Is there a better explanation of Monte Carlo somehere?

I am having great difficulty understanding the reports. The manual uses numerous terms of art without defining them. As a simple example, the term "living standard" is never defined. Why is living standard different from consumption? I won't even start on the explanation of the Monte Carlo reports. ESPlanner is a great product and is very easy to use but the documentation for the reports was written for someone who has a Ph.D. in either economics or statistics, which, unfortunately, I do not.

Is there an ESPlaner Reports for Dummies?


dan royer's picture


It sounds like it would be a good idea for us to develop a shorter guide with tighter explanations.

I can help you with "living standard" and explain the distinction between that term and "consumption." Both terms refer to discretionary spending that is available after one pays for housing, taxes, retirement saving, and term insurance. What's left for the household is "consumption" and you see that amount on the annual recommendation report in the left-most column.

Living standard is derived from this consumption amount. Living standard in ESPlanner usually refers to this consumption amount scaled to "per-adult." So if you run the program as a single person, consumption and living standard are the same amounts. If you run it as a partnered or married couple, then you'll per-adult living standard to be consumption scaled to reflect that two adults in a household live at the cost of 1.6 adults.

So this is why the terms might be used interchangeably.

Monte Carlo analysis refers to a method of analyzing and plotting the effects of investing in different asset classes. The method of analysis has been around for 40 some years but only in the last ten years has it been used by the financial planning industry, and only ESPlanner uses it in a way that shows the impact of your investments on consumption or living standard that also accounts for your fixed-income such as Social Security.

It is a complex concept, so it's not easy to explain in a few sentences. If one takes a particular set of investments and runs them based on historical probabilities, one will see a different "trajectory" each time you run it. In other words, the returns on the investments we make can not be predicted with certainty. The returns vary, but we can predict the range of the variation. We can say with probabilities what might happen to these investments. This is what Monte Carlo analysis does. What ESPlanner does, is it also takes these investment probabilities and shows their impact on our living standard.

Sorry that this sounds so complex.

I hope you stick with it. And I suppose that too is what the forum is for--quality planning is complex but lots of folks on the forum are willing to help out.


Thanks for your reply Dan. I don't think the explanation of the Monte Carlo reports needs to be shorter but it needs to either eliminate the terms of art or define them. I have a 30 year old MBA from the U of Chicago and my wife is a CPA. If we are struggling I suspect others are too.

I think I understand the concept of Monte Carlo simulation but certainly not the mathematics or details. Let me try a couple of specific questions.

One of the things I would like to know from the Monte Carlo simulation is the level of consumption that I can sustain with a 95% confidence level. Is that available in the reports?

I think I understand what the distribution reports are telling me.

Page 44 of the help attempts to explain the trajectory report beginning with the following sentence.

"In a trajectory report, the lines representing a lifetime trajectory are
ranked according to the overall value of the line."

What is a trajectory? What is "the overal value of the line"?

dan royer's picture

Yes, this stuff seems to get pretty complicated. The reports show several different ways of looking at the same thing, and that adds to the complexity I suppose.

In order to get to your question about consumption levels with a 95% chance of sustainability, yes, you can learn that from these reports.

You begin by running your current setup and asset allocation and comparing the living standard distributions in the 5th, 25th, . . . 95th columns. It sounds like you already pretty much understand those. Those columns will help you to see the variation in any given year. So pick a year and read across the row in the grid and see how much difference there is between the 5th and the 95th. Those numbers going down those columns indicate your living standard (not to be confused with "consumption" if you are married). What you are looking for is to see what sort of living standard variation there is in any given year.

But perhaps more what you are looking for is to learn what kind of a living standard you would have if that living standard had a 95% chance of success. So you want to look at the Living Standard Trajectory Report. This will show five columns--very low to very high--and these five columns represent five (out of the 500 possible) living standards that the computer calculated for your particular situation. The "very high" may look very good--you say, yeah, I want that one. But that one appeared in the 95th percentile--that is, it was better than 95 percent of all of the 500 scenarios run. So you would want to look at the 5th percentile and say to yourself: ok, this one doesn't look as good, but I only have to be in the 5th percentile to experience this living standard! In other words, I don't have to be very lucky to have this living standard. In the 95th percentile, you have to be pretty lucky to experience that sort of living standard thread.

By thread or "line" there the Help manual is referring to the line on the chart on that page 44. So you can see in that example that the "Very Low" thread or line is what the computer picked as the lifetime living standard that was ranked in the 5th percentile. If you are comfortable with the living standard that this line traverses as it moves about through life across the chart, then you are in good shape. You can say to yourself, "hey, if I'm only in the 5th percentile--if 95 out of 100 do better than me--I'm still happy. If that living standard seems too low, then you have to either assume more risky investment or find some other way to raise that living standard through optimizing your economy in some way--for example taking SS at 70 instead of 65 or something like that.

Perhaps that's enough for the moment. Does that help? Feel free to ask a follow up. I'm sure that once you get past a few questions it will start making sense. It's just that this is a somewhat different way of looking at things and it takes the mind a bit to grasp things--it did for me anyway, and of course, as you say, perhaps it could somehow be put more clearly than I am doing here.


This has been helpful to me too. I need some clarification on "living standard" within Monte Carlo. I'm assuming it is the same as the "living standard per adult" that is listed in the "Annual Suggestion" table? Or does the "living standard" in the Monte Carlo include the 1.6 multiplier.

dan royer's picture

It's the same per-adult living standard you see in the Annual Suggestions area.

