← The collection

Sequence of Returns Risk.

Move the crash year and try to fund the same withdrawals.

Interactive experimentintuitiveField note ·
Preparing the experiment…
THE SHORT VERSION

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.

01 / THE MECHANISM

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.

02 / FOLLOW IT THROUGH

A worked example

Two invented periods with a withdrawal

  1. Start at 100, take a 30% loss, and withdraw ten: 60 remains after the first period.

  2. A subsequent 30% gain followed by another ten-token withdrawal leaves 68.

  3. 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.

03 / BEYOND THE EXPERIMENT

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.

CHECK YOUR INTUITION

A common misconception

THE TEMPTING CONCLUSION

“Identical average returns imply identical withdrawal outcomes.”

THE MORE USEFUL DISTINCTION

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.
ONE MORE QUESTION

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.

TAKE THE IDEA WITH YOU

Which essential expense would force you to remove funds after a decline rather than wait for an uncertain recovery?

Associated thinkers

Associated withWilliam Sharpe ↗

Associations marked provisional are awaiting source review.

Further reading

Explore the original research or the teaching reference behind this experiment.