ALL 10 STUDY PROGRAM COMPONENTS

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1 ALL 10 STUDY PROGRAM COMPONENTS CAS EXAM 8 ADVANCED RATEMAKING Classification Ratemaking, Excess, Deductible, and Individual Risk Rating and Catastrophic and Reinsurance Pricing SYLLABUS SECTION A: CLASSIFICATION RATEMAKING ARTICLE REVIEW AN ACTUARIAL NOTE ON THE CREDIBILITY OF EXPERIENCE OF A SINGLE PRIVATE PASSENGER CAR Study Program Evaluation Materials Fall 2013 CAS Exam 8 Register for free materials and access our online demo system at

2 Study Program Component A. Study Guide Online STUDY PROGRAM MATERIALS B. Learning Objectives and Knowledge Statements Online C. Article Summary Study Manual D. Past CAS Questions Study Manual E. Solutions to Past CAS Questions Study Manual F. Pre-populated and Blank Notecards Online G. Content Examined by Article- Online H. Content Examined by Syllabus Section- Online I. Article Formulas Online J. Reassembled Past CAS Exams K. Independently Authored Questions and Solutions - In Paper Format (for ultimate study program buyers) L. Modified Past CAS T/F, MC, Computational Questions - Online M. Past CAS Essay Questions Online To provide exam 8 candidates with an example of our study program components, the following is a compendium of the of Study Aids we provide for the exam 8 syllabus reading by Bailey, R.A.; and Simon, L.J., An Actuarial Note on the Credibility of Experience of a Single Private Passenger Car, PCAS XLVI, 1959, pp Including discussion of paper: Hazam, W.J., PCAS XLVII, 1960, pp. These study aids are provided to our customers in a variety of ways: some in study manual format, some in downloadable pdfs, and others in printer friendly HTML versions, the latter being accessible from our website from late June to late October of Study Aids that have been developed, but which are not included in this packet, are: Modified Past CAS T/F, MC, Computational Questions - Online Similar study aids have been developed for the remaining Exam 8 Syllabus Readings. All 10 Study Program Excerpt - ACTUARIAL NOTE ON THE CREDIBILITY OF EXPERIENCE - Fall 2013 Page 2

3 Description of our Study Program Components A. Study Guide Online ( syllabus reading review): Our online study guide provides candidates with article review commentary that ties key content found in the syllabus readings, our Actuarial Notes and past CAS exam questions. It is intended to be read PRIOR to conducting a review of the syllabus reading, our Article Notes, and the working past CAS questions. In more detail, our online study guide provides candidates with the following: Introductory commentary that puts the article in context. Here, you ll get the gist of the article and the high level view so that it s clear where the important topics and concepts fit in. Next, we ll look at how heavily this article has been tested in the past, which helps you get an idea of how much time you should devote to studying it. We list the topics that we ve selected for pre-populated note-cards, since these represent the key concepts in the article. Finally, we point out important sections within the article so that you know to give them special attention while you re studying. Online article review commentary, released every Monday on a weekly basis over a 13 week period, according to our recommended syllabus reading schedule, begins Monday, June 24. B. Learning Objectives and Knowledge Statements - Online Lists the learning objectives, knowledge statements, and the other articles to which they apply, for each article on the exam syllabus. C. Article Summary Study Manual We conduct a page by page review of the most important contact within a syllabus reading, and then summarize it for you. This eliminates hundreds of hours from you doing so during your course of study. D. Past CAS Questions Study Manual. Contains past CAS questions drawn from the content of each article on the current syllabus, dating back to when the article first appeared on the exam. E. Solutions to Past CAS Questions Study Manual. The quality of the solutions in our manuals differentiates us from those found in our competitor's products. We typically spend 2+ hours developing a comprehensive solution to 3-5 point problems asked on past CAS exams. Having spent this amount of time on the hundreds of solutions to past CAS questions dating back to the 1990s, we have produced a first class study aid second to none. Model solutions offered by the CAS are efficient, however they are not educational. They don t explain the rationale behind the solution, often leaving candidates wondering how one gets from one step to the next. Also, they may contain one or several mathematical errors in the solution. These issues lead candidates to spend unnecessary time determining why their solution (which maybe correct) does not agree with the CAS model solution. F. Pre-populated and Blank Notecards Online Having access to pre-populated notecards significantly reduces the amount of time candidates have to devote to accomplishing this task. Even better, the content of these note cards are tied specifically to a CAS learning objective and knowledge statement. Preparing self created notecards, given a thoroughly constructed template for you to use, provides candidates to put down, in their own words, responses to likely CAS essay based questions. Over 250 pre-populated note cards are available. G. Content Examined by Article- Online Lists the points examined over the past 5 years, and the content examined in terms of topics tested, year, question number, question type, and points. Candidates also have to the ability to record the difficulty level of past CAS questions to determine which questions need to be reviewed more closely at a later point in time. H. Content Examined by Syllabus Section- Online This report details the total points tested per article within a given syllabus section over the last three years. All 10 Study Program Excerpt - ACTUARIAL NOTE ON THE CREDIBILITY OF EXPERIENCE - Fall 2013 Page 3

