Several formulations are proposed for the currency portfolio optimization (CPO) problem in this paper, which involves portfolios consisting of currencies and evolving over discrete-time epochs: Firstly, based on linear programming method, the CPO problem is formulated as a basic model to maximize the amount of a particular currency. Then, an equivalent network formulation, as a variant of the maximum amplifying flow problem, is proposed to solve the CPO problem through a new strategy involving max-product operations. The concept of the max-product operation is initially introduced here together with its associative law. Thirdly, by using the strategy of virtual standard currency (VSC), sensitivity analysis methods are developed to estimate the rank-one approximation (ROA) vectors to a forex rate matrix from an augmented or reduced forex rate matrix. The VSC’s role is represented by the virtual standard exchange rates (VSER), which is related to the largest singular value and both left and right singular characteristic vectors of a forex rate matrix. Finally, numerical verifications are presented for illustrating the performance of the ROA approach, the CPO formulations, and the sensitive analysis of a currency basket.