kpmg

Research on the Effectiveness of a Trend Test in the Property/Casualty RBC

Formula

Chris Nyce

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, 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

Our Mission

Began the research with a charge- “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 time horizon, i.e. based on observable data this year, what will happen next year

Status of the Work

Ideas to be discussed here have cleared the Academy RBC committee

Formal report has been written, and is being modified based on comments for review by the AAA counsel

- Note this is the normal procedure for AAA committee work product

Will be submitted to NAIC for consideration at the June meeting

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 ratio- Max of last year and the three year average RBC

decline for each company- Subtract result from current RBC ratio- 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

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 LiquidityReserve

Inadequacies

Poor Profitabilit

y

Fraud

Leverage

Bad Assets Past Capital

Declines

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?

Underwriting Results- 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

ThresholdRatio of failing

cos flaggedFalse

alarms/totalEffectiveness

RatioTotal # of

Companiestrend 62% 47% 50% 480-20% 67% 30% 67% 480-17% 64% 36% 61% 4807% 46% 43% 53% 4805% 46% 37% 59% 480

650% 56% 48% 48% 480350% 54% 46% 51% 480

Composite 64% 34% 63% 480Composite 69% 42% 56% 480-20%/34% 67% 26% 71% 480

Life Trend TestTest Year UW RatioThree Year Average UW Ratio

Composite UW and RunoffComposite uw/runoff/leverageTwo Tiered Underwriting Test

Test Year Runoff RatioThree Year Average Runoff RatioGross Leverage, End of Test YearNet Leverage, End of Test Year

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

An Effective Approach Based on Tests

RBC Ratio

Current Year Combined Ratio

Company Status

200%-300%

Greater than 120% CAL

  Less than 120% No Regulatory Action

300%-350%

Greater than 134% CAL

  Less than 134% No Regulatory Action

Above 350%

All No Regulatory Action