Why does the order of returns matter when money is withdrawn?

State the withdrawal rule first

Use two invented one-year returns, −20% and +20%, an opening $10,000, and a $1,000 withdrawal at each year-end after the return is applied. There are no fees, tax, other cash flows, or changes to the withdrawal amount. Each case uses exactly the same timing rule.

CFA Institute’s wealth-preservation reading identifies adverse early returns during withdrawals as a sequence-risk concern. This worksheet illustrates the mechanics in two years. It does not estimate a sustainable retirement withdrawal rate, longevity, or a probability of running out of money.

Case A: the loss occurs first

After Year 1’s −20%, $10,000 becomes $8,000. The first $1,000 withdrawal leaves $7,000. Apply Year 2’s +20% to that remaining balance: it becomes $8,400. The second $1,000 withdrawal leaves $7,400.

The ledger therefore records $2,000 withdrawn over the two years and $7,400 still invested at the end. The withdrawals are external cash flows, not additional negative investment returns. Keep them in separate columns.

Case B: the gain occurs first

Apply +20% first. The $10,000 becomes $12,000; after the first $1,000 withdrawal, $11,000 remains. A subsequent −20% reduces it to $8,800, and the second $1,000 withdrawal leaves $7,800.

Both cases withdrew the same total and experienced the same two percentage returns, but Case B finishes $400 higher. The difference comes from applying the later return to different balances after the first withdrawal. It is not evidence that either sequence is more likely.

Compare a no-withdrawal control

Without withdrawals, both orders produce $10,000 × 0.80 × 1.20 = $9,600. Multiplying the two growth factors is order-independent in that simple case. The interposed fixed dollar withdrawals create the difference in the other two ledgers.

Changing the timing to beginning-of-year withdrawals, changing the amounts, or making withdrawals a percentage of the current balance would define a different exercise. Do not carry the $400 result into those cases without recalculating. Likewise, this example does not say that every possible withdrawal rule has the same sensitivity.

For each row, check the identity: closing balance equals opening balance multiplied by its growth factor, minus the end-period withdrawal. If a proposed withdrawal exceeds the available amount, mark the scenario’s funding gap rather than silently allowing an unmodelled loan. That would change the cash-flow problem being studied.

Method, sources, and limits

The original ledgers were checked with decimal arithmetic. CFA Institute’s source was opened on 26 October 2026. No historical returns, customer spending, inflation assumptions, or retirement projection were used. The two-year example explains why cash-flow dates belong in a plan; it does not recommend a spending amount or an investment mix. Any real assessment would need a longer, explicit set of assumptions and the person’s actual obligations.