# Skewness

Skewness measures to what direction and degree a set of returns is tilted or “skewed” by its extreme outlier occurrences.

## How Is it Useful?

One way of thinking about skewness is that it compares the length of the two “tails” of the distribution. Another way of thinking of skewness is that it measures whether or not the distribution of returns is symmetrical around the mean. The two are related, because if the distribution is impacted more by negative outliers than positive outliers (or vice versa) the distribution will no longer be symmetrical. Therefore, skewness tells us how outlier events impact the shape of the distribution.

## What Is a Good Number?

Generally speaking one would prefer positive skewness. However, in the real world few investments exhibit a positive skew. Therefore, one might seek investments with skew that is “less negative” than the alternatives.

## What Are the Limitations?

Skewness provides valuable information about the distribution of returns. However, skewness must be viewed in conjunction with the overall level of returns. Skewness by itself isn’t very useful. It is entirely possible to have positive skewness (good) but an average annualized return with a low or negative value (bad).

## What Does the Graph Show Me?

The below graphs illustrate the difference between a negatively skewed distribution on the left and a positively skewed distribution to the right. The distribution formed by the red line and the shaded grey line in both graphs form a symmetrical distribution. The count and scale of observations above the mean is perfectly balanced by the count and scale of observations below the mean, so the left and right sides of the bell curve are mirror images. However, if one side of the distribution is dominated by its outliers, the distribution is said to be skewed. The left graph illustrates a case where the length of the negative tail is dominant, leading to a negative skew. The graph on the right is the opposite case and represents a positive skew.

## What Are Typical Values?

Positive skewness is preferred, but uncommon. Looking across various asset classes and time periods, one notices the prevalence of negative numbers. Knowing how markets behave, this makes sense. When markets melt down, they tend to melt down in a dramatic fashion. Think of the Credit Crisis, the Dot-Com Bust, the Asian Contagion, or the Long Term Capital Management crisis. On the upside, gains tend to be less dramatic. While the overall, long-term returns of the markets are positive, those gains come in slower, steadier gains than big bursts. The worst of the worst months tend to be more extreme than the best of the best months. This is what is meant by negative skewness.

Skewness is also known as the third moment of the distribution. By cubing the differences of the individual observations away from the mean, positive or negative values are possible, which indicate the tilt of the distribution. The process of cubing exacerbates the deviations from the mean, which is why skewness is used for measuring tail risk.

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