4 Description of our Study Program Components I. Article Formulas Online Identifies what formulas were necessary to answer computational based questions appearing on past CAS exams. Over a 13 week period, we spend a significant amount of time developing and updating our online Formula Sheets. Streamline your exam preparation by logging in each Monday, beginning June 24, to printout our Formula Sheets. When faced with a 1.5 to 2 point problem, candidates have approximately minutes to answer it correctly. To answer such a question in the time allotted, candidates need to formulate a step by step problem solving approach, know the formulas needed to answer such a question, and do so in a timely manner. We provide candidates with formula sheets to answer CAS questions dating back to 2000 so that they can solve such problems using a step by step approach. That s a lot of formulas and formula sheets! We know of no other study program provider that does so, and believe this is just one aspect of our study program that sets us apart. J Reassembled Past CAS Exam Questions This set of five exams is made up of computational and essay questions (over 125 in total) that were actually asked of candidates on past CAS exams. These are relevant, meaningful, helpful, and useful tests, since by using actual CAS questions they simulate as closely as possible what you will see when you sit for a real CAS exam. K Independently Authored Questions and Solutions - In Paper Format Our Independently Authored Preparatory Tests comprise: * One set of three MC exams consisting of over 80 modified past CAS MC and computational questions (in Paper Format) * One set of five exams with over 125 challenging questions and solutions (In Paper Format). This set of 5 exams contains computational and essay based questions only. The recommended time to complete each exam is 2.5 hours. These tests also Include questions and solutions to articles added since the release of the 2007 Exam 9 syllabus, since few past CAS questions exist. CAS examiners develop questions that are aligned as closely as possible to the guidance given in the CAS Learning Objectives and Knowledge Statements. Therefore, we've aligned the questions appearing in these independently authored exams with the CAS Learning Objectives and Knowledge Statements. Together, these tests contain a superior set of exam questions relative to having access to only online modified past CAS MC and Computational Preparatory Tests. The results from these exams provide candidates with a good indication of where their strengths and weakness lie, weeks before the Fall 2013 CAS Exam. L Modified Past CAS T/F, MC, Computational Questions Online The modified Past CAS question Tests contain true/false, multiple choice, and computational questions. These preparatory tests comprise a set of five online exams which are auto graded. Each of the exams covers mutually exclusive subsets of the entire syllabus readings for a particular CAS exam. These tests contain the same type of questions, but are different from those questions appearing in K. below. M Past CAS Essay Questions Online (available but not included in this packet) These preparatory tests are comprised of a set of five online exams. The questions on these exams are actual past CAS essay questions. Candidates are encouraged to take these exams and compare their answer to model solutions. Why take these exams? We know of no other way candidates can best prepare themselves to answer essay based questions on the exam, especially since essay based questions represent approximately 30% of the total points that are asked on the exam. Also, by providing candidates with blank notecards for each article, candidates can further prepare themselves to answer essay based questions. Finally, we know of no other study materials provider that emphasizes the importance for candidates to prepare for such questions, let alone, provide them with tools to prepare for essay based questions. All 10 Study Program Excerpt - ACTUARIAL NOTE ON THE CREDIBILITY OF EXPERIENCE - Fall 2013 Page 4

5 Small Default Large Article Notes:...Credibility of Experience of a Single Private Passenger Car - Bailey, R.A. et. al. Article URL: Noteworthy Concepts/Issues within the Article ARTICLE COMMENTARY The Learning Objectives (LOs) and Knowledge Statements (KSs) are highly relevant to preparing for questions associated with this article. In particular, KS a., b. and c. under both LO 1 should be kept in mind when studying this article. CONTENT EXAMINED Number of Questions and Points Tested over the past 5 years Article Total Questions and Points #1, 2.0 pts #1, 3.5 pts #1, 1 pt #1, 3 pt #1, 2.5 pts Article Comp Questions and Points #1, 2.0pts #1, 3.5 pts #1, 1 pt #1, 3pts #1, 2.5 pts PRE-POPULATED NOTECARDS - Topics 1. A generic experience rating modification formula 2. Credibility for classes with claim experience 3. 2 criteria for which credibility for experience rating depends on 4. Differentiate Experience Rating from Class Ratemaking 5. Article Conclusions STUDY MANUAL REVIEW We recommend reading this article several times for a variety of reasons, one being that it is "short and fairly clear". In addition, it's hard for CAS examiners to test "new" content associated with this article since it has been on the syllabus for quite a while. We have added pre-populated notecards for you to print out. Make sure you also print out blank notecards for you to complete now, so that you can simply review them in late October. We suggest that you prepare note cards based on the lists identified in the manual. Knowing this, the key questions you are likely to see on the exam are as follows. Note: There is overlap in the concepts tested (a. through e. listed below). However, such a breakdown helps the candidate focus on the concepts test in categories a. - e. below. a. Compute credibility for classes with and without claim free experience. Work problems: '91,27; '93,6; '94,8; '94,31; '95,30; '00, 32; '02,47; '03,22; '04,2; '06,2; '07,2;'09,4; '10,5 b. Explain why credibility is expected to vary approximately in proportion to the average claim frequency. Work problems: '92,43; '96, 50; '97,19; '98, 26; '01,2; '03,2; c. Explain why credibility for experience periods of one, two and three years would be expected to vary approximately in proportion to the number of years. Read page 160 and reference Tables 3 and 4 and Appendix 1. Work problems: '94,9; '95,32; '99,1; '07,2; '08,5; '11,1 d. According to Hazam, what exposure base does he suggest using and what two conditions must be met to use such an exposure base for computing credibility. Work problems: '95;6; '01,22; '12,6 e. Derive the formula for the credibility assigned to the experience of drivers with one or more claims in the past year. Work problems: '05;6; Bailey Article Formulas

