Skewness and kurtosis are simple statistical concepts. In CFA Level 1, you probably don’t have to memorize the equations. But please make sure you understand the concepts. Especially, how the skewness and kurtosis are related to the returns.

The best way to memorize the meanings of skewness and kurtosis is to compare it with the normal distribution. And indeed, this is want skewness and kurtosis are meaningful to us (the candidates).

Skewness is a measure of symmetry. Compared to a normal distribution (skewness = 0), a skewed-to-left (negative skewed) distribution will have the peak at the right, while a skewed-to-right (positive skewed) distribution will have the peak at the left! This why skewness is confusing! If you are not familiar with this, it is very easy for you to think that having a peak at the left is skewed-to-left, which is wrong! (take a pen and draw it!)

Kurtosis is a measure of the “peaking” of a distribution compared to a normal distribution (Kurtosis = 3). The larger the kurtosis, the more the peaking of the distribution. If it is larger than 3, it is called Leptokurtic and if it is smaller than 3, it is called Platykurtic. Don’t know how to memorize these terms? Well, think of “L” which has a long vertical line. Doesn’t it look like more peaking? So, just remember the word starts with “L” has kurtosis > 3.

Traps and Tips:

E.g. If a portfolio return has positive skew (skewness = 0.6), compared to normal distribution, the portfolio has higher chance of extreme large gain. It also has pretty frequent small loss. Are both statements correct?

Yes. Both are correct. With a positive skew, the peak is at the left. There is a small tail going to the far right, corresponding to extreme high gain. And it also has both frequent small loss and gain, although small gain is more frequent than small loss.