Solutions to Past CAS Questions Associated with NAIC Property/Casualty Insurance Company Risk Based Capital Requirements Feldblum, S.

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1 Solutions to Past CAS Questions Associated with Feldblum, S. Solutions to questions from the 1997 Exam: 18. Calculate the adjusted policyholder surplus for this company. Step 1: Write an equation for adjusted policyholder surplus. Adjusted policyholder surplus = Surplus Non-tabular discounts. Step 2: Identify the non-tabular discounts. On page 378, Feldblum states that tabular discounts represent reserves associated with ALL lifetime pension claims, whether on known or unknown claims, but limited to indemnity cases only. Using this definition, we can determine the non-tabular discounts. Step 3: Using the equation in Step 1, and the data given in the problem associated with non-tabular discounts, calculate the adjusted policyholder surplus. Adjusted policyholder surplus = 500 ( ) = 469. Answer B. Note: per E&Y Total adjusted capital is equal to the company s policyholders surplus from page 3 of the Annual Statement that is reduced by: 1. The amount of non-tabular discount from Schedule P, Part 1, Summary, columns 32 and Tabular discount on medical reserves included in Schedule P, Part 1, Summary, column Which of the following charges is subject to the covariance adjustment? A. Guarantees for affiliates. This is included in R0, which is outside the square root portion of the RBC formula. B. Investments in insurance affiliates. This is included in R0, which is outside the square root portion of the RBC formula. C. Non controlled assets. This is included in R0, which is outside the square root portion of the RBC formula. D. Contingent liabilities. This is included in R0, which is outside the square root portion of the RBC formula. E. Aggregate write-ins for invested assets. This is included in R2, which appears inside the square root portion of the RBC formula. Answer E. Solutions to questions from the 1998 Exam: 23. According to Feldblum, NAIC Property-Casualty Risk-Based Capital Requirements, which of the following are true regarding the risk-based capital calculations? 1. True. Further, this is one of the criticisms levied against the relatively high charge for reinsurance recoverables in the RBC formula. 2. False. This charge is assigned to risk category R False. Investments in non-insurance subsidiaries are included in either the R1 or R2 charge, depending on whether the investments are fixed income or equity securities. Answer A. 49. a. Identify and briefly explain 3 incentives related to the RBC formula that may lead companies to report inadequate reserves. 1. Reducing reserves increases statutory surplus, which increases their RBC ratio. 2. Reducing reserves lowers the reserving risk charge, therefore lowering a company s required capital 3. Reducing reserves lowers the reported adverse development, reducing its reserving risk charge. b. Briefly explain 2 arguments presented by the NAIC working group explaining why the RBC formula should not be modified in response to the criticism above. 1. Ensuring that reserves are adequate is the task of state regulators and company actuaries, and not that of the risk based capital formula. 2. Any reserves that are currently understated will ultimately manifest itself through greater adverse loss development, leading to a higher reserving risk charge. c. Provide 1 reason why insurers want to avoid understating loss reserves. Understated reserves result in increased taxable income. Copyright 2013 by All 10, Inc. Page 1

2 Solutions to questions from the 1999 Exam: 57. According to Feldblum, NAIC Property/Casualty Insurance Company Risk-Based Capital Requirements, the square root rule formula does not have any covariance terms, even though in practice there is some dependence among the risk factors. c. (1 ½ points) One risk charge is outside the square root formula in the risk-based capital calculation. Identify this risk charge and provide the rationale for not including it within the square root formula. The risk charge outside the square root formula is R0 - Investments in Insurance Affiliates. It is outside the square root formula to avoid a reduction of overall capital requirements by simple layering of the company s legal structure. Per E&Y R0 is kept outside of the covariance adjustment because the risk for investments in insurance company subsidiaries is believed to be directly correlated with the combination of the risks specific to the reporting entity (i.e., the other risk charges R1 through R5). 60a. (1/2 point) What is the purpose of the adjustment for investment income factor in the reserving risk calculation? There is an implicit margin in statutory loss reserves because they are undiscounted. This should be removed by the adjustment for investment income factor to avoid a double counting (i.e. an explicit capital requirement held as surplus and an implicit capital cushion held as reserves) of the required capital. 60c. (1/2 point) What is the purpose of the premium concentration factor in the written premium risk calculation? If an insurer writes many lines of business, risk is reduced because the underwriting results of the various lines are not completely correlated with each other. The more diversified the insurer is with respect to lines of business written, the greater the decrease in written premium risk charge. Solutions to questions from the 2000 Exam: 52. True. See page False. Investments in insurance affiliates are included in R 0 risk category. See page a. In both cases, the RBC formulas are using undiscounted values from the AS. Reserving uses undiscounted reserves, while premium uses undiscounted loss ratios. This adds an extra margin for adverse conditions, so to determine RBC requirements, we need to account for this built in margin from investment income so we don t add an RBC margin on top of the built in investment income margin. b. The adjustment for reserves considers the payout pattern after the end of the first year, while the premium payout pattern considers payment in the first year. So, if a large portion of total payments are made during the calendar year, the policy is subject to a long payout of the remaining reserves in the following calendar years, and thus, the discount for reserves will be greater than the discount for premiums. Solutions to questions from the 2001 exam 12. False. See page False. Investments in non-insurance subsidiaries are included in R 1 or R 2, which is subject to the covariance adjustment. See page a. This will have no impact on RBC requirements, since this will go to the R 0 charge which is outside of the square root. Layering has no impact of RBC requirements. b. This will reduce the current A+ RBC requirements since lowering reserves will lower the reserving risk charge, lower adverse development, and raise surplus. However, future RBC requirement will increase since anticipated future adverse development will increase. Copyright 2013 by All 10, Inc. Page 2

