Glide Path Retirement Calculator

Purpose and model boundary

This calculator shows what a glide path does to a retirement plan. A glide path moves the share of the portfolio held in equities (stocks) from a starting share to a share at retirement, as target-date funds do, and splits the rest between bonds and cash. You enter your ages, your savings, contribution and withdrawal, the glide path, and an expected return and volatility for each of the three classes. The spreadsheet works out the mix at every age and simulates 100 possible market futures, one yearly return after another, and reports the share of futures in which the money lasts to the end age, the equity share today, and how the balances spread by age.

It is the glide-path companion of the Monte Carlo Retirement Success Calculator, which simulates one return distribution for the whole plan. Every figure on this page is computed by the spreadsheet; the page adds nothing to it. It is an educational estimate from the assumptions you enter. It does not predict markets, it does not recommend a glide path or a mix, and it is not financial, investment, tax or legal advice.

Inputs and units

• Your age today, the retirement age and the age the money must last to, in whole years. The retirement age is where contributions stop, withdrawals start and the equity share reaches its share at retirement; enter your age if you are already retired. The end age must be above your age and at most 75 years away.
• Age the glide path starts: optional. Blank means 25, or your age if you are younger.
• Starting equity share, equity share at and after retirement, and bonds as a share of the non-equity part, as percentages. The part not in equities is split between bonds and cash.
• Current savings, and the yearly contribution until retirement and the yearly withdrawal in retirement, both in today's dollars.
• Yearly inflation, which raises the contribution and the withdrawal every year, and yearly fees, a share of the balance.
• For equities, bonds and cash: the expected yearly return (an arithmetic mean, before fees) and the volatility (the standard deviation of yearly returns). The correlation of equity and bond returns, from −1 to 1; cash is taken to move independently of both.
• Random seed: the starting number of the spreadsheet's random-number generator. The page does not show it: each press of Simulate first replaces it with the next seed in the stream, except the first press after a worked example or Reset, which keeps that example's seed. Through the API or MCP the seed you pass is used as given; blank means 42, the seed of the worked examples.

Rates are percentages. Money is in dollars and nominal: balances are not deflated, and only the contribution and the withdrawal are stated in today's dollars and grown with inflation.

Governing relationships

The equity share e at age a holds the starting share s₀ up to the glide path start g, moves in a straight line to the share at retirement s_R at the retirement age R, and stays there:

e(a) = s₀ + (s_R − s₀) × (a − g) ÷ (R − g), for g < a < R

With b the bond share of the non-equity part, the bond and cash shares are:

bonds = (1 − e) × b, cash = (1 − e) × (1 − b)

Each year's mix has an expected return and a volatility, the moments of a portfolio rebalanced every year, with ρ the correlation of equities and bonds:

μ = e × μ_E + bonds × μ_B + cash × μ_C

σ = √((e σ_E)² + (bonds × σ_B)² + (cash × σ_C)² + 2 × e × bonds × ρ × σ_E × σ_B)

Each future draws its yearly random numbers from one seeded generator, the minimal standard generator with multiplier 48,271, x(next) = 48271 × x mod (2^31 − 1). Future r owns two consecutive stretches of 64 steps of its stream, so no two futures share a draw and up to 75 years fit. Each state x becomes a uniform draw u = x ÷ (2^31 − 1), and each draw becomes the year's return after fees f through the lognormal distribution matched to that year's mix, with Z the standard normal value whose probability is u:

1 + R = e^(m + s × Z) × (1 − f), with s² = ln(1 + σ² ÷ (1 + μ)²) and m = ln(1 + μ) − s² ÷ 2

Year t of the simulation uses the mix of the age at its start. Until retirement the year's contribution C is added at its start, and from retirement the withdrawal W is taken at its start, both grown with inflation i from the first year:

B(t) = (B(t − 1) + C × (1 + i)^(t − 1)) × (1 + R(t)) before retirement

B(t) = max(0, (B(t − 1) − W × (1 + i)^(t − 1)) × (1 + R(t))) from retirement

Calculation sequence

The spreadsheet first builds the mix for every age from the glide path start to the end age, with its expected return and volatility. It then draws 100 futures of yearly returns, each year at the mix of its age, runs each future's balance from today to the end age, and takes the percentiles of the balances at every age, the share of futures run out by each age and the share that lasts to the end age. Beside the simulation it follows the plan at the average return of each year's mix with no ups and downs.

