiring different rates of return in exchange for taking risks. Ex-post methods of estimating ERP generally do not consider prevailing equity market conditions at or near the valuation date. Until now, there has been no readily available source for calculating the ex-ante ERP in real time or as of a specifi ed date. The RTERP provides this source.

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Overview

The equity risk premium (ERP) represents the expected rate of return on stocks in excess of the risk-free rate. The ERP is a key component in deriving discount rates. For decades, the ERP concept has been debated by academics and practitioners because no method is universally accepted or used for deriving the ERP.

The ERP is typically estimated based on the average historical return of equity securities in excess of the risk-free rate. The ERP is calculated on an annual basis over a long-term historical period. This approach is commonly known as the ex-post method.

The ex-post method has drawn signifi cant criticism in fi nance literature as a result of several faulty assumptions explored in this paper. The most basic of these assumptions is that historical returns are equal to investors’ expectations regarding future returns. However, the ERP represents the returns investors expect to achieve, meaning that ex-post returns provide only a historical data point that may or may not represent investors’ expectations. Hence, many studies have concluded that the ex-post method does not provide a reliable indication of the ERP, as we describe in this paper.

A forward-looking ERP can be determined by using observable market data to extrapolate the future returns expected by investors. This concept is known as the ex-ante method. In a 2005 article, Roger Grabowski addresses the reasoning behind using the ex-ante method:

ERP is a forward-looking concept, as it is an expectation of the valuation date for which no market quotes are observable. While you can observe premiums realized over time by referring to historical data, such calculated premiums serve only as estimates for the expected ERP. If we are to truly mimic the market, then our goal should be to estimate the true expected ERP as of the valuation date. To do that, you need to look beyond the realized premiums (Grabowski, 2005).

Ex-ante methods for estimating the ERP have been published by Brav, Chen, Damodaran, Fama, French, Ibbotson and many other economists, fi nance professionals and academics. Their estimates provide useful data points for demonstrating ex-ante ERPs. However, no process or system reliably calculates an ex-ante ERP as of a specifi c date. The timeliest source currently available is a monthly publication. As a result, practitioners generally estimate an ERP based on a qualitative assessment of dated results from post and ex-ante ERP studies.

In this paper, Grant Thornton LLP (Grant Thornton) introduces the real-time equity risk premium (RTERP). The RTERP is a defi ned process for estimating a customized ex-ante ERP in real time or as of any user-specifi ed historical date within the past fi ve years. The RTERP is an integrated, software-based model with a related database that processes certain market data from third-party data services and employs a proprietary algorithm to determine the ex-ante ERP estimate. The RTERP also provides size and industry risk premium estimates, along with descriptive statistical information such as graphs and charts. Grant Thornton has submitted an application with the U.S. Patent and Trademark Offi ce for a patent on this intellectual property.

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The ERP is the expected future rate of return on equity securities in excess of the risk-free rate. The expected return has far-reaching economic and fi nancial implications for corporations, governments and individuals, because ERP estimates are used for allocating capital, pricing assets and determining quantities reserved for future obligations.

The ERP represents a key assumption in almost every method of deriving discount rates for asset pricing, including the capital asset pricing model (CAPM), the arbitrage pricing model, the multifactor model, the build-up method and others. These discount rates have a direct and signifi cant effect on the value assigned to specifi c assets and liabilities and thus on corporate investment decisions related to projects and acquisitions.

Estimates of expected returns drive investment decisions regarding how capital resources are allocated across

geographies, industries, asset classes and specifi c investments. Such decisions are relevant to all investors: governments, private enterprises and individuals.

Estimates of expected future returns also represent a critical assumption for governments, individuals and corporations when they are determining the amounts required to meet future obligations such as health care, retirement, asset decommissioning and debt payments, to name a few.

Introduction to equity risk premiums

In summary, it is both fundamental and essential for professionals who measure value in our economy to estimate an accurate ERP. A signifi cant body of research has been developed regarding efforts to quantify the ERP. This research typically falls into one of three groups:

1. Surveys — The reporting of ERP estimates based on surveys conducted by investors, academics and fi nancial professionals.

