GF550 Unit 9 Sequence of Returns Retirement Analysis Example

Same Ten Returns, Nine Years Apart: A Unit 9 Longevity and Sequence Analysis of a Million-Dollar Retirement

[Student Name]

Purdue University Global

GF550: Retirement Planning

Unit 9 Longevity and Sequence Analysis

[Instructor Name]

[Date]

The retiree, the returns and every figure are composite and illustrative; the articles and life table cited are real.

The Retiree and the Plan

The retiree is a composite single woman aged 66 with $1,000,000 in a balanced portfolio. She withdraws $48,000 in the first year, 4.8 percent of the starting balance, and raises the withdrawal by 2.5 percent each year for inflation. Withdrawals come out at the start of each year.

The Ten Returns

The returns are negative 15, negative 8, negative 3, 4, 6, 10, 12, 14, 14 and 18 percent. Their arithmetic average is 5.2 percent and their geometric average, the rate at which money actually compounds over the ten years, about 4.68 percent. The same ten numbers are applied in two orders: lowest first, and highest first.

Result 1: The Balance After Ten Years

Losses first. The portfolio falls to about $699,000 after two years as withdrawals are taken from a shrinking base, and ends the decade at about $661,800.

Gains first. The portfolio grows in the early years while withdrawals are small relative to its size, and ends the decade at about $1,047,700.

The ending balances differ by about $386,000, though the returns are identical and so is every withdrawal.

Result 2: How Long the Money Lasts

After the first decade, both paths are carried forward at a flat 5 percent with withdrawals still rising 2.5 percent a year.

Losses first. The portfolio is exhausted at about age 89.

Gains first. It lasts until about age 98.

The order of returns matters because withdrawals are taken from whatever balance exists at the time: losses early force the retiree to sell more of a smaller portfolio, and those shares are not there to benefit when the good years arrive.

Result 3: How Likely Is She to Need the Money?

The Social Security Administration's period life table gives a woman aged 66 roughly a 40 percent chance of reaching 89 and about a 25 percent chance of reaching 92 (Social Security Administration, 2024). In the losses-first path, then, there is about a two-in-five chance she outlives her savings, and with it the plan she thought was adequate. A plan that works on average but fails in a poor sequence two times in five is not adequate for someone who cannot return to work.

Result 4: Two Spending Rules That Respond to Losses

Rule A: skip the inflation raise after a losing year. The withdrawal stays flat in any year following a negative return. In the losses-first path she skips three raises. The decade ends at about $715,300 and the money lasts to about age 91.

Rule B: cut spending 10 percent while the portfolio is below 80 percent of its starting value. The cut applies in years when the balance is below $800,000. The decade ends at about $736,900 and the money lasts to about age 92.

Both rules buy two to three years of income in the bad sequence at the cost of modest, temporary cuts in spending. Research on withdrawal rates finds that flexible spending rules allow higher sustainable spending than a fixed inflation-adjusted withdrawal, because they respond when a poor sequence appears (Blanchett et al., 2014).

Why Averages Mislead

A projection that uses a single average return, like the one in Unit 3, cannot show this risk at all. A 5.2 percent average, or even the 4.68 percent geometric average, would suggest the plan lasts into her nineties regardless of order. Research that estimates the probability of running out of money treats the spending rate, expected return, volatility and horizon together for this reason (Milevsky & Robinson, 2005).

What the Analysis Leaves Out

The model ignores Social Security, which would cover part of her spending whatever the markets do and reduce the share exposed to sequence risk. It uses one sequence in each order rather than thousands of simulated paths. It also holds the post-decade return at 5 percent, which is itself uncertain.

A Check on the Result

The dollar losses tell a surprising story. In the losses-first order, the three negative years cost about $223,000, falling on balances of roughly $952,000, $760,000 and $649,000 after withdrawals. In the gains-first order, the same three negative years cost more, about $343,000, because they hit balances above $1.2 million in years eight to ten. Yet the gains-first path still ends the decade far ahead. The reason is that seven years of withdrawals were funded while the portfolio was growing, so the shares sold to pay them were sold at high prices, and the losses came out of gains already earned rather than out of the original savings.

Recommendations

1. Adopt Rule B, written into the plan in advance so the cut is a rule rather than a judgment made in a bad year.

2. Keep roughly two years of withdrawals in cash and short-term bonds, which lets her ride out an early market drop without selling stock at depressed prices.

3. Revisit the withdrawal rate after any year in which the portfolio falls below $850,000.

References

Blanchett, D. M., Finke, M., & Pfau, W. D. (2014). Low bond yields and safe portfolio withdrawal rates. The Journal of Wealth Management, 16(2), 55-62. https://doi.org/10.3905/jwm.2013.16.2.055

Milevsky, M. A., & Robinson, C. (2005). A sustainable spending rate without simulation. Financial Analysts Journal, 61(6), 89-100. https://doi.org/10.2469/faj.v61.n6.2776

Social Security Administration. (2024). Actuarial life table [Data set]. Office of the Chief Actuary.