Life Cycle Risks
The Risks Related to Mortality
In this section we elaborate on the risk of a premature death:
The ways that mortality risk causes loss
The use of mortality tables and life expectancy tables in assessing the probabilities of premature death
Mortality changes over time
Quantifying the intensity of the risk through the economic value of a person
Our lives involve uncertainties and risks. Sometimes, the uncertainty relates to the question of whether an event will occur (What if I become disabled? Will I reach retirement age?). In other cases, an event, such as death, will definitely occur; therefore, the risk relates to the timing of the event (all people will die, but we don’t know when).
The risk management of individuals is strongly related to mortality because it determines the probabilities of dying and surviving.
It is also related to words and concepts like life expectancy and to the measurement of the financial threats created by the life cycle risks. In the following section, we shall further explore the topic of mortality risk: the risk of premature death.
Financial Implications of Mortality Risk
Speaking in terms of the financial threats and ignoring the very real psychological and emotional elements, we can say that the financial risk of a premature death is mainly borne by the dependents of the deceased person because they relied on the income stream generated by the deceased.
The risk of old age is mainly borne by the person whose life is being assessed-that is, the need to guarantee the livelihood of that person.
The cut-off point to distinguish between a premature death and old age depends on the particular person and family. We shall arbitrarily take a common retirement age, say, sixty-five, as the borderline.
Financial Implications of Mortality Risk (Continued)
The distinction between different effects of mortality risk was made at the beginning of the twentieth century. Human beings, like machines, were assessed according to their ability to contribute to the economy.
The analogy between human beings and machines certainly raises ethical questions, and it may be disliked by most readers, but it is a practical approach that may help us characterize the risks and quantify them purely from a financial perspective.
Like any other risk, we shall try to assess the probabilities and the intensity of occurrences.
A machine is expected to operate during its economic lifetime; it may, however, break down before it reaches its life expectancy, causing its owner to suffer a loss of future income streams.
A machine may exceed its economic life, and this situation brings about increased maintenance costs. It may have a deficient production capacity due to some malfunctioning, and this situation involves increased costs and a lower level of production.
The Risk of Premature Death
A premature death is defined as dying prior to a certain age (commonly, the expected retirement age).
The death of a person typically results in a variety of losses: the direct loss is to the dying person because the person is unable to continue enjoying what he or she was doing and still wished to do. Family members and friends suffer a psychological and emotional loss from the disappearance of their loved one.
However, the economic loss is mainly felt by people who depended financially on the deceased person (e.g., spouse, children, parents) and who lost the future income that would have been earned if the person had not died.
Of course, there are also business interests that could be damaged; for example, the employing firm that lost a key person who held particularly important know-how or who had exceptionally important and strong ties with suppliers, customers, or regulators. Another common type of loss is that of a partnership that lost a key partner, a situation that may endanger the continuation of the business.
Calculating the Probability of Death: Mortality Tables and Life Tables
The probability of dying within a defined period is obtained using a mortality table or a life table)
The risk depends, of course, on the individual features of the particular person: genetics, age, health condition, profession, ethnic origin, lifestyle, hobbies, and so forth.
We are typically unable to tell in advance who will die, when, and how. Nonetheless, we can use population statistics to get estimates of these probabilities.
When actuaries look at large populations, they are able to provide scientific estimates of the probabilities of dying in each age cohort. They can tell us the probability that a person celebrating the x birthday will die before reaching the next birthday (at age x + 1). By common actuarial notation, this probability is denoted by qx.
The mortality rate for males is relatively high at birth, but it declines until age ten. It then rises to a peak between the ages of eighteen to twenty-two (often attributed to risk-taking behavioral patterns) and declines between the ages of twenty-three and twenty-nine.
The rise is continuous for females above age ten and for males after age twenty-nine. The rise is rather slow until middle age, at which point it begins to accelerate. At the more advanced ages, it rises very rapidly.
