Stop repeating the "50% loss requires 100% gain" thing, it's not that insightful

I’m getting fed up with people parroting the line "if you lose 50%, you need to gain 100% to break even" as if it revealed something important about risk. It’s a misleading way to think about how markets work, and those people seem to imply that it's somehow more unlikely for stocks to go back to their previous value after a drop? Otherwise I don't really understand why they keep repeating this line.

Markets move multiplicatively, not additively. Stock prices follow something close to geometric Brownian motion, a random walk **on a log scale**. In a multiplicative world, the symmetry is between ratios, not percent changes.

Assuming no drift, if you look at a stock price **on a log scale**, you will notice that the probability of a green candle and the probability of a red candle of the same size are equal. A 2x gain and a 0.5x loss are symmetric. A -50% drop and a +100% gain are equal and opposite **on a log scale**. Same for -20% and +25% or whatever other example you want to use.

And if you assume even a small positive drift, which reflects long-term market behavior, then the probability of doubling actually becomes **greater** than that of halving.

If a stock lost 50% due to some unexpected bad news, but it later turned out that the news was entirely fake, the price would go back to its original value i.e. +100%. It would not just gain back +50%.

There's nothing deep or meaningful about saying that you need +100% to compensate for -50%. That's just pointing out a basic fact of math and how percentages work, but it's pretty useless to keep repeating this as if it had a deep meaning.