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Why do traditional risk models make you underestimate the possibility of extreme events? Unveiling the mystery of the 'fat tail'!
In risk management and financial analysis, traditional models are often based on normal distribution, but such an assumption may lead to a significant underestimation of the risk of extreme events. In this case, the concept of "fat tail" distribution comes into our view and becomes the key to understanding extreme event models.
A fat-tailed distribution is one in which the tail of a probability distribution exhibits a greater skewness or kurtosis than a normal distribution. In many real-world situations, especially when it comes to financial markets, this distributional nature makes anticipated events appear out of reach, leading to planning and decision-making errors.
When the data comes from a potentially fat-tailed distribution, using a normal distribution model to estimate risk will seriously underestimate the difficulty of prediction and the degree of risk.
Fat-tailed distributions are not easy to spot; they are characterized by the asymptotic nature of the tail and the cumulative probability distribution of many random variables over a certain range. The most extreme fat-tail case is when the tail of the distribution follows a form similar to the "power law", which makes the probability of extreme events significantly higher than that of the normal distribution.
For example, for a normal distribution, an event that deviates five standard deviations from the mean has an extremely low probability of occurring, and is called a "5-sigma event." Under a fat-tailed distribution, the probability of such events occurring may be very different. This inconsistency poses significant challenges to risk managers, who may misassess the risks of extreme events, especially when making critical decisions in the capital markets.
Take the Black-Scholes model as an example. It assumes that asset returns follow a normal distribution, which in practical applications often leads to lower-than-expected option pricing.
In fact, fat tails lead to additional risks. In the financial market, we often encounter some tragic historical events, such as the Wall Street crash in 1929 and the financial crisis in 2008. These events are not only difficult to predict, but also have far-reaching impacts on the market after they occur. In most cases, these events are triggered by some external factors (such as major political changes or economic crises), which usually cannot be simply described by traditional mathematical models.
In the field of behavioral finance, the formation of market turbulence often comes from the fluctuations in investors' emotions, which further deepens the necessary research on fat-tail distribution. Many times, excessive optimism or pessimism in the market can lead to unexpected and extreme market price movements, which cannot be taken into account in the normal distribution forecasting model.
Fat-tailed distributions also find applications in non-financial fields. For example, in marketing, the "80/20 rule" that people often mention is one of the manifestations of fat-tail distribution. In the music market and the commodity market, some songs or commodities may be extremely cheap or expensive, and this phenomenon can also be explained by the fat-tail distribution.
When analyzing market behavior, fat-tailed distributions can better reflect variability and extremes in the data.
In summary, the underestimation of extreme events by traditional risk models stems from incorrect assumptions about data distribution. As we gain a deeper understanding of fat-tailed distributions and their applications, we may be able to more accurately predict and manage risks in the future, and make more informed investment decisions. However, is this shift enough to change the risk management landscape?
