CAS Exam 8 - Actex

Learn Today. Lead Tomorrow. ACTEX Learning

ACTEX Study Manual for

CAS Exam 8 Fall 2017 Edition

Margaret Tiller SherwoodFCAS, FSA, MAAA, FCA, CPCU, ARM, ERMP, CERA

ACTEX LearningNew Hartford, Connecticut

ACTEX Study Manual for

CAS Exam 8 Fall 2017 Edition

Margaret Tiller SherwoodFCAS, FSA, MAAA, FCA, CPCU, ARM, ERMP, CERA

Copyright © 2017, ACTEX Learning, a division of SRBooks Inc.

ISBN: 978-1-63588-067-0

Printed in the United States of America.

No portion of this ACTEX Study Manual may bereproduced or transmitted in any part or by any means

without the permission of the publisher.

Actuarial & Financial Risk Resource Materials

Since 1972

Learn Today. Lead Tomorrow. ACTEX Learning

ACTEX CAS Exam 8 Study Manual, Fall 2017 Edition

ACTEX is eager to provide you with helpful study material to assist you in gaining the necessary knowledge to become a successful actuary. In turn we would like your help in evaluating our manuals so we can help you meet that end. We invite you to provide us with a critique of this manual by sending this form to us at

your convenience. We appreciate your time and value your input.

Your opinion is important to us

Publication:

Very Good

A Professor

Good

School/Internship Program

Satisfactory

Employer

Unsatisfactory

Friend Facebook/Twitter

In preparing for my exam I found this manual: (Check one)

I found Actex by: (Check one)

I found the following helpful:

I found the following problems: (Please be specific as to area, i.e., section, specific item, and/or page number.)

To improve this manual I would:

Or visit our website at www.ActexMadRiver.com to complete the survey on-line. Click on the “Send Us Feedback” link to access the online version. You can also e-mail your comments to [email protected].

Name:Address:

Phone: E-mail:

(Please provide this information in case clarification is needed.)

Send to: Stephen Camilli ACTEX Learning

P.O. Box 715 New Hartford, CT 06057

TABLE OF CONTENTS

A. CLASSIFICATION RATEMAKING 1. ASOP 12 “Risk Classification (for All Practice Areas)” A1 2. Bailey & Simon “An Actuarial Note on the Credibility of Experience” A19 3. Mahler “Example of Credibility and Shifting Risk Parameters” A57 4. Robertson “NCCI’s 2007 Hazard Group Mapping” A79 5. Couret & Venter “Using Multi-Dimensional Credibility for Class Frequency Vectors” A99 6. GLM – Goldburd, “Generalized Linear Models for Insurance Rating” A119 Khare & Tevet

B. EXCESS, DEDUCTIBLE, AND INDIVIDUAL RISK RATING 7. Bahnemann 1 “Distributions for Actuaries” - Introduction B1 8. Bahnemann 2 “Distributions for Actuaries” - Claim Size TBD 9. Bahnemann 3 “Distributions for Actuaries” - Claim Counts TBD 10. Bahnemann 4 “Distributions for Actuaries” - Aggregate Claims TBD 11. Bahnemann 5 “Distributions for Actuaries” - Excess Claims TBD 12. Bahnemann 6 “Distributions for Actuaries” - Limits and Deductibles TBD 13. Bahnemann App “Distributions for Actuaries” - Appendix TBD 14. Fisher et al. 1 “Individual Risk Rating Study Note” - Experience Rating TBD 15. Fisher et al. 2 “Individual Risk Rating Study Note” - Risk Sharing Through TBD Retrospective Rating and Other Loss Sensitive Rating Plans 16. Fisher et al. 3 “Individual Risk Rating Study Note” - Aggregate Excess Loss TBD Cost Estimation 17. Fisher et al. 4 “Individual Risk Rating Study Note” - Concluding Remarks TBD 18. ISO Commercial General Liability Experience and Schedule Rating Plan TBD 19. NCCI 1 - ER Experience Rating Plan Manual for Workers Compensation and TBD Employers Liability Insurance 20. NCCI 2 - RR Retrospective Rating Plan Manual for Workers Compensation and TBD Employers Liability Insurance

