Interactive Calculator#
π² Monte Carlo Retirement Calculator
Simulate your financial future with 10,000 scenarios (up to 100,000)
1. Choose Your Portfolio
Heavy dividend tilt with growth
- VTI: 35% β’ SCHG: 15%
- SCHD: 30% β’ SGOV: 20%
Ultimate simple, diversified portfolio
- VTI: 54% β’ VXUS: 26%
- BND: 20%
All market conditions with gold
- VTI: 30% β’ VXUS: 10%
- SHY: 20% β’ TLT: 20% β’ GLD: 20%
Enhanced diversification + inflation
- VTI: 40% β’ VXUS: 20%
- VNQ: 10% β’ VTIP: 15% β’ BND: 15%
2. Set Your Parameters
π Methodology & assumptions
Engine
- Monthly Geometric Brownian Motion per asset, log-normal compounding (
value × exp(r)) so portfolios can't go below zero. - Cholesky-decomposed correlation matrix drives correlated monthly returns across the assets in the chosen portfolio.
- Fat-tail mode swaps Normal for Student's t (df=5) with variance correction.
- Annual rebalance at year-end. Per-asset withdrawals are taken at target weights, which has a monthly partial-rebalance side effect.
What the metrics actually measure
- Median / 5th / 95th percentile β distribution of terminal portfolio values across paths.
- Depletion risk β share of paths where terminal value < $1.
- Sharpe / Sortino β per-path risk-adjusted return computed from each simulation's gross monthly portfolio returns (annualized), then averaged across paths. Not a cross-path outcome-dispersion proxy.
- Max drawdown β peak-to-trough decline of portfolio value including withdrawals. For retirees this conflates market loss with normal liquidation; expect drawdowns to climb over a long horizon even in benign markets.
- P(beat S&P 500) β the SP500 path shares VTI's correlated monthly shock (empirical Οβ0.98) so the comparison happens in the same market state, not parallel universes.
Assumptions you should know about
- Expected returns and volatilities are conservative empirical estimates (2000-2025 monthly data for US/intl equities, bonds, REITs, TIPS, gold). Bond and TIPS volatility have been bumped to ~4.5-5% to match empirical, not the textbook 3%.
- No taxes. Withdrawals are pre-tax. Your real spending power depends on your jurisdiction.
- No cash buffer mechanic. Real retirees often hold 1-2 years cash; not modelled. Biases outcomes slightly worse than reality for disciplined defenders.
- Asset correlations are historical. Equity/long-bond correlation, in particular, has trended positive since 2022; the simulator uses a benign-decade prior. Treat Golden Butterfly's downside numbers as optimistic.
Plan from the 5th percentile, not the median. Stack a regime-change haircut on top before sizing your spending. Monte Carlo is a stress test, not a forecast.
How to Use This Calculator#
Step 1: Choose Your Portfolio#
Select from four professionally designed portfolios:
| Portfolio | Best For | Expected Geometric Return |
|---|---|---|
| Dividend-Focused | Income seekers, US-focused investors | 8.2% |
| Three-Fund Bogleheads | Most investors (lowest fees, global diversification) | 7.4% |
| Golden Butterfly | Conservative investors worried about crashes | 5.9% |
| Modern Bogleheads | Inflation-conscious investors | 6.8% |
Returns are computed directly from each portfolio's asset assumptions and full covariance matrix using the portfolio-level ItΓ΄ correction (ΞΌ minus half the portfolio variance). The calculator renders the same numbers live on each card.
Step 2: Set Your Withdrawal Rate#
This determines how much you withdraw annually. The calculator supports two strategies:
Constant Dollar (Traditional): Fixed inflation-adjusted withdrawals regardless of portfolio value. Simple but rigid.
Dynamic Spending (Vanguard): Withdrawals adjust based on portfolio performance with floor/ceiling bounds. More sustainable for aggressive rates.
