The equity risk premium (ERP) is the additional return that investors require for investing in the stock market over a risk-free asset (like government bonds). It reflects the compensation investors expect for taking on the higher risk of equities.
There are a few ways to calculate or estimate the ERP:

This method looks at the historical average returns of the stock market relative to a risk-free rate over a long period (typically decades).

Formula: ERP = Average Market Return − Risk-Free Rate

For example, if the historical average annual return of a stock index like the S&P 500 is 10% and the average return on long-term government bonds is 3%, then the ERP is 7%.

Pros: Simple and widely used.

Cons: Assumes that past performance predicts future expectations, which may not be accurate.

This approach calculates ERP based on the current market conditions and expected future cash flows (like dividends and growth).

Process: Use a model like the Dividend Discount Model (DDM) or an Earnings Growth Model to estimate the expected return on the market, and then subtract the current risk-free rate.

For example, if the expected return on the market (from projected dividends or earnings growth) is 8% and the current risk-free rate is 2%, the implied ERP would be 6%.

Pros: Reflects current market conditions and forward-looking expectations.

Cons: Relies on assumptions about future growth rates, which can be uncertain.

This involves asking financial experts or institutions to estimate what they believe the ERP should be based on market conditions.

Many financial institutions conduct regular surveys of economists, analysts, and fund managers to get an estimate.

Pros: Reflects collective market sentiment.

Cons: Subjective and may vary based on the group surveyed.

If the calculation is for a specific country, the ERP might be adjusted based on that country's economic risk relative to the U.S. (or another benchmark country). 
Process: Start with a base ERP (like the U.S. ERP) and add a country risk premium. The country risk premium is often based on the country's credit spread over the U.S. (using bond yields or CDS spreads).

For example, if the U.S. ERP is 5% and the country risk premium for Brazil is 3%, the ERP for Brazil would be 8%.

Pros: Useful for international investors considering country-specific risks.

Cons: Depends on accurate country risk assessments.

The equity risk premium is often determined using the historical approach for a simple average over time or the implied method for a more current, forward-looking estimate. Ultimately, the choice of method depends on the context and purpose, and sometimes analysts may even use a combination of methods to get a well-rounded estimate.