An Overview on Value at Risk Model of Bank Cash Management with Application to Lebanon

This paper develops a model of bank cash management that is simple enough to understand and
apply. The model relies on the joint concepts of Value at Risk (VaR), stress testing, and inventory
optimization. For this the uncertainty in cash withdrawals must be ascertained. This is done through a
predicting regression that describes the fluctuations in cash withdrawals. The standard error of this
regression represents the uncertainty in withdrawals. The model provides for a proper consideration
of integrated statistical processes by selecting and implementing a Hodrick-Prescott filter. The theory
borrows from the newsvendor inventory problem and is applied to the case of Lebanon. A limited
number of parameters is essential as an input, and has to be specified beforehand. Among these
parameters are the service level and the expected stock-out cost per order, which determine the
stock-out probability, and the total stock-out cost. The carrying cost is simply the opportunity cost of
capital. The ex ante and the ex post results are in conformity to theoretical anticipations, and are
definitely quite reasonable.