2011 Research – Short-Term Project Report A Report of the CAS Underwriting Risk Working Party ______________________________________________________________________________ Abstract: At the request of the American Academy of Actuaries, the CAS formed the Risk-Based Capital (RBC) Underwriting Risk Working Party (URWP) to research the current RBC formula for measuring underwriting risk and the procedures for calibrating the formula’s parameters (the Current Calibration Method). The research unveiled various accuracy and consistency issues with the Current Calibration Method. Some alternatives are investigated and areas of further research are suggested, including volume of data, data filtering, curve fitting, the investment income offsets (IIO) discount rate, time horizon, and the relative impact of premium and reserve charges by line. This paper presents results of the URWP’s short-term charge. Keywords. risk-based capital; RBC; underwriting risk, reserve risk; premium risk; risk horizon ______________________________________________________________________________ Underwriting Risk Working Party Emmanuel Bardis Timothy Gault Thomas Loy Robert Butsic Shira Jacobson Daniel Murphy Pablo Castets James Kahn (Chair) Nicole Elliott Allan Kaufman G. Chris Nyce Brian Fannin Alex Krutov Andrew Staudt Sholom Feldblum Giuseppe (Franco) Jennifer Wu Kendra Felisky LePera Linda Zhang EXECUTIVE SUMMARY In 2011 the Underwriting Risk Working Party (URWP) of the Casualty Actuarial Society (CAS) researched the potential for improvements to the calculation of underwriting risk (reserve and premium) charges within the constraints of the current NAIC RBC formula and its current parameter calibration procedures. This report summarizes the results of our short-term charge. • The current data sources—confidential company RBC filings and the most recently available Schedule P—yield too few observations for stable estimates of RBC factors from one calibration cycle to the next. Additional data sources should be investigated. • Filtering eliminates a significant amount of company experience from the current calibration method. For many lines of business the majority of the companies in the industry are eliminated; for two lines, all companies are eliminated. New ways to filter out questionable data should be investigated. Possible alternatives are discussed in the report. • The method of basing the RBC reserve risk factor on empirical reserve run-off ratios is subject to high volatility due to the limited data available and to the natural behavior of mathematical ratios. We are quite confident that it is inevitable that from one calibration cycle to the next RBC factors will change to an unsatisfactorily significant degree. This volatility may be mitigated by additional data, alternative filtering procedures, basing charges on statistics from fitted curves rather than from the empirical data alone, or designing Casualty Actuarial Society E-Forum, Winter 2012-Volume 1 1 A Report of the CAS Underwriting Risk Working Party structural changes to RBC’s reserve risk calculation. • There is evidence that the current calibration method understates the indicated reserve risk charge for companies with smaller booked reserves and overstates the charge for companies with larger booked reserves. Some method of varying the factor by size of booked reserve could be investigated. • The Investment Income Offset (IIO) discount factor of 5% that has always been in place is inconsistent with the current environment. Although selecting the most appropriate discount rate and allowing it to float with the market is not without controversy, research is warranted to improve the implied safety margin of the RBC’s underwriting risk. This research should be coordinated with other RBC risk areas. • There are many differences between the NAIC RBC and the Solvency II approach to risk- based capital. One difference is the time horizon for measuring reserve risk. The Solvency II Standard Formula measures reserve risk over a one-year time horizon while RBC measures reserve risk over the claim run-off period. We illustrate RBC reserve risk factors on the basis of a one-year risk horizon from the RBC data currently available. An analysis of the relative strengths and weaknesses of the current run-off horizon versus a one-year horizon is beyond the scope of the URWP’s short-term charge. • Procedures for comparing the performance of alternative RBC formulas and calibration methods should be investigated. One useful approach investigated in the report is based on pro forma premium to Company Action Level RBC underwriting risk ratios. • A comparison of RBC premium and reserve risk factors suggests that companies entering a line of business may have a lower RBC charge per dollar of premium than established companies. Casualty Actuarial Society E-Forum, Winter 2012-Volume 1 2 A Report of the CAS Underwriting Risk Working Party 1. INTRODUCTION We present a summary of the research as of mid-2011 conducted by the Underwriting Risk Working Party (URWP) of the Casualty Actuarial Society (CAS). 