Chris Nyce, FCAS, MAAA KPMG Senior Manager AAA Updated Research on the NAIC Risk Based Capital (RBC) Formula Research on the Effectiveness of a Trend Test in the Property/Casualty RBC Formula Chris Nyce, FCAS, MAAA KPMG Senior Manager

Disclaimer These results are based on research conducted by a subgroup of the American Academy P/C RBC Committee Views expressed today are based on the research, but do not necessarily reflect the views of the Academy, CAS, KPMG, or the NAIC who of course makes all decisions about changes to the RBC formula Examples used are illustrative, and not a reference to any specific company Anyone who says otherwise is not only wrong, but is itching for a fight

The Mission of the AAA RBC Committee Began the research with a charge NAIC expressed concern that RBC was becoming more of a lagging indicator, not useful in predicting companies that become weaker “Given the use of a trend test in the life RBC formula, is the application of a trend test in the Property/Casualty RBC formula a good idea?” Our interpretation- Not a “Yes/No” question Instead-”What is the most effective way of differentiating between companies above the Company Action Level that are likely to fall below it, and those that are likely to remain above it.” We approached this with a one year future time horizon, i.e. based on observable data this year, what will happen next year

Status of the Work These ideas were presented in the Spring 2004 CAS meeting, prior to release of the Academy report Academy issued a report on August 26, currently featured on the casualty cover page of the Academy website The Academy report did not recommend incorporating the finding in RBC formulas, instead concluded the one certain approach is a “best predictor” of those examined NAIC PC RBC subgroup did recommend on August 31, 2004 that this trend test be incorporated into the RBC formula, and a company being flagged results in CAL Exposure period ends November 11, 2004 NAIC considers comments, votes at December meeting Could vote yes, no, or further deliberation If yes, likely implementation in 2005

Background Life test currently uses a trend test Applies to companies with RBC between 250% and the company action level (“CAL”) of 200% RBC ratio is the ratio of capital to RBC required capital Life test looks at past changes in RBC Max of last year and the three year average decline in margin for each company Apply that change to the current RBC position If below 190%, company is deemed to be at the CAL Note that even before our work, the feeling of committee members was that the life trend test did not work well for P/C companies We quickly confirmed this to be true

Our Approach Basic question-”What is the most effective predictor of decline in capital adequacy?” In general terms, used “Hypothesis Testing” Examined specific cases of past company failures Formulated hypotheses on the causes of RBC decline Tested the hypotheses using statistical tests on annual statement data Conducted additional tests by examining the effectiveness retrospectively Measured the results using a specific set of metrics Selected one approach that produced the best metrics

Boundaries of our Study Did not constrain ourselves to examining the life formula Based on publicly filed data from the NAIC blank And used company level data, due to conclusions in the work leading to the original formula that this was appropriate Outcome has to be intuitively correct, and simple All research also from public data sources For NAIC data, company names remained confidential Outcome had to be based on empirical data, not on our preconceived opinions

Data Considerations For “micro” analysis we used public data sources such as AM BEST and press reports NAIC provided 5 year history of all requested data elements Confidential as to company identifier About 2400 companies Used data through 2002 for statistical tests, updated through 2003 for retrospective test We scrubbed the data, in general separately for each test to maximize data points utilized Screened out invalid entries and extreme values

Micro Results-Initial Hypotheses Companies we examined could be characterized as experiencing trouble due to various causes, such as: High levels of reinsurance recoverables, causing high leverage in estimating reserves, and exposure to disputed balances High leverage of premiums and reserves to surplus Reserve inadequacies coming to roost Poor operating results Fraud and misrepresentation Ill-liquid or incorrectly valued assets Under-funded pensions: (usually a contributor, not a cause)

What is the Best Early Indicator of Future Capital Declines? Lack of Liquidity Reserve Inadequacies Fraud Bad Assets Past Capital Declines Leverage Poor Profitability

Overall “Macro” Approach Performed statistical tests on the NAIC database Explored the basic relationships behind each hypothesis Performed retrospective tests on characteristics of companies just prior to falling to the CAL Set up metrics to evaluate the outcome of the retrospective test Determined recommendations based on all of the above

Statistical Tests Explored relationships between hypothesized variables Performed tests on the NAIC database of 2400 companies for 5 years ending 2002 Looked for statistical tendencies Generally used correlation and regression analysis Examined the percentage of variation explained Calculated the measures of significance Used to corroborate and explain retrospective result Note that a poor result in our tests does not necessarily mean that the measure is not good for IRIS or other financial evaluations And high correlations don’t necessarily mean the hypothesis would form a good trend test

