Study 7: Pricing the Risk - Summary

Question 1

A bucket of premium

Answer 1

• Premiums paid fill up a “bucket of money,” and all claims are paid out of that bucket
• Insurer must ensure they have enough in the bucket to pay claims, as well as other expenses, and still earn a reasonable profit
• Money in the bucket is sum of the pure premium (premium required to pay for insured losses) and expenses

Question 2

Factors for an insurer to consider when setting the price

Answer 2

• Development factors: adjustments to current reserves for claims that have yet to be settled, reflect the estimated final cost for those claims
• Trend factors: adjustments applied to all losses to reflect what they would probably cost if they had occurred next year rather than the past

Question 3

Three types of insurer expenses

Answer 3

• Acquisition costs: costs incurred by the insurer to conclude a contract of insurance with a policyholder
• Commission: fees paid to the agent or broker who mediated the transaction
• Administrative expenses: general expenses the insurer incurs to operate the business (ex. providing and maintaining premises, buying equipment, paying salaries etc.)

Question 4

Insurer profit

Answer 4

• The amount of money left to an insurer after it has paid all of its expenses
• Money in the bucket must always include provision for insurer’s profit
• Profit sometimes gets sacrificed for competitive pressures (ex. an insurer trying to grow the book may quote lower than they should to secure more policyholders)

Question 5

Other factors for premium allocation

Answer 5

• Unallocated loss adjustment expenses (ULAEs): costs which cannot be attached or attributed to a specific claim. Similar to administration costs (i.e. costs for claims department reports, head office support etc.)
• Premium should also be allocated for reinsurance expenses (taxes, licence or other fees)

Question 6

Offsetting underwriting loss with investment income

Answer 6

• Underwriters invest insurer’s capital. For the insurer to make a profit, the premium charged must include allowance for profit.
• If an insurer incurs $1.25 in loss for every $1 received in premium, it must finance the shortfall from its own resources
• Premiums can be invested to offset underwriting losses and produce profit for the insurer, but investment income depends on many factors beyond the insurer’s control and cannot sustain profitability indefinitely

Question 7

The role of the actuary

Answer 7

• Actuaries are professionals skilled in applying mathematics to financial problems
• Apply specialized knowledge of finance, statistics , and risk theory to problems faced by insurers
• Ratemaking (the process of compiling and analyzing data to establish rates that accurately reflect the level of risk) is done by actuaries

Question 8

Rating the risk

Answer 8

• Done by underwriters, and refers to the price of a unit of insurance for the policy period (usually a year)
• Ex. the rate for fire insurance might be $0.50 per $100 of insurance. If a building is insured for $100,000, the rate would be $100,000 x ($0.50 per $100) = $500.

Question 9

Three major components of any rate

Answer 9

• anticipated cost of settling claims;
• acquisition costs of the business, such as commissions; and
• cost of administering the process, including taxes levied on the premiums.

Question 10

The loss ratio

Answer 10

• Costs of settling claims
• Varies from one type of insurance to another, one location to another, and on the basis of various risk factors

Question 11

A rate will be adequate (i.e. sufficient to cover anticipated losses and expenses associated with the risk) when two conditions occur

Answer 11

1. The actuarial forecast of future losses based on past losses is accurate for the population.
2. The sample represented by the book of business written by a particular underwriter or insurer is representative of the population.

Question 12

8 steps to establish rate adequacy

Answer 12

1. Classify risks based on the types of objects of insurance, hazards of exposure, or both
2. Determine the number and nature of the rating classes
3. Select the proper measure of exposure
4. Gather loss statistics
5. Predict future losses based on past losses
6. Calculate the pure premium from the predicted losses
7. Calculate the total premium
8. Calculate the premium rate or unit cost

Question 13

Classify risks based on the types of objects of insurance, hazards of exposure, or both

(Establishing rate adequacy, step 1)

Answer 13

• The insurer’s first step is to decide what objects of insurance it wants to cover (ex auto, property, liability, marine etc.).
• Next, it must decide how to subdivide its chosen classes (ex. property can be divided into residential, commercial, public, etc.)
• Once it has determined the classes of objects, it can determine the exposures that each class represents (ex. residential property might include fire, lightning, windstorm, theft etc.)

