Dynamic Term Structure Models assume that the behavior of the yield curve is fully governed by a set of stochastic state variables. In such a context, bond port- folios selection identifies those state variables as the sources of risk and deals with them to provide the best return given a level of risk. Solution to the optimal portfolio choice problem is available in closed form when state variables are Gaussian and ho- moskedastic. This is hardly the same for heteroskedastic models. This paper explores the optimal bond portfolios choice problem within Quadratic Term Structure Models framework that induce heteroskedasticity. We derive in closed form the optimal bond portfolio and analyze its perfomance. We compare it to those associated to traditional Affine Term Structure Models. We find that the first and second order sensitivities to the underlying sources of risk not only depend on time-to-maturity but also exhibit a stochastic behavior, this last property being in sharp contrasts with Affine Term Structure Models.