Quote from Gordon Gekko:
ok, i think it would work. but, why isn't everyone doing that..if it's so easy... ?? (i don't even do it, and i made this post)
Probably because most people wouldn't feel so hot about taking a random trade. They'd inject thoughts and biases about which way to go, etc.
Also, what you bring up in covered in depth in "Statistical Calculus of Financial Theory." It is part of the "random walk" theory and it goes into binomial, Markov process, etc.
I have a .PDF file that covers everything you'd ever want to know about finance theory, including equations on optimal excerise periods for American Puts and Calls. Actually, it contains everything you'd ever want to know and more.
(It is very heavy into mathematics towards the middle and, if you can stomach it, gets ugly near the end -- but you may be able to pick something out of it).
Here is a question for you, Gordon. It took me some time to figure out the answer because it wasn't obvious.
Let's say a trade has a 50% chance of going to either 48 and 52 from a starting point of 50.
If you were to randomly trade that overtime, you would theoretically break even (ignoring commissions, etc). However, let's change one small parameter.
If the price gets to $48.50, we scale in with another equally weighted position. Since, by the laws of mathematics, it always has a 50% chance of going either direction, if we stop-out, we lose $2.50, but if it goes our way, we make $3.50.
What is the error in this logic?