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In this section we elaborate on the following:
Old-age issues have many aspects: social, psychological, economic, and political. In this text, we focus mainly on the risk management and financial aspect of old age. In the previous discussion, we showed the probability of reaching the old-age group. If we define the group of aged people as those that exceed a common retirement age (like sixty-five), we can easily find the probability of reaching this age by using a life table. We concluded that the probability of a young person reaching retirement age is about 88 percent for males and about 92 percent for females. In the following section, we shall first analyze the probabilities and then discuss the measurement of the financial burden associated with longevity risk. The financial burden is the amount of money that is needed to finance the retirement period. Therefore, we need an estimate for the expected length of this period. Such a measurement can be derived from the life table, and it is related to the concept of life expectancy. Hence, in the following sections we shall discuss survival probabilities and life expectancy figures.
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.
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 lx 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).
Table 17.3 Expectation of Life at Birth for the U.S. Population as Measured in Various Points in Time (1970–2005)
Source: U.S. National Center for Health Statistics, National Vital Statistics Reports (NVSR), Deaths: Final Data for 2005, Vol. 56, No. 10, April 24, 2008, Accessed April 5, 2009, http://www.census.gov/compendia/statab/tables/09s0100.xls.
Longevity risk relates to the duration of the postretirement period, and for that purpose we need to consider conditional life expectancyLife expectancy after retirement.—that is, the life expectancy after retirement (or some other relevant age). These figures are calculated from the life table in a similar way to life expectancy at birth. For example, to calculate the conditional life expectancy at age fifty-five, we have to sum all lx values in the life table (Table 17.1 "Life Table Depicting the Number of Survivors at Age " in the previous section) from age fifty-five to the end of the table to get the number of years lived by the cohort of the people aged fifty-five. This sum must then be divided by l55, the initial number of people in that age. Again, since we used the rough assumption that all people die exactly at their birthdays, even though they die randomly throughout the year, we have to make a correction. Simply deducting half a year (0.5) from the average, we get the life expectancy.
Table 17.4 "Average Number of Remaining Years of Life by Sex and Age (2005)" presents the average number of remaining years of life for the U.S. population. These figures are calculated in the same way as explained above, but they are calculated for the entire U.S. population and not from the 2001 CSO mortality table (Table 17.1 "Life Table Depicting the Number of Survivors at Age " in the previous section) and would therefore be different.
Table 17.4 Average Number of Remaining Years of Life by Sex and Age (2005)
|Age (Years)||Entire Population||Male||Female|
Source: processed by the authors from U.S. National Center for Health Statistics, National Vital Statistics Reports (NVSR), U.S. Decennial Life Tables for 1999–2001, United States Life Tables, vol. 57, no. 1, August 5, 2008, Accessed April 5, 2009, http://www.census.gov/compendia/statab/tables/09s0101.xls.
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.
As a group, young male drivers cause more automobile insurance losses than do young female drivers. A few states, however, no longer allow automobile insurers to charge different rates for males and females. Similarly, over a decade ago, the Supreme Court ruled that employers using annuities to fund retirement benefits could no longer collect higher contributions from women, who were expected to live longer than men, in order to make equal annuity payments during retirement. Employers continuing to pay retirement benefits through annuities were forced by the Supreme Court to use unisex tables. That is, the mortality rates of men and women were pooled to produce an average life expectancy greater than that for men alone and less than that for women alone. Retirement benefits went up for the women and down for the men involved.
Should life insurance rates be made gender neutral as well? The quotes displayed here were requested from Insweb (http://www.insweb.com), an online insurance quotes and distribution company, in August 2005. They show that the premiums for a ten-year term life insurance policy (described in Chapter 19 "Mortality Risk Management: Individual Life Insurance and Group Life Insurance") of $250,000 for a twenty-five-year-old male of perfect health and family history, weight appropriate to height, and no tobacco use, are higher than those for a female with the same attributes. For example, the rate is $13.18 per month for a male as opposed to $11.90 for a female, as shown in the table of quotes below. For newer quotes for your specific age and needs, you can check on line.