Calculating the Probability of Death: Mortality Tables and Life Tables (Continued)
A life table (or survival table) reflects either the probability of survival (one minus the probability of dying), or the number of people surviving at each age.
Mortality tables and life tables are essential tools in the hands of actuaries. The actuary needs only one of the tables for making all the required calculations since one table can be derived from the other.
The most common way to generate a life table is to use the current mortality rates qx (as reflected in a mortality table).
A life table can be constructed by following a cohort of people that were born during a particular year over a long period of time and recording all deaths until the last one dies (generation life table).
Such an approach is naturally not practical because the follow-up has to continue over a century and creates enormous technical problems: replacing researchers, following people wandering all over the globe, and so forth. Moreover, the results could be of some historical interest but of little practical value because they are influenced by the extreme technological changes (including nutrition, health standards, employment, etc.) that have taken place over time.
Calculating the Probability of Death: Mortality Tables and Life Tables (Continued)
Life tables (and mortality tables) are constructed for particular purposes; therefore, they are based on chosen populations.
Many types of mortality tables and life tables exist because they are calculated from different populations according to the particular needs of the actuaries. There are tables for urban or rural populations, tables for people in certain professions, tables for smokers versus nonsmokers, and the like.
Notably, tables exist for the entire population or for only an insured population:
In contrast, ultimate tables are used to make mortality calculations without the selection effects of medical examination.
It is noteworthy that the selection of the period for which a life table is calculated is important because we do not like to have a table that is based on the mortality pattern during a year of plague. To obtain reliable figures, we need fairly large populations and databases, and we have to take great care in data processing.
Insured populations tend to be healthier because they are typically employed and pass medical screenings as a condition of insurability.
Therefore, their mortality rates tend to be significantly lower than those of uninsured populations. Such tables are called select tables.
Such populations include people from a particular geographical region, people with special occupations, males and females, retired or preretired populations, widows and widowers, people with or without certain diseases or disabilities, and more.
Case Study 01- Life Table Example
Please download and study the case study entitled “Life Table Example” from the module resources section for this module.
The case provides an example life table depicting the number of survivors at age x out of an initial population of 1,000,000 people. The case study then continues to discuss the life table in greater detail.
Mortality Changes over Time
The twentieth century has been a period of unprecedented changes in mortality patterns. Most countries experienced enormous improvements (a drastic decline) in mortality rates.
The chart in Figure 17.2 compares the qx values in the mortality tables over two decades (2001 versus 1980). We see that the qx values declined dramatically.
The rate of change is not uniform, however, among various age groups and by gender. What seems to be a very drastic decline of the death probabilities at age ninety-five and above is just a technical result of extending the end of the mortality table from age ninety-nine in 1980 to 120 in 2001.
Figure 17.2 Mortality Changes as Reflected by Comparisons of the 1980 and 2001 CSO Tables
Case Study 02- New Mortality Tables
Please download and study the case study entitled “New Mortality Tables” from the module resources section for this module.
The case study discusses the revisions made to the CSO mortality table reflecting historical improvements in the mortality rate.
Estimating the Economic Value of Life
What is the economic loss value associated with the case of death? It is hard to answer the question without touching on deep ethical questions.  There are no objective market values that can be referred to, and there are no mechanisms in which one could purchase a substitute at a given price. Therefore, we
have to find indirect ways to estimate the hard-to-measure economic value of a human life, while ignoring psychological or emotional elements that are typically attached to death.
The estimation of the value of human life is needed for private and business purposes. From the private point of view, there is often the need to assess how much financial protection a family needs in case of a breadwinner’s death. From a practical business point of view, there are a variety of needs.
For example, there is often a need to assess the loss that an organization will suffer when a key employee dies or to estimate the cash needed to buy out the share of a partner in the case of a partner’s death. We shall focus on the estimation of the economic value of a person from the family’s point of view.
