  We provide an axiomatic foundation for the representation of
num\'{e}raire-invariant preferences of economic agents acting in a financial
market. In a static environment, the simple axioms turn out to be equivalent to
the following choice rule: the agent prefers one outcome over another if and
only if the expected (under the agent's subjective probability) relative rate
of return of the latter outcome with respect to the former is nonpositive. With
the addition of a transitivity requirement, this last preference relation has
an extension that can be numerically represented by expected logarithmic
utility. We also treat the case of a dynamic environment where consumption
streams are the objects of choice. There, a novel result concerning a canonical
representation of unit-mass optional measures enables us to explicitly solve
the investment--consumption problem by separating the two aspects of investment
and consumption. Finally, we give an application to the problem of optimal
num\'{e}raire investment with a random time-horizon.
