Question

what is the purpose of skewness and kurtosis ? How are they “read” from a graph? how do investors/ stock market people use skewness and kurtosis ?

Answer 1

Skewness and kurtosis purpose

Skewness

It is an indicator of lack of equivalence in the frequency distribution.

The term ‘skewness’ is used to mean the absence of symmetry from the mean of the dataset.

Kurtosis

kurtosis is defined as the parameter of relative sharpness of the peak of the probability distribution curve. It ascertains the way observations are clustered around the centre of the distribution. It is used to indicate the flatness or peakedness of the frequency distribution curve and measures the tails or outliers of the distribution.

Skewness shows how much and in which direction, the values deviate from the mean while kurtosis explain how tall and sharp the central peak is

HOW ARE THEY READ FROM GRAPH

Skewness

Positive skewness indicates a distribution with an asymmetric tail extending toward more positive values; negative skewness indicates a distribution with an asymmetric tail extending toward more negative values; zero skewness means the tails are symmetric. Interpreted as downside risk, positive skewness suggests fewer/smaller negative outcomes whereas negative skewness suggest more/greater.

Kurtosis

Kurtosis measures the "tail-heaviness" (as opposed to "peakedness" or "flatness") of a distribution compared against a normal distribution (k = 3).

A "low" kurtosis (k < 3) indicates fewer/smaller outliers whereas a "high" kurtosis (k > 3) indicates more/greater.

With high kurtosis, one will have "fat" tails, higher frequency of outcomes at the extreme negative and positive ends of the distribution curve.

HOW do investors/ stock market people use skewness and kurtosis ?

A stock with negative skewness is one that generates frequent small gains and few extreme or significant losses in the time period considered. On the other hand, a stock with positive skewness is one that generates frequent small losses and few extreme gains. If a stock’s return follows a normal distribution pattern, then their will be no skewness.

The other abnormality that is witnessed in financial data is the possibility of extreme returns, termed as kurtosis. It serves to measure risk, as the abnormal returns on some instances could go beyond 3-times the standard deviation limit, according to the theory of normal distribution.

When data follows normal distribution, the kurtosis has a value of three. Value greater than three means higher instances of abnormal returns, whereas low value of kurtosis (less than three) implies fewer instances of abnormal returns.