Understanding Equity Risk Premium: Definition and Calculation

What Is Equity Risk Premium?

Equity risk premium represents the additional return stocks offer over risk-free investments like Treasury bills, compensating investors for higher risks. It varies with market conditions and requires understanding historical returns to estimate future premiums.

Deep Dive Into Equity Risk Premium  

Stocks are generally considered high-risk investments. Investing in the stock market comes with certain risks, but it also has the potential for big rewards.

So, as a rule, investors are compensated with higher premiums when they invest in the stock market. The extra return you earn over a risk-free investment like a U.S. Treasury bill or bond is the equity risk premium.

An equity risk premium is based on the idea of the risk-reward tradeoff. It is a forward-looking figure and, as such, the premium is theoretical. But there’s no real way to tell just how much an investor will make since no one can actually say how well equities or the equity market will perform in the future.

Instead, the equity risk premium is estimated based on past performance. It observes the stock market and government bond performance over a defined period of time and uses that historical performance to the potential for future returns. Estimates can vary greatly depending on the time frame and calculation method.

Calculating Equity Risk Premium: Methods and Examples

1. Begin with the capital asset pricing model (CAPM): R_a = R_f + β_a (R_m – R_f).
2. Identify the expected return on the equity investment, R_a.
3. Determine the risk-free rate of return, R_f.
4. Calculate beta, β_a, which measures the stock’s volatility against the market.
5. Estimate the market’s expected return, R_m.
6. Use the formula Equity Risk Premium = R_a – R_f, or rework CAPM as β_a (R_m – R_f).
7. Simplify for the stock market by setting β_a = 1 if the investment equals the market.

Real-World Applications of Equity Risk Premium

The equity risk premium isn’t a generalizable concept even though certain markets in certain time periods may display a considerable equity risk premium.

Economists argue that too much focus on specific cases has made a statistical peculiarity seem like an economic law. Several stock exchanges have gone bust over the years, so a focus on the historically exceptional U.S. market may distort the picture. This focus is known as survivorship bias.

Most economists agree that the concept of an equity risk premium is valid. Over the long term, markets compensate investors more for taking on the greater risk of investing in stocks.

In 2024, the S&P 500 with dividends returned 26.1% whereas a Baa rated corporate bond returned 8.7% and a 3-month T-bill returned 5.1%. From 2014 to 2023, the average return of the S&P 500 with dividends was 11.91%, for a Baa rated corporate bond it was 4.32%, and for a 3-month T-bill, it was 1.27%.

 Important Factors in Equity Risk Premium Calculations

The equation noted above summarizes the theory behind the equity risk premium, but it doesn’t account for all possible scenarios.

The calculation is fairly straightforward if you plug in historical rates of return and use them to estimate future rates. But how do you estimate the expected rate of return if you want to make a forward-looking statement?

One method is to use dividends to estimate long-term growth, using a reworking of the Gordon Growth Model: k = D / P + g

where:

• k = expected return expressed as a percentage (this could be calculated for R_a or R_m)
• D = dividends per share
• P = price per share
• g = annual growth in dividends expressed as a percentage

Another is to use growth in earnings, rather than growth in dividends. In this model, the expected return is equal to the earnings yield, the reciprocal of the price-to-earnings ratio (P/E ratio): k = E / P

where:

• k = expected return
• E = trailing twelve-month earnings per share (EPS)
• P = price per share

The drawback of both of these models is that they do not account for valuation. That is, they assume the stocks’ prices are never correct. Since we can observe stock market booms and busts in the past, this drawback is not insignificant. 

Finally, the risk-free rate of return is usually calculated using U.S. government bonds, since they have a negligible chance of default. This can mean T-bills or T-bonds.

To arrive at a real rate of return, that is, adjusted for inflation, it is easiest to use Treasury inflation-protected securities (TIPS), as these already account for inflation. It is also important to note that none of these equations account for tax rates, which can dramatically alter returns.

Using Surveys to Determine Equity Risk Premium 

Another way to calculate the equity risk premium is through the survey method. The survey method involves collecting expectations for future equity returns from finance professionals, analysts, portfolio managers, and academics.

The survey questions typically ask participants to provide their forecasts for the average annual return on a broad stock market index over a specified period, such as the next five to 10 years.

Once the responses are collected, the average expected return on equities is calculated. With this info, the current risk-free rate is determined.

The equity risk premium is then derived by subtracting the risk-free rate from the average expected return on equities. For example, if the survey indicates an average expected return of 8% and the current risk-free rate is 3%, the equity risk premium would be 5%.

This method has advantages. It is forward-looking, capturing current market sentiment and expectations, making the premium relevant.

Also, by gathering insights from market professionals, the method leverages the expertise of people who are deeply engaged in the market and may have a better sense of the equity risk premium.

However, the survey method has some downsides. The results can be influenced by biases, and the accuracy of the equity risk premium estimate depends on the quality and representativeness of the survey sample.

A small or unrepresentative sample can skew results. Plus, during periods of market stress or euphoria, respondents’ expectations may be overly pessimistic or optimistic meaning the survey may be subject to emotions and unfair volatility.

Exploring the Building Block Approach for Equity Risk Premium  

Another option is the risk premium model, also known as the building block approach. The building block involves estimating the equity risk premium by summing up various risk premiums that investors demand for bearing different types of risks. Each component reflects the additional return investors expect for taking on specific types of risk beyond the risk-free rate.

For example, if the risk-free rate is 3%, and investors require additional returns of 4% for business risk, 1% for financial risk, and 1% for liquidity risk, the total expected return on equities would be calculated as 3% (risk-free rate) + 4% (business risk) + 1% (financial risk) + 1% (liquidity risk) = 9%.

Under this method, investors can specifically identify different types of risks, and then assign what they think the appropriate return is for each risk. This gives investors a more dynamic opportunity to evaluate risk at a more granular level, though it may be difficult to assess or assign risk premiums for each intricate type of risk.

Understanding the Fama-French Three-Factor Model

Last, let’s touch on the Fama-French Three-Factor Model. This model extends the traditional CAPM by adding two additional factors to better explain asset returns.

Besides the market risk factor, the model includes size risk and value risk. These additional factors account for the tendencies of smaller companies to outperform larger ones and value stocks to outperform growth stocks.

For example, suppose the risk-free rate is 2%, the expected market return is 8%, the SMB premium is 3%, and the HML premium is 4%. If an asset has betas of 1.2 for the market premium, 0.5 for SMB, and 0.7 for HML, the expected return would be 13.5%. This would be calculated as:

2% + 1.2 beta * (8% – 2%) + (0.5 * 3%) + (0.7 * 4%) = 13.5%

The Fama-French model provides a more nuanced understanding of the factors that can influence equity returns. Its main advantage is being able to capture additional dimensions of risk. However, the model assumes that the factors are consistently priced across different periods and markets which isn’t always the case.

The Bottom Line

Investors seek higher returns by taking on the risks associated with equity investing. The equity risk premium offers insight into how much excess return might be expected over risk-free investments, compensating for higher volatility. While this metric helps estimate potential returns, investors should remember it is derived from historical data, which does not guarantee future outcomes. Multiple methods, including CAPM and the Fama-French model, provide different lenses to calculate this premium, each with its advantages and limitations. Ultimately, understanding the equity risk premium aids in making informed investment choices, though no method ensures absolute accuracy due to market unpredictability.