Fat-tailed distributions are graphical representations of the probability of extreme events being higher than normal. In many domains fat tails are significant, as those extreme events have a higher impact and make the whole normal distribution irrelevant. That is the case when it comes to power laws. Therefore, understanding the properties of those extreme events become critical to business survival and success.
Understanding fat-tailed distributions
Typical bell curve graphs depict the probability distribution of data with the apex of the curve representing the mean, mode, or median. The width of the bell relative to the apex is determined by its standard deviation. This normally distributes the data and forms the shape of the bell curve with two “lean” tails of outlier data on either side.
Normal distributions can be analyzed to predict stock market volatility and make educated predictions around future stock prices. Bell curves can also be used by educators to compare test scores and also in the assessment of employee performance.
However, data are not always normally distributed. Some bell curves have fatter tails with a higher prevalence of data significantly different to the mean. Fat-tailed distributions are said to decay more slowly, allowing more room for outlier data to exist sometimes 4 or 5 standard deviations above the mean. As a result, extreme events are more likely to occur.
Lean tail curves, on the other hand, have distributions that decrease exponentially from the mean. This means that extreme events are highly unlikely, which helps to mitigate risk in a variety of situations.
Examples of fat-tailed distributions
Some of the more obvious fat-tailed distributions include:
Wealth – mean annual income globally is approximately $2,000. Yet there is a high number of millionaires and even billionaires who are many, many standard deviations above this mean.
Urban populations – the vast majority of cities worldwide have populations in the tens to hundreds of thousands, but the increasing prevalence of megacities such as Tokyo, Delhi, and Shanghai skews normally distributed data.
Costs of natural disasters – climate change is increasing the severity of natural disasters, leading to higher insurance claims. For example, the costliest hurricane in the US was Hurricane Andrew in 1992 at $41.5 billion. Just 13 years later, Hurricane Katrina set a new record inflicting $91 billion worth of damage.
Implications for fat-tailed distributions in business
Finance
Normal distributions tend to understate asset prices, stock returns, and associated risk management strategies. This was highlighted during the 2008 Global Financial Crisis (GFC), where conventional financial wisdom was unable to predict fat tail risks brought about by unpredictable human behavior.
Devastating events such as the GFC might have been avoided if preceding periods of financial stress – also represented by fat-tail distribution – were acknowledged and planned for accordingly.
Insurance
Insurance companies rely on normally distributed, historical data to generate profits. However, claims relating to flood and crop damage in particular are challenging historical assumptions of normal distribution. Health insurance claims are also rising as obesity rates soar in many developed western nations.
Companies that offer uncapped insurance contracts are at an increased risk of bankruptcy as climate change and more sedentary lifestyles challenge assumptions of lean-tail distribution.
Key takeaways:
Fat-tailed distributions are found on bell curves with a greater prevalence of outlier data. These distributions suggest a higher probability of extreme events than would be typical in a normally distributed bell curve.
Fat-tailed distributions decay more slowly than lean-tailed distributions, resulting in outlier data that is often 4 or 5 standard deviations above the mean.
Fat-tailed distributions explain variation in the distribution of global incomes and urban population size. In the finance and insurance industries, external stressors are challenging historical assumptions of normal distribution and in turn, profit potential.
The Lindy Effect is a theory about the ageing of non-perishable things, like technology or ideas. Popularized by author Nicholas Nassim Taleb, the Lindy Effect states that non-perishable things like technology age – linearly – in reverse. Therefore, the older an idea or a technology, the same will be its life expectancy.
Technological modeling is a discipline to provide the basis for companies to sustain innovation, thus developing incremental products. While also looking at breakthrough innovative products that can pave the way for long-term success. In a sort of Barbell Strategy, technological modeling suggests having a two-sided approach, on the one hand, to keep sustaining continuous innovation as a core part of the businessmodel. On the other hand, it places bets on future developments that have the potential to break through and take a leap forward.
Another dimension of asymmetric betting is given by how impactful the idea can be to the business. When we have asymmetric bets that can have a high impact and are easy to reverse, we get to the “Jackpot” and go into an “All-In-Mode” of action! And how easy to reverse.
