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##### Subject 2. Equity Risk Premium
The equity risk premium is the excess return that equities provide over a risk-free asset. It can be based on expected return or realized return.

Required return on equity = Risk-free return + Equity risk premium

It is used to estimate the required return on individual stocks. For example:

Required return on share i = risk-free return + βi x Equity risk premium

The question is: how do we estimate the equity risk premium? Two broad approaches are historical estimates and forward-looking estimates.

Historical Estimates

This approach examines the historical data of realized returns of a country's market portfolio and uses the average rate for both the market portfolio and risk-free assets. The historical payoff for risk is a good guide to the future risk premium. An important assumption is that equity returns stationary.

Decisions to make:

• What should be the sample period? The last 30 years, 50 years or 70 years?
• Should we use daily return, weekly return or monthly return?
• Which equity index should we use?
• Arithmetic mean or geometric mean? The arithmetic mean is suitable in single-period models such as CAPM and multifactor models.
• What should represent the risk-free rate? The long-term bond return or the short-term debt instrument return?

Economists have long been puzzled by the high historical equity premium - most theoretical models of investor preferences suggest investors would demand a much lower premium for equity risk. A key contribution to this discussion is the suggestion that history is written by the winners, i.e., that survivorship has a significant effect on the estimate of the equity premium. If so, the historical risk premium estimate should be adjusted downward.

Here is a conceptually related issue this: are we at an artificial peak in the stock market or economy (a bubble) which makes historical growth an upward biased prediction of the future?

Forward-Looking Estimates

This approach is based on current expectational data.

1. Gordon Growth Model Estimates

Many investors estimate the market risk premium using historical averages. However, the Gordon growth model can be algebraically manipulated to create a forward-looking market risk premium based on the current market valuation. Such a model should help estimate the actual return investors should expect from investing in the stock market.

Estimating the risk premium in this way is simple. Start with the dividend yield on the market index, add the consensus long-term earnings growth rate and subtract the current long-term government bond yield.

For example, the dividend yield on the S&P 500 is 2%, the consensus earnings growth rate is about 8% and the yield on the 10-year treasury is about 5%. 2% + 8% - 5% = 5%.

2. Macroeconomic Model Estimates

Analysts can develop equity risk premium estimates using macroeconomic variables. For example, in a supply-side analysis, the total return to equity can be analyzed into four components: expected inflation, expected growth rate in real earnings per share, expected growth rate in the P/E ratio, and expected income component.

3. Survey Estimates

Analysts can also ask a panel of experts (e.g., economists, CFOs) to estimate the future equity risk premium and then take the mean response.

Learning Outcome Statements

b. calculate and interpret an equity risk premium using historical and forward-looking estimation approaches;

CFA® 2023 Level I Curriculum, Volume 3, Module 21

User Comment
AG09429 Hello everyone!
Should that not be: 2% * 1.08 - 5% ?
And in this particular case the equity risk premium goes as - 2.84%, which means that the fixed income instruments are more attractive than equities?