Wade Pfau, Ph.D., CFA, RICP®

# Three Questions To Evaluate Longevity Risk For Retirees

Longevity risk—the risk of running out of assets before running out of time—is fundamental to retirement. We know about the distribution of longevity for the overall population, but an individual cannot know in advance precisely where he or she will fall in the distribution.

The length of your retirement could be much shorter or longer than your statistical life expectancy. Half of the population will outlive their median life expectancy—some will live far beyond it. A long life is wonderful, but it is expensive.

As a first step to measuring longevity risk, it is important to understand what the data says about mortality and survivorship rates. Different data sources provide different longevity estimates for several key reasons:

### (1) From what age is life expectancy being measured?

Life expectancy at birth is the most familiar number, though it is of little relevance for someone reaching retirement. If you have reached age sixty-five, then an obvious point to note is that you did not die prior to age sixty-five. As obvious as it might be, this is important information.

Your life expectancy conditional upon reaching age sixty-five is not the same as your life expectancy at birth. As you age, your remaining life expectancy increases. The remaining number of years one can expect to live decreases, but not on a one-to-one basis with age. This matter leads individuals to underestimate how long they may live in retirement, and we must keep in mind from which age life expectancy is being measured.

### (2) Is life expectancy calculated from current year mortality rates or projected future mortality rates?

Probably the most commonly used source of mortality data is the Social Security Administration’s (SSA) Period Life Tables. A period life table makes calculations about remaining lifetimes using the mortality data from one year. For instance, calculations for the life expectancy of a sixty-five-year old would use the year’s mortality rates for different ages in that one year. How many seventy-year olds died that year? eighty-year olds? and so on.

This method has the advantage of using actual data without requiring any sort of projections, but it is bound to underestimate life expectancies on account of the persistent trends of increasing life expectancies over time. The alternative is to use a cohort life table, which tracks mortality for the same individual over time.

When a sixty-five-year-old in 2016 turns eighty-five in 2036, his mortality rate at eighty-five will most likely be lower than that of an eighty-five-year old in 2016. A cohort life table uses projections for future mortality improvements when calculating life expectancies. Cohort life tables will project longer lives and are surely a better choice for considering longevity when building a retirement income plan.

### (3) What is the underlying population for which mortality and survivorship is being calculated?

It may seem natural to base calculations on the aggregate U.S. population—as is done with the Social Security Administration life tables—but clear socioeconomic differences have been identified in mortality rates. Higher income levels and more education both correlate with longer lifespans.

This may not be a matter of causation (i.e., more income and education cause people to live longer), but perhaps some underlying personality trait leads some people to have a more long-term focus, and that in turn may lead them to seek more education and practice better health habits.

The very fact that you are reading this somewhat technical tome on retirement income suggests you probably have a longer-term focus and can expect to live longer than the average person. In this case, mortality data based on population-wide averages will underestimate your longevity.

This is not because I think my readers are all from Lake Wobegon (where everyone is above average), rather it is because of the important links between income, education, long-term planning, and health. Not everyone will live longer, as unfortunate accidents and illnesses will inevitably befall some along the way. But in a statistical sense, my average reader will live longer than the average person.

The Society of Actuaries (SOA) produced the 2012 Individual Annuity Mortality tables that I think will best reflect the situation for my readers. Their mortality data is for annuity purchasers, who tend to live longer than average. Those with significant illnesses tend to avoid buying income annuities. Their data also reflects estimates for future mortality improvements and is not based only on the situation in one year.

Exhibit 1 helps clarify the distinction between different mortality datasets by showing some key numbers estimated from the Social Security life table and the Society of Actuaries data. I focus on the probability of survival from age sixty-five for males, females, and at least one member of a same-aged couple for different combinations of gender. I also provide life expectancy estimates from age sixty-five for each of these groups.

In terms of remaining life expectancy at sixty-five, the Society of Actuaries data generally shows individuals living about four to five years longer. With SSA data, men can expect to live 17.8 more years to 82.8, while women can expect 20.3 more years to 85.3. For an opposite-sex couple, the longest living member can expect 24.1 more years to age 89.1, on average.

Incidentally, these numbers are 22.7 years for two males and 25.3 years for two females. Meanwhile, with the SOA data, men are looking at life expectancies of 87.6, women of 89.3, and 92.6 for the longest living member of an opposite-sex couple.

Exhibit 1: Longevity Statistics for 65-Year Olds

 At Least One Member of a Couple Male Female One Male – One Female Two Males Two Females Social Security 2013 Periodic Life Table Probability of Living to Age: 70 91% 94% 99% 99% 100% 75 79% 85% 97% 96% 98% 80 63% 73% 90% 86% 92% 85 43% 55% 74% 67% 80% 90 22% 33% 48% 39% 55% 95 7% 13% 20% 14% 25% 100 1% 3% 4% 2% 6% Remaining Life Expectancy 17.8 20.3 24.1 22.7 25.3 Society of Actuaries 2012 Individual Annuity Mortality with Projected Improvements for 65 Year Olds in 2016 Probability of Living to Age: 70 95% 96% 100% 100% 100% 75 89% 91% 99% 99% 99% 80 80% 84% 97% 96% 97% 85 66% 71% 90% 88% 92% 90 45% 52% 74% 70% 77% 95 22% 29% 45% 39% 50% 100 6% 10% 16% 12% 20% Remaining Life Expectancy 22.6 24.3 28.6 27.7 29.4

Exhibit 1 also illustrates longevity risk by showing the probability of survival to different ages beyond sixty-five. For instance, with SSA data, 91% of men are still alive by age seventy (i.e., 9% did not live to their seventieth birthday), 63% are still alive at eighty, and 22% are still alive at ninety. With retirement planning, the trouble is knowing what age to plan for, as this distribution is quite wide.

But more relevant for readers—again because the data reflects people with more similar backgrounds as well as projected improvements in mortality—are the numbers from the SOA data, with mortality improvements projected for a starting year of 2016.

The probability of a sixty-five-year old reaching age ninety-five is 22% for males, 29% for females, and 45% for at least one member of an opposite-gender couple. In 1994, William Bengen chose thirty years as a conservative planning horizon for a sixty-five-year old couple.

But as mortality improves over time, this planning horizon is becoming less conservative. A thirty-year time horizon is not so conservative when we look at data that better reflects higher earning and more highly educated individuals.

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