Chapter 3 - Life Tables, Underwriting, and an Introduction to Mortality Analysis

Question 1

Friendly Societies

Answer 1

Early attempts at life insurance were sponsored by friendly societies in the 17th and 18th centuries. Comprised of individuals who banded together for mutual benefit, including providing the for the widows and orphans of decreased members.

Question 2

Friendly Societies “post death” method

Answer 2

A method of funding death benefits in which each member of the society agreed to pay a specific amount of money when a fellow member died. Society would receive a fee for admin work but the rest would go to the bene - usually family.

Question 3

Friendly Societies “post death” problems (3)

Answer 3

1. Contributions were voluntary and thus the death benefit could not be guaranteed.
2. Unless new members were recruited into the society, the size of the group gradually diminished d/t continued deaths and as a results the death benefits decreased
3. The number of claims increased each year because the group as a whole was aging. Therefore, the amount each bene rec’d further diminished in proportion to the increase in claims.

Question 4

Friendly Societies “post death” - coping with problems

Answer 4

“Assessment method” - in which protection was offered for a specific period of time (usually a year) and the necessary money to fund this plan was raised by assessing each member an equal amount in advance. This resulted in the development of life tables.

Question 5

John Graunt

Answer 5

Credited with the first serious attempt at developing a population life table title “Table of Survivors” [1662]. Based on weekly burial and deaths occurring in London.

Question 6

Calculation of mortality rates

Answer 6

Life tables are constructed using annual mortality rates tabulated by age, sex, and other factors.

Question 7

Mortality rates for different ages

Answer 7

Calculated by observing the number of deaths (d[x]) occurring in the population over a specified period of time (an interval, designated by “x”) and determining the number of individuals exposed to the risk of dying during the interval.

Question 8

Exposure (E[x])

Answer 8

Expressed as the product of the number of individuals who are alive at the beginning of an interval who are exposed to the risk of dying (1[x]) and the duration over which that exposure take place, usually in years. Exposure is almost always expressed as person-years. The interval mortality rate (q[x]) is calculated by dividing the number of deaths occurring during an interval by the corresponding exposure (q[x] =d[x]/E[x])
Mortality rates are typically annual mortality rates.

Question 9

1[x]

Answer 9

Number of individuals alive at the beginning of an interval (x) who are exposed to the risk of dying.

Question 10

d[x]

Answer 10

Number of during an interval.

Question 11

E[x]

Answer 11

Exposure during an interval or
(person exposed to risk of dying)(duration of interval exposure) or
(1[x])(interval duration), usually expressed “in person’ years”

Question 12

q[x]

Answer 12

interval mortality rate, or
deaths/exposure, or
d[x]/E[x]

Question 13

Life insurance pricing

Answer 13

Based on monetary cost of death claims therefore monetary amounts of claims instead of the number of deaths and substitute the total monetary amount of insurance in force for exposure, since this is the total monetary sum that is “exposed to the risk” of being paid out as claims.

Question 14

Viatical and elder life settlement companies

Answer 14

Purchase life insurance policies from policyholders for sums somewhat greater than the policies’ accumulated cash values. When the insured dies, the viatrical or life settlement company received the death benefits. This avoid the policy from lapsing and can lead to an overestimated lapse rates by insurance companies when setting their pricing assumptions.

Question 15

Some types of life tables

Answer 15

1. Population
2. Period
3. Cohort
4. Insured lives life tables

Question 16

Population life tables

Answer 16

based on death rates calculated for large segments of the population without regard to individual health, socioeconomic, or employment status.
Often segments by sex, race, and residence.

Question 17

Period (i.e., current) life tables

Answer 17

Death rates are calculated from data collected over a relatively short period (1 - 3 yrs) and therefore the data is more reliable to the middle of that period. Since the tables reports death rates observed at each age over a relatively short period of time, period tables depict the death rates for a large number of birth cohorts (groups). I.e., deaths from 1989 - 1991, white males, ages 40-41 and 50-51.
The assumption should be that 10 yrs those who were 40-41 would have the same ratio as those 50-51 10 yrs prior.

Question 18

Cohort (generation) life tables

Answer 18

Reports the actual death rates for a group, or cohort, of individual born around the same time. These tables accurately report the historical death rates for a birth cohort up to the time the table was created.

Question 19

Variety of insured lives life tables including

Answer 19

1. Select and ultimate (also known as basic) tables
2. Annuity tables
3. Group life tables
4. Pension life tables
5. Standard and ordinary life tables (Commissioners, Standard Ordinary or CSO Tables)
6. Disabled life tables

Question 20

Insured Lives Life Tables - Basic tables

Answer 20

The mortality of individuals who purchased life insurance at standard or better rates. Usually represent a greater proportion of persons from higher socioeconomic groups and lower proportion of disabled persons w/ ill health. Non-tobacco select mortality rates substantially lower than those in the general population.

Question 21

Basic tables - select period

Answer 21

After policy issue during which the effect of underwriting continues to result in lower death rates compared to the entire pool of policyholders. Death rates immediately following policy are usually the lowest and gradually rise as the underwriting effectiveness wears off

Question 22

Ultimate Rates

Answer 22

The death period following a select period. Often it is assumed underwriting no longer conveys a benefit after 20-25 yrs.
I.e., during the ultimate period, the beneficial effect of underwriting and socioeconomic status usually results in mortality rates below those for the general population.

Question 23

Basic table as cohort table

Answer 23

The annual death rates are the death rates experienced by a cohort of individuals purchasing insurance at the same age.

Question 24

Individual annuity tables

Answer 24

Typically have the lowest mortality rates of any insured lives mortality. Represent the mortality expected for holders of annuity products, the because of their features, as known to attract healthy person having the greatest longevity. I.e., live long enough that the cost of buying the annuity is worthwhile.

Question 25

Group life tables

Answer 25

Aggregate life tables because little, if any, individual underwriting is done. Typically have mortality rates of a par with or slightly higher than individual select and ultimate tables. Requirement that they be actively employed

Question 26

Social Security or pension life table

Answer 26

Typically have a higher mortality rates that are close to, but somewhat less than, population rates because selection is limited to the requirement that persons eligible for social security or pension must have been actively employed at some point.

Question 27

Standard and ordinary tables

Answer 27

CSO Tables
Used by valuation actuaries to set policy reserves and determine basic tables. Usually more conservative d/t the addition of loadings to the underlying basic tables.
The level of mortality reflected in these tables is on par with that of social security and pension life tables.

Question 28

Disabled Lives Life Tables

Answer 28

Reflect mortality rates of persons no longer able to work because of a disability. Mortality rates in these tables are somewhat higher than general population mortality rates.

Question 29

Relative mortality rates in various life tables compared to population mortality

Answer 29

Annuity, Individual Lives -> 20-40%
Select and Ultimate -> 40-60%
          Non-tobacco -> 30-50%
          Tobacco -> 50-80%
Group, Individual Life and Annuity -> 40-60%
Social Security (Pension) -> 85-95%
CSO -> 85-95%
Population -> 100%
Disabled Lives -> 120-140%

Question 30

How to change mortality rates in insured life tables to mortality rates in clinical mortality studies

Answer 30

Often done by assuming that the death rate, expressed as deaths per $1000 insured person per year, is equal to the annual cost of insurance expressed as premium per $1000 of life insurance overage per year plus an additional amount (load) for expenses and profit.

Question 31

Major difficulty encountered when converting clinical mortality

Answer 31

Stems from the difference between the characteristics of the population in clinical studies and of those who purchase life insurance. Those entering clinical studies are usually not selected by factors such as age, socioeconomic status, risk factors, and comorbids, or age.
Therefore results of clinical studies cannot be translated directly to those seen in the insured population.

Question 32

Solution to converting clinical mortality

Answer 32

Mortality rates observed in the clinical population having the impairment in question should first be compared to the mortality rates in another population matched as closely as possible in other respects to the population with the impairment.
In this method, an excess death rate is first calculated using the relationship of observed to expected mortality, in which the expected mortality is the mortality rate in a comparison population closely match to the population having the impairment, except for the presence of the impairment itself.

Question 33

The excess death rate (edr)

Answer 33

Can be used to calculate the amount of extra premium (flat extra premium of FE) the must be charged on an annual basis to cover the excess mortality risk (where extra premium equals the edr plus some additional load for overhead and profit).
Edr can also be compared to select insured lives mortality rates to calculate select relative mortality ratio from which a table rating can be derived.

