Sequencing Risk

Here’s a result that surprises almost everyone. Take a set of yearly returns — say +20%, −30%, +15%, −10%, +25% — and ask: does the order you experience them in change where you end up? If you never add or withdraw money, the answer is a flat no: multiplication commutes, so the final balance is identical no matter how you shuffle them. But the instant cashflows enter — you’re withdrawing in retirement, or contributing while saving — order stops being cosmetic and becomes destiny. The same returns, met in a different order, can leave one investor wealthy and an identical one bankrupt. This is sequence-of-returns risk, and it’s the form of ruin that ambushes retirees and leveraged strategies alike.

No cashflows: order doesn’t matter

Analogy. Imagine stretching and squishing a lump of dough by a series of factors — double it, cut it to 70%, grow it 15%. The final size is the product of all the factors, and you can apply them in any order to reach the same lump. Returns compound the same way: each year multiplies your balance by $(1 + r)$, and multiplication doesn’t care about order.

Definition. With no deposits or withdrawals, an initial balance $B_0$ after returns $r_1, r_2, \dots, r_n$ becomes $B_n = B_0 \,(1 + r_1)(1 + r_2)\cdots(1 + r_n).$ Because multiplication is commutative, any permutation of the $r_i$ gives the identical $B_n$. The order is irrelevant to the endpoint.

Worked example. Start with $100,000 and earn +30%, then −30%: $100\,000 \times 1.30 \times 0.70 = 100\,000 \times 0.91 = \$91\,000.$ Reverse it — −30% then +30%: $100\,000 \times 0.70 \times 1.30 = 100\,000 \times 0.91 = \$91\,000.$ Identical. (Note in passing it’s $91k, not$100k — a +30%/−30% pair is a net loss, because the −30% hits a base inflated by the +30%. That’s the volatility drag from the Kelly/CAGR topic, a different effect from sequencing.) The point here: without cashflows, the path is irrelevant to the destination — only the multiset of returns matters.

Add cashflows and order becomes destiny

Now break the symmetry. The moment you withdraw a fixed dollar amount each year (or contribute one), the returns no longer act on the same base — they act on a base that the cashflows are constantly reshaping. And that makes order matter, violently.

Why. A fixed withdrawal is a larger fraction of a shrunken portfolio. If a crash comes early, you’re forced to sell a big chunk of your now-cheap assets to fund the withdrawal — permanently removing shares that would otherwise have ridden the recovery. The portfolio that meets its bad years late has already grown a buffer, so the same withdrawals and the same crash barely dent it. Same returns, same withdrawals — the timing of the bad years decides who survives.

Worked example — two retirees. Both start with $1,000,000, withdraw$50,000 per year, and earn the same two returns over two years: one year of −40% and one year of +40%, just in opposite order.

Retiree A — bad year first:

• Year 1: $1\,000\,000 \times 0.60 = 600\,000$, then withdraw $50k →$550,000.
• Year 2: $550\,000 \times 1.40 = 770\,000$, then withdraw $50k → **$720,000**.

Retiree B — good year first:

• Year 1: $1\,000\,000 \times 1.40 = 1\,400\,000$, then withdraw $50k →$1,350,000.
• Year 2: $1\,350\,000 \times 0.60 = 810\,000$, then withdraw $50k → **$760,000**.

Same returns, same withdrawals, $40,000 difference after just two years — and the gap compounds and widens over a full retirement. Stretch it to a 30-year horizon with a real bear market up front, and “bad years first” can mean running out of money while “bad years last” leaves a comfortable surplus. The returns were identical; only the order differed.

Retirement sequence risk: the canonical case

The most consequential real-world appearance of sequencing risk is the retirement problem, and it has a precise, well-studied character.

The setup. A retiree spends down a portfolio with fixed (often inflation-adjusted) withdrawals. Their survival depends not on the average return over retirement but on the returns in the first several years. A poor start — a bear market in years 1–5, while withdrawals continue — can be unrecoverable even if the long-run average return is perfectly healthy.

The asymmetry with the accumulation phase. Curiously, sequence risk runs backwards for a saver. During accumulation (contributing, not withdrawing), you actually want the bad years early: a market crash when your portfolio is small and your contributions are buying cheap shares is a gift; the crash you fear is one just before retirement, when the portfolio is largest. So the dangerous window is the years around retirement — late accumulation and early decumulation — when the portfolio is biggest relative to the cashflows, and a crash does the most damage.

Worked intuition. Two retirees, identical 7% average return over 30 years. Retiree X gets −15%, −10%, +5% in years 1–3 (then good years); Retiree Y gets the mirror — good years first, the −15%/−10% in years 28–30. X withdraws through the early crash on a portfolio that never built a buffer, and can deplete the account a decade early. Y withdraws through good years first, builds a huge cushion, and the late crash barely registers against a portfolio that’s already grown. Identical average return, opposite fates — decided entirely by when the bad years landed.

Managing sequencing risk

What to do

• Hold a buffer you can spend from in downturns — a cash/short-bond reserve covering 1–3 years of withdrawals lets you avoid selling risk assets at the bottom, directly defusing the early-crash trap.
• Make spending flexible. Cutting withdrawals after a bad year (variable spending rules) dramatically improves survival versus rigid fixed withdrawals.
• De-risk through the danger zone. Reducing equity exposure in the years immediately before and after retirement (a ‘rising equity glidepath’ or bond tent) shrinks the portfolio’s sensitivity to a badly timed crash.
• Stress-test with Monte Carlo across orderings — not just the average — which is exactly the tool the next lesson builds.

Pitfalls

• Planning on the average return. A plan that ‘works on average’ can fail on a bad ordering; averages hide sequence risk entirely.
• Rigid withdrawals. Fixed real spending through a downturn is the single biggest sequence-risk amplifier.
• Confusing volatility drag with sequencing. Volatility drag (the +30%/−30% net loss) happens even without cashflows; sequencing risk needs cashflows to bite. They’re different effects — don’t conflate them.

Putting it together

With no cashflows, the order of returns is irrelevant: your final balance is the product of $(1+r)$ factors, and multiplication commutes, so any permutation lands in the same place — only the multiset of returns matters. Add withdrawals or contributions and that symmetry shatters: a fixed cashflow is a bigger fraction of a shrunken portfolio, so meeting bad years early (while still withdrawing) forces selling cheap assets and permanently removes the capital that would have ridden the recovery — sequence-of-returns risk. The canonical case is retirement: survival hinges on the first several years’ returns, not the average, and a bad early sequence can deplete a portfolio whose long-run average was perfectly healthy. The risk runs backwards for savers (early crashes are gifts), so the danger zone is the transition around retirement. Manage it with a spendable buffer, flexible spending, and de-risking through the danger zone — and never confuse sequencing (needs cashflows) with volatility drag (happens regardless).

Next up — Monte Carlo ruin curves and stops — we put the whole topic together with simulation: estimating ruin probability by brute force, plotting ruin against risk-per-trade, and the stop-loss arithmetic that turns a risk budget into an exact position size.