Coherent diversification measures in portfolio theory : an axiomatic foundation

We provide an axiomatic foundation for the measurement of correlation diversification in a one-period portfolio model. We propose a set of eight desirable axioms for this class of diversification measures. We name the measures satisfying these axioms coherent correlation diversification measures. We study the compatibility of our axioms with rank-dependent expected utility theory. We also test them against the two most frequently used methods for measuring correlation diversification in portfolio theory: portfolio variance and the diversification ratio. Lastly, we provide an example of a functional representation of a coherent correlation diversification measure.