Life Expectancy

A person’s “life expectancy” is always expressed as of a reference age and equals the average number of years that a group of people with the same starting age will live, assuming that group members experience certain predetermined mortality rates over the course of their remaining lives.

The Social Security Administration’s 2007 Period Life Table is the most recent summary of life expectancy data for the Social Security area population (basically residents of the US and dependent territories plus US citizens and federal employees abroad).

Using death probabilities from the 2007 Period Life Table, Figure 1 below shows how to calculate the number of Remaining Lives each year and a person’s Life Expectancy at any age.

Fig 1. Sample Data to Explain Life Expectancy Calculation

A B C D E F
Exact Age Death Probability Number of Lives Deaths in Each Year Life Expectancy
0 0.7379% 100,000 738 0.5 75.38
1 0.0494% 99,262 49 1.5 74.94
2 0.0317% 99,213 31 2.5 73.98
3 0.0241% 99,182 24 3.5 73.00
4 0.0200% 99,158 20 4.5 72.02
5 0.0179% 99,138 18 5.5 71.03

Column A shows a person’s exact age in full years. Column B shows the probability that a person at each particular age will die within one year. These probabilities are based on actual experience within the Social Security area population during the year 2007.

Column C starts with an assumed population of 100,000 newly-born people (i.e. Exact Age = 0). If the probability of somebody dying in their first year of life, as shown in column B, is 0.7379%, we can estimate that 738 people will die before they reach 1 year of age. This is shown in Column D.

Subtracting this number from the initial 100,000, results in 99,262 people still alive at the age of 1 year, as shown by the second number in column C. Repeating this process year by year results in a declining balance in Column C of people remaining alive.

Life Expectancy at birth is the average number of years that the initial 100,000 population remains alive. From the above calculation we know that 738 of this population are expected to die within one year, as shown in column D. When calculating Life Expectancy, we assume that deaths occur evenly throughout the year. The calculation is the same as assuming that each person dies exactly half-way through their last year of life. The first 738 are therefore assumed to have lived for 0.5 years each.

Similarly, the 49 lives lost between age 1 and 2 are assumed to have lived for a total of 1.5 years and so on for each group, as shown in column E.

Multiplying each entry in column D by its corresponding entry in column E and dividing the result by the sum of all values in column D gives us the average number of years lived by each person in the initial 100,000 population. The result of 75.38, as shown in column F, is this population’s life expectancy at birth.

Life Expectancy for somebody aged 1 year, is the average number of years lived by the 99,262 members of the population who reach that starting age. We therefore repeat the calculation described in the preceding paragraph but omit the first entry in both column D and E.

Half-Life

We noted above that Life Expectancy is the average number of years that a particular group of people is expected to live.

In contrast, “Half Life” means the total number of years required for a group of people with the same starting age to decrease in number by 50%, assuming that group members experience certain predetermined mortality rates over the course of their remaining lives. Thus, if the Half-Life of a 50-year old male is 30 years, half of all 50 year old males are expected to live to age 80.

Life Expectancy and Half Life are not the same.

To illustrate this, Figure 2 shows an extract from the SSA 2007 Period Life Table.

Fig 2. Extract From The SSA Period Life Table 2007

Exact Age Male Number of Lives Male Life Expectancy Female Number of Lives Female Life Expectancy
0 100,000 75.38 100,000 80.43
75 61,612
76 59,147
79 50,591
80 47,974 61,930
81 59,109
83 52,942
84: 49,608

A new-born male has a Life Expectancy of 75.38 years. However, if we look down the columns headed “Male Number of Lives”, we find that even at age 76 years, 59,147 of the original 100,000 males are still alive. In fact, the male population does not drop below 50,000 until somewhere between age 79 and 80 years. Specifically, the Half Life of a new-born male is 79.32 years, whereas their Life Expectancy is 75.38 years.

Similarly, a new-born female has a Life Expectancy of 80.43 years. However, if we look down the columns headed “Female Number of Lives”, we find that at age 81 years, 59,109 of the original 100,000 females are still alive. The Half Life of a new-born female is actually 83.88 years.

Half-Life is Usually Longer Than Life Expectancy

Because Life Expectancy is the more commonly reported number, many people assume that if they add their Life Expectancy to their current age they have a 50:50 chance of living to the resulting total age. In other words, they interpret their Life Expectancy as if it equaled their Half Life. This is incorrect and, in the context of saving for a secure retirement, can lead to people seriously underestimating how many years they might live after retirement. The obvious danger is that if they fail to accumulate enough capital for the longer lifespan, the run a real risk of running out of money at a time when they can do little or nothing about it.

As we noted in the previous section above, at birth Half Life is greater than Life Expectancy for both males and females. I have calculated Half Lives for all ages based on the SSA 2007 Period Life Table. In the case of males, Half Life exceeds Life Expectancy for all years from birth up to and including 69 years of age. The range of values for the calculation Half Life minus Life Expectancy is a maximum of 3.94 years, median of 0.87 years and minimum of -0.70 years.

In the case of females, Half Life exceeds Life Expectancy up to and including 74 years of age. The range of values for the calculation Half Life minus Life Expectancy is a maximum of 3.45 years, median of 1.24 years and minimum of -0.72 years.

Incorporating Lifespan into Retirement Security Analysis

Half Life reflects the probability that 50% of any age group will survive. This means if you use your Half Life value to calculate the amount of money you will need to fund your retirement, you run a 50% chance of living longer and therefore running out of money.

Personally, I would prefer to be more certain that I will not outlive my resources. This leads to the idea of calculating an expected Lifespan at a personally selected confidence level. For example, if you want to be 80% confident of not outliving your retirement capital, base your calculations on the number of years it takes until your age group is expected to fall to 20% of its current size in the SSA Period Life Table. Adding your current age to this number of years gives you your expected Lifespan at an 80% confidence level. For males the median Lifespan across all ages at an 80% confidence level is 89.5 years. The corresponding Lifespan for females is 92.5 years.

These numbers provide a good starting point for considering longevity risk in relation to achieving a secure retirement although detailed discussion of how to manage longevity risk must wait until a later post.

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