First remove cash flows
Let initial capital be 100 notional units. Returns over two periods are minus 20% and plus 20%. With no contributions or withdrawals, the ending amount is 96 regardless of order: 100 × 0.8 × 1.2. The arithmetic average of the returns is zero, but the result is negative because the base changes.
This already shows the limit of a simple average. However, without external flows, the order of the same multipliers does not by itself change the final value. Do not explain a difference through nonexistent “sequence magic” when the problem contains neither cash flows nor other differing conditions.
Add the same withdrawal at the end of each period
Now withdraw 10 units after each year’s result. In the first path, the initial decline reduces capital to 80; after the withdrawal, 70 remains. Twenty-percent growth produces 84, and the second withdrawal leaves 74. Total spending received is 20 and the ending portfolio is 74.
In the second path, growth occurs first: 100 becomes 120; after the withdrawal, 110 remains. The decline of 20% then gives 88, and after the second withdrawal, 78 remains. The payments and returns are identical, but the ending balance differs by 4 units. A positive period before the withdrawal allowed more capital to participate in the next stage.
Payment timing changes the formula
The example withdraws after each period’s return is applied. If the withdrawal occurs at the beginning, subtract the expense first and then apply the value change. Monthly flows also require a new calendar. Do not use year-end timing for one scenario and beginning-of-year timing for another, then attribute the difference to strategy.
An indexed expense adds another dependency: the nominal payment can increase independently of market performance. A fixed percentage of the current balance, by contrast, changes the amount consumed. These are different problems, and comparing only ending capital without the payments actually received is incomplete.
What follows from the example, and what does not
It does not establish a sustainable withdrawal rate or give a probability of exhausting capital. Such an analysis requires the spending horizon, inflation, fees, taxes, portfolio composition and a model of future outcomes. A few successful historical paths do not cover all possible sequences. The SEC warns that hypothetical and past performance do not predict the future.[27](#source-market-performance)
Nor can one promise that extending the horizon will necessarily repair an adverse start. Withdrawn money no longer participates in recovery, and a particular asset may never regain its previous price. If the model allows spending to be deferred, show that as a change in the obligation, not as a hidden correction of a poor result.
The practical educational conclusion is to test several event orders with identical cash-flow rules and preserve consumption amounts separately. The final table should include the minimum balance, completed payments and cases where the goal was breached. This connects returns with the life calendar of capital but does not provide a personal retirement plan or guarantee that a selected portfolio will last for a given period.
Contributions create a different problem
With regular contributions, return order also interacts with when money arrives. Do not automatically transfer conclusions about withdrawals to the accumulation phase: capital is present in each period to a different extent. Preserve the contribution calendar and compare the instrument’s result with the owner’s cash-flow result separately.
If a researcher changes spending after a bad year, that may be an acceptable rule, but the comparison must include the smaller amount actually consumed. A higher ending balance does not necessarily mean better goal achievement when some obligations were simply not met. Show actual payments and deferrals for each sequence.
In an educational check, preserve not only the end of the horizon but also the lowest available balance before a payment. An intrapath breach may matter more than later recovery. This prevents a scenario from being declared successful merely because its final amount looks good while required spending was unavailable on time.
Related foundations
[Portfolio risk: losses, timing and joint asset movements](/guides/portfolio-risk/); [Dividends and total return: do not separate a payment from price](/guides/dividends-total-return/).