6 Small Default Large Article Notes:...Credibility of Experience of a Single Private Passenger Car - Bailey, R.A. et. al. Article URL: Learning Objectives / Knowledge Statements A. Classification Ratemaking Range of weight for Section A: percent Learning Objective: 1. Identify and evaluate possible rate classes. Knowledge Statement: a. Characteristics of appropriate classifications b. Sampling techniques c. Credibility considerations d. Statistical significance Other articles associated with this Learning Objective: Risk Classification SOP (AAA) An Example of Credibility and Shifting Risk Parameters (Mahler, H.C.) NCCI's 2007 Hazard Group Mapping (Robertson, J. P.) Learning Objective: 2. Translate the class differentials into price differences. Knowledge Statement: a. Multidimensional relativities b. Credibility techniques Other articles associated with this Learning Objective: Multi-Dimensional Cred to Est Class Freq Vectors in WC (Couret & Venter)

7 An Actuarial Note On The Credibility of Experience Of A Single Private Passenger Car Bailey and Simon The experience of the Canadian merit rating plan, for private passenger cars, provides a means of evaluating the experience rating credibility of one car. The Canadian experience is drawn from virtually every insurance company operating Canada. Merit Rating in Canada 1. Depends on the number of full years since the insured's most recent accident (or licensing). Ratings A X Y B A+X A+X+Y Description of Ratings Three or more years since the most recent accident. Two years since the most recent accident. One year since the most recent accident. Zero years since the most recent accident. Two or more years accident-free years. One or more years accident-free years. Excerpt from Table 1 Class 1 - Pleasure - no male operator under 25 Claim Frequency Merit Earned Car Earned Premium No. of Claims per $1000 of Relative Rating Years at Present B Rates Incurred Premium to Total * (1) (2) (3) (4) (5) A 2,757, ,108, , X 130,706 7,910,000 13, Y 163,544 9,862,000 19, B 273,944 17,226,000 37, Total 3,325, ,106, , A+X 2,888, ,018, , A+X+Y 3,051, ,880, , Formula (3) / (2) (4) / (4 tot) *(Values in bold used in the next table ) Class 2 - Pleasure - Non principal male operator under Earned Premium is converted to a common rate basis using the relationship A:X:Y:B = 65:80:90: Relative claim frequency is calculated based on premium rather than car years. This avoids the maldistribution that results when higher claim frequency territories produce more X, Y, and B risks, and thus results in higher territorial premiums. 4. Experience rating formula: Modification = ZR + (1-Z). Z = credibility. R = ratio of the actual losses to expected losses. 5. By setting the Modification = the subsequent experience (relative claim frequency) of experience rated risks and R = the past experience, the formula can be solved for the credibility. 0 When R = = 0, as it does for accident free risks, Credibility (Z) = 1 - Modification. E[losses] Copyright 2012 by All 10, Inc. Page 26

8 The Credibility of Experience Of A Single Private Passenger Car Classes with claim free experience Mod = Relative claim frequency = Column (5) from table 1. R = 0 Z = 1 - Mod Classes with claim experience Mod = Relative claim frequency = Column (5) from table 1. R = (1 - e -m ) -1. m = true claim frequency. Z = Mod - 1 R - 1 Tables 2 and 3 based on rounded values in table 1. Class 2-5 results from the reading. Summarization by Class Ratio of Claim 3 year 2 and 3 years of Credibility ( for R=0, Z=1-Modification) Frequency credibility to credibility relative to Class 1 Year 2 Years 3 Years per Car year claim freq 1 year of credibility (6) (7) (8) (9) (10) (11) (12) 1* lowest highest Formula: 1.0-(5)A+X+Y 1.0-(5)A+X 1.0-(5)A (3 tot)/(1 tot) (8)/(9) (7)/(6) (8)/(6) * Based on rounded values in table 1. Class 2-5 results obtained from the reading. If the variation of an individual insureds' chances for an accident were the same within each class (see next paragraph), the credibility would be expected to vary approximately in proportion to the average claim frequency (see the 2nd paragraph below, Appendix 1; and the bold values in the table above). Since classes 2, 3, 4, and 5 are more narrowly defined than Class 1 (see table 1 from the reading), it is expected that there will be less variation in the individual hazards within those classes, (the degree of variation within these classes is similar, as shown in column (10)). Thus, credibility for experience rating depends on: the volume of data in the experience period, and also the amount of variation of individual hazards within the class. If an insured s chance for an accident remained constant from one year to the next, and if there were no risks leaving or entering the class, the credibilities for experience periods of 1, 2 and 3 years would be expected to vary in proportion to the number of years. (see Appendix 1 below). The fact that the relative credibilities in columns (11) and (12) are much less than 2.00 and 3.00 is partially caused by risks entering and leaving the class. But it can be fully accounted for if: (a) an individual insured's chance for an accident changes from time to time within a year, or from one year to the next, or (b) the risk distribution of individual insureds has a marked skewness reflecting varying degrees of accident proneness. Key Definitions: Experience Rating a procedure to find the deviation, of an individual risk, from the average risk. Class Ratemaking a procedure to find the average, and where an increase in the volume of the experience increases the reliability of the indication only in proportion to the square root of the volume. Copyright 2012 by All 10, Inc. Page 27