2. Ex-post method — The derivation of ERP estimates based on historical returns of equity securities in excess of the risk-free rate.

3. Ex-ante method — The derivation of the ERP implied by current market prices and expected future benefi ts (e.g., dividends, stock appreciation).

Few practitioners rely on surveys for precision. While ERP surveys are useful for gauging the general range of ERPs used by various groups, they lack any direct, quantifi able link to the economy or the capital markets. Many qualitative issues exist with surveys, including how questions are presented, the profi le of the respondents, and the timing of the survey. As noted by Damodaran (2010), studies have provided evidence that surveys lack positive predictive power regarding future stock returns and in fact may have an inverse relationship with them. Given the limited use of surveys, this paper focuses on ex-post and ex-ante ERP estimates.

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Ex-post equity risk premiums

“Reliable data to estimate the historical premium of stocks over bonds were only collected in the mid-20th century, and precise econometric estimates of the equity premium only came after the development of the theory that uses it as a central input — the capital asset pricing model, or CAPM” (Goetzmann and Ibbotson, 2005). Since then, the most commonly cited ERP has been the ex-post premium.

Until recently, the ex-post premium was considered to be the best available option because of the weaknesses of surveys and the lack of available information required to construct an ex-ante ERP. While ex-post premiums have been used in academia and practice over several decades, recent research has begun to address the problems of the ex-post premium. We summarize the primary issues with ex-post estimates in the following discussion.

Actual versus expected returns

Ex-post ERPs are based on the premise that past performance is a valid proxy for expectations regarding future results. However, several studies have noted that realized returns are a noisy proxy for expected stock returns (Black, 1986; Merton, 1980; French, Schwert and Stambaugh, 1987; Asness, 2000). Further, signifi cant evidence from several studies indicates that historical returns do not refl ect investors’ actual expectations and that ex-post ERP estimates are a poor predictor of future returns.

In their seminal work, Mehra and Prescott (1985) observed that the high historical returns provided by equities relative to government bonds is inexplicable and implies abnormally high risk aversion in the context of standard economics models. This inexplicably high return on equities relative to government bonds became known as the equity risk premium puzzle. According to many economists, the puzzle provides evidence that historical returns have been signifi cantly higher than expected returns and, therefore, ex-post estimates do not refl ect expected returns.

Using evidence from equity fundamentals such as Sharpe ratios, book-to-market ratios, and income return on investment, Fama and French (2002) concluded that “the average stock return of the last half-century is a lot higher than expected.” As a result, ex-post ERP measurements overstate the premium that investors expected at that time.

In a 1993 publication, Blanchard, Shiller and Siegel concluded that the ex-post ERP — 8.0 percent since 1926 and 6.5 percent since 1871 — “appears far in excess of what is justifi ed by standard asset-pricing models with reasonable levels of risk aversion, given the behavior of the variance-covariance matrix of historical returns on bonds, stocks and consumption” (Blanchard, Shiller, Siegel, 1993).

Elton outlines instances in which observed returns did not align with the given risk of the investment. The McDonald’s effect is one example. Data sets within the second half of the 20th century pertaining to the fast-food chain McDonald’s had abnormally large returns relative to risk. Investors were consistently surprised at the earnings reported by McDonald’s, and those earnings resulted in stock price appreciation

above the expected level of returns. While McDonald’s was a relatively new company when the earnings surprises were occurring, there is ample evidence that mature companies can also have unusually large returns relative to risk (Elton, 1999). Similar examples involve Atlantic Richfi eld with North Shore Oil, Pfi zer with Viagra, and certain corporate restructurings. Anomalies of this kind can also be observed in index returns, such as the 20 percent run-up of annual returns in the Japanese stock market from 1980 to 1990.

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In addition, Elton (1999) asserts that ex-post ERP estimates falsely assume that information surprises cancel out over the measurement period and that realized returns are therefore an unbiased estimate of expected returns. Further, Elton cites “ample evidence that this belief is misplaced” and outlines certain time periods within markets when both stock and bond risk and return do not follow the sensible path. Examples of these periods include:

• periods longer than 10 years in which realized stock market returns are on average less than the risk-free rate (1973– 1984);

• periods longer than 50 years in which risky long-term bonds on average underperform the risk-free rate (1927– 1980); and

• periods during which U.S. equity markets returned over 15%, while the Japanese market experienced a negative return (1990–1999).