Estimating the Economic Value of Life (Continued)
A theoretical correct measurement method may be related to sophisticated theories about personal consumption and savings; however, we do not delve into these theories here. Instead, we focus on the estimated value of human life from the dependents’ point of view.
In principle, there are two alternative ways to estimate the value:
To estimate the value of the income stream that the deceased person would have had if she or he had survived.
To estimate the financial needs of the surviving heirs.
Case Study 03- Assessing Economic Value by Lost Future Income Streams
Please download and study the case study entitled “Assessing Economic Value by Lost Future Income Streams” from the module resources section for this module.
The case study describes the process of estimating the economic value of a human life by calculating the value of the future income stream that will be lost in case of the person’s death.
Assessing Economic Value by Needs Analysis
An alternative way to estimate the financial loss in case of a premature death is to estimate the needs of the surviving members of the family who depended on the deceased person.
The particular needs differ from one family to another; however, certain needs are quite common when the person is a breadwinner for the family.
Most insurance companies and insurance agents are equipped with software to prepare a family needs analysis like that described in the appendix. These programs are useful as a marketing tool by the agents, but they could be used by families in designing their plans.
Many students are unmarried and therefore do not acknowledge the importance of family needs planning. Moreover, people tend to avoid thinking about what could happen in case of their death or their spouse’s death.
However, it is of utmost importance to do so once in a while (at least every ten years) and to keep updating it in accordance with changing personal status and needs (children, marriage, divorce, etc.). It will save many worries for you and your family in case something does go wrong in your life.
Assessing Economic Value by Needs Analysis (Continued)
The financial planning process means creating a cash flow plan that could easily be translated to present values.
It is expected that this method gives a more accurate estimate of financial needs and results in somewhat lower values than the ones obtained by the first approach (the present value of the lost income stream).
The above discussion has shown that the risk of death prior to retirement age is substantial. The probability of occurrence in developed countries could be around 10 to 12 percent for males and around 8 percent for females.
As the present value estimation reveals, the amount of loss is typically around fifteen to twenty times annual income. Therefore, it is not surprising that many institutions are dealing with these risks and offer some sources of financial protection.
This expectation is based on the assumption that the lost income approach overestimates the needs (mainly due to the fact that the dead person stops consuming). It is noteworthy that this hypothesis is not supported by practical experience, and we often find that the two methods result in very similar figures.
The reason for this could be found in the empirical evidence that there is a very strong correlation between the family income and consumption. People get used to a standard of living that is strongly connected to the family’s disposable income, and therefore the financial needs tend to reflect the current consumption pattern of the family while the breadwinner is still alive.
In this section you studied mortality, the risk of premature death:
Mortality risk is borne mainly by the dependents of the deceased.
Mortality tables and life tables can be used to determine the probability of a person dying before a certain age or surviving to a certain age.
Mortality rates of the insured populations tend to be better than those of the uninsured populations.
Actuarially, 8 to 15 percent of the population will die prior to retirement age.
Mortality risk can be quantified by determining the economic value of a person through either the present value of the stream of lost income method or a family needs analysis.
The economic value of life is said to be fifteen to twenty times one’s permanent annual income (or higher when interest rates approach zero).
The economic value of life is inversely related to interest rates.
1. What are life tables used for? How are life tables distinguished from mortality tables?
2. Who primarily bears the risk associated with premature death?
3. Describe briefly some of the changes in mortality patterns that have been observed over the years.
4. Explain how present value can be utilized to estimate the economic value of life.
5. What does it mean to you that your mortality risk may be between 8 and 12 percent? Is this a risk whose probability is so low that you don’t worry about it? Or are the consequences of its occurrence such that it must be dealt with regardless of its likelihood?
 There could be substantial gaps between objective and subjective values, there could be differences between the point of view of the individual versus that of a government, and so forth.
 See Y. Kahane, Life Insurance, Pension Funds, and Retirement Saving Programs: A Handbook for Business and Personal Financial Planning (Isreal: Ateret Publishing House, 1983). Published in Hebrew.
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