Ibbotson’s AnswerAn international consulting firm provides a solution for calculating the equityrisk premium for international markets.

Michael W. Barad, Ibbotson Associates

One of the most important elements in anybusiness valuation is the equity risk premium.There are many variations to estimating theequity risk premium, consequently, the ulti-mate value of a business will depend on thechosen approach.

While the underlying assumptions for deter-mining the appropriate method of calculation arestill widely debated, the equity risk premium pre-sented by Ibbotson Associates (Ibbotson) is one ofthe most frequently cited. This article explorescalculation assumptions behind the Ibbotson eq-uity risk premium, as well as its applications tointernational markets.

Use of the Equity Risk PremiumThe equity risk premium is a critical parame-

ter for a variety of valuation models. The buildupmethod, capital asset pricing model (CAPM), andFama-French 3-factor model all use the equityrisk premium in determining an appropriate cost ofequity.

The buildup method sums various risk premia,including the equity risk premium and a risk-freerate. The CAPM is similar to the buildup method,except the equity risk premium is multiplied bythe systematic risk, or beta, of the entity before therisk-free rate (and possibly a size premium) isadded. The Fama-French 3-factor model is an ex-tension of the CAPM, with two factors in additionto the market that are expected to influence stockmovements. The Fama-French model includes afactor for size, financial distress, and market risk(equity risk premium).

Numerous international cost of equity modelsutilize the equity risk premium from one countryas a base for calculations in another. The interna-tional CAPM and relative standard deviation mod-els, along with the globally nested CAPM andcountry spread models, developed by AndrewClare and Paul Kaplan, are examples of modelsthat use the equity risk premium in similar form.

Definition and CalculationThe expected equity risk premium is defined

as “the additional return an investor expects to

receive, to compensate for additional risk associ-ated with investing in equities as opposed to risk-less assets.”

It is important to note that the equity risk pre-mium used in business valuation is a forward-looking concept. In business valuation, the entityis typically viewed as a going concern, meaningthat operations are expected to continue indefi-nitely.

Calculating the equity risk premium is rela-tively straightforward, once the assumptions havebeen determined. The basic equity risk premiumpresented by Ibbotson takes the arithmetic meantotal return of stocks and subtracts the arithmeticmean income return of bonds.

Simply stated, we are interested in the excessreturn of stocks over bonds.

Benchmark SelectionIbbotson uses the S&P 500 as the market

benchmark, from which the income return on theappropriate horizon Treasury bond is subtracted,in calculating the equity risk premium for theUnited States.

Since most business valuations are performedas going concerns, a long-horizon (20-year) bondis an appropriate representation of the riskless as-set in calculation of the equity risk premium.Broader market benchmarks, such as the NewYork Stock Exchange weighted index, may beused as well.

Ibbotson has chosen the S&P 500 for itsbroad industry and equity capitalization coverageas well as its wide acceptance as a market proxy.Long-term bonds of different maturity, such as 10-year and 30-year bonds, are also acceptable alter-natives to proxy the riskless asset.

While changes in the market benchmark canalter the equity risk premium between 0 and 100basis points, changes in the long-term horizons onthe riskless asset benchmark amount to small dif-ferences.

The same principle applies to benchmark se-lection when calculating the equity risk premiumfor countries other than the United States. In Can-ada, for example, the Toronto Stock Exchange(TSE) 300 is an acceptable stock market bench-mark. While availability of data is always an issue,Morgan Stanley Capital International (MSCI)provides a number of equity market indices formany different countries that can work well in theequity risk premium calculation. Finding data onthe riskless asset also can be difficult. The Inter-national Monetary Fund’s “International Finan-cial Statistics” data provides yield series for a va-riety of countries that can be converted to incomereturn series.

Any series used in the analysis should containquality financial data from a reliable source andmust have a significant history of data to drawfrom.

Appropriate Time PeriodWhile some claim that surveys and forecasts

are appropriate for determining the equity riskpremium going forward, most believe that the useof an appropriate historical time period is the bestestimate of future performance. For those whoagree on the use of historical data, the argument

then turns toward the appropriate length of timefrom which to take the data.

Serial correlation is one test that can be ap-plied to verify whether prior year’s returns can aidin predicting subsequent year’s performance. Val-ues range from “–1” to “1,” with zero signifyingcomplete randomness (no predictability) and theextremes representing a perfect negative or posi-tive relationship (strong predictability), respec-tively.

