Percentile

Explanation

When the app runs thousands of simulations, it needs a way to describe the whole range without listing every result. Percentiles do this. Sort all outcomes from worst to best; the Pth percentile is the value with P% of outcomes below it.

• 10th percentile: 10% of outcomes were worse. A reasonable “bad luck” case, though not the worst.
• 50th percentile (median): half were worse and half better. It is often lower than the average, because a few very good outcomes pull the average up.
• 90th percentile: only 10% were better. A “good luck” case.

Percentiles describe the simulation, not a guarantee. A 10th-percentile result means 1 in 10 trials did worse, and real-world outcomes can fall outside every simulated band if the assumptions are wrong.

A fan chart plots several percentiles for each year, showing how uncertainty widens over time. Note that each year’s band is computed separately: the path along the 10th percentile line is not necessarily a single trial’s path.

In scenarios, Monte Carlo results show percentile bands for balances (in nominal or today’s dollars) and percentile figures for ending wealth.

Example

A plan is simulated 1,000 times, and the ending balances are sorted from lowest to highest.

• The 10th percentile is around the 100th value: say $180,000.
• The 50th percentile is around the 500th value: say $1,450,000.
• The 90th percentile is around the 900th value: say $4,200,000.

Read it as: in 10% of simulated futures you ended with less than $180,000; in half, more than $1,450,000; in 10%, more than $4,200,000.

With a tiny sample of five results, $200,000, $600,000, $900,000, $1,500,000 and $3,800,000, the median is the middle value, $900,000, while the average is $7,000,000 ÷ 5 = $1,400,000, pulled up by the best result.