If you are like most people, you occasionally see the phrase “we used a Monte Carlo Simulation to...” If you are a rare person, you have thought about that phrase and may have wondered what the deal is with Monte Carlo simulations and why they are supposed to lend credence to whatever is said in the sentence after that phrase.
I ran thousands of Monte Carlo simulations during my thirty-something year career as an actuary. During that time I often saw people who misunderstood “Monte Carlo” and what can and cannot be learned from such a simulation. In this post I will discuss what they are and what they are not, and how we can use a Monte Carlo simulation to make more nuanced decisions.
Computer Model of a Real World Process
First let’s talk about a non-Monte Carlo simulations; a simulation is a computer modeling of a real world process. It has many values, such as allowing us to study how each different input affects the process, or the effect of introducing a new input.
What is a Monte Carlo Simulation?
Now let’s deal with the “Monte Carlo” bit. It’s simply meant to convey that the inputs to the simulation have been allowed to vary during each simulation, and that the simulation is run many times to test the variability of the entire process. This means, for example, that we don’t just assume we have an 8% stock market gain each simulated year. Instead we allow the return to vary so that some simulated years will have great returns while others will have bad losses.
I’m sure that, at some point in history, the name “Monte Carlo” was chosen because of the famous casino in Monte Carlo. Over the years, the name “Monte Carlo simulation” has (at least for some people) taken on a certain gravitas, perhaps due to the old world/money association with Monte Carlo.
While I enjoyed giving my work that kind of prestige by saying “I performed a Monte Carlo simulation on this and (average result)”, the real value of those simulations was the information they gave beyond the average result, like how often we should expect to end up losing money. After reading this blog post, you will know how to get the additional value that “Monte Carlo” brings to a simulation.
Here’s a concrete example: driving to a destination
Although much of financial planning is about saving for retirement, that can have a lot of complicated elements so let me do a simpler example first; since saving for retirement can be compared to driving to a destination, let’s start with that as an example:
My GPS has a “simulator mode” that allows me to see how do the 45ish minute drive from home to the office. If I watch it over and over it might help me to memorize the turns and the speed limits on different roads, but every time I watch it the trip will take 45 minutes.
Because I do stuff like that, I timed my actual drive time for a couple of years and found that 45 minutes was pretty accurate on average. The thing is, my actual experience showed the trip rarely took exactly 45 minutes. There were often delays, usually due to traffic, but other days the roads were clear and I hit every green light so the trip was shorter.
Limits of using a simulation
The GPS was useful the first few times I drove to the office, but after I had memorized the route the question I needed answered changed from “How do I get there?” to “If we have an 8am meeting every morning, what time do I need to leave the house to ensure I won’t be late?”
Once I had done the commute a few million times I got a pretty good idea of when I need to leave to be safe. But that didn’t help me if I had a new destination (like a meeting in a client’s office); in that case I was stuck with the GPS’s single estimate.
Saving For Retirement: Monte Carlo Simulation Example
Similar to getting to an 8am meeting, I don’t just want to know how much money a simulation shows I’ll spend in an average retirement; I need to have a safety margin because there might be “slow traffic” in the form of an illness or drop in the stock market that would result in my running out of money too soon. (On the other hand, I might happen to retire during a good run in the stock market and have much more money than I had anticipated in retirement.)
It’s not a problem if I need less in retirement, of course, but it is a problem if I end up needing more than my savings and investments bring me because I’m probably not going to want to go back to work when I’m in my 90s.
The internet has a lot of basic financial tools that are like my GPS; they’ll tell us whether our current savings rate will allow us to accumulate a certain amount of assets by some age (typically 65) on average, and then how many years those assets will last in retirement (again, on average.)
A Thousand Swings At The Bat
A Monte Carlo retirement simulation, on the other hand, lets us simulate our remaining life thousands of times, and each of these simulations will incorporate random good or bad luck in each of the inputs for each simulation. Sometimes good luck in some inputs will offset bad luck in others so we’ll end up close to the average, while other times there’ll be more good luck than bad, or more bad luck than good. By simulating thousands of remaining lives, the Monte Carlo simulation gives us a better idea of what kind of safety margin we will want to have before retiring.
Does this mean that the result of a Monte Carlo simulation will be correct? Before we answer that, let’s make sure how we’re defining “correct”; if what you’re asking whether the average outcome of the “Monte Carlo” is going to be your average outcome, then you’re not thinking about a “Monte Carlo” simulation correctly!