C. CATASTROPHIC AND REINSURANCE PRICING 21. Grossi & Kunreuther 2 “An Introduction to Catastrophe Models and Insurance” C1 22. Grossi & Kunreuther 3 “The Risk Assessment Process” C15 23. Grossi & Kunreuther 4 “Use of Catastrophe Models in Insurance Rate Making” C21 24. Grossi & Kunreuther 5 “Sources, Nature, and Impact of Uncertainties on Catastrophe Modeling” C27 25. Grossi & Kunreuther 6 “Insurance Portfolio Management” C37 26. Clark “Basics of Reinsurance Pricing” C43 27. Bernegger “Swiss Re Exposure Curves and the MBBEFD Distribution Class” C119

NOTES

This is a limited edition of the CAS Exam 8 Study Guide that reflects the current readings on Parts A and C of the syllabus. The complete edition that includes the substantial syllabus changes on Part B is expected to be released mid-July. This limited edition reflects the relevant 2016 exam problems, as well as some I created for the new material. This is my fourth update of the manual originally written by Peter J. Murzda, Jr., FCAS, ASA and previously updated by Dean A. Westpfahl, FCAS, MAAA. At this point, there have been enough syllabus changes that most of the outline material is mine. For the current update, I reflected the 2017 syllabus material and included problems from the 2016 exam. For the many readings that are no longer on the exam, I retained those problems from past exams that I think are relevant to the current readings, making changes to reflect the new syllabus material where appropriate. Questions and parts of some solutions have been taken from material copyrighted by the Casualty Actuarial Society. They are reproduced in this study manual with the permission of the CAS solely to aid students studying for CAS exams. Students may also request past exams directly from the CAS or find them on the CAS website. I am very grateful to the CAS for its cooperation and permission to use this material. The CAS is not responsible for the structure or accuracy of this manual. In some cases, questions and answers have been edited or altered to be more accurate, reflect syllabus changes, or provide a better organized manual. Students should keep in mind that there may be more than one correct way to answer a question even if only one is shown. Exam questions are identified by numbers in parentheses at the end of each question. Questions have four numbers separated by hyphens: the year of the exam, the number of the exam, the number of the question, and the points assigned. There are some questions labelled 14-8-MTS-(point value). These are questions I added in 2014 on the syllabus material that was new in 2014. There also are some questions labelled 17-8-MTS-(point value). These are questions I added in 2017 for the syllabus material that is new in 2017. The past exam problems that are retained for which I made significant changes so that they reflect the new syllabus material are designated by: the year of the exam, the number of the exam, the number of the question & MTS, and the points assigned. I made a conscientious effort to eliminate mistakes and incorrect answers, but a few may remain. I am grateful to students who previously pointed out errors and encourage those who find others to bring them to my attention. Please check the ACTEX website for corrections subsequent to publication.

Margaret Tiller Sherwood FCAS, FSA, MAAA, FCA, CPCU, ARM, ERMP, CERA

June 2017

Section A

Classification Ratemaking

ASOP 12 A1

ACTEX Learning Classification Ratemaking CAS Exam 8 – Sherwood

Actuarial Standards Board, “Actuarial Standard of Practice No. 12, Risk Classification (for All Practice Areas),”

December 2005, Updated for Deviation Language Effective May 1, 2011

OUTLINE

I. SECTION 1. PURPOSE, SCOPE, CROSS REFERENCES, AND EFFECTIVE DATE

A. Purpose – Provides guidance to actuaries when performing professional services with respect to designing, reviewing, or changing risk classification systems.

