This study started with a simple thought experiment. Suppose you lose 50% in year one and then grow steadily for 19 years. Now suppose instead that you grow steadily for 19 years and lose 50% in the final year. You end up with the same pile of money — or do you?
For retirees, this question is close to existential. Retirement is when the saving stops and the withdrawing starts, and the order in which returns arrive — sequence-of-returns risk — is widely described as the defining risk of the withdrawal phase. Before getting to what this study means for retirees, it is worth seeing what the raw arithmetic actually says, because the arithmetic turns out to be both more boring and more interesting than intuition suggests.
The warm-up: a toy example
Start with the simplest possible version. One thousand dollars, twenty years, a single 50% loss, and a steady 10% growth rate in every other year.
- Scenario A ("lose first"): −50% in year 1, then +10% for 19 years.
- Scenario B ("lose last"): +10% for 19 years, then −50% in year 20.
- Benchmark: a steady 4% every year, for reference.
Both scenarios end at exactly $3,057.95, versus $2,191.12 for the 4% benchmark. Multiplication commutes: 0.5 × 1.1¹⁹ is the same number as 1.1¹⁹ × 0.5, regardless of where the 0.5 sits. The terminal value does not care about the order.
But the journeys could hardly be more different:
| Year | Lose first (A) | Lose last (B) | 4% benchmark |
|---|---|---|---|
| 1 | $500.00 | $1,100.00 | $1,040.00 |
| 15 | $1,898.75 | $4,177.25 | $1,800.94 |
| 19 | $2,779.96 | $6,115.91 | $2,106.85 |
| 20 | $3,057.95 | $3,057.95 | $2,191.12 |
The "lose last" path led the benchmark by 190.3% at year 19 — and then a single −50% year cut that lead to 39.6%. The "lose first" path, meanwhile, sat underwater for a decade and a half: it did not catch the 4% benchmark until year 15. Same destination; one path was a victory lap that ended in a gut punch, the other was fifteen years of looking wrong before being proven right.
That was the toy. The natural next question: does the same identity hold when the loss and the growth rate come from real market history instead of round numbers?
Method: rearranging real history
To keep the experiment honest, the loss and the growth rate were taken from each index's own real 20-year record rather than invented:
- Starting capital: $1,000. Horizon: 20 years.
- The loss: each index's actual historical maximum drawdown over the window — the real worst peak-to-trough fall, with its real dates.
- Scenario A ("lose first"): one year at the index's actual max drawdown, then 19 years at a constant growth rate *g*.
- Scenario B ("lose last"): 19 years at *g*, then the max-drawdown year at the end.
- Benchmark: 4% compounding every year.
- A third column shows the index's actual year-by-year buy-and-hold path, for comparison.
The constant *g* is not arbitrary. It is solved fairly: one crash plus 19 years of *g* must reproduce the index's actual 20-year terminal value. This matters because the index's historical CAGR already contains the crash — using the raw CAGR as *g* would double-count the drawdown. Solving for *g* keeps the experiment apples-to-apples: all three paths (lose first, lose last, real history) end at the same real terminal value by construction.
Data: Yahoo Finance daily adjusted closes for QQQ and SPY, October 9, 2006 through October 2, 2026. Year boundaries fall on each October 9 anniversary (snapped to the nearest trading day); year 20 uses the last available close.
Honest limitations, stated up front: the model assumes no taxes, no fees, no trading costs, and — critically — no withdrawals. Constant growth at rate *g* is a fiction; real markets never compound smoothly. This is a single 20-year window that happens to contain the Global Financial Crisis, the worst drawdown in the modern history of both indexes. A different window would give different numbers. The conclusions below are about arithmetic, not predictions.
QQQ: the −53.40% experiment
QQQ's real parameters over the window: maximum drawdown −53.40% (peak October 31, 2007 → trough November 20, 2008), 20-year CAGR 16.49%, turning $1,000 into $21,108.43. The fairly-solved growth rate is *g* ≈ 22.23%.
