Casualty Actuarial Society E-Forum, Fall 2014-Volume 2
Casualty Actuarial SocietyE-Forum, Fall 2014-Volume 2
The CAS E-Forum, Fall 2014-Volume 2The Fall 2014-Volume 2 Edition of the CAS E-Forum is a cooperative effort between the CAS EForum Committee and various other CAS committees, task forces, or working parties.This E-Forum contains Report 9 of the CAS Risk-Based Capital Dependencies and CalibrationWorking Party (Reports 1 and 2 are posted in E-Forum Winter 2012-Volume 1; Reports 3 and 4 inE-Forum Fall 2012-Volume 2; Report 5 in E-Forum Summer 2012; Report 6 in E-Forum Fall 2013;Report 7 in E-Forum Fall 2013; and Report 8 in E-Forum Spring 2014).Risk-Based Capital Dependencies and Calibration Research Working PartyAllan M. Kaufman, ChairpersonKaren H. AdamsEmmanuel TheodoreBardisJess B. BroussardRobert P. ButsicPablo CastetsDamon Chom, ActuarialStudentJoseph F. CofieldJose R. CouretOrla DonnellyChris DoughertyNicole ElliottBrian A. FanninSholom FeldblumKendra FeliskyDennis A. FranciskovichTimothy GaultDean Guo, Actuarial StudentJed Nathaniel IsamanShira L. JacobsonShiwen JiangJames KahnAlex KrutovTerry T. KuruvillaApundeep Singh LambaGiuseppe F. LePeraZhe Robin LiLily (Manjuan) LiangThomas Toong-Chiang LoyEduardo P. MarchenaMark McCluskeyJames P. McNicholsGlenn G. MeyersCasualty Actuarial Society E-Forum, Spring 2014Daniel M. MurphyDouglas Robert NationG. Chris NyceJeffrey J. PflugerYi PuAshley Arlene RellerDavid A. RosenzweigDavid L. RuhmAndrew Jon StaudtTimothy Delmar SweetserAnna Marie WetterhusJennifer X. WuJianwei XieJi YaoLinda ZhangChristina Tieyan ZhouKaren Sonnet, Staff Liaisoni
CAS E-Forum, Fall 2014-Volume 2Table of ContentsCAS Research Working Party ReportRisk Based Capital (RBC) Underwriting Risk Charges: Differences inPremium and Reserve Risk Charges by Ceded Reinsurance UsageReport 9 of the CAS Risk Based Capital (RBC) Research Working PartiesIssued by the RBC Dependencies and Calibration Working Party (DCWP) . 1-53Independent ResearchOn the Use of Stock Index Returns from Economic Scenario Generators inERM ModelingMichael G. Wacek, FCAS, CERA, MAAA . 1-11Casualty Actuarial Society E-Forum, Fall 2014-Volume 1ii
E-Forum CommitteeDennis L. Lange, ChairpersonCara BlankMei-Hsuan ChaoMark A. FlorenzMark M. GoldburdKarl GoringDerek A. JonesDonna Royston, Staff Liaison/Staff EditorBryant RussellShayan SenRial SimonsElizabeth A. Smith, Staff Liaison/Staff EditorJohn SopkowiczZongli SunBetty-Jo WalkeQing Janet WangWindrie WongYingjie ZhangFor information on submitting a paper to the E-Forum, visit http://www.casact.org/pubs/forum/.Casualty Actuarial Society E-Forum, Fall 2014-Volume 1iii
Risk Based Capital (RBC) Underwriting Risk Charges:Differences in Premium and Reserve Risk Charges by CededReinsurance UsageReport 9 of the CAS Risk Based Capital (RBC) Research Working PartiesIssued by the RBC Dependencies and Calibration Working Party (DCWP)Abstract: The paper examines the extent to which indicated Premium Risk Factors (PRFs) and Reserve RiskFactors (RRFs) are related to ceded reinsurance usage.Prior DCWP work found that company insurance impairment probabilities generally increase as cededreinsurance usage increases.1In this report, we show that that PRFs and RRFs are higher for companies with an elevated reinsurance usage forall-lines combined, for nearly all lines of business (LOBs) and generally across LOB-sizes than for companieswith lower usage. This result allows us to connect the earlier impairment rate findings, which did not implyparticular capital charges to mitigate the increased risk, to the indicated risk charges for the RBC formula.This is one of several papers being issued by the Risk Based Capital (RBC) Dependencies and CalibrationWorking Party.Keywords: Risk-Based Capital, Capital Requirements, Analyzing/Quantifying Risks, Assess/Prioritizing Risks,Integrating Risks1. INTRODUCTION AND FINDINGS1.1 Prior DCWP ResearchDCWP Report 4, Review of Historical Insurance Company Impairments,2 showed that relativeimpairment probability increased