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 49 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.
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.
Blanchard, R.S., “Accounting Concepts for the Actuary,” CAS Study Note, June 2003.
Casualty Actuarial Society Enterprise Risk Management Committee, “Overview of Enterprise Risk Management,” Casualty Actuarial Society Forum, Summer 2003, Section 3 and Appendix B.
Friedland, Jacqueline F. Estimating Unpaid Claims Using Basic Techniques. Casualty Actuarial Society. July 2009.
Past Casualty Actuarial Society exams: 2008 Exam 6.
Original Problems and Solutions from The Actuary’s Free Study Guide
Problem S6-49-1. Similar to Question 23 from the 2008 CAS Exam 6.
(a) What is the “10-10” rule for risk transfer for reinsurance contracts?
(b) Give an example of a quota share reinsurance treaty for which the “10-10” rule does not hold, but which nonetheless entails significant risk transfer.
(c) Give an example of an excess-of-loss reinsurance treaty for which the “10-10” rule does not hold, but which nonetheless entails significant risk transfer.
Solution S6-49-1. (a) The “10-10” rule states that, in order for risk transfer to occur under a reinsurance contract, the reinsurer must have a 10% loss with at least a 10% probability – i.e., a 10% or greater loss exists at the 90th percentile of the loss distribution.
(b) A quota share can be with respect to a book of business of a highly profitable primary insurer that only experiences a loss less than 10% of the time. Since the reinsurer shares in the primary insurer’s fortunes, even a substantial quota share can result in the reinsurer experiencing profits 90% or more of the time. Thus, the “10-10” rule fails, but there is unambiguous risk transfer, as the reinsurer is assuming responsibility for a substantial share of the primary insurer’s book of business.
(c) An excess-of-loss treaty, especially a catastrophe treaty, may have a high attachment point that is rarely reached, but, when reached, is often exceeded substantially. For instance, assume a catastrophic event that occurs with 5% probability and brings about $4,000,000 in losses. If an excess-of-loss treaty has an attachment point of $1,000,000, then the reinsurer will have no losses 95% of the time and immense $3,000,000 losses 5% of the time. This is clearly a situation of risk transfer, but the “10-10” rule fails.
Problem S6-49-2. Similar to Question 24 from the 2008 CAS Exam 6. How might the “Notes and Disclosures” section of a financial report address the following topics: (a) uncertainty, (b) future developments, and (c) accounting practices?
Solution S6-49-2. The “Notes and Disclosures” section of a financial report may (a) discuss uncertainty associated with various insurance liability estimates and values that may not be possible to estimate with precision, (b) address estimates of future events and earnings that have not yet occurred as of the report’s publication date, and (c) discuss what accounting policies were used in the financial statements’ creation. (See Blanchard, “Accounting Concepts for the Actuary”, p. 6.)
Problem S6-49-3. Similar to Question 26 from the 2008 CAS Exam 6. A quota share treaty has the following conditions:
Ceded share: 44%
Ceding commission: 30%
Subject earned premium: $500,000
Ultimate loss and ALAE on subject business: $250,000
(a) What is the net earned premium for the ceding insurer?
(b) What is the ultimate retained loss for the ceding insurer?
(c) What is the reinsurer’s gain or loss?
(d) What are two reasons for which the primary insurer may be interested in this quota share treaty?
Solution S6-49-3. (a) The net earned premium for the ceding insurer is the subject earned premium multiplied by (1 – ceded share): 500000*(1-0.44) = $280,000.
(b) The ultimate retained loss for the ceding insurer is the ultimate loss and ALAE multiplied by (1 – ceded share): 250000*(1-0.44) = $140,000.
(c) The reinsurer receives 500000*0.44 = $220,000 in premium and also pays 30% of this amount as ceding commission, thus keeping only 220000*0.7 = $154,000. The reinsurer’s share of losses is 250000*0.44 = $110,000, meaning that the reinsurer’s net result is $154,000 – $110,000 = a gain of $44,000.
(d) The primary insurer may be interested in this quota share treaty to (1) obtain surplus relief for a rapidly growing book of business and (2) increase large line capacity and insure risks with a higher total insured value than would otherwise be possible.
Problem S6-49-4. Similar to Question 27 from the 2008 CAS Exam 6. You have the following information for an insurer by accident year (AY).
Reported loss as of December 31, 2044: 20300
Selected IBNR as of December 31, 2044: 4000
Reported loss as of December 31, 2045: 23500
Reported loss as of December 31, 2044: 12444
Selected IBNR as of December 31, 2044: 10340
Reported loss as of December 31, 2045: 21230
Reported loss as of December 31, 2044: 6005
Selected IBNR as of December 31, 2044: 18000
Reported loss as of December 31, 2045: 13000
You also have the following selected reported loss development factors to ultimate:
From 12 months: 2.602
From 24 months: 1.983
From 36 months: 1.252
From 48 months: 1.055
(a) Based on the selected IBNR and the selected reported loss development factors, what is the expected loss emergence during calendar year 2045 for AY 2042 through AY 2044?
(b) Based on the data and calculations, what conclusions can be drawn regarding the accuracy of the expected loss emergence estimate, compared to actual loss emergence?
Solution S6-49-4. (a) We calculate the expected loss emergence for each accident year as
(Selected IBNR)*((LDF as of Dec. 31. 2044)/(LDF as of Dec. 31. 2045) – 1)/((LDF as of Dec. 31. 2044) – 1).
Expected loss emergence for AY 2042: 4000*(1.252/1.055 – 1)/(1.252 – 1) = 2963.965007.
Expected loss emergence for AY 2043: 10340*(1.983/1.252 – 1)/(1.983 – 1) = 6141.579373.
Expected loss emergence for AY 2044: 18000*(2.602/1.983 – 1)/(2.602 – 1) = 3504.340484.
(b) We calculate the actual loss emergence.
For AY 2042: 23500 – 20300 = 3200.
For AY 2043: 21230 – 12444 = 8786.
For AY 2044: 13000 – 6005 = 6995.
For each accident year, actual loss emergence considerably exceeds expected loss emergence. Thus, we can conclude that the selected reserving method is prone to underreserving.
Problem S6-49-5. Similar to Question 41 from the 2008 CAS Exam 6.
(a) Why does a focus solely on increasing the stock price of a company inconsistent with the definition of Enterprise Risk Management (ERM)?
(b) What broad categories of risk are considered under an ERM approach?
(c) With respect to financial risks, why does a focus solely on avoiding or reducing these risks not qualify as ERM?
Solution S6-49-5. (a) The definition of ERM requires both a short-term and a long-term focus on the firm’s value – and the focus is on value for all stakeholders, not just shareholders. Focus on the stock price only reflects a short-term value for stockholders.
(b) The four categories of risk considered under an ERM approach are (1) operational risk – related to business operations such as human resources, leadership, information technology, and information reporting; (2) hazard risk – physical damage and injuries and the resulting loss of revenue; (3) financial risk – including commodity risk, credit risk, foreign exchange risk, and risk posed by macroeconomic factors such as inflation; and (4) strategic risk – risks arising from such phenomena as competition, reputational damage, technological innovation, and regulatory and political trends. (See CAS Overview of Enterprise Risk Management, p. 111.)
(c) ERM focuses not just on reducing or avoiding risks, but also on exploiting them when this can raise the value of the firm. Some exposure to risk may be preferable for increasing the firm’s value than no exposure at all. Calculated risks in the financial market may thus be pursued and not avoided.
See other sections of The Actuary’s Free Study Guide for Exam 6.