This paper assumes an investor who has a non-traded position operating in a stochastic interest rates environment. The investor trades continuously either distinct futures contracts or distinct forward contracts in order to maximize his expected utility of terminal wealth. In order to reach the welfare level of the first best optimum, the investor must incorporate into his portfolio either two distinct futures contracts or two distinct forward contracts. The optimal forward contracts dynamic spreading strategy has two components, a speculative component and a minimumvariance hedging component. The minimum-variance hedging component is composed of a short position in the nearby contract and a long position in the deferred contract. The speculative component serves to replicate the growth optimum portfolio. The speculative component is composed of a short position in the contract which is the most negatively correlated with the growth optimum portfolio and a long position in the other contract. The marking-to-market procedure of the futures positions forces the investor to hold less futures contracts than the corresponding forward contract positions. The analysis is also extended to incomplete markets and to inter-market spreading.