What is the equity risk premium?

The equity risk premium is the additional return investors earn — or expect to earn — for holding stocks instead of a risk-free investment such as short-term government bills. It is the reward for bearing the risk that stocks can fall sharply and stay down for years. Without it, there would be no reason to hold stocks at all.

The formula

The realized equity risk premium over a period is simply:

\text{ERP} = R_{\text{stocks}} - R_f

where $R_{\text{stocks}}$ is the return of the stock market and $R_f$ the risk-free rate over the same period.

Looking forward, it can be estimated from today's valuations. One common approach uses the earnings yield — earnings divided by price, the inverse of the price-earnings ratio — as a rough estimate of the expected real return of stocks, and subtracts the real yield on safe government bonds:

\text{ERP}_{\text{expected}} \approx \frac{E}{P} - r_{\text{real, bonds}}

A simple illustration

A stock market trades at 20 times earnings — an earnings yield of 5% — while inflation-linked government bonds yield 1.5% in real terms:

\text{ERP}_{\text{expected}} \approx 5\% - 1.5\% = 3.5\%

Stocks would be expected to earn about 3.5 points a year more than safe bonds, in real terms. If prices rise until the market trades at 25 times earnings, the earnings yield falls to 4% and the expected premium to 2.5%: higher prices today mean lower expected returns later.

What history shows

Long-run studies of global markets over more than a century, such as those by Dimson, Marsh and Staunton, have found an average premium of global stocks over short-term government bills of roughly 4–5% a year. The premium has varied enormously by period and by country, and there have been whole decades in which stocks earned less than safe assets.

Why it matters

It is the basis of long-term planning. Assumptions about stock returns are, in effect, assumptions about the risk-free rate plus the equity risk premium.
It explains the trade-off. A portfolio with more stocks has a higher expected return precisely because it takes more risk; the premium is the price of that risk.
It depends on the starting point. Expected premiums are lower when stocks are expensive and higher after large falls.

Limits

It cannot be observed in advance. Every forward-looking estimate rests on a model and its assumptions.
It is not guaranteed over any horizon. The premium is an average; over ten or even twenty years, stocks have sometimes returned less than bonds.

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