The equity risk premium compares equity returns with a safer benchmark, with distinct expected, historical, arithmetic, and geometric measures.
The equity risk premium (ERP) is the expected or required return on a broad equity investment above a specified lower-risk benchmark, usually a risk-free rate. A historical ERP instead measures the excess return equities actually produced over a completed period; it is evidence, not a promised future premium.
For an expected premium:
where:
E(R_e) is the expected return on the selected equity market or portfolioR_f is the matched risk-free rateFor a completed historical period, replace expected returns with realized returns and clearly label the result realized or historical ERP.
Assume a valuation policy uses these hypothetical expectations:
3.0%8.0%The expected ERP is:
If a comparable company’s adjusted equity beta is 1.20, a CAPM-style cost-of-equity estimate is:
Raising only the ERP to 6.0% increases the estimate to 10.2%. That higher discount rate generally reduces the present value of the same expected equity cash flows. The calculation illustrates model sensitivity; it does not establish that either premium is correct or that the shares will earn the modeled return.
| Usage | What it represents | Typical application | Caution |
|---|---|---|---|
| Expected ERP | Forecast equity return above a matched safer rate | Asset allocation and expected-return analysis | Depends on uncertain expectations |
| Required ERP | Compensation investors are assumed to demand for equity risk | Cost of equity and valuation | Usually inferred rather than observed |
| Historical ERP | Realized equity return minus realized benchmark return | Long-run evidence and research | Highly sensitive to market, period, and averaging |
An article or model that simply states “the ERP is 5%,” for example, is incomplete unless it identifies which meaning, market, benchmark, currency, horizon, date, and method apply.
The historical method subtracts returns on a safer asset from returns on a broad stock-market index. It is reproducible when the analyst documents:
A long sample reduces dependence on one business cycle but may combine very different monetary, regulatory, tax, and market regimes. A short sample may better reflect recent structure but contain too few observations for a stable estimate.
An implied ERP starts with current equity-market prices and projected aggregate cash distributions or earnings. The analyst solves for the expected return and subtracts the selected risk-free rate.
The method responds to current prices, but the result depends on growth, payout, terminal-value, and cash-flow assumptions. An implied ERP is not directly observed merely because current prices are observable.
Surveys collect expected-return or premium assumptions from market participants, academics, or finance professionals. Organizations may also adopt a policy ERP to keep valuations comparable across teams and dates.
Survey and policy estimates should identify their population, date, horizon, currency, and intended use. Consensus does not remove estimation risk, and a policy value is not necessarily the market’s current required premium.
An arithmetic historical premium is the average of the period-by-period equity return minus the matched benchmark return. With identical observations and weights, it also equals the difference between the two arithmetic average returns.
A common geometric historical premium convention instead subtracts the benchmark’s compound annual growth rate (CAGR) from the equity market’s CAGR. NYU Stern’s valuation-method summary uses that difference-of-geometric-averages convention.
This is not the same calculation as compounding annual excess-return differences or measuring growth in equity wealth relative to benchmark wealth. State the formula, not just the word “geometric.”
Assume these two hypothetical annual total returns, including reinvested distributions, with no taxes, fees, or external cash flows:
| Year | Equity return | Safer-benchmark return | Equity minus benchmark |
|---|---|---|---|
| 1 | +50% | +10% | +40 percentage points |
| 2 | -20% | +10% | -30 percentage points |
The arithmetic historical premium is +5 percentage points per year: the average of +40 and -30. Yet $100 invested at the start ends at $120 in equities and $121 in the benchmark. Equity wealth grew by 20%, while benchmark wealth grew by 21%.
The annual compound rates are:
Subtracting those CAGRs gives a historical geometric premium of approximately -0.46 percentage points per year. The positive arithmetic average did not mean a buy-and-hold equity investment finished ahead.
A different measure is the annualized change in the equity-to-benchmark wealth ratio:
The -0.41% relative-wealth growth rate and the -0.46-percentage-point CAGR spread both describe this path, but they are not interchangeable. Compounding +40% and -30% as though the annual excess-return differences were returns on a funded investment gives neither comparison.
These two years illustrate arithmetic, not a reliable premium estimate. For each individual return series, the geometric mean cannot exceed the arithmetic mean when all gross returns are positive. It does not follow that the difference between two geometric means must always be below the difference between their arithmetic means; the variability of both series matters.
The capital asset pricing model uses an equity-market premium when a broad equity index serves as the market proxy:
The resulting cost of equity may feed into a dividend discount model, discounted cash-flow model, residual-income model, or weighted average cost of capital.
Input consistency matters:
The terms often refer to the same numerical input, but they emphasize different definitions.
| Equity risk premium | Market risk premium |
|---|---|
| Excess return on a defined equity basket | Excess return on CAPM’s market portfolio |
| Can be expected, required, or historically realized | Usually discussed as the expected market-factor premium in CAPM |
| Benchmark may be a Treasury instrument or another defined safer asset | Benchmark is CAPM’s matched risk-free rate |
CAPM’s theoretical market portfolio includes all investable risky assets. Practical CAPM estimates often use a broad equity index instead, making the practical MRP and ERP the same only when all other conventions also match.
An ERP estimated from one country’s equity history may not represent another market’s political, currency, liquidity, legal, or economic risks. Some valuation methods start with a mature-market ERP and add a separately estimated country risk premium. Others estimate local market returns directly.
There is no adjustment that is universally correct. The analysis should disclose the method, avoid embedding the same risk in several inputs, and keep cash-flow scenarios consistent with the discount rate.
For a reviewable valuation, retain the source file or link, retrieval date, market, series definitions, formula, and any overrides. A number copied from a presentation without those details is weak evidence.
ERP can be a useful organizing assumption, but it does not capture every source of equity risk or settle whether a specific security is attractive.
This article provides general financial education. Equity-premium and valuation inputs are uncertain and do not constitute personalized investment, tax, legal, accounting, or valuation advice.