We analyse how money as a store of value affects the decisions of a representative household under diversifiable and non-diversifiable risks given that the central bank successfully stabilizes the rate of inflation at a low level. Assuming exponential utility allows us to derive an explicit relationship between optimal money holdings, the household?s desire to tilt, smooth and stabilize consumption as well as minimize portfolio risk. In this context we also show how the correlation between stochastic labour income and stock returns impact the store-of-value function of money. Finally we prove that the store-of-value benefits of money holdings continue to hold even if we take riskless alternatives into account.