These are two different representations of the potential risk in the financial markets. Let us now understand more about the dissimilarities between them below:
Table of Contents
What Is Fat Tail Distribution?
Fat tail distribution measures future risk possibilities in the financial markets by identifying which probability distribution is most likely to have extreme outcomes or values. Indeed, it often makes a bell-shaped distribution asymmetrical, where one of the sides represents a fatter tail.
In stock markets, such extreme results can lead to sudden profit or loss for traders or investors. Moreover, it is difficult to predict such possibilities since the usual risk management strategies and forecasting methods fail to determine the potential change in future values. Indeed, for better prediction, a sample size of approximately 2000 to 10000 data points is required.
Key Takeaways
- A fat tail distribution is a probability distribution that shows a higher-than-expected probability of obtaining extreme values, signifying a greater future risk involvement in the financial market.
- These are bell-shaped distributions that are skewed at one or both ends, thus forming thick and long tails that show significant chances of considerable loss or gain if the market condition changes.
- Conventional predictive tools are inefficient in predicting the future performance of financial instruments in an extremely volatile market; instead, non-Gaussian models work best in such cases.
How Does Fat Tail Distribution In Finance Work?
A fat tail distribution in finance indicates a higher probability of the presence of extreme outliers in the financial market than that expected by traders or investors. The 2008 financial crisis cleared the myth that probability distributions are generally normal and that conventional financial theories are apt for determining the expected future outcomes of the financial markets. However, real-world finance indicates that there are frequent possibilities of having extreme market outcomes, which leads to the formation of this distribution.
Such a distribution usually has a higher 3 kurtosis and is skewed at one or both the tails. Also, the mean, mode, and median don't fall close to one another. The tails are, therefore, long and thick, creating room for significant potential losses or gains during market fluctuations. Moreover, it has questioned the efficiency of the other models whose fundamental assumption is normality, including the Black-Scholes Option Pricing Model.
An example of such a distribution is the Pareto distribution, which provides instability even with a large data set of 2,000 to 10,000 values. Further, it requires a proper risk management strategy, unlike the thin-tail distribution. Also, investors and traders can undertake various hedging strategies, such as liability hedging and diversification, to enhance profits, limit losses, and ensure long-term protection from adverse events like financial crises.
Graph
As wisely noted, all risks and opportunities of a potential investment are at the tail of its probability distribution; it becomes even more relevant when the distribution is fat-tailed. Given below is a general representation of a fat tail distribution on a graph showing the possible outcomes:
Considering the stock trading perspective, when a distribution is fat-tailed instead of normal, it is highly skewed at the tails. Hence, the chances of either incurring a considerable loss or making a large profit become extremely high in such a condition. These are the times when the market experiences a crash or boom, elevating the potential risk involved in such investments.
Examples
A distribution with a thin tail is more reliable and predictable compared to the one with a fat tail. Let us now have a look at the following examples to understand the practical sense of this statement:
Example #1
Suppose stock A is a small-cap stock that is highly volatile and shows extreme price movements. James, an investor, collects the past 2,500 price movements data to understand the future risk and return potential of the stock. He finds out that the stock has a fat tail distribution using advanced forecasting methods, i.e., it involves an extreme potential loss if the market crashes. However, the bright side is that the shares would perform equally well in the market boom. Now, the investment decision is entirely dependent upon the risk-taking appetite of the investor.
Example #2
As per an article published on July 22, 2024, Bitcoin traders are hoping for potential extreme price movements, i.e., a fat tail distribution in lieu of Donald Trump's speech at the Nashville Bitcoin conference on July 27, 2024. Deribit's data on the options market tracked by Amberdata signals an expected surge in volatility, potentially improving the performance of the butterfly index.
Greg Magadini, Amberdata, shows optimism towards a significant rise in 25-delta wings compared to at-the-money (ATM) volatility, thus indicating a possibility of higher return distribution kurtosis for the traders. Eventually, the optimistic traders are purchasing out-of-the-money (OTM) options to prepare for unexpected market shifts. Moreover, traders and market experts expect an announcement of Bitcoin's inclusion for a strategic role in the U.S. financial system would cause a significant price surge. Meanwhile, Markus Thielen, 10x Research, expressed the high-risk possibilities in buying Bitcoins before the speech.
Other than Bitcoins, various other factors are elevating the market uncertainty, such as the upcoming launch of spot ether ETFs in the U.S. and concerns about tail risks from the FOMC meeting on July 31, 2024. Additionally, the potential Federal Reserve's rate cuts and the demand for Bitcoins are majorly reliant upon the upcoming U.S. economic data for June 2024 on GDP growth estimates, durable goods, core PCE prices, and retail sales.
Fat Tail Distribution Vs. Thin Tail Distribution
| Basis | Fat Tail Distribution | Fat Tail Distribution |
|---|---|---|
| 1. Definition | It is a probability distribution with a long and thick tail, resembling the high possibility of obtaining extreme values in the future. | It is a short-tailed probability distribution that indicates a more reliable and accurate prediction of the expected future values. |
| 2. Identification | Long and thick tail at one side of the probability distribution. | Short and narrow tail formation at one of the sides of a distribution. |
| 3. Expected Future Risk | Signifies the possibility of extreme values due to excessive volatility and unpredictable nature. | Comparatively, expected outcomes are more stable and predictable due to low variability. |
| 4. Data Required | A meaningful result can only be drawn with a large sample size of around 2,000 to 10,000 data points. | A meaningful result can only be drawn with a large sample size of around 2,000 to 10,000 data points. |
| 5. Forecasting | Difficult to predict the possible outcome due to mean value skewness because of the extremely high data values | More reliable and accurate predictions of possible outcomes because such a distribution has nearly similar mean, mode, and median values. |
| 6. Planning | Forecasting methods like Little's Law fail to determine the exact possibilities, making it unreliable and difficult to plan investments and strategies for stocks with such a distribution pattern. | However, with the use of various forecasting techniques and equations, planning for thin-tail investments becomes much easier and more reliable. |
| 7. Risk Management | Requires a more complex strategy and approach to avoid losses. | It is easy to determine using standard risk management tools and practices. |
| 8. Examples | A distribution with the mean, median, and mode of $10, $18, and $25 | A distribution with the mean, median, and mode of $10, $18, and $25 |
Frequently Asked Questions (FAQs)
1
How to model fat tail distribution?
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What is true about fat tail distribution?
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What is the difference between long tail and fat tail distributions?
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Is exponential distribution a fat tail distribution?
