Today, I added a note about the usage of log returns in finance to my second brain, and thought it might be interesting to some people. The most valuable videos on the topic are referenced below. I suggest watching all three videos as each gives a different angle to the subject. If you prefer a written article over videos, you can check out this article about the usefulness of log returns and the second part of the article with an Excel implementation.

A log return is calculated by dividing the current price of an asset by the past price of an asset and taking the natural logarithm: $ln(price_{t}/price_{t-1})$.

We use log returns because the product of normally-distributed variables is not normal. But the sum of normally-distributed variables follows a normal distribution. A product of simple gross returns will not be normally distributed! A time series of $1\%$ price increases would look like this when aggregated, but the returns will not be normally distributed: $1.01 * 1.01 * 1.01 …$

Have you ever wondered why, when a portfolio loses $-20\%$ and then gains $20\%$, we do not end up at the value we left off? Log returns solve this issue! What is also nice is that log returns are time-additive (time-consistent). But they are not portfolio-additive. See also this video:

When you add log returns, you will have to $exp()$ the result to get the percentage return. See also this video, starting at about 7:30min:

The following video is the most comprehensive one with 25min length. As you can see in this video after 4:30min, the geometric average is another concept related to log returns:

After studying these videos, I became a bit of a fan of log returns. I hope they make your life easier as well.