Sequence of Returns Risk Calculator

A sequence of returns risk calculator shows how the order in which investment returns occur can dramatically affect a retirement portfolio's longevity. It is essential for anyone in or approaching retirement who is making regular withdrawals from a portfolio. Two investors with identical average returns can end up with vastly different outcomes depending on whether poor returns happen early or late in retirement.

How to Use the Sequence of Returns Risk Calculator

1. Enter your starting portfolio value at retirement.
2. Input your planned annual withdrawal amount (in today's pounds or dollars).
3. Set an expected average annual return and a standard deviation to model volatility.
4. Choose the number of years to simulate (commonly 25 to 30 years).
5. Review the projected portfolio value across different return sequences, including best-case, worst-case, and median outcomes.

The Formula

Sequence of returns risk does not have a single formula; it is demonstrated through simulation. The key principle is that withdrawals interact with returns in an asymmetric way.

Portfolio Value (year N) = Previous Year Value multiplied by (1 plus return rate) minus annual withdrawal

When returns are negative early in retirement, withdrawals force you to sell assets at depressed prices, locking in losses and leaving fewer shares to benefit from future recovery. This is the sequence of returns problem.

A Monte Carlo simulation runs hundreds or thousands of return sequences drawn from a probability distribution to estimate the likelihood that a given withdrawal strategy survives the full retirement period.

Real-World Example

Two retirees each start with £500,000 and withdraw £25,000 per year. Over 10 years, both experience the same average return of 5% per year, but in opposite order.

Retiree A experiences: minus 20%, minus 15%, 8%, 10%, 12%, 15%, 10%, 10%, 8%, 7%. Retiree B experiences: 7%, 8%, 10%, 10%, 15%, 12%, 10%, 8%, minus 15%, minus 20%.

Retiree A, who faces poor returns early, may exhaust the portfolio within 20 years. Retiree B, who faces the same poor returns but later, preserves far more wealth because the portfolio had years of growth before the losses hit.

After 10 years, the difference in portfolio values can exceed £100,000 even though the average return is identical. This illustrates why sequence risk is most damaging in the first decade of retirement.

Protecting Against Sequence of Returns Risk

Several strategies can reduce the impact of poor early returns.

A cash buffer or bucket strategy involves holding one to three years of living expenses in cash or short-term bonds. This allows you to avoid selling equities during a downturn, giving the portfolio time to recover.

A flexible withdrawal strategy means reducing withdrawals in years when the portfolio has fallen significantly. Even cutting spending by 10% to 15% in a bad year can extend portfolio longevity by several years.

The glide path approach involves gradually reducing equity exposure as retirement approaches and in early retirement, reducing the impact of a market crash on the portfolio balance.

Annuitising a portion of retirement income through a guaranteed product removes some of the sequence risk by providing income that does not depend on portfolio performance.

Frequently Asked Questions

How is sequence of returns risk different from average return risk? Average return risk is simply the risk that your long-run returns are lower than expected. Sequence of returns risk is specifically about the timing of those returns. You can achieve your target average return and still run out of money if negative returns happen early in retirement when the portfolio is largest and withdrawals begin.

Does sequence of returns risk affect the accumulation phase? During accumulation, sequence of returns risk works in your favour. Poor returns early in saving mean you are buying units cheaply, and when markets recover you benefit from pound-cost averaging. The risk reverses at retirement because you switch from buying to selling.

What withdrawal rate best protects against sequence risk? The widely cited 4% rule was designed with sequence of returns risk in mind, based on historical US market data. However, starting at a lower rate (3% to 3.5%) provides greater protection, particularly in the current lower-yield environment. Flexibility to adjust withdrawals based on portfolio performance is also valuable.

Can diversification reduce sequence of returns risk? Diversification across asset classes reduces portfolio volatility, which indirectly reduces sequence risk. A less volatile portfolio experiences smaller drawdowns, meaning withdrawals have a lesser impact during downturns. Adding bonds, property, or other assets with low correlation to equities helps smooth the return sequence.

The two retirees, numbered

The example above asserts that the two orderings diverge. Working the arithmetic year by year shows how far, and where the damage happens.

