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.
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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.
Case Studies
Book Publishing:
Scenario: A publishing house is analyzing the sales of their books over a decade.
Normal Distribution: A certain consistent number of books sell around 10,000 copies.
Fat-tailed Distribution: Occasionally, a breakout bestseller, like a new fantasy series, might sell millions, skewing the average sales distribution. Most books don’t achieve this level of success, but those that do have a significant impact on the publisher’s revenue.
Viral Videos:
Scenario: A content creator uploads videos on a platform like YouTube.
Normal Distribution: Most of their videos get a consistent 5,000 views.
Fat-tailed Distribution: Occasionally, one video might go viral and achieve 5 million views. This outlier drastically affects the creator’s average view count and potential revenue.
Startup Success:
Scenario: An investor is examining the returns from their portfolio of tech startups.
Normal Distribution: Many startups yield moderate returns or even fail.
Fat-tailed Distribution: Occasionally, a startup might become the next unicorn, like Uber or Airbnb, and provide returns many times over the initial investment, overshadowing the performance of other investments.
Natural Disasters:
Scenario: An insurance company is assessing claims related to natural disasters over several years.
Normal Distribution: Most years, claims remain within a certain predictable range.
Fat-tailed Distribution: Some years, a catastrophic event like a super typhoon or a mega earthquake can lead to claims that are multiple times the average, affecting the insurance company’s profitability.
Healthcare:
Scenario: A hospital is analyzing patient admission rates.
Normal Distribution: On most days, the hospital admits a consistent number of patients.
Fat-tailed Distribution: Occasionally, events like a disease outbreak can lead to a sudden spike in admissions, requiring the hospital to mobilize extra resources.
Stock Market:
Scenario: An investor is examining stock returns.
Normal Distribution: Most of the time, stock returns fluctuate within a certain expected range.
Fat-tailed Distribution: Rare events, like a global financial crisis or a pandemic, can lead to extreme stock market crashes, causing severe losses for investors.
Internet Traffic:
Scenario: A website owner is analyzing daily website traffic.
Normal Distribution: The website receives a consistent number of daily visitors.
Fat-tailed Distribution: Occasionally, being featured on a popular site or getting shared by a celebrity can cause a surge in visitors, overwhelming the server.
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.
Key Insights
Fat-Tailed Distributions: Graphical representations of the probability of extreme events being higher than normal, with a greater prevalence of outlier data.
Normal Distributions: Typical bell curve graphs with lean tails and normally distributed data.
Properties of Fat-Tailed Distributions: Decaying more slowly than lean-tailed distributions, resulting in a higher probability of extreme events occurring.
Examples of Fat-Tailed Distributions: Wealth distribution with a high number of millionaires and billionaires, urban populations with increasing prevalence of megacities, and costs of natural disasters with rising severity.
Finance: Normal distributions understate asset prices and risk management strategies, leading to challenges during financial crises.
Insurance: Historical assumptions based on normal distributions face challenges due to climate change, flood and crop damage, and rising health insurance claims.
Fat-tailed distributions have a higher probability of extreme events.
They decay more slowly than lean-tailed distributions.
They explain variations in global incomes and urban populations.
In finance and insurance, challenges arise when dealing with extreme events.
Convergent thinking occurs when the solution to a problem can be found by applying established rules and logical reasoning. Whereas divergent thinking is an unstructured problem-solving method where participants are encouraged to develop many innovative ideas or solutions to a given problem. Where convergent thinking might work for larger, mature organizations where divergent thinking is more suited for startups and innovative companies.
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.
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.
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 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.
Antifragility was first coined as a term by author, and options trader Nassim Nicholas Taleb. Antifragility is a characteristic of systems that thrive as a result of stressors, volatility, and randomness. Therefore, Antifragile is the opposite of fragile. Where a fragile thing breaks up to volatility; a robust thing resists volatility. An antifragile thing gets stronger from volatility (provided the level of stressors and randomness doesn’t pass a certain threshold).
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
Systems thinking is a holistic means of investigating the factors and interactions that could contribute to a potential outcome. It is about thinking non-linearly, and understanding the second-order consequences of actions and input into the system.
Vertical thinking, on the other hand, is a problem-solving approach that favors a selective, analytical, structured, and sequential mindset. The focus of vertical thinking is to arrive at a reasoned, defined solution.
