MT423 Unit 9 Sequence Risk Illustration Example

The Same Ten Returns in a Different Order: An MT423 Unit 9 Sequence Risk Illustration From 65 to 95

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Purdue University Global

MT423: Asset Allocation and Risk Management

Unit 9 Sequence Risk Illustration

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[Date]

Denise Hartley's balance and withdrawals are composite and in today's dollars; the Social Security figure stands in for her statement's estimate, the return set is constructed for the illustration, and the sources cited are real.

Inputs

Denise starts retirement at 65 with $936,000, the projected resources from earlier units rounded to the nearest thousand. All figures are in today's dollars and all returns are real. She withdraws $62,000 at the start of each year at 65 and 66, the bridge years before Social Security. From 67 her benefit of about $31,800 a year begins, and her withdrawals fall to $30,200. Withdrawals are taken at the start of each year, before that year's return, so a loss applies to what is left after she has drawn the year's spending.

The Return Set

The same ten returns are used in every run: nine years of 5.0 percent and one year of minus 20.0 percent. Their arithmetic average is 2.5 percent and their compound average about 2.18 percent in every run. The only thing that changes is which of the ten years carries the loss. After the tenth year, every run continues at a flat 2.5 percent real until 95, so the later decades are identical too.

Keeping the set identical is the whole point. An illustration that compared a good decade with a bad one would mix two effects, the level of returns and their order, and could not show that order alone matters.

Four Runs

With the loss in year one, at age 65, the balance at 75 is about $685,704 and at 95 about $332,871.

With the loss in year three, at 67, the balance at 75 is about $719,228 and at 95 about $387,804.

With the loss in year six, at 70, the balance at 75 is about $748,158 and at 95 about $435,210.

With the loss in year ten, at 74, the balance at 75 is about $780,700 and at 95 about $488,533.

A single chart overlays the four paths from 65 to 95. They begin together, separate in the year each loss arrives and then run roughly parallel, never converging, because the 2.5 percent return after 75 applies to whatever balance each run has reached.

Moving one bad year from age 74 to age 65 costs about $155,700 by 95, with every return the same.

The Mechanism

The difference comes from withdrawals. In the first run, Denise withdraws $62,000 at 65 and the remaining $874,000 falls 20 percent, to $699,200. She then withdraws another $62,000 from that reduced balance. Money withdrawn at the bottom is gone; it is not there to benefit from the 5 percent years that follow. In the last run, the same 20 percent loss falls at 74, after nine years of 5 percent growth have built the balance up and after the largest withdrawals have already been taken, so the loss bites into a larger base that is no longer being drawn down as fast.

A portfolio with no withdrawals would end each run at exactly the same value, since multiplication does not depend on order. Withdrawals are what make the order matter.

Why Her Early Years Are More Exposed

Denise's early withdrawals are about twice her later ones, because Social Security begins only at 67. A loss in the bridge years therefore hits a balance from which the largest amounts are being taken. If her first two withdrawals were no larger than the later ones, less would be drawn from a fallen balance in the worst run, and the gap between runs would narrow. Milevsky and Robinson (2000) showed that the chance of exhausting savings depends strongly on the pattern of withdrawals and returns early in retirement, and Denise's bridge years concentrate that exposure into the first two years.

What the Illustration Implies

Three decisions in her plan respond directly to this result. The glide path in Unit 7 places her lowest stock share at 65, when a loss would do the most damage, the shape Pfau and Kitces (2014) tested for this reason. Her safe assets at 65, about $561,000, can cover the bridge years and more without selling stocks after a fall, so the withdrawals in a bad early year need not come from the fallen holding. And if a large loss does arrive early, a modest cut in spending for a few years, for example drawing $55,000 rather than $62,000 in the bridge years, would reduce what is taken from the fallen balance.

Bengen (1994) built his widely cited withdrawal guideline on the worst historical sequences for exactly this reason: a spending rate that survives a bad start will survive most others.

Limits

The illustration uses a constructed return set, not a forecast, and a single loss rather than the clusters of bad years that occur in practice. Its purpose is to show that order matters and why, not to predict her balance at 95.

References

Bengen, W. P. (1994). Determining withdrawal rates using historical data. Journal of Financial Planning, 7(4), 171-180.

Milevsky, M. A., & Robinson, C. (2000). Self-annuitization and ruin in retirement. North American Actuarial Journal, 4(4), 112-124. https://doi.org/10.1080/10920277.2000.10595940

Pfau, W. D., & Kitces, M. E. (2014). Reducing retirement risk with a rising equity glide path. Journal of Financial Planning, 27(1), 38-45.