B. Scope

1. Applies to all actuaries when performing professional services with respect to designing, reviewing, or changing risk classification systems used in connection with financial or personal security systems regarding the classification of individuals or entities into groups intended to reflect the relative likelihood of expected outcomes.

a. Expert testimony b. Regulatory activities c. Legislative activities d. Statements concerning public policy

2. Also applies when giving advice with respect to a risk classification system. 3. Risk classification can affect and be affected by many actuarial activities, such as:

a. Setting rates, contributions, reserves, benefits, dividends, or experience refunds b. Analysis or projection of quantitative or qualitative experience or results c. Underwriting actions d. Development assumptions

4. Standard applies when activities directly or indirectly involve designing, reviewing, or changing a risk classification system.

5. Also applies when performing such activities if those activities directly or indirectly are

likely to have a material effect on the intended purpose or expected outcome of the risk classification system.

6. Departures from this standard should be disclosed.

C. Cross References 1. Referenced documents are as amended, restated, or succeeding. 2. If there is a material difference from the originally referenced document, the actuary

should consider the guidance in this standard to the extent it is applicable and appropriate.

D. Effective Date – Any professional service commenced on or after May 1, 2006.

A2 ASOP 12


II. SECTION 2. DEFINITIONS

A. Advice - An actuary’s communication or other work product in oral, written, or electronic form setting forth the actuary’s professional opinion or recommendations concerning work that falls within the scope of this standard.

B. Adverse Selection - Actions taken by one party using risk characteristics or other information

known to or suspected by that party that cause a financial disadvantage to the financial or personal security system (sometimes referred to as antiselection).

C. Credibility - A measure of the predictive value in a given application that the actuary attaches to a

particular body of data (predictive is used here in the statistical sense and not in the sense of predicting the future).

D. Financial or Personal Security System - A private or governmental entity or program that is

intended to mitigate the impact of unfavorable outcomes of contingent events. Examples of financial or personal security systems include auto insurance, homeowners insurance, life insurance, and pension plans, where the mitigation primarily takes the form of financial payments; prepaid health plans and continuing care retirement communities, where the mitigation primarily takes the form of direct service to the individual; and other systems, where the mitigation may be a combination of financial payments and direct services.

E. Homogeneity - The degree to which the expected outcomes within a risk class have comparable

value. F. Practical - Realistic in approach, given the purpose, nature, and scope of the assignment and any

constraints, including cost and time considerations. G. Risk(s) - Individuals or entities covered by financial or personal security systems. H. Risk Characteristics - Measurable or observable factors or characteristics that are used to assign

each risk to one of the risk classes of a risk classification system. I. Risk Class - A set of risks grouped together under a risk classification system. J. Risk Classification System - A system used to assign risks to groups based upon the expected cost

or benefit of the coverage or services provided.

III. SECTION 3. ANALYSIS OF ISSUES AND RECOMMENDED PRACTICES

A. Introduction

1. Approaches to risk classification can vary significantly. 2. It is appropriate for the actuary to exercise considerably professional judgment.

B. Considerations in the Selection of Risk Characteristics

1. Relationship of Risk Characteristics and Expected Outcomes

a. The actuary should select risk characteristics that are related to expected outcomes.

ASOP 12 A3


b. A relationship exists if it can be shown that the variation in actual or reasonably anticipated experience correlates to the risk characteristic.

c. To demonstrate a relationship can use:

Analysis of available data Clinical experience Expert opinion

d. Rates are considered to be equitable (fair) if the differences in rates reflect

material differences in expected cost for risk characteristics. e. The actuary should consider the interdependence of risk characteristics and

make appropriate adjustments if their impact on the operation of the risk classification system is expected to be material.

f. It may be appropriate for the actuary to make inferences without specific

demonstration. For example, it might not be necessary to demonstrate that persons with seriously impaired, uncorrected vision would represent higher risks as operators of motor vehicles.

2. Causality – It is not necessary to establish a cause and effect relationship between the

risk characteristics and expected outcome. 3. Objectivity – The actuary should select risk characteristics that are capable of being

objectively determined. 4. Practicality – The actuary’s selection of a risk characteristic should reflect the tradeoffs

between practical and other relevant considerations such as:

a. Cost, time, and effort needed to evaluate the risk characteristic b. The ongoing cost of administration c. The acceptability of the usage of the characteristic d. Potential usage of different characteristics that would produce equivalent results

5. Applicable Law – The actuary should consider whether compliance with applicable law creates significant limitations on the choice of risk characteristics.

