## What Is Equity Risk Premium?

The term equity risk premium refers to an 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.

### Key Takeaways

• An equity risk premium is an excess return earned by an investor when they invest in the stock market over a risk-free rate.
• This return compensates investors for taking on the higher risk of equity investing.
• Determining an equity risk premium is theoretical because there's no way to tell how well equities or the equity market will perform in the future.
• Calculating an equity risk premium requires using historical rates of return.

## How Equity Risk Premiums Work

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 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.

Because equity risk premiums require the use of historical returns, they aren't an exact science and, therefore, aren't completely accurate.

To calculate the equity risk premium, we can begin with the capital asset pricing model (CAPM), which is usually written as Ra = Rf + βa (Rm - Rf), where:

• Ra = expected return on investment in a or an equity investment of some kind
• Rf = risk-free rate of return
• βa = beta of a
• Rm = 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 = Ra - Rf = βa (Rm - Rf)

If we are simply talking about the stock market (a = m), then Ra = Rm. 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 βa = βm = 1. Rm - Rf is known as the market premium, and Ra - Rf is the risk premium. If a is an equity investment, then Ra - Rf is the equity risk premium. If a = m, then the market premium and the equity risk premium are the same.

According to some economists, this isn't a generalizable concept even though certain markets in certain time periods may display a considerable equity risk premium. They 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. How exactly to calculate this premium is disputed. A survey of academic economists gives an average range of 3% to 3.5% for a one-year horizon, and 5% to 5.5% for a 30-year horizon. Chief financial officers (CFOs) estimate the premium to be 5.6% over T-bills. The second half of the 20th century saw a relatively high equity risk premium, over 8% by some calculations, versus just under 5% for the first half of the century. Given that the century ended at the height of the dotcom bubble, however, this arbitrary window may not be ideal.

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## 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 Ra or Rm)
• 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 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.

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