In this paper, we investigate the problem of how to cache a set of media files with optimal streaming rates, under HTTP adaptive bit rate streaming over wireless networks. The design objective is to achieve the optimal expected QoE under a limited storage budget, which is measured by the logarithmic relation between the required bit rate and the actual streaming bit rate. We formulate the content cache management of streaming files as a constrained optimization problem. Lagrange multiplier method is employed, and we obtain the numerical solution of the optimal streaming files. Particularly, we characterize the properties of the solution, and find there is a fundamental phase change in the optimal solution as the number of cached files grows. Moreover, the simulation results indicate that with the increase of cache size, more copies of different bit rate should be cached for a better QoE. Our comprehensive investigation reveals insightful guidelines to provide HTTP ABR streaming services over wireless networks.