Assorted Exam-Style Questions for Actuarial Exam 6 -- Part 19

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.

Some of the problems in this section were designed to be similar to problems from past versions of Exam 6, offered by the Casualty Actuarial Society. They use original exam questions as their inspiration - and the specific inspiration is cited to give students an opportunity to see the original. All of the original problems are publicly available, and students are encouraged to refer to them. But all of the values, names, conditions, and calculations in the problems here are the original work of Mr. Stolyarov.

Sources:
Blanchard, R.S., "Accounting Concepts for the Actuary," CAS Study Note, June 2003.

Friedland, Jacqueline F. Estimating Unpaid Claims Using Basic Techniques. Casualty Actuarial Society. July 2010.

Past Casualty Actuarial Society exams: 2008 Exam 6 and 2009 Exam 6.

Original Problems and Solutions from The Actuary's Free Study Guide

Problem S6-46-1. Similar to Question 15 from the 2008 CAS Exam 6. You are performing a retrospective test for reserve accuracy and find the following deviations of the reserve estimates from actual results. All differences are expressed in the format (Amount at AY+1, Amount at AY+2, Amount at AY+3, Amount at AY+4), where AY is the accident year in question.

Percentage Deviations
AY 2032: (12.5%, -2%, -8%, 4%)
AY 2033: (6%, 12.4%, -4%)
AY 2034: (-4%, 4%)
AY 2035: (6.5%)

You are also given loss reserves distributed by year of payment as follows.
AY 2033: **********************Starting with (AY + 4): (234)
AY 2034: ***************Starting with (AY + 3): (2222, 255)
AY 2035:********Starting with (AY + 2): (3444, 2455, 300)
AY 2036: Starting with (AY + 1): (8000, 3555, 2600, 240)

(a) Find the weighted-average bias as of December 31, 2036. Use as your weights the contributions to the total reserve by payment year.

(b) If you used a straight arithmetic average of biases instead, identify two problems you would encounter.

Solution S6-46-1.

(a) First we select our percentage deviations for each payment year.

For AY + 1, we select the arithmetic mean of the four given percentages:
(12.5% + 6% - 4% + 6.5%)/4 = 5.25%.

We likewise select arithmetic means for the other payment years:
For AY + 2: (-2% + 12.4% + 4%)/3 = 4.8%.
For AY + 3: (-8% -4%)/2 = -6%.
For AY + 4: 4%.

We can also select our weights for each payment year by adding the reserves for that payment year.
For AY+1: 8000
For AY+2: 3444 + 3555 = 6999
For AY+3: 2222 + 2455 + 2600 = 7277
For AY+4: 234 + 255 + 300 + 240 = 1029.

Our weighted-average bias is thus
(8000*5.25% + 6999*4.8% + 7277*(-6%) + 1029*4%)/(8000 + 6999 + 7277 + 1029) = +1.546844025%.

(b) The following are two problems that would arise from using a straight arithmetic average of biases in this case:

1. There would be an overemphasis of the deviation for AY+4. Since the last payment year does not see nearly as much development as the others, it is appropriate to place a smaller weight on the deviation for that payment year.

2. There would be a general overestimation of the bias, as the simple arithmetic average would be (5.25% + 4.8% -6% + 4%)/4 = +2.0125%. Thus, the analyst might get the impression that the reserving method is more biased than is actually the case.

Problem S6-46-2. Similar to Question 19 from the 2008 CAS Exam 6. Match the following statements to the accounting paradigm to which they best pertain. Your choices are either (1) the deferral/matching paradigm or (2) the asset/liability paradigm.

(a) This paradigm emphasizes the income statement more than the balance sheet.

(b) This paradigm emphasizes the balance sheet more than the income statement.

(c) This paradigm focuses on temporal matching of revenues with expenses.

(d) This paradigm recognizes revenues and expenses as they are incurred, even if revenues are thereby separated from corresponding expenses.

(e) This paradigm allows for a "deferred expense" asset.

(f) This paradigm is more appropriate for a policy where coverage is provided over time in exchange for premium.

Solution S6-46-2.

(a) (1) The deferral/matching paradigm emphasizes the income statement more than the balance sheet.

(b) (2) The asset/liability paradigm emphasizes the balance sheet more than the income statement.

(c) (1) The deferral/matching paradigm focuses on temporal matching of revenues with expenses.

(d) (2) The asset/liability paradigm recognizes revenues and expenses as they are incurred, even if revenues are thereby separated from corresponding expenses.