3 Solutions to questions from the 2002 exam 20. False. The reserving risk charge measures the susceptibility of loss reserves to adverse developments. The charge is quantified separately by line of business, using Schedule P data for the past ten years. See page 324. Per E&Y: The company RBC percent is the crux of the reserve risk charge. According to the NAIC RBC instructions, These factors are designed to provide a surplus cushion against adverse reserve development 63. (4.5 points) Based on Feldblum, "NAIC Property/Casualty Insurance Company Risk-Based Capital Requirements," and the above information, answer the following. Show all work. a. (3 points) Calculate XYZ's 2001 risk-based capital requirement. Show the calculation of each risk charge category, R0 through R5, separately. Step 1: Write an equation to determine XYZ's 2001 risk-based capital requirement. R 0 + [(R 1 ) 2 + (R 2 ) 2 + (.50*R 3 ) 2 + (R *R 3 ) 2 + (R 5 ) 2 ].50 Step 2: Develop a table similar to the one below in order to define the risk category and to compute the risk charges for categories R0 through R5 separately. Step 3: Review the given information to determine what risk categories require computation beyond the amounts given in the problem. Based on the given additional information, and Feldblum s discussion with respect to Credit Risk, recognize that a 10% credit risk charge for reinsurance recoverables and a 5% credit risk charge for miscellaneous receivables needs to be determined. Risk Category Description Computation R 0 Inv in affiliates & off-balance risks None needed. Given as 3,000 R 1 Fixed income securities None needed. Given as 11,000 R 2 Equity investments None needed. Given as 26,250 R 3 Credit risk charge (see below) a. 10% charge for reinsurance recoverables: b. 5% charge for miscellaneous receivables: (.10 * 15,000) + (.05 * 10,000) = 2,000 R 4 Reserving risk None needed. Given as 8,000 R 5 Premium risk None needed. Given as 12,000 Step 4: Using the equation and Step 1, and the results from Steps 2 and 3, compute XYZ's 2001 risk-based capital requirement RBC requirement = 3,000 + [11, , (2,000-1,000) 2 + (8, ,000) ,000 2 ].50 = 35,188 See pages See Table 60 in the E&Y test for a detailed illustration of the R3 charge b. (0.5 point) Calculate XYZ's 2001 risk-based capital ratio. The risk based capital ratio is the ratio of adjusted surplus to risk-based capital surplus. Thus, the risk based capital ratio equals 20, % 35,188 See page 382. Copyright 2013 by All 10, Inc. Page 3

4 Solutions to questions from the 2002 exam (continued): Question 63 (continued) c. (1 point) If the authorized control level benchmark is set at 60% of the risk-based capital standards, comment on what level of action will be required given this result. The levels of regulatory action depends upon the ratio of the company s adjusted surplus to the risk-based capital authorized control level (ACL) benchmark. Thus, the risk-based capital authorized control level (ACL) benchmark equals (.60 * 35,188) = 21,113 The ratio of the company s adjusted surplus to the risk-based capital authorized control level (ACL) benchmark is 20, % 21,113 Given that the above ratio is within % of the ACL benchmark, the authorized control level is invoked. When the authorized control level is invoked, the insurance commissioner is authorized to take control of the company, but regulatory action is still discretionary. See page 384. Solutions to questions from the 2004 exam: 21. Rank the companies in order of increasing ratios of Adjusted Surplus to Authorized Control Level (ACL): Step 1: Write an equation to determine the ratio of Adjusted Surplus to ACL: Adjusted Surplus Adjusted Surplus ACL =.50[R + R + R + (.50R ) + (R +.50R ) + R ] Step 2: Using equation from Step 1, and the data given in the problem, solve for, and then rank the ratio of Adjusted Surplus to ACL 5000 Company X: ratio = (100 [ *(750) + (1, ) 2,500 ] ) ,800 Company Y: ratio = (100 [ *(500) (1, ) 1,100 ] ) Company Z: ratio = 1, Therefore, Z < Y < X. Answer D 37. (2 points) a. n/a b. (1 point) Briefly describe the response taken by the regulator in response to the RBC calculation. The ratio of the insurer s Adjusted Surplus to the Authorized control level RBC determines the regulator s response. (Adjusted Surplus)/ (ACL RBC) Regulator Response 150% - 200% Company Action Level company submits plans to increase capital and reduce risks to capital. 100% - 150% Company submits plan as above; regulation may take some corrective action. 70% - 100% Regulator is authorized to (may) take control. < 70% Regulator is authorized to (must) take control. See pages Copyright 2013 by All 10, Inc. Page 4

5 Solutions to questions from the 2004 exam (continued): Question 43 (continued): d. (0.5 point) Discuss an argument for and an argument against a formula that assesses a higher Risk-Based Capital charge to alien subsidiaries. FOR: Assessing the financial status of an alien insurer is more difficult since they are not subject to the same regulatory requirements as US subsidiaries. This fact increases the risk of investing in Alien subsidiaries and therefore should require a higher RBC charge. AGAINST: It may discourage investment in Alien subsidiaries which reduces the diversity of the portfolio. Reduced diversity produces increased risk of a large loss due to one event. See pages (1 point) Many industry analysts have argued property/casualty industry reserves are more than $50 billion deficient (approximately 12.5% of total industry reserves). Assuming the deficiency is spread evenly as a percentage of statutory surplus and all companies adjusted their reserves to the perceived adequate level, how would this affect the regulation of insurance companies with respect to risk based capital standards? Initial comment: When formulating an answer to a question like this, skim through the question for key information. Here, we are asked how the regulation of insurance companies would be affected when accounting for industry wide reserve deficiencies. This may lead you to discuss actions that regulators may take, prompting you to discuss issues associated with regulatory authorized control level (ACL) action. All companies would appear weaker to regulators since surplus would decrease while the reserving risk charge would increase. However, the actual strength of the companies would not change. It would therefore make sense to lower the authorized control level from 50% of the risk-based capital charge. 66. (3.5 points a. (1 point) Calculate the two-year reserve development total that would appear on this Schedule P. See the solutions to the Schedule P article. b. (2.5 points) Calculate the reserving risk charge percentage under the Risk Based Capital rules. Step 1: Write an equation to determine the reserving risk charge percentage: Co Avg Dev *Ind RBC% Ind RBC% Ind AvgDev Res Risk Charge % 1 Adj for II The RBC charge is given as.21, the discount factor is given as.942, and the industry average development factor is given as Step 2: Compute the company average development factor: Company average development factor is the ratio of the following amounts: i. current incurred losses = the sum of incurred losses at the current statement date for the nine accident years prior to the current year = = 6,909 ii. initial incurred losses = the sum of incurred losses at the initial statement dates for the nine accident years prior to the current year = = 6,580 Thus, the company average development factor 6,909/6,580 = 1.05 Step 3: Using the eq. in Step 1, the Step 2 result, and the given data given, solve for the res risk charge % 1.05 * Res Risk Charge % % 2 Copyright 2013 by All 10, Inc. Page 5

