A negatively skewed distribution is the opposite of a positively skewed distribution. A negatively skewed distribution has a disproportionately large amount of outliers on its left side. In other words, a negatively skewed distribution is said to have a long tail on its leftside.
q: Define and interpret kurtosis and explain why a distribution might have positive excess kurtosis.
Kurtosisdeals with whether or not a distribution is more or less "peaked" than a normal distribution.

  • A distribution that is more peaked than normal is leptokurtic. A leptokurtic return distribution will have more returns clustered around the mean and more returns with large deviations from the mean (fatter tails).

  • A distribution that is less peaked, or flatter than normal is said to be platykurtic.

For all normal distributions, kurtosis is equal to three. Statisticians, however, sometimes report excess kurtosis, which is defined as kurtosis minus three. A normal distribution has excess kurtosis equal to zero, a leptokurtic distribution has excess kurtosis greater than zero, and platykurtic distribution will have excess kurtosis less than zero.
r: Explain why a semi-logarithmic scale is often used for return performance graphs.