1.1 Research Context At the request of the American Academy of Actuaries the CAS formed the Underwriting Risk Working Party (URWP) to conduct research regarding the Underwriting Risk (Premium and Reserves) components of the NAIC’s Risk-Based Capital (RBC) formula. The Academy requested the research to take place in two stages, through a long-term and a short-term charge. 1.1.1 Long-Term Charge Provide general research that identifies better ways to quantify reserve and premium risks in solvency monitoring, and to determine capital charges to account for those risks. The measurement of underwriting risk would involve identification of an amount of capital for each company that specifically reflects the company’s underwriting risk profile to the extent practical in an RBC context. To accurately reflect risk, detailed measurements might use techniques that differ from the current RBC formula, and development of such techniques is left as a long-term research subject. 1.1.2 Short-Term Charge Research ways to improve the calculation of reserve and premium charges within the constraints of the current NAIC RBC formula and the current parameter calibration procedures. The URWP recognizes that accurate measurement of risk may require structural changes to the measurement formula. However, in the short term, we analyze some of the assumptions and implications in the current RBC formula and propose possible improvements within the existing framework. Casualty Actuarial Society E-Forum, Winter 2012-Volume 1 3 A Report of the CAS Underwriting Risk Working Party 1.2 Objective We provide details on our investigation into the short-term charge and explain the long-term issues that we may address in future research. 1.3 Disclaimers The analysis and opinions expressed in these pages are solely those of the Working Party members, and in particular are not those of the members’ employers, the Casualty Actuarial Society, or the American Academy Actuaries. Equivalent values in separate tables may differ due to rounding. 1.4 Outline The remaining sections in this report are as follows: Section 2: Background and Methods Section 3: Results and Discussions (Short-Term Issues addressed in this report) Section 3.1 Filtering Section 3.2 Risk Charge Measurement Section 3.3 Investment Income Offset (IIO) Section 3.4 Observations Regarding Solvency II Section 3.5 Pro Forma Premium to Company Action Level (CAL) RBC Underwriting Risk Ratios Section 4: Conclusions and Areas of Further Research Acknowledgements and Appendices Casualty Actuarial Society E-Forum, Winter 2012-Volume 1 4 A Report of the CAS Underwriting Risk Working Party 2. BACKGROUND AND METHODS 2.1 Introduction to the Current Calibration Method When RBC was established in 1993, premium and reserve risk charges were based on analysis and judgment. The factors were updated in 2008, 2009, and 2010. The RBC factors are currently based on an approach we call the Current Calibration Method. The selected factors adopted for 2008, 2009 and 2010 were the factors indicated by the Current Calibration Method subjects to limitations (“caps”) in movement of ±15% each year for 2008 and 2009. In 2010, the cap was ±5%. The Current Calibration Method begins with 10x10 triangles (ten accident years by ages 1 through 10 years) for all lines of business for all companies. The source is Schedule P data for long-tailed lines and the RBC filing for short tail lines1. Data for certain companies is removed from this data set and extreme values for some data points are limited based on criteria which we discuss below. We refer to this data editing as “filtering.” Filtering in the Current Calibration Method is described in section 3.1. Reserve Risk For calculation of the reserve charges, the Current Calibration Method uses nine data points for each selected company by RBC line of business. The first of these data points is the total reserve development on total reserves from the oldest evaluation date to the current statement date, representing nine years of development. The next data point is total reserve development from the second-oldest evaluation date to the current statement date, representing eight years of development. The subsequent points follow the same pattern. The Current Calibration Method then calculates a statistic, currently the 87.5th percentile, from these data, which, after investment income offset, is considered the indicated “INDUSTRY LOSS & EXPENSE RBC%” factor that would otherwise appear in Line 04 in report PR016 for the relevant line of business. This indicated factor is subject to the following limitations before becoming the final selected factor (or “RBC charge”) for that line: • The selected INDUSTRY LOSS & EXPENSE RBC% cannot be less than 5% (the “5% minimum charge”). • The change in the selected factor from year to year is “capped.” • Other potential NAIC overrides. 