On the steady state of the replicating portfolio: accounting for a growth rate

For the risk management and transfer pricing of non-maturity liabilities, banks in Europe often use a so-called replicating portfolio technique. A commonly used implementation is replication of a fixed investment rule every time period. This paper deals with the development of the portfolio in the long run, when using this methodology. Applying this replicating portfolio technique yields, after a while, a steady state. Besides the straightforward result when volume is constant, we solve the steady states for the case where the funds (volume) grow with a fixed rate (e.g. due to credited interest or growth in GDP). We therefore define a system growth process, alternative to the Markov process (when volume is constant). From a transfer pricing and risk-management point of view, the resulting portfolio should satisfy certain requirements concerning return and flexibility. Once the steady state can be calculated for given growth rates, the investment policy can be specified. The importance of taking account of a growth rate is illustrated. Growth in volume implies that a different rule will converge to the desired steady state. This is illustrated analytically and with numerical examples. The purpose of the paper is not to find the ideal hedge strategy for non-maturity liabilities, but to improve the existing risk management without any implementation costs for the banks. Given the currently used methodology, accounting for a growth rate can significantly improve the risk management of non-maturity liabilities.