9 The Credibility of Experience Of A Single Private Passenger Car Summary: The experience for 1 car for 1 year has significant and measurable credibility for experience rating. In a highly refined private passenger rating classification system which reflects inherent hazard, there would not be much accuracy in an individual risk merit rating plan, but where a wide range of hazard is encompassed within a classification, credibility is much larger. If we are given 1 years experience and add a 2nd year, we increase the credibility roughly 2/5. Given 2 years experience, a 3rd year will increase the credibility by 1/6 of the two year value. (See the relative credibility values in Table 4 of the reading). Appendix 1: Illustrates that the credibilities would vary approximately in proportion to the number of years. This illustration uses a Poisson distribution. Since an increase in the annual frequency has the same effect as an increase in the length of time, it can be similarly shown that the credibilities would vary approximately in proportion to the average annual frequency. Consider 3 types of risks with an inherent hazard measured by a Poisson frequency distribution: P(x) = m x e -m / x!, where the number of risks and their true claim frequency are shown respectively in columns (b) and (a) below. Note: For a person accident free for 1 year, P(x) = e -m. Also, the sum of Poisson random variables are Poisson distributed with a parameter = the sum of the parameters. Claim No. of people claim-free for the past t years No. of claims in the subsequent year Frequency t=0 t=1 t=2 t=3 t=0 t=1 t=2 t=3 (a) (b) (c) (d) (e) (f) (g) (h) (i) ,000 95,123 90,484 86,071 5,000 4,756 4,524 4, ,000 90,484 81,873 74,082 10,000 9,048 8,187 7, ,000 40,937 33,516 27,441 10,000 8,187 6,703 5,488 Total 250, , , ,594 25,000 21,992 19,415 17,200 Formulas (b)*e -(a) (b)*e -2(a) (b)*e -3(a) (a)*(b) (a)*(c) (a)*(d) (a)*(e) Results based on the above t=0 t=1 t=2 t=3 Claim Frequency of the Total Group: Claim Frequency relative to t = 0: Z = 1 - Relative claim frequency (Mod): Credibility relative to t = 1: Number of years Thus, credibilities vary approximately in proportion to the number of years. Copyright 2012 by All 10, Inc. Page 28

10 The Credibility of Experience Of A Single Private Passenger Car Appendix 2: Calculation of the average number of accidents for risks with 1 or more claims in the previous year (Class 1B). Class 1B risks are risks having had one or more claims in the past year. The number of persons having 0 claims last year = Ne -m, where N = the number of persons in the population and m = the claim frequency. Thus, the number of risks having had one or more claims in the past year (Class 1B risks) = N(1-e - m ). The number of claims produced by the entire group is Nm. Nm m Therefore, the average number of accidents for Class 1B risks = -m -m N(1- e ) (1- e ) Example: The class 1 claim frequency, as shown in table 2 =.087. Thus, risks having 1 or more claims last year (and are Class 1B this year) had an average.087 of = claims (1- e ) Mod In addition, Z R - 1 (1- e ) - 1. See page 160. Discussion by Hazam "While the data underlying the paper are exclusive to the Canadian Merit Rating Plan, the conclusions are not so geographically restricted." 1. Premium as a base eliminates maldistribution only if high frequency territories are also high premium territories AND if territorial differentials are proper. However, premium, although not perfect, is an improvement over exposure as a base for this type of study. Also, the fact that these assumptions do not always exist, does not detract from the qualitative nature of the conclusions. 2. "Credibilities for experience periods of one, two and three years would be expected to vary approximately in proportion to the number of years." This is true only for low credibilities and even then the theoretical credibilities, based on P/(P + K), are < 1.00, 2.00, and 3.00 for the one, two and three claim free years. For example, using the actuarially accepted formula P/(P + K), (where K = 2074 was derived on the assumption of 100 claims per year producing a one-year credibility of.046), the theoretical relativities to.046 are: Credibility Relative Z Observed Result (Table 3) [100/ ] = [200/ ] = [300/ ] = In a balanced merit rating plan there is not enough credibility by class to warrant the magnitude of credits now being offered by many plans. Although adding convictions no doubt helps substantiate larger credits, it is dubious that it will support current merit rating differentials. Copyright 2012 by All 10, Inc. Page 29

11 PAST CAS QUESTIONS ASSOCIATED WITH Questions from the 1991 Exam: 27. (2 points) A simplified merit rating plan splits a class of insureds into three groups based entirely upon claim frequency as described in "An Actuarial Note on the Credibility of Experience of a Single Private Passenger Car" by Bailey and Simon. Based upon the following chart and a standard rate of $1,500, what is the rate for an insured who has had no claims for at least one year? Number of Years Earned Premium Number Since Last at of Accident Present Rates Claims Two or more $100, One 40, None 10, Questions from the 1992 Exam: 43. (2 Points) You are given the following private passenger auto results from State X. Answer the questions below based on Bailey and Simon's paper An Actuarial Note on the Credibility of a Single Private Passenger Car Claim 1-year 3-year Frequency Credibility Credibility Pleasure Class A Business Class B a. Which class has less within class variability in claim frequency? Explain your answer. b. Which class has a more stable claim frequency over three years? Assume that no exposures enter or leave either class during the experience period, and that the risk distribution in both classes is not markedly skewed. Explain your answer. Questions from the 1993 Exam: 6. (1 point) Insureds in Territory A experienced a claim frequency of.08 in 1991, and insureds statewide, including Territory A, experienced a claim frequency of.05 in In 1992, the Formula Relative Claim Frequency for Territory A was Based on Bailey & Simon's paper An Actuarial Note on the Credibility of Experience of a Single Private Passenger Car, what is the one-year credibility implied for risks in Territory A? A. <.200 B. >.200 but <.400 C. >.400 but <.600 D. >.600 but <.800 E. >.800 Questions from the 1994 Exam: 8. According to Bailey and Simon, in "An Actuarial Note on the Credibility of Experience of a Single Private Passenger Car", which of the following statements are true? 1. For accident-free risks, the credibility is equal to {1.000 minus the modification}. 2. One reason that relative credibilities calculated for two and three years are lower than expected is that the chance of an accident for an individual can change during the year. 3. Experience rating is a procedure used to find the deviation of an individual risk from the average. A. 1 only 2 B. 1 and 2 C. 1 and 3 D. 2 and 3 E. 1, 2 and 3 Copyright 2013 by All 10, Inc. Page 30