1 It is not uncommon for companies to complete their RBC filings for short tail lines with only the most recent evaluation (i.e., the list diagonal of the accident year triangle). Since incomplete triangles flag companies to be eliminated in the filtering process (see Section 3.1), such “shortcut” company practices curtail the volume of data for short tail line RBC calibration. Casualty Actuarial Society E-Forum, Winter 2012-Volume 1 5 A Report of the CAS Underwriting Risk Working Party Premium Risk For calculation of the premium charges, the Current Calibration Method uses the ten accident year loss ratios evaluated at the current date by RBC line of business. The maturity of this loss ratio for the oldest accident year in Schedule P is ten years; for the second-oldest accident year, nine years; and so forth. The Current Calibration Method then calculates a statistic, currently the 87.5th percentile, from these data, which, after investment income offset, is considered the indicated “INDUSTRY LOSS & EXPENSE RATIO” factor that would otherwise appear in Line 04 in report PR017 for the relevant line of business. This indicated factor is subject to the following limitations before becoming the final selected factor (or “RBC charge”) for that line: • The selected INDUSTRY LOSS & EXPENSE RATIO plus the industry average company operating expense ratio (27.5% currently) less unity cannot be less than 5% (the “5% minimum charge”). • The change in the selected factor from year to year is “capped.” • Other potential NAIC over-rides. Casualty Actuarial Society E-Forum, Winter 2012-Volume 1 6 A Report of the CAS Underwriting Risk Working Party 3. RESULTS AND DISCUSSION 3.1 Filtering Filtering in the Current Calibration Method is primarily accomplished by eliminating entire companies from the RBC database according to the following rules. For reserve risk, a company is eliminated if it has: • negative paid values in any AY as of any statement date. • negative reserve values in any AY as of any statement date. • negative incurred loss and DCC in any AY as of any statement date. • fewer than ten accident years with non-zero loss data as of some evaluation date. For premium risk, a company is eliminated if it has: • average AY earned premium less than $500,000. • any AY loss ratio <= 0%. • less than eight AYs with net earned premium greater than 20% of its average earned premium for all AYs. • fewer than ten years of earned premium. For companies that remain, filtering takes the form of constraints on the observations that appear in the RBC database: • For the calculation of premium risk, loss ratios are capped at 300%. • For reserve risk, reserve run-off ratios, expressed as the ratio of reserve development to booked reserves, are constrained to lie between -100% and 400%. Filtering in the Current Calibration Method eliminates a large portion of industry data for all lines of business. In most lines, less than 50% of available industry observations are used in developing reserve and premium charges, as shown in Exhibit 1 below.2 2 Unless otherwise noted the RBC data used in this report is as of 12/31/2008. Casualty Actuarial Society E-Forum, Winter 2012-Volume 1 7 A Report of the CAS Underwriting Risk Working Party Exhibit 1: Current Company Filtering Percentage of Industry Data Utilized Line Reserve Reserve Premium Premium Line Letter Dollars Companies Dollars Companies (1) H/F A 81.7% 39.0% 95.7% 57.0% (2) PPA B 85.1% 42.5% 95.6% 57.0% (3) CA C 80.6% 40.2% 90.5% 53.7% (4) WC D 82.5% 41.4% 91.1% 54.9% (5) CMP E 71.0% 40.3% 93.0% 56.7% (6) MM Occurrence F1 43.0% 10.7% 74.0% 20.3% (7) MM CM F2 59.2% 14.2% 71.9% 21.3% (8) SL G 64.5% 18.7% 83.3% 31.2% (9) OL H 64.4% 27.7% 89.8% 43.5% (11) Spec Prop I 29.9% 26.9% 89.0% 51.8% (12) Auto Phys Damage J 31.3%* 12.8%* 95.8% 56.9% (10) Fidelity & Surety K 29.8% 8.6% 88.9% 31.2% (13) Other L 25.7% 10.5% 68.7% 22.6% (15) International M 20.5% 1.4% 28.9% 1.9% (16) Reins Property & Financial N&P 34.3% 7.7% 63.3% 20.9% (17) Reinsurance Liab O 15.9% 4.4% 49.9% 13.8% (18) Products Liability R 48.4% 19.7% 75.1% 31.0% (14) Fin & Mort S ** ** ** ** (19) Warranty T ** ** ** ** Average 67.1% 31.7% 91.3% 51.6% *Salvage and subrogation development often produces negative reserves which result in many companies being excluded from the reserve data by the current filter. ** Not enough data Dollar measure is based on total reserve dollars utilized divided by total reserve dollars for industry Company measure is based on number of companies utilized divided by total number of Companies Average is weighted average using 2008 industry data To measure the effect on risk charges of the filtering in the Current Calibration Method, we tested the effect of an alternative filtering process that eliminates