6 Solutions to questions from the 2005 exam: 34. (3.25 points) a. (3.25 points) Calculate the company's RBC requirement. Show calculations for each risk charge category R 0 through R 5. Step 1: Write an equation to determine the company s risk-based capital requirement. R 0 + [(R 1 ) 2 + (R 2 ) 2 + (.50*R 3 ) 2 + (R *R 3 ) 2 + (R 5 ) 2 ].50 Step 2: Develop a table similar to the one below in order to define the risk category and to compute the risk charges for categories R0 through R5 separately. Risk Category Description Computation R 0 Contingent & off-balance risks Given as 1,000 and 2,000 respectively R 1 Fixed income securities (bonds) Given as 10,000 R 2 Equity investments (stocks) Given as 15,000 R 3 Credit risk charge Computed as.50 * reinsurance recoverables =.50 * 4,000 = 2,000 R 4 Reserving risk (includes basic Given as 8,000 and 5,000 respectively = 13,000 and growth reserving charge) R 5 Premium risk (includes basic and growth reserving charge) Given as 11,000 and 3,000 respectively = 14,000 Step 3: Using the equation and Step 1, and the results from Step 2, compute the company s risk-based capital requirement RBC requirement = 3,000 + [10, , (2,000) 2 + (2, ,000) ,000 2 ].50 = 30,386 See pages b. (1.5 points) Based on the answer to part a. above, identify the RBC Action Level for this company and briefly describe the action required for both the company and the regulator. The ratio of the insurer s Adjusted Surplus to the Authorized control level RBC determines the regulator s response. (Adjusted Surplus)/ (ACL RBC) Regulator Response 150% - 200% Company Action Level company submits plans to increase capital and reduce risks to capital. 100% - 150% Company submits plan as above; regulation may take some corrective action. 70% - 100% Regulator is authorized to (may) take control. < 70% Regulator is authorized to (must) take control. Write an equation to determine the ratio of Adjusted Surplus to ACL: Adjusted Surplus Adjusted Surplus = ACL.50[R + R + R + (.50R ) + (R +.50R ) + R ] , %.50[30,386] This ratio falls into the Authorized Control level. Regulators may take control of the company, but it is within their discretion to do so. The company should create plan of action to fix the problem. The regulator may agree, recommend other action, or take control. See pages c. (0.5 point) If the company purchases a U.S. insurance subsidiary that has a total RBC charge of $10,000, what effect, if any, will this have on the company's RBC? The entire 10K RBC charge would be passed to parent, increasing R0 and the entire RBC charge by 10K. Copyright 2013 by All 10, Inc. Page 6

7 Solutions to questions from the 2005 exam: Question 35 a. (3 points) Calculate the reserving risk charge. Initial comments: Two alternative solutions were accepted by CAS examiners to part a. of this question. This stems from the fact that to compute the reserving risk charge, the company needs to have enough years of company experience to opt for computing its reserving risk charge based on its own experience. a. First alternate answer Step 1: Write an equation to determine the reserving risk charge percentage: Co Avg Dev *Ind RBC% Ind RBC% Ind AvgDev Res Risk Charge % 1 Adj for II RBC charge is given as.275, the discount factor is given as.936, and the industry average development factor is given as Step 2: Compute the company average development factor: Company average development factor is the ratio of the following amounts: i. current incurred losses = the sum of incurred losses at the current statement date for the nine accident years prior to the current year = = 797 ii. initial incurred losses = the sum of incurred losses at the initial statement dates for the nine accident years prior to the current year = = 755 Thus, the company average development factor 797/755 = Step 3: Using the equation in Step 1, the result from Step 2, and the data given in the problem, solve for the reserving risk charge percentage * Res Risk Charge % % 2 a. Second alternate answer Because the company needs to have enough years of experience to opt for computing its reserving risk charge based on its own experience (note it only has four years of experience), the reserving risk charge should be computed as follows: Reserving Risk Charge % = [(1+ RBC charge)(discount Factor) - 1.0] = ( ) * = * 500M = 96.7M b. (0.25 point) Briefly describe what the reserving risk charge is designed to measure. It is designed to measure susceptibility to adverse development. Copyright 2013 by All 10, Inc. Page 7

8 Solutions to questions from the 2006 exam: Question 29. a. (2.25 points) Calculate R0 through R5 as used in the formula for risk based capital. Show all work. CAS Model Solution 1: R0 = 3,000 R1 = 2, ,000 = 11,000 R2 = 6, ,000 = 10,000 R3 = 1, = 500 R4 = 15,000 + (0.5 x 1,000) = 15,500 R5 = 12,000 Note: Assumed R3 has not been adjusted. Thus ½ R3, the credit risk charge, was removed and added to R4. CAS Model Solution 2: R0 = Inv in ins affiliates + off balance sheet items = 3,000 R1 = Fixed investment charges = Bonds charge + Cash charge = 2, ,000 = 11,000 R2 = Equity investment charges = common stocks +Real Estate charges = 6, ,000 = 10,000 R3 = Credit Risk Charge = 1,000 R4 = Reserving Risk Charge = 15,000 R5 = Premium Risk Charge = 12,000 b. (0.5 point) Calculate XYZ's total risk based capital requirements. Show all work. CAS Model Solution 1: RBC = 3,000 (11,000 10, ,500 12,000 3,000 24,607 27,607 CAS Model Solution 2: RBC Charge = = R 0 + R 1 + R 2 + (.50R 3) + (R R 3) + R ,000 (11,000 10, (500 15,000) 12,000 3,000 24,607 27,607 Copyright 2013 by All 10, Inc. Page 8