| Year | Lose first (A) | Lose last (B) | 4% benchmark | Real QQQ |
|---|---|---|---|---|
| 0 | $1,000.00 | $1,000.00 | $1,000.00 | $1,000.00 |
| 1 | $465.96 | $1,222.26 | $1,040.00 | $1,288.77 |
| 2 | $569.52 | $1,493.92 | $1,081.60 | $763.43 |
| 3 | $696.11 | $1,825.96 | $1,124.86 | $1,034.35 |
| 4 | $850.82 | $2,231.79 | $1,169.86 | $1,222.24 |
| 5 | $1,039.93 | $2,727.83 | $1,216.65 | $1,384.64 |
| 6 | $1,271.06 | $3,334.12 | $1,265.32 | $1,682.67 |
| 7 | $1,553.57 | $4,075.16 | $1,315.93 | $1,953.04 |
| 8 | $1,898.86 | $4,980.91 | $1,368.57 | $2,493.70 |
| 9 | $2,320.90 | $6,087.96 | $1,423.31 | $2,772.28 |
| 10 | $2,836.75 | $7,441.07 | $1,480.24 | $3,137.38 |
| 11 | $3,467.24 | $9,094.92 | $1,539.45 | $3,920.09 |
| 12 | $4,237.87 | $11,116.36 | $1,601.03 | $4,810.97 |
| 13 | $5,179.78 | $13,587.08 | $1,665.07 | $5,059.34 |
| 14 | $6,331.03 | $16,606.94 | $1,731.68 | $7,767.19 |
| 15 | $7,738.17 | $20,298.00 | $1,800.94 | $9,870.91 |
| 16 | $9,458.05 | $24,809.43 | $1,872.98 | $7,326.77 |
| 17 | $11,560.20 | $30,323.57 | $1,947.90 | $10,149.42 |
| 18 | $14,129.56 | $37,063.28 | $2,025.82 | $13,748.13 |
| 19 | $17,270.00 | $45,300.96 | $2,106.85 | $17,117.09 |
| 20 | $21,108.43 | $21,108.43 | $2,191.12 | $21,108.43 |
A few things stand out. The "lose first" path trailed the 4% benchmark for five full years and did not pull ahead until year 6 ($1,271.06 vs. $1,265.32) — a far faster recovery than the toy example's fifteen years, because 22.23% fills a hole much faster than 10%. The "lose last" path is the dramatic one: at year 19 it sat at $45,300.96, leading the benchmark by roughly 2,050% — and then a single −53.40% year erased nearly all of it, landing at exactly $21,108.43, the same dollar as every other path.
The real QQQ column tells its own story: the actual index trailed the benchmark in years 2 and 3 (the crisis), then pulled away for good from year 4. Buy-and-hold investors who lived through 2008 spent two years "behind" a hypothetical 4% account before the recovery took hold.
SPY: the −55.19% experiment
SPY's real parameters: maximum drawdown −55.19% (peak October 9, 2007 → trough March 9, 2009), 20-year CAGR 11.11%, turning $1,000 into $8,212.01. The fairly-solved growth rate is *g* ≈ 16.54%.
| Year | Lose first (A) | Lose last (B) | 4% benchmark | Real SPY |
|---|---|---|---|---|
| 0 | $1,000.00 | $1,000.00 | $1,000.00 | $1,000.00 |
| 1 | $448.11 | $1,165.41 | $1,040.00 | $1,180.02 |
| 2 | $522.23 | $1,358.17 | $1,081.60 | $698.48 |
| 3 | $608.60 | $1,582.82 | $1,124.86 | $847.43 |
| 4 | $709.27 | $1,844.63 | $1,169.86 | $938.94 |
| 5 | $826.59 | $2,149.74 | $1,216.65 | $982.59 |
| 6 | $963.31 | $2,505.32 | $1,265.32 | $1,210.27 |
| 7 | $1,122.65 | $2,919.72 | $1,315.93 | $1,420.29 |
| 8 | $1,308.34 | $3,402.66 | $1,368.57 | $1,685.21 |
| 9 | $1,524.75 | $3,965.48 | $1,423.31 | $1,795.87 |
| 10 | $1,776.95 | $4,621.40 | $1,480.24 | $1,969.67 |
| 11 | $2,070.87 | $5,385.80 | $1,539.45 | $2,360.84 |
| 12 | $2,413.41 | $6,276.65 | $1,601.03 | $2,720.58 |
| 13 | $2,812.60 | $7,314.85 | $1,665.07 | $2,812.01 |
| 14 | $3,277.82 | $8,524.77 | $1,731.68 | $3,413.35 |
| 15 | $3,820.00 | $9,934.82 | $1,800.94 | $4,369.68 |
| 16 | $4,451.85 | $11,578.10 | $1,872.98 | $3,647.23 |
| 17 | $5,188.21 | $13,493.19 | $1,947.90 | $4,448.31 |
| 18 | $6,046.37 | $15,725.04 | $2,025.82 | $6,019.14 |
| 19 | $7,046.48 | $18,326.06 | $2,106.85 | $7,084.80 |
| 20 | $8,212.01 | $8,212.01 | $2,191.12 | $8,212.01 |
The SPY experiment is the slower, more grinding version of the same story. Real SPY trailed the 4% benchmark for five straight years (years 2–6) during and after the crisis — the longest stretch of "looking wrong" in either index — before catching up in year 7. The hypothetical "lose first" path needed until year 9 to catch the benchmark. And once again, all three paths converge to the same $8,212.01 at year 20. The identity held a third time.