12 PAST CAS QUESTIONS ASSOCIATED WITH Questions from the 1994 Exam (continued): 9. According to Bailey and Simon, in "An Actuarial Note on the Credibility of Experience of a Single Private Passenger Car", which of the following statements are true? 1. Credibility for experience rating depends not only on the volume of data in the experience period, but also on the amount of variation of individual hazards within the class. 2. Credibility for experience rating should increase in proportion to the square root of the volume of data. 3. The fact that the relative credibilities calculated for two and three years of experience are lower than expected is partially caused by risks entering and leaving the class. A. 1 and 2 B. 1 and 3 C. 2 and 3 D. 1, 2 and 3 E. None of A, B, C, or D 31. (2 points) Based on the methodology and notation used by Bailey and Simon in "An Actuarial Note on the Credibility of a Single Private Passenger Car" and the table below, calculate the credibility for category B risks (i.e., risks whose number of claim-free years equals zero) for a one-year experience period. (You can assume that the Poisson distribution reasonably approximates the distribution of observed claim counts among risks from all merit rating groups combined.) Show all of your work. Merit Rating (No of Earned Premium at Number of accident free years) Earned Car Years Present Category B rates Claims incurred A (3+) 3,005, ,400, ,000 X (2) 148,000 10,700,000 18,000 Y (1) 184,000 13,200,000 25,000 B (0) 330,000 23,000,000 46,000 Total 3,667, ,300, ,000 Questions from the 1995 Exam: 6. According to Hazam's discussion of Bailey and Simon's paper '"An Actuarial Note on the Credibility of Experience of a Single Private Passenger Car," which of the following are true? 1. For a study like that presented by Bailey and Simon, the use of premium as a base is an improvement over the use of exposure as a base. 2. Using a premium base eliminates the mal-distribution only if high frequency territories are also high premium territories or if territorial differentials are proper. 3. Bailey and Simon's statement "the credibilities for experience periods of one, two, and three years would be expected to vary approximately in proportion to the number of years" holds largely true only for low credibilities. A. 1 only B. 2 only C. 1 and 3 D. 2 and 3 E. 1, 2 and 3 Copyright 2013 by All 10, Inc. Page 31

13 PAST CAS QUESTIONS ASSOCIATED WITH Questions from the 1995 Exam (continued): Question 30. Based on Bailey and Simon's paper "An Actuarial Note on the Credibility of Experience of a Single Private Passenger Car" and the information given below, calculate the credibilities that can be assigned to the experience of a single private passenger car from each of the following two groups: A. (1.5 points) The group of risks that have been claim free for two (2) or more years B. (1.5 points) The group of risks that have been claim free for no (0) years Show all work Number Number of Years Earned Earned Premium of Claims Group Claim Free Car Years at Present D Rates Incurred A 3 or more 650, ,000,000 54,250 B 2 200, ,000,000 21,000 C 1 75,000 45,000,000 10,125 D 0 75,000 45,000,000 14,625 Total 1,000, ,000, ,000 Question 32. (3 points) You have been retained as a consulting actuary for Hi Risk Auto Insurance Company. The company has asked for you to determine if any of the three classifications in use is possibly in need of further refinement. The only data available are shown below: Claim Frequency Per $1,000 Earned Premium Class A TOTAL Class B TOTAL Class C TOTAL Only Risks with 3 or More Years Loss Free Earned Premium Per Earned Car Year Credibility of a Single Risk Class A $ Class B $ Class C $ Using the procedures and formulas from Bailey and Simon's paper "An Actuarial Note on the Credibility of Experience of a Single Private Passenger Car," determine whether one or more of the current classes exhibit(s) more variation of individual hazards than do(es) the other(s). Assume that the earned premiums are adjusted to a common current rate level. Show all work Copyright 2013 by All 10, Inc. Page 32

14 PAST CAS QUESTIONS ASSOCIATED WITH Questions from the 1996 Exam: 50. You are given the following private passenger automobile results for a hypothetical state. Using the techniques from Bailey and Simon's "An Actuarial Note on the Credibility of a Single Private Passenger Car," answer the questions below: Class Description A Pleasure Class - Unmarried Male Operator under age 25 B Pleasure Class - Unmarried Female Operator under age 25 C Pleasure Class - Operator over age Claim 1995 One-year Three- Class Frequency Credibility Year Credibility A B C a. (1 point) Which class has a more stable claim frequency over the three year period? Assume that there is no change in the exposures in each class during the three years and that the risk distribution in each class is not markedly skewed. Explain your answer. b. (1 point) Which class has less variability in claim frequency within its class? Explain your answer. Questions from the 1997 Exam: 19. According to Bailey and Simon s An Actuarial Note on the Credibility of Experience of a Single Private Passenger Car, which of the following are true? 1. Relative claim frequency is calculated on a premium basis to avoid biases due to the fact that exposure based frequency varies by territory. 2. Credibility for experience rating depends only on the volume of data in the experience period. 3. The experience for one car for one year has significant and measurable credibility for experience rating. A. 3 B. 1, 2 C. 1, 3 D. 2, 3 E. 1, 2, 3 Copyright 2013 by All 10, Inc. Page 33