6. Industry Practices – The actuary should consider usual and customary risk classification

practices for the type of financial or personal security system under consideration. 7. Business Practices – The actuary should consider limitations created by business

practices related to the financial or personal security system as known to the actuary and consider whether such limitations are likely to have a significant impact on the risk classification system.

A4 ASOP 12


C. Considerations in Establishing Risk Classes

1. Intended Use a. A risk classification system should be appropriate for the intended use. b. Different sets of risk classes may be appropriate for different purposes. 2. Actuarial Considerations

a. Adverse Selection

Likely to occur if the variation in expected outcomes within a risk class is too great.

To the extent practical, the actuary should establish risk classes such that each has sufficient homogeneity with respect to the expected outcomes to satisfy the purpose for which the risk classification system is intended.

b. Credibility

It is desirable that risk classes be large enough to allow credible statistical inferences regarding expected outcomes.

When this is not possible, the actuary should balance considerations of predictability with considerations of homogeneity.

The actuary should use professional judgement to achieve this balance.

3. Other Considerations – The actuary should: a. comply with the applicable law; b. consider industry practices for that type of financial or personal security system

as known to the actuary; and c. consider limitations created by business practices of the financial or personal

security system as known to the actuary.

4. Reasonableness of results – The actuary should consider the reasonableness of results that proceed from the intended use of the risk classes such as:

a. consistency of the patterns of rates; b. consistency of values; and c. consistency of factors among risk classes.

ASOP 12 A5


D. Testing the Risk Classification System

1. Upon the establishment of the risk classification system and upon subsequent review, the actuary should, if appropriate, test the long-term viability of the financial or personal security system.

2. When performing such tests subsequent to the establishment of the risk classification

system, the actuary should evaluate emerging experience and determine whether there is any significant need for change.

3. Effect of Adverse Selection

a. Can potentially threaten the long-term viability of a financial or personal security system.

b. If the effects of adverse selection are expected to be material, the actuary should,

when practical, estimate the potential impact and recommend appropriate measures to mitigate the risk.

4. Risk Classes Used for Testing

a. The actuary should consider using a different set of risk classes for testing long-term viability than was used as the basis for determining the assigned values.

b. This is likely to improve the meaningfulness of the tests.

5. Effect of Changes – The actuary should consider testing the effects of changes:

a. if the risk classification system has changed; or b. business or industry practices have changed.

6. Quantitative Analyses – Depending on the purpose, nature, and scope of the assignment, the actuary should consider performing quantitative analyses of the impact of the following to the extent they are generally known and reasonably available to the actuary:

a. significant limitations due to compliance with applicable law; b. significant departures from industry practices; c. significant limitations created by business practices of the financial or personal

security system; d. any changes in the risk classes or the assigned values based upon the actuary’s

determination that experience indicates a significant need for a change; and e. any expected material effects of adverse selection.

E. Reliance on Data or Other Information Supplied by Others – Refer to ASOP No. 23, Data Quality.

A6 ASOP 12


F. Documentation

1. The actuary should document the assumptions and methodologies used in designing, reviewing, or changing a risk classification system in compliance with the requirements of ASOP No. 41, Actuarial Communications.

2. The actuary should also prepare and retain documentation to demonstrate compliance

with the disclosure requirements in Section 4.1 of this standard.

IV. SECTION 4. COMMUNICATIONS AND DISCLOSURES

A. Communications and Disclosures (Section 4.1)

1. When issuing actuarial communications under this standard, the actuary should comply with ASOP Nos. 23 and 41.

2. In addition, the actuarial communications should disclose any known significant impact

resulting from the following to the extent they are generally known and reasonably available to the actuary:

a. significant limitations due to compliance with applicable law; b. significant departures from industry practices; c. significant limitations created by business practices related to the financial or

personal security system; d. a determination by the actuary that experience indicates a significant need or

change, such as changes in the risk classes or the assigned values; and e. expected material effects of adverse selection; f. the disclosure in ASOP No. 41, section 4.2, if any material assumption or method

was prescribed by applicable law (statutes, regulations, and other legally binding authority);

g. the disclosure in ASOP No. 41, section 4.3, if the actuary states reliance on other

sources and thereby disclaims responsibility for any material assumption or method selected by a party other than the actuary; and

h. the disclosure in ASOP No. 41, section 4.4, if, in the actuary’s professional

judgment, the actuary has otherwise deviated materially from the guidance of this ASOP.

