The Effects of Risk Reduction in Universal Life Insurance, Part II

Abstract

The first part of this essay argued for a reformation of the life insurer and the purge of the positive covariance that exists between the savings and protection elements of conventional life insurance products. The separation of these elements has a beneficial impact on the risk structure of the rudimentary promises of prepaid life insurance. The second part of the essay develops the tools for pricing both conventional and universal life insurance on a chance-constrained basis. It shows that the universal life scheme costs less than traditional cash value products when the probabilities of ruin are equal for a closed cohort of lives. The cleansing of the risk-increasing properties of conventional life insurance by fracture of the mortality and investment guarantees across two independent promises was broached in Part I of this essay. A reformation scenario was envisioned that would annihilate the positive covariance that was shown to exist within the risk structure of the savings and protection elements. The blend of these two elements in conventional life insurance produces an enigma-both desirable and undesirable attributes can be identified. Certainly, the risk-creating properties of cash value life insurance must be counted among the latter. Part II of this essay examines the relative attractiveness of universal life, which may preserve the better features while eliminating the undesirable risk structure of conventional life insurance. In particular, the costliness of conventional and universal life insurance is compared in the final section of the paper. The pricing of the alternatives is performed on a chance-constrained basis so that the probability of ruin under each approach is the same. Sections William C. Scheel is Associate Professor of Finance at the University of Connecticut. He holds the Ph.D. degree and is a frequent contributor to this Journal and other scholarly and professional journals. Professor Scheel holds the CPCU designation. The clarity of this essay has been improved by the commentary of three anonymous referees and a Journal editorial board member. The considerable insight given by James C. Hickman during the development of the essay was invaluable and also greatly appreciated. Whatever cloudy thinking remains is clearly the author's undoing. Editor's Note: As Professor Scheel's paper was too long to be included in one issue, he graciously consented to divide the paper into two parts. This article is Part II. Part I was published in the June 1979 issue of this Journal. The equations in Part I were numbered through 12. Part II continues with the numbering sequence. Therefore, the first equation here is numbered 13. Part II also includes Appendix B. Appendix A was published with Part I. R.I.M.