Educational information, not individual financial advice.
Key Takeaways
Every financial projection makes assumptions about future returns. The most important distinction is whether those assumptions are fixed (deterministic) or variable (probabilistic). The choice dramatically changes what the forecast can tell you.
A deterministic forecast uses fixed assumed rates of return, inflation, and expenses. "My portfolio will earn 7% per year for 30 years" is a deterministic assumption.
Under 7% constant returns, a $1M portfolio with $50k annual withdrawals survives:
Clean answer. But misleading, because actual markets don't deliver constant 7% every year. Real returns are a sequence of wildly different annual returns that average out to something near 7% over long periods.
The problem is sequence risk. Consider two investors, both drawing $50k from $1M portfolios, both averaging 7% returns:
Investor A: Year 1: −40%. Year 2: +15%. Year 3+: +7% steady. Investor B: Year 1: +7%. Year 2: +7%. Year 3+: +7% steady.
Both have the same arithmetic average. But Investor A's portfolio hits $550k at the start of year 2. They withdraw $50k ($500k left), earn 15% on $500k = $575k. Then they're compounding at 7% going forward from a damaged base. By year 30, Investor A has maybe $100k; Investor B has $2M.
A deterministic forecast using "7% average" would show both the same. Reality doesn't work that way.
Monte Carlo simulation runs your plan through thousands of different return sequences, drawn from a distribution that matches historical volatility. Instead of "here's what happens," the output is "here's the distribution of what could happen."
Outputs typically include:
Range of outcomes. A plan might show a median outcome of $2M and a 10th percentile outcome of $200k. That 10× range isn't visible in a deterministic forecast.
Sensitivity to sequence. Monte Carlo exposes sequence risk because some trials happen to draw bad early returns and show the resulting damage.
Failure modes. Deterministic says "it works." Probabilistic says "it works in 85% of scenarios, and the 15% that fail look like this."
Robustness. A plan that works at the median and the 25th percentile is robust. A plan that works only at the median but fails below is fragile.
Monte Carlo is an improvement over deterministic, but it has its own limitations:
Input-driven. The output is only as good as the assumed distributions. If your assumed stock return distribution is wrong (too high, too low, wrong volatility), the results will be misleading. Garbage in, garbage out.
Historical bias. Most Monte Carlo uses historical data as the reference. The 20th century may not repeat.
Tail events. Normal distributions understate the frequency of extreme events. Real markets have fatter tails than Gaussian assumptions. Horizons uses correlated factor models that capture some of this, but no model fully captures tail risk.
Assumed independence. Simple Monte Carlo models treat asset returns as drawn independently each year. Real markets have some mean reversion and autocorrelation that complicates the picture.
Static assumptions. Most MC holds asset allocation, savings rate, and withdrawal strategy constant. Real investors adjust. Dynamic MC models exist but add complexity.
Best practice uses both:
Deterministic for quick what-if analysis, showing the average-case trajectory, testing plan mechanics.
Probabilistic for the serious analysis, understanding the range of outcomes and identifying failure modes.
Think of deterministic as a sketch — useful for quick answers — and probabilistic as the real map.
A common mistake: interpreting success rates too precisely. "95% success" vs "90% success" differs by 5 percentage points, which is within the uncertainty of the underlying models. Don't fine-tune plans to chase 95% vs 93%.
Instead, use probability thresholds as rough guardrails:
Horizons runs both deterministic and Monte Carlo forecasts. The primary Retirement page dashboard and readiness score use Monte Carlo output (risk-weighted, percentile-based). Individual scenarios and the walkthrough use deterministic for clarity. Toggle between them depending on the question you're asking.
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