I have a question regarding kurtosis and skewness.

In investment terms skewness is supposed to mean “bias toward positive or negative return”.

Kurtosis captures the tendency of the price of this investment to jump either direction. In FRM, I’ve encountered EVT, and its objective is to capture severe events. These severe events come with fat-tail, and fat-tail is higher kurtosis. My question is then, what is the difference between skewness and kurtosis?

If a distribution exhibits skewness, doesn’t that also imply that it has a tendency to move toward either directions, which eventually leads to higher kurtosis than normal distribution? For example, let’s say a statician is conducting a research to find out the average income of people in a town, and there is one very rich guy. The average of the people’s income excluding him is 100$, and if he is included the average jumps up to one million$. The skewness is definitely positive, and doesn’t this also exhibit high kurtosis, since he’s a really big outlier and an extreme event?