9 Solutions to questions from the 2006 exam (continued): c. (2 points) Identify and describe the four RBC Action Levels, including the consequences of each. Initial comments: Feldblum states that company or regulatory action levels may be stated as % s of the RBC standard or as a % of the ACL (e.g. the company action level is 75% to 100% of the risk-based capital standard, or 150% to 200% of the authorized control level benchmark). The following two model solutions use these different % s applied to different bases in describing the four RBC Action Levels. CAS Model Solution 1: Company Action Level: 150% < [Adjusted surplus/acl RBC] < 200% No action required by the regulation. Company must submit plan on how they plan to increase their surplus. Regulatory Action Level: 100% < [Adjusted surplus/acl RBC]< 150% Company action is same as listed above. Regulator has discretion to take action against the company. For example the regulator could ask the company to reduce its writings. Authorized Control Level: 70% < [Adjusted surplus/acl RBC]< 100% Regulator is authorized to take over the company. Mandatory Action Level: [Adjusted surplus/acl RBC]< 70% Regulator is required to liquidate or rehabilitate the company. CAS Model Solution 2: Company Action Level When RBC ratio = [Adjusted Surplus/ RBC Requirement] = 75% - 100% Company is required to submit a plan for how capital will be increased or risk reduced in order to increase RBC ratio. No action require by regulator. Regulatory Action Level RBC ratio is between 50% and 75%. Same action required by insurance company as with company action level and regulator is not required to do anything but may put restrictions on insurer such as not allowing new business to be written. Authorized Control Level RBC ratio is between 35% and 50%. Regulator is authorized to take control of the company but not required to. Mandatory Control Level RBC ratio less than 35%. Regulator is required to liquidate or rehabilitate the company. d. (0.75 point) Identify the Action Level indicated in part b. above. Show all work. CAS Model Solution 1: [Adjusted surplus/acl RBC] = (20,000 2,500) / (0.5 x 27,607) = 127% ACL RBC Regulatory Action Level CAS Model Solution 2: Adjusted Surplus = Statutory Surplus Non-tabular discount = 20,000 2,500 = 17,500 RBC Ratio = 17,500/27, = Falls within the Regulatory Action Level Copyright 2013 by All 10, Inc. Page 9

10 Solutions to questions from the 2006 exam (continued): 30. (3.5 points) Use the given information to answer the following questions about risk based capital requirements. a. (3 points) Calculate the basic written premium risk charge. Show all work. Step 1: Write an equation to determine the basic written premium risk charge WP Charge = Written Premium * {[(Adjustment*Discount Factor) + Expense Ratio] - 1.0}. Adjustment 10 year company avg LR [ ( industry worst case LR ( industry worst case LR* ] 10 year industry avg LR 2 Discount factor = adjustment for investment income factor Expense ratio = the company's Annual Statement reports an expense ratio for all lines. Step 2: Using the equation in Step 1, and the data given in the problem, solve for the written premium risk charge. The Industry Worst Case Loss Ratio = 91% (from 1997) Industry 10-year average loss ratio = 78.1% Company 10-year average loss ratio = 76.4% Company adjusted worst case LR = 91.0% x (76.4 / 78.1) = 89.0% Adjustment = Average of industry and company adjusted worst-case LR = ( ) / 2 = 90.0% WP Charge = Written Premium * {[(Adjustment*Discount Factor) + Expense Ratio] - 1.0}. = 75M * {[(0.90 * 0.924) ] - 1.0} = 75M * = 8.4M. b. (0.5 point) Describe what the written premium risk charge is designed to measure. Designed to measure risk that written business will be unprofitable and will require resources from surplus to cover these future loses. Copyright 2013 by All 10, Inc. Page 10

11 Solutions to questions from the 2007 exam: 34. (3.25 points) a. (1.75 points) Calculate RO through R5 as used in the formula for risk based capital. Show all work. b. (0.5 point) Calculate the company's total risk based capital requirement. Show all work. c. (1 point) Identify the RBC Action Level for the company and describe the resulting actions by the regulator and/or company, if any. Show all work. Question 34 - Model Solution 1 a. and b.. Step 1: Write an equation to determine the company s risk-based capital requirement. R 0 + [(R 1 ) 2 + (R 2 ) 2 + (.50*R 3 ) 2 + (R *R 3 ) 2 + (R 5 ) 2 ].50 Step 2: Develop a table similar to the one below in order to define the risk category and to compute the risk charges for categories R 0 through R 5 separately. Risk Category Description Computation *R 0 Affiliates & off-balance risks * (16) = 28 R 1 Fixed income securities (bonds) 200 * 0 = 0, assuming 0% charge for govt. Bonds R 2 Equity investments (stocks).15 * 100 = 15, assuming common stock charge of 15% R 3 Credit risk charge Computed as.10 * reinsurance recoverables =.10 * 40 = 4, assuming recoverable charge of 10% R 4 Reserving risk (includes basic Given as 30 and growth reserving charge) R 5 Premium risk (includes basic and growth reserving charge) Given as 20 * the RBC charge for an alien insurance subsidiary is 50% of the reported value of the company or of the securities that it has issued, such as stocks and bonds. Step 3: Using the equation and Step 1, and the results from Step 2, compute the company s risk-based capital requirement RBC requirement = 28 + [ (2) 2 + (2 + 30) ].50 = See pages c. The ratio of the insurer s Adjusted Surplus to the Authorized control level RBC determines the regulator s response. (Adjusted Surplus)/ (ACL RBC) Regulator Response 150% - 200% Company Action Level company submits plans to increase capital and reduce risks to capital. 100% - 150% Regulatory Action Level - Company submits plan as above; regulation may take some corrective action. 70% - 100% Regulator is authorized to (may) take control. < 70% Regulator is authorized to (must) take control. Write an equation to determine the ratio of Adjusted Surplus to ACL: Adjusted Surplus Adjusted Surplus ACL [ R R R (.50 R ) ( R.50 R ) R ] = 146%.50[68.657] Regulatory action level requires the company to submit a plan on how capital will be increased or risk decreased. Regulator has the authority to restrict future writing of business. Copyright 2013 by All 10, Inc. Page 11

