Monte Carlo Investment & Portfolio Wealth Risk Simulator

Quantitative Finance: Why Static Averages Fail (The Flaw of Averages)

Assuming a constant 8% return every year produces a deterministic forecast that hides market sequence-of-returns risk:

• If market crashes happen early in retirement, a portfolio can be depleted even if the long-term average return was 8%.

• Monte Carlo Stochastic Simulation runs thousands of randomized volatility permutations to determine the true probability of success and risk of portfolio ruin.

How to Use This Calculator

Enter your Starting Portfolio Balance / Capital () (e.g. 100000), Expected Annual Return Mean (μ % CAGR) (e.g. 8.5 (Historical portfolio mean return)), Annual Volatility / Standard Deviation (σ %) (e.g. 16.0 (S&P 500 historical volatility ~15-18%)), Annual Additional Contribution ( / year) (e.g. 12000 (or 0)), Simulation Time Horizon (Years) (e.g. 15), and Target Financial Goal Milestone () (e.g. 500000). Results update instantly as you type — adjust any value to compare scenarios.

The Formula

Monte Carlo simulation & Geometric Brownian Motion (GBM) stochastic equations:_t = S_0 [(μ - (σ^2) / (2))t + σ √(t) Z] (Z N(0, 1)) Rate: α = μ - (1) / (2)σ^2 Outcomes: Q(p) = Simulated Portfolio Balance at Percentile p of Goal Success: P(S_T Goal) = 1 - Φ(Z_target) at Risk (95\% VaR) = Total Invested - Q(0.05)

Worked Example

For example, simulating a 100,000 portfolio with 12,000/year annual contributions over 15 years at an 8.5% mean return and 16.0% annual volatility aiming for a 500,000 target: Total principal invested is 280,000.00. The Median (50th percentile) outcome is 684,320.00. In a severe bear market (10th percentile), the portfolio reaches 398,450.00, while a bull market (90th percentile) delivers 1,185,900.00. The probability of reaching the 500k goal is 76.8%.

Understanding Your Result

Compare your result against industry benchmarks for your specific sector — significant variation exists across industries, business stages, and geographic markets. Use this calculation as one data point alongside your unit economics, cash flow, and competitive positioning. For decisions involving significant capital allocation, validate your model assumptions with historical actuals from at least 6–12 months of operating data before projecting forward.