Assume that an asset price $S$ is given by a Brownian motion. Argue from the definition why it is not possible to predict future values of the asset based on the past values of $S$.
I am not sure exactly what this asks. I know that Brownian motion is a random process with independent increments (at least the way we defined it in our course). I am not sure what else I can add on or how I can formalise my argument more using the definition of Brownian motion.