The preceding discussion provides evidence that actual historical returns may not provide an accurate estimate of investors’ expectations about future returns.

Time-period sensitivity

Ex-post ERP measurements are sensitive to the time period selected for calculation of the premium. Ex-post studies of historical returns on stocks and bonds have been performed using periods as far back as the 1870s, while other such studies look at returns beginning in 1926 or in the mid-1950s and the 1960s. Each selected time period yields signifi cantly different ERP estimates. “Because the state-of-the-art model assumes a constant variance rate, the large differences in variance rates among the various subperiods cause the model’s estimates to be quite sensitive to the time period of history used” (Merton, 1980).

The table illustrates the signifi cantly different results provided by ex-post ERP calculations using different historical time periods.

Time period ERP estimate (arithmetic average)

1926–20091 6.66%

1963–20091 4.25%

1997–20082 -3.68%

1802–18703 2.20%

1871–19253 2.90%

1 Sources: Morningstar Inc. Ibbotson SBBI 2010 Valuation Yearbook, 2010.; Duff & Phelps Risk Premium Report, 2010

2 Source: Damodaran, Aswath, Equity Risk Premiums (ERP): Determinants, Estimation and Implications — The 2010 Edition

3 Source: Siegel, Jeremy, Stocks for the Long Run, Second Edition, McGraw-Hill, 1998

Until recently, the ex-post premium was considered to be the best available option

because of the weaknesses of surveys and the lack of available information required to

construct an ex-ante ERP.

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Statistical reliability

As previously noted, empirical studies have concluded that historical returns are a noisy proxy for expected future returns. The statistical noise can be measured using the standard errors in ex-post estimates. The table below illustrates the standard errors in these estimates for various time periods ending in 2009 (Damodaran, 2010).

As shown above, shorter time periods have extremely high standard errors. However, even the longer time periods have signifi cant standard errors relative to the size of the ERP itself.

Survivorship bias and special events

Historical stock market returns contain an upward survivorship bias. Goetzmann and Ibbotson (2005) provide evidence that ex-post ERP estimates are affected by these survival issues. Because the returns are measured by the performance of the S&P 500, there is a focus on surviving companies, and the failure of many fi rms is neglected. The survivorship bias is exacerbated by the focus on domestic U.S. markets, which represent the best-performing markets over the periods typically used for ex-post ERP estimates. The survivorship bias results in ERP estimates that exceed expected returns.

There has been signifi cant debate regarding which time period is most relevant for estimating the current ERP. Longer time periods are advocated by many analysts because of the reduced statistical noise associated with longer-term estimates, while shorter time periods are advocated by others who argue that risk aversion has changed over time, causing recent returns to better refl ect current investors’ expectations. However, the arguments presented by both sides of this debate provide evidence that neither side may be correct. The events and issues listed below are commonly cited as problems with certain historical time periods:

• The concentration of railroad stocks prior to the 1860s • Regulatory changes in the NYSE in the 1860s

• The unreliability of data prior to 1926

• The bull market of the late 1920s followed by the 1929 stock market crash

• The postwar economic boom in the 1930s and 1940s • The low interest rates from the 1930s through the 1950s • Dramatically rising interest rates since the 1950s

• Signifi cant changes in investment income tax structure since the 1950s

• Recent decades’ bond market volatility relative to more stable equity markets

• The high standard errors indicated in 10-year and 20-year estimates

It is evident that every historical time period presents its own set of problems and results in a signifi cantly different ex-post ERP.

Time period Standard error (20% ÷√n)*

5 years 8.94%

10 years 6.32%

25 years 4.00%

50 years 2.83%

80 years 2.23%

* 20% represents the standard deviation in stock prices between 1926 and 2008. Damodaran (2010) notes that the standard errors are likely understated because they assume uncorrelated annual returns, while there is empirical evidence that these returns may be correlated over time.

