What is Excess Kurtosis and Why is it Important in Financial Analysis?

  • Context: Undergrad 
  • Thread starter Thread starter bballwaterboy
  • Start date Start date
  • Tags Tags
    Gaussian Statistics
Click For Summary
SUMMARY

Excess kurtosis is a statistical measure that indicates the presence of 'fat tails' in a distribution, which signifies that there is more probability weight in the tails compared to a normal distribution. This concept is crucial in financial analysis, as it highlights the limitations of assuming that economic variables follow a Gaussian distribution. The collapse of Long-Term Capital Management in 1998 exemplifies the dangers of relying on normality assumptions. Understanding excess kurtosis and its implications is essential for accurate risk assessment in finance.

PREREQUISITES
  • Understanding of Gaussian statistics and Normal Distribution
  • Familiarity with statistical moments, specifically kurtosis and skewness
  • Basic knowledge of financial risk management principles
  • Awareness of historical financial events, such as the Long-Term Capital Management collapse
NEXT STEPS
  • Study the concept of kurtosis in-depth, focusing on its mathematical definition and implications
  • Explore Benoit Mandelbrot's work on fractals and the limitations of Gaussian assumptions in finance
  • Learn about statistical tools for testing normality, such as the Shapiro-Wilk test
  • Investigate alternative distribution models used in finance, such as the Student's t-distribution
USEFUL FOR

Financial analysts, risk managers, statisticians, and anyone involved in quantitative finance who seeks to understand the impact of distribution assumptions on risk assessment and decision-making.

bballwaterboy
Messages
85
Reaction score
3
I heard a guy mention in a debate that some math calculation didn't obey Gaussian statistics. It was a debate re: the economy (not important here, though).

I was curious what was meant by "Gaussian statistics" and would appreciate if anyone could offer a sort of layman's definition. Thanks so much!
 
Physics news on Phys.org
He was probably saying that some economic random variable did not have a Normal Distribution. The Normal Distribution is also known as the 'Bell Curve' as well as the 'Gaussian distribution' (because it was first invented by CF Gauss). Many random phenomena are assumed to be Normally Distributed because it makes calculations about them easier. But in some cases that assumption is very inaccurate, and that can cause big, unforeseen accidents.
The collapse of the hedge fund Long-Term Capital Management in 1998 is believed to have arisen from the fund managers assuming that certain economic variables were Normally Distributed when they were not.
 
andrewkirk said:
believed to have arisen from the fund managers assuming that certain economic variables were Normally Distributed when they were not.

I'd be interested in reading more about that, but I didn't see much about it in the wiki.
 
ElijahRockers said:
I'd be interested in reading more about that, but I didn't see much about it in the wiki.
This short article is more helpful, and points to a book by Benoit Mandelbrot all about the danger of the Gaussian assumption.

'Kurtosis' - the fourth moment of the distribution - measures how 'fat' the 'tails' of the distribution are. 'Excess kurtosis' is when there is more probability weight in the tails of a distribution than in a normal distribution with the same first two moments. Excess kurtosis - aka 'fat tails' - along with asymmetry (aka skew - related to the third moment) are problems that get a great deal of attention in finance these days, where it has belatedly been realized that testing the validity of assumptions of normality is very important.
 
  • Like
Likes   Reactions: ElijahRockers

Similar threads

  • · Replies 9 ·
Replies
9
Views
2K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 1 ·
Replies
1
Views
3K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 18 ·
Replies
18
Views
7K
  • · Replies 7 ·
Replies
7
Views
2K
Replies
8
Views
3K
Replies
1
Views
2K
  • · Replies 2 ·
Replies
2
Views
3K