(e) (1) The deferral/matching paradigm allows for a "deferred expense" asset.

(f) (1) The deferral/matching paradigm is more appropriate for a policy where coverage is provided over time in exchange for premium.

Problem S6-46-3. Similar to Question 20 from the 2008 CAS Exam 6. Identify whether each of the following statements applies to generally accepted accounting principles (GAAP) or statutory accounting principles (SAP):

(a) Used to evaluate an insurer's solvency.

(b) Allow for a "deferred expense" asset that is amortized over time.

(c) Require all acquisition expenses to be recognized immediately.

(d) Focus on the money that could be obtained if the firm were liquidated immediately.

(e) Used by investors and creditors to evaluate an insurer's position.

Solution S6-46-3.

(a) SAP are used to evaluate an insurer's solvency.

(b)GAAP allow for a "deferred expense" asset that is amortized over time.

(c) SAP require all acquisition expenses to be recognized immediately.

(d) SAP focus on the money that could be obtained if the firm were liquidated immediately.

(e) GAAP are used by investors and creditors to evaluate an insurer's position.

Problem S6-46-4. Similar to Question 21 from the 2008 CAS Exam 6. You have the following information about an insurer as of December 31, 2040:

Bonds - market value: $5555
Bonds - amortized value: $5100
Agents' balances - under 60 days: $540
Agents' balances - 60-90 days: $400
Agents' balances - 90+ days: $300
Deferred acquisition costs: $250
Bills receivable past due: $102
Furniture: $444
Loss and LAE reserve: $1341
Unearned premium reserve: $2322

What are the insurer's (a) GAAP assets, (b) GAAP liabilities, (c) SAP assets, and (d) SAP liabilities.

Solution S6-46-4. We consider which of the above will be recognized as assets by GAAP and SAP. GAAP recognize bonds at market value, while SAP recognize bonds at their amortized value (predetermined and independent of market changes). SAP do not recognize agents' balances in excess of 90 days or bills receivable past due. Also, SAP do not allow deferral of acquisition costs and do not recognize furniture as an asset. Both sets of principles will recognize the loss/LAE reserve and unearned premium reserve as liabilities.

(a) GAAP assets:
Bonds - market value: $5555
Agents' balances - under 60 days: $540
Agents' balances - 60-90 days: $400
Agents' balances - 90+ days: $300
Deferred acquisition costs: $250
Bills receivable past due: $102
Furniture: $444
Total: $7591

(b) GAAP liabilities:
Loss and LAE reserve: $1341
Unearned premium reserve: $2322
Total: $3663

(c) SAP assets:
Bonds - amortized value: $5100
Agents' balances - under 60 days: $540
Agents' balances - 60-90 days: $400
Total: $6040

(d) SAP liabilities:
Loss and LAE reserve: $1341
Unearned premium reserve: $2322
Total: $3663

Problem S6-46-5. Similar to Question 22 from the 2008 CAS Exam 6.

(a) What is the difference between a loss reserve and a premium deficiency reserve?

(b) Calculate the premium deficiency reserve as of December 31, 2025, given the following information:

Unearned premium reserve as of December 31, 2025: $4,340,000
Expected loss ratio on the unearned premium reserve as of December 31, 2025: 90%
Loss from occurrence on December 24, 2025, reported on January 6, 2026: $600,000
Estimated marginal expenses related to the runoff of the unearned premium reserve: $500,000
Ratio of fixed and general overhead expenses: 25%

Solution S6-46-5.

(a) A loss reserve is an estimate of unpaid losses as of a particular date. A premium deficiency reserve is set up relative to an unearned premium reserve, when the amount of the unearned premium reserve is not sufficient to cover all the future losses and expenses that would be associated with the unearned premium in question.

(b) This is somewhat of a trick question, because two of the given quantities are irrelevant to the premium deficiency reserve. Fixed and general overhead expenses are not used in determining whether there is a premium deficiency. Moreover, the loss occurring on December 24, 2025, will be considered in the loss reserve for 2025, irrespective of when it was reported.

Our premium deficiency is thus
Unearned premium reserve as of December 31, 2025 -
Expected losses on the unearned premium reserve -
Estimated marginal expenses related to the runoff of the unearned premium reserve =
$4,340,000 - 0.9*($4,340,000) - $500,000 = -$66,000.

Thus, the premium deficiency reserve should be $66,000.

See other sections of The Actuary's Free Study Guide for Exam 6.