  The probability distribution for the relative return of a portfolio
constructed from a subset n of the assets from a benchmark, consisting of N
assets whose returns are multivariate normal, is completely characterized by
its tracking error. However, if the benchmark asset returns are not
multivariate normal then higher moments of the probability distribution for the
portfolio's relative return are not related to its tracking error. We discuss
the convergence of generalized tracking error measures as the size of the
subset of benchmark assets increases. Assuming that the joint probability
distribution for the returns of the assets is symmetric under their
permutations we show that increasing n makes these generalized tracking errors
small (even though n<<N). For n>>1 the probability distribution for the
portfolio's relative return is approximately symmetric and strongly peaked
about the origin. The results of this paper generalize the conclusions of
Dynkin et. al. (2002) to more general underlying asset distributions.
