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This paper describes multi-portfolio `internal' rebalancing processes used inthe finance industry. Instead of trading with the market to `externally'rebalance, these internal processes detail how portfolio managers buy and sellbetween their portfolios to rebalance. We give an overview of currently usedinternal rebalancing processes, including one known as the `banker' process andanother known as the `linear' process. We prove the banker processdisadvantages the nominated banker portfolio in volatile markets, while thelinear 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 ingeneral 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 calledthe `iterative proportional fitting procedure') for biproportional matrices. Weshow 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 tothe significance of these results.

Internal multi-portfolio rebalancing processes: Linking resource allocation models and biproportional matrix techniques to portfolio management