Metaphorical thinking describes a mental process in which comparisons are made between qualities of objects usually considered to be separate classifications. Metaphorical thinking is a mental process connecting two different universes of meaning and is the result of the mind looking for similarities.
Maslow’s Hammer, otherwise known as the law of the instrument or the Einstellung effect, is a cognitive bias causing an over-reliance on a familiar tool. This can be expressed as the tendency to overuse a known tool (perhaps a hammer) to solve issues that might require a different tool. This problem is persistent in the business world where perhaps known tools or frameworks might be used in the wrong context (like business plans used as planning tools instead of only investors’ pitches).
The Peter Principle was first described by Canadian sociologist Lawrence J. Peter in his 1969 book The Peter Principle. The Peter Principle states that people are continually promoted within an organization until they reach their level of incompetence.
The straw man fallacy describes an argument that misrepresents an opponent’s stance to make rebuttal more convenient. The straw man fallacy is a type of informal logical fallacy, defined as a flaw in the structure of an argument that renders it invalid.
The Google effect is a tendency for individuals to forget information that is readily available through search engines. During the Google effect – sometimes called digital amnesia – individuals have an excessive reliance on digital information as a form of memory recall.
The Streisand Effect is a paradoxical phenomenon where the act of suppressing information to reduce visibility causes it to become more visible. In 2003, Streisand attempted to suppress aerial photographs of her Californian home by suing photographer Kenneth Adelman for an invasion of privacy. Adelman, who Streisand assumed was paparazzi, was instead taking photographs to document and study coastal erosion. In her quest for more privacy, Streisand’s efforts had the opposite effect.
Single-attribute choices – such as choosing the apartment with the lowest rent – are relatively simple. However, most of the decisions consumers make are based on multiple attributes which complicate the decision-making process. The compromise effect states that a consumer is more likely to choose the middle option of a set of products over more extreme options.
In business, the butterfly effect describes the phenomenon where the simplest actions yield the largest rewards. The butterfly effect was coined by meteorologist Edward Lorenz in 1960 and as a result, it is most often associated with weather in pop culture. Lorenz noted that the small action of a butterfly fluttering its wings had the potential to cause progressively larger actions resulting in a typhoon.
The IKEA effect is a cognitive bias that describes consumers’ tendency to value something more if they have made it themselves. That is why brands often use the IKEA effect to have customizations for final products, as they help the consumer relate to it more and therefore appending to it more value.
The overview effect is a cognitive shift reported by some astronauts when they look back at the Earth from space. The shift occurs because of the impressive visual spectacle of the Earth and tends to be characterized by a state of awe and increased self-transcendence.
The house money effect was first described by researchers Richard Thaler and Eric Johnson in a 1990 study entitled Gambling with the House Money and Trying to Break Even: The Effects of Prior Outcomes on Risky Choice. The house money effect is a cognitive bias where investors take higher risks on reinvested capital than they would on an initial investment.
As highlighted by German psychologist Gerd Gigerenzer in the paper “Heuristic Decision Making,” the term heuristic is of Greek origin, meaning “serving to find out or discover.” More precisely, a heuristic is a fast and accurate way to make decisions in the real world, which is driven by uncertainty.
The recognition heuristic is a psychological model of judgment and decision making. It is part of a suite of simple and economical heuristics proposed by psychologists Daniel Goldstein and Gerd Gigerenzer. The recognition heuristic argues that inferences are made about an object based on whether it is recognized or not.
The representativeness heuristic was first described by psychologists Daniel Kahneman and Amos Tversky. The representativeness heuristic judges the probability of an event according to the degree to which that event resembles a broader class. When queried, most will choose the first option because the description of John matches the stereotype we may hold for an archaeologist.
The take-the-best heuristic is a decision-making shortcut that helps an individual choose between several alternatives. The take-the-best (TTB) heuristic decides between two or more alternatives based on a single good attribute, otherwise known as a cue. In the process, less desirable attributes are ignored.
The bundling bias is a cognitive bias in e-commerce where a consumer tends not to use all of the products bought as a group, or bundle. Bundling occurs when individual products or services are sold together as a bundle. Common examples are tickets and experiences. The bundling bias dictates that consumers are less likely to use each item in the bundle. This means that the value of the bundle and indeed the value of each item in the bundle is decreased.
