Rapidity asymmetry ($Y_\mathrm{asym}$) of K$^{*0}$ (red circles) and $\phi$ (blue squares) meson production as a function of $p_\mathrm{T}$ in the rapidity range 0 $<$ $|y|$ $<$ 0.3 for various multiplicity classes in p$-$Pb collisions at $\sqrt{s_{\rm NN}}$ = 5.02 TeV. The statistical uncertainties are shown as bars whereas the boxes represent the systematic uncertainties on the measurements.