Lesson 9

Question 1

State the main function of an actuary. Identify the duties performed by actuaries
that enable them to perform this function.

Answer 1

One of the main functions of actuaries is to help businesses measure, manage and
mitigate the risk of certain events occurring

Actuaries assemble and analyze data to estimate the probability and likely cost of an event

actuaries help design insurance policies, pension
plans and other financial strategies in a manner that helps ensure plans are
maintained on a sound financial basis

Question 2

9.1.2 Explain what an appointed actuary is responsible for in insurance companies.

Answer 2

1) Reporting to an insurer’s management and directors and imminent risks that could imperil the company and for reporting to the superintendent of financial institutions

They certify policy liabilities, protect the policyholder’s interests including monitoring fairness and equity

Question 3

9.2.1 List the three general properties of probability

Answer 3

1) The probability of an event is between 0 and 1
2) The probability of an impossible event is 0
3) the probability of a certain event is 1

Question 4

9.2.2 Last year, one city reported that 50 people under the age of 20 died. If the population
of people in the city under the age of 20 was 50,000, calculate the probability of
someone under the age of 20 dying

Answer 4

0.1%

Question 5

8.2.3 An observed group has 80 people living one year after they all became 88 years of
age; 20 people of that age group died during the year. Calculate the rate of mortality
at the age of 88

Answer 5

20%

Question 6

9.2.4 Explain compound probability and how it is calculated

Answer 6

Compound probability is the probability of two independent events both occurring.

You simply multiply the probability of the two events occurring independently.

P(A and B) = P(A) x P(B)

Question 7

9.2.5 If the probability that an individual will live one year is 0.900 and the probability of
dying in the following year is 0.120, calculate the probability that an individual will
survive both years.

Answer 7

.792

Question 8

9.2.6 Explain the difference between compound probability (A and B) and the probability
of A or B. Show how the latter probability is calculated. Provide examples.

Answer 8

P(A and B) = P(A)xP(B)

P(A or B) = P(A) + P(B) if the events are mutually exclusive

Question 9

9.2.7 Explain how the statistical concept known as the law of large numbers applies to
group life insurance.

Answer 9

The larger the group the more the events will tend towards the mean probability of occurrence. Larger groups have higher credibility. For large groups chance events become predictable

Question 10

9.3.1.a Identify the two basic sources of mortality statistics

Answer 10

Population data and insurance data

Question 11

9.3.1.b Describe the effect of population data on mortality tables

Answer 11

Population data is compiled by Stats Can every 5 years and is broken down by province, sex, and cause of death.

This data can be subject to inaccuracies or missing information

Question 12

9.3.1.b Describe the effect of insurance data on mortality tables

Answer 12

Generally more accurate as the insurance company carefully documents dates of birth and death

Question 13

9.3.2 Explain how group insurance mortality data is collected and used in Canada

Answer 13

The CIA compiles and analyzes individual insurance data from a number of companies.

It issues mortality tables for males/females, smokers/non, annuitants and insured lives

Most insurers use this data to some degree although larger companies tend to rely on their own experience studies

Question 14

9.3.3 Describe the information that is provided in a mortality table

Answer 14

A mortality table shows the rate of death in a given population during a selected time interval

Question 15

9.3.4 Explain the impact of a reduction in mortality rates at the younger ages on the rate
of mortality at the older ages.

Answer 15

A reduction in mortality at younger ages has no impact on older ages.

However the same conditions tend to impact mortality across the ages.

Question 16

9.3.5 Explain how the gradual long-term improvement in mortality rates is reflected in
annuities.

Answer 16

It is common to price annuities using a mortality table that has lower mortality than that shown in the static table

Question 17

9.3.6 Explain what is meant by the term “graduation” as it applies to mortality tables.

Answer 17

Graduation is a mathematical process that introduces smoothness and regularity to the mortality rates while preserving the basic characteristics of the observed data

Question 18

9.3.7 Explain when valuation mortality tables are used.

Answer 18

A valuation motility table is used as the basis for calculating minimum reserves and cash surrender values.

These tables usually have margins that render them conservative. Their use is prescribed by law

Question 19

9.3.8 Describe the impact of smoking on mortality rates.

Answer 19

Increases mortality rates substantially leading to higher premiums

Question 20

9.3.9 Explain why margins are included in the mortality rates of a valuation mortality
table

Answer 20

In the interest of conservatism, as a sound business practice

In tables for life insurance mortality is higher than actually expected. In tables for annuities it is the opposite

Question 21

9.3.10 Explain why annuitant mortality tables contain lower mortality rates than life
insurance mortality tables.

Answer 21

A margin is built in to the tables. Also individuals in poor health don’t usually purchase annuities whereas they do purchase life insurance

Also this allows for a margin of safety given increasing lifespans

Question 22

9.3.11 Describe select and ultimate mortality tables and explain why they are not used
in the group life insurance industry.

Answer 22

Select tables account for the fact that mortality for people who have just proven their good health is lower than those who haven’t. Ultimate tables are mortality rates after the effect has worn off.

They aren’t used for group insurance because no proof of health is required

Question 23

9.4.1 Describe the impact of smoking on morbidity rates.

Answer 23

Smokers have a higher rate of death, disability and higher health costs than non smokers

Question 24

9.4.2 State when morbidity tables are used.

Answer 24

To forecast the frequency of claims as well as the size and duration of the claim

Question 25

9.4.3 Discuss why data from published morbidity tables are of limited use in pricing
health care insurance (2 reasons)

Answer 25

1) Numerous variables affect health care costs such as geographic area and socioeconomic group which cannot be reflected in morbidity data
2) Published tables aren’t updated as frequently as is desirable since the data on healthcare becomes out of date quickly and insurer updates proprietary data more frequently than publishers do

Question 26

9.4.4 In general, describe 5 of the differences between mortality tables and
morbidity tables.

Answer 26

1) mortality tables are used to price policies with a specified claim amount whereas for morbidity the claim amount is unknown
2) Mortality tables are used only only to forecast death and date of onset of an insured event. Morbidity tables include size, severity and duration of the claim
3) it is more difficult to predict morbidity than mortality since there are fewer sources of credible data
4) One basic mortality table can be used for most life insurance policies whereas numerous morbidity tables are needed for most policies
5) Changes in mortality have trended slowly downward, morbidity can trend either direction an can move suddenly. The tables become out of date much more quickly

Question 27

9.4.5 If the probability of death at a certain age is 0.15 and the probability of disability
is 0.03, calculate the probability of living one year.

Answer 27

.85