3. The actuarial communications should also disclose any recommendations developed by

the actuary to mitigate the potential impact of adverse selection.

ASOP 12 A7


PAST CAS EXAMINATION AND NEW QUESTIONS 1. The Supreme Court's decision in the Norris case eliminated the use of sex as a rating variable in

pensions. Discuss the potential implications of this decision on automobile insurance classification in the context of the considerations in the selection of risk characteristics discussed in ASOP 12.

(84–9–9 & MTS–3) 2. A property insurance company is considering adding a new classification rating variable to its

homeowners insurance program based on an individual risk's actual loss experience over the past five year period as follows:

Class A – no claims Class B – one or two claims Class C – three or more claims Considering the considerations in the selection of risk characteristics discussed in ASOP 12, would you recommend the addition of this new classification? Why or why not? (96–9–48b & MTS–1.5)

3. As the personal lines actuary for the department of insurance in the state of Crazyfornia, you have been

asked by the state's insurance commissioner to comment on Proposition 99.

Proposition 99 – The ratemaking for personal automobile insurance should be based on a new classification system using the following six criteria:

a) Insureds are to be classified based on nationality. b) Insureds are to be classified based on the ability to pass an annual random drug test. c) Insureds are to be classified based on whether they can pass a comprehensive, individually

administered eight-hour driving test every year. d) Insureds are to be classified based on their weights. e) Insureds are to be classified as either good eyesight or bad eyesight. Each eye doctor can have

his/her own definition of good/bad eyesight. f) Insureds are to be classified as right-handed or left-handed.

For each criterion, identify which one of the considerations in the selection of risk characteristics discussed in ASOP 12 is violated. You may not use the same consideration for more than two criteria. (97–9–48 & MTS–0.5/0.5/0.5/0.5/0.5/0.5)

A8 ASOP 12


1. ASOP 12 lists the following considerations in the selection of risk characteristics:

1) There should be a relationship between the risk characteristics and the expected outcome. 2) The risk characteristics should be objective. 3) The risk characteristics should reflect the tradeoff between practicality and other considerations. 4) Risk characteristics should comply with applicable law. 5) The actuary should consider industry practices in selecting risk characteristics. 6) The actuary should consider business practices in selecting risk characteristics. If the Norris case were applied to automobile insurance, it would violate 1) because the risk classification system would not reflect expected costs as males would be undercharged and females overcharged as one relevant cost-related factor would be disregarded. The resulting risk classification would meet considerations 2), 3), and 4). It would not meet 5) or 6).

2. See #1 for the list of considerations.

1) The proposed system would not reflect cost differences among risks or distinguish among risks on cost-based factors because past loss experience may not be a good indicator of future loss experience.

2) The system could be applied objectively. 3) The new system would entail extra costs without comparable benefits. In addition, public

acceptability would be questionable, given the random penalties the system would produce. 4) Whether the new system complies with the applicable law would have to be determined for each

state. 5) The new system is not current industry practice, which could be an advantage or disadvantage. 6) The new system is not current business practice and would add expense. On balance, I would not recommend the new classification.

3. See #1 for the list of considerations.

a. Need one of these. It is not objective (2). It does not comply with applicable law (4). b. Need one of these. There may not be a relationship between the risk characteristic and the

expected outcome (1). There is not practical due to the added expense (3). It may not comply with applicable law; this would have to be determined for each state (4).

c. It is not practical due to the added expense (3). d. There probably is not a relationship between the risk characteristic and the expected outcome

(1). e. It is not objective (2). f. There is no relationship between the risk characteristic and the expected outcome (1).