Statistical Test of Life Type Trend Test Does a simple life type of trend test work? Correlation between year to year changes in RBC ratio for all companies= -23% (wrong sign) For only companies near the CAL = 1% In 2001 and 2002, the direction of the change in subsequent years was only the same 41% of the time Changes in market asset valuations dominated any characteristics of companies themselves Implication: Life type of trend test is worse than random guessing for P/C Companies

What About Underwriting Results and Reserve Runoff? Correlation between subsequent year combined ratios= 25% to 34% between 2000-2002 For only companies near CAL correlation is 33% to 75% (highly significant) Reserve Runoff Correlation between subsequent year runoff ratios=33% to 37% between 2000 and 2002 For only companies near CAL correlation is 29% to 35% This is good and bad news Statistical relationship is strong But still only predicts a portion of the subsequent year outcome

What is the Predictive Power of Leverage? Gross Leverage Correlation between gross leverage and subsequent year RBC ratio change= -1% to 1% between 2000-2002 For only companies near CAL correlation is –5% to –3% (not significant) Net Leverage Correlation between net leverage and subsequent year RBC ratio change= 3% to 4% between 2000-2002 For only companies near CAL correlation is 1% to 16% (wrong sign) This is not a good outcome Statistical relationship is weak and sign is sometimes wrong

Well then it must be Liquidity? Correlation between liquid assets to surplus and subsequent RBC change is –4% to 1% over 2001 to 2002 Depending on sample, relationship is not significant, or sign is wrong

In 2002 and 2003, Portion of Companies Falling to CAL RBC Ratio in Prior Year Total Companies in Sample Number of Companies Falling to CAL Percentage Falling to CAL 200% to 300% 314 30 9.6% 300% to 350% 166 9 5.4% 350% to 400% 205 4 2.0% 400% to 450% 176 3 1.7% Greater than 200% 3582 55 1.5%

Retrospective Tests Performed on NAIC database of 2400 companies ending 2003 Generally “Yes/No” Measured whether the hypothesis accurately predicted the subsequent year outcome, or not Therefore, scrubs were oriented toward invalids, but not toward extremes Measured on three metrics Effectiveness-Percentage of overall correct predictions False alarms-Percentage of companies flagged that did not deteriorate to CAL Failing Companies Flagged-Percentage of companies that subsequently declined to the CAL that were correctly flagged

Retrospective Approach Started by setting a threshold such as leverage above industry average, or combined ratio above 110%, etc. Based on the threshold, companies were “flagged” or “not flagged” Allowed for mixed approaches; Leverage, reserve runoff, and combined ratio Reserve runoff and combined ratio Three year tests of reserve runoff and combined ratio Adjusted the threshold to optimize the metrics Based on trial and error Understand, this test tells us not what causes RBC decline, but what best predicts it Although the implication for the cause is pretty clear

Retrospective Metrics

An Effective Approach Based on Tests RBC Ratio Current Year Combined Ratio Company Status 200%-300% Greater than 120% More Likely to Decline to CAL-”flagged”   Less than 120% Less Likely to Decline to CAL 300%-350% Greater than 134% Less than 134% Above 350% All

Further Metrics from the Combined Ratio Trend Test   Total Companies % Flagged % Of Companies Falling <200% in Subsequent Year Flagged Not Flagged Total Two-Tiered CR Test for Companies 200%<RBC<250% 143 47% 17.9% 6.6% 11.9% Two-Tiered CR Test for Companies 250%<RBC<300% 171 33% 2.6% 7.6% Two-Tiered CR Test for Companies 300%<RBC<350% 166 16% 14.8% 3.6% 5.4% Total Population 200%<RBC<350% 480 31% 17.3% 3.9% 8.1%

Why not 100% Effective Formula approach doesn’t account for capital changes (contributed, dividend) Financial statements can always be subject to restatement RBC ratio decline could involve fraud, or an other wise solid looking asset losing value Or pension funding The statistical relationship is strong, but is not 100% predictive of direction and magnitude Need to keep the test simple

Could a PC RBC Trend Test be Appropriate? Hypothetical Formula Change Additional Companies at CAL Resulting True Alarms, Those Falling <200% False Alarm True Alarms to Total Flagged Change the CAL to 250% 143 17 126 11.9% Implement a “Life” type trend test for Companies 200%<RBC<250% 117 13 104 11.1% Implement a combined ratio trend test for Companies 200%<RBC<250% 67 12 55 17.9% Implement a combined ratio trend test for Companies 200%<RBC<300% 123 22 101 Implement a combined ratio trend test for Companies 200%<RBC<350% 150 26 124 17.3%