The equity risk premium (ERP) is the expected return on a broad equity market above the risk-free rate, measured on a consistent basis. It is an input to asset allocation and the cost of equity: changing the assumed premium changes how attractive risky equities look relative to cash and how future equity cash flows are discounted.
For a one-year simple-return comparison, write
is the market's total return, including dividends under the stated reinvestment convention. is a return fixed at the start for the same period and currency. The subscript on the expectation means “using information available at time .” The premium concerns an uncertain future return; it is not a payment promised by the market. Damodaran's definitions distinguish this expected premium from the premium earned in historical data.
The bad year does not contradict the premium
Consider hypothetical one-year nominal USD returns, before fees and taxes. The supplied expected broad-equity total return is 8% and the matched risk-free return is 3%. The expected ERP is therefore 5 percentage points:
Now suppose the equity market actually returns −12% over that year while the cash investment delivers the stipulated 3%. The realised excess return is
On equal USD 100 starting investments, the supplied expected equity wealth was USD 108 versus USD 103 in cash. The realised equity wealth is USD 88, leaving it USD 15 behind cash. The −15-point outcome does not by itself establish a negative expected premium.
Original hypothetical comparison. Both panels use the same one-year nominal USD simple-return scale. The cash return is fixed at the start; the realised equity loss is one possible outcome, not a revised estimate of expected return.
For a concrete consistency check, a fictional market with equally likely returns of −12% and +28% has expected return 8%. It can have a positive expected premium and still deliver the loss. This distribution is an illustration, not a forecast.
Three numbers that can all be called “ERP”
| Measure | What produces it | What it tells you |
|---|---|---|
| Expected premium | A conditional expectation of future equity return less a matched risk-free return | The forward-looking quantity an allocation or valuation model needs; it is not directly observable. |
| Historical premium | Observed equity returns and risk-free proxy returns over a specified sample | What investors earned in that sample. Using it for the future assumes that the sample is informative about future conditions. |
| Model-implied premium | A return backed out from market prices and assumed future cash flows, less a stated risk-free rate | The premium consistent with those prices and those modelling assumptions. Changing growth or payout assumptions can change it. |
Historical averages have sampling uncertainty, and the underlying expected premium can change. An implied estimate also depends on its model; it is not an expectation read directly from a price screen. Damodaran's discussion of the price of risk explains these historical and forward-looking approaches and their limitations.
When someone quotes an ERP, ask which of these quantities they mean before comparing numbers.
The measurement choices belong beside the number
Match the currency, horizon and return basis. Compare USD equity returns with a USD risk-free benchmark, not a rate in another currency. A one-year return is not directly comparable with an unconverted monthly rate. Keep both sides nominal or both sides real, and disclose taxes and fees. Price-only index gains omit dividends and do not measure the equity total return used here.
Name the risk-free proxy. A default-free nominal zero-coupon payoff in the same currency and at the horizon gives a clean theoretical comparison. Rolling short bills over a longer horizon introduces uncertainty about reinvestment rates. A long government bond's quoted yield is not its guaranteed return over a shorter holding period: its sale price can change. Historical “stocks minus bills” and “stocks minus bonds” can consequently answer different questions.
State arithmetic or geometric averaging. In a separate synthetic history, equities earn +20% then −10% in two consecutive years while cash earns 3% in each year. The arithmetic average equity return is 5%, so its arithmetic average excess return is 2 percentage points per year. Reinvested equity wealth grows from USD 100 to USD 108, however, giving an annualised geometric return of
The difference between that equity growth rate and cash's 3% geometric rate is approximately 0.92 percentage points per year. This difference of compound growth rates is not the arithmetic mean of annual excess returns, nor the annualised growth rate of the equity-to-cash wealth ratio. Label the convention rather than treating the numbers as interchangeable.
SelfMadeQuant's Equities, Indices and Corporate Actions develops the dividend, corporate-action and index-return conventions needed before estimating a historical premium. The page has a public preview; the full lesson requires membership.
Why investors might require it
Equity is risky partly because it can pay poorly in states where investors most need wealth. In consumption-based pricing, a payoff that is low when marginal utility of consumption is high needs compensation in expected return. That is a statement about the economic timing of risk, not a promise that more volatile investments always earn more or that a positive premium is guaranteed over any realised holding period.
The market ERP also differs from a single company's required excess return. In the capital asset pricing model, the market premium is multiplied by the company's beta; it is not simply added unchanged to every company's risk-free rate. The model's assumptions and the choice of market proxy remain part of that calculation.
Sources
- Aswath Damodaran, NYU Stern — Financial Ratios and Measures. Expected and historical ERP definitions and the cost-of-equity connection.
- Aswath Damodaran, NYU Stern — The Price of Risk: Looking Back and Forward, slides 7, 15–19 and 29–31. Historical estimation, implied returns, changing premiums and model choices. Historical figures in these slides are not used as current estimates here.
- Edwin J. Elton, Martin J. Gruber, Stephen J. Brown and William N. Goetzmann, Modern Portfolio Theory and Investment Analysis, 9th edition, Wiley, 2014, Chapter 10, pp. 208–211, and Chapter 13, p. 305. Expected-return estimation, historical evidence and estimation risk; covariance with the stochastic discount factor.
All numerical examples are original synthetic illustrations. They are not live ERP estimates or investment forecasts.