Survival Probabilities

Survival probabilities can be derived from Table 17.1 "Life Table Depicting the Number of Survivors at Age " of the previous section. We can see that out of the initial population of 1,000,000 people at age zero, about 985,668 people will be living at age twenty-five. At age sixty-five, the expected number of survivors is 834,036. We can say that the probability of a twenty-five-year-old male surviving to age sixty-five is 84.6 percent (834,036/985,668). About 59 percent of all the people that have reached age sixty-five are expected to survive beyond eighty years old (491,853 out of 834,036). In the 1950s, this figure was substantially lower, typically below 40 percent. The survival rates in less-developed countries are by far smaller, and in many cases are very close to zero.

Longevity riskLife cycle risk of living too long, such that one’s advanced age hinders one’s ability to continue adequately providing for oneself. can be defined simply as the risk of living too long such that one’s advanced age hinders one’s ability to continue adequately providing for oneself. To characterize the risk, we have to show also the costs involved in aging. Old age may bring about severe financial implications for the individual. Surviving for many years after retirement involves high costs of current maintenance (housing, clothing, food, entertainment, and the like) and frequently involves increased medical expenses (hospitalization, senior citizen housing, special care, and the like). Retired people often do not have the resources needed to finance these costs. They often lack current income sources and do not have sufficient properties. Moreover, they often face difficulties in generating adequate income from the properties they do hold. The risk of extended life without sufficient financial resources could be severe and more frequent than people think. Surveys often show that aged people have far lower income than they used to have during their employment period, and many report financial stresses.

In the following section, we shall give a general review of the cost of aging, from the individual’s point of view. Like the cost of premature death, we have to talk in general terms about populations and averages rather than relate to particular individuals. The first term to be discussed is life expectancy (at birth). We shall then discuss the average number of postretirement years.

Life Expectancy

The financial burden of aging is a direct function of the number of years that the individual will live beyond retirement. A common term that is related to the issue is life expectancyMeasures the average length of life in a population; in a stable population, it would be an approximation of the average age of deceased people.. Although this term is commonly used in the literature, there are misunderstandings concerning its meaning. Thus, we start by explaining this measure. Life expectancy measures the average length of life in a population. In a stable population, it would be an approximation of the average age of deceased people.

Life expectancy figures are calculated from the life table. Assume for a moment that mortality has a strange pattern: all people are expected to die during the year and to die immediately before they touch the birthday cake just prior to the next birthday. From the life table, actuaries can determine the total number of years that the cohort of people presented has lived (which is simply the sum of all l_x values from age zero to the end of the life table). If this figure is divided by the number of people that were assumed to be alive at age zero, the average age of death, or life expectancy, is the result. Actuaries do make a small correction to this figure: we have assumed that all people die at the end of the year, whereas people normally die throughout the year, so we have to deduct 0.5 from the average figure we got. We can deduce from the life table in Table 17.1 "Life Table Depicting the Number of Survivors at Age " that all 1,000,000 males of the cohort are expected to live a total of 77,119,302 years, or 77.119 years per person on the average. Deducting 0.5, we see that life expectancy at birth as determined from the life table is 76.6 years. Similarly, life expectancy for females is 80.8 years. These values are based on the CSO table and are higher than the life expectancy of the general population.

Life expectancy depends, of course, on the nutrition, sanitation, life style, genetics, and general well-being of the population. Therefore, it is no wonder that it is chosen as one of the leading indicators for the developmental stage of a country. Because of that, we have this measure for most countries in the world, including the least-developed countries.

In a cross-section analysis, World Health Organization (WHO) statistics show that life expectancy for the entire population (males and females) is below sixty for less developed countries (in some countries it could even be as low as forty). On the other hand, developed and advanced countries experience life expectancy figures around seventy-seven to eighty-two (for the entire population). Will life expectancy continue to increase at the same rate in the future? Is there a limit to the human life span? These are critical questions for retirement planning. Scientists cannot give us a definite answer yet. Some claim that the body cells are designed to last only for a certain period; for example, heart cells are assumed to have a limited number of beats, perhaps 2 billion. Others believe that we are on the verge of deciphering the mechanism that determines the aging of cells, and we will learn the way to control it. Meanwhile, we experience a continuous increase in life expectancy due to the cumulative effect of gradual improvements in a wide variety of medical technologies. Modern medicine can replace failing organs through transplants, open clogged arteries, and administer drugs that immunize against and cure many diseases.