ASOP 12 A9


4. You are the actuary for Aggressive Mutual Insurance Company. The marketing department has approached you with a plan to increase business by liberalizing protection class definitions. The new definition would allow you to classify any risk within eight miles of the nearest fire department using the protection class of that town, without any verification of its ability to respond to the location of that risk.

a. Discuss this based on the relationship of risk characteristics and expected outcomes discussed in ASOP 12?

b. Based this discussion, what would you tell the marketing director about the appropriateness of

the proposed class definitions?. (99–9–43 & MTS–0.75/0.25)

5. Adverse selection is a financial threat to an insurance program's solvency. Based on ASOP 12, answer

the following.

a. Briefly describe adverse selection. b. Briefly explain when it is likely to occur in a risk classification system.

c. Briefly explain how to control it through the risk classification system.

(00–9–35 & MTS–0.5/0.5/0.5)

6. Which of the following describes a risk classification system that complies with the recommended

practices in ASOP 12? For each one that does not apply, make the appropriate correction or comment.

a. The system should be applied subjectively. b. The system should produce prices based on the observed actual losses of each risk. c. The system should reflect expected cost differences. d. The system should be based solely on complying with the law. e. The system should be the same for all competitors. (02–9–20 & MTS –0.25/0.25/0.25/0.25/0.25)

A10 ASOP 12


4. a. 1) The risk characteristics do not relate to the expected outcomes since those having a lower risk because they live next to a fire department are charged the same rate as those who a higher risk living almost eight miles away.

2) This system is not fair since those having a lower risk are charged the same as those

having a higher risk.

b. I would tell the marketing director this is not a good idea and recommend it not be carried out.

5. a. Adverse selection is the actions taken by one party using risk characteristics or other information known to or suspected by that party that cause a financial disadvantage to the financial or personal security system.

b. Adverse selection is likely to occur if the variation in expected outcomes within a risk class is

too great. c. To the extent practical, the actuary should establish risk classes such that each has sufficient

homogeneity with respect to the expected outcomes to satisfy the purpose for which the risk classification system is intended.

6. a. No – Substitute “objectively” for “subjectively.” b. No – Substitute “expected” for “observed actual.”

c. Yes. d. No –Complying with the law is only one of several factors. e. No – This is not mentioned.

ASOP 12 A11


7. Your company is planning to purchase a block of boatowners insurance business from Zeron. Zeron has raised overall rates on this block of business for three consecutive years, but does not classify risks by age or size. Despite the rate increases, loss ratios continue to worsen and growth remains high.

a. Explain how adverse selection could be impacting the seller's poor results. b. Using the information below, calculate rates to address the adverse selection problem. Briefly

justify your methods in light of the considerations in establishing risk classes discussed in ASOP 12.

Age Boat Ethnicity Group Size Group Exposures Premium Losses 1 Large A 75 15,000 4,600 1 Medium A 35 7,000 3,200 1 Small A 5 1,000 350 1 Large B 15 3,000 1,100 1 Medium B 20 4,000 1,800 1 Small B 45 9,000 6,500 2 Large A 100 20,000 11,000 2 Medium A 60 12,000 8,500 2 Small A 20 4,000 2,500 2 Large B 25 5,000 2,600 2 Medium B 25 5,000 2,800 2 Small B 50 10,000 7,200

(02–9–48 & MTS–1/3)

A12 ASOP 12


7. a. Age Boat Ethnicity Group Size Group Loss Ratio 1 Large A 0.307 1 Medium A 0.457 1 Small A 0.350 1 Large B 0.367 1 Medium B 0.450 1 Small B 0.722 2 Large A 0.550 2 Medium A 0.708 2 Small A 0.625 2 Large B 0.520 2 Medium B 0.560 2 Small B 0.720

Although loss ratios are lower for age group 1, larger boats, and in most cases ethnicity group A, Zeron charges them all the same rate. If a competitor of Zeron has a classification system that separates insureds based on these variables and charges appropriate premiums, insureds in low-risk groups are likely to switch to the competitor since they will receive a lower rate. As this happens, Zeron's book comes to be composed more and more of high-risk insureds and until its rates reflect this greater proportion of such insureds, it will have a higher loss ratio. If the switching to a competitor is gradual, what will happen is a continuing series of rate increases as each rate increase spurs other lower-than-average risk insureds to leave, creating the need for another rate increase.

b. Since using ethnicity as a variable is probably illegal and could create a business public perception problem if not, separate insureds by age group and size to calculate proposed premiums.

