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Why the 'fat-tail' distribution can reveal risk secrets you never thought of?
Fat-tailed distributions are gaining attention in many scientific fields, and their peculiar statistical properties may change our understanding of risk. As the name suggests, the tail of the fat-tailed distribution is fatter than that of the normal distribution, that is, as the sample size increases, there will continue to be a large number of atypical events, and the frequency of these events is much higher than what we generally expect. .
The tails of a fat-tailed distribution show a higher incidence of extreme events that would be barely noticeable in a normal distribution.
The traditional normal distribution tells us that the probability of an event that is five standard deviations away from the mean, that is, a "5-sigma event", is very small. However, in fat-tailed distributions, such "extreme events" are not uncommon. For example, the Cauchy distribution is a fat-tailed distribution with undefined variance, which means that when we use the normal distribution model to estimate risk during risk assessment, we may actually underestimate the potential risk and prediction difficulties.
Well-known scholars such as Benoit Mandelbrot and Nassim Taleb have pointed out the shortcomings of normal distribution models in risk management and advocated the use of fat-tailed distributions to understand the return risk of financial assets.
Fat-tail distributions are widely used in finance, especially in the management of asset return risk. Assuming that the expected return of an investment strategy is five times its standard deviation, under normal distribution, the probability of project failure is extremely low, even less than one in a million. In reality, however, market events can be much more volatile, in stark contrast to what a normal distribution would predict. Historical financial crises, such as the Wall Street crash in 1929 and the global financial crisis in 2008, can be seen as the result of the fat tail effect. The impact of these events is very huge and difficult to predict.
The contradiction between market uncertainty and predictability is precisely one of the risk secrets revealed by the fat-tail distribution.
In addition to financial markets, fat-tail distribution also has applications in other fields. For example, in marketing, the well-known 80/20 rule, which states that “20% of customers contribute 80% of revenue,” is a manifestation of fat-tail distribution. We also see shadows of fat-tail distribution in the merchandise or record markets, especially in the promotion of new albums, where a very small number of new albums will attract the majority of sales.
These findings make us reflect: In these uncertain times, do we fully understand the risks surrounding fat-tailed distributions?
In summary, the existence of fat-tailed distribution challenges the traditional risk assessment method and reminds people to be cautious when making risky investment decisions. This is also one of the reasons why the financial community is paying more and more attention to the fat tail phenomenon. Stepping out of the conventional framework, let us seek a more comprehensive understanding and response in the face of uncertainty. The risks currently visible are still just the tip of the iceberg, and there are many untapped potential risks waiting for us to think about and respond to. Are we ready to face such potential challenges and opportunities?