12 Solutions to questions from the 2007 exam (continued): Question 34 - CAS Model Solution 2 a. R0 = *.5 = 28 R1 = 0 (no charge for US gov. bonds) R2 = 100*.15 = 15 R3 =.1 *40 *.5 = 2 R4 =.1 *40 * = 32 R5 = 20 b. RBC req. = 28 + ( ) = $68.657M c. Adjusted surplus/rbc Req. = 50/ = 72.8% The company is in the regulatory action level. The company must submit a plan to the domiciliary insurance department detailing the changes it intends to make to return to an adequate RBC level. The insurance commissioner has the right but not the obligation to take action against the company such as by restricting new business. 35. (1 point) Provide two arguments to support the following statement: "The risk-based capital formula adds additional incentives for companies to report inadequate reserves." Question 35 - CAS Model Solution 1 1. By reporting inadequate reserves the calculated reserving risk charge is lower, in turn, the RBC requirement is reduced 2. As a liability, lower reserves than needed increases policyholders surplus greater surplus increases the RBC ratio Question 35 - CAS Model Solution 2 1. The RBC formula provides incentives for companies to reduce reserves since this increases PHS and therefore, increases the RBC ratio since adjusted RHS is in the numerator. 2. The RBC formula provides incentives for companies to reduce reserves since reducing reserves will lower adverse development and therefore, the reserving risk charge will be lower. Copyright 2013 by All 10, Inc. Page 12

13 Solutions to questions from the 2008 exam: Question 28- Model Solution a. (2 points) Calculate XYZ's reserving risk (R4) charge. Step 1: Write an equation to determine R4. R4 = {[Loss Reserves + Non-Tabular Discount] * Reserving Risk Charge %} - [Unadjusted RBC charge](.25)(.30), where.30 is the Loss Sensitive Offset, and.25 is the % of WC reserves written on loss sensitive contracts Step 2: Write an equation to determine the reserving risk charge percentage: Co Avg Dev *Ind RBC% Ind RBC% Ind AvgDev Res Risk Charge % 1 Adj for II Givens: The RBC charge =.273, the discount factor =.872, and the ind avg development factor = Step 3: Using the equation in Step 1, the result from Step 2, and the data given in the problem, solve for R * Res Risk Charge % % 2 [Loss Res + Non-Tabular Discount] * Reserving Risk Charge % =.108 (500, ,000) = 56,841 [Unadjusted RBC charge](.25)(.30) = 4,263 R4 = 56,841 (56,841)(.25)(.30) = 52,578 b. (2 points) Calculate XYZ's written premium (R5) risk charge. Step 1: Write an equation to determine R5 WP Charge = WP * WP Risk Charge % - [Unadjusted RBC charge](.20)(.30), where.30 is the Loss Sensitive Offset, and.20 is the % of WC written premium written on loss sensitive contracts. Step 2: Using the equation in Step 1, and the data given in the problem, solve for R5 WP Risk Charge % = [(Comp Avg L&LAE Ratio/Ind Avg L&LAE Ratio) * Ind L & ALAE Ratio + Ind L & ALAE Ratio)/2] * Adj II + Comp Underwriting Expense Ratio 1.0 (0.85 / 0.901)* WP Risk Charge % * % 2 Written Premium * WP Risk Charge % = 300,000 *.069 = 20,700 [Unadjusted RBC charge](.20)(.30) = 20,700 *.2 *.3 = 1,242 R5 = 20,700 1,242 = 19,458 c. (1 point) Calculate XYZ's total risk-based capital requirements. Show the value of each risk charge category, R0 through R5, separately. R 0 = 1,000 (capped at carrying value); R 1 = 10,000 and R 2 = 15,000 and R 3 = 4,000 were given R 4 = 52,578 and R 5 = 19,458 were calculated in parts a. and b. above. R3 (after adjustment) requires that ½ of R3 be removed and added to R4. RBC requirement = 1,000 + [(10,000) 2 + (15,000) 2 + (4,000 2,000) 2 + (52, ,000) 2 + (19,458] 1/2 =61,715 Copyright 2013 by All 10, Inc. Page 13

14 Solutions to questions from the 2008 exam: Question 28 - Model Solution (continued): d. (0.5 point) Calculate XYZ's risk-based capital ratio. Write an equation to determine the ratio of Adjusted Surplus to ACL: Adjusted Surplus PHS - NonTabular Discount 75,000-25, % ACL [ R R R (.50 R ) ( R.50 R ) R ].50[61,584] e. (0.75 point) Identify the RBC action level and briefly describe the responses required of the company and of the state insurance commissioner under this level. The ratio of the insurer s Adjusted Surplus to the ACL RBC determines the regulator s response. (Adjusted Surplus)/ (ACL RBC) Regulator Response 150% - 200% Company Action Level company submits plans to increase capital and reduce risks to capital. 100% - 150% Regulatory Action Level - Company submits plan as above; regulation may take some corrective action. 70% - 100% Regulator is authorized to (may) take control. < 70% Regulator is authorized to (must) take control. Since 1.62 is >1.5 and < 2, the company is at the company action level. It must submit a plan for how it will get ratio above 2.0. No action by the regulator is required. Solutions to questions from the 2009 exam: Initial comments. The two model solutions are nearly identical with the exception of how the risk reserving charge is calculated in part a. In the first model solution, reserves equal [Loss Reserves + Non-Tabular Discount] while in the second model solution, reserves equal Loss Reserves only. Per E&Y, the Reserve Risk Charge % is applied to Company Net Loss & LAE Unpaid, gross of non-tabular discount + Other Discount Amount Not Included in Unpaid Loss & LAE. See table 62 Question 32 - Model Solution 1 a. (2 points) Calculate the reserving risk charge for Workers' Compensation. Step 1: Write an equation to determine R4. R4 = {[Loss Reserves + Non-Tabular Discount] * Reserving Risk Charge %} Step 2: Write an equation to determine the reserving risk charge percentage: Co Avg Dev *Ind RBC% Ind RBC% Ind AvgDev Res Risk Charge % 1 Adj for II Given: The Ind L+LAE ratio=.273, the adj for II=.872, and the ind average development factor is given as Step 3: Using the equation in Step 1, the result from Step 2, and the data given in the problem, solve for R * Res Risk Charge % % 2 R4 = [Loss Res + Non-Tabular Discount] * Reserving Risk Charge % =.108 (1, ) = Copyright 2013 by All 10, Inc. Page 14

