DEFINITION
OF 'KURTOSIS'
Like skewness,
kurtosis is a statistical measure that is used to describe the distribution.
Wherea skewness differentiates extreme
values in one versus the other tail, kurtosis measures extreme values in either
tail. Distributions with large kurtosis exhibit tail
data exceeding the tails of the normal distribution (e.g., five or more
standard deviations from the mean). Distributions with low kurtosis exhibit
tail data that is generally less extreme than the tails of the normal
distribution. For investors, high kurtosis of the return distribution implies
that the investor will experience occasional extreme returns (either positive
or negative), more extreme than the usual + or - three standard deviations from
the mean that is predicted by the normal distribution of returns. This
phenomenon is known as kurtiousis
Kurtosis is a
measure of the combined weight of a distribution's tails relative to the center
of the distribution. When a set of approximately normal data is graphed via a
histogram, it shows a bell peak and most data within + or - three standard
deviations of the mean. However, when high kurtosis is present, the tails
extend farther than the + or - three standard deviations of the normal
bell-curved distribution. Kurtosis is sometimes confused with a measure of the
peakedness of a distribution. However, kurtosis is a measure that describes the
shape of a distribution's tails in relation to its overall shape. A
distribution can be infinitely peaked with low kurtosis, and a distribution can
be perfectly flat-topped with infinite kurtosis. Thus, kurtosis measures
“tailedness,” not “peakedness.
Types of
Kurtosis
There are three
categories of kurtosis that can be displayed by a set of data. All measures of
kurtosis are compared against a standard normal distribution, or bell curve.
mesokurtic.The
first category of kurtosis is a mesokurtic distribution. This distribution has
kurtosis statistic similar to that of the normal distribution, meaning that the
extreme value characteristic of the distribution is similar to that of a normal
distribution
leptokurtic. The second category is a
leptokurtic distribution. Any distribution that is leptokurtic displays greater
kurtosis than a mesokurtic distribution. Characteristics of this type of
distribution is one with long tails (outliers). The prefix of
"lepto-" means "skinny," making the shape of a leptokurtic
distribution easier to remember. The “skinniness” of a leptokurtic distribution
is a consequence of the outliers, which stretch the horizontal axis of the
histogram graph, making the bulk of the data appear in a narrow (“skinny”)
vertical range. Some have thus characterized leptokurtic distributions as
“concentrated toward the mean,” but the more relevant issue (especially for
investors) is that there are occasional extreme outliers that cause this
“concentration” appearance. Examples of leptokurtic distributions are the
T-distributions with small degrees of freedom.
platykurtic.The final type of
distribution is a platykurtic distribution. These types of distributions have
short tails (paucity of outliers). The prefix of "platy-" means
"broad," and it is meant to describe a short and broad-looking peak,
but this is an historical error. Uniform distributions are platykurtic and have
broad peaks, but the beta(.5,1) distribution is also platykurtic and has an
infinitely pointy peak. The reason both these distributions are platykurtic is
that their extreme values are less than that of the normal distribution. For
investors, platykurtic return distributions are stable and predictable, in the
sense that there will rarely (if ever) be extreme (outlier) returns.
figure1:
Types Of Kurtosis A Grahical Representation
Table no1: Ststistical Analysis Tabular Column
STSTISTICS
|
VALUE
|
KURTOSIS
|
3.18
|
SKEWNESS
|
0.11
|
SHARP
RATIO
|
1.34
|
STANDARD
DEVIATION
|
6.77
|
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