What Is Equity Risk Premium, and How Do You Calculate It?

What Is Equity Risk Premium?

Equity risk premium is the excess return that investing in the stock market provides over a risk-free rate. This excess return compensates investors for taking on the relatively higher risk of equity investing. The size of the premium varies and depends on the level of risk in a particular portfolio. It also changes over time as market risk fluctuates.

Understanding 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. Whatever return you earn above a risk-free investment such as a U.S. Treasury bill (T-bill) or a bond is called an 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, an equity risk premium is an estimation as a backward-looking metric. 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. The estimates vary wildly depending on the time frame and method of calculation.

How to Calculate Equity Risk Premium

To calculate the equity risk premium, we can begin with the capital asset pricing model (CAPM), which is usually written as R_a = R_f  β_a (R_m - R_f), where:

• R_a = expected return on investment in a or an equity investment of some kind
• R_f = risk-free rate of return
• β_a = beta of a
• R_m = expected return of the market

So, the equation for equity risk premium is a simple reworking of the CAPM which can be written as Equity Risk Premium = R_a - R_f = β_a (R_m - R_f)

If we are simply talking about the stock market (a = m), then R_a = R_m. The beta coefficient is a measure of a stock's volatility—or risk—versus that of the market.

The market's volatility is conventionally set to 1, so if a = m, then β_a = β_m = 1. R_m - R_f is known as the market premium and R_a - R_f is the risk premium. If a is an equity investment, then R_a - R_f is the equity risk premium. If a = m, then the market premium and the equity risk premium are the same.

Equity Risk Premium in Reality

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.

The majority of economists agree, though, 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%.

Special Considerations

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.

Equity Risk Premium and the Survey Method

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 several advantages. It is forward-looking, capturing current market sentiment and future expectations, making the premium more 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, there are some downsides to the survey method. 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.

Equity Risk Premium and the Building Block Approach

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.

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 take risks to earn the highest possible return within their risk tolerances. Calculating the equity risk premium can indicate to investors how much more return they'll achieve than if they opted for a risk-free rate. However, this is not a true mechanism to gauge potential returns as the calculation relies on historical data, which is never indicative of future performance.