The Use of Archimedean Copulas to Model Portfolio Allocations

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 firstand 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.