Skewness

Skewness is a statistical measure of asymmetry in a distribution. It shows whether data concentrate more on one side of the central value (mean) and whether extreme values (tails) are heavier on one side.

Key points

• Zero skewness: symmetric (e.g., ideal bell curve).
• Positive (right) skew: long/fatter tail to the right; mean > median.
• Negative (left) skew: long/fatter tail to the left; mean < median.
• High skew can indicate outliers or heavy tails (related to kurtosis).
• Skewness locates the side where extremes occur but does not count how many outliers there are.

Types of skew

• Right-skewed (positive): most values are left of the mean; rare large positive values pull the mean to the right.
• Left-skewed (negative): most values are right of the mean; rare large negative values pull the mean to the left.
• Symmetric (zero skew): values balance around the mean.

Measuring skewness

Two common measures are Pearson’s first and second coefficients:

Pearson’s first coefficient (mode-based):
Sk1 = (mean − mode) / s

Pearson’s second coefficient (median-based):
Sk2 = 3 × (mean − median) / s

where:
* mean = average value
* median = middle value
* mode = most frequent value
* s = sample standard deviation

Use the first coefficient if the data have a clear mode; use the second if the mode is weak or multiple modes exist.

Interpretation for investors

Skewness matters because many financial return distributions are not symmetric. Relying solely on standard deviation (which assumes normality) can underestimate the likelihood of extreme outcomes when data are skewed.

• Skewness risk: the chance that an asset’s return distribution has extreme outcomes on one side. Models assuming normality may understate this risk.
• Short- and medium-term investors pay attention to skew and kurtosis because extremes (rare large gains or losses) can dominate realized performance.

Examples

Roulette: A single-number bet usually loses $100, but rarely pays a large sum. Most outcomes are losses, with a small chance of a big win—this produces a strongly right-skewed distribution.

Household income: Often right-skewed because a small portion of households earn very high incomes relative to the majority.

Equity returns: The aggregate market and individual stocks are sometimes observed to exhibit negative (left) skew — frequent small gains but occasional large losses.

Why skewness occurs

Skewness arises when observations cluster on one side of the central values while a few extreme values extend the tail on the other side. The relative frequency and magnitude of those extremes determine the skew.

Is skewness normal?

Yes. Many natural and economic variables are skewed (for example, lifespans and incomes). Skewness is a normal feature of many real-world data sets and should be expected rather than assumed away.

Simple explanation (ELI5)

Skewness is like a seesaw where most kids sit on one side. If a few very heavy kids sit on one end, the seesaw tips that way—skewness tells you which side is tipped and how extreme the tip is.

Bottom line

Skewness indicates the direction and extent of asymmetry in a distribution. Positive skew means the right tail is heavier, negative skew means the left tail is heavier. For analysts and investors, recognizing skewness helps assess the likelihood and direction of extreme outcomes that standard deviation alone may miss.