Retirement Sequence of Returns Calculator
Use this calculator to see how the order of returns can change a retirement withdrawal plan. It compares the same return set with the bad years first, bad years last, and a constant-return benchmark.
Maximum first-year withdrawal in adverse sequence$30,934.19
- Adverse-sequence starting withdrawal rate
- 3.09%
- Implied normal-year return
- 9.2%
- Bad years first: ending balance
- $0.00
- Bad years last: ending balance
- $2,038,700.67
- Constant-return ending balance
- $1,104,575.85
- Sequence-of-returns gap
- $2,038,700.67
- Bad-years-first depletion year
- Year 19
Year by year sequence test
| Year | Withdrawal | Bad-first return | Bad-first balance | Bad-last return | Bad-last balance | Constant balance |
|---|---|---|---|---|---|---|
| 1 | $40,000.00 | -10% | $861,840.00 | 9.2% | $1,045,699.20 | $1,015,056.00 |
| 2 | $41,000.00 | -10% | $736,909.11 | 9.2% | $1,094,388.70 | $1,029,918.11 |
| 3 | $42,025.00 | -10% | $623,832.21 | 9.2% | $1,146,308.20 | $1,044,548.78 |
| 4 | $43,075.62 | -10% | $521,374.22 | 9.2% | $1,201,718.15 | $1,058,907.64 |
| 5 | $44,152.52 | -10% | $428,425.79 | 9.2% | $1,260,901.52 | $1,072,951.33 |
| 6 | $45,256.33 | 9.2% | $417,375.00 | 9.2% | $1,324,165.84 | $1,086,633.31 |
| 7 | $46,387.74 | 9.2% | $404,105.29 | 9.2% | $1,391,845.35 | $1,099,903.66 |
| 8 | $47,547.43 | 9.2% | $388,387.78 | 9.2% | $1,464,303.40 | $1,112,708.86 |
| 9 | $48,736.12 | 9.2% | $369,972.37 | 9.2% | $1,541,934.97 | $1,124,991.58 |
| 10 | $49,954.52 | 9.2% | $348,585.85 | 9.2% | $1,625,169.55 | $1,136,690.44 |
| 11 | $51,203.38 | 9.2% | $323,929.80 | 9.2% | $1,714,474.13 | $1,147,739.74 |
| 12 | $52,483.47 | 9.2% | $295,678.35 | 9.2% | $1,810,356.57 | $1,158,069.22 |
| 13 | $53,795.55 | 9.2% | $263,475.67 | 9.2% | $1,913,369.22 | $1,167,603.76 |
| 14 | $55,140.44 | 9.2% | $226,933.31 | 9.2% | $2,024,112.86 | $1,176,263.09 |
| 15 | $56,518.95 | 9.2% | $185,627.25 | 9.2% | $2,143,241.01 | $1,183,961.46 |
| 16 | $57,931.93 | 9.2% | $139,094.69 | 9.2% | $2,271,464.63 | $1,190,607.33 |
| 17 | $59,380.22 | 9.2% | $86,830.57 | 9.2% | $2,409,557.18 | $1,196,102.98 |
| 18 | $60,864.73 | 9.2% | $28,283.81 | 9.2% | $2,558,360.22 | $1,200,344.16 |
| 19 | $62,386.35 | 9.2% | $0.00 | 9.2% | $2,718,789.46 | $1,203,219.70 |
| 20 | $63,946.01 | 9.2% | $0.00 | 9.2% | $2,891,841.33 | $1,204,611.03 |
| 21 | $65,544.66 | 9.2% | $0.00 | 9.2% | $3,078,600.18 | $1,204,391.83 |
| 22 | $67,183.27 | 9.2% | $0.00 | 9.2% | $3,280,246.09 | $1,202,427.47 |
| 23 | $68,862.86 | 9.2% | $0.00 | 9.2% | $3,498,063.42 | $1,198,574.55 |
| 24 | $70,584.43 | 9.2% | $0.00 | 9.2% | $3,733,450.04 | $1,192,680.35 |
| 25 | $72,349.04 | 9.2% | $0.00 | 9.2% | $3,987,927.49 | $1,184,582.31 |
| 26 | $74,157.76 | 9.2% | $0.00 | -10% | $3,513,586.77 | $1,174,107.40 |
| 27 | $76,011.71 | 9.2% | $0.00 | -10% | $3,086,083.01 | $1,161,071.48 |
| 28 | $77,912.00 | 9.2% | $0.00 | -10% | $2,700,585.52 | $1,145,278.67 |
| 29 | $79,859.80 | 9.2% | $0.00 | -10% | $2,352,756.52 | $1,126,520.64 |
| 30 | $81,856.30 | 9.2% | $0.00 | -10% | $2,038,700.67 | $1,104,575.85 |
Withdrawals are taken at the beginning of each year before that year's return is applied.
