  Within the $\Lambda$CDM cosmology, dark matter haloes are comprised of both a
smooth component and a population of smaller, gravitationally bound subhaloes.
These components are often treated as a single halo when halo properties, such
as density profiles, are extracted from simulations. Recent work has shown that
density profiles change substantially when subhalo mass is excluded. In this
paper, we expand on this result by analysing the change in three specific host
halo properties -- concentration ($c_{\rm{NFW}}$), spin ($\lambda_{\rm
Bullock}$), and shape ($c/a$), -- when calculated only from the smooth
component of the halo. This analysis is performed on both Milky Way-mass haloes
and cluster-mass haloes in high-resolution, zoom-in, $N$-body simulations. We
find that when subhaloes are excluded the median value of (1) $c_{\rm{NFW}}$ is
enhanced by $\approx 38 \pm 12\%$ and $\approx 88 \pm 7.7\%$ for Milky Way mass
($10^{12.1}\,\text{M}_\odot$) and cluster mass ($10^{14.8}\,\text{M}_\odot$)
haloes respectively, (2) $\lambda_{\rm Bullock}$ is reduced for Milky Way mass
by $\approx 16 \pm 6.8\%$ and cluster mass haloes by $\approx 32 \pm 8.9\%$.
Additionally, with the removal of subhaloes, cluster mass haloes tend to become
more spherical as the ratio of minor-to-major axis, $c/a$, increases by
$\approx 12 \pm 4\%$, whereas Milky Way mass haloes remain approximately the
same shape with $c/a$ changed by $\approx 1.2 \pm 5.6\%$. The fractional change
of each of these properties depends primarily on the amount of mass that is
removed from the halo system and, to a lesser extent, mass accretion history.
Our findings demonstrate that the properties of the smooth components of dark
matter haloes are biased relative to the total mass of the halo including
subhaloes.
