A Model for Policy-Size and Diversification Discounts
By Jay Michael Call
An actuarial approach for calculating a relativity based on geographic diversification is presented. The method models correlation as a function of distance between two exposures, and uses that to calculate a risk margin for each policy. It assumes that any premium provision for a company risk margin is currently allocated in proportion to policy risk-free premium, which results in a uniform risk-loading uprate for all policies. It is suggested that a better approach would be to allocate com-pany risk margin in proportion to policy risk margin so that more diverse policies incur a smaller risk factor. This approach results in a range of diversification relativities that tends to be very narrow, so a revenue-neutral method for magnifying the impact of the diversification relativity is also presented. Approaches for reflecting non-geographic forms of diversification (such as for package policies) are also discussed. And, since policies with many insured items have a greater potential for diversity than policies with fewer insured items, the diversification relativities presented herein could also be viewed as a type of policy-size relativity.
Keywords Diversification relativity, risk-free premium, risk margin, risk factor, coefficient of variation, book diversification ratio, geographic diversification, distance-correlation model, geocode, distance formula