Are Monte Carlo Simulations a Waste of Time?
Abstract: Monte Carlo simulations are great because they run thousands of predictions, showing which outcomes are most likely. Or perhaps Monte Carlo simulations are terrible because they destroy carefully collected data by overlaying random numbers. So what is the answer? At a minimum, Monte Carlo simulations are fine because, with enough simulations, the random numbers eventually refind the original accuracy. But are they an efficient use of time and computing power? The conclusion of this article is that when we dig deeper, the benefit of being able to customise individual parts of the model (reflecting the “messiness” of the real world) makes a Monte Carlo simulation clearly the best approach.
Monte Carlo simulations are great because they run thousands of predictions, showing which outcomes are most likely
The touted selling point of Monte Carlo simulations is that they simulate hundreds, thousands, tens of thousands or even more versions of the future.
A model will have been created to describe something (for example the various risks associated with a particular business). Many (perhaps all) elements of this model will have a probability associated with it; the model can then calculate how likely each risk is to happen in a given year.
And this model is what is used to make the simulation. If we imagine just one small part of a typical model: Perhaps it is thought that there is a ten-percent chance of very heavy rain during the winter in a particular region. And it is thought that such heavy rain causes logistical hold-ups. And so, as the number of simulations increase, the proportion of them that feature heavy rain (that causes a hold-up) will approach this ten-percent probability.
Clearly if only one simulation is run, then we have a single random example of what might happen in the future. And we would not know whether this particular simulation was showing us a likely overall outcome, an unlikely one or an extreme one.
However, the idea is to run a large number of simulations. We can then get a sense for which outcomes are relatively common, which are unlikely and so on. This is often presented in the form of a graph.
Example of the result of a large number of Monte Carlo simulations
Monte Carlo simulations are terrible because they destroy carefully collected data with random-number smudging
So, having just given a romantic description of how wonderful Monte Carlo simulations are, let’s consider whether it is a self-fulfilling prophecy.
“Oh, how wonderful! Notice how a large number of simulations allows us to overcome the randomness of the random numbers!” cry sarcastic opponents of the Monte Carlo approach.
What, say Monte Carlo opponents, if we simply didn’t do any of this at all? We already know that ten per cent of the time, the heavy rain would cause a logistical hold-up. We could instead simply add all these “average” values together and get an average outcome for any given year. This is a very useful number.
Additionally, if we really want to, we can get a mathematician to calculate perfect distributions of likely, unlikely and extreme outcomes. This is complicated but doable mathematics. And it is worth it to gain the perfect answer!
Checkmate! This has to be the best. The same outcome, the same data and graphs can be produced. And no accuracy is lost. And we are not constantly running a large, clunky model.
So is this the answer, are Monte Carlo simulations a waste of time?
Even strong advocates of Monte Carlo simulations will concede that: where you have access to a mathematician (or a team of such) and a certain type of problem, yes an analytical approach can be neater (ignoring issues such as cost).
But the debate is not yet won.
Regardless, Monte Carlo simulations are fine because, with enough simulations, the random numbers eventually refind the original accuracy
It is important to note at this point that Monte Carlo simulations are not giving incorrect results. Those who argue against it are typically arguing in terms of efficiency or in terms of it being neater and simply to do a bit of mathematics instead.
If we ignore efficiency or “neatness”, then we can focus on accuracy. And as long as we run enough simulations, a Monte Carlo simulation is accurate.
And the real world is messy
The real world is messy. Analytical mathematics has given way to computer modelling in most sectors now. Formula-one teams use three-dimensional simulations. Modern aeroplanes are constantly making calculations onboard to correct instabilities in their flight; they are not surfing the waves of a neatly calculated equation, instead they are constantly adjusting to the chaotic turbulence of high-speed flight.
Monte Carlo simulations (with the name being an accident of history that we will not dwell on) are exactly the same kind of powerful computational approach that has enabled humans to start mastering the “messiness” of the real world.
To infinity and beyond
Imagine a company that has a factory. This factory will have cost a finite amount of money to build. It will not have cost an infinite amount of money (remembering that the practical effect of “infinite” is that it permits a number to become extremely large, beyond the physically meaningful).
But this is mathematically “messy”. A statistical distribution generally continues to infinity. And so, this statistical distribution is telling us that, in very rare cases, your factory fire could have an impact of hundreds of trillions of dollars. A factory fire with an impact of this magnitude would take down the global economy with it! This is not realistic.
So, when modelling events, such as the impact of a factory fire, we need to recognise there are hard limits so that it cannot become too large. This is just one example of a vast number of such “real-world fixes” that are applied to the mathematics.
Monte Carlo simulations are a tool
So, in conclusion, Monte Carlo simulations are perhaps pilloried by some because they are being knocked down due to not being something they were not supposed to be in the first place! True, we can show that the core functionality of a Monte Carlo model is simply reproducing (in a complicated way) what can be achieved through pure mathematical analysis.
However, the whole point is that a Monte Carlo simulation is a tool (or perhaps better, a “framework”) that enables tens, hundreds or thousands of little “corrections” to bring the mathematics in line with the real world.
A Monte Carlo simulation is an incredibly powerful technique; when you have a real-world situation that needs modelling statistically.
It is like a cake: the lovely sponge within is the frame onto which decorations are attached.
It is like a football team: a solid framework of goalkeeper, defenders, midfielders and forwards becomes fluid and adaptive as the game is actually played.
It is like a perfect date: a restaurant followed by the cinema is actually more than just this framework because simply eating in silence and then watching a film would likely be considered a failure.
What do you think?
We would love to hear your thoughts in the comments below or contact us directly. Or you might share this article and add your personalised comments for your colleagues or friends to read.