Evaluating annuities using data from the SSA life tables

Using the 2006 Social Security Administration Period Life Tables for evaluating Annuities Gaetan “Guy” Lion June 2010

Introduction
At retirement, people purchase annuities from life insurance companies.
By doing so, one avoids market risk affecting retirement funds; And, as a trade off takes on counterparty risk on the life insurer that provides the annuity.
Evaluating an annuity for life (the most common option) entails figuring out your remaining life expectancy. This can be done using the Social Security Administration Period Life Tables.

Period Life Tables Definition
A period life table is based on the mortality experience of a population during a relatively short period of time. For the 2006 table, the period life expectancy at a given age represents the average number of years of life remaining if a group of persons at that age were to experience the mortality rates for 2006 over the course of their remaining life.

Life Expectancy, a few interesting considerations (using SSA data)…

Life Expectancy Probability Density Women live much longer than men with a mean life expectancy at birth of 80.2 years vs 75.1 years for men.

Life Expectancy Probability Density starting at age 65 Focusing on Women account for a majority of the elder-age cohorts.

The remaining life expectancy gender gap declines rapidly at middle age and beyond At birth women remaining life expectancy is 5 years longer than men. By age 55 the difference shrinks to 3.4 years. By 75, it is only 2 years.

Difference in remaining life expectancy at age 65 + Focusing on age cohorts 65+ is an effort to eliminate risk taking behavior differences between the genders earlier in life.

Survival Rate Curve Women account for a majority of the elder-age cohorts.

Survival Rate Curve starting at 65 This is important information, we will soon regress those curves in order to evaluate annuities for male and female.

Is an Annuity an attractive investment? This table was copied from a real life insurer. Are those monthly payments providing the annuity investor with an attractive rate of return?

Annuitizing at 65 years old Men receive higher monthly annuity payments resulting in higher IRR for any given life span. But, women live longer. However, we know the remaining life expectancy gender gap decreases rapidly beyond 65. Are those returns fair gender wise? Assuming long term inflation is around 3% to 3.5%, males have to live till 82.5 years old and females till 86 years old for the respective IRRs to meet inflation levels. If you factor in taxes, individuals have to live even longer.

Regressing Probability of Survival
To evaluate if the returns are fair gender wise, we have to regress the probability of survival for each gender.
The regression models include the following time series variables:
1) Age 1/2
2) Age
3) Age 2
4) Age 3
The resulting models nearly perfectly replicate the curves shown at right (R Square ~ 1). And, the resulting Standard Error is only 0.08% for Males and 0.27% for Females.

Annuities return @65 This table shows that given a Survival Probability of 50% associated with specific respective age(s) a Male will earn an IRR of 3.27% and a Female an IRR of 3.32%. Those IRRs, not factoring taxes, are close to reasonable inflation expectations. This table shows that given a 3.0% IRR a Male has a 51.9% probability of reaching the required age to earn such IRR and a Female has a 53.4% probability.

Gender Fairness? Green areas are relatively favorable to a gender. Red areas are unfavorable to a gender. It boils down to Males having a slightly broader distribution of IRR outcomes vs Females. But, the outcomes are pretty much centered around the same values (IRRs associated with 50% survival probability.

Annuities return @70 We did the same exercise for annuitants starting at age 70 instead of 65. We developed two regression models with the same variables to replicate the Survival Probability Curves. They also fit such curves very closely with R Square ~ 1 and Standard Errors of only 0.04% for Males and 0.14% for Females. As for the 65 year old annuitants, we conclude that the distribution of IRR outcomes is a bit wider for Males. But, such outcomes are centered around pretty much the same values (Medians) suggesting the annuities are reasonably fair to both genders.

Annuities @65 vs @70 With this life insurer, it does not pay to defer taking annuity payments from 65 to 70 years old. Somehow, the annuity at 70 years old is too low. What should the @70 annuity be reset at to be equivalent to the @65 one?

Annuities @65 vs Adjusted @70 We increased the @70 annuity so that the probability of reaching a 3% IRR was closed to even between the @65 vs @70 annuity.

Conclusion
Using the SSA life tables and modeling the resulting survival probabilities allowed us to evaluate those annuities on several counts.
1) On an after-tax basis, those annuities will probably not return an IRR matching or exceeding the prospective inflation rate. Those low IRRs may reflect the life insurer hedging against future period survival rates rising over what they were in 2006;
2) The annuities treat both genders fairly in terms of returns associated with similar survival probabilities;
3) The @70 annuity is mispriced and needs to be increased by slightly over 5% to provide returns similar to the @65 annuity.

Evaluating annuities using data from the SSA life tables

by Gaetan Lion

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Evaluating annuities using data from the SSA life tables Presentation Transcript