15 PAST CAS QUESTIONS ASSOCIATED WITH Questions from the 1998 Exam: 26. Based on Bailey and Simon s An Actuarial Note on the Credibility of Experience of a Single Private Passenger Car, answer the following questions. a. (2 points) Using the information below, calculate the number of claims incurred for Group C. Show all work. Number of Years Earned Car Years Earned Premium at Present D Rates (000) No. of Claims Incurred Group Claim Free (1) (2) (3) A 3 or more 700, ,000 62,376 B 2 175, ,000 15,957 C 1 100,000 60,000????? D 0 25,000 15,000???? Total 1,000, ,000 98,000 Credibility for the group of risks with one or more claim-free years (Z) = b. (0.5 point) What conclusion do the authors reach with respect to merit rating using one year s worth of experience? c. (0.5 point) In a highly refined private passenger rating classification system, what relative credibilities would the authors conclude should be assigned to the experience of an individual risk compared to the experience of a class? Questions from the 1999 Exam: 1. In Bailey and Simon's "An Actuarial Note on the Credibility of Experience of a Single Private Passenger Car," the authors state that under certain conditions, the credibilities associated with experience periods of one, two, and three accident-free years for insureds within a given class would be expected to vary approximately in proportion to the number of years. Which of the following are reasons why this would not be true? 1. Changes in an individual insured's chance for an accident within a year 2. Skewness in the risk distribution of individual insureds 3. The impact of risks entering and leaving the class A. 1 B. 1, 2 C. 1, 3 D. 2, 3 E. 1, 2, 3 Copyright 2013 by All 10, Inc. Page 34

16 PAST CAS QUESTIONS ASSOCIATED WITH Questions from the 2000 Exam: 32. Based on Bailey and Simon s An Actuarial Note on the Credibility of Experience of a Single Private Passenger Car and the table below, answer the following. Private Passenger Automobile Liability - Non-Farmers Class 3 - Business Use Merit Rating Earned Car Years Earned Premium at Present B Rates Number of Claims Incurred Claim Frequency per $1,000 of Premium Relative Claim Frequency A 247,424 $25,846,000 31, X 15,868 $1,783,000 2, Y 20,369 $2,281,000 3, B 37,666 $4,129,000 7, Total 321,327 $34,039,000 45, where: Class A - Three or more years claim free Class X - Two years claim free Class Y - One year claim free Class B - Zero years claim free a. (1.5 points) Calculate the credibilities for a single private passenger car for one year, two years, and three years. Show all work. b. (0.5 point) Briefly describe the relationship that Bailey and Simon expect between the three credibilities from part a. c. (1 point) Do the credibilities calculated in part a. follow the relationship described in part b.? Briefly explain why or why not. Questions from the 2001 Exam: 2. According to Bailey and Simon s An Actuarial Note on the Credibility of Experience of a Single Private Passenger Car, which of the following is false? A. The experience for one car for one year has significant and measurable credibility for experience rating. B. Credibility for experience rating depends on the variation of individual hazards within the class. C. In a highly refined private passenger rating classification system that reflects inherent hazard, there would not be much accuracy in an individual risk merit rating plan. D. In experience rating, an increase in the volume of data in the experience period increases the reliability of the indication in proportion to the square root of the volume. E. None of A, B, C, or D are false. Copyright 2013 by All 10, Inc. Page 35

17 PAST CAS QUESTIONS ASSOCIATED WITH Questions from the 2001 Exam (continued): 22. (2.5 points) Use Bailey and Simon s An Actuarial Note on the Credibility of Experience of a Single Private Passenger Car, and Hazam s discussion to answer the following questions. a. (1.5 points) Using the information below, calculate the credibility for 1-year and 2-year claim free periods for Class 1. Show all work. Number of Years Claim Free Earned Premium at Present Rates Number of Claims Incurred Earned Car Years Class 1 2 or more $5,000,000 7,000 15,000 1 $7,000,000 10,000 12,250 0 $1,000,000 2, Total $13,000,000 19,000 27,650 b. (0.5 point) What exposure base do the authors use? Explain why. c. (0.5 point) According to Hazam, what two conditions must be met to use the exposure base described in part b.? Questions from the 2002 Exam: 47. (2 points) a. (1.5 points) Given the following data, calculate the credibilities for 1-year and 2-year claim free periods. A represents 3 or more years since the most recent accident. X represents 2 years since the most recent accident. Y represents 1 year since the most recent accident B represents 0 years since the most recent accident Earned Premium Earned Car at Present Class Number of Group Years B Rates Claims A 50,000 $5,500,000 5,000 X 6,500 $682,500 1,000 Y 5,000 $535, B 4,500 $490, Total $66,000 $7,208,000 $7,750 b. (0.5 point) Give two possible reasons that the 2-year credibility is less than 2 times the 1-year credibility. Questions from the 2003 Exam: 2. Which of the following statements is false for private passenger auto experience rating? A. Credibility assigned to an individual risk within a highly refined classification rating plan would be higher than the credibility assigned in a less refined rating plan. B. Credibility for experience rating depends on the amount of variation of individual hazard within the class. C. Credibility for experience rating is significant & measurable when based on data from one car for 1 year. D. Credibility for classification rating increases in proportion to the square root of the volume of data. E. Credibility within a highly refined private passenger classification rating system would be larger where a wide range of hazard is encompassed within a classification. Copyright 2013 by All 10, Inc. Page 36

