## Monte Carlo

Last updated:
July 2, 2021

We provide many projections within My Financial Plan. How we handle each income, expense, asset, and debt projection is covered in separate articles. In addition, we have a post about the more holistic scenarios we offer in an article called “Potential Impacts of Economic Scenarios”.

Almost all the asset projections in My Financial Plan are based on a mathematical methodology called “Monte Carlo”. Broadly speaking, Monte Carlo is a way of estimating what will happen in the future by repeating an experiment and observing the probability of each experimental outcome.

For example, if you wanted to guess the future likelihood of a coin toss, you could flip a coin 10,000 times and keep track of how many times each toss came up heads or tails. After that work, you could be confident that the next time you flipped that coin, there would be an equal chance of each result.

Here is a more complicated example. Let’s say you wanted to be able to estimate a future roll of two six-sided dice. The Monte Carlo methodology for figuring that out would be to roll two six-sided dice thousands of times and keep track of the results. You would end up with a chart that looked like this:

You can see that the most likely result from rolling a pair of dice will be rolling a 7, with lower probabilities for 6, 8 and so on.

Projecting the future value of assets with the Monte Carlo method is like the coin or dice experiments, but with many more variables.

For the My Financial Plan Monte Carlo projections, we use FinMason, a leading provider of data for financial planning institutions. To determine the projected values of your investments, we send an anonymized version of your investment portfolio to FinMason. FinMason calculates 10,000 different future values for your portfolio and replies with three projected outcomes for your assets.

Those outcomes are displayed in My Financial Plan as 10th, 50th and 90th percentile values from the overall Monte Carlo projection. The projected outcomes that fall within the 50th percentile are the most likely to occur, like rolling a seven in the dice experiment above. These are the projected asset values that we show by default.

Outcomes in the 10th percentile are lower than 89 percent of the experiments run. In My Financial Plan we show these outcomes if you select “Pessimistic” with the “Show Projection Probabilities Control” selector.

Outcomes in the 90th percentile are higher than 89 percent of the experiments run. In My Financial Plan we show these outcomes if you select “Optimistic” with the “Show Projection Probabilities Control” selector.

#### Key Assumptions

FinMason Monte Carlo projections are determined by the anonymized current market value of the investor’s portfolio, as well as expected return and expected volatility analytics of the portfolio. Expected return and expected volatility analytics are calculated as follows:

• Expected returns are the long-term future returns for an investment or portfolio, which are determined by analyzing the sensitivity of the portfolio to various macroeconomic factors alongside estimates of the long-run future impact for each of those macroeconomic factors. Macroeconomic factors' estimated impacts on returns are calculated using various academically-accepted methodologies depending on the factor. FinMason determines the exposure of a portfolio or investment to a set of macroeconomic factors called the FinMason Global Factor Set. FinMason then calculates the portfolio’s expected return by analyzing the expected impacts of the various factors and the portfolio’s sensitivities to those factors.
• Expected volatility is the long-run estimate of the future volatility of an investment or portfolio based upon its exposure to various macroeconomic factors and the investments' behavior over the last 20 years. Expected volatility depends on the sensitivity of the investment or portfolio to the same FinMason Global Factor Set. This describes the portfolio not as a group of investments, but as a group of exposures to various economic factors (generally less than 20). The calculation measures how volatile each of the factors have been over the last 20 years and how those factors have interacted with each other over that time (correlation).

#### Important Information

A Monte Carlo analysis models the probability of different investment outcomes. It does not imply or guarantee future returns. FinMason calculates a 10,000-iteration Monte Carlo analysis that produces probability distributions over time. The inputs used in the Monte Carlo calculations are based on current portfolio balances and holdings, as well as the FinMason expected return and expected volatility analytics, both of which are calculated using FinMason’s factor-based approach. The models may use market proxies, individual fund returns, or security level returns where relevant data is available. The hypothetical expected case (50th percentile), pessimistic case (10th percentile), and optimistic case (90th percentile) are for illustrative purposes only, and not a guarantee of future returns.

For more details on how FinMason uses Monte Carlo projections, download the "FinMason Monte Carlo Engine for Goals Based Planning" white paper.