The Barnum Effect is a cognitive bias where individuals believe that generic information – which applies to most people – is specifically tailored for themselves.
The anchoring effect describes the human tendency to rely on an initial piece of information (the “anchor”) to make subsequent judgments or decisions. Price anchoring, then, is the process of establishing a price point that customers can reference when making a buying decision.
The decoy effect is a psychological phenomenon where inferior – or decoy – options influence consumer preferences. Businesses use the decoy effect to nudge potential customers toward the desired target product. The decoy effect is staged by placing a competitorproduct and a decoy product, which is primarily used to nudge the customer toward the target product.
Commitment bias describes the tendency of an individual to remain committed to past behaviors – even if they result in undesirable outcomes. The bias is particularly pronounced when such behaviors are performed publicly. Commitment bias is also known as escalation of commitment.
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.
Goodhart’s Law is named after British monetary policy theorist and economist Charles Goodhart. Speaking at a conference in Sydney in 1975, Goodhart said that “any observed statistical regularity will tend to collapse once pressure is placed upon it for control purposes.” Goodhart’s Law states that when a measure becomes a target, it ceases to be a good measure.
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.
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.
Moore’s law states that the number of transistors on a microchip doubles approximately every two years. This observation was made by Intel co-founder Gordon Moore in 1965 and it become a guiding principle for the semiconductor industry and has had far-reaching implications for technology as a whole.
Disruptive innovation as a term was first described by Clayton M. Christensen, an American academic and business consultant whom The Economist called “the most influential management thinker of his time.” Disruptive innovation describes the process by which a product or service takes hold at the bottom of a market and eventually displaces established competitors, products, firms, or alliances.
Value migration was first described by author Adrian Slywotzky in his 1996 book Value Migration – How to Think Several Moves Ahead of the Competition. Value migration is the transferal of value-creating forces from outdated business models to something better able to satisfy consumer demands.
The bye-now effect describes the tendency for consumers to think of the word “buy” when they read the word “bye”. In a study that tracked diners at a name-your-own-price restaurant, each diner was asked to read one of two phrases before ordering their meal. The first phrase, “so long”, resulted in diners paying an average of $32 per meal. But when diners recited the phrase “bye bye” before ordering, the average price per meal rose to $45.
Groupthink occurs when well-intentioned individuals make non-optimal or irrational decisions based on a belief that dissent is impossible or on a motivation to conform. Groupthink occurs when members of a group reach a consensus without critical reasoning or evaluation of the alternatives and their consequences.
A stereotype is a fixed and over-generalized belief about a particular group or class of people. These beliefs are based on the false assumption that certain characteristics are common to every individual residing in that group. Many stereotypes have a long and sometimes controversial history and are a direct consequence of various political, social, or economic events. Stereotyping is the process of making assumptions about a person or group of people based on various attributes, including gender, race, religion, or physical traits.
Murphy’s Law states that if anything can go wrong, it will go wrong. Murphy’s Law was named after aerospace engineer Edward A. Murphy. During his time working at Edwards Air Force Base in 1949, Murphy cursed a technician who had improperly wired an electrical component and said, “If there is any way to do it wrong, he’ll find it.”
The law of unintended consequences was first mentioned by British philosopher John Locke when writing to parliament about the unintended effects of interest rate rises. However, it was popularized in 1936 by American sociologist Robert K. Merton who looked at unexpected, unanticipated, and unintended consequences and their impact on society.
Fundamental attribution error is a bias people display when judging the behavior of others. The tendency is to over-emphasize personal characteristics and under-emphasize environmental and situational factors.
Outcome bias describes a tendency to evaluate a decision based on its outcome and not on the process by which the decision was reached. In other words, the quality of a decision is only determined once the outcome is known. Outcome bias occurs when a decision is based on the outcome of previous events without regard for how those events developed.
Hindsight bias is the tendency for people to perceive past events as more predictable than they actually were. The result of a presidential election, for example, seems more obvious when the winner is announced. The same can also be said for the avid sports fan who predicted the correct outcome of a match regardless of whether their team won or lost. Hindsight bias, therefore, is the tendency for an individual to convince themselves that they accurately predicted an event before it happened.
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.
