As I understand it, one can model changing variance of a time series process with a GARCH model. What I don't understand is, how can one actually make predictions with this? Since $$ y_t = \sigma_t \epsilon_t $$ with $\epsilon_t$ being a Gauss distributed random variable, the expectationa value of this is always zero. So how does it help to know, how big the variance is, when both, a up and a down is equally likely? Or did I understand something wrong?

As I understand it, one can model changing variance of a time series process with a GARCH model. What I don't understand is, how can one actually make predictions with this? Since $$ y_t = \sigma_t \epsilon_t $$ with $\epsilon_t$ being a Gauss-distributed random variable, the expected value of this is always zero. So how does it help to know, how big the variance is, when both an up and a down are equally likely? 
Or did I understand something wrong?