Outputs and interpretation

The headline is the share of the 100 futures in which the balance is still above zero at the end age. It is an estimate: at 100 futures its 95 percent sampling margin is about 9.8 percentage points, which the page reports. Beside it are the equity share today, the seed used and the workbook's self-check. The bond and cash shares today, the expected return and volatility of today's mix, the median and the 10th and 90th percentile balances, the balances at the average returns at retirement and at the end age, and the number of futures simulated (always 100) are returned to the API and MCP, and the tables give the shares and the balances by age.

The allocation chart draws three overlapping areas from zero, all classes first, then equities and bonds, then equities, so the bands seen are equities, bonds and cash from the bottom; the top of each area is a running total, and the allocation table gives each share on its own. The balance chart shows the 10th, 25th, median, 75th and 90th percentile balances by age and the plan at the average returns of the mix. Under the default assumptions the fixed 60/40 worked example lasts in somewhat more of its futures than the default glide path (76 against 70 of 100, within the sampling margin), mostly because thirty years at a 30% equity share grow less; this is what the assumptions imply, not a recommendation.

Validation and status logic

The workbook evaluates the conditions below from top to bottom and returns the first matching status.

NOT VALID is a refusal, not a numeric answer: every number reads zero and the tables are empty. CHECK accompanies a computed result but calls for the stated review. The self-check is reported separately as arithmetic-integrity evidence; it does not replace this ordered status chain.

Assumptions and limitations

Each year the mix is drawn as one lognormal return with the mean and volatility of an annually rebalanced mix, an approximation of a mix of three assets with their own distributions. Cash is taken as independent of equities and bonds. Returns are independent from year to year, with no fat tails, mean reversion or change of market regime. Equities are one class, not split into domestic and international. There are no taxes, Social Security, pensions or other income, no spending that changes in retirement other than with inflation, no flows during the year and no rebalancing costs. Balances are nominal. One hundred futures give an estimate with the sampling margin shown, not a forecast.

Restrictions and non-computing states

This calculator enforces its numeric limits before it accepts a result, and the workbook also refuses the combinations a single limit cannot express: an end age not above your age or too far away, a retirement age outside your age and the end age, and a glide path start after your age. A retained seed remains part of every simulation.

Errors and warnings

A request rejected by the page's input limits is not a computed result. A transport or service failure cannot establish a fresh workbook answer. Review the workbook's References and Disclaimer, and check any plan with a qualified professional before using a result for a real decision.

Sources and further reading

The model's amounts, ages, shares and return assumptions come from the inputs, not market data. The workbook's References sheet identifies the calculation sources. The links below explain the ideas behind them; they do not endorse this calculator.

• The U.S. Securities and Exchange Commission's investor bulletin Target Date Funds explains a glide path: a mix that moves from stocks toward bonds as the target date nears, and paths that stop at the date or continue through it.
• H. Markowitz, “Portfolio Selection”, The Journal of Finance 7(1), 1952, gives the variance of a portfolio from its weights, volatilities and correlations, the formula behind the volatility of each year's mix.
• S. K. Park and K. W. Miller, “Random number generators: good ones are hard to find”, Communications of the ACM 31(10), 1988, and the Park–Miller–Stockmeyer 1993 correspondence describe the generator family. The workbook uses multiplier 48,271 and modulus 2³¹ − 1.
• The NIST/SEMATECH e-Handbook's lognormal distribution section and Microsoft Support's NORM.S.INV and PERCENTILE.INC documentation describe the distribution and percentile functions used by the workbook.

This is an educational estimate, not financial, investment, tax or legal advice. Check any plan with a qualified professional.