Whole Life Cost Comparisons Based upon the Year of Required Protection

Abstract

Whole Life Cost Comparisons Based Upon the Year of Required Protection ABSTRACT The traditional measures of Interest Adjusted Surrender Cost and Linton's rate of return are computed for 68 whole life policies. Similar measures are obtained via linear programming where cash flows are discounted using several different external interest rates. With the linear programming method, year of insurance protection is varied to include year 0, year 10 and year 20. If protection is required in year 20, several policies are infeasible (incapable of generating any insurance protection). Upper limits for rates of return are calculated. Infeasibility occurs for a given policy if the external rate of return exceeds the upper limit. Introduction The purpose of this article is to use a linear programming (LP) method for measuring the cost of whole life insurance. The method is applied to policies offered in 1984 by 68 different insurers. For comparative purposes, the traditional methods of interest adjusted surrender cost (IASC) and Linton's rate of return are applied to the same set of policies. The insurers and policies were selected using criteria established in an earlier study by Hutchins and Quenneville [3]. Consequently, the results of this study of 1984 policies may be compared to a set of similar policies offered in 1972. The LP method is similar to both IASC and Linton methods in several respects. Specifically, all three methods assume deterministic projected dividends and a fixed horizon of 20 years. The LP technique can be used to derive level interest adjusted costs similar to the IASC and internal rates of return on equity similar to the Linton rate of return. Nevertheless, both the IASC method and Linton's method rely on assumptions not required by the LP method. The LP method requires only an assumption of a rate of return that is relevant to the policyholder. Conceptually, the IASC and Linton's method treat the whole life insurance policy as providing the two products of protection and savings. The IASC attempts to measure the level cost of protection while the Linton method attempts to measure the rate of return on the savings component. The IASC requires an interest rate for discounting whereas Linton's method requires various term insurance rates. As a consequence of these different required assumptions, rankings obtained by these two methods will not be perfectly correlated. The LP method, by contrast, does not attempt to directly separate protection and savings. The method assumes that the insured individual requires a given level of protection. It is irrelevant to the insured how the insurer provides the protection. In other words, the insured is unconcerned with how the insurer divides the premium into loading charges, reserves, and so forth. The LP method has the additional flexibility of considering the point in time at which the insured requires protection. Neither the IASC nor Linton method explicitly address issues related to timing of insurance protection. The flexibility of varying the year of required protection is the primary characteristic of the LP method that differentiates it from the traditional methods. The IASC, for example, implicitly assumes that coverage is required at the time the policy becomes effective. The IASC, however, does not recognize the reduction in the insured's wealth resulting from the premium payment. The LP method recognizes premium payments by increasing the policy face value by a corresponding amount. With the LP method, premiums are compounded and accumulated at the relevant interest rate to the year in which protection is required. This accumulation of premiums may be large if protection is required 15 or 20 years into the future. For large interest rates the accumulated premiums will, at some point, exceed the face value of the policy. …