Question 14

Determining the number and nature of the rating classes

(Establishing rate adequacy, step 2)

Answer 14

The insurer should choose a rating class, which should be large enough to allow a reasonable amount of data to be collected for it. The rate class should also reasonably discriminate between insureds so that it reflects the probable frequency and severity of loss that would be experienced by that class.

Question 15

Selecting the proper measure of exposure

(Establishing rate adequacy, step 3)

Answer 15

The proper measure is the exposure base (the denomination in which the unit of exposure is expressed). “Gross sales” can be an exposure base and is used for some classes of liability insurance. Ideally, the exposure base will reflect the frequency and severity of loss that the risk experiences.

Question 16

Gathering loss statistics

(Establishing rate adequacy, step 4)

Answer 16

Once rating classes and exposure bases have been determined, the insurer must gather information about loss experience for insureds that reflect those choices. The General Insurance Statistical Agency (GISA) is an independent agency which provides statistics for insurers.

Question 17

Three mandatory plans administered by GISA

Answer 17

• The Automobile Statistical Plan (ASP), commonly known as the Green Book, which applies to insurers in all nine of the jurisdictions for which GISA acts as statistical agent
• The Ontario Statutory Accident Benefits Statistical Plan (OSABSP)
• The Ontario Commercial Liability Statistical Plan (OCLSP)

Question 18

Predicting future losses based on past losses

(Establishing rate adequacy, step 5)

Answer 18

Predicting future losses involves applying the law of large numbers (a given probability becomes more reliable the larger the number of trials or cases in the sample) and the theory of probability (the likelihood of an occurrence, expressed by a ratio of the number of actual occurrences to the number of possible occurrences)

Question 19

Three factors that determine how reliable a prediction about loss experience will be

Answer 19

• The size of the sample: 1 house fire out of 10 houses is less useful than 100 house fires out of 10,000
• The time period over which the sample was taken: results which are duplicated over a number of years become more reliable than results from a single year
• Past and future conditions: the usefulness of statistics depends on how conditions have changed between past years and future years with the same results (ex. house fires may be more common in past years when there were fewer safety features)

Question 20

Calculating the pure premium from the predicted losses

(Establishing rate adequacy, step 6)

Answer 20

The pure premium is the premium required to pay claims.

Question 21

Calculating the total premium

(Establishing rate adequacy, step 7)

Answer 21

A dollar of insurance premium includes both the pure premium as well as the additional funds required to pay expenses. To calculate the total premium, the insurer must add amounts to the pure premium to account for these expenses.

Question 22

Calculating the premium rate or unit cost

(Establishing rate adequacy, step 8)

Answer 22

The premium rate or unit cost of insurance is calculated by dividing the total premium by the exposure unit

Question 23

Ratemaking for different lines of insurance

Answer 23

• The general process of ratemaking is refined for each type or class of risk
• For property risks, COPE factors will be looked at
• For auto risks, the classification and use of the vehicle and its territory will play a factor
• For liability, the nature and extent of potential liability exposures are examined
• Statistics must be collected over a long time and must represent as large a sampling as possible

Question 24

Class rating

Answer 24

• Class rating is used when statistics can be gathered on a large number of risks that share common characteristics
• Ex. same basic risk factors are present or absent for most automobile and homeowners risks
• Statistics gathered by the Insurance Bureau of Canada for the whole industry reflect a better average class cost per unit insured
• Rates developed by class rating method are applicable to broad groups of risks

Question 25

Schedule rating

Answer 25

• Some classes are individually rated because of their complexity and the need for underwriting judgement
• This is called schedule rating, and is used when the body of statistical data is too fragmented to permit class rating
• Rates are based on a schedule or manual that lists a multitude of characteristics identified by underwriters
• Involves the fixing of a base rate or key rate, which is used as the initial charge. Debits and credits are then applied based on factors that make the risk better or worse.

Question 26

The role of the underwriter in ratemaking

Answer 26

• Degree of flexibility available to an underwriter varies by the type of insurance and size of risk
• Rating and ratemaking are not purely science, but rather a combination of art and science. Underwriters must still apply practical experience and theoretical knowledge to do either one well.