When we compare a particular man to a particular woman of the same age and seemingly the same state of insurability (health, lifestyle, occupation, financial condition, and so forth), the man may outlive the woman, but, as you know, insurers pool cohorts of insureds rather than the individual. Insurers observe difference in average experience for large groups of males and females to justify different life rates based on gender, arguing that doing so creates actuarial equity. That is, premiums should differ because expected outcomes (death benefits multiplied by probabilities) are different for groups of males and females. In the past two decades, the gender mortality gap has begun to close. While female longevity has risen, male life spans have increased at a faster rate, due in part to medical advances in treating conditions like heart disease, which traditionally kills more men than women. Recently, companies have begun to incorporate data from the early 1990s. Yet even with a smaller gap between men’s and women’s longevity, insurance rates for women are still lower than for equally aged and healthy men.
Questions for Discussion
|Monthly Premium for a 10-year Level Term Life Policy*|
|* Quotes based on a composite of participating carriers, which have at least an A rating by S&P. Your rate may differ due to your health, smoking, or other activities. Rates subject to underwriting and state availability. InsWeb is a service offered by InsWeb Insurance Services, Inc., a licensed agency in most states (CA #0C24350).|
Source: InsWeb, rates effective as of August, 2005, used with permission
Sources: Ron Panko, “Closing the Gender Gap,” Best’s Review, August 2000, accessed April 4, 2009, http://www3.ambest.com/Frames/FrameServer.asp?AltSrc=23&Tab=1&Site=bestreview&refnum=10974; Insweb, http://www.insweb.com, accessed August 2005.
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.
Table 17.5 The Effect of Interest Rates on the Accumulation of Retirement Savings
|(Future Value of an Annuity)|
|Saving Period (Years to Retirement)||0%||2%||4%||6%|
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:
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.
The interest rate is a major economic parameter that affects and is affected by a variety of complicated political and economic processes. These processes are becoming very complex in the current “flat world” global economy, and they create frequent changes and fluctuations in the interest rates. This introduces a substantial financial risk factor into financial and retirement planning. It is hard to predict future interest rates in the world markets without a reliable, complex econometric model. One feature, though, seems to be quite certain: most developed countries are going to suffer a reduction in the numbers of the working-age population, and they will therefore experience a concomitant decline in the growth potential. The developing countries, on the other hand, will have substantial population and industrial growth, but they will probably soon be facing constraints on their growth due to market limitations. This may indicate that the real interest rates will not exceed, for example, 3 percent in the long run and that the risk factor resulting from interest rate uncertainties is significant.
Some countries have successfully stabilized their social insurance systems (as will be discussed at length in Chapter 18 "Social Security") by directly and indirectly guaranteeing interest rates. The current trend, however, puts the entire burden of interest risks on individuals. This element requires special treatment in the risk management of our personal risks. Low interest rates means that, on the average, the retirement of most people will be financed mainly by the direct contribution (by employers, employees, and the government), and only a relatively small part will be financed by interest accumulation. And the result will be that the burden of financing the retirement system will remain quite heavy.
In the United States, the government does not guarantee market interest rates, but it does influence them through monetary policy. The Federal Reserve (the Fed), for example, directly controls the federal funds rate. This is the rate that private banks charge each other for loans, and it is manipulated to alter the supply of money. The federal funds rate is a determinant of the prime rate, or the interest rate that banks charge their most credit-worthy customers. On the other hand, the rate that banks pay customers on their savings investments will generally be something below the prime rate (so that positive returns on lending activities are not canceled out). In light of the 2008–2009 economic recession, the Fed adjusted the federal funds rate to a target between 0 and 0.25 percent on December 16, 2008, in a radical move designed to increase lending.Board of Governors of the Federal Reserve System, “Press Release,” December 16, 2008, http://www.federalreserve.gov/newsevents/press/monetary/20081216b.htm (accessed March 10, 2009). In response, prime was lowered to 3.25 percent.Wall Street Journal, Market Data Center: Money Rates, March 9, 2009. http://online.wsj.com/mdc/public/page/2_3020-moneyrate.html. Accessed March 10. 2009. While this was good news for people holding outstanding bank notes, mortgages, or credit card debt, it was bad news for those counting on interest rates to help fund their retirements. Of course, banks are hardly the only source of interest rate returns for individuals saving for retirement.
