Beyond the United States: Anarkulova, Cederburg and the world sample
The whole safe withdrawal rate tradition, from Bengen to Trinity and on to nearly every online simulator, rests on one data set: US markets since 1926 (Bengen, the Trinity study, and the birth of the safe withdrawal rate). The twentieth-century United States is not a neutral sample. It is the country that won the last century.
Since the 2010s, a line of research has redone those calculations on the full experience of the developed world: Dimson-Marsh-Staunton, Wade Pfau, and above all Aizhan Anarkulova, Scott Cederburg and Michael O'Doherty. The results are uncomfortable. The world safe withdrawal rate sits well below 4%, and bond-heavy portfolios protect less than we thought. This page walks through that work, its numbers, and the fair criticisms of it. It also shows how a simulator turns it into something usable, the model known as the broad sample, and what you need to know to read it without overreading it.
Geographic survivorship bias§
Start with the problem. The Ibbotson data begins in 1926 in New York. It holds the Great Depression and the stagflation of the 1970s, but it also describes a country never invaded, never in default on its domestic debt, whose currency became the world's reserve and whose stock market was the great winner of the century. Pick that country as your only sample and you calibrate your plan on the winning lottery ticket.
The developed twentieth century produced plenty of what the US sample does not contain: stock markets shut down or expropriated (Germany 1948, Japan 1946), hyperinflations that pulverize bonds (Hyperinflation and extreme scenarios), lost decades (Japan after 1990, stocks below their real peak for more than thirty years), defaults and financial repression. A German, Japanese, French or Italian retiree who left between 1900 and 1960 with an American-style plan was ruined in a fair share of cases. Not through bad luck in the sequence, but because their country lived through history.
Dimson, Marsh and Staunton, the London Business School trio behind the Global Investment Returns Yearbook, put a number on the gap back in 2002. Real stock returns from 1900 to 2020 ran about 6.5% a year in the United States against about 4.5% outside it. And in half the countries, government bonds did worse than 0% real over long stretches. Wade Pfau applied Bengen's method to 17 countries as early as 2010. The 30-year SAFEMAX, about 4% in the United States, falls below 3% in a third of them and below 1.5% in the worst, Japan, Italy and France among others, sunk by their postwar inflations.
Anarkulova, Cederburg and O'Doherty: the modern method§
The work of Anarkulova, Cederburg and O'Doherty ("The Safe Withdrawal Rate: Evidence from a Broad Sample of Developed Markets", 2023, cosigned with Sias, plus the sister papers, among them "Beyond the Status Quo", 2023) modernizes the question on three fronts.
The data. The cleanest developed-market database available, built on the GFD reference set and on long-run academic work. It covers 38 developed countries and roughly 2,500 country-years of real returns in stocks, bonds and cash. The care taken over survivorship and look-ahead bias is unusual: a country enters the sample when it was developed at the time, not in hindsight. Argentina, rich in 1900, is therefore in. That is the sore point, and we come back to it.
The method. Instead of replaying windows from a single country, a block bootstrap. Ten-year blocks are drawn from the whole grid of countries and eras, which preserves clusters, trends and regimes (Sequence of returns risk: the retiree's real enemy). Those blocks are then assembled into synthetic retirements of whatever length you want. Each simulated retirement lives the history of one coherent developed country, piece by piece, disasters included. That machinery is what the broad-sample models copy, on a more modest database, since the authors' own is not open (Historical windows, bootstrap, parametric: the three families of models).
Mortality. Instead of a fixed 30-year horizon, a 65-year-old couple tracked through real mortality tables. Retirements therefore run for a random length, sometimes 35 years and more.
Here are the headline results for a 65-year-old couple holding a domestic 60/40. The rigid 4% rule fails in about 17% of cases, against roughly 2% on US data alone. The rate carrying a 5% failure probability comes out near 2.26%. For an early retiree with a longer horizon it is worse still. The same team draws an even more uncomfortable conclusion in "Beyond the Status Quo": in their sample, all-equity portfolios diversified internationally beat stock-bond mixes over long horizons. The reason is that bonds get destroyed by inflation every so often, in exactly the eras that flatten local stocks. International diversification in equities protects better than domestic bonds do (International diversification (and home bias), Bonds in retirement: types, duration, the exact job).
Three samples travel under the same flag, and mixing them up wrecks any reading. Here is what separates them.
| Sample | Data and draw | Portfolio | Horizon | Published figure |
|---|---|---|---|---|
| The paper (2023) | 38 developed countries (GFD), blocks from every country | domestic 60/40 | real mortality, 65-year-old couple | ~17% failure at 4%; 2.26% at a 5% failure probability |
| The broad-sample model | 16 countries (JST panel, 1870 to 2020), blocks from one country | domestic 60/40 | your plan's | world basket at 3.3% over 30 years |
| US history | United States since 1926, rolling windows | 50/50 to 75/25 | fixed 30 years | SAFEMAX ~4.15%; ~2% failure at 4% |
Read that last column carefully, because the three numbers do not measure the same thing. The first is a probability over retirements of random length; the other two are worst-vintage rates, one across a basket of countries, the other for a single one. The databases differ too. On the panel behind the figure above, the United States carries only 3.75%, where the Bengen tradition prints 4.15%.
