Investment markets operate on relative gain, not absolute gain. E.g.: if you invest in a stock and it gains $5, this would be a great return for a $1 stock but a poor one for a $1000 stock, so the absolute gain doesn't mean anything on its own. A 5% return always means that you've gained 5% on your investment.

Would it be the same (valid) with percentage returns?

Less so. Log-normal returns are better because they have the property that a summation of log-normal returns over contiguous intervals is equal to the log-normal returns of the combined interval. In other words: Losing 5% and then gaining 5% doesn’t put you back at exactly 100%, and log-normal fixes that.

In the extreme, two successive trades, where the first gains 110% and the second loses 100%, “average” out to a 5% return. However, you don’t want to make that pair of trades.

Ah, that makes sense. Many thanks.

I think their point is that predicting that "the stock will go up by 1$" or "the stock will go down by 1$" is worse than "the stock will go up by 0.05%" and "the stock will go down by 0.05%" because of this little paradox:

50$ increase from 50$ is 100% increase 50$ decrease from 100$ is 50% decrease

e.g., if the model finds 50$ increase/decreases, that actually corresponds to very different wealth changes

Here you go:

https://financetrain.com/why-lognormal-distribution-is-used-...

Thank you.

Well, just at a minimum... There's the fact that the majority of large gains and losses exist over single-day frames. That is, guessing "right" or "wrong" on movement means little when one slip on the wrong day will decimate your returns.