Equity risk premium methodology

What is published

For each country and date we publish five figures, all in percent except the ratio:

Each component carries a basis of observed, modelled or table. The mature market has no country premium: its spread is 0, its ratio is empty and its total equals its mature premium.

A country appears only when every input it needs is available. A missing input leaves the country out; nothing is filled in or carried forward silently.

Formulas

Mature-market implied premium. Take the cash that listed companies return to investors in a year (dividends plus share buybacks) as a fraction of their market value, y. Let it grow at rate g for five years (the length of the growth stage; g itself is measured over the past ten years of earnings, below), then grow at the risk-free rate rf for ever. The implied expected return r is the discount rate at which that cash is worth exactly today's market value:

1 = sum for t = 1..5 of  y (1+g)^t / (1+r)^t  +  [ y (1+g)^5 (1+rf) / (r - rf) ] / (1+r)^5
mature_erp = r - rf

The right side falls steadily as r rises above rf, so exactly one r solves the equation. We find it numerically. If no rate below 100% solves it, no figure is published.

Country default spread. For euro-area countries the spread is the country's 10-year government bond yield minus Germany's, both in euro, never below zero. It measures the extra yield over Germany, the reference for the euro area, and is added to the United States premium as the country's default-risk increment; it is not a difference against the United States bond. Nine euro-area countries whose series we may not use are modelled (see below). Every other country is taken from the public country risk table (see below).

Volatility ratio. The standard deviation of weekly equity returns divided by the standard deviation of weekly returns on a constant-maturity 10-year government bond, over the same weeks. The bond return in a week is the price change of a par bond bought at the previous week's yield and valued at the new yield. The three curves are not the same kind: the United States risk-free rate is a par yield, while the Bundesbank and Bank of Canada series are zero-coupon (spot-curve) estimates, and the OECD euro-area spreads use secondary-market yields. The difference is small next to the spreads it is compared with, but it is not zero.

Country risk premium and total.

country_risk_premium = country_default_spread x volatility_ratio
total_erp            = mature_erp + country_risk_premium

The figures we publish add up: the total is the sum of the published mature premium and the published country premium, and the country premium is the product of the published spread and ratio.

Inputs and their source type

The cash yield is measured on United States filers only: every active common-stock primary listing in the United States whose accounts follow US GAAP and whose latest annual report ended within the last 18 months; other countries' companies do not enter the aggregate. The figures are those of each company's latest fiscal year. A company whose latest annual report has a cash-flow statement but no dividend line, or no share-buyback line, counts as zero for that line: it did not report paying one. A missing dividend line is first taken from the dividends declared per share times the share count. A missing share count on the cover is replaced by the weighted average share count of the same year; when the two differ by more than 1.5 times (a split or a large issue between them), the company has no market value and is left out; an average stated in thousands or millions without a scale is recognised by that factor and does not count as a difference. Companies with no cash-flow statement, a wrongly signed figure, a different reporting currency or no market value are left out of the aggregate and counted. No market value means no share count in any form (some companies with several share classes, among them a few very large ones, report none we can use) or no quote; filers whose accounts are in another currency than their US quote (mostly depositary receipts of foreign companies) are also left out. At the first release 3,770 of 4,454 companies were counted, 99.96% of the market value of the companies that had one; the others were left out and are not added by estimate. Growth is measured on counted companies that report net income at both ends of the ten-year window (the latest fiscal year and the year ten fiscal years earlier), so a company with a shorter history is not in the growth sample, though it is in the cash yield; no premium is published when either total is not positive, when the companies with both ends hold less than half of the counted companies' market value, or when the ten-year growth is above 20% a year (a stop, not a ceiling: such a figure points to a data fault, and nothing is published until it is looked at). The number of companies in the growth sample and their share of the counted market value are kept with every release. At the first run (28 October 2026) the mature-market premium came out at 3.2230% a year; the ten-year growth was 10.580% a year, measured on 2,364 of the 3,770 counted companies, which hold 88.2% of the counted market value. The growth used is the ten-year rate as it is, never below zero. A closing price dated more than five days before the run counts as missing, and a run whose risk-free yield is more than seven days old does not publish.

Observed and modelled

A component is observed when it is computed directly from market or official data for that country: a spread from a bond pair, a ratio from both a price series and a yield series.