Each annual growth factor applies the modeled gross return and then 0.25% in fees.
How to use this calculator
- Enter the starting portfolio and the first annual withdrawal taken from it.
- Choose the retirement length and the annual increase applied to later withdrawals.
- Enter the average return, number of bad years, bad-year return, and annual fees.
- Compare the ending balances, depletion year, sequence gap, and adverse-sequence withdrawal limit.
How the sequence test is calculated
Sequence-of-returns risk is the risk that losses arrive when withdrawals are already pulling money out of the portfolio. The average return can be the same, but a loss early in retirement hurts more because later gains compound on a smaller balance.
This calculator builds two block-return paths from the same assumptions. Let P be the starting portfolio, W the first-year withdrawal, n the retirement years, i the annual withdrawal increase, m the average return, k the number of bad years, b the bad-year return, and f annual fees. All rates are converted to decimals for the math.
The non-bad-year return is chosen so the full set has the average return you entered:
g = (n x m - k x b) / (n - k)
The withdrawal in year t is:
W_t = W x (1 + i)^(t - 1)
For that year's gross return r_t, the after-fee growth factor is:
a_t = (1 + r_t) x (1 - f)
Withdrawals are modeled at the beginning of each year. Starting with B_0 = P, each ending balance is:
B_t = max(0, (B_(t - 1) - W_t) x a_t)
The bad-years-first path uses the bad return for the first k years and the implied normal return after that. The bad-years-last path reverses the blocks. The constant path uses the average return every year, which is the conventional projection benchmark but not a sequence-risk test.
How the withdrawal limit is solved
The headline is the first-year withdrawal that leaves exactly zero at the end of the bad-years-first path before rounding. It uses the same beginning-of-year withdrawal timing:
W_max = P x product(a_j) / sum((1 + i)^(t - 1) x product(a_j from t to n))
That value is not a safe withdrawal recommendation. It is a stress-test boundary for the particular block sequence, fees, inflation adjustment, and retirement length entered here.
What moves the result most
The result is usually most sensitive to the first few returns, the starting withdrawal, and the withdrawal increase. A larger bad-year block, a deeper bad-year loss, or higher fees lowers the adverse-path balance. A higher average return can help, but if it requires an unusually high implied normal-year return, the scenario may be mathematically balanced while still being a strained assumption.
What this calculator leaves out
This is a deterministic stress test, not a forecast or a probability model. It does not use historical return series, Monte Carlo simulation, taxes, required minimum distributions, account types, Social Security, pensions, spending changes, rebalancing rules, or changes in asset allocation. It is best read as a way to make return order visible before doing fuller retirement planning.
Worked example
Suppose retirement begins with $1,000,000, the first portfolio withdrawal is $40,000, withdrawals rise by 2.5% per year, the retirement period is 30 years, the average gross return is 6%, there are five bad years at -10%, and annual fees are 0.25%.
The implied normal-year return is 9.20%, so both sequence paths use five years at -10% and 25 years at 9.20%. With the bad years first, the portfolio cannot fund the scheduled withdrawal in year 19 and the ending balance is $0. With the bad years last, the ending balance is about $2,038,701. The same return set therefore creates a sequence gap of about $2,038,701.
The constant-return benchmark ends near $1,104,576. Under the adverse bad-years-first order, the reverse-solved maximum first-year withdrawal is about $30,934, or 3.09% of the starting portfolio.
Common questions
What is sequence-of-returns risk?
Sequence-of-returns risk is the risk that poor investment returns happen early in retirement while withdrawals are also reducing the portfolio. Early losses leave less money invested for later recoveries. That is why two portfolios with the same average return can end with different balances.
Why does return order matter more after retirement?
During accumulation, contributions can buy into downturns and the exact order of returns matters less for a fixed ending average. During retirement, withdrawals remove shares after losses, so later gains apply to a smaller base. The cash flow changes the effect of the sequence.
What does the implied normal-year return mean?
It is the return required in every non-bad year so the full return set has the arithmetic average you entered. For example, a severe bad-year block may require a high normal-year return to preserve the average. That can be useful for a controlled stress test, but it is still only an assumption.
Why are withdrawals modeled at the beginning of each year?
Beginning-of-year withdrawals are a conservative annual convention because spending leaves the portfolio before that year earns a return. Many retirees withdraw throughout the year, and some planning tools use end-of-year cash flows. Changing the timing would change the ending balances.
Does this use historical or simulated market returns?
No. The calculator uses a deterministic block of bad years and a matching block of normal years. It is meant to isolate return order, not estimate the probability that a real portfolio succeeds.
How can lower early withdrawals reduce sequence risk?
Lower early withdrawals leave more money invested while the portfolio is recovering from losses. In this model, reducing the first-year withdrawal also reduces each later inflation-adjusted withdrawal. That raises the bad-years-first ending balance and can delay or avoid depletion.