Fat Tails & the Risk Hidden Underneath the Lines

If you do not know already, Lucratyva, LLC is completely student-run. When we sit in class and learn about finance, economics, and mathematical distributions, we tend to see correlation and connection between the three topics.

Often, we find the teachings incredibly helpful and informative to our own operations, but sometimes, we and other students across American campuses are taught a cookie-cutter curriculum about finance and financial modeling that fit the traditional mold (quite literally the bell curve mold). While these are incredibly important fundamentals to learn, it does not mean it should be applied everywhere and every time.

Our minds love patterns, normalcy, and linearity. It just makes sense to us. This is why normal distribution curves, or bell curves, are blatantly overused. We take this fundamental mathematical principle and apply to everywhere (sounds very cookie-cutter to me). But let us see the flaw in this with an example, one used by renowned statistician Nassim Taleb:

In this example, we have two scenarios. Imagine we initially have a group of 5 people. The average weight of this group is 157 lbs. Let us say that the chance that a 500 lb individual joins the group is 0.01% and assume that a 500 lb individual does join the group.

The average weight now goes up to 214 lbs, a percent change of 36%. In scenario B, we have the same group of people and their average net worth is $495,040. Again, let us say that the chance that an individual with a net worth of $1 billion is 0.01%, and assume that a billionaire joins the group. Now, the average net worth shoots up to $167,079,200, or a change of 336%.

What does this mean?

When extremities occur, the averages shift to a new “normal,” but the change in averages is important. In both scenarios, the chance of the extremity happening was 0.01% but the change in averages were 36% for the weight scenario and 336% for the net worth scenario. For a probability of 0.01%, an average change of 336% is far more significant than a change of 36%.

Imagine the stock market crashing tomorrow. How much will your portfolio change by? 10%, 100%, 100000%? A black swan event is an extremity, meaning very low probability of occurrence. In reality, the S&P 500 dropping 20% on Monday has a 0.000165% of occurring, or once in every 25 years. But according to the normal distribution model, that chance is 1.8 x 10–79%. This shows that the current mathematical models used, primarily normal distribution curves, are innately flawed. We saw that it worked for many other criteria like the average weight scenario, but it did not work for the net worth scenario. Both scenarios had a 0.01% chance of occurrence, but one extremity had a larger impact on the average than the other.

This same principle can be applied to finance. If I told you that the S&P 500 dropping 20% in a single day only happens once every 2 x 1076 years, would you be worried about your portfolio? Absolutely not, that is not even in your lifetime. But what if I told you that the S&P 500 dropping 20% occurs once every 25 years? Now, I have your attention.

So what is the alternative to normal distribution? Fat-Tails

Ed Carver of JP Morgan explained this concept perfectly:

“The idea that returns from financial assets are normally distributed underpins many traditional financial theories, but the reality is that many (even most) assets do not conform to this. Instead, empirical distributions exhibit higher peaks and fatter tails — returns are mostly clustered within a small range around the mean but extreme moves occur more frequently than a normal distribution would suggest.”

Fat-tails are not about the frequency of low probability events, but it is the contribution of these events to the total property. Even if the probability is low, the impact of the event can fundamentally change your portfolio, indexes, markets, and economy. This is just like the average net worth example.

The probability of a billionaire walking into the room is very low, but if it does happen, the average net worth changes by 336%. In fat-tail distribution curves, the tail of the curve quite literally looks more “fat,” meaning that the probability of extreme events is higher and has a greater impact on the average compared to a normal curve. A fat-tail distribution curve can predict a 20% single day drop in S&P 500 once every 25 years while normal distribution predicts that the event would happen in thousands of millennia.

Not everything is so cookie-cutter. We saw that normal distribution works for the example about weight but does not work well with the net worth scenario. The same thing goes with finance. Normal-distribution curves work for subset of assets, but it may not work for all.

The teachings of scholars like Taleb is just one of the many that we utilize at Lucratyva. Other than an economic and financial background, our STEM backgrounds have allowed us to approach markets in a far more scientific and mathematically-oriented manner. Sometimes, you must go against the grain, against the herd mentality to gain a lucrative reward.

If you would like to learn more about fat-tails, I recommend you check out some of Taleb’s work and some interesting articles:

https://www.businessinsider.com/normal-distribution-versus-fat-tails-2016-10

https://www.sr-sv.com/the-dangerous-disregard-of-fat-tails-in-quantitative-finance/

https://www.statisticshowto.com/fat-tail-distribution/

Disclaimer: The content of this post has been prepared by Lucratyva, LLC for informational purposes only and does not constitute legal financial advice. The information on this post shall not be construed as an offer to invest or manage a portfolio for you, nor is it intended to create, nor shall the receipt of such information constitute, an manager-investor relationship. We hope that you will find the information informative and useful, and we would be delighted to speak with you to answer any questions you may have about our firm. Internet users, subscribers and readers should not act upon the information on this blog post or decide not to act based upon the information on this post, without first seeking appropriate professional counsel from a licensed financial professional in the user’s jurisdiction. No content or media on any Internet platform, such as but not limited to the firm’s website or social media accounts, are used in any way to solicit, advertise, or market the firm or to obtain accredited investors.