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Geometric versus arithmetic mean

There is an ongoing debate over how to average historical data in calculating an ex-post ERP. Two schools of thought center on the geometric mean and the arithmetic mean. The geometric mean represents the compound annual return over the estimation period, while the arithmetic mean measures the simple average of annual returns over that period.

Many believe that the geometric mean provides a better estimate of long-term returns, while the arithmetic mean provides a better estimate of the next period’s returns. Neither averaging technique has been selected as the preferred method in practice. However, the two types of averaging result in extremely different ERP estimates (see below).

The averaging problem presents another unresolved dilemma with ex-post estimates, where the various options result in different ERP indications.

Time period ERP estimate ERP estimate

(arithmetic average) (geometric average)

1928–2008 5.56% 4.29%

1967–2008 4.09% 2.74%

1997–2008 -3.68% -7.22%

Source: Damodaran, Aswath, Equity Risk Premiums (ERP): Determinants, Estimation and Implications — The 2010 Edition

Volatility of expected returns

There is substantial evidence that expected returns change over time. In general, “expected returns are lower when economic conditions are strong and higher when conditions are weak,” as determined based on a statistical analysis of default spreads and dividend yields by Fama and French (1989).

“[F]rom the work of Rosenberg (1972) and Black (1976) as well as many others, the hypothesis that the variance rate on the market remains constant over any appreciable period of time can be rejected at almost any confi dence level” (Merton, 1980). “Moreover, there are two schools of thought on how to explain the variation in expected returns. Some attribute it to rational variation in response to macroeconomic factors [Fama and French (1989), Blanchard (1993) and Cochrane (1994)], while others judge that irrational swings in investor sentiment are the prime moving force [e.g., Shiller (1989)]” (Fama and French, 2002).

However, regardless of the underlying reason for the variation in the ERP, the ex-post method cannot provide results refl ecting expected returns, which are constantly changing. Long-term averages used in the ex-post method smooth the variation in expected returns and conceal the true ERP.

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Ex-ante equity risk premiums

The problems with ex-post ERP estimates are well-documented in economic and fi nancial literature. Ex-ante ERP estimates avoid those problems, while providing a more theoretically sound and measurable estimate of returns expected by investors at the relevant date.

Some authors, including Fama and French (2002) and Claus and Thomas (2001), provide empirical evidence that ex-ante ERP estimates are more accurate than ex-post estimates based on standard errors, ratio analyses and valuation theory. However, most practitioners have been forced to use realized returns as a proxy for expected returns because of the lack of data required to determine an ex-ante ERP. Fortunately, the amount of relevant data has increased signifi cantly over time, and research within the past several years has yielded substantial progress in developing ex-ante ERP estimates.

Ex-ante ERP estimates are derived by populating generally accepted fi nancial and economic models such as the CAPM, utility functions and the arbitrage pricing theory (APT) with observable market data and then solving for the ERP as the remaining unknown variable.

Economic variables — such as trading prices, dividend yields, forward-looking analyst estimates, volatility and default spreads — can be used to derive market evidence of investors’ expected returns. This is done by applying the variables to demand-side models such as the CAPM, utility functions or the APT.

Most ex-ante studies have compared future economic benefi ts expected from stocks (e.g., dividends, earnings, stock appreciation) with their observable market prices to solve for the expected percentage rate of return. The ERP is then determined by using demand-side models such as the CAPM and APT, in which all inputs are observable except the ERP itself.

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The real-time equity risk premium

The RTERP is a defi ned process by which the ex-ante ERP may be estimated in real time or as of a historical date specifi ed by the user. The RTERP is an integrated, software-based model with a related database that processes certain market data from third-party data services and uses that data, along with a proprietary algorithm, to determine the ex-ante ERP estimate.

The RTERP output also includes size and industry risk premium estimates, along with descriptive statistical information such as graphs and charts. The integrated database stores output from the model as of the end of each trading day in order to make historical output available without rerunning the entire RTERP process. The RTERP has a graphical user interface and may be made available through the Internet, intranets, third-party database queries (e.g., an application programming interface), or a prepackaged software application.