individual data points rather than entire companies. Exhibit 2 shows the charges that would result from the use of a filter based on the size of the underlying data which targets use of 90% of industry premium dollars or reserve dollars, as appropriate. In the case of the Homeowners/Farmowners line, for example, the alternative filter eliminated all reserve run-off ratio observations where total booked reserves (the denominators of the reserve run-off ratios) are less than $9.4 million for calculating the reserve charges, and eliminated all loss ratios where the earned premium is less than $30.5 million for calculating the Casualty Actuarial Society E-Forum, Winter 2012-Volume 1 8 A Report of the CAS Underwriting Risk Working Party premium charges. As a result, 90% of Homeowners/Farmowners industry dollars are used in the calibration calculations (a decrease from the Current Calibration Method for premium). Appendix A shows the thresholds and the dollar utilization percents by line of business. The alternative filter ensures that 90% of industry dollars are used for all lines of business. Filtering by data point also allows data from insolvent, run-off, withdrawn, and new companies to be reflected in the RBC charges. Lines of Business with Insufficient Data Post-Filter For International and Financial/Mortgage Guarantee there was not enough data after the Current Filter to calibrate factors. The NAIC judgmentally set the 2010 International charge equal to its previous value prior to application of the IIO. The Financial/Mortgage Guarantee charge was also set equal to its previous value and then increased due to the housing market collapse by the maximum amount allowable under the post-IIO 5%-cap constraint. The Indicated values for these two lines are shown as “N/A” (not available) in column (4) of Exhibit 2. The Alternative Filter keeps enough data to calibrate factors for International but not for Financial/Mortgage Guarantee. The “Average” values include no adjustment for loss sensitive business or diversification by line of business. The averages also do not include provision for the other quantities included in the RBC’s R4 and R5 calculations – reinsurance (R4 only), excessive premium growth, and A&H business. Casualty Actuarial Society E-Forum, Winter 2012-Volume 1 9 A Report of the CAS Underwriting Risk Working Party Exhibit 2: Effect of Alternative Company Filtering Reserving RBC charge Premium RBC Charge (1) (2) (3) (4) (5) (6) (7) (8) Current Alternative Current Alternative 2010 Filter Filter 2010 Filter Filter Line Line Letter Actual Indicated Indicated Actual Indicated Indicated (1) H/F A 0.127 0.127 0.080 0.169 0.152 0.149 (2) PPA B 0.106 0.050 0.050 0.171 0.138 0.118 (3) CA C 0.121 0.121 0.120 0.154 0.099 0.106 (4) WC D 0.099 0.111 0.092 0.142 0.125 0.111 (5) CMP E 0.283 0.283 0.214 0.100 0.069 0.055 (6) MM Occurrence F1 0.238 0.053 0.213 0.672 0.572 0.541 (7) MM CM F2 0.153 0.156 0.118 0.178 0.392 0.352 (8) SL G 0.119 0.050 0.100 0.087 0.075 0.066 (9) OL H 0.287 0.303 0.479 0.125 0.093 0.094 (11) Spec Prop I 0.151 0.231 0.244 0.168 0.050 0.067 (12) Auto Phys Dam J 0.085 0.050 0.191 0.094 0.065 0.050 (10) Fidelity & Surety K 0.246 0.229 0.821 0.073 0.160 0.050 (13) Other L 0.133 0.115 0.268 0.121 0.119 0.153 (15) International* M 0.160 N/A 0.155 0.333 N/A 0.270 (16) Reins Property & Financial N&P 0.159 0.424 0.150 0.480 0.823 0.536 (17) Reinsurance Liability O 0.482 0.975 0.554 0.446 0.601 0.424 (18) Products Liability R 0.382 1.030 0.899 0.215 0.272 0.110 (14) Fin & Mort* S 0.111 N/A 0.111 0.585 N/A 0.585 (19) Warranty** T 0.246 0.229 0.821 0.073 0.160 0.050 Average 0.201 0.254 0.255 0.155 0.135 0.116 * Not analyzed. Factors judgmentally set. Refer to text. ** Set equal to Fidelity & Surety due to limited data. Charges are shown after IIO and are subject to the 5% minimum charge. Average is weighted average using 2008 industry data. For the purpose of averaging, N/As in columns (4) and (5) were replaced by the column (3) value; in columns (7) and (8) by column (6). Premium RBC charges in this and all other exhibits based on industry average expense ratio of 27.5%. Note: In this and subsequent exhibits the “2010 Actual” factors reflect the cap on changes in the factors selected by the NAIC to be 5% in 2010. Factors labeled as “indicated” reflect no such caps. We note that the current filtering was intended to avoid distorting effects due to new companies and run-off companies; we believe the distortions, if any, might not be as large as feared and could be eliminated by other means. We also note that the current filtering was intended to generate a database of companies that all have the same number of loss ratio observations (ten) and the same number of reserve run-off ratio observations (nine). With alternative filtering that eliminates data points rather than entire Casualty Actuarial Society E-Forum, Winter 2012-Volume 1 10