  The stability of income payments in a pooled annuity fund is studied. In
those funds, members receive a fluctuating income depending on their
experienced mortality in exchange for their pension savings. The focus is on
describing the influence of different initial savings on the ability of the
fund to provide a stable income in retirement. Because of this, members
coincide in their characteristics except for their initial savings. We identify
a term, which we dub ``implied number of homogeneous members'', that directly
links the initial savings to the size of the income fluctuations. Our main
contribution is the analysis of this term and the development of a criterion to
answer the question of whether or not a given group of same-aged people should
pool their funds together.
