What is Skewness
Skewness is the degree of distortion from the symmetrical bell curve, or normal distribution, in a set of data. Skewness can be negative, positive, zero or undefined.
Breaking Down Skewness
Skewness is positive if the tail on the right side of the distribution is longer or fatter than the tail on the left side. The mean and median of positively skewed data will be greater than the mode. Skewness is negative if the tail of the left side of the distribution is longer or fatter than the tail on the right side. The mean and median of negatively skewed data will be less than the mode If the data graph symmetrically, the distribution has zero skewness, regardless of how long or fat the tails are.
There are several ways to measure skewness. Pearson’s first and second coefficients of skewness are two common ones. Pearson’s first coefficient of skewness, or Pearson mode skewness, subtracts the mode from the mean and divides the difference by the standard deviation. Pearson’s second coefficient of skewness, or Pearson median skewness, subtracts the median from the mean, multiplies the difference by three and divides the product by the standard deviation.
Pearson’s first coefficient of skewness is useful if the data exhibit a strong mode. If the data have a weak mode or multiple modes, Pearson’s second coefficient may be preferable, as it does not rely on mode as a measure of central tendency.
Skewness in Business and Finance
Investors note skewness when judging a return distribution because skewness, like kurtosis, considers the extremes of the data set rather than focusing solely on the average. Short- and medium-term investors in particular need to look at extremes because they are less likely to hold a position long enough to be confident that the average will work itself out.
Investors commonly use standard deviation to predict future returns, but standard deviation assumes a normal distribution. As few return distributions come close to normal, skewness is a better measure on which to base performance predictions. This is due to skewness risk.
Skewness risk is the increased risk of turning up a data point of high skewness in a skewed distribution. Many financial models that attempt to predict the future performance of an asset assume a normal distribution, in which measures of central tendency are equal. If the data are skewed, this kind of model will always underestimate skewness risk in its predictions. The more skewed the data, the less accurate this financial model will be.