Model overview

The RTERP model employs a bottom-up approach to calculating an ex-ante ERP, as follows:

1. Determining the long-term expected rate of return for each constituent of a market index such as the S&P 500. This calculation is based on the internal rate of return (IRR) required to reconcile each constituent’s stock price with the present value of future cash fl ows, based on consensus analyst estimates.

2. Estimating the long-term expected rate of return on the index by calculating a market capitalization-weighted average of the IRRs identifi ed in step 1 above. The expected rate of return on the index represents the implied cost of equity capital for the index.

3. Applying the CAPM framework to solve for the implied ERP. The risk-free rate is subtracted from the index-level cost of equity to estimate the ERP.

The RTERP process is agnostic with regard to the sources of market data. Bloomberg, Morningstar, Thomson Financial Network, Reuters, Edgar Online, Capital IQ, Standard & Poor’s, and Compustat top the list of reliable data sources.

The RTERP is a defi ned process by which the ex-ante ERP may be estimated

in real time or as of a historical date specifi ed by the user.

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IRR for index constituents

As described on the previous page, using a bottom-up ERP model involves calculating the implied cost of equity for each index constituent. That amount can be determined by solving for the discount rate (in this case, the IRR) that makes the present value of future cash fl ows equal to the company’s stock price. The resulting discount rate represents the implied cost of equity, assuming that consensus analyst estimates represent the general expectations of the market.

Cash fl ows

From a fundamental perspective, the economic returns to equity holders can be measured by free cash fl ow to equity (FCFE), defi ned as after-tax operating cash fl ow less capital expenditures and debt principal payments. FCFE is available to return value to equity holders in the form of dividends, share buybacks, growth through acquisitions, and risk reduction by means of holding additional cash reserves.

The RTERP uses FCFE forecasts as the primary measure of expected future returns. The data necessary to calculate FCFE forecasts are pulled from a third-party database of consensus analyst estimates (e.g., Thomson Reuters, Capital IQ). The forecasted components of FCFE are available for the majority of index constituents.

For companies that do not have consensus estimates for their FCFE components, the RTERP uses earnings per share (EPS) as a proxy for cash fl ows. Finally, for companies that do not have FCFE or EPS consensus estimates, the RTERP uses dividends per share (DPS) estimates. FCFE, EPS and DPS are referred to collectively as cash fl ow measures.

Utilities and fi nancial institutions generally do not have FCFE estimates available through the data sources mentioned above. Given that these companies typically issue dividend-paying stocks, DPS estimates are used in lieu of FCFE and EPS, because DPS estimates provide the most relevant measure

Stock prices

The stock price of each index constituent, as of the date of the ERP estimate, is pulled from a data source.

IRR calculations

IRR calculations are performed in the context of a discounted future cash fl ow (DCF) analysis. The RTERP uses a three-stage DCF model:

First stage — Discrete period forecasts of cash fl ow measures are based on consensus analyst estimates as of the date of the ERP estimate. The forecast horizon is fi ve years. For companies without fi ve years of analyst estimates available, the RTERP estimates the remaining discrete periods based on each company’s growth rate in the latest forecasted period available. Blanchard (1993) suggests that a DCF “is likely to be a good approximation of expected rates of return over fi nite but suffi ciently long periods — say, fi ve years or more.”

Second stage — For RTERP modeling purposes, the smoothing period represents the second stage, in which growth transitions in a linear manner from the discretely forecasted periods to the stable growth rate used in the terminal period. The model assumes a two-year smoothing period. “The rather smooth transition toward the long-run growth rate is probably a more realistic assumption than the sudden change in the two-stage model” (Schröder 2007). An H-model is used to implement the smoothing period during the sixth and seventh years.

Third stage — This stage represents the terminal value (i.e., the present value of cash fl ows from the eighth year into perpetuity). Cash fl ows are capitalized using a Gordon growth model with a terminal growth rate equal to the risk-free rate, as measured by the yield on 20-year U.S. government bonds as of the date of the risk premium estimate.