as the ceded reinsurance usage increased (Report 4 Table 7). Thispattern applied to all group sizes combined and separately to each size group, except for the smallest20%, of company-sizes (Report 4 Tables 7 - 10).Further not-yet-published DCWP research, using a multi-factor regression model, also showedthat elevated ceded reinsurance usage (“Elevated Re”) generally implied higher relative impairmentprobabilities, after controlling for company characteristics such as size, LOB concentration, andstate concentration.1.2 FindingsIn this report, we test the extent to which Elevated Re is associated with higher indicated PRFsA Review of Historical Insurance Company Impairments (Report 4), CAS E-Forum, Fall RBC-DCWPRpt4.pdf2 Ibid.1Casualty Actuarial Society E-Forum, Fall 2014-Volume 21
Differences in Premium and Reserve Risk Charges by Ceded Reinsurance Usage (Report 9)and RRFs 3In DCWP Reports 6 and 74 indicated PRFs and RRFs by line of business (LOB) are determinedusing accident year (AY) premiums and loss ratios (Report 6) and initial reserves and reserve runoffratios (Report 7) net of ceded reinsurance. The PRFs and RRFs by LOB indicated by the methodsdescribed in Reports 6 and 7 are determined using data from all companies, regardless of the level ofceded reinsurance usage. For this analysis, we segment the companies based on the cededreinsurance usage.Table 1.1 on the next page shows that PRFs and RRFs increase as reinsurance usage increases.The horizontal axis in Table 1.1 represents the percentage of ceded reinsurance that is used toseparate the data between Base ceded reinsurance usage (“Base Re”) and Elevated Re. The PRF orRRF for Base Re is the PRF or RRF indicated using the data points with reinsurance usage at orbelow the selected Separation Point, (“Reinsurance Separation Point” or “Separation Point”). ThePRF or RRF for Elevated Re is the PRF or RRF indicated using the data points with reinsurancepercentage usage above the selected Separation Point.The vertical axis is the difference between PRFs or RRFs for the data points with Elevated Recompared to the PRFs or RRFs for the data points with Base Re. For example, the vertical axis valueof approximately 20% at the horizontal value of 50% reinsurance Separation Point means that theindicated PRF for all data points with reinsurance usage above 50% is 20% of Net Earned Premium(NEP) higher than the indicated PRF for all data points with ceded reinsurance usage of 50% orless.3Ahigher value of the 87.5th percentile of loss ratios or runoff ratios could be due to higher mean values, greatervariability around the mean or a combination thereof.4 Casualty Actuarial Society E-Forum, CAS Research Working Party on Risk-Based Capital Dependencies andCalibration (DCWP), Risk Based Capital (RBC) Premium Risk Charges – Improvements to Current Calibration Method,Report 6, Fall 2013, andCasualty Actuarial Society E-Forum, CAS Research Working Party on Risk-Based Capital Dependencies and Calibration(DCWP), Risk Based Capital (RBC) Reserve Risk Charges – Improvements to Current Calibration Method, Report 7,Winter 2014.Casualty Actuarial Society E-Forum, Fall 2014-Volume 22
Differences in Premium and Reserve Risk Charges by Ceded Reinsurance Usage (Report 9)Table 1.1PRF and RRF Variations by Reinsurance UsageDifferences in Indications between Elevated Re vs. Base ReAll Lines CombinedIn addition to the all-lines combined analysis summarized in Table 1.1, we also examined theexperience at three sub-levels: (a) by company-size for all-lines combined, (b) by LOB4 and (c) byLOB-size5 within each LOB. By all-lines company-size: We also observed higher indicated PRFs/RRFs for ElevatedRe. The differences were largest for the smallest company-size group and the differencesgenerally decreased with company size.By LOB: Weobserved higher indicated PRFs/RRFs for Elevated Re for most LOBs.By LOB-size groups: The same pattern was evident, but less consistent. The smallestLOB-size group (first 15th percentile) showed the largest yet most variable differences. AsLOB-size grew above the 50th percentile size group, the differences between Base andElevated PRFs/RRFs are typically smaller. The 75th-95th percentile LOB-size group hadseveral LOBs where Elevated Re produced lower (rather than higher) PRFs and RRFs.Table 1.2 below summarizes the analysis and the tables found in Section 3.5For LOBs and LOB-size groups with more than a minimum number of data points (50) in Elevated Re.Casualty Actuarial Society E-Forum, Fall 2014-Volume 23
