Equity risk premium explained: formula and estimates

The equity risk premium is the additional return investors require, or expect, for owning stocks instead of a risk-free investment such as a US Treasury security. It is the "price of risk" that sits at the heart of valuation, because it determines how heavily future stock cash flows are discounted. It is also unobservable, which means every number you see is an estimate.

What is the equity risk premium in simple terms?

The equity risk premium (ERP) is the extra return investors expect for holding stocks instead of a risk-free investment such as a US Treasury security. It is the reward for accepting the chance of large losses. It is sometimes called the market risk premium, and in practice the two terms are often used interchangeably. Nobody can observe it directly, so every figure you see is an estimate.

The definition

Equity risk premium (ERP) = expected return on the stock market
                          - risk-free rate

If the risk-free rate is 4% and investors expect 9% from the broad stock market, the ERP is 5%. The premium compensates for the possibility of large losses, such as those in bear markets, and for the fact that returns are uncertain.

Note that this is an expectation, not a guarantee. Over any particular period, stocks can earn less than the risk-free rate. If that never happened, there would be no risk and no premium.

Why it matters

The ERP is one of the three inputs to the CAPM:

Cost of equity = risk-free rate + beta x ERP

Beyond individual stocks, it influences how the entire market is valued. A higher premium means investors demand more compensation, lowering what they will pay for a given stream of cash. See discount rates and the CAPM and beta.

Three ways to estimate it

1. Historical premium

Average the difference between past stock returns and past returns on Treasury securities over a long period. It is easy to explain, but results depend on:

• The period chosen. Different start and end dates give noticeably different answers.
• Which risk-free security is used (short-term bills or longer-term bonds).
• Arithmetic versus geometric averaging.
• Survivorship. The US market was a historical success story, and studies relying on US data may overstate what investors could reasonably have expected in advance.

Historical estimates also carry large statistical error. Annual stock returns are so volatile that even decades of data pin down the average only loosely.

2. Survey-based premium

Ask investors, professionals or corporate finance officers what they expect. This reflects current opinion, but opinions are influenced by recent performance and can be inconsistent between surveys.

3. Implied premium

Work backward from today's index level. Given the current price of the market and a forecast for dividends, buybacks and growth, solve for the discount rate that makes the present value of the expected cash flows equal to the price. Subtract the risk-free rate, and the remainder is the implied ERP. This approach is forward-looking and uses current market data, but it relies on the cash flow forecast.

Aswath Damodaran, an academic who publishes widely used valuation datasets, is one prominent source of implied premium estimates. StocksXray draws on his datasets for betas and the equity risk premium.

Implied premiums move with prices. If stock prices fall while expected cash flows stay the same, the implied premium rises, because buyers are paying less for the same expected cash. If prices rise in an extended rally, the implied premium tends to fall. This is a mechanical property, not a forecast.

What is the US equity risk premium?

The US equity risk premium is the premium for the US stock market measured against US Treasury yields, which is also what people mean by the "US market risk premium". There is no official number. The historical, survey and implied methods above give different answers, and the implied premium moves as stock prices and Treasury yields move. StocksXray's valuation models take the equity risk premium from Aswath Damodaran's public datasets, which are refreshed each January, and use the US 10-year Treasury yield as the risk-free rate (see the methodology).

Example (illustrative numbers)

The risk-free rate is 4%. How much does the choice of ERP matter?

A two-point range in the premium shifts the cost of equity by two points for a beta-1 stock and 2.6 points for a beta-1.3 stock. In a DCF, that is the difference between a stock that looks cheap and one that looks expensive.

How is the equity risk premium used in valuation and WACC?

In the CAPM the ERP is multiplied by the stock's beta and added to the risk-free rate to get the cost of equity. That cost of equity is then blended with the cost of debt, weighted by how the company is financed, to give the weighted average cost of capital used to discount cash flows in a DCF. A higher premium raises the discount rate and lowers the present value of the same cash flows, all else equal.

Rules of thumb

• Never rely on a single value. Use a range, and show how the result changes across it.
• Make it consistent with the risk-free rate. Pair a Treasury-based risk-free rate with an ERP estimated against Treasuries, in the same currency.
• Use a country risk adjustment for non-US markets, since the premium for investing abroad can be higher.
• Remember that the premium can change over time and with market conditions. A single historical figure is not a law of nature.

Common mistakes

• Treating the historical average as a promise about the next decade.
• Mixing an ERP measured against short-term bills with a long-term Treasury yield.
• Using different ERPs to obtain a desired valuation.
• Confusing the ERP with expected return. The ERP is the excess over the risk-free rate, not the total.
• Forgetting that the risk-free input moves with interest rates; see bond yields and prices for how those yields behave.

A long-running puzzle

Economists have long debated why stocks have historically outperformed bonds by as much as they have, a question often called the equity premium puzzle. The debate illustrates a practical point: there is no settled "true" number, and the premium you choose is a judgment.

Frequently asked questions

What is the equity risk premium? It is the additional return investors expect from the stock market over a risk-free investment such as a US Treasury security. It compensates for the risk of large losses and uncertain returns, and it is an expectation, not a guarantee.

How do you calculate the equity risk premium? Subtract the risk-free rate from the expected return on the stock market. Because the expected return cannot be observed, it is estimated from history, from surveys or by working backward from today's index level, which gives the implied premium.

What is a good or typical equity risk premium? There is no single correct number. Estimates differ with the method, the period, the risk-free security and the date. The illustrative table above uses premiums of 4%, 5% and 6% to show how much the choice matters, but those are examples, not forecasts.

Why does the equity risk premium change over time? The implied premium moves with prices and yields. If stock prices fall while expected cash flows stay the same, the implied premium rises, and in an extended rally it tends to fall. Historical estimates also change with the period chosen.

What is the difference between the equity risk premium and expected return? The expected return is the total return investors expect from stocks. The premium is only the excess over the risk-free rate, so the expected return is the risk-free rate plus the premium.

Is the size premium part of the equity risk premium? No. A size premium is an extra return some analysts add to the cost of equity for smaller companies, on top of the CAPM result. It is an add-on to the cost of equity, not part of the ERP, and whether and how much to add is debated. See WACC and the cost of capital.

Does a higher equity risk premium lower stock prices? In valuation, a higher premium raises the discount rate, which lowers the present value of the same expected cash flows. In market terms the implied premium rises when prices fall, so the link runs both ways.

Key takeaways

• The ERP is the expected return on the stock market minus the risk-free rate.
• It can be estimated from history, surveys or implied by today's prices, and each method has weaknesses.
• Small changes in the ERP have large effects on discount rates and valuations.
• Use a range and keep it consistent with the other inputs.