In October 2015 the European Parliament has established a Market Stability Reserve (MSR) in the Phase 4 of the EU-ETS, as part of the 2030 framework for climate policies. In this paper we model the EU-ETS in presence of the Market Stability Reserve (MSR) as it is defined by that decision and investigate the impact that such a measure has in terms of permits price, output production and banking strategies. To do so we build an inter-temporal model in which polluting firms competing in an homogeneous good market are price takers in a permits market and face an uncertain demand. Our main finding is that the MSR succeeds in increasing the permits' price correcting an excess supply (and conversely decreasing it in case of excess demand). However, when the output demand is stochastic, the MSR may alter the arbitrage conditions that determine permits' prices. In some cases which depend on the extend of the demand variation, unintended effects on the price pattern appear. This in turns may adversely affect welfare.