Differences in Premium and Reserve Risk Charges by Ceded Reinsurance Usage (Report 9)Table 1.2Summary of FindingsPRFs and RRFs for Elevated Re vs. Base ReTable(s)3.1a-3.1bData GroupAll lines combined3.2a-3.2bAll lines combinedBy company sizeFindingsPRF/RRF differences grow as the SeparationPoint between Elevated versus Base Re grows.At the 40% Separation Point, the comparison ofElevated to Base Re is:- PRF is 15.5% of NEP higher- RRF is 13.0% of initial reserveshigher.PRFs/RRFs for Elevated Re are higher than forBase Re across all company-size groups.The smallest companies have the largestdifferences.3.3a-3.3bBy LOBAll sizes combinedFor most lines, PRFs at Elevated Re are at least12% higher than at Base Re, and RRF’s are atleast 10% higher.Exceptions are usually LOB’s with a lowernumber of data points.3.3a-3.3b,3.4a-3.4b andAppendix ABy LOB;by LOB-size groupWith Elevated Re, PRFs and RRFs are generallyhigher across all size groups.The smallest LOB-sizes have the largestdifferences.PRFs, compared to RRFs, show more consistentdownward trend in difference as the LOB-sizegroup increases.In the remainder of this report: Section 2 provides more detail regarding (a) the ceded reinsurance data (b) and the riskdata used to establish the PRFs and RRFs.Section 3 presents the results of our analyses.Section 4 discusses the relationship between the findings in this report and thereinsurance credit risk charge in R3.Section 5 provides thoughts on further research.Section 6 is a glossary of key terms.Appendix A provides further detail regarding risk factor differences between Base andElevated Re, by LOB and LOB-size group.Appendix B provides a summary of an analysis using ceded reinsurance data fromSchedule F, to compare to the analysis in Section 3 based on ceded reinsurance data fromSchedule P.Casualty Actuarial Society E-Forum, Fall 2014-Volume 24
Differences in Premium and Reserve Risk Charges by Ceded Reinsurance Usage (Report 9) Appendix C provides further detail on filtering of data points used in the analysis.Appendix D shows that the maturity of PRF and RRF data points does not affect ourfindings.1.3 Terminology, Assumed Reader Background and DisclaimerThis paper assumes the reader is generally familiar with the property/casualty RBC formula6 andhas a working knowledge of DCWP Reports 6 and 7.In this paper, references to “we” and “our” refer to the principal authors of this paper. The“working party,” and “DCWP” refer to the CAS RBC Dependencies and Calibration Working Party.The analysis and opinions expressed in this report are solely those of the authors, and inparticular are not those of the authors’ employers, the Casualty Actuarial Society, or the AmericanAcademy of Actuaries.DCWP make no recommendations to the NAIC or any other body. DCWP material is for theinformation of CAS members, policy makers, actuaries and others who might makerecommendations regarding the future of the P&C RBC formula. In particular, we expect that thematerial will be used by the American Academy of Actuaries.This paper is one of a series of articles prepared under the direction of the DCWP.2. DATAIn our analysis we use two types of data: Information to assess indicated PRFs and RRFs (Risk Data). Information to determine ceded reinsurance usage (Reinsurance Usage Date).The sections below discuss risk data (2.1) and reinsurance usage data (2.2).2.1 Risk DataThe data we used to determine indicated PRFs and RRFs is as described in DCWP Reports 6 and7.In brief, the premium risk data consists of AYs 1988-2010 