18 PAST CAS QUESTIONS ASSOCIATED WITH Questions from the 2003 Exam (continued): 22. (3 points) You are given the following data: Actual Earned Years since Premium at Earned Car Number of Class last accident Present B Rates Years Claims A ,000 2, X 2 15, Y 1 22, B 0 37, Assume that the same rate is charged to all insureds within a class and there have been no rate changes in or since the experience period. a. (1 point) What is the credibility of 3 or more accident-free years of experience? b. (1 point) What is the credibility of 1 or more accident-free years of experience? c. (1 point) Give two possible reasons why the answer in part a. is not 3 times the answer in part b. Questions from the 2004 Exam: 2. Given the following information: Number of Years Earned Earned Number Since Most Car Premium at of Class Recent Accident Years Present B Rates Claims A 3 or more 10,000 $1,000,000 1,000 X 2 7,000 $770,000 1,155 Y 1 5,000 $625,000 1,250 B 0 2,000 $400,000 1,000 Total 24,000 $2,795,000 4,405 Calculate the credibility of one or more accident-free years of experience. A B C D E Questions from the 2005 Exam: 3. (3 points) a. (2 points) Given the following information: N= the number of drivers in the population, m = the mean claim frequency for all drivers, Mod = the credibility weighted modification factor for risks with one or more claims in the past year. Derive the formula for the credibility assigned to the experience of drivers with one or more claims in the past year. Assume that claim frequency follows a Poisson distribution. b. (1 point) If there is a switch from a less refined class plan to a highly refined class plan, describe the likely change in the credibility assigned to an individual risk. Copyright 2013 by All 10, Inc. Page 37

19 PAST CAS QUESTIONS ASSOCIATED WITH Questions from the 2006 Exam: 2. (4 points) a. (3 points) Given the following information about an automobile insurance portfolio: Number of Accident-Free Group Years A 3 Earned Premium at Present Group D Rates $25,000,000 Number of Claims Incurred 40,000 B 2 $8,000,000 15,000 C 1 $13,000,000 25,000 D 0 $8,000,000 30,000 Calculate the credibility of a single car for each of the following: one-year, two-year, and three-year accident-free periods. b. (1 point) In performing the analysis in part a. above, would using car years instead of earned premium as an exposure base be more preferable? Explain why or why not. Questions from the 2007 Exam: 2. (3.5 points) a. (2 points) The following data were compiled from the ABC automobile insurance portfolio: Group Number of Accident-Free Years Earned Premium at Present Group D Rates Number of Claims Incurred A 3 or More $ 100,000, ,000 B 2 $ 10,000,000 25,000 C 1 $ 17,000,000 44,000 D 0 $ 10,000,000 36,000 Calculate the credibility of a single car for each of the following ranges of accident-free years: i. 1 or more ii 2 or more iii.3 or more b. (1 point) The following table provides the single car credibility for the XYZ automobile insurance portfolio: Accident-Free Years Single Car Credibility 1 or More or More or More 0.06 Discuss two conclusions than can be drawn from the different credibility results of the ABC and XYZ portfolios. c. (0.5 point) Explain why analysis of two portfolios with different classification plans could assign different values to the credibility of the experience of a single car. Copyright 2013 by All 10, Inc. Page 38

20 PAST CAS QUESTIONS ASSOCIATED WITH Questions from the 2008 Exam: 5. (2 points) A liability insurer collects the following data for a particular class of private passenger auto risks: Accident-Free Years Earned Exposures Incurred Losses ($) 2 or more 2,500 1,000, , ,000 2,500,000 Total 4,000 4,000,000 Assume the following: The base rate is $1,250 per exposure. An experience rating factor is the only factor applied to the base rate. a. (1 point) Calculate the credibility of an exposure that is accident-free for 1 or more years. b. (1 point) Calculate the premium for an exposure that is accident-free for 2 or more years. Questions from the 2009 Exam: 4. (3.5 points) The following information can be used to calculate the credibility assigned to the experience of a single private passenger car: Years Since Earned Last Earned Car Premium at Number of Group Accident Years Present B Rates Claims A 3 or more 650, ,000,000 50,000 X 2 230, ,000,000 20,000 Y 1 100,000 75,000,000 12,000 B 0 M 45,000,000 18,000 Total 980,000 + M 670,000, ,000 Assume claim counts follow a Poisson distribution. a. (2.5 points) Calculate M, the earned car years for Group B, given that the credibility for an insured that has had no claim-free years is equal to b. (1 point) Calculate the credibility for the group of risks that have been claim-free for two or more years. Questions from the 2010 Exam: 5. (1 point) An insurance company has a private passenger auto book of business with the following claims experience: Earned Premium at Number of Present Number of Accident Group D Claims Group Free Years Rates Incurred A 3 or More 60,000,000 45,000 B 2 15,000,000 15,000 C 1 20,000,000 29,300 D 0 5,000,000 18, ,000, ,000 Calculate the credibility of a single car for a driver with one or more accident-free years. Copyright 2013 by All 10, Inc. Page 39

21 PAST CAS QUESTIONS ASSOCIATED WITH Questions from the 2011 Exam: 1. (3 points) An insurance company is using a merit rating plan for drivers in two states. State X has the following claims experience: Number of Earned Premium Number of Accident-Free at Present Group Claims Group Years D rates Incurred A 3 or more $500, B 2 $150, C 1 $200, D None $300, Total $1,150, State Y has the following relative claim frequencies for accident-free experience: Number of Relative Claim Accident-Free Frequencies to Years Total 3 or more or more 0.77 I or more 0.84 Assuming that no new risks enter or leave either state, use relative credibility to explain which state has more variation in an individual insured's probability of an accident. Questions from the 2012 Exam: 6. (2.5 points) An insurance company has a private passenger auto book of business with the following claims experience: Earned Premium at Years Present Rates for Since Last Two Years Since Earned Car Number of Territory Accident Last Accident Years Claims Incurred Loss 1 0 $15,000,000 15,000 5,000 $9,000, $125,000, ,000 41,000 $75,000, $230,000, ,000 76,000 $138,000, $25,000,000 25,000 7,000 $16,000, $310,000, ,000 84,000 $187,000, $550,000, , ,000 $328,000, $10,000,000 10,000 4,000 $7,000, $80,000, ,000 35,000 $43,000, $160,000, ,000 60,000 $100,000,000 Choose an appropriate exposure base for calculating credibility. Justify the selection. Copyright 2013 by All 10, Inc. Page 40