Range Of Outcomes, Not A Single Answer
Remember that the result of your Monte Carlo simulation won’t be a single answer; it will be a range of outcomes; you’ll fall short in some of those simulated outcomes, while in others you’ll have plenty of money. As the saying goes, “your results may vary”.
The value of the Monte Carlo simulation isn’t in the average; it’s in the range of outcomes because that is what allows us to make rational decisions about our actions. Here’s some examples to show why I say that:
- Let’s say I do a Monte Carlo simulation and it shows that I have a 55% chance of having enough money if I retired today. A non-Monte Carlo simulation would show that I have enough money to retire but, for me, a 45% chance of falling short would be too high, so I would probably continue to work longer than simulated, or I’d rethink my retirement lifestyle.
- Let’s say it shows that I have a 98% probability of having enough if I retire at 65, and 95% if I retire at 63. Well, that’s an interesting finding, and I might well decide retiring a couple years early is worth the 3% increase in my probability of falling short. (Or maybe I wouldn’t decide that – the point is that now I can now make an informed choice.)
- Let’s say it shows I’m 95% likely to have enough. Let’s also say I’ve always dreamt of buying a certain exotic sports car; if I redo the simulation starting with X dollars less than before (I’ll ignore maintenance and stuff like that because no one ever thinks about that stuff when buying a sports car) and it shows that purchase only reduces my odds to 94%, then I’d probably try to convince my wife to indulge my dream. If, on the other hand, my chances go down to 80%, then I’d try to think of a different way to finance that particular dream.
The Value Of Monte Carlo Simulations: More Nuanced Answers To Financial Questions
These examples show the value of Monte Carlo simulations; it gives us a much more nuanced answer to financial questions, and so allows us to make decisions on questions where just plain “yes” or “no” aren’t enough to feel like we’re making the best decisions for ourselves and our families.
So, now, getting back to the question of whether the Monte Carlo simulation is correct, I hope you see that the answer to that question does just not lie in the average, but in how well the range of results reflect the actual range of outcomes we can expect.
Ask About The Inputs
Since we only experience retirement once, we can’t directly test the variability. What we can do, though, is ask our advisor some questions to see how the inputs to the Monte Carlo simulation are allowed to vary and decide if they are realistic:
- How are the investment returns varied? Stock and bond returns are endlessly analyzed, so historical variability is quite well known and should be reflected in the simulation. Don’t accept “the variabilities from 10 year periods” or anything like that – multiyear periods smooth out variance. While that may be appropriate for deciding on an investment mix, our actual retirements will be lived year by year, so that’s the kind of variability we need to plan for.
- How frequently are “black swan” events assumed to occur? I remember discussing a Monte Carlo simulation with its designer who told me the “great recession” was modeled as a once in 200 year event. I asked him if he’d ever heard of the “great depression” and hung up the phone.
- How is catastrophic illness modeled? The correct answer to this will vary for each of us, of course, because diseases may run in our families. You definitely want to make sure the simulation reflects the possibility of catastrophic illness, but you might have to use your judgement to decide if the frequency derived from the population adequately reflects the risk for you and your family.
- What kind of variability in length of life is incorporated? If it just simulates out to a maximum 30 years of retirement then you should demand a different simulation, especially if people tend to have long lives in your family.
- How many simulations are run? For an actuarial analysis, I want at least 10,000, but don’t let someone cow you by saying they did millions of simulations; my experience is that the results don’t vary much once you get past 10,000. (If a planner tries to tell you that’s wrong, ask them how many simulations are required for convergence. “Convergence” means that you don’t get much additional variance after a certain point so that, for example, the 75th percentile point will be pretty much the same whether you run 10 thousand simulations or 10 million. )
The list of possible items to vary is too long for a single blog post, but these are the kind of items you should look for; don’t be shy about asking your planner what has been allowed to vary in the simulation, and the basis for how variable they are allowed to be! (Don’t be surprised if your planner has to get back to you on some things.)
The value of a Monte Carlo simulation is in the variability
“Monte Carlo” is often taken to convey some sort of gravitas to the average of a bunch of simulations, but the real value of those simulations is not in their average; it’s in their variability. We can use the knowledge gained about that variability to improve our decision making, whether it’s deciding what time we need to leave the house in the morning, or the serious decisions we make about our financial futures.
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