Skewness is the degree of asymmetry observed in a probability distribution. When data points on a bell curve are not distributed symmetrically around the median, the bell curve is skewed. Distributions can be positive and right-skewed, or negative and left-skewed. A normal distribution exhibits zero skewness.
Key Takeaways
- Skewness is the asymmetry observed in a probability distribution.
- Distributions can be positive and right-skewed, or negative and left-skewed. A normal distribution has zero skewness.
- Skewness is often noted in stock market returns or the distribution of average individual income.
Discover the Types of Skew Worldwide
- Negative or left-skewed: Refers to a longer or fatter tail on the left side of the distribution.
- Positive or right-skewed: Indicates a longer or fatter tail on the right side.
The diagrams below depict probability distributions that are increasingly right-skewed. The mean of positively skewed data will be greater than the median. Conversely, in a left-skewed distribution, the mean will be less than the median.
Mastering the Art of Measuring Skewness
Pearson’s First Coefficient of Skewness: (Mean - Mode) / Standard Deviation
Pearson’s Second Coefficient of Skewness: 3 * (Mean - Median) / Standard Deviation
Choose Pearson’s first coefficient when the data exhibit a strong mode; the second is better for data with a weak mode or multiple modes. Skewness tells you where the outliers are, though it doesn’t indicate the quantity.
Mathematical Representation
Skewness (S_k) can be measured through two primary methods:
- S_k1 = \(\frac{ \bar{X} - Mo }{ s}\)
- S_k2 = \(\frac{ 3 ( \bar{X} - Md ) }{ s}\)
Where:
- \bar{X}: Mean
- Mo: Mode
- Md: Median
- s: Standard Deviation
How Skewness Informs Investment Strategies
Investors pay attention to skewness when evaluating return distributions because, like kurtosis, it considers extreme values within the data set beyond the mere average. Risk becomes crucial for short- and medium-term investors who don’t hold a position long enough to see the average resolve.
Investors usually turn to standard deviation to predict future returns, but standard deviation assumes a normal distribution. Given that few return distributions are truly normal, skewness offers a more accurate measure for performance predictions.
Skewness Risk
Skewness presents additional risk (known as skewness risk) because financial models typically assume normal distributions. The more skewed the data, the less reliable the prediction, increasing skewness risk.
Unveiling Skewness in the Economy
The broader stock market often displays a negative skew. The general perception is a market that commonly shows small positive returns with occasional significant negative losses. Studies indicate that individual firm equity often leans toward left-skewed distributions as well.
Household income distribution in regions like the United States frequently offers a common example of skewness.
Understanding the Causes of Skewness
Skewness results from data concentrated heavily in one range and less in another. For instance, Olympic long jump scores might display many high-distance jumps and fewer short-distance jumps, leading to right-skewness.
Embracing Skewness as a Normal Scenario
While analyzing data sets, one often finds inherent skewness, reflective of real-life situations like the average human lifespan. This skewness is anticipated and considered part of the data’s natural makeup.
The Conclusion: Embrace Skewness for Better Insights
Skewness indicates whether a distribution is distorted or symmetrical. A right-skewed distribution is positive and left-skewed is negative. Understanding skewness allows for a richer analysis of data distributions and the recognition of extreme values within a data set.
Related Terms: Kurtosis, Standard Deviation, Return, Risk, Distribution.
References
- Oxford Academic. “The Skewness of the Stock Market Over Long Horizons”.
