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 a fixed value is applied year over year, Monte Carlo applies 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 there have been years of returns in excess of 30%, there have been years of losses of the same magnitude. And years still where the market ended up at the same place in December as it 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, Monte Carlo does 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, interquartile ranges are used 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 you 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.
Our Monte Carlo engine uses a normal distribution to produce variance on a monthly basis. Basically, the rate of return for a given account is plugged in and used as an "average." We then take the rate of return for the account and map it to a % to be used as a standard deviation.
The standard deviation, while not explicitly disclosed, closely mirrors historical returns. In general, it starts with rates of return of 0% having a standard deviation of 0%, and as the rate of return increases, so too does the standard deviation. This represents the following:
Cash accounts with a rate of return of 0% will never grow, modeling the stable nominal value of cash accounts.
Low rate of return accounts, such as an account holding bond funds, will have a low standard deviation, and thus will not be very volatile. Although unlikely, monthly rates of return less than 0% are possible.
Higher rate of return accounts (>6%) will have a significantly higher standard deviation and thus will be much more volatile. Very positive monthly rates of return (>50%), as well as very negative monthly rates of return (<-50%), are possible, however very unlikely.