1) Calculate relativities for each combination of age group and boat size: Average Loss Ratio = (Total Losses)/(Total Premiums) = 52,150/95,000 = .549

Age group 1 Large boats 5,700/18,000 = .317 .317/.549 = .577 Medium boats 5,000/11,000 = .455 .455/.549 = .829 Small boats 6,850/10,000 = .685 .685/.549 = 1.248 Age group 2 Large boats 13,600/25,000 = .544 .544/.549 = .991 Medium boats 11,300/17,000 = .665 .665/.549 = 1.211 Small boats 9,700/14,000 = .693 .693/.549 = 1.262

2) Calculate the indicated premium:

Average Premium = (Total Premiums)/(Total Exposures) = 95,000/475 = 200

Age group 1 Large boats (200)(.577) = 115.40 Medium boats (200)(.829) = 165.80 Small boats (200)(1.248) = 249.60 Age group 2 Large boats (200)(.991) = 198.20 Medium boats (200)(1.211) = 242.20 Small boats (200)(1.262) = 252.40

ASOP 12 A13


8. List five considerations in establishing risk classes mentioned in ASOP 12. (17-8-MTS-1.25) 9. a. According to ASOP 12, what two items should an actuary balance regarding credibility? b. How should an actuary accomplish this balance? (17-8-MTS-0.5/0.5) 10. List four considerations in selecting risk characteristics mentioned in ASOP 12. (17-8-MTS-1.0) 11. Discuss casualty as a risk characteristic based on ASOP 12. (17-8-MTS – 1.0)

A14 ASOP 12


8. Any five of these are acceptable.

The considerations in establishing risk classes in ASOP 12 are: 1. A risk classification system should be appropriate for the intended use.

2. To the extent practical, the risk classes should have sufficient homogeneity with respect to the expected outcomes to satisfy the purpose for which the risk classification system is intended. 3. It is desirable that the risk classes be large enough to allow credible statistical inferences regarding expected outcomes. 4. The risk classes should comply with applicable law. 5. The actuary should consider industry practices in determining the risk classes. 6. The actuary should consider business practices in determining the risk classes. 7. The risk classes should produce reasonable results that proceed from the intended use of the risk classes.

9. a. An actuary should balance considerations of predictability with considerations of homogeneity.

b. An actuary should use professional judgment in achieving this balance.

10. Any four of these are acceptable.

1) There should be a relationship between the risk characteristics and the expected outcome. 2) The risk characteristics should be objective. 3) The risk characteristics should reflect the tradeoff between practicality and other considerations. 4) Risk characteristics should comply with applicable law. 5) The actuary should consider industry practices in selecting risk characteristics. 6) The actuary should consider business practices in selecting risk characteristics.

11. While the actuary should select risk characteristics that are related to expected outcomes, it is not

necessary for the actuary to establish a cause and effect relationship between the risk characteristics and expected outcome in order to use a specific risk characteristic.

