A distribution can either be symmetrical over the mean or skewed in one direction. If the tail on one side is longer than the other side of the mean, then the distribution is said to be skewed towards the longer side. So, if the returns on the right side of the mean have a longer tail than the returns on the left side, then the distribution is said to be right-skewed or positively skewed. If the returns on the left side of the mean have a longer tail than the returns on the right side, then the distribution is said to be left-skewed or negatively skewed.
A return distribution with a positive skew has frequent small losses and a few extreme gains. A return distribution with a negative skew has frequent small gains and a few extreme losses.
The mean is greater than the median, which is greater than the mode for a unimodal positively skewed distribution. The mode is greater than the median, which is greater than mean for a unimodal negatively skewed distribution.
For positively skewed distribution: Mean > Median > Mode
For negative skewed distribution: Mean < Median < Mode
For symmetrical distribution (normal distribution): Mean = Median= Mode
Diagram:
Previous LOS: Coefficient of variation and Sharpe ratio
Next LOS: Measures of sample skewness and kurtosis
