Inflation Based Variable Life Insurance Models

Abstract

The variable life insurance models developed to date do not have an explicit tie with an inflation index, and according to historically-based simulations of these products, their face value is not likely to keep pace with inflation in the early years of the policy. This paper develops and tests several variable life insurance models which are designed to minimize the difference between the face of the policy and an inflation index. It is concluded that the modified level additions model is likely to be the most effective inflation based variable life insurance design. life insurance (VLI) represents a significant development within the insurance industry for many reasons, not the least of which is the prospect of marketing an inflation-fighting insurance product. If the past investment performance of the Standard and Poor's stock price index is indicative of future returns on a broadly diversified equity portfolio, the face value of three VLI designs analyzed by Miller can be expected to increase rather significantly in future years.' On the other hand, if future inflation follows the historical pattern as traced by the Consumer's Price Index (CPI), the face value of these three policies is likely to lag behind the inflation index for a significant period of time after issuance of the policy and eventually Howard E. Winklevoss, D.B.A., is Assistant Professor of Insurance in The Wharton School of the University of Pennsylvania. The author would like to thank David G. Adams and Dr. J. David Cummins for their helpfill cnmments. This paper was submitted in May, 1973. 1'Walter N. Miller, Variable Life Insurance Product Design, Journal of Risk and XXXVIII (December, 1971),p. 527. surpass the inflation index by a wide margin.2 In addition, the three VLI models are particularly vulnerable to the inflation risk during a downward movement in the equity market at a time of persistent inflation. Thus, while VLI is likely to be an effective inflation-fighting product in the long run, it is not at all clear that adequate protection will be provided in the early years of the policy or during a sharp downturn in the equity market. The purpose of this paper is to develop several VLI models designed to enhance the inflation-fighting aspects of the product. The distinguishing characteristic of these inflation-based models is the method by which the face of the policy is adjusted in response to favorable and unfavorable investment performance, an approach designed to minimize the difference between the face value and an inflation index. The constraints on this minimization objective include the cost of insurance protection, and of course, the 2 Douglas C. Olson and Howard E. Winklevoss, Equity Based Life Insurance, Wharton Quarterly (Summer, 1971), p. 26.