So, referencing the Monte Carlo living standard report, if one of the items in the 5 percentile column says $30,000 then can I take this number and multiply it by 1.6 to get the family living standard number (i.e. 2 can live cheaper together)? This would mean that the 5 percentile number represents a "Consumption" value of $48K?
Just want to make sure I understand this number.

dan royer's picture

Yes, that's true in many cases. But remember, "discretionary spending" or household spending also includes children in the home. So multiply by 1.6 only works if there are no children in the home in that year.

Great. Thanks! This helps a lot. Yes, in my case, kids are out of the house and it's just my wife and I. So 1.6 should work well.

dan royer's picture

I forgot: the "overall value of the line" . . .

The Monte Carlo (MC) runs 500 different times, each one generating a slightly different path or living standard that is a consequence of your particular economic situation that includes your Social Security and your investments and everything.

So it could show you all 500 of those living standard columns of numbers (or lines if put on a graph) but of course it is most useful if they are sorted somehow. So they sort them from low to high. But what does that mean? Well, Kotlikoff has figured out some math using "present value" (you probably understand that better than me) so that numbers early in the life are weighted to be more valuable than numbers later in life. I trust that it makes sense. So when it's all said and done, each of those 500 paths or trajectories has a value that makes it better or worse than the other 499 (even though as the path progresses from left to right on the chart, it might actually dip below or above a competing path).

But rather than show you all 500, he's just showing you five that represent Very Low, Low, etc. so that you can get the general idea rather than see all 500.

So that's what's meant by "overall value of the line." The line or path or trajectory--I suppose it would help to use but one metaphor instead of three? indicates that each of these trajectories has an "over all value" that has a ranking against the other 499. The program shows you a representative five of the 500.

does that help?


Is the Monte Carlo "randomized?" Meaning if I keep the input exactly the same and rerun the calcs, will the results be subtly different? Of is it programmed to run through the same 500 scenarios in the same order each time?

dan royer's picture

Yes, it is random, but I recall one of the programmers saying that you probably won't see even subtle differences each time because of some variable in the program that is recalled each time the program does the math on the same data set. But if you were to create a whole new profile, then you'd see the very subtle variations given the same data.

Thanks Dan. Your two messages answered most of my questions. I just have one more at the moment. On the Variability of Living Standard report, what does the Projected Trajectory column represent?


dan royer's picture

I'm going to cheat on this one and copy an answer from Kotlikoff elsewhere in the forum. The short answer is that it is the average return on assets held in that year. So "projected" means "expected" as used here. Here's Kotlikoff's answer:

When you run the program with Monte turned on, all the numbers shown in the Main and Detailed reports are generated assuming you earn, each year, the mean (expected or average) return on the assets you tell the program you'll be holding in that year.

In other words, when you run the Monte, the Main and Detailed reports are generated just as they'd be if you ran the program with Monte turned off except they use each year's expected return for that year's rate of return rather than use a single rate for all future years.

In the Monte Reports, on the other hand, we are showing the results of running/simulating 500 life paths. To see what's going on, imagine you run the program this year with Monte turned on and spend based on recommendation in the Main Report. Now a year goes by, and it's January 1, 2008. You earned a return on your assets in 2007 that differs from the mean return, which is what the Main Report assumed. Your assets on January 1, 2008 are, thus, going to be different from what the Main Report for 2007 said they'd be in 2008. So you run the program again for 2008 and it tells you, in the Main Report, what to spend. You spend this and cotinue in this manner through time. Each year you'll have a recommened level of spending and an associated living standard. At the end of your life, you'll look back and see a path of past living standards. This is one of the 500 paths of living standards that we generate and then use to show the variabiilty across the 500 paths of your living standard in each future year.

Now I realize that what we are showing here is the results of very agressive assumed spending behavior. (Our next variant of the Monte Carlo program will modify this assumption and base spending/draw down rates on what's called expected utility maximization, which will take into account users' risk aversion.) But I wanted to show users who might be basing their spending on expected returns that spending this way will lead to a lot of downside living standard risk as they age if they invest in risky assets.

Any chance a video tutorial, specifically on understanding Monte Carlo reports is forthcoming?

Thanks again. I believe that I have the information I need now.

Please see the attached image of my Living Standard Trajectory report for the Monte Carlo Simulation. I'm confused about the numbers. I thought that they would get bigger as you moved from the "very low" (5th %ile) to the "very high" (95th %ile) columns, as in the row circled in blue. However, in the row circled in red, this is not the case. Am I misunderstanding the meaning of "very low" and "very high?"

Comment Image: 

It's tough to understand MC results even with your own profile when you know your inputs and tougher to do this confidently with someone else's data, goes.

First, I'm guessing your Spending Behavior is set to "spend aggressively". That would seem to make sense from the graphic.

The first couple of years often have (in my words) somewhat questionable numbers. The team is working on enhancing MC and hopefully this will make the red section values appear more realistic. Honestly, I discount the first 3 years or so especially since you are a decent way out from retirement. There can be constraints in your profile when run through MC that cause "very high" results to be lower than you expect. Partly, this is due to actual/potential constraints as the 500 MC runs are made.

As you look at the columns (VL, L, M, H, VH), they generally increase up to the H column, as expected. The VH column, I'm guessing, is lower because of constraints in regular assets in your profile, but that's just a guess.

When you move to age 62 (blue circle), I'm guessing that you are retiring or starting Social Security or starting some withdrawals from retirement assets or possibly your mortgage is paid off at this point or similar change. That seems reasonable for why you see the big jump in values. Also, you'll notice that for the VH column, the numbers are higher, suggesting that you are no longer constrained in regular assets.

There may be options to smooth and raise your consumption. Various forum posts discuss this so I won't get into details here.

I hope this is helpful.


Thanks, Brian. That is somewhat helpful. I do hope Monte Carlo improvements and better explanations of the reports are forthcoming.

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