Right, here's a guide. As I say I've no idea if this will work but you can try it.
After the Life Invader keynote mission and the shares plummet, I went straight to Franklin and invested my 500k. This is BEFORE Lester emails and tells you to. Right after the mission.
At this point, the shares should still be falling for the next week or so, but head to Franklin's house and save your game.
Wake up, and the shares should still be falling. They start off at around $27 dollars right after the keynote IIRC but after they will start falling through $16, $10 and on mine they've fallen as low as $3 after a week. In my experience the value doesn't matter, sell them anyway.
Go to your portfolio, click Life Invader, press sell and then sell all. This will take you to a confirmation screen, which in my experience now shows that you're making a profit. Sell them, save the game. Wake up, buy, save. Sell, save. Etc. The profit should be rising at a ridiculous rate each time. Over 10x, I think, but I wasn't really counting.
You will hit a point, after about 10 times of this, where you can't sell your shares and the Sell All button won't work because you've hit the cap. In this instance you can sell a substantial amount, after which the sell all button will work one final time, leaving you with around 2.1bn. After that you'll be stuck with about 54 million shares which you can't get rid of.
Now, after this I discovered this also works with Michael and WITHOUT saving. You can just buy, sell, buy, sell, right after one another, and watch it tick up, without having to save. I started with 8 grand on Michael, did it three times and was at 500K. I stopped there because I don't really want to make the whole moneymaking schemes of the game pointless. (Worth noting I also invested with Michael right after the LI mission too. Don't know if this would work if you hadn't.)
That's a really rough guide I know but as I say I really only stumbled across it and wasn't paying that much attention to what I was doing. I think the key is investing right after the keynote. My friend also recreated this on both characters with those instructions. Neither of us have done any of the heists or assassinations or have Trevor available yet, so this is kind of game breaking that early on.
Is it too late to this with after Trevor arrives in Los Santos?