We study optimal investments in rolling-horizon bond portfolios. Combinations of a money-market account and 1 to 3 rolling-horizon bonds are considered. Forward interest rates are modelled using finite dimensional realizations of HJM-models. Money-market account has return being the implied short rate from the forward interest rate model. We state minimal realizations of the forward interest rate models in terms of diffusion processes. From the definition of self-financing roll-over strategy, we state the value process of rolling-horizon bonds. We solve optimal control problems by means of direct approach when the volatility has constant-, exponential-, hump-shapedand combined constant and exponential structure. We state the Hamilton-Jacobi-Bellman equation of the stochastic control problem when the volatility structure is given by constant function. Further, we consider fixed-fraction rolling-horizon bond portfolios. By means of Monte Carlo simulations we are able to determine optimal fixed-fraction portfolios.