The main objective of this paper is to address, in an a continuous-time framework, the issue of using storable commodity futures as vehicles for hedging purposes when, in particular, the convenience yield as well as the market prices of risk evolve randomly over time. Following the martingale route and by operating a suitable constant relative risk aversion utility function (CRRA) specific change of numéraire, we solve the investor's dynamic optimization program to obtain quasi analytical solutions for optimal demands, which can be expressed in terms of two discount bonds (traded and synthetic). Contrary to the existing literature, we explicitly derive the individual optimal proportions invested in the spot commodity, in a discount bond and in the futures contracts, which can be computed in a simple recursive way. We suggest various decompositions allowing an investor to assess the sensitivity of the optimal demands to the state variables and to specify the role played by each risky asset. Empirical evidence shows that the convenience yield has a strong impact on the speculation and hedging positions and the interaction among time-varying risk premia determines the magnitude and the sign of these positions.