What is Monte Carlo analysis?

This article explains what Monte Carlo simulations are and how they play a key role in a comprehensive financial plan Written by Davorin Robison
Updated over a week ago

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.

For a deeper look into how NewRetirement's Monte Carlo simulator works, please watch the following snippet from the Build Your NewRetirement Plan course:

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.

We cannot go into specifics into the actual calculation used, but 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.

Consider adjusting your optimistic and pessimistic assumptions and experiment with reducing expenses or saving more to see how the insights change. You may choose to make adjustments to your plan based on the additional information.

If you enter different optimistic and pessimistic values that end up changing the average, you will get a different standard deviation, but if you switch between optimistic and pessimistic views of your plan, the standard deviation stays the same since you aren't doing anything to affect the average rate of return for the account.

If you change the optimistic and pessimistic values in such a way that average does not change (say go from 4%/2% to 5%/1% so the average always stays at 3%), standard deviation does not change for that account.The Standard Deviation is based on the account’s mean (i.e. average) growth rate, which is, in turn, determined by the midpoint of the optimistic and pessimistic rates (i.e. (optimistic+pessimistic) / 2). To achieve a Standard Deviation of ~20% would require a mean growth rate of at least 9%.