This article proposes a methodology to calculate the upper boundary of the revenue available from the storage and time-shifting of electrical energy. The inputs to the mathematical model are a discrete time-series of the market index prices over a particular period of interest, and also specific energy storage device parameters. By using a Monte Carlo based optimisation method, the upper boundary of the revenue from time-shifting energy is determined. The method is explained and validated by showing that it finds the optimum solution that is the upper boundary for time-shifting revenue. In other words, a storage operator could never derive more revenue than this value from time-shifting alone and calculating this upper-boundary gives a reference value to compare the efficacy of other methods of estimation. The user defined storage device parameters include: fixed efficiencies for charging and discharging (%), the maximum capacity of the storage device (kWh), the charging and discharging power limits (kW), and the inclusion of an additional time-dependent efficiency that models the self-discharge of storage devices (% loss per hour). The combination of these parameters enables this method to give an objective comparison between different storage devices in terms of maximum arbitrage revenue. The output of the model provides not only a single value of the upper boundary revenue, but also the corresponding charging/discharging schedule.