Hypothetical worked example and primary educational references; not observed market data.
Return order interacts with cash flows
When there are no external flows, multiplying the same annual growth factors in a different order produces the same endpoint. Withdrawals change that result because money leaves the portfolio between returns. Investor.gov's allocation guidance ties decisions to horizon and goals, while FINRA distinguishes financial capacity from willingness to bear risk. The sequence illustration here is independent portfolio mathematics supporting those planning concepts. It does not establish a safe withdrawal rate or predict retirement outcomes. Its narrower purpose is to show why the timing of losses can matter when investments simultaneously support spending.
Supporting references: 1. Investor.gov: Asset Allocation and Diversification
State when spending occurs
Assume a hypothetical portfolio begins with USD 100,000 and withdraws 10,000 at the end of each of two years, immediately after that year's investment return. One path earns minus 20% followed by plus 25%. The other earns plus 25% followed by minus 20%. Taxes, fees, inflation, and further flows are excluded. Naming the withdrawal timing is essential because beginning-of-year spending would produce different figures. The percentages and spending amounts are invented for a two-period demonstration. They are not expected returns, observed statistics, or recommendations for how much an investor should withdraw.
Hypothetical worked example
Identical returns in reverse order
Model setup
Read these assumptions before comparing the scenarios.
- All monetary amounts in this example are hypothetical U.S. dollars (USD), not current prices, quoted account terms or observed market data. Percentages, counts, time periods and index levels retain their stated units.
- Initial value is 100,000; 10,000 is withdrawn after each annual return.
- Two invented returns are -20% and +25%; no other flows or costs.
After second withdrawal (USD)
- -20%, +25%77,500
- +25%, -20%82,000
Expanded scale, not zero-based; dots show small differences.
- Lowest displayed value
- 77,500.00
- Highest displayed value
- 82,000.00
Hypothetical cases from the table below, in the stated units. Not market observations, a forecast or a recommended choice. Read the scenario assumptions before comparing.
| Return order | After first withdrawal (USD) | After second withdrawal (USD) |
|---|---|---|
| -20%, +25% | 70,000 | 77,500 |
| +25%, -20% | 115,000 | 82,000 |
Calculation details
- Loss-first year one
- 70,000.00 USD
((100000 * 0.80000000000000004) - 10000) - Loss-first ending
- 77,500.00 USD
((((100000 * 0.80000000000000004) - 10000) * 1.25) - 10000) - Gain-first year one
- 115,000.00 USD
((100000 * 1.25) - 10000) - Gain-first ending
- 82,000.00 USD
((((100000 * 1.25) - 10000) * 0.80000000000000004) - 10000) - Ending difference
- 4,500.00 USD
(82000 - 77500)
Follow the loss-first path
After the first 20% decline, the account is 80,000. The first 10,000 withdrawal leaves 70,000. A subsequent 25% gain raises that remaining balance to 87,500, and the second withdrawal leaves 77,500. The early loss reduces the capital available for the rebound, and spending removes additional units before the recovery period. Without any withdrawals, the same two returns would bring 100,000 back to 100,000 because 0.8 multiplied by 1.25 equals one. This isolates how cash-flow timing changes the result rather than attributing the difference to a worse overall no-flow return.
Follow the gain-first path
In the reversed path, the first 25% gain produces 125,000. After the first withdrawal, 115,000 remains. The subsequent 20% decline reduces it to 92,000, and the second withdrawal leaves 82,000. The ending balance is 4,500 higher than the loss-first path despite identical returns in reverse order and identical total withdrawals of 20,000. The comparison is deliberately short and deterministic. It shows the mechanism without assigning probabilities or implying that favorable sequences can be reliably selected. Investors cannot infer future return order from the fact that the algebra distinguishes these two constructed paths.
Different planning tools address different pressures
A liquidity reserve can reduce the immediate need to sell volatile assets, flexible spending can change withdrawals, and a suitable allocation can change exposure to losses. Each approach has costs, constraints, and uncertainties. A reserve may reduce market exposure; spending reductions may be difficult for fixed obligations; diversification does not guarantee losses disappear. Evaluate these tools against actual liabilities rather than declaring any one a complete solution. The relevant capacity question is whether the household can continue meeting essential commitments after an unfavorable sequence. The mathematical example alone cannot answer that household-specific question.
Supporting references: 2. FINRA: Know Your Risk Tolerance
Keep the conclusion within its boundaries
A two-year scenario does not establish long-term sustainability, a withdrawal threshold, or the superiority of a particular asset mix. Longer analysis would need changing spending, taxes, mortality or goal horizon, investment uncertainty, and implementation costs. Contributions can also create sequence effects during accumulation, though the direction and objective differ. Record the timing of all external flows before comparing strategies. The central lesson is that a summary return does not fully describe a spending portfolio: the path and withdrawals interact. Planning should consider that interaction while avoiding forecasts disguised as guaranteed smooth annual growth.
Test another situationChanging withdrawal timing changes the exposed capital
A separate hypothetical case. Its inputs differ from the main worked example above.
Changing withdrawal timing changes the exposed capital
Start two hypothetical accounts with USD 20,000 each. Both experience a 20% annual loss followed by a 30% annual gain and fund USD 2,000 of spending in each year. One pays at each year's beginning, the other at each year's end. At the common endpoint, beginning-year spending leaves exactly USD 80 less than end-year spending. The difference comes entirely from when money stops participating in returns. This is not a recommendation to postpone essential payments, which may have fixed dates. The model illustrates why a spending simulation must reproduce the actual cash calendar rather than use an unspecified annual withdrawal.
Test spending adjustments against actual discretion
Investor.gov ties allocation to horizon and tolerance. When extending sequence analysis, classify withdrawals by whether the household can reduce or defer them. A model allowing all spending to shrink after losses may misrepresent a household with substantial fixed obligations. A model forbidding every adjustment can miss flexibility that actually exists. Record the consequence of each proposed reduction rather than treating it as painless. Also keep a reserve's withdrawals in the household ledger even if they are outside the investment account. Moving the source of spending does not make the expenditure vanish or establish a sustainable long-term withdrawal rate.
Supporting references: 1. Investor.gov: Asset Allocation and Diversification
Check this case’s calculations
- End-year withdrawal endpoint
- 16,200.00 USD
((((20000 * 0.80000000000000004) - 2000) * 1.3) - 2000) - Beginning-year withdrawal endpoint
- 16,120.00 USD
((((20000 - 2000) * 0.80000000000000004) - 2000) * 1.3) - Endpoint difference from withdrawal timing
- 80.00 USD
(16200 - 16120)
Limits of this additional case
- The two-year deterministic paths omit inflation, costs and continuing spending, so they cannot establish retirement sustainability.
Limits of this analysis
- This two-period example does not estimate long-term withdrawal sustainability.
- Changing withdrawal timing changes the results.
- No probability, asset recommendation or safe withdrawal rate is implied.
Sources and scope
- Investor.gov: Asset Allocation and Diversification
Allocation, diversification and rebalancing address different portfolio decisions.
Scope: U.S. investor education; supports the stated mechanism, not the hypothetical scenario or a forecast.. Reference accessed 2026-10-06.
- FINRA: Know Your Risk Tolerance
Willingness to accept risk can differ from financial ability to absorb it.
Scope: U.S. investor education; supports the stated mechanism, not the hypothetical scenario or a forecast.. Reference accessed 2026-10-06.
Illustrative calculations are not forecasts or personal recommendations. Editorial standards
