Skip to main content

Safe withdrawal rate simulator

Test how long a portfolio lasts under different withdrawal rates. See the failure rate, not a promise.

Currency:
Simulation Survival Rate
91.2%
In 4,562 of 5,000 simulated retirements, the portfolio lasted 30 years.
Depletion rate: 8.8% (438 failures)

Portfolio & Spending Inputs

Stochastic parameters update the simulation model in real time.

$1,000,000
Initial Annual Withdrawal
4% = $40,000/yr
30 Years
60% Stocks / 40% Bonds
Conservative (20/80)Balanced (60/40)All Equity (100/0)
Static purchasing power: spends the exact same real dollar amount each year regardless of market trends.
3%

Portfolio Fan Chart (Percentile Bands)

Simulated real portfolio purchasing power across 10th, 25th, 50th, 75th, and 90th percentiles.

Median (50th) 10th–90th Band
Loading fan chart...
Year 0: $1,000,000Median Year 30: $1,046,44210th %ile: $30,38490th %ile: $3,251,885
Median Ending Balance$1,046,442Year 30 real purchasing power
10th Percentile Balance$30,384Unfavorable market tail (bottom decile)
Median Depletion YearYear 27Across 438 failed paths
What this means: At 4% over 30 years, 9 in 10 simulated retirements lasted without running out of money. At 5%, 7 in 10 did. There is notable sequence risk in bottom decile market paths.

Success Rate by Withdrawal Rate

Evaluates survival probability from 3.0% to 6.0% in 0.25% increments across identical market sequences.

Highest rate ≥ 95% survival: 3.5%Highest rate ≥ 90% survival: 4%
Loading sweep curve...

Strategy Comparison

Comparing survival rate and terminal capital at 4% initial rate over 30 years.

Fixed Real (Classic 4%)Selected91.2% Success
Median Ending: $1,046,442Failure ~Yr 27
Fixed % of Portfolio100% Success
Median Ending: $1,041,3660 Depletions
Guardrails (±10% Adjustment)100% Success
Median Ending: $1,069,0640 Depletions

Asset Allocation Sensitivity

Success rates across equity allocations at 4% withdrawal over 30 years.

40% Stocks / 60% Bonds90.7% Success
60% Stocks / 40% BondsCurrent91.2% Success
80% Stocks / 20% Bonds90.2% Success
100% Stocks / 0% Bonds88.1% Success

The 4% Rule: Origin, Boundaries & Assumptions

The 4% rule originated in a 1994 paper by certified financial planner William Bengen, later corroborated by the 1998 Trinity Study (Cooley, Hubbard, and Walz). Analyzing US historical market returns from 1926 through the mid-1990s, Bengen discovered that across any rolling 30-year period, an initial 4% withdrawal adjusted annually for inflation never depleted a portfolio holding 50% to 75% large-cap equities.

However, Bengen’s findings carry crucial boundary conditions:

  • Horizon constraint: The study explicitly tested 30-year horizons. Early retirees planning 40, 50, or 60 years of retirement face sustained exposure to market downturns and lower survival odds at 4%.
  • Asset allocation: Portfolios held exclusively US large-cap equities and intermediate government bonds.
  • Rigid spending assumption: It assumes the retiree never adjusts spending downwards during market crashes.
Early retirees: a 40–50 year retirement is outside the original study’s assumptions. Try 45 years.

Disclaimer: Educational tool only, not financial advice. Simulations show how outcomes could vary under stated assumptions. They are not predictions. Real markets, taxes, fees and spending change over time.

How this is calculated

Mathematical specification of the discrete simulation engine and order of operations.

1. Annual Balance Recurrence & Order of Operations

Balance_{t} = (Balance_{t-1} - NetWithdrawal_t) * (1 + NetRealReturn_t)

Withdrawal is deducted at the start of each year. If withdrawal exceeds current balance, depletion is triggered immediately. Remaining capital then compounds at net real return.

2. Net Real Return Calculation

NetRealReturn_t = (w_stocks * r_stocks + w_bonds * r_bonds) - annualFee

Annual rebalancing maintains static asset weights. Real returns are drawn from correlated bivariate lognormal distributions.

3. Withdrawal Strategy Rules

Fixed Real: W_t = W_0
Fixed %: W_t = Balance_{t-1} * rate
Guardrails: W_t = W_{t-1} * (1 ± 0.10) if rate drifts ±20%

Models spending responsiveness during market stress.

4. Success Rate Metric

Success Rate = Successful Runs (Ending Balance > 0) / Total Runs

Evaluated across 5000 stochastic retirement paths.

Frequently Asked Questions

Common questions on the 4% rule, safe withdrawal rates, early retirement horizons, and guardrail rules.

Related Systems Resources

Complementary calculators, deep-dive guides, and definitions on retirement planning and compounding.

Calculator

FIRE and Coast FIRE Calculator

Find your baseline FIRE target portfolio, calculate your Coast FIRE point, and simulate month-by-month accumulation.

Open calculator
Systems Guide

Compound Interest Explained as a Feedback Loop

Understand exponential capital accumulation, recurrence relations, and the cost of delay through software systems mental models.

Read guide
Glossary Definition

Compounding in the Systems Glossary

Formal equations, mathematical notation, and variable definitions for compounding mechanisms and safe withdrawal boundaries.

View definition