15 Solutions to questions from the 2009 exam (continued): Question 32 - Model Solution 1 (continued) b. (1 point) Calculate the loss concentration factor and the net Loss and Loss Adjustment Expense (LAE) RBC charge for reserves. Loss concentration factor = 70% + 30% Largest Line Reserve = 70% + 30% % Total Reserves 1500 Net loss and LAE RBC Charge For Reserves = LCF * [RBC charge + Tabular Discount] =.90( ) = Question 32 - Model Solution 2 a) Reserving Risk. 1. Co. Adj = ( ) / Industry Adv L + LAE = RR % = (0.273 x ) x (II Adj = 0.872) 1 = 10.8% RR Charge for WC= 1,000 x 10.8%= 108 b. Loss concentration factor = 70% + 30% Largest Line Reserve Total Reserve Reserving charge = ( ) x 90% =187.2 = 70% + 30% % 1500 Solutions to questions from the 2010 exam: Question 30 - Model Solution 1 RBC Reserve Risk Charge = [ ½ (Industry Avg Dev + Comp Arg Dev)/Industry Avg Dev * Industry worstcase+1] * Interest Margin -1 GL RBC Reserve = [ ½ ( )/1.075 * ]/ 1.075]* = (1.035 * ) * Risk Charge % = 19.3% WC RBC Reserve = [ ½ ( )/1.030 * ] * = (0.993 * ) * Risk Charge %= 10.8% GL RBC Reserve Risk Charge = Unpaid Loss * GL RBC Charge % =1 5,000,000 * 19.3% = 2,895,000 WC RBC Reserve Risk Charge % = unpaid loss * WC RBC Charge% = 6,000,000 * 10.8% =648, % Retro-rated Adjusted = 648,000 * (1 40% * 30% ) WC RBC Charge = 570,240 Loss Concentration Factor = 70 % +30 % *(Largest line reserve/ total reserve) = 70% +30%*15,000,000/(15,000, ,000,000) = 70% + 30% * = Company s RBC = (2,895, ,240) * Reserves Risk Charge = 3,167,229 Copyright 2013 by All 10, Inc. Page 15

16 Solutions to questions from the 2010 exam (continued): Question 30 - Model Solution 2 GL: (1 + (1.150/ 1.075)) / 2 = Risk Load % = ( * 1.035) * = GL Risk Charge = 15M * = $2,889, WC: (1 + (1.015/1.03)) / 2 = Risk Load % = ( *.9927) * = 10.83% WC Risk Charge = 6M * 10.83% = 649, Now Adjust WC for the retro-rated plans WC Risk Charge = 649, * [ * (1 0.3)] = $571, Now concentration factor = * (15/(15+6) = R4 = [2,889, ,943.24] * = $3,164, Question 30 - Model Solution 3 RBC Reserving Risk Charge % = [ ½ (Company coverage/ industry coverage * industry worst case + industry worst case) + 1] * discount rate 1 GL = [ ½ (1.15/1.275 * ) + 1] * = WC = [ ½ (1.035/1.03 * ) + 1] * = RBC Reserve Risk Charge = RBC % * unpaid losses GL= (15,000,000) = 2,889,621.8 WC = (6,000,000) = 649,935.5 WC charge needs to be reduced by 30 % for retrospective policies WC charge [649,935.5(.4)(.7) + 649,935.5 * (.60 )] = 571, Total Reserving Risk Charge = 2 889, , = 3,461, This needs to be adjusted for the loss concentration factor =70% * 30% * (reserves in largest line/ total reserves) = 70% + 30% * (15,000,000/21,000,000) = RBC Reserve Risk Charge= 3,461, * = 3,164,859.5 Copyright 2013 by All 10, Inc. Page 16

17 Solutions to questions from the 2010 exam: Question 36 - Model Solution A. Denominator = 50 % * RBC requirement < 70% Mandatory Action Level 70 % to 100% Authorized Action Level 100 % to 150% Regulatory Action Level 150 % to 200% Company Action Level B. Statutory Surplus/(RBC *.50) = 150/(32*.50) = 937.5% >200% C % * 61 = % * 150 = [150 X]/(32*.50) < 200% x > 118 The min [7.32, 30, 118 ] = 7.32 Also, Loss and LAE reserve may increase to 70, which is an increase of = 9 D. 9 > Thus, a risk of material adverse deviation exists E. XYZ next to RBC action level: Company action level Commissioner: no action needed XYZ: Submit a report to commission, let commission know how XYZ will increase capital. Question 36 Additional Model Solutions parts a. and b. A. RBC Range Company 75%-100% Regulatory 50%-75 % Authorized 35%-50% Mandatory < 35% Denominator = RBC requirement, in this case 32 B. RBC ratio = Adjusted Surplus/RBC Requirement ( I am assuming there are no non-tabular discounts) =150/32 = 4.68 There is no current action level. The company has sufficient surplus to capital. Copyright 2013 by All 10, Inc. Page 17

