We analyse 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 modelled by means of a trinomial probability distribution. Monte Carlo simulations cofirm 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. (C) 1999 Elsevier Science B.V. All rights reserved.