Safe withdrawal rates and what they assume

A safe withdrawal rate is not a spending style. It is a specific rule, and the precision of the definition is what makes it testable at all.

Pick a percentage of the portfolio's value on the day the withdrawals start. Take that amount in year one. In every year after, take the same amount adjusted for inflation, whatever the portfolio has done in the meantime. Continue for a stated number of years. The rate counts as safe for that horizon if the balance never reached zero before the horizon ended.

Four assumptions are buried in that paragraph.

• The percentage is of the starting value. After year one the withdrawal has no arithmetic connection to the current balance at all.
• Spending is fixed in real terms. The rule requires the withdrawal to rise after a crash, which is the opposite of what a person would do.
• The horizon is finite and chosen in advance. Thirty years is conventional, not derived.
• Safe means did not reach zero. A plan finishing with almost nothing scores exactly the same as one finishing many times larger, and a rule reported as 95 percent safe is one that emptied the portfolio in one window out of twenty.

The practical use runs backwards. If $w$ is the initial rate, the portfolio has to be worth

$$\text{portfolio} = \frac{\text{first year spending}}{w}$$

which turns a spending figure into a target and back again.

The rate applies to the portfolio, not to total spending. Any income that arrives whatever the market does, such as a state pension or an annuity, is subtracted from spending first, and the portfolio only has to cover the gap that is left.

William Bengen, writing in the Journal of Financial Planning in 1994, took United States stock and bond returns from 1926, where the standard series begins, and ran a retirement beginning in every year. For each start he asked what initial rate, raised with inflation, the portfolio would have carried for 30 years without emptying. The worst one set the answer. He called it SAFEMAX, and for portfolios between half and three quarters stocks it landed a little above 4 percent. Cooley, Hubbard and Walz at Trinity University followed in 1998 with success rates across a grid of rates, horizons and stock weightings rather than a single worst case. Those two papers are the source of the familiar figure.

Three features of that derivation travel with the number.

• One country. The sample is the United States, among the most successful equity markets of the twentieth century, so picking it is picking a winner already known. The same rule applied to seventeen developed markets from 1900 onward put the United States near the favourable end, and in most of the others it would have exhausted a portfolio in at least one 30-year window. The usual reply is that nobody has to hold one country: a portfolio spread across world markets lifts the worst case above the worst single market, without lifting it as far as the United States result.
• One period, counted many times. Starting a 30-year window in every year from 1926 gives one retirement date for every year with 30 further years of data after it, which on a century of history is roughly seventy. Neighbouring windows share 29 of their 30 years, and a century holds three non-overlapping 30-year periods. Seventy results are not seventy pieces of evidence.
• A handful of binding years. The worst cases in the United States data are few and famous: 1929, 1937 and above all 1966, whose retiree met a decade of poor real returns and then inflation raising the required withdrawal into the hole. The number is the outcome of those years and nothing else.

Even its author moved it: Bengen's later work, over a wider set of asset classes, put his own figure above the original.

With no money going in or out, the order of returns is irrelevant. Multiplication commutes, so the same set of yearly returns in any sequence produces the same ending value. Withdrawals break that, and they break it in one direction.

A withdrawal taken from a fallen portfolio is a larger share of what remains, and the units sold to fund it are not there when the recovery arrives. Below, one unit of money meets the same five yearly returns in opposite orders, with 0.05 taken out at the start of every year and no inflation adjustment, so that the ordering is the only thing that differs.

Both portfolios started at 1.0000, both handed over 0.25 in total, and both met exactly the same five returns. Order B finishes about 14 percent ahead. Take the withdrawals away and both orders finish at 1.1730, not approximately but exactly, because multiplication does not care about order and there is nothing left for the sequence to act on.

The sign of the order effect flips while money is being paid in. A saver who meets the bad years early buys more units cheaply and finishes ahead of one who meets them late. Same market, same investor, opposite conclusion, and the thing that switches it is the direction the cash is travelling.

This is why the first decade of a drawdown carries far more weight than any later one, and why risk and return has to be read differently once withdrawals start. Sequence of returns risk works the arithmetic through in full, and the sequence of returns explorer lets you reorder a run and watch the ending balance move.

If returns were known and steady there would be no argument, because the answer would be arithmetic. The rate that exactly exhausts a portfolio earning a constant real return $r$ over $n$ years is the capital recovery factor:

$$w = \frac{r}{1 - (1+r)^{-n}}$$

Every figure in the table is that rate, written as a percent of the starting value. The formula as written takes the withdrawal at the end of each year, which is the convention that makes the last column come out at exactly the return. Taking it at the start of the year instead divides every figure by $(1+r)$: at 3 percent real over 30 years that moves 5.10 to 4.95. The convention is worth stating because a reader who assumes the other one will not reproduce the table.