Both retirees start with 500,000 and withdraw 25,000 at the end of each year. The returns are the two orderings given above. Retiree A meets the losses first, then the gains. Retiree B meets the same returns in reverse order.

After ten years the gap is 137,812.79, and it is widest in year 8 at 433,695.74. Both figures come from the same ten returns in a different order, so the whole difference is timing.

Retiree A ends the decade with less than the starting balance, having taken out 250,000 and gained nothing net. Retiree B ends with 484,181.84, which is barely below the start despite the same 250,000 of withdrawals. The ordering, not the average, produced the difference.

One correction belongs with this table. The sequence above has an arithmetic mean of 4.5% a year, not the 5% stated in the example. Adding the ten figures gives 45, and 45 divided by 10 is 4.5. The geometric mean of the same sequence is 3.82%. The table above uses the printed returns exactly as they stand, so a reader reproducing it will get the figures in the rows.

The rise a fall has to recover

Losses and gains are not symmetric, and the arithmetic behind that asymmetry is short. A portfolio that falls from 100 to 90 needs a rise of 11.11% to get back to 100, not 10%: the gain applies to the smaller balance.

The formula is one divided by one minus the fall, minus one. A 20% fall needs 1 divided by 0.8, which is 1.25, minus 1, which is 0.25. A 50% fall needs a doubling to recover.

What a percentage withdrawal changes

The fixed withdrawal is where the sequence damage enters. A withdrawal of 25,000 from a 500,000 portfolio is 5% at the start. After the first year the portfolio has fallen to 400,000 before the withdrawal, and the same 25,000 is 6.25% of it. After the second year it is 7.84%, then 7.88%, 7.78% and 7.53% in the years that follow.

The withdrawal rate drifts upward exactly when the portfolio can least afford it, because a fixed money amount divided by a shrinking balance is a rising percentage. That is the mechanism the cash buffer and the flexible withdrawal strategies above are designed to break.

A percentage rule removes the drift by construction. Withdrawing 5% of the balance in the first year takes 20,000 rather than 25,000 from a portfolio that has fallen to 400,000, which leaves more capital invested for the recovery. The cost is that the income moves with the market, and a retiree whose spending is fixed cannot absorb a 20% cut in income in a bad year. Most practical plans combine the two, with a cash buffer covering the years when a percentage rule would cut too far.

What a sequence simulation assumes

The projection above holds several things still, and each assumption is a way the real outcome can differ.

Returns arrive in annual steps and withdrawals happen at the end of the year. A withdrawal taken at the start of each year is worse for the portfolio in every bad year, because the money leaves before the loss applies. No fees, no taxes and no fund charges appear, and a charge of 0.5% a year compounds into a material figure over a thirty-year retirement. Inflation does not appear either, so the 25,000 withdrawal keeps its face value while its purchasing power falls.

A Monte Carlo run adds a distribution rather than a sequence, and the assumptions move into the distribution itself. The choice of average return, the volatility, and whether returns are drawn independently all change the survival figure. Real returns show some persistence rather than independence, and ignoring that makes a simulation understate the run of bad years that does the damage.

The output to act on is a range and a failure rate, not a single balance. A plan that survives 90% of simulated sequences still fails in one sequence out of ten, and the retiree lives one sequence rather than a thousand. That is the reason the strategies above are about reducing the size of the bet rather than about finding the withdrawal rate that never fails.

The same decade at a four percent withdrawal

The 4% rule sets a starting withdrawal of 4% of the portfolio, which is 20,000 on 500,000. Run the same unlucky sequence against that withdrawal and the decade looks different.

The five thousand a year difference is worth 76,216.52 after ten years. The 20,000 rule never falls below 300,000 across the decade, while the 25,000 rule spends three years below that line. The 20,000 rule also takes 50,000 less out of the portfolio, so part of the gap is money the retiree kept rather than money the portfolio earned.

That is the trade the 4% rule makes. A lower starting rate buys a wider margin against a bad sequence, and it costs income every year the sequence turns out to be kind.

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