Product Walkthrough

How the Simulation Engine Works

Most retirement calculators assume returns follow a bell curve and assets move independently. Both assumptions are wrong. Here is what Retirement Lab models instead - and why each choice changes your projected success rate.

Monte Carlo Engine

How Monte Carlo Retirement Simulation Works

Rather than projecting a single "average" outcome, the engine runs thousands of independent scenarios - each with a different sequence of annual returns drawn from your configured distribution. The result is a probability spread: not just "will I run out of money?" but "in what percentage of futures does each outcome occur?"

Under the hood

Each iteration runs your full retirement timeline year by year. For each year, the engine draws a correlated return vector, applies it to the portfolio, deducts your spending (adjusted for your strategy and inflation), and credits any income streams like Social Security or pensions. This repeats until the portfolio is depleted or the timeline ends. At 50,000 iterations, tail probabilities stabilize - the difference between an 87% and 89% success rate is meaningful when planning 30 years of withdrawals.
50,000 iterations per run on Pro - 1,000 on free - enough to measure tail risk reliably
Seeded PRNG for reproducible results: same inputs always produce the same distribution
Fan chart shows the 25th, 50th, and 75th percentile paths - the gap between them is the uncertainty
Success rate: the share of scenarios where the portfolio survives to the end of your timeline
Retirement Lab simulation output - probability fan chart showing pessimistic, typical, and optimistic portfolio projections with success rate
Retirement Lab distribution settings - Student's t-distribution degrees of freedom and Fernandez-Steel skewness parameter
Fat-Tail Distributions

Why Normal Distributions Underestimate Retirement Risk

The standard Monte Carlo assumption - that annual returns follow a Gaussian bell curve - dramatically understates the frequency of severe losses. Real equity markets produce 30%+ annual drops far more often than the normal distribution predicts. The Student's t-distribution corrects for this: lower degrees of freedom produce heavier tails, meaning catastrophic return sequences appear in more simulated scenarios. DOF=3 is more severe than DOF=5 - you choose based on how conservative you want the model to be.

Under the hood

The skewness parameter handles a second asymmetry: markets crash sharply but recover gradually. A symmetric distribution implies that extreme upside years are just as likely as extreme downside years - which is not what history shows. The Fernandez-Steel parameter tilts the distribution to weight the downside more heavily. On identical inputs, switching from Gaussian to fat-tail typically lowers the modeled success rate - not because the plan got worse, but because the assessment became more realistic.
Student's t-distribution: DOF=3 (severe tails) or DOF=5 (moderate) - both heavier than Gaussian
Fernandez-Steel skewness: tilts the distribution asymmetrically toward the downside
Toggle on or off to directly compare Gaussian vs fat-tail success rates on the same inputs
Impact Insights card shows the exact percentage-point shift fat tails apply to your success rate
Correlated Asset Returns

Stocks, Bonds, and Alternatives Move Together - Not Independently

If stocks and bonds are treated as independent, a bad equity year has no statistical relationship to that year's bond return in the simulation. That fails exactly when it matters most. In 2022, stocks and long-duration bonds both fell sharply at the same time - breaking the negative correlation that 60/40 portfolios rely on for protection. In 2008, correlations across asset classes converged as investors fled to cash. These joint movements define the worst retirement sequences.

Under the hood

Cholesky decomposition translates your configured correlation matrix into a transformation applied to each joint return draw. The default stock/bond correlation is negative, reflecting their typical diversification benefit - but you can adjust it. Setting it toward zero stress-tests a world where diversification breaks down; a positive value models a 2022-style scenario where both fall together. The effect is most visible in the worst-case percentiles rather than the median outcome.
3x3 Cholesky decomposition across stocks, bonds, and alternatives
Configurable correlation matrix - set stock/bond correlation from negative to positive
Each iteration draws a correlated return vector; the three assets never move independently
Available on the free plan - not gated behind Pro
Retirement Lab correlation matrix and market assumptions - configurable stock, bond, and alternatives correlation coefficients
Retirement Lab withdrawal strategy selector - floor and ceiling strategy with configurable annual rate, monthly floor, and monthly ceiling
Spending Strategies

How You Withdraw Matters as Much as How Much You Save

Fixed withdrawals are simple and predictable but take no account of what the market is doing. Withdrawing the same amount in year 3 of a bear market as in a bull year accelerates depletion. Dynamic strategies reduce this risk by linking spending to portfolio performance - which can improve survival rates substantially, at the cost of some income predictability in bad years.