loss and loss adjustment expenseratios, net of reinsurance, at the latest available maturity from Schedule P, Part 1, in the 1997-2010Annual Statements, by LOB and by company for individual companies and DWCP-defined grouppools, as indicated. Thus, each data point is a single AY and LOB for a single company or poolFor a detailed description of the formula and its basis, see Feldblum, Sholom, NAIC Property/CasualtyInsurance Company Risk-Based Capital Requirements, Proceedings of the Casualty Actuarial Society, 1996and NAIC, Risk-Based Capital Forecasting & Instructions, Property Casualty, 2010.6Casualty Actuarial Society E-Forum, Fall 2014-Volume 25
Differences in Premium and Reserve Risk Charges by Ceded Reinsurance Usage (Report 9)(LOB-Company-AY).7Similarly, the reserve risk data consists of reserve runoff ratios for initial reserve dates 1988-2009.The ratios, net of reinsurance, are through the latest available maturity from Schedule P, Parts 2 and3, in the 1997-2010 Annual Statements, by LOB and company for individual companies andDWCP-defined group pools, as indicated. Thus, each data point is the runoff ratio from a singleinitial reserve date and LOB for a single company or pool (LOB-Company-Initial Reserve Date).For this analysis, we also constructed all-lines data points. For PRFs, the all-lines premium foreach company-AY data point is the sum of the NEP for all LOBs in the PRF data set. The all-linesloss ratio is the all-lines average loss ratio weighted by NEP by LOB for the LOBs included in thePRF data.8 For RRFs, the all-lines reserve for each company-initial reserve date is the sum of theinitial reserves for all LOBs in the RRF data set. The reserve runoff ratio is the all-lines averagereserve runoff ratio weighted by initial reserve by LOB.2.2 Reinsurance Usage DataFor each LOB-Company-AY PRF data point and each LOB-Company-Initial Reserve Date RRFdata point, the ceded reinsurance percentage is the AY Ceded Premium divided by AY Direct plusAssumed Premium by LOB by company, from the 1998-2010 Annual Statements (i.e., values inSchedule P, Part 1, column 2 divided by column 1.)For the PRF data points this reinsurance usage ratio closely matches the premium in the datapoint, and the RBC charge is based on that premium. For RRF data points, the reinsurance usageratio in the initial reserves would be the most closely related reinsurance usage ratio. However, theceded reinsurance reserves for initial reserve dates earlier than 1996 cannot be obtained from theAnnual Statements available for our research. Therefore we use the ceded premium reinsurancepercentage as a proxy for the ceded reinsurance applicable to reserve runoff ratios. The effect usingthe premium proxy is a matter for further research. We did find the RRF results using a loss-basedreinsurance usage ratio (the three-year ceded AY incurred loss, including IBNR, divided by thethree-year direct plus assumed AY incurred loss) produced results that were very close to the resultsusing the premium-based reinsurance ratio from the PRF analysis.2.3 FilteringWe excluded data points that had negative direct plus assumed earned premium or cessionpercentages equal to or greater than 100%. We also used a minimum cession percentage of 0% when7 In constructing the PRF and RRF data sets we removed certain data points using the filtering process explained inSection 3.2.2 of DCWP Reports 6 and 7, for premium risk and reserve risk, respectively.8 Because the all-lines data points are constructed from the filtered LOB data points, the all-lines data only includes linesin which the LOB component of the LOB data point satisfied the Report 6 and 7 filtering tests.Casualty Actuarial Society E-Forum, Fall 2014-Volume 26
