This section of sample problems and solutions is a part of The Actuary’s Free Study Guide for Exam 6, authored by Mr. Stolyarov. This is Section 56 of the Study Guide. See an index of all sections by following the link in this paragraph.
Some of the questions here ask for short written answers. This is meant to give the student practice in answering questions of the format that will appear on Exam 6. Students are encouraged to type their own answers first and then to compare these answers with the solutions given here. Please note that the solutions provided here are not necessarily the only possible ones.
Blanchard, R.S., “Premium Accounting,” CAS Study Note, May 2005.
Original Problems and Solutions from The Actuary’s Free Study Guide
Problem S6-56-1. In “Premium Accounting” (p. 10), Blanchard describes two distinct roles that unearned premium may be seen as having. Describe these two roles and identify a situation in which they may result in different values for unearned premium.
Solution S6-56-1. The two roles described by Blanchard for unearned premium are
1. Estimating the insurer’s refund liability in the event the policy is cancelled and
2. Deferring revenue so that the timing of the insurer’s revenue matches the timing of the associated expenses.
If an insurer charges the policyholder a penalty when the policyholder initiates cancellation of the policy, then the unearned premium under approach 1 above would be lower than under approach 2, since the insurer would not be liable to refund the amount of the penalty to the policyholder.
Problem S6-56-2. Describe four situations in which it would probably not be appropriate to consider premium as being earned over time in a pro rata fashion. (See Blanchard, “Premium Accounting”, p. 10.)
Solution S6-56-2. In the following situations, it would probably not be appropriate to consider premium as being earned over time in a pro rata fashion:
1. Seasonal risks, where the exposure to risk varies depending on the time of year.
2. Aggregate excess-of-loss reinsurance policies, where the probability of exceeding the attachment point is higher at the end of the policy period than at the beginning.
3. Warranty products, where the risk is greater when the product subject to the warranty is older.
4. Performance bonds, where the risk of non-performance increases with the age of the contract. (See Blanchard, “Premium Accounting”, p. 10.)
Problem S6-56-3. (a) Define how the premium deficiency reserve is calculated and comment regarding the only situations in which a premium deficiency reserve would be established. (See Blanchard, “Premium Accounting”, p. 12.)
(b) If a balance sheet is established as of January 1, 2034, but events on March 1, 2034, substantially change the insurer’s estimate of future losses and expenses, should the unearned premium reserve and the premium deficiency reserve be effected? (See Blanchard, “Premium Accounting”, p. 13.)
(c) Give a numerical example of how the level of aggregation of an insurer’s operations can materially affect the premium deficiency reserve calculated for the insurer.
Solution S6-56-3. (a) A premium deficiency reserve is the difference between (1) “the losses and expenses expected from the runoff of the unexpired policy term” and (2) “the unearned premium liability already held with respect to the unexpired policy term” (Blanchard, “Premium Accounting”, p. 12). Note that fixed expenses are not considered. The only time a premium deficiency reserve is established is when the difference above is positive, i.e., losses and expenses expected from the runoff of the unexpired policy term exceed the unearned premium liability already held with respect to the unexpired policy term. Otherwise, no premium deficiency reserve is established.
(b) No, the unearned premium and premium deficiency reserves should not be affected by events that occur after the balance sheet date; these reserves are estimates of the insurer’s liability as of the balance sheet date and so should only be based on information known up to that date or anticipated as of that date.
(c) Many examples are possible. Here is a sample answer.
An insurer has two operations, 1 and 2, with the following characteristics:
Unearned Premium Liability of $4000
Estimated losses from the unearned premium runoff of $3610
Estimated expenses remaining from the runoff of the unearned premium liability: $300
Unearned Premium Liability of $5000
Estimated losses from the unearned premium runoff of $4800
Estimated expenses remaining from the runoff of the unearned premium liability: $500
There are two ways to aggregate: by operation or in total.
If the aggregation is performed by operation, then the premium deficiency reserve for Operation 1 is max(0, (3610 + 300) – 4000) = max(0, -90) = 0, and the premium deficiency reserve for Operation 2 is max(0, (4800 + 500) – 5000) = max(0, 300) = 300, for a total premium deficiency reserve of 0 + 300 = 300.
If the aggregation is performed for the entire insurer, then the premium deficiency reserve is max(0, (3610 + 300 + 4800 + 500) – (4000 + 5000)) = max(0, 210) for a total premium deficiency reserve of 210.
Problem S6-56-4. (a) On what basis are expected deficiencies in reserves typically allocated between the unearned premium reserve and the loss reserve? (See Blanchard, “Premium Accounting”, p. 14.)
(b) Explain the distinction between “finance charges” and “service charges” in U.S. regulatory accounting (See Blanchard, “Premium Accounting”, p. 15.)
(c) Assume an inflationary environment in which the annual inflation rate for expected losses is 30%.What fraction of the premium should be considered earned on a four-year insurance policy for the second year of the policy? Assume that the insurer wants an exact match between expected exposure to loss and earned premium.
Solution S6-56-4. (a) Expected deficiencies associated with events that have not yet occurred are typically reflected in the unearned premium reserve. Expected deficiencies associated with events that have already occurred are typically reflected in the loss reserve.
(b) In U.S. regulatory accounting, “finance charges” are payments pertaining to an installment plan that are a function of the amount of premium paid (and therefore have a similar role to that of interest). “Service charges” on the other hand are fixed monetary amounts that do not vary based on the amount of premium paid.
(c) We can assume that the expected loss is as follows:
1 in Year 1, 1.3 in year 2, 1.32 in year 3, 1.33 in year 4. If premium is earned in proportion to expected loss, then the fraction earned in year 2 would be 1.3/(1 + 1.3 + 1.32 + 1.33) = 0.2101179893 = 1300/6187.
Problem S6-56-5. (a) Explain the concept of “earned but unbilled” (EBUB) or “earned but not reported” (EBNR) premium and where it would be applied. (See Blanchard, “Premium Accounting”, pp. 16-17.)
(b) Explain how U.S. regulatory accounting requires the insurer’s liability for extended reporting periods to be treated. (See Blanchard, “Premium Accounting”, p. 17.)
Solution S6-56-5. (a) EBUB or EBNR premium occurs when the insurer can reasonably expect (on aggregate) that a certain amount of audit premium or reinstatement premium would be due to it, but has not established the exact amounts for specific insureds – as the audits or the events requiring reinstatement have yet to occur. The specific parties from which such premiums are to be due have not yet been identified, but the effect on the insurer’s accounting figures can nonetheless be considerable.
(b) U.S. regulatory accounting requires that the insurer’s liability for finite extended reporting periods be treated as unearned premium reserves and the liability for indefinite extended reporting periods be treated as loss reserves.
See other sections of The Actuary’s Free Study Guide for Exam 6.