Investors around the world face in principle the same investment performance opportunity on the Foreign Exchanges, as they do on the capital markets. This principle can be demonstrated to hold only if the logarithmic measure is used in the calculation of the exchange rate returns and not the conventional arithmetic measure. Only then a situation of equal opportunity may arise within the standard mean/variance portfolio optimisation framework. In mathematical terms, the logarithmic norm ensures that the return/risk opportunity space is defined in a consistent way, in the sense that it complies with the fundamental Euclidean properties of length and distance. If the algebraic rules are being applied regardless in non-Euclidean space, undue situations arise that can be shown to be incompatible with the equal opportunity principle. Two domains in the currency literature are reviewed where this mistake is recurrently committed, one concerning the Uncovered Interest Rate Parity and the other the International Capital Asset Pricing Model.
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