There is a much easier way to grasp what is happening here. Often in finance, securities are assumed to follow something like a geometric Brownian pattern. Thi

There is a much easier way to grasp what is happening here. Often in finance, securities are assumed to follow something like a geometric Brownian pattern. This is the idea behind the Black-Scholes model, for instance. This means that you view your price ticker as a random Gaussian walk (e.g. Brownian motion) when your ticker is placed on a logarithmic scale. One way to think of this is that, given some (sufficiently large) unit of time, you have an equal chance of your security either doubling or halving in value. Or being multiplied/divided by 1.5, or 1.1, or any other figure you like, given whatever unit of time you like. It's really easy to see how this basic pattern has a positive expected value. Suppose you put $1 into a fair coin toss game, and if you win it doubles and if you lose it halves. You stand to win $1 or lose only $0.5, thus the expected value is $1.25. Now suppose, to keep it simple, you have a ridiculously volatile security which doubles or halves in value every day. So the ideal trading strategy is to choose some betting amount, say $1000, and just put it in at the start of the day. Then the next day, just reset your position size to $1000, either taking your $1000 in profit or kicking in another $500 to cover losses. You will quickly become a trillionaire.