1. Liability and total plan surplus volatility decompositions based on average plan data from NISA’s Pension Surplus Risk Index (PSRX) as of 03/31/2013. Correlation between mortality surprises and economic variables are assumed to be zero.
2. One-year increase is calibrated on a 65-year old participant. Other participants’ life expectancies may change by different amounts.
3. The assumed liability cash flow structure has a duration of 13 years and is similar in profile to pension liability cash flows we have seen. It is composed of a basket of annuities assumed to be from a half male, half female work force. For simplicity, no spousal benefits are assumed. We assume the retirement age is 65 and the mortality rate of a 120 year old is 100% (no pension participants will live to their 121st birthday.) The liability is discounted at the Citigroup Pension Discount Curve as of 02/28/2013.
4. The possibility that rare events may have extreme effects introduces “tail risk” to the pension plan. A medical advance that dramatically lengthens lifespans or widespread pandemics that shorten it could materially alter the value of the liability. These types of events are inherently challenging to quantify, and we do not attempt to do so in this paper. This is to say, we do not attempt to dimension model risk – the amount of uncertainty related to the possibility that the model doesn’t reflect the complete understanding of what reality brings to bear on the pension plan.
5. See Appendix for more details.
6. A cursory investigation suggests this sampling error falls to about one-tenth the magnitude of our longevity risk estimate as plans exceed 10,000 employees.
7. We would like to thank Ronald Lee for his assistance with mortality models, and his comments and suggestions in this regard. Any and all errors, however, are the responsibility of NISA.
8. Ronald Lee and Lawrence Carter, Modeling and Forecasting U.S. Mortality (1992), Journal of the American Statistical Association, Vol. 87, No. 419, pp. 659-671.
9. For a survey of mortality models, see Andrew J. G. Cairns, David Blake, Kevin Dowd, Guy D. Coughlan, David Epstein, Alen Ong, and Igor Balevich, A Quantitative Comparison of Stochastic Mortality Models Using Data from England & Wales and the United States (2009), North American Actuarial Journal, Vol. 13, No. 1, pp. 1-35.
10. See Appendix for more details.
11. Discounted using Citigroup Pension Discount Curve as of 02/28/2013
12. Reported annualized longevity risk of 0.4% is calculated based on the first year of simulated results. The annual longevity volatility would change with plan demographics – in general, it would fall as the duration of a plan shrinks and the average age of the beneficiaries increases over time.
13. The current low interest rate environment further increases economic sensitivity to longevity by increasing the value of and sensitivity to cash flows occurring in later years. In fact, we estimate that if interest rates were 3% higher than at present, longevity risk would drop by nearly one-third to 1.7% and 0.8% for higher and lower longevity uncertainty, respectively.