  Observations of the Cosmic Microwave Background (CMB) have revealed an
unexpected quadrupole-octopole alignment along a preferred axis pointing toward
the Virgo cluster. We here investigate whether this feature can be explained in
the framework of the concordance model by secondary anisotropies produced by
the non-linear evolution of the gravitational potential, the so-called
Rees-Sciama (RS) effect. We focus on the effect caused by the local
superclusters, which we calculate using a constrained high-resolution
hydrodynamical simulation, based on the IRAS 1.2-Jy all-sky galaxy redshift
survey, which reproduces the main structures of our Universe out to a distance
of 110 Mpc from our Galaxy. The resulting RS effect peaks at low multipoles and
has a minimum/maximum amplitude of -6.6\mu K 1.9\mu K. Even though its
quadrupole is well aligned with the one measured for the CMB, its amplitude is
not sufficient to explain the observed magnitude of the quadrupole/octopole
alignment. In addition, we analyze the WMAP-3 data with a linear matched filter
in an attempt to determine an upper limit for the RS signal amplitude on large
scales. We found that it is possible to infer a weak upper limit of 30\mu K for
its maximum amplitude.
