Sequence of Returns Risk, explained.
Sequence of returns risk arises when changing the order of returns changes an outcome because money enters or leaves along the way. Withdrawals make the timing of losses consequential.
Why it happens
A withdrawal after a decline removes a larger fraction of the remaining balance. Later gains then apply to less capital. Without cash flows, reordering these fixed multiplicative factors leaves the endpoint unchanged, although the interim balances differ.
Sequence risk is the sensitivity of a portfolio with external cash flows to the order of returns. Withdrawals after early losses can leave less capital participating in later recoveries.
Read the result
Move the five cards earlier or use Put gains first. Compare your final balance with the reversed path and inspect unpaid withdrawals. Set the withdrawal to zero before comparing again to isolate the cash-flow mechanism.
A worked example
Two invented periods with a withdrawal
Start at 100, take a 30% loss, and withdraw ten: 60 remains after the first period.
A subsequent 30% gain followed by another ten-token withdrawal leaves 68.
Reverse those returns: 100 becomes 120 after the first withdrawal, then 74 after the second. The return product is the same; the withdrawal timing differs.
OPTIONAL DEEPER DETAILGo deeper: inside the model
Inside this model
Start at 100. Five fixed returns are −30%, −10%, +10%, +20%, +30%. After each return, withdraw the selected 0–20 tokens. Wealth cannot fall below zero; any unpaid withdrawal accumulates as a shortfall. A reversed path supplies the comparison.
Where this idea is useful
A practical use
Two hypothetical retirees with the same return factors can end with different balances when they both make withdrawals.
A common misconception
“Identical average returns imply identical withdrawal outcomes.”
Cash flows interact with the changing portfolio. Their timing and size matter alongside the return factors and the way an average is calculated.
What this explanation leaves out
- Five invented periods and fixed nominal withdrawals do not estimate retirement success. Inflation, longevity, taxes, and other income are omitted.
What does an unpaid withdrawal mean here?
If the balance cannot meet the requested payment, it pays what remains and records the gap. The game does not assume borrowing or secretly allow negative portfolio wealth.
Which essential expense would force you to remove funds after a decline rather than wait for an uncertain recovery?
Associated thinkers
Associations marked provisional are awaiting source review.
Further reading
Explore the original research or the teaching reference behind this experiment.