Estimating international adverse selection in annuities

North American Actuarial Journal, Oct 2002 by Mitchell, Olivia S, McCarthy, David

Mortality tables may differ across segments of the population for various reasons, one of which is adverse selection, which could arise, for example, if purchasers of annuities are more likely to live longer than average. In such a case, the observed mortality pattern for annuitants would be lower than that of the general population, requiring that separate mortality tables be prepared for the annuitants and the general population. How important this adverse selection effect may be in the annuity market is likely to depend on the extent to which annuitization is optional. In the U.K., for instance, a portion of retirement benefits is often subject to mandatory annuitization, whereas other benefits may be voluntarily annuitized. As a result, separate U.K. mortality tables have been generated for voluntary as well as compulsory-purchase annuitants, both of which differ from that of the general population (Finkelstein and Poterba 1999; Murthi et al. 1999). In the U.S., retirement benefits paid under the current Social Security system are annuitized, but corporate pensions are increasingly paid as lump sums rather than the conventional annuities of times past (Mitchell 1999). As a consequence of the fact that some retirees purchase annuities while others do not, U.S. mortality tables are published for both annuitant purchasers and for the general population, with the latter having higher mortality than the former (Brown et al. 2000).

Mortality tables also change over time as a result of past and projected future improvements in life expectancies. Over the last several decades, mortality among older people has dropped rapidly in developed countries, and there is reason to believe that this will continue in the future (Executive Committee 1999). Actuaries tend to handle this problem by estimating so-called period mortality tables from past data and then devising separate, forward-looking cohort mortality tables by extrapolating future trends in mortality. Of course, anticipated future declines in mortality built into cohort tables are only estimates based on past trends. Nevertheless these must be incorporated in valuing annuities because future mortality estimates are needed to determine the money's worth of retirement income flows for people alive today, some of whom will survive into the future.

A. Metrics for Comparing Mortality Tables

There is no single generally accepted method that can be used to compare mortality tables across countries. In this section, we propose five metrics to be used for comparing mortality tables: plots of survival frequency distributions, the A/E method, the expected remaining life method, the present value of a life annuity metric, and a measure we call the internal rate of return. We illustrate the different answers these five metrics yield by using them to compare the 1998 U.S. and U.K. mortality tables for men and women currently age 65.

Plots of Survival Frequency or Age at Death Distributions

A conventional way to compare mortality tables is to plot expected survival frequencies by age and examine them visually. To compare different mortality tables, this approach would graph the percentage of individuals who attain age x given that they reached age 65. An advantage of the graphical approach is that it affords an illustration of which mortality curve is higher (or lower) at given ages. A major disadvantage of this technique is that it does not offer any measure for "how far apart" two mortality or survival tables might be.