22 Solutions to questions from the 1991 Exam: Question 27. Step 1: Step 2: Write a formula for the insured's rate: Insured's rate = Standard Rate * Modification factor. = Standard Rate * Relative claim frequency. Set up a Bailey type exhibit to compute relative claim frequency: Claim Frequency Merit Earned Car Earned Premium No. of Claims per $1000 of Relative Rating Years at Present B Rates(000) Incurred Premium to Total (1) (2) (3) (4) (5) (3) / (2) (4) / (4 A X Y B Total A+X Formula (3) / (2) (4) / (4 Step 3: Using the formula in step 1 and the results of step 2, compute the insured's rate: Insured's rate = Standard Rate * Modification factor = $1,500 * = $1, Solutions to questions from the 1992 Exam: Question 43. Step 1: Set up a Bailey type exhibit similar to Tables 2 and 3: 3- Year Class Credibility Claim Frequency Ratio of 3 year Cred to Freq. (1) (2) (3) (4) = (2) / (3) A B Step 2: Evaluate the results: If the variation of an individual insureds' chances for an accident were the same within each class, the credibility would be expected to vary approximately in proportion to the average claim frequency Class B has less within class variability. Bailey states that for class comparison purposes, smaller column (4) ratios confirm the expectation that there is less variation of individual hazards in those classes. (b) Bailey states that if an insured s chance for an accident remained constant from one year to the next, and if there were no risks leaving or entering the class, the credibilities for experience periods of 1, 2 and 3 years would be expected to vary in proportion to the number of years. Credibility Class 1- Year 3- Year 3 year to 1 year (1) (2) (3) (4) = (3) / (2) A B This relationship is more closely exemplified by Class A. Page 41

23 Solutions to questions from the 1993 Exam: Question 6. Step 1: Recall the following relationships: Modification = ZR + (1 - Z), where the Modification = Relative Claim Frequency. Z = credibility R = ratio of the actual losses to expected losses Step 2: Using the given information, solve for Z: 1.50 = Z(.08/.05) + (1 - Z). Z = Answer E. Solutions to questions from the 1994 Exam: Question T. Keep the following table in mind: Classes with claim free experience Mod = Relative claim frequency = Column (5) from table 1. = ZR + (1 - Z). R = 0 Z = 1 - Mod Classes with claim experience Mod = Relative claim frequency = Column (5) from table 1. = ZR + (1 - Z). R = (1 - e -m ) -1. m = true claim frequency. Z = Mod - 1 R T. Bailey states the following two reasons: "The fact that the relative credibilities in columns (11) and (12) (on page 2 of the summary) are much less than 2.00 and 3.00 is partially caused by risks entering and leaving the class. But it can be fully accounted for if: (a) an individual insured's chance for an accident changes from time to time within a year, or from one year to the next, or (b) if the risk distribution of individual insureds has a marked skewness reflecting varying degrees of accident proness." 3. T. Experience Rating - a procedure to find the deviation, of an individual risk, from the average risk. Answer E. Question T. Bailey states the following: Thus, credibility for experience rating depends on: the volume of data in the experience period, and also the amount of variation of individual hazards within the class. 2. F. Class Ratemaking - a procedure to find the average, and where an increase in the volume of the experience increases the reliability of the indication only in proportion to the square root of the volume. 3. T. Refer to quote cited in the solution to question 8, statement 2. Answer B. Page 42

24 Solutions to questions from the 1994 Exam (continued): Question 31. Step 1: Step 2: Write a formula for the Credibility for classes with claim experience: Z= Mod - 1 R - 1. Mod = Relative claim frequency. R = (1 - e -m ) -1. m = true claim frequency for the class in total. Set up a Bailey type exhibit to compute relative claim frequency: Claim Frequency Merit Earned Car Earned Premium No. of Claims per $1000 of Relative Rating Years at Present B Rates Incurred Premium to Total * (1) (2) (3) (4) (5) A X Y B 330,00 23,000,000 46, Total 3,667, ,300, , Formula (3) / (2) (4) / (4 tot) Step 3: Compute m: m = 349,000/3,667,000 = Step 4: Using the formula in step 1 and the results of steps 2 and 3, solve for Z: ( ) Z = = [(1.0 - e ) - 1.0] Solutions to questions from the 1995 Exam: Question 6. According to Hazam, premium as a base eliminates maldistribution only if (1) high frequency territories are also high premium territories AND (2) territorial differentials are proper. However, premium, although not perfect, is an improvement over exposure as a base for this type of study. Also, the fact that these assumptions do not always exist, does not detract from the qualitative nature of the conclusions. Thus, 1 is true and 2 is false. Credibilities for experience periods of one, two and three years would be expected to vary approximately in proportion to the number of years." This is true only for low credibilities and even then the theoretical credibilities, based on P/(P + K), are < 1.00, 2.00, and 3.00 for the one, two and three claim free years. Thus, 3 is true. Answer C. Page 43