Under the hood

Guyton-Klinger defines two guardrails: if your withdrawal rate as a share of current portfolio rises above the upper threshold (the portfolio has shrunk), spending is cut by a configurable percentage. If it falls below the lower threshold (the portfolio has grown), spending is raised. Floor and ceiling works differently - it withdraws a percentage of current portfolio value but caps the monthly amount between a hard minimum and maximum, giving portfolio-responsiveness within a predictable income range. All four strategies apply inflation from your current age, so all amounts reflect today's purchasing power.
Fixed amount - constant monthly withdrawal, with or without inflation adjustment (free)
Guyton-Klinger guardrails - configurable upper and lower thresholds trigger spending cuts and raises (Pro)
Percentage of portfolio - highest survival rate but most variable income; scales directly with portfolio value (Pro)
Floor and ceiling - percentage-based with a guaranteed monthly minimum and capped maximum (Pro)
Black Swan Events

Model Sudden Market Shocks at Any Point in Your Retirement

Fat-tail distributions generate extreme return sequences randomly across your scenarios. Black swan events are different: a deterministic shock at a specific age, applied to every single iteration. If you set a 35% drawdown at age 65, every simulated retirement experiences that drawdown that year - then continues from the reduced portfolio. This answers a specific question: how does my plan hold up if a major crash happens right as I retire?

Under the hood

The timing matters more than the magnitude. A 35% crash at age 65 - large portfolio, withdrawals just beginning - has a very different impact than the same crash at age 75, when the portfolio is smaller but you also have fewer years of withdrawals ahead. You can add multiple events at different ages to model a scenario with more than one shock. In iterations where the black swan year coincides with a bad fat-tail draw, the two effects compound - which defines the true floor of your plan.
Deterministic shock at a user-specified age and magnitude - applied to every iteration
Multiple events supported: test a crash at retirement age plus a second shock later
Compounds with fat-tail draws in the same year - the worst scenarios reflect both
Impact Insights card shows the exact success-rate shift the event applies
Retirement Lab black swan events configuration - discrete portfolio crash at a specified age with configurable drop percentage
Retirement Lab historical stress test - draggable sliding window over 97 years of real S&P 500 and Treasury returns from 1928 to 2025
Historical Stress Test

Test Your Plan Against 97 Years of Real Market Returns

The historical stress test runs your exact plan - spending strategy, income streams, allocation, tax settings - against every actual retirement window in the historical record. The window length matches your configured retirement duration. A 30-year retirement is tested against 1928-1958, then 1929-1959, then 1930-1960, and so on. When the record runs out before the window ends, the engine falls back to your configured expected returns for the remaining years.

Under the hood

The result is a historical success rate: what share of all possible retirement start years would have left you with money at the end. This number is entirely independent of your distribution assumptions - fat tails, skewness, and correlation are not involved. It is a direct empirical check on your plan. If your Monte Carlo says 85% but only 60% of historical windows succeed, that gap is a signal that your return assumptions may be more optimistic than history warrants. The Great Depression start years are typically the hardest - not because 30-year total returns from 1929 were catastrophic, but because the first three years destroy a withdrawing portfolio before any recovery can compound.
Damodaran dataset: real annual S&P 500 and 10-year Treasury returns, 1928-2025
Window size matches your retirement duration - each starting year gets a full run
Historical success rate across all windows - independent of your distribution settings
Great Depression, Oil Crisis, Dot-Com, 2008, COVID annotated directly on the chart
Simulation Comparison

Compare Two Scenarios Side by Side to Make Better Decisions

The value of a retirement decision - retiring two years earlier, shifting from 60/40 to 70/30, switching from fixed withdrawals to Guyton-Klinger - depends entirely on your specific inputs. Generic rules of thumb do not apply when your portfolio size, spending level, and income streams are all variables. Running both scenarios and comparing them gives you the actual number for your situation.

Under the hood

The comparison view has three tabs. The metrics tab shows success rate, terminal wealth at the 25th and 75th percentile, and depletion risk side by side for both scenarios. The projection tab overlays the fan charts from both simulations on a single chart, so you can see at which age the paths start to diverge and by how much. The parameter diff lists every input that changed, field by field - so if you adjusted three things at once, you can still read exactly what differed.
Metrics tab: success rate, terminal wealth at P25 and P75, depletion risk - both scenarios side by side
Projection tab: overlaid fan charts showing where and when the two outcomes diverge
Parameter diff: structured field-by-field list of every input that changed
Available on the free plan - no upgrade required
Retirement Lab simulation comparison - side-by-side metrics, overlaid projection charts, and parameter diff between two saved simulations

See it in action with your own numbers.

Free plan runs 1,000 iterations with correlated multi-asset modeling and simulation comparison. Pro unlocks the full engine.

30-day money-back guarantee on Pro. No questions asked.