Five things this study taught its author
1. Order does not change the terminal value. This is a mathematical identity — multiplication commutes — and it verified three times: in the toy example, in QQQ, and in SPY. Losing first versus losing last ends at the identical dollar, provided the capital is left untouched.
2. But order completely changes the journey. Same destination, radically different psychological path. "Lose last" leads for nineteen years and then gets cut in half. "Lose first" trails the benchmark for 6 to 15 years before recovering. An investor living through either path experiences something totally different from what the terminal number suggests — and most investors make their biggest decisions mid-journey, not at the destination.
3. One big drawdown can erase years of outperformance. A 190% lead became a 39.6% lead after a single −50% year; a roughly 2,050% lead in the QQQ "lose last" path was cut back to the common terminal value by one −53.40% year. This is the mathematical case for a hard maximum-drawdown line: the deeper the hole, the more of the compounding story gets rewritten by a single bad year.
4. Recovery speed is a function of the growth rate. Same hole (roughly −50%), very different fill times: 15 years at 10%, 9 years at 16.54%, 6 years at 22.23%. The case for pursuing a high CAGR is not only a bigger terminal value — it is a faster recovery from drawdowns. Growth rate is the shovel; drawdown depth is the hole.
5. Buy-and-hold's real cost is time, not volatility. Real QQQ trailed the benchmark in years 2–3; real SPY for five straight years (2–6). Nobody paid those years in dollars — the terminal values were spectacular — but they were paid in patience, and in the temptation to abandon the strategy at exactly the wrong moment. Long-term holders win not by avoiding drawdowns but by surviving them.
The part that matters most if you are retired
Everything above comes with one enormous asterisk, and it deserves its own section rather than a footnote: this study modeled capital that was never touched. No withdrawals, no distributions, no spending. That is precisely why the order of returns did not matter.
For a retiree who withdraws a fixed amount each year to live on, the math changes completely. Take the "lose first" path and add annual withdrawals: the early −50% now hits a portfolio that is simultaneously being drained, so there is less capital left to compound during the recovery years. No later growth rate can fully repair that, because the shares sold at the bottom are gone forever. This is true sequence-of-returns risk — and it is the reason the study's "order doesn't matter" result must never be read as "timing doesn't matter for retirees." It applies to untouched capital only.
This distinction is the whole reason withdrawal-phase planning exists as a discipline separate from accumulation-phase investing: cash buffers to avoid selling into drawdowns, dynamic spending rules that tighten when the portfolio falls, and drawdown guardrails that trigger before the hole gets too deep. The arithmetic in this article explains *why* the withdrawal phase needs its own playbook — it does not substitute for one, and nothing here is a recommendation about any individual's withdrawal strategy.
Limitations and disclosures
This is a hypothetical exercise, and its simplifications all point in the same direction — toward cleaner results than real life produces. The constant growth rate *g* is a mathematical convenience; real returns arrive lumpy, and lumpiness interacts with drawdowns in ways this model smooths away. There are no taxes, no fees, no trading costs, and no withdrawals in the model — each of which would change every number in the tables. The window is a single 20-year period containing the Global Financial Crisis; a different 20 years would produce different drawdowns, different growth rates, and different recovery times. Adjusted closes assume dividends reinvested; indexes themselves are not directly investable, and real index funds carry expense ratios and tracking differences. Annual snapshots also hide the intra-year path — the −53.40% and −55.19% drawdowns unfolded over months, and living through them month by month felt nothing like reading a yearly table suggests.
Suitability varies enormously by individual circumstance: time horizon, income needs, tax situation, risk tolerance, and health all change which lessons of this study apply and how. Nothing in this article is a recommendation to buy, sell, or hold any security, nor a suggestion about any personal withdrawal or allocation strategy.
Sources
- Market data: Yahoo Finance daily adjusted closing prices, QQQ and SPY, October 9, 2006 – October 2, 2026. Max drawdowns, CAGRs, terminal values, and the fairly-solved growth rates were computed from this data; scenario paths are arithmetic constructions described in the Method section.
- Background concepts on retirement risk and investor education: U.S. Securities and Exchange Commission Investor.gov and FINRA investor-education materials.