The Use of Archimedean Copulas to Model Portfolio Allocations

Source abstract

A copula is a means of generating an n ‐variate distribution function from an arbitrary set of n univariate distributions. For the class of portfolio allocators that are risk averse, we use the copula approach to identify a large set of n ‐variate asset return distributions such that the relative magnitudes of portfolio shares can be ordered according to the reversed hazard rate ordering of the n underlying univariate distributions. We also establish conditions under which first‐ and second‐degree dominating shifts in one of the n underlying univariate distributions increase allocation to that asset. Our findings exploit separability properties possessed by the Archimedean family of copulas.