Well I spent some time mainly just looking at the LCN yesterday. And first of all, this concerns only the prices moving on their own without any in game action involvement (mission or something else). After completing the main story in my case.
One thing to note for starters.. The blue graph lines that you see for the index and all of the stocks, you can forget about them. They stay completely static all the time and do not change AT ALL.
Only the days on the bottom keep moving to represent the day you are in the game. Also when looking at the market list, all of the precentage changes you see do not move AT ALL either. The info that you see there about the highest and lowest prices next to the graphs is also pretty much irrelevant, the stocks will never reach those levels, unless they happen to be already very close to one of them.
But still, the prices do change obviously, not by much, but they do. The thing I noticed was they seem to change by few decimals at a time, quite slowly, whether its a lower price stock or vice versa. So in that case for any reasonable profits, you'd only want to look for the cheapest stocks. It's all about percentage after all.
I started watching the 3 cheapest ones in the list for a while. Which were Lifeinvader (LFI), Redwood (RWC) and Logger (LOG).
During few in-game days, their prices moved like this (lowest-highest price spotted):
LFI: 2.66 - 3.29
RWC: 7.0 - 9.11
LOG: 8.17 - 9.47
Naturally they didn't go from lowest to highest in a linear way, but there were ups and downs in between. With only LFI I managed to make $200k quite easily couple of times, with a 10m buy. So thats only a 2% profit. 10% or close seemed easily possible for all of those stocks.
Of course I can't say if the general price ranges are same for everyone. These
should be the cheapest stocks for everyone I'd think though.
Easy way to follow the movements is just to buy one stock of anything, and keeping an eye how the stock price starts to move.
Thats it for now.