This paper studies risk-aware day-ahead scheduling and real-time dispatch for plug-in electric vehicles (EVs), aiming to jointly optimize the EV charging cost and the risk of the load mismatch between the forecasted and the actual EV loads, due to the random driving activities of EVs. It turns out that the inclusion of the load mismatch risk in the objective function complicates the risk-aware day-ahead scheduling and indeed the optimization problem is nonconvex. A key step is to utilize the hidden convexity structure to recast it as a two-stage stochastic linear program, which can be solved by using the L-shaped method. Further, we develop a distributed risk-aware real-time dispatch algorithm, where the aggregator only needs to compute the shadow prices for each EV to optimize its own charging strategy in a distributed manner. We show, based on real data, that the proposed risk-aware day-ahead scheduling algorithm can reduce not only the overall charging cost, but also the peak demand of EV charging.