Equity risk premium (ERP) is the difference between the benchmark risk-free rate and expected equity return. It is used to calculate a company's cost of equity, which is the sum of the equity risk premium and the benchmark risk-free rate.

r_e = r_f + (ERP + IRP)

Where:
ERP = Equity risk premium (Market risk premium for bearing the systematic risk of investing in equities).
IRP = Idiosyncratic risk premium (Company-specific risk premium).

Historical Approach

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? The length of the historical period impacts the accuracy of the estimate. A longer data period may be problematic because the past may not represent the current market environment in a market. Fluctuating market volatility has an insignificant effect on estimates from long data series. A shorter period has a greater likelihood of noise in the ERP estimate.
• Should we use daily return, weekly return or monthly return?
• Which equity index should we use? It should represent the returns equity investors earned in a market (e.g., S&P 500).
• 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? What is the best proxy for the risk-free rate? The long-term bond return or the short-term debt instrument return?

Considerations:

• Market Conditions: ERPs can vary over time. Changes in market conditions, such as economic crises, can influence the historical ERP.
• Survivorship bias: 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.

Forward-looking Approach

The forward-looking approach estimates the ERP based on current market expectations and forecasts. We discuss a few common models.

Survey-based Estimates

This approach involves gauging expectations by asking people questions. 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. The limitation of using surveys is that estimates are sensitive to recent market returns. Such estimates are often subject to response and sampling and behavioral biases such as confirmation and recency biases.

Dividend Discount Model

The dividend discount model expresses the value of a share as the present value of future expected dividends. Gordon's growth model is a simplified DDM used to estimate ERP: D₀ = D₁/(r_e - g)

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. The forward-looking ERP estimate is:

ERP = E(D₁/V₀) + E(g) - r_f

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%.

Limitation: DDM assumes the P/E is constant when dividends, earnings growth, and prices differ.

Macroeconomic Modeling

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.