The Equity Risk Premium

Reading-order note. Numbered #4 and drafted second, after the risk-free rate and before CAPM, because the premium is defined relative to the risk-free rate and CAPM is built from both. All figures come from the hub's canonical parameter set and are illustrative teaching values, not market data or estimates of any current premium; the three estimation methods are described with their strengths and weaknesses and none is endorsed.

Important, because it is the largest component of almost every cost of equity, so every discounted valuation inherits whatever assumption was made about it. Unknowable, because it is an expectation: it describes what people require of the future, and the future has not happened. Everything else in this article follows from that tension.

Expected and realised are two different quantities

The distinction the whole subject turns on is between the premium investors demanded and the premium they got. The expected (ex ante) premium is forward-looking and unobservable; it lives in the heads of investors and can only be inferred. The realised (ex post) premium is what history actually delivered, and it is measurable to the decimal place. These are routinely treated as the same number. They are not, and the gap between them is not noise: if equities did unusually well over some period, the realised premium is high precisely because the expected premium turned out to be too conservative; the good outcome and the low prior expectation are the same fact viewed twice. Using a high realised premium as an estimate of the expected one therefore builds the past's good luck into the future's forecast. This pillar uses 5.0%, per the hub. It is a teaching value chosen for arithmetic cleanliness, not an estimate of any actual premium.

Three ways to estimate it, and why they disagree

Historical. Measure the realised excess return of equities over the risk-free asset across a long past period. Its virtue is that it is grounded in data rather than opinion. Its problems are severe and worth naming individually. Which period? Different start and end dates give materially different answers, and no start date is neutral. Which risk-free proxy? The premium over bills and the premium over long bonds are different numbers, and both are called "the" equity risk premium. Arithmetic or geometric mean? Treated below, because it is the single most common source of confusion. And which market? Long-run series are most available for markets that did well and survived, which is survivorship bias operating on an entire dataset rather than on individual funds. Studies covering many countries, including those with interruptions, wars, and expropriations, generally produce lower premia than studies of the single most successful market. Forward-looking (implied). Start from current prices and ask what premium the market must be assuming, typically by taking observed prices, adding expected dividends or cash flows and a growth assumption, and solving for the discount rate. Its virtue is that it reflects today's conditions rather than history's. Its problem is circularity of a kind: the answer is only as good as the growth assumption fed in, and reasonable people supply different growth assumptions. Survey. Ask academics, analysts, or company finance officers what premium they use. Its virtue is that it captures what practitioners actually apply, which is what really moves valuations. Its problems are that respondents are influenced by recent returns, they often disagree by several percentage points, and asking people what they expect is not the same as observing what they require.

Arithmetic, geometric, and the statistical problem nobody advertises

Two means, two different questions, and mixing them up shifts the premium by whole percentage points. The arithmetic mean is the average of annual returns and answers "what is the expected return in a single year?" The geometric mean is the compound annual growth rate actually achieved and answers "what did a holder end up with?" For any series with variation, the arithmetic mean is always higher, and the gap widens with volatility. On the illustration below, five years of realistic equity returns give an arithmetic mean of 8.00% and a geometric mean of 6.11%, a gap of 1.89 percentage points, which is larger than many disputes about the premium itself. Neither is wrong; using the arithmetic figure where the geometric belongs simply overstates what a long-term holder receives.

Now the problem that ought to govern how confidently anyone quotes this number. Equity returns are volatile: 16.0% annualised standard deviation, per the hub's canonical set. The precision of an average estimated from volatile data improves only with the square root of the sample length, which means even a century of data leaves the premium estimate genuinely imprecise. With 16.0% volatility, the standard error of a mean estimated over 100 years is 1.60 percentage points, so a point estimate of 5.0% carries a 95% confidence interval of roughly 1.9% to 8.1%. Over 50 years the interval widens to about 0.6% to 9.4%; over 25 years it is so wide it fails to exclude zero. This is not a criticism of any particular study; it is arithmetic that applies to all of them, and it explains why serious sources disagree by several points without any of them being incompetent. The honest conclusion is that the equity risk premium is a range, not a number, and any analysis presenting it as a precise input is claiming a precision the data cannot supply.

What to do with a number this uncertain

Not abandon it: the premium is real, and the alternative to estimating it badly is not estimating it at all, which is worse. Equities have historically compensated holders for bearing risk, that compensation is what makes the asset class rational to own, and a valuation with no premium implies shares should be priced like government debt. The practical response has three parts. State the assumption explicitly, with its source and method, so a reader can substitute their own. Present the output as a range across a defensible span of premia rather than as a point value, since the point value implies precision the input lacks. And separate the disagreement: when two valuations differ, establish whether they differ about the business or merely about the discount rate, because those are entirely different conversations and only the first is analysis. The broader habit this article should leave behind is scepticism toward any confident-sounding statement about what equities "return": over a decade, realised outcomes are dominated by starting valuations and luck, and the premium is a long-run tendency rather than a schedule. CAPM takes this number as an input and inherits every one of its uncertainties.