Interest rates higher than those offered through private banks are available to individuals investing in mutual funds, money market accounts, corporate debt, and other long- and short-term investment vehicles. The interest rate will vary considerably depending on the source, but there is a national indicator often used as a benchmark in rate making: the U.S. Treasury bill (T-bill). T-bills are government bonds paying guaranteed, fixed interest rates. Because the government cannot default on its loan obligations, the yield on a T-bill can be said to be a risk-free rate of return. Thus, investments in the private sector must offer a risk premium to entice investors into taking on greater risk. No one would invest in risky private securities if the same return was available from risk-free government bonds. The ten-year annual T-bill rate for 2008 was 3.66 percent. In comparison, the rate on AAA-rated corporate bonds was 5.63 percent. The average ten-year annual T-bill rate since 2000 has been 4.6 percent. However, this compares with a 6.7 percent average for the decade of the 1990s.Board of Governors of the Federal Reserve System, “Federal Reserve Statistical Release: Selected Interest Rates,” http://www.federalreserve.gov/releases/h15/data.htm (accessed March 10, 2009).
The crux of this discussion is that investing for retirement entails its own longevity risk due to interest rates. Consider, for example, an individual who retired in 1999 at the age of sixty-five. What if he were born ten years later and retired in 2009 at the age of sixty-five? Examining interest rates alone, it is hard to imagine this retiree being better off today than if he retired ten years ago. The boom period of the 1990s produced much higher returns, on balance, than are available today. Certainly, one’s personal investment savvy is an important factor in the performance of his portfolio. However, when even the risk-free rate of return yielded 2 percent more during the 1990s, it is easy to see how a conservative, unsophisticated investor would be in a better position if he had to rely on his retirement savings in that decade. Equity investments, too, performed better in the 1990s than in the 2000s. The Dow Jones Industrial Average trended upward for the entire 1990s, peaking on the last day of the decade. The 2000s has seen more volatility in the Dow and a sharp dropoff in 2007.Dow Jones Indexes, “The Dow Through History and Interactive Timeline,” http://www.djaverages.com/ (accessed March 10, 2009). Diversification can improve one’s portfolio, but in a time when both the equity and bond markets are not what they once were, it may be impossible to restore what was lost. Indeed, many individuals who felt secure in building their nest eggs for retirement in the 1990s and again in the mid 2000s have seen those gains erased by the 2008–2009 recession when the Dow lost 50 percent of its value by March 2009. Some of the specific effects will be discussed in Chapter 21 "Employment-Based and Individual Longevity Risk Management". In short, just as longevity risk can be equated as the risk of living too long, so too can it be examined from the standpoint of investing for too long in volatile markets. We cannot control when we are born, nor can we predict the future, so saving for retirement is a delicate balance involving short- and long-term investment mixes and asset diversification.
Most countries do not have a mandatory retirement age but some do. Given the great importance of the retirement age in determining Social Security and other pension arrangements (see Chapter 18 "Social Security" and Chapter 21 "Employment-Based and Individual Longevity Risk Management"), and due to the significant implications for socioeconomic issues, it is time to reexamine this parameter. We do not intend to go into the complex issue of the optimal retirement age, but it is clear that this topic justifies a deep and thorough study from a balanced social, political, and economic point of view.
One possible way to mitigate the increased longevity problem is by deferring the retirement age.Orio Giarini, Dialogue on Wealth and Welfare, Report to the Club of Rome (Oxford, England: Pergamon Press, 1980). When retirement ages were first determined by the government of Germany in 1873, less than 40 percent of the people survived to the age of sixty-five. Today, 80 to 85 percent of males and more than 90 percent of females in developed countries live to that age and beyond. People reaching the age of sixty-five today are often in good physical and mental shape and are often willing to continue working. Some countries are actively moving toward the deferment of the retirement age, and some are already accepting a retirement age of sixty-seven. However, this trend conflicts with another major force of the declining demand for labor.Orio Giarini and Patrick M. Liedtke, The Employment Dilemma: The Future of Employment (Geneva, Switzerland: Dossiers of the Geneva Association, 1997). The present production capacity of developed countries is large, and it can be achieved with only part of the potential labor force. To mitigate the effects of the resulting growth of unemployment, some European countries are reducing the monthly working hours of employees. There is an inevitable clash between the forces driving toward a higher retirement age and the pressures on young populations that have to join the labor force.
Longevity is one of the most important risks that affect our economies. Planners of retirement systems typically focus on the economic and financial aspects and often ignore the basic demographic considerations. Nonetheless, the drastic changes in longevity and life expectancies should not be ignored.
In this section you studied the following about longevity, the risk of living too long: