ALU 202 ACTUAL FINALS QUESTIONS AND
ANSWERS SET A+
✔✔Disabled lives life tables - ✔✔- reflect mortality rates of persons no longer able to
work because of a disability.
- mortality rates are somewhat higher than general population mortality rates.
✔✔The excess death rate (edr) - ✔✔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
✔✔The EDR can be used to calculate - ✔✔Can be used to calculate the amount of
extra premium (flat extra premium if FE) that must be charged on an annual basis to
cover the excess mortality risk.
✔✔Base pricing assumptions for life insurance products reflect - ✔✔the mortality
expected for individuals who are in good health and who are free from impairments that
would be expected to increase their risk of dying
✔✔Individuals excluded from the base pricing assumption - ✔✔individuals who have
impairments or risk factors at the time of policy issue that would be expected to
significantly increase their mortality risk
✔✔The excess mortality risk of impairments resulting in offers of insurability at
substandard rates is commonly expressed in one of two ways: - ✔✔-As an excess
death rate (edr)
-As a relative mortality ratio (rmr)
✔✔Relative mortality ratio (rmr) or mortality multiples - ✔✔- the ratios between
observed mortality rates and expected mortality rates.
- form the basis of a classification system for rating substandard
,✔✔Two commonly used conventions for designating table ratings - ✔✔1. Each 25% of
extra risk is referred to as one table.
2. The other convention uses letters to designate the number of tables of extra
premium.
✔✔Table Rating - ✔✔if excess mortality risk increases with each duration that the policy
remains in force, this can be the most appropriate way to charge the extra premium
necessary to cover that mortality cost.
✔✔Flat Extra Premium - ✔✔if the excess mortality risk is thought to remain constant,
then this type of premium is commonly charged in addition to the standard premium
✔✔Temporary Flat Extra - ✔✔- special circumstances in which excess mortality risk
decreases with time.
- usually the charge is expressed in terms of the average cost of the extra premium per
1 thousand dollars of coverage and the duration in years over which that extra risk is
expected to be present.
✔✔Select factors - ✔✔scalar factors applied to life tables to reduce projected mortality
rates to levels thought to be attractive to potential life insurance buyers while
maintaining achievable mortality goals through the combination of target market
selection, underwriting and anticipated secular (general population) mortality
improvements
✔✔Select period - ✔✔is the period from life insurance policy issue to the time at which
the effect 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 to 25 years).
✔✔Ultimate period - ✔✔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 to
25 years after underwriting).
✔✔dx = - ✔✔= interval deaths = number of deaths occurring during the interval, x to
x+1
✔✔Calculation: dx = 1x+1-1x-wx - ✔✔dx =
✔✔qx = - ✔✔= interval probability of death = probability of death during the interval x to
x+1.
✔✔Calculation is the number of deaths occurring during the interval divided by the
interval exposure: dx/Ex - ✔✔qx =
,✔✔px = - ✔✔= interval probability of survival = probability of survival during the interval
x to x+1
✔✔Calculation 1-qx also, Px/Px+1 - ✔✔px =
✔✔edrx - ✔✔= 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 1 thousand individuals exposed to
the risk of dying during the interval x.
✔✔Calculation edrx = 1,000(dx-d'x/Ex) = qx-qx' - ✔✔edrx
✔✔Mr = - ✔✔= interval mortality ratio = the ratio of the observed death rate (q) to the
expected death rate (q') during interval x.
✔✔Calculation mrx = qx/qx' - ✔✔Mr =
✔✔1x = - ✔✔= number of lives entering interval x = the 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.
✔✔Calculation 1x = 1(x-1)-w(x-1)-d(x-1) and 1(x+1) = 1x-wx-dx - ✔✔1x =
✔✔Lx = - ✔✔= average number of individuals alive during the interval x. = the average
number of individuals alive during an interval is equal to the number of individuals
entering the interval less half of those dying during the interval.
✔✔Calculation Lx = 1x-0.5(dx) - ✔✔Lx =
✔✔wx = - ✔✔= number of withdrawals during interval x. = number of individuals
entering an interval who withdraw from the study during the interval x. In practice, wx
usually also includes those lost (untraced) to follow-up (ux) during the interval.
✔✔Ex = - ✔✔= 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.
✔✔Calculation Ex = (1x)(interval duration)
Ex = 1x (intervak duration) - wx (one half the interval duration)
Ex = 1x - wx (0.5) - ✔✔Ex =
✔✔x = interval - ✔✔as in px or qx = interval one of a series of successive periods of
time during which mortality is studied.
, ✔✔' = - ✔✔= expected as in px' or qx' = the expected probability of survival (px') or
death (qx') during the interval, x.
Expected probabilities of survival or death are usually taken from a life table.
✔✔v = - ✔✔= geometric annual average, as in geometric average probability of death (v
qx) or survival (v px)
✔✔D = - ✔✔= cumulative (overall) deaths from beginning of the study to end of interval
of interest.
✔✔Q = - ✔✔= cumulative (overall) probability of death from beginning of the study to
end of interval of interest.
✔✔P = - ✔✔= cumulative (overall) probability of survival from beginning of the study to
end of interval of interest.
✔✔Framingham Study - ✔✔US Public Health and Service selected those from the town
of Framingham, MA to help Americans nationwide understand their coronary risk
factors.
✔✔Included in the Framingham Study - ✔✔medical history, physical measurements,
height weight, blood pressure, resting EKG, chest x-ray and blood chemistries.
✔✔Conservation of Deaths - ✔✔- This model assumes there is a correlation between
the percent qualifying for a preferred risk class and the mortality discount.
- The fewer individuals that qualify for the preferred class, the greater the mortality
discount.
✔✔Hazard Ratios (HR) - ✔✔- results presented in the study.
- The baseline is 1.0. (equivalent to 0 debits or 100%)
✔✔The multivariate Cox proportional hazard model is - ✔✔-Is the basis behind the
Framingham Point Score.
-The goal of the model is to define the mortality risk associated with a variable.
✔✔Point System - ✔✔- can take favorable and unfavorable risk factors into
consideration at the same time without allowing one factor to overwhelm the decision by
itself, unless it is extreme.
- fewer points mean lower risk.
- Lower points represent favorable risks, whereas higher point values represent higher
mortality risk
ANSWERS SET A+
✔✔Disabled lives life tables - ✔✔- reflect mortality rates of persons no longer able to
work because of a disability.
- mortality rates are somewhat higher than general population mortality rates.
✔✔The excess death rate (edr) - ✔✔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
✔✔The EDR can be used to calculate - ✔✔Can be used to calculate the amount of
extra premium (flat extra premium if FE) that must be charged on an annual basis to
cover the excess mortality risk.
✔✔Base pricing assumptions for life insurance products reflect - ✔✔the mortality
expected for individuals who are in good health and who are free from impairments that
would be expected to increase their risk of dying
✔✔Individuals excluded from the base pricing assumption - ✔✔individuals who have
impairments or risk factors at the time of policy issue that would be expected to
significantly increase their mortality risk
✔✔The excess mortality risk of impairments resulting in offers of insurability at
substandard rates is commonly expressed in one of two ways: - ✔✔-As an excess
death rate (edr)
-As a relative mortality ratio (rmr)
✔✔Relative mortality ratio (rmr) or mortality multiples - ✔✔- the ratios between
observed mortality rates and expected mortality rates.
- form the basis of a classification system for rating substandard
,✔✔Two commonly used conventions for designating table ratings - ✔✔1. Each 25% of
extra risk is referred to as one table.
2. The other convention uses letters to designate the number of tables of extra
premium.
✔✔Table Rating - ✔✔if excess mortality risk increases with each duration that the policy
remains in force, this can be the most appropriate way to charge the extra premium
necessary to cover that mortality cost.
✔✔Flat Extra Premium - ✔✔if the excess mortality risk is thought to remain constant,
then this type of premium is commonly charged in addition to the standard premium
✔✔Temporary Flat Extra - ✔✔- special circumstances in which excess mortality risk
decreases with time.
- usually the charge is expressed in terms of the average cost of the extra premium per
1 thousand dollars of coverage and the duration in years over which that extra risk is
expected to be present.
✔✔Select factors - ✔✔scalar factors applied to life tables to reduce projected mortality
rates to levels thought to be attractive to potential life insurance buyers while
maintaining achievable mortality goals through the combination of target market
selection, underwriting and anticipated secular (general population) mortality
improvements
✔✔Select period - ✔✔is the period from life insurance policy issue to the time at which
the effect 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 to 25 years).
✔✔Ultimate period - ✔✔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 to
25 years after underwriting).
✔✔dx = - ✔✔= interval deaths = number of deaths occurring during the interval, x to
x+1
✔✔Calculation: dx = 1x+1-1x-wx - ✔✔dx =
✔✔qx = - ✔✔= interval probability of death = probability of death during the interval x to
x+1.
✔✔Calculation is the number of deaths occurring during the interval divided by the
interval exposure: dx/Ex - ✔✔qx =
,✔✔px = - ✔✔= interval probability of survival = probability of survival during the interval
x to x+1
✔✔Calculation 1-qx also, Px/Px+1 - ✔✔px =
✔✔edrx - ✔✔= 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 1 thousand individuals exposed to
the risk of dying during the interval x.
✔✔Calculation edrx = 1,000(dx-d'x/Ex) = qx-qx' - ✔✔edrx
✔✔Mr = - ✔✔= interval mortality ratio = the ratio of the observed death rate (q) to the
expected death rate (q') during interval x.
✔✔Calculation mrx = qx/qx' - ✔✔Mr =
✔✔1x = - ✔✔= number of lives entering interval x = the 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.
✔✔Calculation 1x = 1(x-1)-w(x-1)-d(x-1) and 1(x+1) = 1x-wx-dx - ✔✔1x =
✔✔Lx = - ✔✔= average number of individuals alive during the interval x. = the average
number of individuals alive during an interval is equal to the number of individuals
entering the interval less half of those dying during the interval.
✔✔Calculation Lx = 1x-0.5(dx) - ✔✔Lx =
✔✔wx = - ✔✔= number of withdrawals during interval x. = number of individuals
entering an interval who withdraw from the study during the interval x. In practice, wx
usually also includes those lost (untraced) to follow-up (ux) during the interval.
✔✔Ex = - ✔✔= 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.
✔✔Calculation Ex = (1x)(interval duration)
Ex = 1x (intervak duration) - wx (one half the interval duration)
Ex = 1x - wx (0.5) - ✔✔Ex =
✔✔x = interval - ✔✔as in px or qx = interval one of a series of successive periods of
time during which mortality is studied.
, ✔✔' = - ✔✔= expected as in px' or qx' = the expected probability of survival (px') or
death (qx') during the interval, x.
Expected probabilities of survival or death are usually taken from a life table.
✔✔v = - ✔✔= geometric annual average, as in geometric average probability of death (v
qx) or survival (v px)
✔✔D = - ✔✔= cumulative (overall) deaths from beginning of the study to end of interval
of interest.
✔✔Q = - ✔✔= cumulative (overall) probability of death from beginning of the study to
end of interval of interest.
✔✔P = - ✔✔= cumulative (overall) probability of survival from beginning of the study to
end of interval of interest.
✔✔Framingham Study - ✔✔US Public Health and Service selected those from the town
of Framingham, MA to help Americans nationwide understand their coronary risk
factors.
✔✔Included in the Framingham Study - ✔✔medical history, physical measurements,
height weight, blood pressure, resting EKG, chest x-ray and blood chemistries.
✔✔Conservation of Deaths - ✔✔- This model assumes there is a correlation between
the percent qualifying for a preferred risk class and the mortality discount.
- The fewer individuals that qualify for the preferred class, the greater the mortality
discount.
✔✔Hazard Ratios (HR) - ✔✔- results presented in the study.
- The baseline is 1.0. (equivalent to 0 debits or 100%)
✔✔The multivariate Cox proportional hazard model is - ✔✔-Is the basis behind the
Framingham Point Score.
-The goal of the model is to define the mortality risk associated with a variable.
✔✔Point System - ✔✔- can take favorable and unfavorable risk factors into
consideration at the same time without allowing one factor to overwhelm the decision by
itself, unless it is extreme.
- fewer points mean lower risk.
- Lower points represent favorable risks, whereas higher point values represent higher
mortality risk
