Sequence-of-returns risk: why the order of returns matters and the vulnerable first decade
See with identical returns in different orders how withdrawals turn the order of returns into a decisive risk, and learn how to measure your exposure in the first years.
What you will learn
- Why the order of yearly returns is irrelevant without withdrawals but decisive with them.
- How to run a simple sequence simulation on paper with two orders of the same returns.
- Why the first five to ten years of retirement carry most of the risk.
- Which gauge, the current withdrawal rate, tells you early whether a plan is drifting into danger.
Explanation
Sequence-of-returns risk is the risk that poor returns occur early in a period of regular withdrawals. Compound growth was covered in the course ETFs, Funds & Long-Term Investing; here we add withdrawals.
Without cash flows, multiplication is commutative: −20 percent then +25 percent ends where +25 percent then −20 percent ends (0.8 × 1.25 = 1.0). With withdrawals the order matters, because each withdrawal is taken from a different base. If you sell €40,000 after a 20 percent fall, you sell more units at low prices, and those units never recover for you. The final value with yearly withdrawal W and returns r1 … rn is
V = (((P − W)(1 + r1) − W)(1 + r2) − W) …
and the early returns multiply the largest number of later terms.
In the saving phase the effect is mirrored: early losses are harmless because contributions buy cheaply, while a crash in the last years before retirement is damaging. The years from about five before to ten after the retirement date are therefore called the retirement risk zone. After the first decade a portfolio that has grown is far less sensitive to a bad year, because the withdrawal has become a smaller share of it.
The practical gauge is the current withdrawal rate: this year's withdrawal divided by the current portfolio value. A plan that starts at 4 percent and climbs to 6 or 7 percent in the first years is in danger, even if the 30-year average return turns out fine. Dynamic rules (lesson 4), cash buckets (lesson 5), a rising equity glide path (lesson 11) and flexibility levers (lesson 12) all address this one problem. Remember that a diversified portfolio has fallen by 50 percent in past crises; a plan must survive that in year one.
Worked example
Hypothetical example: ten yearly returns, −20, −10, +3, +6, +8, +10, +12, +15, +20 and +25 percent. Their arithmetic mean is 6.9 percent and their geometric mean about 6.1 percent per year. Starting portfolio €1,000,000, withdrawal €40,000 at the start of every year, no inflation adjustment, no fees or taxes.
No withdrawals: in any order the portfolio ends at €1,000,000 × 1.8043 = €1,804,260.
Order A, worst years first: year 1: (1,000,000 − 40,000) × 0.80 = €768,000. Year 2: (768,000 − 40,000) × 0.90 = €655,200. Year 3: 615,200 × 1.03 = €633,656. Year 4: 593,656 × 1.06 = €629,275. Continuing with +8, +10, +12, +15, +20 and +25 percent gives €636,417; €656,059; €689,986; €747,484; €848,981; and finally €1,011,226.
Order B, best years first: year 1: 960,000 × 1.25 = €1,200,000. Year 2: 1,160,000 × 1.20 = €1,392,000. Year 3: 1,352,000 × 1.15 = €1,554,800. Continuing with +12, +10, +8, +6, +3, −10 and −20 percent gives €1,696,576; €1,822,234; €1,924,812; €1,997,901; €2,016,638; €1,778,974; and finally €1,391,179.
| Order A (bad first) | Order B (good first) | |
|---|---|---|
| Total withdrawn | €400,000 | €400,000 |
| Lowest value | €629,275 (year 4) | €1,000,000 (start) |
| Highest current withdrawal rate | 40,000 / 629,275 = 6.4 % | about 4 % |
| Value after 10 years | €1,011,226 | €1,391,179 |
Same returns, same average, same total withdrawals: a difference of €379,953, about 38 percent of the starting capital. In order A the retiree watched the portfolio lose 37 percent while spending 4 percent a year and had to hold on through year 4 at a 6.4 percent current rate. With inflation-adjusted withdrawals and a 40-year horizon, order A would be close to failure. Excluded: fees, taxes and inflation, each of which makes the bad sequence worse.
Common mistake
Practice activity
On paper: portfolio €500,000, withdrawal €20,000 at the start of each year, three yearly returns of −30, +10 and +20 percent. (a) Compute the ending value for the order −30, +10, +20 and for the order +20, +10, −30. (b) What is the ending value in both cases without withdrawals? (c) What is the highest current withdrawal rate in the bad order?
Show solution
(a) Bad first: (500,000 − 20,000) × 0.70 = 336,000; (336,000 − 20,000) × 1.10 = 347,600; (347,600 − 20,000) × 1.20 = €393,120. Good first: 480,000 × 1.20 = 576,000; 556,000 × 1.10 = 611,600; 591,600 × 0.70 = €414,120. Difference €21,000. (b) Without withdrawals: 500,000 × 0.7 × 1.1 × 1.2 = €462,000 in both orders. (c) Year 2 withdrawal €20,000 against €336,000 = 6.0 percent (the starting rate was 4.0 percent).
Limitations: three years and fixed withdrawals; a real plan would raise withdrawals with inflation and run for decades, which magnifies the gap.
Key takeaways
- Order of returns is irrelevant without cash flows and decisive with regular withdrawals.
- Early losses force you to sell more units at low prices; those units never recover for you.
- The first decade after retirement is the vulnerable period; afterwards sensitivity falls.
- Track the current withdrawal rate; a climb from 4 to above 6 percent is an early warning.
Next step
Lesson 4 compares the dynamic withdrawal rules, guardrails, percentage-of-portfolio, floor-and-ceiling and CAPE-based rates, that are designed to answer a bad sequence.
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