Output Statistics

At each month-end, wealth across all paths is sorted and the P5, P25, P50, P75 and P95 quantiles are recorded. The chart is available on a nominal and an inflation-adjusted basis, with a linear/log axis toggle, the goal and wealth-floor lines drawn on their matching basis, and the engine's deterministic invested-capital schedule overlaid on the nominal view.

Goal probability is the fraction of paths whose terminal wealth meets or exceeds your goal. A goal is evaluated against exactly one terminal series, chosen explicitly and stored with the result:

With tax disabled but a non-zero trade cost, liquidation-net wealth still differs from pre-tax wealth. A liquidation-net goal line is deliberately not drawn on the pre-tax fan chart, because those axes are not comparable and overlaying them would be misleading.

Alongside the terminal figure, a pathwise per-month goal-attainment series with per-point Wilson intervals is reported as the goal-probability-over-time chart. When the goal basis is liquidation-net, that monthly curve monitors the pre-tax counterpart and says so on the chart, because monthly wealth is tracked pre-tax.

A probability estimated from a finite number of paths carries sampling error. Goal, terminal-depletion, wealth-floor and withdrawal-health probabilities all carry a 90% Wilson score interval:

The Wilson interval is used rather than the textbook normal approximation because the latter breaks down exactly where these probabilities matter most. Near 0 or 1 it produces intervals that extend outside [0, 1] and whose actual coverage is far below nominal. A goal probability of 0.98 is precisely the case where you want the interval to be trustworthy, and Wilson stays well behaved there.

Maximum drawdown and the longest underwater spell are computed daily inside every path, then summarized across paths. Computing them from monthly snapshots would systematically understate both, because a sharp intra-month decline and recovery would never appear.

The underwater spell is the longest consecutive stretch during which wealth sat below its running peak. Spells still unrecovered at the horizon are right-censored, and P(unrecovered at horizon) is reported beside the duration distribution. Silently treating a censored spell as if it ended at the horizon would bias the reported durations downward, which is the classic survival-analysis error.

Dense P0 to P100 quantile grids are reported for maximum drawdown, longest underwater spell and the one-year NAV return, along with P(negative one-year NAV return) and its Wilson interval.

One-year VaR is stored as a signed lower-tail return: the 5th percentile at the 95% level, or the 1st percentile at 99%. CVaR is the signed average return beyond that cutoff. Negative values are losses, so a VaR of −0.28 means a 28% loss. No sign flipping is applied anywhere, which removes an entire category of misreading.

The two are computed independently and returned with separate bootstrap interval blocks, because they are different estimators with different sampling behaviour. Each CVaR bootstrap replicate recomputes both its own VaR cutoff and its tail mean, rather than holding the cutoff fixed at the point estimate. The shared interval metadata records the confidence level, bootstrap method, resampling unit, signed-tail semantics, and the model-conditional scope.

Tail estimates need enough extreme paths to mean anything. The result includes expected and observed tail counts plus a reliability warning when fewer than 25 tail observations are expected, which is exactly the situation where a 99% CVaR from a small run would otherwise look authoritative while resting on a handful of paths.