# Monte Carlo Reports

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ESPlanner is able to use Monte Carlo simulation to provide a very powerful statistical analysis to help you understand how risk factors into or changes how we view what is otherwise an average or ideal trajectory of our retirement income and living standard. We can tell the program in the assumptions inputs that we expect to earn an 8.5% return on our retirement investments. But of course the chance of this 8.5% recurring year after year without variation is not likely, to say the least. So although we might get 8.5% on average over a long period of time, what might our living standard and sources of income really look like as we live through this variation each year from now until we die? This is what the Monte Carlo reports help us to understand.

Its simulations show that a household’s living standard will not necessarily soar if its portfolio value doubles because of the extra taxes it will have to pay, nor plummet if its portfolio value drops because of the concomitant decline in its taxes.

Note well that the Monte Carlo reports in ESPlanner provide information—not just about a single pool of retirement assets as do most Monte Carlo reports in other software—but rather something much more valuable: the distribution and trajectory of living standard. Why is this more valuable information? It’s more valuable because retirement assets are only a part of what supplies us with living standard. Indeed, with pensions and Social Security in the mix, we want to learn about the upside and downside of our living standard (discretionary spending) not merely one pool of assets.

## Trajectory Reports

These reports are given not in percentile ranking or probability ranges like the other two kinds of reports because the emphasis here is not on variability or probability of the scenarios in any given year, but rather on the entire trajectory or life span of the portfolio—and for this we must view a whole column. Like the other two kinds of reports, the trajectory report has generated behind the scenes 500 different economic lives lived with the one data set. The Trajectory reports are showing just five of these 500 paths (as columns). They are not average paths, but rather five very particular paths generated from among the total of the 500 generated by the software. In order to determine which five to show us, the software calculates the internal value of each of the 500 paths and ranks the paths or columns and arranges them beside each other from lowest to highest. It may be interesting to note that the internal value of a given path or column is not just the sum of the numbers in that path, but the present value of each of these numbers. In other words, each number down the path from early in life to the year we die is “weighted” to reflect its present value in relation to whether the number is, early or late in our life. The main point, however, is that these five columns represent the 500 columns or paths generated (again, showing you all 500 would be overwhelming) and represent the 5th (very low), 25th, 50th, 75th, and 95th (very high) percentile ranking of the columns or paths relative to each other (described in the column header as very low to very high). We use the “very low” and “very high” designations so as to not confuse them with the distribution reports. Remember, any particular number in a row in the trajectory may even seem out of place if a number in a left row is greater than a number to its right in the same row. But these trajectories are arranged as columns, and any one row across columns is a minor factor relative to the value of the column as a whole trajectory set.

The point of displaying these trajectory columns is to indicate that even though you may do well, on average, with respect to the returns you earn over your lifetime and end up with a very high level of lifetime consumption, you’ll experience a lot of variability in your living standard down that column path from year to year because your returns will be high in some years and low in others, even though they’ll generally be high, if you are looking at the “high” or “very high” column. In a nutshell, the trajectory reports show that doing well or poorly over your lifetime with respect to the returns you earn, doesn’t mean you’ll do well or poorly each and every year.

In trajectory report we are focusing on the change or variation down a path or column and comparing it to one of the other four paths generated by the same data set. Thus we tend to look first at a trajectory report by scanning down the column to see how much variation there is as we scan down the column in each of the five represented trajectories or paths.

It may also be interesting to note that if we do read across the row of a particular year, jumping from one path (column) to the next, we should not expect to always see the number be larger in the corresponding year of a different path even when that path is to the right, thus indicating that the path, taken as a whole, is a better path than to the one to its left. It other words, it may be better or worse in any given year, but taken as a whole, the path or trajectory to the right will be of higher value than the column to its left. Consider, for example, that you are viewing the 250th path out of the 500 paths generated (the median path or middle column). If the software were to show you path number 249 (which it does calculate but doesn’t show you) you might see a much higher number in year 2041. But taken as a whole, path (column) number 250 is slightly more valuable than path number 249. Again, there is no reason to view all 500 paths. Five is sufficient for most users to get the point.

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