Monte Carlo Simulation of the S&P 500
Executive Summary
As of this writing, there are many prominent financial figures discussing the probability of a recession, given the hawkish Federal interest rate hikes to combat inflation. With layoffs in the tech sector, the S&P 500 has already taken a battering - but is there more to come, and if so, can we predict it?
Monte Carlo Simulation
In essence, we run a simulation multiple times, in order to try and predict the likelihood of different scenarios playing out.
Step-by-Step
We create a simulation
We run it many times over (in this case, 1000 times)
We analyze the scenarios cumulatively
Average, standard deviation, etc.
Graphs (data visualization)
What are the benefits and drawbacks of simulation modeling?
Benefits: objective predictions based upon the combination of
Drawbacks: external factors remain unaccounted for
Can this Monte Carlo, or any other simulation, accurately predict what the S&P 500 will do?
In a word, no. But there is much value to be found here. We can observe the basics of what is and is not within the realm of likelihood, by putting the simulations into buckets and seeing which buckets fill. The “empty buckets” are not impossible - but they are highly unlikely. For example, it is likely the S&P 500 will increase or decrease somewhat over the course of the next year, but it is unlikely it will half or double in value. We can use statistics to visualize this.
What will the S&P 500 be next week?
Using weekly data from the past five years, we can start crafting the initial simulation. This data starts with the S&P 500 closing with 2,651.50 points the week of December 4th, 2017. It ends with the SP 500 closing with 3,963.51 points the week of December 5th, 2022. Much has happened in between - COVID, elections, and international conflict. This simulation just looks at the numbers - it can’t tell what the world will do next, but it can predict how the SP 500 will act in a vacuum - which is a useful tool.
Here we can see the average and standard deviation of the SP500 for the past five years - as well as the percentage changes week-to-week. I have also calculated the average and standard deviation of the percentage changes as well.
Now, let’s see what the SP 500 may look like next week, which as of the time of this writing, is December 12th, 2022. We know that the SP 500 closed with 3,963.51 points the week of December 5th, 2022. We also know that the standard deviation of the last five years, week-to-week, is approximately 672 points. This means that next week, the SP 500 is likely to change by, at most, 672 points up or down. Given the width of this standard deviation, it may be prudent to stay within a half-standard deviation - this means that we will likely lose up to 336 points, or gain up to 336 points - or something in between. For our purposes, we can then make a formula in Excel that looks something like this:
This formula is saying:
Give me a random number, between…
Last week’s points, minus 336 points (minus 1/2 std. dev.)
Last week’s points, plus 336 points (plus 1/2 std. dev.)
Obviously, this could result in a multitude of answers.
What will the S&P 500 be on the Week of January 1st, 2024?
We can use our prior predictive model to drag out what with happen the week of January 1st, and then, copy that a thousand times. This is called a Monte Carlo simulation.
Using our same formula, we get a scenario in which the S&P 500 is at 4,308 points. Then we copy that formula a thousand times. One can observe that percentages are calculated here as well - which is where much value can be derived from these simulations. We can see that, of course, the S&P 500 is likely to stay within the realm of reason. There is only one out of a thousand scenarios in which it goes over nine thousand points, and only five in which it crashes down to zero (the simulation will make some of these negative, but since that isn’t possible, we count them as zeroes).
