MaxiFi uses the term "trajectories" in our Living Standard Monte Carlo analyses (Full Risk Investing and Upside Investing). However, you may not be familiar with the term, and even if you are familiar with trajectories from other financial planning Monte Carlo analyses, ours are quite different. It's important to understand how they are calculated and used.
How a Trajectory is Calculated
In the Base Plan there is typically no variation in the plan's return rates from year to year. MaxiFi calculates your highest sustainable living standard, so usually you see a perfectly smooth discretionary spending path. In the chart below, the Base Plan is a constant $100,000, starting in the current year (2024) and extending for the life of this 20-year plan.
In building a trajectory, MaxiFi starts in the current year and essentially runs a base plan, using the return rate assumptions you've set. This first year projection will always equal the Base Plan:
Next, MaxiFi uses Monte Carlo techniques to determine return rates for your assets at the end of the current year. These are random return rates, but realistic based on the history of the assets in your investment strategies. MaxiFi then advances to the next year (2025 in this case), and re-runs your "base plan" from the perspective of 2025. In this case, the current year Monte Carlo returns were better than expected so your asset balances are higher than expected. So, when the plan is run from 2025, the spending projections are higher!
Now the process is repeated for determining random return rates for 2025 and advancing to 2026. Unfortunately, returns were poorer than expected in 2025, so you enter 2026 with less assets and therefore, the base plan projections from 2026 forward are lower.
MaxiFi repeats this same process over and over for the duration of your plan. Each year, determining the next year's asset balances based on simulated market returns, but then projecting for the future based on the assumed return rates of your base plan. It is just like if you were a time traveller (and a loyal MaxiFi user) and each year you ran and spent according to your Base Plan projections. Each year you would have higher or lower assets than expected because the actual returns for the year would never match your assumptions. You'd rerun your Base Plan and adjust your spending according to the new Base Plan.
The end result of this process is a trajectory like that shown below, and which you will see on the charts shown in the Living Standard Monte Carlo reports. The level changes each year, though usually not by much because the impact of the higher or lower asset balances is smoothed out over the remainder of the plan.
How Trajectories Are Used in Analysis
But MaxiFi does not just run one trajectory. It simulates hundreds of these trajectories for each Living Standard Monte Carlo report. In order to make sense of the results, we don't show all the hundreds of trajectories. We rank them according to the average standard of living for the whole trajectory, and then show the 5th, 25th, 50th, 75th, and 95th "percentile" trajectories.
The 5th percentile trajectory, for example, is the trajectory where 5% of all trajectories had a lower average standard of living and 95% of trajectories had a higher standard of living. We say this trajectory is when your investments performed "Very Poorly."
The 95th percentile trajectory, on the other hand, is the one where 95% of all trajectories had a lower average standard of living and only 5% had higher. We say this is when your investments performed "Very Well."
In terms of performance, the 25th percentile is "Poorly," the 50th is "At Median," and the 75th is "Well."