Understanding MaxiFi’s Monte Carlo Risk Analysis

MaxiFi’s risk analysis recognizes that you are investing at risk, i.e., that you can’t tell precisely what real rates of return (returns adjusted for inflation) you will earn each year on your regular and retirement account assets. We call a particular sequence of annual real returns that you may receive a trajectory of returns.

Your investment strategy – the assets you tell MaxiFi you’ll invest in through time – determines what trajectories of real returns you may experience. Suppose your investment strategy is to hold stocks for 15 years and then switch to bonds. On average, stocks yield higher annual real returns than do bonds. But their annual real returns are far more variable. Hence, your trajectories of real returns will be generally high, but very variable for the first 15 years and generally low and smooth thereafter.

Or your investment strategy may entail holding half of your assets in stocks and half in bonds on an ongoing basis. In this case, your real return trajectories will generally lie midway between the typical all-stocks or all-bonds return trajectories. This mixed investment strategy would exhibit less real return variability than the all-stocks strategy, but more variability than the all-bond strategy.

For any given investment strategy, the particular trajectory of real returns you end up receiving will differ from the average real returns trajectory because of the random nature of the real returns you earn on your investments. In other words, you can’t expect to earn the average real return every year. Instead, there will be high and low real returns along any trajectory. You can also experience lots of low real returns or lots of high real returns in a row.

MaxiFi can’t tell you what trajectory of real returns you’ll receive through time. It can and does show you the range (distribution) of real return trajectories and associated living standards you may experience given your investment strategy. Keep in mind that the historical real return data we use to help predict future real returns are no guarantee of future returns. It’s also important to bear in mind that you only go through life once and will only experience one trajectory of real returns.

Translating a Real Returns Trajectory Into a Living Standard Trajectory

The trajectory of real returns you experience will help determine, along with your other economic and demographic inputs, the living standard your household will experience each year. We call a trajectory of annual living standards a living standard trajectory. For each real return trajectory you may experience, there is a corresponding living standard trajectory.

There is another key factor that enters into the determination of your living standard trajectory given your real return trajectory and other inputs. This other factor is your spending behavior, which you control by setting an annual safe rate of return. This is the return you can count on receiving, on average. We ask you to be cautious in setting your safe rate of return as well as all other inputs.

In traditional Monte Carlo analysis, households are assumed to spend the same amount no matter what returns they receive. No reasonable household would act this way. In contrast, MaxiFi’s Monte Carlo analysis assumes households adjust their spending each year in light of the returns they received the year before.

Indeed, MaxiFi’s Monte Carlo simulates the annual spending a user would do (and annual living standard they would experience) were they a) to run their Basic Report each year with their assets updated based on the returns received to date and b) spend each year what the Basic Report says to spend in the year they run it. I.e., MaxiFi’s Premium’s Monte Carlo is simulating, for a given randomly selected path of returns, how you’d fare is you were to use MaxiFi Standard on an ongoing basis. Stated differently, our Monte Carlo analysis is entirely consistent with ongoing us of our software.

Once you’ve specified your investment strategy and safe rate of return. MaxiFi produces hundreds of possible living standard trajectories to show you the range of living standard trajectories you may experience.

Using MaxiFi’s Monte Carlo Risk Analysis

Once you’ve run MaxiFi’s risk analysis based on your specified investment strategy and spending behavior (determined by your specified safe real rate of return), you can try other investment strategies and spending behaviors. You’ll see that less aggressive investing will lead to living standard trajectories that are lower, but less variable. You’ll also see that less aggressive spending, generated by a lower assumed safe real rate of return, will produce living standard trajectories that start out lower, but have less chance of being low in the future.

Bear in mind that you will experience just one trajectory of returns through time and one living standard trajectory based on that trajectory of returns and your spending strategy. Consequently, you face three risks when it comes to deciding how aggressively to invest and save:

  1. You’ll end up on a living standard trajectory that’s lower, on average, than you’d like.
  2. You’ll end up with more annual variability in your living standard than you’d like.
  3. You’ll experience more downside living standard risk toward the end of your life than you’d like.

MaxiFi doesn’t suggest what investment and safe rate of return you should adopt. This depends on your attitudes toward risk. What MaxiFi does is show you the implications of investing and spending more or less aggressively to assist you in deciding how to invest and spend through time.