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As populations increase in arid regions of the world, investment in water infrastructure improves resource management by increasing control over the location and timing of water allocation. Many studies have explored freer trade as a substitute for additional infrastructure investment. We instead quantify how water allocation institutions, reservoir management objectives, and storage capacity influence the value derived from a reservoir system. We develop a stochastic dynamic programming model of a reservoir system that faces within-year variation in weather-dependent water demand as well as stochastic semiannual inflows. We parameterize the model using the Colorado-Big Thompson system, which transports stored water from the West Slope of the Rocky Mountains to the East Slope. We then evaluate the performance of the system under five institutional settings. Our results suggest that rigid allocation mechanisms and inefficient management objectives result in a decrease of up to 13% in the value generated from stored water when compared to a free trade scenario, an impact on par with predicted losses associated with climate-change-induced inflow reductions. We also find that under biased management objectives, increasing storage capacity can decrease the social value obtained from stored water.