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Audit the future. Run 1,000 simulations of your portfolio growth to visualize the range of probable outcomes.
Step-by-step breakdown of the underlying equations.
In 1,000 simulations, your capital of $100000 grew to a median of $326,440. However, volatility (σ) means there is a 5% chance your portfolio could be worth as little as $204,908. This "fat-tail" risk is what Monte Carlo analysis aims to quantify.
The Portfolio Monte Carlo Simulator models the statistical probability distribution of future investment wealth over long multi-year horizons. Unlike static linear calculators that assume constant annual growth rates, Monte Carlo analysis generates 1,000 randomized market paths using Geometric Brownian Motion to capture sequence-of-returns risk, market drawdowns, and tail-risk volatility.
Worked 20-Year Simulation Example:\nAn investor deposits $100,000 into a balanced global equity portfolio (S_0 = $100,000) with a 7.0% historical mean return (μ = 0.07) and a 15.0% annual standard deviation (σ = 0.15) over a 20-year horizon (t = 20):\n• Static Constant Calculator (7% compound): $100,000 × (1.07)^20 = $386,968 (Provides a false sense of linear certainty).\n• Monte Carlo 1,000-Path Distribution:\n - 50th Percentile (Median Path): ~$325,000 (Lower than deterministic compounding due to volatility drag: σ² ÷ 2 = 1.125% annual drag).\n - 5th Percentile (Worst 5% of economic histories): ~$128,000 (Illustrates prolonged bear market / stagflation scenarios).\n - 95th Percentile (Top 5% secular bull markets): ~$845,000.\n• Takeaway: Planning for retirement requires stress-testing against the 5th and 10th percentiles, not merely assuming the average.
The 50th percentile is your most probable median portfolio outcome. Pay close attention to the 5th percentile (Worst Case): if this lower bound is insufficient to fund your retirement withdrawal plans, you must increase annual savings or adjust your asset allocation to reduce portfolio volatility (σ).
This is caused by 'volatility drag' (variance drain). When an asset drops 50%, it requires a 100% gain just to break even. High volatility mathematically reduces compound geometric returns below simple arithmetic average returns by approximately half the variance: Geometric Return ≈ Arithmetic Return − (σ² ÷ 2).
Sequence-of-returns risk is the danger that severe market downturns occur in the first few years of retirement when an investor begins withdrawing living expenses. Liquidating assets during deep market crashes permanently impairs portfolio recovery.
A 100% S&P 500 equity portfolio historically exhibits ~16% annual volatility. A classic 60/40 stock/bond portfolio exhibits ~10% to 12% volatility. A conservative 20/80 portfolio typically exhibits ~5% to 7% volatility.
Standard GBM assumes log-normal price distributions. While accurate for long horizons, real-world financial markets exhibit 'fat tails' (leptokurtosis) and volatility clustering, meaning extreme market shocks happen more frequently than pure Gaussian distributions predict.
For retail retirement planning and portfolio estimation, 1,000 iterations provide robust median and 5th/95th percentile confidence intervals. Institutional hedge funds and quantitative risk desks often run 10,000 to 100,000 iterations.
Data verified: September 2026