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Ratemakingby Charles L. McClenahan

Copyright 2004 by All 10, Inc.

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Topic 1 : Basic Ratemaking Terminology & The Rating Plan

Exposures

While written exposures are the most common exposure base, it is not unusual to use statistics based onearned exposures orin-force exposures. The table below demonstrates the differences in these exposurebases.

4 Factors Affecting the Selection of an Exposure Base1. Reasonableness - the exposure unit should be a reasonable measure of the exposure to loss -

it will be difficult to establish a rate for the exposure when the variation inloss potential per exposure unit is large

2. Ease of Determination - if it is not measurable (i.e. # products in use) the insurer will never receivethe proper premium for the exposure

3. Responsiveness toChange

- exposure bases such as payroll, which change with exposure to loss, arepreferable to those which do not change as the exposure to loss changes

4. Historical Practice - a change from the historical exposure base could render historical dataunusable

Losses and Loss Adjustment Expenses

Claim data is generally aggregated based on the accident year(AY) and then evaluated at successive intervals as more losses arepaid and more information becomes available on unpaid claims. Asshown in Figure 1, AY case-incurred losses tend to increase overtime as they approach their ultimate value. This pattern is largelythe result of the reporting of claims which were not present atearlier evaluations. By introducing the concept of AY age, theindividual evaluations of AY case-incurred losses can be tracked inan orderly fashion. By convention, age is measured in months andthe last day of an AY is said to be age 12 months.

Probably the single most widely-used statistic in the analysisof insurance losses is the loss ratio, or losses divided bypremium.

Term DefinitionExposure The basic unit underlying an insurance premiumEarned Exposure The exposure units actually exposed to loss during the period in question

In-Force Exposure The exposure units actually exposed to loss at a given point in timeWritten Exposure The units of exposure on policies written during the period in question

Effective Written Exposures Earned Exposures In-ForceDate 1987 1988 1987 1988 @ 1/1/1988

1/1/1987 1.00 0.00 1.00 0.00 0.004/1/1987 1.00 0.00 0.75 0.25 1.007/1/1987 1.00 0.00 0.50 0.50 1.00

10/1/1987 1.00 0.00 0.25 0.75 1.00

Total 4.00 0.00 2.50 1.50 3.00

Term Abbreviation DefinitionAllocated LAE ALAE LAE which can be related to a specific claimLoss Adj Expense LAE The expenses associated with the claims settlement processUnallocated LAE ULAE LAE which cannot be related to a specific claim

Figure 1

AY Case-Incurred Loss Development

0

20

40

6080

100

0 6 12 24 36 48 60

Accident Year Age in Months

7/28/2019 e5sm Excerpt

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Ratemakingby Charles L. McClenahan

Copyright 2004 by All 10, Inc.

Page 3

Topic 1 : Basic Ratemaking Terminology & The Rating Plan (cont)

Frequency, Severity, Pure Premium, Rates and Policy Premium

As demonstrated above, pure premium, P, is a product of the frequency perunit of exposure, F1, and severity, S. In order to determine the rate or price of a

specific coverage, provision must also be made for profit, contingencies andexpenses (other than the LAE included in the pure premium). Generally, aportion of the expenses will be fixed (i.e., it is independent of the premiumvolume) while the remainder of the expenses and the profit and contingencieswill vary directly with the rate or price.

Finally, the policy premium is computed by multiplying the rate by the individualexposures covered by the policy.

The Rating Plan

The 3 Goals of Ratemaking are to determine rates which will:provide1. Sufficient Funds - provide sufficient funds to pay expected losses and LAE

2. Adequate Margin - maintain an adequate margin for adverse deviation3. Reasonable Return - produce a reasonable return on funds provided by investors

In addition to the ratemaking goals, rates are also subject to the regulatory standard that rates shall not beinadequate, excessive, or unfairly discriminatory between risks of like kind and quality. The primaryresponsibility of the actuary in this regard is to recommend rates which can be reasonably expected to beadequate over the period in which they are to be used. The various elements or classifications in the ratingplan allow identifiable differences in loss propensity to be reflected in the manual rating process.

2 Situations Resulting From the Failure to Reflect Differences in Loss Propensity:1. Skimming the Cream - if the rating plan does not reflect a positive characteristic (i.e. reduces loss

propensity), the rate applied to risks with that characteristic will be too highencouraging companies to insure these better risks to the exclusion ofother risks

2. Adverse Selection - if the rating plan does not reflect a negative characteristic, the rate will be toolow for those risks possessing the negative characteristic and will be toohigh for those risks which do not possess the negative characteristic. Ifother companies are reflecting this characteristic in their rating plans, therisks which do not possess the negative characteristic will be able to obtaininsurance more cheaply from other insurance companies and only thepoorer risks will purchase insurance from the insurer which does not reflectthe negative characteristic in its rating plan.

C = Claim Count E = Exposure Units F = Fixed Expenses

k = Scale Factor L = Losses P = Pure PremiumQ = Profit and Contingencies Factor R = Rate V = Variable Expenses

Term Symbol Definition FormulaFrequency Fk Number of claims per k exposure units F

k C

Ek =

*

Severity S Average loss per claimS

L

C=

Pure Premium P Average loss per unit of exposure1

L C LP F S

E E C= = =

Development of the Rate perUnit Exposure

R P F + VR QR = + +

( )R V Q- VR - QR = R = P + F1

RP F

V Q=

+

1