Question 34

Base pricing assumptions

Answer 34

Reflect mortality expected for individual who are in good health and who are free from impairments that would be expected to increase their risk of dying.
Can be subdivided to reflect mortality expected amount various classes of better risk (preferred pricing)

Question 35

The excess mortality risk of impairment resulting in offers of insurability at substandard rates is commonly expressed in 2 ways

Answer 35

1. Excess death rate (edr)

2. Relative mortality ratio (rmr)

Question 36

Express Death Rate

Answer 36

The difference in death rates observed in the population having the impairment compared to the death rates expected in an otherwise matched population without the impairment.
Observed death rate is designated as “q”
Expected death rate is designated as “q’”
Therefore edr = q - q’
In insured lives studies q’ represents the baseline mortality assumption.

Question 37

Relative Mortality Ratio (aka mortality multiples)

Answer 37

Ratios between observed mortality rates (q) and expected mortality rates (q’). Thus rmr =q/q’.
Relative mortality ratios form the basis of a classification system for rating substandard mortality risks in which a “table” of excess mortality risk represents a 25% increase in risk over the expected standard mortality risks,

Question 38

Substandard Ratings

Answer 38

Pricing varies by the nature and severity of the impairment or risk factor. Ideally, substandard rates would be derived from an analysis of insured liver mortality experience similar to that used to set standard premium rates. For this to work, a sufficient number of individual with that impairment would need to be followed until death.
Therefore many companies share their mortality data on substandard issues to create pooled date for inter-company mortality studies.

Question 39

Table Ratings

Answer 39

The pattern of extra premium charges should mirror the pattern of excess mortality risk. Thus, if the excess mortality risk increased with each duration that the policy remains in force, a table rating can be the most appropriate way to charge the extra premium necessary to cover that excess mortality cost.

Question 40

Flat Extra Premium

Answer 40

If the excess mortality risk is thought to remain constant, then a flat extra premium is commonly changed in addition to the standard premium. (i.e., occupation, avocation, or foreign travel related risks.

Question 41

Temporary Flat Extras

Answer 41

Special circumstance in which excess mortality risk decreases with time.

Question 42

Temporary Flat Extras - strategy objectives

Answer 42

1. Postponement period avoids assuming speculative risks during the earliest durations when the mortality is very high.
2. A finite period over which a more modest temporary flat extra premium is charged allows most individuals to purchase insurance at affordable prices when the risk has diminished to more predictable levels. This minimizes the anti-selection risk that would otherwise result if the cost of covering all durations of risk were so expensive that only individuals with high mortality risks (who could not obtain coverage elsewhere) purchased insurance.
3. Returning to standard pricing at the later duration is designed to minimize the anti-selection that would otherwise result from selective lapsation, if extra premium were charged beyond the time when the mortality risk had returned to baseline levels.

Question 43

Annuity life tables

Answer 43

A type of insured lives’ life table tabulating the mortality rates of individuals who have purchased annuities. Consider to represent the lower mortality rates among insured lives.

Question 44

Basic Life tables

Answer 44

Also known as select or ultimate tables. A type of insured lives’ life table tabulating the death rates for individuals who purchased insurance at standard or better (preferred) rates. Subdivided by tobacco use and by select and ultimate periods

Question 45

Cohort (generation) life table

Answer 45

A type of life table tabulating the year-to-year death rates for a group (cohort) of individuals born around the same time (e.g., same year).

Question 46

Disabled lives life table

Answer 46

A life table tabulating the mortality rates of persons no longer able to work due to a disability.

Question 47

Flat Extra rating

Answer 47

A method used in underwriting to account for extra (substandard) mortality risk by charging constant extra premium in addition to the base (standard) premium.

Question 48

Period (current) life tables

Answer 48

A life table tabulating death rates for a particular period of time for individuals of different ages at the time of mortality data was collected (different birth cohorts).

Question 49

Population life table

Answer 49

A life table tabulating death rates for large segments of the population without regard to individual health, socioeconomic status, or employment status.

Question 50

Select Factors

Answer 50

Scalar factors applied to life tables to reduce projected mortality rates to levels thought to be attractive to potential life insurance buyers while remaining achievable through the combination of target market selection, underwriting, and anticipated secular (general population) mortality improvements.

Question 51

Select period

Answer 51

The periods from life insurance policy issue to the time at which the effects of underwriting has been assumed to no longer be effective in selecting standard or better risks from among the entire pool of insured persons. Often considered to be about 20-25 years.

Question 52

Social security (pension) life tables

Answer 52

A type of population life table tabulating the mortality rates of individuals who were actively employed at some time.

