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The 'Fat Tail' Stories Behind the Financial Crisis: How Do These Historical Events Affect Your Investment Decisions?
In financial markets, investors often rely on normal distribution models to predict future market trends. However, as numerous financial crises over the past centuries have shown, these models often underestimate the chances of extreme events. These extreme events are called "fat tail events", and their existence puts investors at higher risk. This article will explore the concept of fat tail distribution and its potential impact on investment decisions.
The fat tail distribution is a probability distribution that exhibits greater skewness or kurtosis relative to the normal or exponential distribution.
Characteristics of fat-tailed distribution
The characteristic of the fat tail distribution is that the probability of extreme events is not just a theoretical calculation, but is embedded in actual market behavior. This distribution is common in many fields such as physics, economics, and political science. Different research communities may differ in their definitions, but fat tail distributions are generally believed to include those attenuated by power law. This type of distribution is particularly important in financial markets because they provide a theoretical framework for why major market crashes occur frequently.
In the normal distribution, the probability of events deviating from the mean by more than five standard deviations is very low, while the fat tail distribution is different, and the probability of extreme events is much higher than that of the normal distribution.
Mistakes in risk estimation
Many financial models, such as the Black-Scholes option pricing model, assume that asset returns follow a normal distribution. However, if the actual distribution is fat-tailed, these models will fail to price forward options correctly because the probability of major outlier events is underestimated. This means that when markets experience extreme volatility, investors may be exposed to higher risk than they anticipated.
Many prominent finance scholars, such as Paul Volcker and Nassim Taleb, have highlighted the inadequacy of the normal distribution model and have proposed that fat-tailed distributions are more dominant in asset returns.
Review of historical events
Looking back at history, we can find many examples of fat-tail events. The Wall Street Crash of 1929, Black Monday of 1987, the dot-com bubble of 2000, and the financial crisis of 2007-2008 were all extremely rare extreme situations in the market under normal forecasting models. However, the occurrence of these events demonstrates the importance of fat-tail distributions in financial reality.
These crises are often triggered by non-mathematical factors, such as political unrest or supply chain disruptions, that do not conform to assumptions of normal distribution. In fact, behavioral finance factors generated in the process, such as investors' excessive optimism or pessimism, also play an important role in the fat-tail distribution.
Fat Tail and Income Distribution
Fat-tail distribution can also explain certain sociological phenomena, such as the "80/20 rule," which states that 20% of customers contribute 80% of revenue. This phenomenon is particularly evident in market behavior, where a few people or companies are able to dominate the market while the majority are relatively insignificant.
In some commodity markets or the music industry, the probability density function of sales data also exhibits a fat-tail characteristic, indicating that new record promotions have a strong impact on sales.
Facing the challenges of the future
Looking ahead, investors should be aware of the risks of fat-tail events and adjust their investment strategies accordingly. Models that rely on normal distributions can result in significant capital losses, especially during periods of significant and unusual market movement. Investors need to adopt a diversified strategy to offset these risks and correct for potential biases in risk management models.
How will future financial markets evolve to cope with the frequency and impact of fat-tail events?
