What is a fat tail in a distribution?
A fat-tailed distribution is a probability distribution that exhibits a large skewness or kurtosis, relative to that of either a normal distribution or an exponential distribution.
Which kurtosis has fat tails?
Leptokurtic distributions are statistical distributions with kurtosis greater than three. It can be described as having a wider or flatter shape with fatter tails resulting in a greater chance of extreme positive or negative events. It is one of three major categories found in kurtosis analysis.
Which distribution has heavier tails?
In probability theory, heavy-tailed distributions are probability distributions whose tails are not exponentially bounded: that is, they have heavier tails than the exponential distribution.
What is a measure of how fat or thin the tails of a distribution are?
Kurtosis describes the “fatness” of the tails found in probability distributions. The normal distribution has a kurtosis of exactly 3.0, and is known as mesokurtic.
What do fat tails look like?
As a synonym for heavy tailed distribution
In other words, the tails simply look fatter. As the tails have more bulk, the probability of extreme events is higher compared to the normal. This definition, where “heavy tail” and “fat tail” mean the same thing, is especially common in trading and other areas of finance.
Are fat tailed distributions skewed distributions?
Any symmetric distribution will have a skewness of zero – no matter how fat its tails. This is because of the third power in its definition, which allows deviations in both tails to cancel out. Thus, there is no relationship between skewness and tail fatness.
What does fatter tails mean in kurtosis?
Kurtosis measures the “fatness” of the tails of a distribution. Positive excess kurtosis means that distribution has fatter tails than a normal distribution. Fat tails means there is a higher than normal probability of big positive and negative returns realizations.
What are the three types of kurtosis?
The three categories of kurtosis are:
- Mesokurtosis: An excess kurtosis of 0. Normal distributions are mesokurtic.
- Platykurtosis: A negative excess kurtosis. Platykurtic distributions are thin-tailed, meaning that they have few outliers.
- Leptokurtosis: A positive excess kurtosis.
How do you determine if a distribution is heavy-tailed?
What is a Heavy Tailed Distribution? A heavy tailed distribution has a tail that’s heavier than an exponential distribution (Bryson, 1974). In other words, a distribution that is heavy tailed goes to zero slower than one with exponential tails; there will be more bulk under the curve of the PDF.
Is gamma distribution heavy tail?
Traditionally, the wet-day daily rainfall has been described by light-tailed distributions like the Gamma distribution, although heavier-tailed distributions have also been proposed and used, e.g., the Lognormal, the Pareto, the Kappa, and other distributions.
What does a kurtosis of 1 mean?
For kurtosis, the general guideline is that if the number is greater than +1, the distribution is too peaked. Likewise, a kurtosis of less than –1 indicates a distribution that is too flat. Distributions exhibiting skewness and/or kurtosis that exceed these guidelines are considered nonnormal.” (Hair et al., 2017, p.
What is a good kurtosis value?
2.3.
A standard normal distribution has kurtosis of 3 and is recognized as mesokurtic. An increased kurtosis (>3) can be visualized as a thin “bell” with a high peak whereas a decreased kurtosis corresponds to a broadening of the peak and “thickening” of the tails. Kurtosis >3 is recognized as leptokurtic and <3.
What causes fat tails?
Understanding Tail Risk
The fat tails indicate that there is a probability, which may be larger than otherwise anticipated, that an investment will move beyond three standard deviations. Distributions that are characterized by fat tails are often seen when looking at hedge fund returns, for example.
What is a fat tail risk?
By definition, a fat tail is a probability distribution which predicts movements of three or more standard deviations more frequently than a normal distribution. Even before the financial crisis, periods of financial stress had resulted in market conditions represented by fatter tails.
What is a fat tail event when looking at distribution of data?
Fat tails are defined as rare but significant market events which can cause extreme gains or losses in a portfolio. In recent years, these events can be attributed to unconventional policy intervention, partisan divide in local governments and geopolitical risk factors.
What kurtosis tells us?
Kurtosis is a statistical measure that defines how heavily the tails of a distribution differ from the tails of a normal distribution. In other words, kurtosis identifies whether the tails of a given distribution contain extreme values.
How do you interpret kurtosis values?
Which measure is used to determine whether the distribution is heavy-tailed or light tale?
A normal distribution is generally thought of mesokurtic, i.e. having normal kurtosis, with kurtosis of 3. Anything less than 3 is described as platykurtic (“light tailed”) and larger than 3 as leptokurtic (“heavy tailed”). Some people subtract 3 from kurtosis so that 0 is a normal value.
How do you know if a distribution is heavy-tailed?
Is Laplace distribution heavy-tailed?
The Laplace distribution is the distribution of the difference of two independent random variables with identical exponential distributions (Leemis, n.d.). It is often used to model phenomena with heavy tails or when data has a higher peak than the normal distribution.
What kurtosis is acceptable?
A standard normal distribution has kurtosis of 3 and is recognized as mesokurtic. An increased kurtosis (>3) can be visualized as a thin “bell” with a high peak whereas a decreased kurtosis corresponds to a broadening of the peak and “thickening” of the tails. Kurtosis >3 is recognized as leptokurtic and <3.
What is a bad kurtosis?
Data with a skew above an absolute value of 3.0 and kurtosis above an absolute value of 8.0 are considered problematic.
What is a tail risk strategy?
The art of tail‐risk protection is to asymetrically protect against left‐hand events (those which are loss making) while maintaining participation in those events on the right (which are profit making).
Is high kurtosis good or bad?
Kurtosis is only useful when used in conjunction with standard deviation. It is possible that an investment might have a high kurtosis (bad), but the overall standard deviation is low (good). Conversely, one might see an investment with a low kurtosis (good), but the overall standard deviation is high (bad).
What is an acceptable kurtosis value?