The honest criticisms§
This work has serious opponents, ERN first among them, who has devoted several analyses to it, and the objections are worth knowing, because they bound the pessimistic reading the way the American bias bounds the optimistic one.
The weight of military catastrophe. A large share of the sample's failures comes from world wars fought on home soil (Germany, Japan, Austria, France) and the hyperinflations that followed. If your capital-destruction scenario is a military occupation, an ETF portfolio is not your real problem anyway. The counter: strip out the wars and you also strip out the only observations of political tail risk anyone has, and events of that class, confiscation, financial repression, a currency destroyed, do not require a world war.
Argentina, and where the sample stops. Including countries that were developed at the time and later fell behind, Argentina among them, is defensible. It is exactly the survivorship bias you want to avoid: in 1900, nobody knew who would fall behind. But it does drag the numbers down for an investor in today's core countries.
The simulated investor is domestic. The simulated retirements live one country's history, in local stocks and local bonds. A globally diversified investor today, holding an unhedged world equity fund, would not have taken Japan 1990 or Italy 1970 full in the face: international diversification cushions precisely the worst blocks of the sample. This is probably the most important criticism in practice, and it argues for diversification (International diversification (and home bias)) more than it argues against the study.
Overlapping blocks and the real sample size. Two thousand five hundred country-years sounds like a lot. But the draw pulls ten-year blocks out of overlapping windows, so the same German or Japanese decade shows up in a great many simulated retirements, and a single disaster weighs on thousands of paths. Crises are global and correlated on top of that: 1929, 1973 and 2008 hit everyone. The sample of independent disasters stays small, and the uncertainty around these numbers is itself wide.
The reasonable synthesis: the true risk facing a globally diversified investor today sits somewhere between US history and the domestic world sample, and nobody knows where. So here is the rule to work by, whatever tool you use. Keep both bounds on screen, side by side, all the time, and distrust any verdict that shows only one.
What it changes for your plan§
The rigid rate you size with. If you size with no margins (How much you need), the world bound argues for 3 to 3.5% rather than 4%. What it really rules out is calling 4% "scientifically safe" over 45 years. But aiming at 2.3% (43 times your spending!) out of pure literalism would be an overreaction. That is the domestic worst-case bound, and your real margins, a pension, flexibility, diversification, dominate it comfortably.
How to read a broad-sample model. That model is not your portfolio, and your return assumptions change nothing in it, since it draws only from real data. If your plan holds there, it holds in the harshest developed world on record. That is the best robustness label available. If it does not hold, look at where the scenarios fail, usually in inflationary blocks (Inflation and the withdrawal rate: the exact link), and at what your portfolio lacks for those regimes (All-weather portfolios: Browne, All Weather, Golden Butterfly, Dragon, Defensive assets: the map and the roles).
The portfolio. Two direct lessons. International equity diversification is not a refinement: it is the defense against the dominant risk of the sample, one country falling behind, yours included. And domestic nominal bonds are not the safe asset of a long horizon, because their worst enemy, sustained inflation, is the retiree's worst enemy too (Inflation-linked bonds: the only contract written in real terms, Gold in a retirement portfolio).
The essentials§
- US history is the century's winning lottery ticket: calibrate a plan on it and you inherit its optimism; the full developed world tells a harder story.
- Anarkulova-Cederburg-O'Doherty (38 countries, block bootstrap, real mortality): the rigid 4% rule fails about 17% of the time, and the rate carrying a 5% failure probability comes out near 2.3% for a domestic 60/40 couple; domestic bonds protect less than international equity diversification does.
- The criticisms (wars, Argentina, the domestic investor, correlated crises) are serious: the truth for a globally diversified investor lies between the two bounds, and nobody knows where.
- In practice: 3 to 3.5% rigid for sizing, the broad sample as a robustness label, international diversification and inflation-resistant assets as the answers to the failure modes it reveals.
- You can run this evidence on your own plan: a broad-sample model replays the JST panel (16 countries, 1870 to 2020). How it is built is spelled out in Under the hood: how the simulator computes this book.
Going further§
- Anarkulova, Cederburg, O'Doherty & Sias, "The Safe Withdrawal Rate: Evidence from a Broad Sample of Developed Markets" (2023) and Cederburg et al., "Beyond the Status Quo: A Critical Assessment of Lifecycle Investment Advice" (2023): the source papers (SSRN, free access).
- Dimson, Marsh & Staunton, Triumph of the Optimists (2002) and the Global Investment Returns Yearbook (annual, UBS): the world century in numbers.
- Wade Pfau, "An International Perspective on Safe Withdrawal Rates" (2010): the forerunner.
- Early Retirement Now on these studies, in the parts he devotes to them: the counter-case, argued (ERN's Safe Withdrawal Rate series: a reader's guide).
- Jorda, Knoll, Kuvshinov, Schularick & Taylor, "The Rate of Return on Everything, 1870-2015": the academic panel behind the broad-sample model.