Skew Or Skewness

Skew (or skewness) measures the extent to which a set of data differs from a normal (or symmetrical) distribution, which is characterised by a bell curve shape of the data and a similar spread of data on either side of both the median and mode values.

Types Of Skew

There are two types of skew:

  1. Positively skewed, where there is more data on the right hand side of the distribution, and thus the mean is higher than the median and mode and
  2. A negatively skewed distribution, where the opposite applies (the mean is below the median and mode due to the presence of more extreme negative values on the left side of the chart).

How To Use Skew In Trading

In finance, it is often assumed that returns to investments are normally distributed (via a bell curve), but in reality, they are not, especially in regards to non-linear assets (such as options, and to a lesser extent bonds via convexity).

A positively skewed profile might imply frequent small losses alongside irregular large gains.

This is usually deemed acceptable as the small number of gains will outweigh the large number of small losses.

In a negatively skewed distribution, the opposite applies (consistent small gains with the possibility of occasional large losses) – this is most often seen in traders’ position books which feature a high degree of short options exposure.

The extent of skewness can be calculated in a number of ways, one of which is known as Pearson’s co-efficient of skewness, whereby:

3x (mean-median)/Standard Deviation = degree of skewness.

A high degree of skewness in either direction may lead to misleading results when employing conventional statistical analysis. Thus, data transformation tools, such as log transformation are used to reduce the natural skew of the data, thereby making it easier to perform statistical tests, which in practise reduces the error term of the analysis.