Quick guide:
- 2.5-3.0% = Very conservative (50-year horizons)
- 3.0-3.5% = Moderate (40-year horizons)
- 4.0%+ = Aggressive (30-year horizons or with flexibility)
Step 3: Set Duration#
Enter years until age 100 (or your planning horizon). Add 5-10 years as a buffer.
Step 4: Add Fees (Optional)#
Beyond ETF expense ratios, add any advisor or platform fees:
- 0.00% - DIY at Vanguard/Fidelity/Schwab
- 0.25% - Robo-advisors
- 1.00% - Traditional advisor (costs ~39% of wealth over 50 years!)
Step 5: Run Simulation#
Click Run Simulation and wait 2-10 seconds. The default run is 10,000 scenarios. For tighter percentiles bump to 50,000 or 100,000 from Advanced Options (slower, more accurate).
Understanding Your Results#
| Metric | What It Means |
|---|---|
| Median Outcome | Most likely result (50th percentile) |
| 5th Percentile | Your safety net. Plan around this number, not the median. |
| Depletion Risk | Probability of running out of money |
| Sharpe/Sortino Ratio | Risk-adjusted return (higher = better). Computed per simulation path from gross monthly returns, then averaged across paths. |
| Growth potential context | A sentence under the cards shows your median outcome without withdrawals and how much spending cost you in compound growth. Anchors the magnitude of the headline numbers. |
| Growth chart, dashed brass line | The median path of a parallel portfolio that compounds with the same market shocks but never withdraws. The gap between it and the solid green median is the real, year-by-year cost of your retirement spending. |
| Max Drawdown | Worst peak-to-trough decline. Includes the withdrawal effect, so retirement runs naturally show larger drawdowns than markets alone. |
Depletion risk guidelines:
- 0-5% = Very safe
- 5-10% = Acceptable
- 10%+ = Consider reducing withdrawal rate
Advanced Options#
Fat-Tail Mode: Layers a Student's t-distribution (df=5) on top of the default log-normal compounding to model extreme events (crashes and booms) more realistically than the bell curve alone. Recommended for conservative planning. If your plan survives fat-tail mode at a punishing withdrawal rate, your plan is genuinely robust.
Dynamic Spending Bounds: Adjust floor (-2.5% default) and ceiling (+5% default) to control withdrawal variability.
Privacy & Accuracy#
All calculations run in your browser. No data is collected or stored.
The engine is professional-grade:
- Monthly Geometric Brownian Motion per asset. Returns compound via
value Γ exp(r), so portfolios mathematically cannot fall below zero. - Cholesky-decomposed correlation matrix drives correlated monthly shocks across the assets in the chosen portfolio.
- Fat-tail mode swaps the Normal driver for a variance-corrected Student's t-distribution (df=5).
- Annual rebalance at year-end. Withdrawals are taken at target weights (this has a monthly partial-rebalance side effect, disclosed in the methodology box inside the calculator).
- Sharpe and Sortino are computed per simulation path from monthly gross portfolio returns, then averaged across paths. That's the textbook formulation, not a cross-path outcome-dispersion proxy.
- S&P 500 comparison shares VTI's correlated monthly shock (empirical correlation 0.98). The "probability of beating the S&P" is therefore measured in the same market state, not in two parallel universes.
- Expected return labels on each portfolio card are derived directly from the asset assumptions plus the full covariance matrix, not hardcoded marketing numbers.
- Parallel no-withdrawal portfolio runs alongside the main simulation using the same Cholesky-correlated monthly shocks. Its median terminal value (and its full annual path on the chart) anchors the cost of your spending. If your median outcome is $16M and the no-withdrawal median is $40M, withdrawals cost you $24M of compound growth. The dashed brass line on the growth chart is that parallel portfolio's median path over time.
Open the Methodology and assumptions disclosure inside the calculator for the full set of caveats (no taxes, no cash buffer, historical correlations, the drawdown-includes-withdrawals convention).
