Monte Carlo Simulation Explained

The basic idea

Rather than assuming returns are constant, Monte Carlo:

1. Defines a probability distribution for each uncertain variable (stock returns, bond returns, inflation, housing prices, etc.).
2. Runs your plan through the forecast period many times — hundreds or thousands of "trials."
3. Each trial draws new random samples from the distributions for each year.
4. Collects all the results and reports the distribution of outcomes.

The output isn't "your portfolio will be $2.3M." It's "50% of trials end with $1.8M–$3.1M, 10% of trials end below $800k, and 5% of trials end with the portfolio exhausted."

What goes into the model

Horizons' Monte Carlo uses six correlated market factors:

• Aggressive-strategy returns (stocks, growth-oriented)
• Moderate-strategy returns (balanced)
• Conservative-strategy returns (bonds, income-oriented)
• Interest rates (affecting borrowing costs, bond values)
• Inflation (affecting expenses and real returns)
• Housing appreciation (affecting home equity)

Each factor has:

• A mean (long-run expected return).
• A standard deviation (volatility).
• Correlations with other factors (stocks and bonds, inflation and rates, etc.).
• AR(1) persistence for rates and inflation (high inflation tends to persist, then mean-revert).

Correlated factors matter

Naive Monte Carlo models treat each asset class as independent. Real markets don't work that way. Some examples of correlations:

• Stocks and bonds. Sometimes positively correlated, sometimes negatively — and the relationship shifts.
• Inflation and rates. Highly positively correlated (rising inflation drives rate increases).
• Rates and bond prices. Strongly inversely correlated.
• Inflation and stock returns. Varies by regime; high-inflation periods are often bad for stocks.

Horizons' factor model captures these correlations explicitly. When inflation spikes in a trial, interest rates rise, bond prices fall, and stock returns are typically affected — all consistent with how real markets have behaved.

Number of trials

Statistical precision improves with trials, but with diminishing returns:

• 50 trials: rough picture, moderate precision on the middle; noisy tails.
• 200 trials: good for most planning questions. Percentile bands stable.
• 1,000 trials: precise enough for most analysis. Rare events captured.
• 10,000+ trials: useful for very rare event analysis.

Horizons defaults to 200 trials, which balances speed and accuracy. For planning decisions with significant dollar stakes, consider 1,000+ trials.

Trial results

Each trial produces:

• Monthly net worth trajectory across the entire forecast period.
• Final portfolio value at the forecast horizon.
• Path of withdrawals vs spending needs.
• Intermediate checkpoints (balance at key ages, first year spending shortfall if any).

Across all trials, Horizons aggregates:

• Percentile bands of portfolio value by year.
• Success rate (fraction of trials with positive portfolio at horizon).
• Risk of ruin (fraction that exhausted the portfolio before horizon).
• Distribution of final values.
• Drawdown analysis (worst 12-month experience across all trials).

Reading Monte Carlo output

A fan chart shows the range of portfolio values over time:

• Dark center line: median (50th percentile) outcome.
• Dark shaded band: 25th–75th percentile range (the middle half of outcomes).
• Lighter band: 10th–90th percentile range (80% of outcomes).
• Outer edges: extreme outcomes.

If your fan chart fans out wildly, you have high uncertainty. If it stays tight, your plan is consistent across scenarios.

The shape of the fan tells a story:

• Wide and rising: most trials grow; high upside, but wide range.
• Wide and falling: many trials drain; sequence risk significant.
• Narrow and flat: stable outcome with limited upside and downside.
• Fan that bends down over time: withdrawals are outpacing growth in many scenarios.

Common misinterpretations

"Success rate is too precise." A success rate of 91.3% vs 89.8% looks different but reflects modeling noise. Treat as approximate.

"Monte Carlo guarantees outcomes." The output reflects the input distributions. If real-world returns are different from assumed (as they likely will be), real outcomes will differ.

"Tail events will happen as shown." Tails depend on distribution choice. Normal distribution understates real-world extremes.

"One trial is informative." Any single trial, even the median one, is just one possible future. The distribution is the output, not any individual path.

Comparing plans

Use Monte Carlo to compare alternatives:

• Plan A: 92% success, median final value $1.8M, 10th percentile $300k.
• Plan B: 88% success, median final value $2.5M, 10th percentile $400k.

Plan B has lower success but better median AND better bottom 10%. Depending on your goals (maximize expected, minimize downside, optimize survival), either could be preferred.

How Horizons uses this

Horizons' Monte Carlo runs in parallel using multiple CPU cores for speed. The engine takes your specific plan — every asset, liability, income, expense, and their interactions — and runs it through 200+ independent market scenarios. The Retirement page aggregates all outputs into the readiness score, survival curves, and drawdown curves you see.

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