Question 53

Standard and ordinary life tables

Answer 53

Aggregate insured lives’ life tables in which select and ultimate mortality rates are combined to arrive at aggregate death rates fro each age, thus ignoring most of the effect of selection resulting from underwriting. Death rates in such a table are somewhat higher (more conservative) than those in the basic select and ultimate tables.

Question 54

Table ratings

Answer 54

A method used in underwriting to account for extra (substandard) mortality risk by charging extra premium based on a multiple of the base (standard premium).

Question 55

Ultimate period

Answer 55

The period after the select period during which the effect of underwriting is assumed to no longer be effective in selecting standard or better risks from the entire pool of insured persons. Often considered to be the period beyond 20-25 yrs after underwriting.

Question 56

d[x]

Answer 56

Interval deaths -> The number of deaths occurring during the interval, x to x+1
** d[x] = 1[x+1] -1[x]-w[x]

Question 57

q[x]

Answer 57

Interval probability of death -> Probability of death during the interval, x to x+1
** Number of deaths occurring during the interval, divided by the interval exposure, d[x]/E[x]

Question 58

p[x]

Answer 58

Interval probability of survival -> Probability of survival during the interval, x to x+1
** 1-q[x], also P[x]/P[x+1]

Question 59

edr[x]

Answer 59

Interval excess death rate -?> Excess death rate during the interval, x to x +1. It is the observed death rate less the expected death rate during interval x. Usually expressed as the number of extra deaths per 1000 individuals exposed to the risk of dying during the interval, x
** edr = 1,000(d[x]-d’[x]/E[x]) = q[x]-q[x]’

Question 60

mr

Answer 60

Interval mortality ratio -> The ratio of the observed death date (q) to the expected death rate (q’) during interval x.|
** mr[x] =q[x]/q[x]’

Question 61

1[x]

Answer 61

Number of lives entering interval x -> Number of individuals exposed to the risk of dying at the beginning of interval, x. It is equal to the number of individuals entering the previous interval (x-1) less the number of individuals withdrawn or lost to follow up and the number of individuals dying during the previous interval
** 1[x] = 1[x-1]-w[x-1]-d[x-1] and 1[x+1] = 1[x]-w[x]-d[x]

Question 62

L[x]

Answer 62

Average number of individuals alive during the interval, x -> The average number of individuals alive during the interval is equal to the number of individuals entering the interval less half of those dying during the interval.
** L[x] -1[x]-0.5(d[x])

Question 63

w[x]

Answer 63

Number of withdrawals during interval x -> Number of individuals entering an interval who withdraw form the studying during the interval, x. In the practice w[x] usually also includes those lost (untraced) to follow up (u[x]) during the interval.

Question 64

E[x]

Answer 64

Exposure in (person x years) -> Number of individuals exposed to the risk of dying during the interval, x. Exposure is calculated by multiplying the number of persons entering interval by the duration they are exposed to the risk of dying. Since the length of an interval is usually taken to be one unit long (e.g., usually 1 year) and since those withdrawing or lost to follow-up are considered to have withdrawn at the midpoint of the interval, their contribution to the overall interval exposure is 1/2 of those remaining in the study.
** E[x] = (1[x])(interval duration)
E[x] = 1[x](interval duration)
w[x](one half the interval duration)
Ex = 1[x]-w[x](0.5)

Question 65

x

Answer 65

Interval, as in p[x] or q[x] -> Interval one of a series of successive period of time during which mortality is studied.

Question 66

’

Answer 66

Expected, as in p[x]’ or q[x]’ -> The expected probability of survival (p[x]’) or death (q[x]’) during the interval, x. Expected probabilities of survival or death are usually taken from a life table.

Question 67

-

Answer 67

Aggregate annual average interval as in:
\_\_\_       \_\_\_
p[x] or q[x]
The averal annual probability of survival or dying over the interval x to x+n/
** SEE equation in textbook **

Question 68

v

Answer 68

Geometric annual average as in geometric annual average probability of death or survival
v v
(q[x]) (p[x])
** SEE equation in textbook **

Question 69

D

Answer 69

Cumulative (overall) deaths from beginning of the study to end of the interval of interest.

Question 70

Q

Answer 70

Cumulative (overall) probability of death from beginning of the study to end of interval of interest|

Question 71

P

Answer 71

Cumulative (overall) probability of survival from beginning of the study to end of interval of interest.