The Impact of Lapse Rates on Life Insurance Prices

Abstract

The purpose of this paper is to measure the effect of changes in lapse rates on the price of life insurance protection to policyholders. The magnitude of the changes in lapse rates to be considered is determined by reference to data on lapse rates in various companies. Then, the impact of changes in lapse rates is compared to the impact of changes in mortality rates. The conclusions are that lapse rates have a substantial effect on price, and that consideration should be given to the use of expected lapse experience in the classification of life insurance applicants. The discontinuation of life insurance Joseph M. Belth, Ph.D., C.L.U., C.P.C.U., is Associate Professor of Insurance in the Graduate School of Business at Indiana University. He is author of Participating Life Insurance Sold by Stock Companies (1965), for which he received the 1966 Elizur Wright Award of the American Risk and Insurance Association, The Retail Price Structure in American Life Insurance (1966), and A Report on Life Insurance (1967). Dr. Belth is a frequent contributor to this Journal and serves as its Communications Editor. He has received four N.A.I.I. awards for papers published in this Journal. This paper was first presented on September 1, 1966, at the Fourth Annual Risk Theory Seminar of the American Risk and Insurance Association. The author wishes to acknowledge the financial support provided to the Risk Theory Seminar by the Cooperative League of the United States of America, including the following companies: Desjardins Mutual Life Insurance Company, Mutual Service Insurance Company, Cooperators Insurance Association, Co-operative Insurance Services, Ltd., La Societe d'Assurance des Caisses Populaires, Nationwide Insurance Company, and League Life Insurance Company. The author also wishes to acknowledge the asistance of Cheyeh Lin, then a doctoral candidate in Indiana University's Graduate School of Business and presently Assistant Professor of Finance at the University of Cincinnati, who handled a considerable portion of the data processing and tabulation of the results. The author alone, however, assumes full responsibility for the views expressed in the paper and for any errors that may remain. The computer used was the CDC 3600 in Indiana University's Research Computing Center. policies by policyholders prior to maturity or death is recognized as an important factor in the prices that life insurance companies charge their policyholders. For example, the tendency of increased lapse rates to increase the level of life insurance prices is generally cited as one of the primary reasons for discouraging the replacement of existing policies.' Nevertheless, the lapsation problem is usually referred to only in general terms, and, as far as the author has been able to determine, no specific analysis of the impact of lapse rates on prices has ever been published. The purpose of this paper, therefore, is to attempt to measure the effect of changes in lapse rates on the price of life insur-