compoundsimSequence of Returns Risk: Why an Early Crash Hurts Retirement
The same market crash costs far more early in retirement than ten years in. A Monte Carlo simulation of sequence of returns risk shows how much.
Published
The same market crash costs far more early in retirement than ten years in. A Monte Carlo simulation of sequence of returns risk shows how much.
Published
Sequence of returns risk (or sequence risk) is the risk that the order of good and bad years changes your result even when the average return is the same. While you are drawing money down in retirement, the earlier a market crash comes, the more it takes. In a simulation that withdraws 4% a year from a 60/40 mix of stocks and bonds, the same crash left a median balance after 20 years of 63% of the starting sum when it struck right at retirement, and 98% when it struck ten years in. Only the timing of the crash differed.
We ran 1,000 paths the way the withdrawal simulator does, with these settings:
Each path draws its monthly returns from the model fitted to the full history. We then put the same crash into every path: the portfolio falls 30% (in nominal terms, before inflation) over 12 months. It goes in at one of two points, right at retirement (year 1) or ten years in (year 11). Apart from the crash, both cases use the same months in the same order.
| Balance after 20 years (start = 100%) | 10th percentile | Median | 90th percentile | Money lasted 20 years |
|---|---|---|---|---|
| No crash added (for reference) | 60% | 179% | 415% | 99.4% |
| Crash at retirement | 4% | 63% | 177% | 91.4% |
| Crash ten years in | 25% | 98% | 242% | 98.0% |
At the median, the same crash left 63% of the starting balance after 20 years when it came at retirement, and 98% when it came ten years in. In the worst tenth of the paths (the 10th percentile) it was 4% against 25%: several times as much was left after the later crash. The share of paths whose money lasted is lower for the early crash too.
The shaded band is where the middle 80% of the 1,000 paths fall (the 10th to 90th percentile). With the same crash, what happens afterwards in the market still spreads the balance after 20 years widely. In the top panel, with the crash at retirement, the bottom of the band sinks to 4% by year 20. The thin lines are single paths: the same four in both panels, with only the timing of the crash changed.
After a crash at retirement, the median stays close to where the crash left it for the next 20 years. The yearly withdrawals use up what the recovery adds.
The order changes the result because money is coming out. With nothing paid in or taken out, the order of returns has no effect on the final sum. If $100,000 rises 50% in the first year and falls 50% in the second, or falls 50% first and then rises 50%, it ends at $75,000 either way.
The same holds in the simulation above. Stop the withdrawals, and every path ends at the same balance after 20 years whether its crash came at retirement or ten years in. All of the gap in the table comes from the timing of the crash combined with the withdrawals.
If the portfolio falls 30% right at retirement, the same withdrawal becomes a bigger share of what is left: about 5.7% instead of 4% (simple arithmetic, ignoring the first year's withdrawals). What you sell while prices are low does not come back when the market recovers, because there is less money left to recover with.
A crash ten years in is different. If the balance has grown in the meantime (the median in this simulation was 129% of the start at year 10), it falls from higher up, so the withdrawal does not take as large a share. And only ten years of withdrawals follow the crash.
For saving, the timing works the other way round. While you are still paying in, a crash early on, when the balance is small, loses less money than the same fall near the end, when the balance is large. That the timing of a crash changes a monthly plan is also touched on in How Monte Carlo simulation works for investing.
The experiment above put in a crash of a set size at a set time. The withdrawal simulator adds no crash: each of its 1,000 paths draws its months from the model one after another. The model moves between a calm regime, when prices move gently, and a wild regime, when they swing more and tend to fall, so the wild months come at a different time on every path. Each path is a future with its own order of months.
The success rate ("Money lasted") is the share of paths that still have money left at the end. Checking with 4% withdrawn from a 60/40 mix over 30 years, most paths that ran out had a first five years with returns below the middle of all the paths. The success rate already includes this effect of the order.
In the simulator you can compare:
Cutting withdrawals in bad years would make the money last longer, but the simulator does not adjust withdrawals to the market, so that effect does not show in its figures. Nor does it include income such as a pension.