Materials engineering is a key for the enhancement of photovoltaics technology. This is particularly true for the novel class of perovskite solar cells. Accurate theoretical modelling can help establish general trends of behavior when addressing structural changes. Here, we consider the effects due to halide substitution in organohalide CH3NH3PbX3 perovskites exploring the halide series with X = Cl, Br, I. For this task, we use accurate DFT and GW methods including spin-orbit coupling. We find the expected band gap increase when moving from X = I to Cl, in line with the experimental data. Most notably, the calculated absorption coefficients for I, Br and Cl are nicely reproducing the behavior reported experimentally. A common feature of all the simulated band structures is a significant Rashba effect. This is similar for MAPbI3 and MAPbBr3 while MAPbCl3 shows in general a reduced Rashba interaction coefficient. Finally, a monotonic increase of the exciton reduced masses is calculated when moving from I to Br to Cl, in line with the stronger excitonic character of the lighter perovskite halides.