How we calculate retirement success

A Monte Carlo simulation builds thousands of return sequences and reports how often a portfolio survives. Ours does this by resampling contiguous multi-year blocks of real history (a block bootstrap), so every path carries the inflation regimes and recoveries that actually happened, recombined into new orders. It is forward-looking and valuation-agnostic: it does not try to read today’s market and adjust.

A historical backtest replays the actual return sequences that happened — every overlapping window in more than 150 years of Shiller data (1871 to present). Instead of resampling, it asks: across every real starting year on record, how often would this plan have lasted?

Because the Monte Carlo now resamples the same history the backtest replays, the two largely agree. The backtest uses the fixed set of real windows; the Monte Carlo recombines them into many novel sequences and reports smooth percentile bands. The comparison below shows how closely they line up.

The Monte Carlo engine resamples real annual returns from the Shiller series in contiguous multi-year blocks, so it preserves the mean reversion and inflation regimes of the real record. The long-run real return and volatility of that series are summarized below — deliberately conventional, close to the numbers most retirement researchers use for US stocks and bonds after inflation. These are also the inputs to an optional simpler “Standard” Monte Carlo (independent yearly draws) we keep available for side-by-side comparison.

The default engine preserves the order and clustering of history (a roughly 10-year average block bootstrap), so a bad decade and its recovery travel together. The optional Standard engine instead draws each year independently. The historical backtest uses no assumptions at all — it replays the real Shiller return series directly.

The standard benchmark is Wade Pfau’s 2015 update to the Trinity Study (Journal of Financial Planning). His Table 1 reports historical portfolio success rates at a 4% inflation-adjusted withdrawal over 30 years, by stock allocation. Here is our historical backtest against it — and our Monte Carlo, which now resamples the same history and lands close to both.

The solid line (our backtest) tracks the dashed line (Pfau’s historical Table 1) closely — within about 7.1 percentage points across the realistic 50–100% stock range — and the Monte Carlo line now rises with both rather than sitting flat. The small residual differences come from documented data choices: we use Shiller data back to 1871 with long-term government bonds; Pfau used 1926–2014 with intermediate-term bonds. Those differences bite hardest at the all-bond end, where the 1966–1981 inflationary destruction of bonds is a larger share of Pfau’s shorter sample.

This is not a one-time check. 66 automated tests re-run our backtest against Pfau’s table on every build, across three withdrawal rates, three horizons, and five allocations. If our numbers ever drift off the published benchmark, the tests fail before anything ships.

The Monte Carlo line rises with allocation and sits close to the backtest because both draw on the same real record. Real history has mean reversion and inflation regimes: a terrible decade tends to be followed by a recovery, and bonds can bleed real value for years at a stretch (1966–1981). By resampling contiguous blocks of history rather than rolling independent dice, our engine keeps those patterns intact — so a stock-heavy plan earns its historical edge and a bond-heavy plan carries its historical inflation risk.

An honest limit: with about 155 overlapping years of data (roughly a dozen independent decade-long blocks), the bootstrap mostly re-expresses the historical record as a smooth probability distribution — many novel paths, percentile bands — rather than adding genuinely new information beyond the backtest. We show both engines precisely so the agreement, and its source, are visible.

A simpler Standard Monte Carlo, which draws each year independently from the average return and volatility above, produces a flatter and generally more conservative curve — it manufactures more unlucky-in-a-row sequences than history ever ran. We keep it available for comparison; the Allocation Comparison tool shows the Standard engine, this regime-aware engine, and the historical backtest side by side.

Pfau’s paper has a second table — a Monte Carlo built on 2015 market conditions. That was the paper’s headline: with bond yields near zero at the time, his low-yield Monte Carlo produced far lower success rates. Our Monte Carlo does not match it, and the gap is informative.

The two agree closely at high stock and diverge sharply toward all-bonds. The reason is the bond treatment: Pfau’s Table 2 priced bonds off roughly 0% real 2015 yields, so a bond-heavy portfolio cratered. Our main engine resamples the full real bond record (1871 to present, averaging about 2% real) rather than pricing off one low-yield snapshot, so its bond-heavy survival stays higher.

That is a deliberate design choice. Our headline projection is valuation-agnostic: it uses long-run averages rather than chasing the current market, so the answer does not swing with this month’s yields. If you want a number that does condition on today’s valuations, that is exactly what the CAPE-conditioned panel in our SWR comparison tool is for.