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Abstract:
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In the global financial and business world, the wealth that an entity owns usually is measured by the amount of different currencies, whose value is dependent on the fluctuation of the foreign exchange rates and has an impact on potential decisions about the wealth’s maximization. Since the maximization of an entity’s wealth is one of the important concerns to market strategists, financial planners or risk managers, it induces a fundamental problem such as how to measure the wealth objectively. A concept of the virtual standard currency(VSC) is proposed in the paper as a strategy to objectively measure the wealth in a currency portfolio together with eliminating uncertainties arising from the choice of a particular currency and the interactive effects among cross currency rates. The VSC can be regarded as a virtual base currency such that any real foreign exchange rate matrix can be approximated by a rank one matrix consisting of two virtual exchange rate vectors. The existence of the VSC is proved through an optimal solution to the basic rank one approximation problem, which also leads to the virtual exchange rates between the VSC and real currencies.
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