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June 18, 2020

Mathematics and Predictions

Author: Kristopher W. Carroll, CFA®, CFP®


I started life as a mathematician. In fact, through the first few years of college, I still considered myself a mathematician. When I started studying finance, I thought of finance as the mathematics of business, and in many aspects it is. As I continued to study and really started to focus on investments, I realized that investing is not all math. I vividly remember my father telling me that there was an art to investing as well as a science. To this day I still believe he is right.


Dealing With Unknown Unknowns
In many ways, investing deals with uncertainty. Mathematics deals with uncertainty quite well. It even has these wonderfully complex words like “stochastic random variables” that allow us to describe uncertainty. Unfortunately, mathematics focuses on what I would call “known unknowns”. Variables where there is uncertainty, but we know something about them. Maybe we know the standard deviation or the probability. That is where mathematics can handle uncertainty. Too often in investing, we deal with “unknown unknowns”. There is randomness, there are things we do not understand and outcomes we cannot predict. We don’t know what we don’t know. I am not sure I have ever had a better example of that than when dealing with the coronavirus outbreak or the current state of our economy.

If you asked me at the beginning of 2020 about the probability that unemployment would reach 15% in the next six months, I would have had to evaluate scenarios that would cause that to happen. I am not sure I would have said 0% chance, but I am confident I would have come up with a very small number, something less than 1%. Clearly, I underestimated the “unknown unknowns”. Today, so many of our clients are asking us: “What’s next?”, “What is going to happen to the economy?”, “What is going to happen with the markets?” At the bottom of the market on March 23rd of this year, if I had told anyone that I thought the market would be close to even for the year by June, they would have told me I was crazy. Once again, I do not know what the probability of that happening was. But today, as I am writing this, we sit pretty close to even for the year. That does not mean everyone is right back to where they were, but it does mean that we have seen a substantial rebound in markets… not so much in the economy though.

Today, I feel like there are so many more “unknown unknowns” in play. How will this virus be dealt with? How will it work its way through the system? Will there be a second wave? How will the economy react to a second wave if it occurs? How will the economy react to the amount of money and stimulus that the government has put into the economy? How will we work out of that stimulus and remove the excess money in the coming years? When I think about this, it is so hard to judge mathematically. It is hard to make predictions in the face of so many “unknown unknowns”.


Sticking To Your Plan
In thinking about these predictions, I am reminded of one of my students at Winthrop University. His name is Don and he is a retired engineer. He takes classes at Winthrop because he is fascinated with finance and managing his own assets in retirement. Don, like many engineers, looks at investing as a problem to be solved. He looks at it as if there should be a solution to how he invests. I think it is better to look at investing as a discipline rather than to look at it as a problem. We make the best decisions we can, we follow the rules of rational investing and we try to avoid doing what our gut tells us to do. So often our gut is wrong, and the rational choice is the best solution, but what is rational in the face of so many “unknown unknowns”? To me, I must fall back on the basic rational tenants of investing:

  • Stay diversified.
  • Understand the risk you are taking.
  • Keep a long-term view.
  • Stay the course.
  • Pick a plan and stick to it.

If I ignore the path that the market took from where it started the year to where it sits today, I would conclude that this is very normal market volatility. In fact, it has been anything but normal. But in the longer term we will look back at this as just a blip from an investing perspective.


What We Can Learn
I do think there are things to learn from this. The experience reminds us that the “unknown unknowns” do exist and that they are often bigger than we think they are. Some investors refer to these as black swans. While I am not sure if the coronavirus swan is black, I do think that we went through an unusual period of the market and continue to live through a very unusual time in our economy. I do not want to make predictions about the next six months or even twelve months based on this black swan. I will tell you a longer-term prediction though. In the end, the losses are temporary, and the gains are permanent.


Bottom Line: I don’t know what things will look like in the next year, but I do believe in five or even ten years from now we will remember the coronavirus by how it affected our personal lives, not how it affected our finances. The best thing you can know about math is: no mathematician could have reasonably predicted the volatility we have seen in the past four months. With that said, investing discipline should never be changed based on the experience we have over such a short period of time.

In the News, Market Volatility

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