Financial planning requires many assumptions: Your rates of return, views on inflation, medical spending, cost of living adjustments, how much you may earn, and even your longevity age. Nothing is truly certain (except for maybe death and taxes). So how can we model into the future in a way that accounts for the uncertain nature of the future?

Enter Monte Carlo simulations.

Monte Carlo is a way to introduce probability into financial planning. Instead of using "linear" projections, whereby we apply a fixed value year over year, we allow variance month to month.

Although the average long-term annual return of the S&P 500 is 10–11%, the market has not steadily marched up and to the right at that pace. Just as we've seen years of returns in excess of 30%, we've seen years of losses of the same magnitude. And years still where we ended up at the same place in December as when we started in January. Linear projections simply cannot capture this volatility, while Monte Carlo allows us to do so.

Instead of applying, say, 10% growth to your accounts each year, Monte Carlo breaks the compounding up by month and applies a degree of probability to each month of projecting. Using this method of projecting from today until longevity is fine and good, but by only doing it once, it isn't all that different from linear modeling. So instead of doing it just once, we do it many times. 1,000 times, to be exact.

Each one of these 1,000 "iterations" has a different curve over time. In order to make sense of this spread of 1,000 iterations, we use interquartile ranges to show the probability of ending up at a certain place. The 50th percentile shows the "middle" result of the simulation, while the area between the 25th and 75th percentiles shows the middle 50% of outcomes. Lastly, our "Chance of Success" metric is based on the percentage of iterations that did not end up running out of money by longevity.

What we are left with is a spread of results that starts off tight and predictable, and as we project further into the future, becomes more scattered and variable. This is in fact representative of the world we live in. As much as we may wish to have a crystal ball and know what will happen, the further out we plan, the more that can end up happening.