Week 45 Day 1: Monte Carlo Simulation: Running Your Retirement 10,000 Times

Think of it like shuffling a deck of market returns and dealing them in random order. Sometimes you get great returns early (your plan thrives). Sometimes you get terrible returns early (your plan struggles). The Monte Carlo simulation runs all possible orderings and tells you what percentage of the time your money lasts. It is the closest thing to a crystal ball that math can provide.

How Monte Carlo works: (1) Inputs: current portfolio value ($1,000,000), asset allocation (70/30 stocks/bonds), annual withdrawal ($40,000, inflation-adjusted), time horizon (30 years), expected stock return (10% average, 16% standard deviation), expected bond return (5% average, 5% standard deviation). (2) Process: the simulation generates 10,000 possible 30-year return sequences. Each year's return is randomly drawn from a distribution with the specified average and standard deviation. Returns in each simulation are independent (though more sophisticated models can incorporate serial correlation). (3) For each simulation: apply the annual returns to the portfolio, subtract annual withdrawals, and track whether the portfolio runs out. (4) Output: 'Success rate' -- the percentage of 10,000 simulations where money lasted the full 30 years. Example results: $40,000/year withdrawal (4%): 95% success. $50,000/year (5%): 82% success. $60,000/year (6%): 65% success. $35,000/year (3.5%): 98% success. Target: 85-95% success. Below 80% is risky. Above 95% means you are likely underspending. Interpreting success rates: 95% = 1 in 20 chance of running out (good). 90% = 1 in 10 chance (acceptable with guardrails). 85% = 1 in 7 chance (acceptable if flexible). 80% = 1 in 5 chance (warrants adjustment). 70% = concerning. 60% = plan is underfunded. Free tools for running simulations: cFIREsim, FIRECalc, Boldin, Portfolio Visualizer (all have Monte Carlo or historical simulation features).

Monte Carlo simulation (MCS) for retirement planning uses random sampling from assumed return distributions to estimate the probability distribution of retirement outcomes. The standard approach assumes returns are drawn from a normal or lognormal distribution with specified mean and standard deviation, independently across time periods. This assumption is computationally convenient but empirically questionable: actual stock returns exhibit (a) fat tails (more extreme events than the normal distribution predicts), (b) volatility clustering (high-volatility periods tend to persist), and (c) mean reversion at long horizons (above-average returns tend to be followed by below-average returns at multi-year horizons). More sophisticated MCS implementations use: (1) bootstrapping from historical returns (preserving the empirical distribution, including fat tails), (2) block bootstrapping (preserving serial correlation and volatility clustering by sampling consecutive multi-year blocks), (3) regime-switching models (allowing the return distribution to differ across market regimes -- bull, bear, crisis), and (4) vector autoregression (VAR) models (incorporating the correlation between returns, inflation, interest rates, and dividend yields over time). Pfau (2014) showed that the assumed return distribution significantly affects success rates: using 10% expected returns (historical average) yields much higher success rates than using 7% (a more defensible forward-looking estimate based on current valuations). The lesson: a Monte Carlo simulation is only as good as its inputs. Overly optimistic return assumptions produce a false sense of security. Conservative inputs (7-8% stocks, 3-4% bonds) provide a more honest assessment.