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The three-stage DCF model for calculating the IRR is as follows:

CF1 CF2 CF3 CF4 CF5 1 CF5✱ H✱ (gS - gL) CF5(1+gL)

(1+k) (1+k)2 (1+k)3 (1+k)4 (1+k)5 (1+k)5 (k - g

L) (k - gL)

S = Stock price at the date of the risk premium estimate CFt = Forecasted cash fl ow measure for year t

gS = Short-term growth rate during the smoothing period of the H-model:

CF5 CF4

gL = Long-term projected growth rate into perpetuity

H = Half-life of the smoothing period stated in years (i.e., for a two-year smoothing period, H = 1) k = IRR, also the cost-of-equity component

The observed market inputs are applied in an IRR calculation using the above framework to solve for k, which represents the implied cost of equity for the subject stock. This calculation is performed for each constituent of the market index.

gS = – 1

S= + + + + +

[

+

[

Market capitalization and the weighted average

After the implied cost of equity is calculated for all market index constituents, the index-level cost of equity is calculated based on the market capitalization-weighted average cost of equity. Each index constituent’s market capitalization is pulled from a data source and used to weight the respective costs of equity in calculating the weighted average. That weighted average represents the implied expected return on the index.

ERP estimates and the CAPM framework

The CAPM framework provides an analytical basis for determining the ERP from the index-level rate of return implied by observable market data.

The index’s IRR is then applied to the CAPM in the following manner:

ki = Rf + β*(ERP)

ki = Cost of equity capital (i.e., the index-level expected rate of return)

Rf = The risk-free rate, assumed to equal the yield on 20-year U.S. government bonds as of the date of the risk premium estimate.

β = Market beta defi ned as 1 because the index is considered to be the market ERP = Equity risk premium

Given that beta is equal to 1 for the index, the CAPM formula is simplifi ed to the following:

ki = Rf + ERP

The RTERP model solves for the ex-ante ERP by deducting the risk-free rate from ki:

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Size premium estimates

Practitioners frequently use data sources that provide size premiums based on the excess historical returns of small stocks relative to the returns calculated using the CAPM. These historical measures have most of the same weaknesses as ex-post ERP estimates described earlier in this paper.

An ex-ante size premium estimate can be calculated in much the same way as an ex-ante ERP estimate. The following steps are used by the RTERP to calculate ex-ante size

premiums:

1. Computing the long-term expected rate of return for the market index based on the market capitalization-weighted average IRR for index constituents (see the calculation referred to above).

2. Determining the long-term expected rate of return for a small company group by using the IRR calculation and weighted average referred to above. The constituents of the small company group are not required to be constituents of the index. Size can be measured by several characteristics: market capitalization, enterprise value, total assets, book value, revenue, various earnings measures and fi nancial ratios, and other indicators.

3. Calculating the implied size premium as the excess of the expected return for the small company group relative to the index.

Industry risk premium estimates

Currently, practitioners use data sources that provide industry risk premiums based on historical returns. Again, however, these measures have most of the weaknesses of ex-post ERP estimates.

An ex-ante industry risk premium estimate can be calculated in much the same way as an ex-ante size premium estimate. The following steps are used by the RTERP to calculate ex-ante industry risk premiums:

1. Computing the long-term expected rate of return for the market index based on the market capitalization-weighted average IRR for the index constituents (see the calculation referred to above).

2. Determining the long-term expected rate of return for an industry group by using the IRR calculation and weighted average referred to above. The constituents of the industry group are not required to be constituents of the index.

3. Calculating the implied industry premium as the excess of the expected return for the industry group relative to the index.

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Conclusion

It is vital to estimate expected equity returns properly, because these estimates have far-reaching economic and fi nancial implications for corporations, governments and individuals across all sectors of the global economy. Expected returns affect critical decisions such as allocating capital resources, pricing assets, and determining quantities reserved for future obligations.

The RTERP is an innovative process that uses software and database programming, combined with economic and fi nancial modeling, to provide estimates of the ex-ante ERP and size and industry risk premiums, along with relevant graphs and statistics. The RTERP represents the only available source for ex-ante risk premiums in real time or as of a historical date specifi ed by the user. The RTERP has a graphical user interface and may be made available through the Internet, intranets, third-party database queries (via an application programming interface), or prepackaged software applications.