Serial correlation for the annual excess returnsof the equity risk premium in the U.S., Canada,Japan, Germany, and many other countries areclose to zero. This means that the equity risk pre-mium is random or unpredictable if based on theprior year’s performance.

Therefore, the most recent time period is nobetter or worse at predicting next year’s equityrisk premium than has been any other time in thepast. For these reasons, the appropriate historicalperiod of data to use is the longest period of qual-ity data available. Exhibit 1 illustrates the randomcharacter of the equity risk premium on an annualbasis.

While data is available as far back as the1800s for the U.S., Ibbotson has determined thatthe highest quality data extends back to 1926, ashas been provided by the Center for Research in

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Exhibit 1

Annual U.S. Equity Risk Premium 1926-2000

Security Prices (CRSP). Ibbotson uses data backto 1919 for the UK, 1936 for Canada, and as farback as possible for other countries.

Total Return vs. Income ReturnCalculating the Ibbotson equity risk premium

considers the “total return” of stocks, minus theincome return of bonds.

Total return is used for stocks because it rep-resents the return an investor will actually experi-ence from an equity investment. Price return(capital appreciation) plus income return combineto form an asset’s total return. In forming an eq-uity risk premium, total return is not appropriatefor measurement of the riskless asset because totalreturns include price return, which fluctuates in-versely with interest rates.

There is much uncertainty surrounding fluc-tuation of a bond’s (positive or negative) capitalappreciation. The income return from a bond is theappropriate measure of the truly riskless portion ofthe bond and should be used as the measure of theriskless asset in the equity risk premium calcula-tion.

Arithmetic vs. Geometric MeansAn equity risk premium that is to be used in

discounting future cash flows should be calculatedusing arithmetic computations. The arithmeticmean takes into account uncertainty of period-to-period returns.

The greater the standard deviation for a returnseries, the higher the arithmetic mean will becompared to the geometric mean. This type of pe-riod-to-period riskiness must be accounted forwhen forecasting.

Ibbotson does provide geometric means andgeometric calculations of the equity risk premium,but these are intended for audiences interested inpurely historical analysis. The compound averageis appropriate for analyzing past returns, while thearithmetic average is appropriate for forecasting.

International AnalysisOnce the assumptions for calculation of the

equity risk premium are agreed upon, the premiumcan be calculated for any country with enoughquality data. Exhibit 2 compares the equity riskpremium across different countries over a com-mon time period of 1970-2000.

Data has been presented in both U.S. dollarsand in each country’s local currency. This graphuses 1970 as a common starting point acrosscountries. Since many of these countries havemore data available than presented here, eachcountry should be evaluated individually to deter-mine the appropriate historical range to calculateits equity risk premium.

While this chart presents data for only sixcountries, Ibbotson calculates the equity risk pre-mium for sixteen developed nations.

An issue concerning international investorshas been the idea that the world is becoming aglobal market. Specifically, equity marketsworldwide are reacting to each other with highercorrelation than in the past, thereby lessening theeffects of diversification.

One interesting example can be found by ex-amining the equity risk premium of the UnitedKingdom and that of the United States over thepast ten years. Graph 3 shows the similarity ofmovement in the equity risk premium of both na-tions.

SummaryWhile there is still much debate about which

methods to use when calculating the equity riskpremium, it is important to understand the under-lying assumptions Ibbotson has made.

The first is that the appropriate historical timeperiod to measure the equity risk premium from isthe longest period over which quality financialdata exists. Since the equity risk premium in oneyear cannot predict returns in the next, choosing

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Exhibit 2

Per Country Comparison ofEquity Risk Premium 1970-2000

only recent data is not the most prudent choice asit can overemphasize unusual events.

Further, the income return is the correctmeasure of the riskless asset as it is the portion ofa bond’s return guaranteed by the government.

Finally, when aggregating the total return onstocks and the income return on bonds, arithmeticmeans are appropriate for creating a forwardlooking equity risk premium while geometricmeans are used in purely historical analysis.

The assumptions set forth here can be appliedto a wide range of international markets, subject todata availability. While there is no doubt that thedebate over calculation of the equity risk premiumwill continue, this article presents a fairly simplemethod for which data on many countries can beobtained and applied.

Michael Barad is Manager, Valuation & LegalServices at Chicago-based Ibbotson Associates.Readers wanting to learn more about the equityrisk premium and Ibbotson’s methodolgy cancontact him by telephone at (312) 616-1620 or viae-mail at mbarad@ibbotson.com.

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Exhibit 3

UK vs. U.S. Annual Equity Risk Premium (in Dollars)