Sequence of Returns Risk: Why Order Changes Your DCA Outcome

#Where the effect comes from

For a single lump sum left untouched, order genuinely does not matter. Multiplication is commutative: growing by 20 percent and then falling by 10 percent gives the same result as falling 10 percent and then growing 20 percent. If nothing enters or leaves the account, the sequence is irrelevant.

The moment money moves in or out, that stops being true. Each return now applies to a different balance depending on when it occurs, and the balances differ because contributions have been accumulating. Order stops being cosmetic and starts determining the outcome.

#The arithmetic, worked through

Take a simple case. Three years, $10,000 contributed at the start of each year, and returns of +30 percent, 0 percent, and −20 percent in some order. Same three returns, same contributions, different sequence.

Identical contributions, identical returns, a difference of $10,000. The second ordering finished 38 percent higher.

#Why the bad-year-first ordering won

The reason is straightforward once you see it. A percentage applies to a balance, and the balance grows over time as contributions accumulate. So the largest return should ideally land on the largest balance.

In the second sequence, the −20 percent year hit a balance of only $10,000, costing $2,000. The +30 percent year hit a balance of $28,000, gaining $8,400. In the first sequence the reverse happened: the +30 percent was applied when just $10,000 was invested, and the −20 percent struck $33,000.

#The retirement case, where it reverses

Everything above applies to the accumulation phase. Once you are withdrawing rather than contributing, the effect flips sign and becomes considerably more dangerous.

A retiree drawing a fixed amount from a portfolio that falls early is selling more shares to fund each withdrawal, at depressed prices. Those shares are gone permanently and cannot participate in the recovery. The portfolio can be structurally impaired even if the market subsequently returns to its long-run average.

Two retirees with identical average returns over a thirty-year retirement can end with wildly different outcomes purely on the basis of whether the bad years came first or last. This is the reason retirement planning gives so much weight to the years immediately before and after the retirement date, and why glide paths reduce equity exposure as that date approaches.

#Why this matters for reading a backtest

A backtest reports one sequence: the one that actually happened. The annualized return it produces is specific to that ordering, and a different ordering of the same years would produce a different figure for the same plan.

This is one reason the same fund can show meaningfully different annualized returns depending on the start date, even for windows of equal length. It is not only that different years are included. It is that the same years arrive in a different position relative to your accumulated balance.

The 2000 to 2010 decade is the clearest available example. A contribution plan running through it did modestly better than a lump sum precisely because the worst years arrived while comparatively little was invested, and the recovery arrived once far more had accumulated.

#What this does and does not imply

• →It does not mean you should try to time contributions. You cannot know the sequence in advance, and attempting to guess it reliably underperforms simply contributing.
• →It does mean an early decline is much less alarming than it feels, if you are still contributing and intend to continue.
• →It does mean the years immediately around retirement deserve disproportionate attention, because that is when sequence risk is at its maximum.
• →It does mean a single backtest's annualized return should be read as one draw from a distribution, not as the plan's characteristic return.

#How to see it in the tool

Run the same ticker and the same contribution plan across several different ten-year windows, for example starting in 1998, 2000, 2003, 2007, and 2012. The spread in annualized returns across those runs is sequence risk made visible, using nothing but real historical data.

Then run each window as a lump sum instead. The spread will generally be wider, because a lump sum concentrates all of its exposure into a single entry point and has no subsequent contributions to average across the sequence.