A component is modelled when the data it needs is not available to us for that country:

• Spread, observed. For euro-area countries the spread is the country's monthly 10-year government bond yield minus Germany's, taken from the OECD's monthly series. Each country's series is supplied to the OECD by a named national source. Germany's series is supplied by the Deutsche Bundesbank. We use a country's series only when the source the OECD names for it is the one we reviewed; if the name changes or cannot be read, the country is left out of that run. This gives observed spreads for Austria, Belgium, Finland, France, Germany (zero by definition, as the reference), Greece, Ireland, Italy, Luxembourg, the Netherlands, Portugal and Spain. A spread older than four months is not used.
• Spread, modelled. For Bulgaria, Croatia, Cyprus, Estonia, Latvia, Lithuania, Malta, Slovakia and Slovenia, whose series we may not use, the spread is estimated by a straight line fitted by least squares on the countries above, with one input: the current-account balance as a percent of GDP (latest value from 2023 on, World Bank). It is fitted on at least eight countries. A country whose balance lies outside the range of the fitted countries gets no modelled figure of ours (nothing is extrapolated) and is taken from the public table instead. The modelled spread is never below zero. With so few countries the fit is weak: its average error when each fitted country is left out in turn is recorded with every modelled figure and stated at the end of this section. It is good enough to place a country inside the euro-area range, not to say more. The fit is for countries inside one currency union and is not applied to any other country.
• Spread outside the euro area. Taken from the public country risk table ("Spread, table" below). We compute none ourselves, and the model is not applied to them.
• Spread, table. For every other country, and for a euro-area country whose own figure is missing in a month (a spread older than four months, a series whose named source could not be confirmed or read, or a country outside the model's range), the spread is the adjusted default spread of the public country risk table, and the country risk premium is the table's own. The volatility_ratio of such a country is the quotient of the two (empty where both are zero), so the published figures still add up: the premium is approximately the product of the spread and the ratio (the ratio is rounded to four decimals), and the total is exactly our mature-market premium plus the table's country risk premium. All five components of such a row carry the basis table, except mature_erp, which is ours and stays observed.
• Ratio, observed. A ratio needs at least 100 weekly observations of both the equity series and the bond series. We measure it for the United States (a broad equity fund against the Treasury 10-year yield), Germany (a broad fund quoted in euros against the Bundesbank's 10-year yield) and Canada (a broad fund quoted in Canadian dollars against the Bank of Canada's 10-year yield), over the three years before the run date. A country is measured only if its fund and its yield are in the same currency.
• Ratio, constant. Every other country uses one constant: the average of the ratios measured above. It is a pooled number, not that country's own volatility. A country that uses it has a modelled ratio, and so a modelled country premium and total. The constant exists only when all three ratios are measured; otherwise the country run fails and no country figure is published.

country_risk_premium and total_erp are modelled whenever the spread or the ratio is, and table whenever they come from the public table. mature_erp is observed: it is solved from observed inputs and involves no fitted model.

At the first release (28 October 2026) the line was fitted on 11 euro-area countries. Leaving each country out in turn, its average error was 0.21 percentage points, against 0.28 for simply predicting the average spread of the others. Of the nine, seven received a modelled spread; Bulgaria and Cyprus lie outside the fitted range, have no figure of ours and are taken from the public table.

Countries taken from a public table

Where our own series do not reach a country, we use the public country risk table that Aswath Damodaran (NYU Stern) publishes at pages.stern.nyu.edu/~adamodar, using the last good stored copy of it (a copy is replaced only by a newer one that passed our checks); the update of that copy is stored with every row we publish from it. Only two of its columns are used: the adjusted default spread and the country risk premium. The sovereign rating column and the equity risk premium column of the table are not used or republished; our total is our own mature-market premium plus the table's country risk premium. Using a published table is not a claim that it is our measurement: the rows are marked table so that you can tell.

The countries that come from the table are:

• every country the table lists, except the United States (the mature market, solved by us) and the countries that have a row of ours that month: Austria, Belgium, Finland, France, Germany, Greece, Ireland, Italy, Luxembourg, the Netherlands, Portugal and Spain with an observed spread, and Croatia, Estonia, Latvia, Lithuania, Malta, Slovakia and Slovenia with a modelled one (Bulgaria and Cyprus only when the model's range allows it);
• any of those countries in a month when its own figure cannot be built (see "Spread, table" above), for that month only.