ASOP 12 A15


12. a. You are given the following information: Type of Earned Number of Pure Vehicle Exposures Claims per Year Premium Cars 100,000 5,000 $200 Trucks 75,000 4,000 300

Would a classification plan that assigns cars and trucks to different classes make sense based on ASOP 12 requirements? Explain why or why not.

b. You are given the following information: Type of Earned Number of Pure Vehicle Exposures Claims per Year Premium

Type A 99,950 4,950 $199 Type B 50 5 2,199 Would a classification plan that assigns type A and type B cars make sense based on ASOP 12

requirements? Explain why or why not (04–9–23 & MTS–1.5/1.5)

13. A company is considering changing its age-of-home rating system, which has been in use for five years,

and has compiled the following data: Current ________________2005–7 Combined_____________ 2007 Age of Home Age Discount Earned Exposures Earned Premium ($)* Loss Ratio Loss Ratio 0 5% 40,000 28,000,000 54% 27% 1 5% 35,000 23,625,000 65% 62% 2 5% 35,000 23,100,000 65% 50% 3 3% 25,000 16,125,000 60% 48% 4 3% 20,000 12,600,000 45% 40% 5 3% 25,000 15,375,000 60% 53% 6+ 0% 30,000 18,000,000 60% 59% Total 210,000 136,825,000 63% 50% *At current discounts

Provide a recommendation whether the company should adopt each of the three changes below. Defend the recommendation on the basis of ASOP 12.

a. Set the discount for age 0 (new homes) to 15%, leaving other discounts unchanged.

b. Set the discount for age 4 to 25%, leaving other discounts unchanged.

c. Disaggregate the age 6+ group and implement discounts of 2% for age 6 and age 7 and 1% for age 8 and age 9, leaving discounts for age 10+ at 0%

(08–9–2 & MTS–1/1/1)

A16 ASOP 12


12. a. Frequency for cars = 5,000 / 100,000 = 0.050 Frequency for trucks = 4,000 / 75,000 = 0.053 Although the frequencies are similar, the pure premiums are very different. Each group has

enough vehicles to allow credible statistical inferences regarding expected outcomes. Therefore, it makes sense put cars and trucks in different rating classes.

b. Frequency for Type A cars = 4,950 / 99,950 = 0.050 Frequency for Type B cars = 5 / 50 = 0.100 Severity for Type A cars = 199 / 0.050 = 3,980 Severity for Type B cars = 2,199 / 0.100 = 21,990 Both frequency and severity are different, but Type B does not have enough vehicles to allow

credible statistical inferences regarding expected outcomes. Therefore, it does not make sense to put Type A and Type B cars in different rating classes.

13. a. Premium without discount = 28,000,000 / 0.95 = 29,473,684 Three-year losses = 28,000,000 x 0.54 = 15,120,000 Premium with proposed discount = 29,473,684 x 0.85 = 25,052,631 Three-year loss ratio with proposed discount = 15,120,000 / 25,052,631 = 60% It should adopt the discount. The classification is the one with the largest number of earned exposures, has sufficient credibility, and has a three-year loss ratio that brings the loss ratio with the proposed premium in line with those of the other rating classes.

b. Premium without discount = 12,600,000 / 0.95 = 13,263,158 Three-year losses = 12,600,000 x 0.45 = 5,670,000 Premium with proposed discount = 13,263,158 x 0.75 = 9,947,368 Three-year loss ratio with proposed discount = 5,670,000 / 9,947,368 = 57% It should not adopt the discount. Even though the three-year loss ratio with the proposed premium would be in line with those of most of the other rating classes, this is the classification with the fewest earned exposures. There also would be extreme premium discontinuities with ages 3 and 5 that would be problematic to explain to policy holders as their houses age.

c. The data presented are insufficient to make a recommendation regarding the proposed discount.

Splitting one classification into the several proposed should increase homogeneity, but the number of exposures in the three new groups might be too small to be credible.

14. The actuary should considerer:

1) the consistency of the pattern of rates; 2) the consistency of values; and 3) the consistency of factors.

ASOP 12 A17


14. This three items that the actuary should consider that proceed from the intended use of the risk classes in terms of whether or not the results are reasonable based on ASOP 12.

(17-8-MTS-0.75) 15. See Robertson 5c.

A18 ASOP 12


14. The actuary should considerer:

1) the consistency of the pattern of rates; 2) the consistency of values; and 3) the consistency of factors among risk classes.

15. See Robertson 5c.

CAS Exam 8 - Actex

Documents

Transcript of CAS Exam 8 - Actex