Differences in Premium and Reserve Risk Charges by Ceded Reinsurance Usage (Report 9)the calculated ratio indicated a negative cession.We also excluded data points in which there was a significant inconsistency in the AY NEPbetween the risk data and the Schedule P data. These inconsistencies are all in the “two-year” lines,9and the extent of the inconsistencies is summarized in Appendix C. These inconsistencies arisebecause the risk data is obtained from the NAIC 10 year RBC reporting of “two-year” lines whilethe reinsurance usage data is from the two years of data publically available in Annual Statements.We looked at the effect of including or excluding the data points with these inconsistencies and wefound that the impact was negligible.2.4 Schedule FSchedule F provides an alternative way to assess reinsurance usage. In Appendix B, we show theeffect of using Schedule F data for reinsurance usage rather than the Schedule P data. Schedule Fdata is less useful in that it is not available by LOB, it is not available by accident year and it is onlyavailable for 1996 and subsequent evaluation dates. On the other hand, Schedule F allows us toseparate reinsurance with affiliates from other reinsurance. The Schedule F results are similar to theSchedule P results.3. ANALYSISWe measured the effect of ceded reinsurance usage on PRFs and RRFs at four levels of detail: All LOBs combined, all company-size groups combined By company-size, all LOBs combined By LOB, all LOB-size groups combined By LOB-size group, by LOBThe analyses are discussed in sections 3.1, 3.2 and 3.3 below.3.1 All Lines Combined / All Company-Sizes CombinedIn this section we describe the analysis of Elevated Re on PRFs and RRFs for all lines/allcompany-sizes combined. In this analysis, we used the all-lines PRF and RRF risk data pointsconstructed as described in Section 2.1. Each all-line data point is assigned a Schedule P cededreinsurance percentage described in Section 2.2. At each Reinsurance Separation Point from 10% to90%, in 10% increments, and we calculated the difference between:a) the all-lines indicated PRFs and RRFs for data points with ceded reinsurance above theSeparation Point, i.e., Elevated Re and9Special Property, Auto Physical Damage, Fidelity and Surety, and OtherCasualty Actuarial Society E-Forum, Fall 2014-Volume 27
Differences in Premium and Reserve Risk Charges by Ceded Reinsurance Usage (Report 9)b) the all-lines indicated PRFs and RRFs for data points with ceded reinsurance at or below theSeparation Point, i.e., Base Re.Table 3.1a below shows the results. Column (1) shows the Separation Points. Column (2) showsthe PRF for Base Re given the Column (1) Separation Point. Column (3) shows the PRF forElevated Re given the Column (1) Separation Point. The difference between the two is shown inColumn (4). Column (5) shows the percentage of PRF data points that had ceded percentages lessthan or equal to the ceded percentage in Column (1). Columns (6) through (9) show the sameinformation as Columns (2) through (5) but for RRFs.For example, the 30% row in Table 3.1a column (4) shows that premium risk data points with aceded reinsurance percentage more than 30% have a PRF 10.6% of NEP higher than the PRF datapoints with ceded reinsurance percentages of 30% or less. Looking at the share of data points,column (5), 61.8% of PRF data points have a ceded reinsurance percentage of 30% or less.Similarly, the 30% row in Table 3.1a column (8) also shows that that reserve risk data points withceded reinsurance percentage of higher than 30% have a RRF 11.9% of reserves higher than theRRF data points with ceded reinsurance percentage 30% or less. Looking at the share of data points,column (9), 62.5% of RRF data points have a ceded reinsurance percentage of 30% or less.Table 3.1aPRF and RRF Variations by Reinsurance UsageDifference in Indications between Elevated Re vs. Base ReAll-Lines CombinedReins. ‐‐‐‐‐‐‐‐‐ PRF ‐‐‐‐‐‐‐‐B
Mar 29, 2013 · The Fall 2014-Volume 2 Edition of the CAS E-Forum is a cooperative effort between the CAS E-Forum Committee and various other CAS committees, task forces, or working parties. This E-Forum contains Report 9 of the CAS Risk-Based Capital Dependencies and Calibration Working Party (Reports 1 and 2 are posted in E-Forum
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