Sequence-of-Returns Risk: When the Same Returns Produce Different Outcomes
Suppose three annual returns are +30%, −20% and +10%. Does rearranging them change the ending balance? It depends. Sometimes order is irrelevant; in other circumstances it determines the outcome. This guide explains the boundary.
First: Without cash flows, order does not change the product
If money remains invested without deposits or withdrawals, reordering identical percentage returns leaves the ending balance unchanged. Multiplication is commutative.
+30% → −20% → +10%:
13,000 → 10,400 → $11,440.
−20% → +10% → +30%:
8,000 → 8,800 → $11,440.
+10% → +30% → −20%:
11,000 → 14,300 → $11,440.
1.30 × 0.80 × 1.10 = 1.144.
The order does not change this product.
This is a basic property of compounding. “Order matters” is therefore not universally true. It matters when cash moves during the path, a threshold interrupts the account, or behavior changes. Consider four conditions.
Condition 1: Fixed withdrawals
Keep the same +30%, −20% and +10% returns, but withdraw $1,000 at each year-end.
Good years first: +30% → +10% → −20%.
13,000−1,000 = 12,000.
13,200−1,000 = 12,200.
9,760−1,000 = $8,760.
Middle ordering: +30% → −20% → +10%.
13,000−1,000 = 12,000.
9,600−1,000 = 8,600.
9,460−1,000 = $8,460.
Bad year first: −20% → +10% → +30%.
8,000−1,000 = 7,000.
7,700−1,000 = 6,700.
8,710−1,000 = $7,710.
Identical returns and withdrawals;
a $1,050 difference.
The withdrawal is a different fraction of the remaining balance each time. $1,000 is 14.3% of $7,000 but 8.3% of $12,000. Early losses force a larger proportional withdrawal from a smaller account, leaving less principal for later recovery.
The same structure affects trading accounts that fund fixed monthly living expenses. Identical performance can leave different balances depending on whether drawdown arrives early.
Condition 2: Fixed contributions reverse the comparison
When money is being added, the comparison reverses in this example. The bad year first is more favorable, allowing later contributions to participate in recovery.
Good year first: +30% → −20% → +10%.
13,000+1,000 = 14,000.
11,200+1,000 = 12,200.
13,420+1,000 = $14,420.
Bad year first: −20% → +10% → +30%.
8,000+1,000 = 9,000.
9,900+1,000 = 10,900.
14,170+1,000 = $15,170.
Early decline is $750 more favorable in this contribution example.
Early declines can help during accumulation and hurt during withdrawal, given the illustrated subsequent returns. This calculation explains part of how dollar-cost averaging behaves during declines. Identify which phase your account is in before interpreting sequence risk.
Condition 3: A threshold ends the account
The most severe case occurs when early losses exhaust the account, so later winning trades cannot be taken, despite identical nominal win and loss counts.
Losses first: LLLLWWWW.
7,500 → 5,000 → 2,500 → 0.
Account exhausted; four remaining wins cannot execute.
Ending balance: $0.
Alternating: WLWLWLWL.
12,500 → 10,000 → 12,500 → 10,000 …
Ending balance: $10,000.
Identical nominal counts and stakes;
order alone determines exhaustion.
With leverage, liquidation can create this stopping boundary. Once liquidation occurs, later hypothetical statistics cannot restore the position. See risk of ruin and volatility drag for the relationship between exposure and growth.
Under a simplified model, staking a fixed percentage removes this particular zero-balance mechanism. Losing 2% of the remaining balance repeatedly never reaches exactly zero, and identical proportional outcomes have the same product regardless of order. Actual execution constraints are addressed below. See position sizing.
Condition 4: A person changes the rules midway
The first three conditions are mathematical; behavioral changes are common in practice. Early losses can prompt larger recovery bets or fear-driven skipping of valid signals.
Then the premise of continuing the same strategy at the same size breaks, separating the live account from its backtest. Early losing streaks can reflect sequence rather than skill. Misinterpreting them and changing rules introduces another source of loss. This motivates pre-established boundaries such as a daily loss limit.
Proportional withdrawals remove ending-balance dependence in this model
Replace fixed withdrawals with a fixed percentage of the balance: 10% at each year-end.
Ending balance = 10,000 × 1.30 × 0.80 × 1.10 × 0.9³.
= 11,440 × 0.729.
The original guide reports $8,339.8 for this product.
Its reported result is the same for:
+30% → −20% → +10%;
−20% → +10% → +30%;
+10% → +30% → −20%.
Fixed withdrawals: $7,710–$8,760, a $1,050 range.
Proportional withdrawals: the same product in every order.
Withdrawal becomes multiplication by 0.9, leaving a product of factors. The tradeoff is that the amount available to spend varies each year. If the first year loses 20%, its withdrawal falls to $800. Ending-balance sequence dependence is exchanged for fluctuating withdrawals.
A hybrid approach keeps ordinary withdrawals fixed but reduces them in years when the balance falls below a threshold. It is less mathematically clean than pure proportional withdrawals, but reduces principal depletion during early losses.
Checking whether favorable sequencing helped your record
If trade records exist, replay reordered outcomes. The actual path is just one possible sequence.
1. Export the original percentage return of each trade.
2. Shuffle the order and replay 1,000 times.
3. Examine the distribution of ending balances and maximum drawdowns.
Check:
Does an adverse path reach a liquidation boundary?
Where does the actual path sit?
The guide treats a top-5% placement as evidence of unusually favorable sequencing.
This is a form of Monte Carlo simulation. Averages can remain similar, while maximum drawdown and boundary crossings vary substantially. The adverse tail matters more than the average for survival.
Several simultaneous assets can concentrate sequence risk because correlated assets suffer bad periods together. See correlation and diversification traps for why asset count is less informative than actual co-movement.
Five practical checks
① Identify whether the account is accumulating or withdrawing. Early losses affect these phases differently under the illustrated return paths.
② Consider proportional rather than fixed-dollar stakes. The exact exhaustion mechanism in condition 3 depends on fixed stakes under its simplified assumptions.
③ Consider balance-based withdrawals. Reducing withdrawals after losses can reduce this form of sequence risk.
④ Do not judge skill from an early losing streak alone. Small samples can be dominated by ordering. Evaluate after a preselected observation count; a trading journal is necessary to make that assessment.
⑤ Examine sequence distributions as well as win rate. Identical win rates and payoff ratios can produce different minimum balances. Size exposure with account survivability in mind.
Three key points
① Without intervening cash flows or stopping conditions, reordering identical percentage returns leaves the final product unchanged. Cash flows and stopping boundaries make order matter.
② Early declines hurt the withdrawal example and help the contribution example. With fixed-dollar stakes, four wins and four losses can exhaust an account solely because of ordering.
③ Proportional withdrawals and stakes leave multiplicative factors, removing this ending-balance dependence in the simplified model. Avoiding hasty skill judgments after early losses addresses the behavioral version.
Caution
Returns, withdrawals, stakes and balances are hypothetical calculations, not measured strategy or exchange results. Fees, slippage, funding and tax are omitted, so actual results can be worse. The theoretical claim that fractional stakes never reach zero assumes no minimum order sizes, liquidation or price gaps; live trading may violate those assumptions. Leverage can lose all principal. Decisions and responsibility remain with the investor.
NOONOO TRADING invites you to follow live trading in our free chat.
Start in the bot📈 OKX trading fee discount for new registrations
Register for the OKX Fee Discount →