18 Solutions to questions from the 2011 exam: Question 4 CAS Model Solutions parts a - d a. RBC ratio = Adjusted Surplus RBC Action level 75% - 100% Company Action level 50% - 75% Regulatory Action level 35% - 50% Authorized Control level 1. Company action level: 75% - 100% of RBC or 150% - 200% of ACL 2. Regulatory action level: 50% - 75% of RBC or 100% - 150% of ACL 3. Mandatory control level: <35% of RBC or <70% of ACL 1. Company: 150% - 200% of authorized control level (=50% x RBC) 2. Regulatory: 100% - 150% of authorized control level 3. Authorized: 70% - 100% of authorized control level b. 1. Company Action Level: Company submits written plan for RBC ratio improving; regulator does nothing. 2. Regulatory Action Level: company submits written plan for RBC ratio improvement, regular may take some supervisory action at his discretion. 3. Authorized Control Level: Company submits written plan for RBC ratio improvement, regulator may take control of the company. 1. Company submits a plan of action about how it intends to raise surplus. Regulatory action not required. 2. In addition to above regulators now authorized to take action against company, such as restricting new business. 3. Regulators must now take control of company and put it into receivership as a prelude to liquidation or rehabilitation. 1. Company must submit plan of action for how they will increase surplus; regulator takes no action. 2. Company must submit plan of action for how they will increase surplus; regulator may step in and put restriction on company such as ordering them to reduce writings. 3. Company must submit plan and also take direction from regulators; commissioner now authorized to take over company but is not required to do so. c. 1. Minimum capital requirements: RBC replaces or supplements existing ad hoc minimum capital and surplus requirements. 2. Solvency monitoring: provides tool for regulators to ascertain if company is in financial distress. 3. Legal Authority: provides authority for regulators to restrict actions or take control of company. d1. To identify a level above which a company s surplus must stay. d2. To regulate the solvency of a company. d1. Ratemaking: use of RBC to determine rates consumers should be charged. d2. Marketing: use of RBC to advertise a company s financial strength. d1. Calculating profit provision within rates using RBC. d2. Marketing insurer s strength to the public. Copyright 2013 by All 10, Inc. Page 18

19 Solutions to questions from the 2011 exam (continued): 23a. (0.5 point) Determine the Industry Loss and LAE RBC Percentage for each line of business. 23b. (1.5 points) Determine the Base Loss and LAE Reserve RBC for this insurer (the R4 Charge before application of the Loss-Sensitive Discount, Claims-Made Discount and Loss Concentration Factor). 23c. (0.75 point) Calculate the Loss-Sensitive Discount amount (in dollars) for Workers' Compensation. Question 23 CAS Model Solutions part a a1. - WC: Industry Loss and LAE RBC% = the highest worst case scenario avg adverse development = 27% - MM: Industry Loss and LAE RBC% = the highest worst case scenario avg adverse development = 57% a2. - Industry loss and LAE RBC % is the worst case factor. WC: highest is 27% in 2005 MM: highest is 57% in 2003 Question 23 CAS Model Solutions part b Step 1: Write an equation to determine R4. R4 = {[Loss Reserves] * Reserving Risk Charge %} Step 2: Write an equation to determine the reserving risk charge percentage: Reserving Risk Charge % = [(1.0 + Adjustment * Ind L+LAE ratio)(adj for II) - 1.0], where Adjustment [ ( industry avg dev factor company avg dev factor) 2] industry avg development factor For WC, the Ind L+LAE ratio is given as.27, the adjustment for II is given as.89, the company avg development factor is given as 1.21 and the industry avg development factor is given as For MM, the Ind L+LAE ratio is given as.57, the adjustment for II is given as.81, the company avg development factor is given as 1.08 and the industry avg development factor is given as Step 3: Using the equation in Step 1, the result from Step 2, and the data given in the problem, solve for R WC Reserving risk charge % 1 *.27 * % 2* MM Reserving risk charge % 1 *.57 * % 2*1.04 Thus, WC R4 = [Loss Res] * Reserving Risk Charge % =.146 (500,000) = 73,010 Thus, MM R4 = [Loss Res] * Reserving Risk Charge % =.2806 (1,500,000) = 420,868 Copyright 2013 by All 10, Inc. Page 19

20 Solutions to questions from the 2011 exam (continued): Question 23 CAS Model Solutions part b b , * 1 * , WC: ,500, * 1 * , MM: Initial R4 73, , ,878 b2. - WC: MM: *.27 1 * , , Total 73, , , ,500, ,863 b3. - WC Company Loss and LAE RBC % Basic R 4 % ½ *27% 28.8% (1.07) WC Basic R 4 % 128.8% * % WC basic R 4 charge 14.6%*500,000 73,000 -MM Company Loss and LAE RBC % ½ *57% 58.1% 1.04 Basic MM R 4 % % * % MM Basic R 4 charge 28.1%*1,500, ,500 Total Basic Loss and LAE Reserve RBC = WC + MM 73, , ,500 Copyright 2013 by All 10, Inc. Page 20

21 Solutions to questions from the 2011 exam (continued): 23c. (0.75 point) Calculate the Loss-Sensitive Discount amount (in dollars) for Workers' Compensation. Question 23 CAS Model Solutions Part c Of the insurer s $500,000,000 in WC reserves, 50%, or $250,000,000, is for accidents on business written on retrospectively rated plans. This business gets the 30% reduction for loss-sensitive contracts. Two step computation: 1. The loss-sensitive discount equals the % of loss-sensitive business * the loss-sensitive offset factor * the "Base Loss + LAE Reserve RBC" 2. The final reserving risk charge is the initial reserving risk charge loss sensitive discount c1. - Discount % * Dollar Discount.15* 73, ,952 c % reduction for primary business that is loss sensitive:.3 *.5 * 73, , 952 This will reduce the 73,010 charge to 62,059 c3. - WC Loss Sensitive Discount 30%* Loss Sensitive %* Basic WC R 4 30%*50%*73, ,950 Copyright 2013 by All 10, Inc. Page 21

