Tools · Sequence of returns
The order only matters when money moves.
Compound the same returns in any order and the result is identical. Start withdrawing, and the order becomes one of the largest factors in the outcome. This shows the size of that difference for a series and a withdrawal you choose.
Calculator
This page is showing a worked example. The figures below use 8 annual returns, a starting balance of 100 and a withdrawal of 5 a year. Enable JavaScript to enter your own; the table, chart and method on this page do not need it.
Read as per cent if any value carries a % sign or exceeds 1 in size, and as decimal fractions otherwise. At least two years are needed.
- As entered
- 91.1
- ending balance
- Reversed
- 103.3
- same returns, opposite order
- No withdrawal
- 145.5
- identical in either order
Both lines use exactly the same set of returns. The only difference is which years come first, and whether the early years fall while money is being taken out.
Year by year
Where the two paths separate.
The worked example: 8 years, starting at 100, withdrawing 5 at the end of each year after the return is applied.
| Year | Return | Balance | Reversed | Balance | No withdrawal |
|---|---|---|---|---|---|
| 1 | −20.0% | 75.0 | +6.0% | 101.0 | 80.0 |
| 2 | +15.0% | 81.2 | +12.0% | 108.1 | 92.0 |
| 3 | +10.0% | 84.4 | +8.0% | 111.8 | 101.2 |
| 4 | −5.0% | 75.2 | +18.0% | 126.9 | 96.1 |
| 5 | +18.0% | 83.7 | −5.0% | 115.5 | 113.4 |
| 6 | +8.0% | 85.4 | +10.0% | 122.1 | 122.5 |
| 7 | +12.0% | 90.6 | +15.0% | 135.4 | 137.2 |
| 8 | +6.0% | 91.1 | −20.0% | 103.3 | 145.5 |
The last column is the same series with nothing withdrawn. It ends at 145.5 whichever order the returns arrive in, because multiplication does not care about order. The first two columns do care, because a withdrawal made after a fall removes units that are never bought back.
Method
Why the order matters at all.
Without flows
final = start × ∏(1 + r)
A product is commutative: rearranging the factors cannot change the answer. Any claim that the order of returns matters for a portfolio with no contributions or withdrawals is simply wrong.
With flows
vₙ = vₙ₋₁ × (1 + rₙ) − w
Now each return is applied to a balance that depends on every withdrawal before it. A withdrawal after a fall takes a larger share of what remains, and that share cannot participate in the recovery. The same logic runs in reverse for contributions, which benefit from early falls.
Limits
What this leaves out.
- The withdrawal is fixed and nominal. It does not rise with inflation and does not adjust when the balance falls. A withdrawal that flexes with the balance changes the outcome substantially, and is one of the standard responses to this problem.
- Timing within the year. The withdrawal is taken at the end of each year, after the return. Taking it at the start, or monthly, gives different numbers.
- Costs and tax are not modelled. The returns you enter are treated as the returns actually received.
- Reversing is an illustration, not a forecast. It is the clearest way to show the size of the effect using the same numbers. It is not a claim about which order is more likely.
- The balance stops at zero. If withdrawals exhaust the balance the path ends there rather than going negative, so a depleted path and a nearly depleted path can look similar at the end.
This calculator is provided for general information only and is directed to wholesale and professional investors. It is not personal advice: it does not take into account the objectives, financial situation or needs of any person, and it is not an offer, invitation or recommendation to acquire any financial product. Investing involves risk, including the possible loss of capital. Past performance is not a reliable indicator of future performance.
Definitions
Terms on this page.
Each links to the glossary entry, which states the convention the term assumes as well as what it means.
- Sequence of returns risk — why the order of returns matters once money is moving.
- Cumulative return — the total, which the order does not change on its own.
- Maximum drawdown — the fall that does the damage early in a withdrawal.
Questions
Common questions.
What is sequence of returns risk?
The risk that the order in which returns arrive, rather than their average, determines the outcome. It applies whenever money is being added or taken out. A run of poor years early in a withdrawal period does lasting damage, because the withdrawals take a larger share of a smaller balance and that capital is not there for the recovery.
Does the order of returns matter if I am not withdrawing?
No, not at all. With no contributions or withdrawals the final value is the product of the returns, and a product is unchanged by reordering. This is the third column in the table above.
Does it work the other way for contributions?
Yes. While money is being added, weak early years buy more units at lower prices, so a rising-later sequence helps. The effect has the same cause and the opposite sign.
What reduces sequence risk?
In general terms: smaller drawdowns, flexible rather than fixed withdrawals, and holding assets that do not all fall together. This page describes the mechanism; it is not advice about any particular arrangement, and what suits one investor will not suit another.