Read across a row and it prices the horizon. At a 3 percent real return, 20 years supports 6.72 percent and 50 years supports 3.89. The effect is large and it flattens: each extra decade costs less than the one before, because a long horizon converges on the return itself. Nothing withdrawn forever can exceed the real return, whatever else is assumed.

Read down a column and it prices a percentage point of return, which is also what a percentage point of costs takes away, since a fee is subtracted before anything compounds. Over 30 years, going from 3 percent real to 2 percent moves the sustainable rate from 5.10 to 4.46, a cost of about 0.64 points. The same point of fee costs about 0.70 points over 50 years, and on a perpetual withdrawal it costs the full point.

Now the gap that matters, and the reason it is so often described wrongly. A steady 5 percent real return supports about 6.51 percent for 30 years, while backtests of real portfolios have produced worst-case sustainable rates well below that. Three separate things sit in the gap and they are worth keeping apart. A varying series compounds at less than the arithmetic average of its yearly returns, so a portfolio whose yearly returns average 5 percent grows at less than 5 percent before anyone withdraws anything, which is volatility drag and not sequence at all. Next, a worst case is a worst case: the window that set the number had a lower compound return than the century that contains it. Only what is left after those two is the price of not knowing the order, and it is the part a constant-return table can never show, because a constant return has no order to get wrong.

A withdrawal rate is an output, not an input. Change any of these and the number changes with it.

The allocation row is the one most often misread. Both ends of the range are bad for different reasons, so the studies tend to find a broad plateau rather than an optimum: too little stock and inflation grinds the real value of a fixed-income portfolio down over 30 years, too much and the depth of the falls does the grinding instead. Inside that plateau the rate barely moves, which means precision in the allocation buys much less than the argument about it suggests.

Tax is jurisdictional and belongs in the calculation as a rate adjustment made against local rules. In the United States, money taken from a tax-deferred account is generally taxed as income in the year it is withdrawn, while a taxable account is taxed on gains as they are realised, so the same spending figure needs a different gross withdrawal depending on where it comes from. Some systems also force a minimum withdrawal from tax-deferred accounts past a set age, which can exceed what the plan would otherwise take. Which rules apply, and at what point, is a matter of local law rather than arithmetic.

One more assumption sits underneath: that spending rises with a published inflation index every year. Studies of retiree spending in the United States find real spending typically drifting down through the middle of retirement and rising again late as health costs arrive, which is a different shape from a straight line. How much of that drift is a choice and how much is a budget running out is disputed, and the two readings point in opposite directions, so it is weaker evidence for a higher rate than it first looks. A published index is also an average across a whole population rather than a measure of any one household's costs.

The classic rule never adapts, which is exactly what makes it a hard test and a poor description of how anyone actually spends. Every alternative trades some certainty of income for some certainty of survival.

The second row is worth sitting with. Taking a fixed percentage of the current balance cannot reach zero, because each withdrawal shrinks with the portfolio. Nothing has been solved, only moved: the risk has been transferred from the portfolio to the income, and an income that falls by a third in a bad year is a real problem even though the account survives.

The last row hides the same trick. A floor is secure against the market, which is not the same as secure. An income fixed in cash terms loses purchasing power for exactly as long as it goes on being paid, so over a 30-year horizon a nominal floor is a shrinking one, and whether an inflation-linked floor can be bought at all depends on the country and on what governments and insurers are offering.

A ladder of inflation-linked government bonds changes the question rather than answering it. Buy a bond maturing in each year of a fixed horizon and the rate it supports is the capital recovery factor at the real yield you can actually buy, which is arithmetic rather than a probability. Two things are being assumed away rather than solved: the ladder stops on its last maturity, so the horizon has to be guessed exactly as before, and the real yield can be negative, in which case the arithmetic returns a rate below one divided by the number of years rather than above it. It does show why the certain answer moves with real yields, since the yield is the only input it has.

What the concept is good for is sizing and direction. It converts a spending figure into a portfolio target, and it shows which assumptions the target is resting on when it comes out of range: the length of the horizon, the cost of the investments, and whether the spending is allowed to bend. Treating any particular percentage as a settled fact asks a backtest of one country over one century to do work it cannot do. This page is educational material and not financial advice about your own money.