Parts of a country that the table lists on their own (emirates, for example) are not used. The table is read from the page each month before the run, checked, and kept as a copy of its own, replaced only by a copy that passed the checks. Our own rows are written first, and the table is a separate step after them, using the last good copy: a table that cannot be read never holds our rows back, and only that step is retried (three attempts at most, six hours apart). The table is refused whole when its structure is not the one we reviewed: its columns, the update it names, a country count far below the usual, or a country listed twice. A single row that names a country we do not recognise, has no figure, or fails a plausibility check is left out and logged by name, and the other rows are used. Where a country was published from the table in an earlier month, its earlier revision stays available through the history endpoint; nothing is carried forward into the new month.

Updates

The monthly job is built and is switched on at launch; until then figures are computed by hand for single dates. Quotes are read slowly so the run takes about an hour and a half. Only the market-value total and the yield are kept; individual prices are not stored.

History is not yet built. The cash yield needs the market value of all United States companies at each past month-end, which needs historical prices that we do not yet hold; we plan to build monthly history later, and until then the history endpoint holds only the dates that have been computed.

Every release is a new revision of its date, and earlier revisions stay available through the history endpoint. as_of is the date the figures describe.

Limits

• No credit ratings and no credit default swaps in our own spreads. Our own spreads come from bond yields or from a model. Where ratings or swap prices would say something different, we do not see it. The spreads of the public table are, by its author's method, derived from sovereign credit ratings; for those countries the spread is his, and it is only as current as his update.
• Backward-looking growth. Growth is the past ten years of earnings, not analysts' forecasts, and it has no ceiling. A decade smooths the swings of a single cycle but still looks back: after a lasting change in earnings growth the estimate lags, and it can differ from forecast-based estimates by several tenths of a point. It is measured on the companies that have ten years of reported net income.
• Sample. The cash yield covers the listed companies in our filings data, weighted by market value; it is not the cash yield of a named index.
• Currency. The figures are in US dollar terms. A local-currency discount rate needs the inflation difference between the two currencies added.
• Modelled countries. A modelled spread is an estimate with real error. Use the basis field to see which figures are which.
• Coverage. The United States, the euro-area countries listed above and the nine modelled euro-area countries have our own figures; every other country the public table lists is published from it, marked table, with the volatility ratio taken as the table's own premium over its spread. These rows are as current as the table: they move when its author publishes a new one, not with our monthly bond yields.
• One fund per country. A country's volatility ratio uses one broad equity fund, not the whole market.
• Cash yield sample. Multi-class companies are counted by their primary share class only, which understates their market value and raises the yield slightly.
• Table countries and the mature base. The table's country premiums are measured against its author's own zero-risk base, while ours is added to our implied premium for the United States, whose own row in his table carries a small positive spread; the totals of table countries can therefore run slightly high against his method.
• Not advice. The figures are estimates for analysis, not financial, investment, legal or tax advice.

Method source

The method follows the approach published by Aswath Damodaran (NYU Stern; see his paper "Equity Risk Premiums (ERP): Determinants, Estimation and Implications"), whose dataset pages are at pages.stern.nyu.edu/~adamodar, consulted 27 October 2026: an implied premium for the mature market, a default spread, a volatility ratio, and the sum. Our inputs differ:

• We use the trailing ten-year growth of earnings from filings, with no ceiling; the published method uses analysts' forecasts of growth.
• We take default spreads from bond yields or a fitted model where we can; the published method takes them from sovereign ratings, and for the countries we cannot reach we use his table.
• We publish a basis on every component.

The only table of another provider that we use is the country risk table described above, for the two columns named there; we do not republish its ratings or its premium for any country we compute ourselves.

Sources and attribution

• Government bond yields: official sources, as published on each curve's page (United States Treasury, Deutsche Bundesbank, Bank of Canada).
• Euro-area monthly 10-year government bond yields: OECD (2026), Financial market, OECD Data Explorer, https://data-explorer.oecd.org/ (accessed on 28 October 2026). Each country's series is supplied by the national source the OECD names; Germany's by the Deutsche Bundesbank.
• Market prices: licensed market data, used for the market-value total, the equity fund series and nothing else.
• Company filings: public filings with the United States Securities and Exchange Commission.
• Country default spreads and country risk premiums for countries outside our own series: Aswath Damodaran, NYU Stern, Country Default Spreads and Risk Premiums, the update of the last good stored copy.
• World Bank, World Development Indicators, CC BY 4.0. Values normalised and combined by us; the World Bank does not endorse the result.