It’s clear that then the mean return is the dividends paid and can be negative if the exit price is sufficiently low. I think by a bit of squinting (using the central limit theorem) you can say that this should be normally distributed as long as entry_price and exit_price have the same distribution
Coming back to options world, entry_price is a constant when opening the contract, let's ignore dividends, the formula is (exit_price - entry_price) / entry_price = exit_price/entry_price - 1 = exit_price/constant - 1.
This is normally distributed if, and only if exit_price is normally distributed. You'd want to to add back the 1, log() it, add back the log(constant) to cancel it out and just work on the log(exit_price) normally distributed random variable.
Stock return really is not normally distributed. Log(stock return) is normally distributed (under B-S, it's an assumption after all). Stock return is log-normally distributed. Multiply by 1/entry_price and subtract 1 to get your version of stock returns.
Stock return = (exit_price - entry_price + dividends) / entry_price.
It’s clear that then the mean return is the dividends paid and can be negative if the exit price is sufficiently low. I think by a bit of squinting (using the central limit theorem) you can say that this should be normally distributed as long as entry_price and exit_price have the same distribution