In statistics, the Simpson Paradox happens when a trend clearly shows up in clusters/brackets of data. But it disappears or at worse it reverses when the data is grouped and combined. In short, the Simpson paradox shows that when the data moves from clusters to combined data, it hides several distributions, which end up creating a biased overall effect.
Ergodicity is one of the most important concepts in statistics. Ergodicity is a mathematical concept suggesting that a point of a moving system will eventually visit all parts of the space the system moves in. On the opposite side, non-ergodic means that a system doesn’t visit all the possible parts, as there are absorbing barriers
First-principles thinking – sometimes called reasoning from first principles – is used to reverse-engineer complex problems and encourage creativity. It involves breaking down problems into basic elements and reassembling them from the ground up. Elon Musk is among the strongest proponents of this way of thinking.
The ladder of inference is a conscious or subconscious thinking process where an individual moves from a fact to a decision or action. The ladder of inference was created by academic Chris Argyris to illustrate how people form and then use mental models to make decisions.
The Six Thinking Hats model was created by psychologist Edward de Bono in 1986, who noted that personality type was a key driver of how people approached problem-solving. For example, optimists view situations differently from pessimists. Analytical individuals may generate ideas that a more emotional person would not, and vice versa.
Second-order thinking is a means of assessing the implications of our decisions by considering future consequences. Second-order thinking is a mental model that considers all future possibilities. It encourages individuals to think outside of the box so that they can prepare for every and eventuality. It also discourages the tendency for individuals to default to the most obvious choice.
Lateral thinking is a business strategy that involves approaching a problem from a different direction. The strategy attempts to remove traditionally formulaic and routine approaches to problem-solving by advocating creative thinking, therefore finding unconventional ways to solve a known problem. This sort of non-linear approach to problem-solving, can at times, create a big impact.
Moonshot thinking is an approach to innovation, and it can be applied to business or any other discipline where you target at least 10X goals. That shifts the mindset, and it empowers a team of people to look for unconventional solutions, thus starting from first principles, by leveraging on fast-paced experimentation.
The concept of cognitive biases was introduced and popularized by the work of Amos Tversky and Daniel Kahneman in 1972. Biases are seen as systematic errors and flaws that make humans deviate from the standards of rationality, thus making us inept at making good decisions under uncertainty.
Bounded rationality is a concept attributed to Herbert Simon, an economist and political scientist interested in decision-making and how we make decisions in the real world. In fact, he believed that rather than optimizing (which was the mainstream view in the past decades) humans follow what he called satisficing.
The Dunning-Kruger effect describes a cognitive bias where people with low ability in a task overestimate their ability to perform that task well. Consumers or businesses that do not possess the requisite knowledge make bad decisions. What’s more, knowledge gaps prevent the person or business from seeing their mistakes.
Occam’s Razor states that one should not increase (beyond reason) the number of entities required to explain anything. All things being equal, the simplest solution is often the best one. The principle is attributed to 14th-century English theologian William of Ockham.
The Mandela effect is a phenomenon where a large group of people remembers an event differently from how it occurred. The Mandela effect was first described in relation to Fiona Broome, who believed that former South African President Nelson Mandela died in prison during the 1980s. While Mandela was released from prison in 1990 and died 23 years later, Broome remembered news coverage of his death in prison and even a speech from his widow. Of course, neither event occurred in reality. But Broome was later to discover that she was not the only one with the same recollection of events.
The bandwagon effect tells us that the more a belief or idea has been adopted by more people within a group, the more the individual adoption of that idea might increase within the same group. This is the psychological effect that leads to herd mentality. What in marketing can be associated with social proof.
Gennaro is the creator of FourWeekMBA, which reached about four million business people, comprising C-level executives, investors, analysts, product managers, and aspiring digital entrepreneurs in 2022 alone | He is also Director of Sales for a high-tech scaleup in the AI Industry | In 2012, Gennaro earned an International MBA with emphasis on Corporate Finance and Business Strategy.
