The currents that cause magnetic storms are usually characterized by the hourly Dst and Asym indices. It is observed and expected physically that the ring current is asymmetric during the main phase of a magnetic storm and becomes symmetric in the recovery phase. We report work utilizing 1-min resolution Sym-H* and Asym-H to study the time development of these currents. As an index of the degree of ring current symmetry we use the ratio (-Sym-H/Asym-H). We show that this index does not behave as expected. Corrections for solar wind dynamic pressure do not change this behavior. We find that the ring current is always asymmetric. Using ~160 magnetic storms, we have determined the median response of these indices as a function of time relative to the time of minimum Sym-H. We find that both indices appear to contain offsets. Sym-H* appears to be -19.7 nT too low, and Asym-H appears to be 18.8 nT too high. We also find that in the main phase both median curves can be represented by a single exponential with nearly identical growth times: ~6 hours. In the recovery phase double exponentials are needed to obtain reasonable fits to the median curves. The time constants for Sym-H* (5.25 and 64.3 hours) are nearly twice as long as those for Asym-H (2.2 and 20.9 hours). If we subtract the calculated offsets from the measured indices, we obtain a corrected ratio that behaves as expected. In the main phase the ratio is close to 1.0, implying equal Sym-H* and Asym-H, i.e., that either the two currents grow together or that both ground disturbances are caused by the same current. In the recovery phase the ratio increases continuously until both corrected indices approach zero and the ratio becomes meaningless. This is the expected behavior with the main phase current system being converted to a symmetric ring as the ring current decays.