Sequence of returns risk

2026-11-03

With a fixed balance and no flows, the order of returns does not matter — multiplication commutes. The moment money is being added or withdrawn, order matters a great deal, and an average return stops describing the outcome.

This is why a projection built from an average return is not the average of the projections, and why “my strategy returns 2% a month” is an incomplete description of what happens to an account.

When order does not matter

Start with 10,000 and no contributions. Returns of +20%, −10%, +5%, in any order:

10,000 × 1.20 × 0.90 × 1.05 = 11,340
10,000 × 0.90 × 1.05 × 1.20 = 11,340
10,000 × 1.05 × 1.20 × 0.90 = 11,340

Identical, because multiplication is commutative. Every ordering is the same product.

So for a buy-and-hold balance with no flows, sequence genuinely is irrelevant. This is the case most compounding intuition is built on, and it is the case that does not describe an account you are trading.

When order matters

Add a contribution of 1,000 at the end of each period. Now the same returns produce different results, because each contribution experiences only the periods after it arrives:

Good returns first (+20%, −10%, +5%):

10,000 × 1.20 = 12,000 + 1,000 = 13,000
13,000 × 0.90 = 11,700 + 1,000 = 12,700
12,700 × 1.05 = 13,335 + 1,000 = 14,335

Bad returns first (−10%, +5%, +20%):

10,000 × 0.90 =  9,000 + 1,000 = 10,000
10,000 × 1.05 = 10,500 + 1,000 = 11,500
11,500 × 1.20 = 13,800 + 1,000 = 14,800

14,335 versus 14,800 — same returns, same contributions, a 465 difference from ordering alone.

Here the bad-first ordering wins, because contributions bought in after the decline and participated in the recovery. That is the general rule while you are adding: poor early returns affect a smaller balance, and later contributions benefit from the eventual gains.

Withdrawals reverse it. Taking money out during an early decline realises the loss and removes capital that would have participated in the recovery. For an account being drawn down, bad returns early are considerably worse than bad returns late — the same set of returns, a materially different outcome.

Why averages mislead

The compounding calculator applies a constant rate, which is the cleanest possible model and removes sequence entirely. That is useful for seeing the shape of the curve, and it is exactly what makes it a model rather than a projection.

Two specific ways an average return overstates what you get:

Volatility drag. A sequence averaging zero ends below where it started, because losses and the gains that undo them are not symmetric — as the drawdown recovery calculator shows. A +10%/−10% pair leaves 99%. The arithmetic mean says zero; the realised result is negative, and the gap widens with the size of the swings.

The average is not the experience. An account that averages 2% a month via a +15% month and several −1% months is a different thing to live with than one that returns 2% every month, even though the arithmetic mean matches.

What this implies

For an account you are adding to: early volatility is tolerable and can even help, provided you keep contributing through it. The failure is stopping — a contribution schedule abandoned during a decline converts the favourable ordering into the unfavourable one. This is the mechanical argument for DCA as a rule rather than an intention.

For an account you are drawing from: early losses are disproportionately damaging and cannot be averaged away. The protection is having a smaller drawdown, not a higher average return.

For trading accounts generally: the sequence you actually get is unknown, so the robust move is to reduce the size of the bad periods rather than to improve the average. That is what a daily loss limit does, and it is why the limit is worth more than the losses it prevents.

The connection to sizing

Risk of ruin is sequence risk in its harshest form: a losing streak arriving early, at a size the account cannot absorb, ends the sequence before the edge has a chance to express itself.

The same set of trades in a different order might have been fine. You do not get to choose the order, which is why the term you control is the risk fraction — and why it does more work than any improvement in win rate.

FAQ

What is sequence of returns risk?

The risk that the order in which returns arrive changes your outcome, even when the set of returns is identical. It has no effect on a static balance, since multiplication commutes, but it matters as soon as money is being contributed or withdrawn — because each flow only experiences the periods after it happens.

Does the order of returns matter if I am not adding or withdrawing money?

No. With no flows, any ordering of the same returns produces the same ending balance. What still applies is volatility drag: a sequence averaging zero ends below where it started, because a loss and the gain that undoes it are not the same size. That is a separate effect from sequence risk.

Is early volatility good or bad?

It depends on the direction of your cash flows. While contributing, early declines mean later contributions buy in lower and participate in the recovery, which tends to help. While withdrawing, early declines realise losses and remove capital that would have recovered, which hurts. Same returns, opposite conclusion.

Why does a constant-rate calculator overstate my likely result?

Because it removes both sequence and volatility drag. A real series with the same arithmetic mean compounds to less than a constant series at that mean, and the gap grows with the size of the swings. Use a constant-rate projection to understand the shape of compounding, not to predict a balance.