22 Solutions to questions from the 2012 exam Question 4 - Sample Answer - Part a Two triggers for Mandatory Corrective Action: Fact finding by regulator indicates policyholders may be at risk Poor results on financial examinations RBC Ratio is within Regulatory Action Level ( or 50-75) RBC Ratio is below Company Action Level IRIS ratios show abnormality / fail IRIS ratios Insurer s ability to pay claims has deteriorated (Close to) Insolvency Liabilities are greater than assets Company has problems paying claims / obligations Insurer experiencing excessive growth Reserve inadequacy Large Catastrophe Loss Insurer Fraud Two actions for Mandatory Corrective Action: Submit a plan to improve financial status Suspend or limit dividends to policyholder/stockholders Limit or withdraw from specified investments Require insurer increase capital / surplus Restrictions on writing or renewing business Limit renewal of non-guarantee renewable policies Require insurer to reduce liabilities Require increased reinsurance (reduce liabilities) Limit expenses (commission expenses, general expenses) Require insurer to document the adequacy of its rates Two triggers for Administrative Supervision Mandatory Corrective Action fails Financial Conditions are worse than previous level Fact finding by regulator indicates policyholders may be at risk Poor results on financial examinations RBC Ratio is within Authorized Control Level ( or 35-50) RBC Ratio is below Regulatory Action Level Failing multiple IRIS ratios (Close to) Insolvency Liabilities are greater than assets Company has problems paying claims / obligations Insurer experiencing excessive growth Reserve Inadequacy Large Catastrophe Loss Insurer Fraud Copyright 2013 by All 10, Inc. Page 22

23 Solutions to questions from the 2012 exam Question 4 - Sample Answer Two Actions for Administrative Supervision Insurer will need regulator s consent/approval for the following (or regulator may limit/restrict/prohibit): Incur new debt/financing Issue new or renewal policies Renewing policies that are not guaranteed-renewable Writing premiums Purchase Reinsurance Merge with another insurer Sell or transfer assets or in-force business Change Management Changes to Executive / management compensation Making certain investments Withdrawing or lending funds PART b When company is in financial distress and must surrender the company to the commissioner and they determine the fate of the company (liquidate/rehab). Must access assets and liabilities to determine position as well as reserve adequacy. When a receiver is assigned to manage a company s assets and distribute funds for obligations faced. Receiver is a disinterested person assigned to be in charge of a company s receivership. Receivership is when a receiver (an unbiased disinterested third party) takes control of an insurer and its assets in attempts to stabilize cash flows. Receiver is established to stabilize assets and liabilities leading to either rehabilitation or liquidation. When judge declares insurer insolvent, places company in court ordered receivership, in which regulator designates receiver to assume control and act to safeguard interests of policy holders/taxpayers during rehab and/or liquidation process. PART c Liquidation is when a company cannot rehabilitate and all the assets are sold to make payments for everyone owed. Must follow a certain order in making payments (UEP return is usually last). Rehabilitation insurer continues to service policy holders with creditors satisfying claims from future earnings. One outcome is liquidation when the assets are sold off to pay off the company s debts. Liquidation all assets are liquidated to pay as many liabilities as possible and company is dissolved. Copyright 2013 by All 10, Inc. Page 23

24 Solutions to questions from the 2012 exam Question 4 - Examiner s Report Part a The most common incorrect answers confused Mandatory Corrective Action with the Mandatory Control Level of the RBC. Mandatory Corrective Action aligns with the Regulatory Action Level, which is not as severe. Some candidates only provided the triggers, but not the actions that the regulator could take under each of the levels. If a candidate did not read the entire question, they may have missed that they needed to provide actions as well. Also, many candidates only gave one trigger (instead of two) for each level. Part b Many candidates knew that a receivership involved the regulator taking control of the company (or putting it in the hands of a third party). However, some candidates neglected to provide the receiver s goals or obligations. Part c The two correct answers were rehabilitation and liquidation. Candidates who failed to get full credit often did not explain these two events sufficiently. Solutions to questions from the 2012 exam: 20a. (4.25 points) Determine the written premium RBC charge (in dollars) after application of the losssensitive discount, claims-made discount and premium concentration factor. General information from the Feldblum RBC article is presented here. It is included as a prelude to solving the problem since many of the concepts discussed in this excerpt apply to the types of calculations needed to be performed to solve question 20 from the 2012 exam. Note: E&Y do not mention the discount for CM. Workers Compensation Of the company's $500,000,000 in WC WP, 20%, or $100,000,000, is written on retrospectively rated plans. o This business gets the 30% reduction for loss-sensitive contracts, so the final RBC charge is multiplied by (30%)*(20%) = 94%. o The adjustment to the RBC Charge Factor is [( )/2]/0.901 = o The adjusted loss & LAE ratio is *1.008 = The capital charge before the loss-sensitive contract offset is Written Premium *{[(Adjusted RBC Charge Factor*Discount Factor) + Expense Ratio] 1.0} o $500,000,000 * { [( * 0.836) ] 1} = $34,419,170. o $34,419,170 * 94% = $32,354,020, the final WP charge. Two step computation. o The loss-sensitive discount is 6% * $34,419,170 = $2,065,150. o The final written premium charge is $34,419,170 - $2,065,150 = $32,354,020. Medical Malpractice (but not mentioned in the E&Y text) The MM charge has an offset of 20% for CM business. Since 53.3%, or $80,000,000, of the $150,000,000 premium is written on CM business, the final RBC charge is multiplied by (20%)*(53.3%) = 89.33%. o The company adjustment to the RBC Charge Factor is [( ) + 2] = o The adjusted loss & LAE ratio is *1.472 = The capital charge before the CM business offset is Written Premium * {[(Adjusted RBC Charge Factor * Discount Factor) + Expense Ratio] 1.0. o $150,000,000* {[(1.494*0.778) ] 1} = $61,890,615. o $61,890,615 * 89.33% = $55,294,075, the final charge. Copyright 2013 by All 10, Inc. Page 24