Human society is the only one among all animals that values longevity as a goal. It is not improbable that this value will be challenged in the future, and that societies finding it difficult to cope with the soaring costs of retirement and of health-related expenses will put constraints on medical treatment to aged people. This involves ethical problems that go far beyond the scope of this discussion.

During the last century, the developed countries have experienced an unprecedented increase in longevity. This increasing life expectancy is in direct correlation to the sharp reduction in mortality rates. At the beginning of the twentieth century, life expectancy at birth (corrected for mortality in the first few months after birth) was around forty-five to fifty years in most currently developed countries. A century later, at the beginning of the twenty-first century, life expectancy is around seventy-six years for males and approximately eighty years for females. In other words, life expectancy at birth has increased on the average by one year for every three to four calendar years! In 1900, the life expectancy of white males and females in the United States was 48.2 and 51.1, respectively. The parallel figures in 2002 are 75.1 and 80.3, respectively. The figures for the entire population differ, of course, from the figures of the CSO tables, which are based on the insured population, which in turn is typically healthier than the general population. Therefore, the life expectancy found in the CSO tables tends to be higher than that of the general population. The latest findings from the U.S. Census Bureau provide an excellent illustration of the life expectancy improvements in the United States over time, as seen in Table 17.3 "Expectation of Life at Birth for the U.S. Population as Measured in Various Points in Time (1970–2005)".U.S. Census Bureau, “The 2009 Statistical Abstract,” The National Data Book, http://www.census.gov/compendia/statab/cats/births_deaths_marriages_divorces/life_expectancy.html (accessed April 4, 2009).

Financial Implications of Longevity Risk

To estimate the financial needs to confront the risk of longevity, we must look more carefully at the meaning of life expectancy. We will assume a very basic model, where people join the labor force at the age of twenty and retire at the age of sixty-five. In addition, assume that life expectancy is seventy-five and is not expected to change, and that interest rates can be ignored. Assume also that the annual consumption of a retired person is similar to that of a working person (a realistic assumption in view of studies showing that the total consumption is quite stable, although its composition changes significantly with age). These basic parameters seem to generate a simple retirement model: during forty-five years of work, people are supposed to accumulate sufficient funds to cover an additional ten years, that is, put aside about 10/45, or 22 percent, of their annual income.

There are two major flaws in this basic model, and both of them stem from a misinterpretation of the concept of life expectancy. First, relying on an average number (life expectancy) may be fine for a financial institution that holds a large portfolio of many insured people. An individual, however, is not supposed to plan her insurance needs according to average figures and must instead prepare for the extreme cases. Life expectancy is an average figure. A high proportion of retired people will live far longer than the assumed life expectancy (age seventy-five). What will all these people do when the funds are depleted at the end of the assumed ten-year postretirement period?

Second, when people refer to life expectancy, they commonly refer to the published figure, which is life expectancy at birth (the average age of death). The remaining life expectancy is a complicated function of age. If life expectancy at birth is seventy-five years, the remaining life expectancy at the age of sixty-five may be substantially higher than ten years insofar as those who reach age sixty-five have survived the childhood diseases, the motorcycle accidents, the risks of military service, and so forth. The U.S. Vital Statistics, for example, show that the life expectancy at birth of white males in 2005 was 75.2 (see Table 17.3 "Expectation of Life at Birth for the U.S. Population as Measured in Various Points in Time (1970–2005)"). However, the remaining (conditional) life expectancy at age sixty-five is not just ten years, but rather 17.2 years, as shown in Table 17.4 "Average Number of Remaining Years of Life by Sex and Age (2005)" above.

