# Equity Risk Premium Article Michael Annin, CFA and Dominic Falaschetti, CFA

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4 4 K = R + ( β ERP) s f s where, K s = cost of equity for company s; R f β s ERP = risk-free rate; = beta of company s; and, = equity risk premium. The CAPM states that the cost of equity is equal to the risk-free rate plus the equity risk premium multiplied by the company beta or measure of systematic risk. In many cases it is also appropriate to add a size premium to the CAPM. Fama-French Three Factor Model The Fama-French three factor model is a further extension of the CAPM. The regression equation to estimate the cost of capital using the Fama-French model can be written as follows: R R = β ( R R ) + ( s SMB) + ( h HML) i f i m f i i where, R i R f = risk premium for company i; β i,s i,h i = regression coefficients for company i; R m R f SMB = expected equity risk premium; = Size factor risk. Expected return of a portfolio of small stocks minus the expected return on portfolio of big stocks; and, HML = Distress factor risk where distress is measured by book equity divided by market equity. Expected return of a portfolio of high book-to-market stocks minus the

6 6 The Ibbotson Associates Equity Risk Premium Ibbotson Associates produces several publications that provide various cost of capital measures. One of these, the Stocks, Bonds, Bills and Inflation (SBBI) Yearbook provides one of the most commonly cited equity risk premium estimates in the field of valuation. Calculation Methodology The equity risk premium (ERP) is calculated by Ibbotson Associates using the returns on the S&P 500 over the income return on the appropriate horizon Treasury security. SBBI provides equity risk premium calculations for short-, intermediate-, and long-term horizons. However, companies are entities that have no defined life span and are assumed to be going concerns for extended time periods. In determining a company s value, it is important to use a long-term discount rate because the life of the company is assumed to be infinite. This holds true even if the time horizon of the investor is for a short amount of time. The long horizon ERP is simply the arithmetic average total return for the S&P 500 less the average income return of long-term Treasury bonds measured from 1926 to present. The History Behind the Seventy-one Year History The Ibbotson Associates equity risk premium covers the time period from 1926 to present. The original data source for the time series comprising the equity risk premium is the Center for Research in Security Prices (CRSP) at the University of Chicago. The CRSP time series start in CRSP determined that the time period around 1926 was approximately the time period where quality financial data became available. Nineteen twenty-six was also chosen by CRSP because it includes one full business cycle of data before the market crash of This is the most basic reason why the Ibbotson Associates ERP calculation window starts in 1926.

7 7 The period from 1926 to present is relevant because of the number of different economic scenarios represented by the time period. Some practitioners argue for a shorter historical time period, such as thirty years. This is based on the assumption that it is improbable that events of the more distant past will not be repeated in the future. However, as is discussed later in this article, even the most recent periods contain unique events. The Income Return Versus the Total Return The use of the income return, as opposed to the total return, for the appropriate horizon Treasury as a representation of the riskless rate is another area of discussion. Ibbotson uses the income return in calculating the ERP rather than the total return since it represents the truly riskless portion of the return. Yields have been rising generally over the period causing negative capital appreciation on the long-term bond series. This negative return is due to the risk of unanticipated yield changes. Any anticipated changes in yields will already be priced by the market into the bond. Therefore, the total return on the bond series does not represent the riskless rate of return. It includes the effects of unanticipated interest rate changes. The income return better represents the riskless rate of return since an investor can hold a bond to maturity and be certain of obtaining the income return and return of principal with no capital loss. The Appropriate Market Benchmark The Ibbotson Associates equity risk premium is based on the S&P 500 as its market proxy. The S&P 500 is chosen to represent the market because it is a broad based index, covering a large portion of the overall market in term of equity capitalization. It is also a widely cited proxy for the market as a whole.

9 9 assumes that the equity risk premium will be the same for each and every future time period. That is, the market benchmark will achieve the same excess return over every future time period. We know that this is not the case. Exhibit 1 shows the equity risk premium for each year based on the arithmetic mean returns of the S&P 500 and the income return on long-term government bonds. There is considerable volatility in the year-by-year calculation of the equity risk premium. At times the equity risk premium is even negative. The arithmetic average acknowledges the fact that market returns vary over time. Yet, the average equity risk premium realized will be the arithmetic average. However, the numbers will vary from period to period. To illustrate the difference between the arithmetic and geometric mean, suppose the expected return on a stock is 10 percent per year with a standard deviation of 20 percent. Also assume that only two outcomes are possible each year +30 percent and -10 percent (or rather, the mean plus or minus one standard deviation). The probability of occurrence for each outcome is equal. The growth of wealth over a two-year period is illustrated in below.

10 10 \$1.70 \$1.69 \$1.30 \$1.17 \$1.00 \$0.90 \$0.81 \$ Years 2 The most common outcome of \$1.17 is given by the geometric mean of 8.2 percent. However, the expected value is predicted by compounding the arithmetic, not the geometric mean. The probability weighted average of all possible outcomes is: (0.25 x 1.69) = (0.26 x 1.17) = (0.27 x 0.81) = The rate that must be compounded to achieve the terminal value of \$1.21 after two years is 10 percent, the arithmetic mean. The arithmetic mean equates the expected future value with the present value, therefore it is the appropriate discount rate. The Equity Risk Premium Over Time As seen in Exhibit 1, the equity risk premium varies considerably from year-to-year. The table below also indicates that the equity risk premium varies considerably by decade, from a high of 17.9 percent in the 1950s to a low of 2.3 percent in the 1930s. In the recent periods, the equity risk premium has been higher than its long-term average of 7.5 percent.

14 14 the calculation. Therefore, these periods carry more weight in the ultimate equity risk premium determined under this approach. Summary and Conclusion The equity risk premium is and will probably be one of the more widely debated topics in the area of cost of capital and valuation. The ERP is wildly debated because of its impact on the ultimate value derived. It is also widely debated since it represents the expectation of what the future returns on equities will be on average. In this article we have outlined various EPR methodologies. We have also outlined some of the strengths and weaknesses of these methodologies. Whether or not you agree with the Ibbotson Associates ERP methodology, it is important to understand how and why it is calculated in this manner. The issues addressed and assumptions made underlying the Ibbotson Associates ERP must also be addressed in any ERP calculation.

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