Monte Carlo Capital Simulation
Traditional investment calculators project growth using a constant interest rate. However, real-world market returns fluctuate randomly. Firewire Analytics incorporates a Monte Carlo simulation engine (10,000 iterations) to evaluate plan resilience under volatility and Sequence of Returns Risk.
1. Why Monte Carlo Simulation?
Even if historical stock return averages $14\%$ per year, a portfolio might face negative returns during early withdrawal years (e.g. $-20\%$, $-15\%$). Withdrawing funds during market drops depletes capital much faster than deterministic models predict.
The Monte Carlo method simulates 10,000 independent future paths, capturing bull markets and market crashes.
2. Geometric Brownian Motion Model
Portfolio valuation $S_t$ at each time step $\Delta t$ is calculated using Geometric Brownian Motion (GBM):
Screenshot: Interactive Monte Carlo calculator displaying capital trajectory fan and probability histogram
where:
- $S_t$ — portfolio capital at year $t$;
- $C_t$ — net annual cash flow ($C_t = \text{Inflows} - \text{Outflows}$);
- $\mu$ — expected return;
- $\sigma$ — annualized volatility;
- $Z_t \sim \mathcal{N}(0, 1)$ — standard normal random variable.
3. Scenario Percentiles ($P_{10}$, $P_{50}$, $P_{90}$)
- Median scenario ($P_{50}$) — $50\%$ of simulations performed better, $50\%$ worse.
- Optimistic scenario ($P_{90}$) — top $10\%$ quantile corresponding to strong bull markets.
- Conservative scenario ($P_{10}$) — bottom $10\%$ quantile representing severe early downturns.