We analyze the time series of overnight returns for the bund and btp futures exchanged at LIFFE (London). The overnight returns of both assets are mapped onto a one-dimensional symbolic-dynamics random walk: The `bond walk'. During the considered period (October 1991 - January 1994) the bund-future market opened earlier than the btp-future one. The crosscorrelations between the two bond walks, as well as estimates of the conditional probability, show that they are not independent; however each walk can be modeled by means of a trinomial probability distribution. Monte Carlo simulations confirm that it is necessary to take into account the bivariate dependence in order to properly reproduce the statistical properties of the real-world data. Various investment strategies have been devised to exploit the `prior' information obtained by the aforementioned analysis.