In summary, the RTERP provides more accurate ERP estimates than were previously available. As a result, investors, academics, practitioners and governments may be able to improve their ability to estimate key inputs affecting important decisions.

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Damodaran, Aswath, Equity Risk Premiums (ERP):

Determinants, Estimation and Implications — The 2010 Edition, Stern School of Business, February 2010.

Dimson, Elroy; Marsh, Paul; and Staunton, Mike, “Global Evidence on the Equity Premium,” The Journal of Applied Corporate Finance, 15-4, Summer 2003.

Duff & Phelps Risk Premium Report, 2008. Duff & Phelps Risk Premium Report, 2010.

Elton, Edwin J., “Expected Return, Realized Return, and Asset Pricing Tests,” Journal of Finance, pp. 1199–1220, 54-4, 1999. Fama, Eugene, and French, Kenneth, “The Equity Premium,” Journal of Finance 637, 75-2, April 2002.

Fama, Eugene, and French, Kenneth, “The Cross-Section of Expected Stock Returns,” Journal of Finance, pp. 427–465, 47-2, 1992.

Fama, Eugene F., and French, Kenneth R., “Dividend Yields and Expected Stock Returns,” Journal of Financial Economics, pp. 3–26, Vol. 22, No. 1, October 1988.

Fama, Eugene F., and French, Kenneth R., “Business Conditions and Expected Returns on Stocks and Bonds,” Journal of Financial Economics 25, pp. 23–49, 1989.

Freeman, Mark, “Explaining the Declining Ex-Ante Equity Risk Premium,” School of Business and Economics at the University of Exeter, 2004.

French, Kenneth R.; Schwert, G. William; and Stambaugh,

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About the authors

Bryan Benoit

Partner, Valuation Services and Central Region Leader T 832.476.3620

E [email protected]

Bryan Benoit is a Valuation Services partner in Grant Thornton’s Advisory Services practice in Houston. He has more than 20 years of experience and specializes in the valuation of complex businesses and assets.

A specialist in corporate fi nance and accounting, Benoit is familiar with business and asset valuations related to transactions, estate and gift tax, family limited partnerships, corporate tax, transfer pricing, international tax, litigation support, and fi nancial reporting.

Prior to joining Grant Thornton as a partner, Benoit was the managing director in charge of the Houston offi ce of Standard & Poor’s and Duff & Phelps.

Benoit has provided consulting services to clients in numerous industries, including energy, consumer and industrial products, computer software and hardware, integrated health care, life sciences, telecommunications, and fi nancial services. Benoit is the author of a number of published works and seminars and has been quoted in The Wall Street Journal, Bloomberg and Harvard Business School case studies.

Taylor West

Senior Manager, Valuation Services T 832.476.3722

E [email protected]

Taylor West is a Valuation Services senior manager in Grant Thornton’s Advisory Services practice in Houston.

West has 10 years of corporate advisory experience focused on the valuation of corporate securities, partnership interests, and intangible assets of privately held and publicly traded businesses. His valuation projects relate to M&A, fi nancial and tax reporting, litigation, and general corporate planning. West also manages projects involving forensic accounting, litigation consulting and intellectual asset management.

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Content in this publication is not intended to answer specifi c questions or suggest suitability of action in a particular case. For additional information on the issues discussed, consult a Grant Thornton client service partner.

National Partner-in-Charge Neil Beaton 206.398.2487 Atlanta Steven Krug 404.475.0041 Boston James Dondero 617.848.4890 Cincinnati Chuck Williams 513.345.4542 Charlotte Mark Edwards 704.632.6926 Chicago Massimo Messina 312.602.8247 Dallas Todd Patrick 214.283.8195 Detroit Phil Gaglio 248.213.4219 Houston Bryan Benoit 832.476.3620 Los Angeles Edward Karstetter 213.596.6762 McLean Venkat Komarlingam 703.847.7656 Milwaukee Dean Polenz 414.277.1512 Valuation practice leaders

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References

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