This paper provides an axiomatic foundation of the measurement of diversication in a one-period portfolio theory under the assumption that the investor has complete information about the joint distribution of asset returns.
Four categories of portfolio diversication measures can be distinguished: the law of large numbers diversication measures, the correlation diversication measures, the market portfolio diversication measures and the risk contribution diversication measures.
The authors propose the first step towards a rigorous theory of correlation diversication measures. They propose a set of nine desirable axioms for this class of diversication measures, and name the measures satisfying these axioms coherent diversication measures that they distinguish from the notion of coherent risk measures.
They provide the decision-theoretic foundations of their axioms by studying their compatibility with investors' preference for diversication in two important decision theories under risk: the expected utility theory and Yaari's dual theory.
They explore whether useful methods of measuring portfolio diversication satisfy their axioms.
They also investigate whether or not their axioms have forms of representation.
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