  The I-band brightness of clump stars has been used recently to determine the
distance to the bulge, the LMC and SMC, and to M31. It was assumed to be a
standard candle based on the observational fact that it is independent of
(V-I)-colour in all observed populations. The calibration was done using nearby
clump stars with HIPPARCOS-parallaxes. The most surprising result of this
procedure was the claim that the distance to the LMC was only 18.04 mag. In the
present paper we show that with a population synthesis approach we can
reproduce the constancy of M_I with colour for the local Hipparcos clump
sample. Nevertheless, M_I is not a constant among different populations, but
depends on metallicity. As a result, the determined distance modulus to the LMC
of 18.28+-0.18 mag is in better agreement with standard values. This resolves,
at least partially, the controversial result obtained by the assumption of a
universal value for M_I. We also find and discuss substructures in the clump:
we predict that stars slightly heavier than the maximum mass for developing
degenerate He cores should define a secondary, clumpy structure, about 0.3 mag
below the bluest extremity of the red clump. This secondary clump can be
clearly identified in the HIPPARCOS database of stars. We argue that there
remain severe uncertainties in the use of clump stars as a distance indicator.
