Financial planning for retirement can be a tricky exercise, requiring both the client and the planner to make many assumptions about an uncertain future. Monte Carlo simulations try to address this uncertainty by acknowledging the very wide range of possible outcomes in a portfolio’s value over time and assigning a probability to the outcomes based on thousands of random trials.

A Monte Carlo simulation is a statistical tool that has been used in many disciplines to look at the variety of outcomes from a given set of inputs. It gets its name from the random results of throwing dice in gambling. (The simulation technique was first developed by scientists working on the Manhattan Project for the atomic bomb!)
Straight line extrapolation, which was the method used prior to Monte Carlo simulation’s widespread availability, gives a more narrow and unrealistic answer to the question of future portfolio worth. In financial planning, Monte Carlo simulations can give us more informed answers about how a portfolio may behave under a variety of circumstances.
We need six inputs to run a Monte Carlo Simulation:

1. Current Portfolio Size
2. Portfolio Asset Allocation (% Stock/% Bond/% Cash)
3. Projected Annual Withdrawal
4. Projected Annual Deposits
5. Inflation Estimate
6. Time Horizon

The resulting simulation will give us a range of possible outcomes, and a probability of the portfolio supporting the annual withdrawals. Where straight line extrapolation gives us a single answer, Monte Carlo simulations give us a confidence band, or range of expected values.

As the chart shows, a \$1 million portfolio with a 70% Equity and 30% Bond allocation with an annual 2% withdrawal would be about \$3M after 20 years assuming an average return. With the Monte Carlo simulation, we get a range of values, from a low of \$2M to a high over \$4.6M, within a given probability – in this case, a 60% probability. In other words, 60% of the time, the account will be valued between \$2M and \$4.6M. Twenty percent of the time it will be lower than \$2M, and 20% of the time, it will be higher. Statisticians often look at the 95% confidence interval, or the range of values that will occur 95% of the time. For this portfolio, that gives us a range of \$1.3M to \$7.6M, meaning 2.5% of the time, it will be less than \$1.3M, and 2.5% of the time, it will be more than \$7.6M.

There are many valid criticisms of Monte Carlo Simulations in financial planning, such as assuming constant inflation and the lack of Black Swan events like 2008. However, understanding that a financial plan is a fluid document that needs revisiting, Monte Carlo simulation results can be a useful starting point in planning for retirement.