  Is the large influence that mutual funds assert on the U.S. financial system
spread across many funds, or is it is concentrated in only a few? We argue that
the dominant economic factor that determines this is market efficiency, which
dictates that fund performance is size independent and fund growth is
essentially random. The random process is characterized by entry, exit and
growth. We present a new time-dependent solution for the standard equations
used in the industrial organization literature and show that relaxation to the
steady-state solution is extremely slow. Thus, even if these processes were
stationary (which they are not), the steady-state solution, which is a very
heavy-tailed power law, is not relevant. The distribution is instead
well-approximated by a less heavy-tailed log-normal. We perform an empirical
analysis of the growth of mutual funds, propose a new, more accurate
size-dependent model, and show that it makes a good prediction of the
empirically observed size distribution. While mutual funds are in many respects
like other firms, market efficiency introduces effects that make their growth
process distinctly different. Our work shows that a simple model based on
market efficiency provides a good explanation of the concentration of assets,
suggesting that other effects, such as transaction costs or the behavioral
aspects of investor choice, play a smaller role.