The above figures mean that when the U.S. white male in our model reaches retirement, he had better have sufficient funds for 17.2 years, on the average, rather than just ten years, as the model has assumed (and this figure is subject to the first comment about the use of averages in personal planning). Putting aside savings for 17.2 years over forty-five years of assumed employment is almost double the calculation that assumed a 10/45 ratio.

The problem of females is even more pressing in practice. Females are the biologically more resilient gender, and their life expectancy at birth is typically greater than that of males. In 2005, for example, life expectancy at birth for white U.S. females was 80.4 (compared to only 75.2 for males). However, females tend to retire earlier than men, say, at the age of sixty, and the remaining life expectancy at that age is twenty-four years. Earlier retirement, however, also means a shorter working period, perhaps only forty years. Traditionally, many women also spend a few years out of the wage-earning labor force to raise the family. The average working period for women can actually be reduced to thirty years or less. One needs to be a financial magician to be able to accumulate enough savings to finance a postretirement period of twenty-four years over approximately thirty years of work. The longevity differences between men and women are reflected in prices for life insurance, as discussed in “Should Life Insurance Rates Be Based on Gender” below.

Interest Rate Considerations in Retirement Planning

The rough retirement model that has been discussed so far ignores the interest rate, changes in the purchasing power of money, and changes in the general standard of living. It must be corrected to deal with these factors, which can be done in an accurate actuarial manner, but the following less accurate way gives a better general picture.

A retirement plan has the advantage that its financing can be spread over a relatively long period: the employment period and the retirement period. Over such a long period, interest rates cannot be ignored. Thus, we shall examine some simple interest rate calculations. Imagine a person saves $1 per year over forty-five years. The amount saved by the end of the period (the future value of the stream of savings—as discussed in Chapter 4 "Evolving Risk Management: Fundamental Tools") depends on the interest rate. If the money is saved at 0 percent interest, the person will accumulate $45. At 2 percent interest, the amount saved by the end of the period will be $72. (The first dollar gained interest for forty-five years, the second for forty-four years, and so forth.) In other words, interest added approximately 60 percent to the $45 principal. At 4 percent, the amount jumps to $121, meaning that for each dollar saved, the (compounded) interest contributes approximately another $2. At 6 percent, the interest effect is even more impressive: each dollar saved brings in close to $4 in interest. With such a high interest rate, the total amount of the savings at the end of the period is about $212, approximately five times larger than the amount saved. These computations are summarized in Table 17.5 "The Effect of Interest Rates on the Accumulation of Retirement Savings" below.

This simple illustration demonstrates that the interest rate cannot be ignored in long-range planning. One must make a decision: Who should work for retirement—oneself or the interest rate? And the answer is obvious. Being able to finance retirement throughout forty-five years, at an interest rate of 6 percent, means that the financial burden that we discussed earlier could be about five times smaller than with zero percent interest.

There are a couple of caveats to the above discussion:

1. Compounding has a strong effect when the savings period is long. One must start the retirement planning at a young age in order to leave enough time for compounding to have a significant effect. A shorter savings period drastically cuts the contribution of the interest in the saved fund. Unfortunately, most young people joining the labor force do not think about their retirement and by the time they start thinking about it, they have to do most of the saving by themselves without much support from the interest rate.
2. Significant effects are reached only with high interest rates. Factors like inflation or a continuous increase in the standard of living operate in the opposite direction to the incoming interest rate. Deducting such factors from the interest rate and accumulating the savings at the lower real (net) effective interest rate results in lower real savings at the end of the period.

From the individual’s point of view, the interest rate is an exogenous parameter. However, there is a very strong connection between retirement savings and market interest rates. The above discussion demonstrates that people are expected to save a substantial part of their income just to finance their retirement. These savings are a major component of the aggregated national savings, which in turn affect economic growth and the market interest rate.Martin Feldstein, “Social Security, Induced Retirement, and Aggregate Capital Accumulation,” Journal of Political Economy 82, no. 5 (September/October 1974): 905–26.