Charge-dependent anisotropy Fourier coefficients (
v
n
) of particle azimuthal distributions are measured in
p
Pb
and
PbPb
collisions at
√
s
NN
=
5.02
TeV
with the CMS detector at the LHC. The normalized difference in the second-order anisotropy coefficients (
v
2
) between positively and negatively charged particles is found to depend linearly on the observed event charge asymmetry with comparable slopes for both
p
Pb
and
PbPb
collisions over a wide range of charged particle multiplicity. In
PbPb
, the third-order anisotropy coefficient
v
3
shows a similar linear dependence with the same slope as seen for
v
2
. The observed similarities between the
v
2
slopes for
p
Pb
and
PbPb
, as well as the similar slopes for
v
2
and
v
3
in
PbPb
, are compatible with expectations based on local charge conservation in the decay of clusters or resonances, and constitute a challenge to the hypothesis that, at LHC energies, the observed charge asymmetry dependence of
v
2
in heavy ion collisions arises from a chiral magnetic wave.