  This paper describes multi-portfolio `internal' rebalancing processes used in
the finance industry. Instead of trading with the market to `externally'
rebalance, these internal processes detail how portfolio managers buy and sell
between their portfolios to rebalance. We give an overview of currently used
internal rebalancing processes, including one known as the `banker' process and
another known as the `linear' process. We prove the banker process
disadvantages the nominated banker portfolio in volatile markets, while the
linear process may advantage or disadvantage portfolios.
  We describe an alternative process that uses the concept of
`market-invariance'. We give analytic solutions for small cases, while in
general show that the $n$-portfolio solution and its corresponding
`market-invariant' algorithm solve a system of nonlinear polynomial equations.
It turns out this algorithm is a rediscovery of the RAS algorithm (also called
the `iterative proportional fitting procedure') for biproportional matrices. We
show that this process is more equitable than the banker and linear processes,
and demonstrate this with empirical results.
  The market-invariant process has already been implemented by industry due to
the significance of these results.
