Casualty Actuarial Society Review and Comparison of Rating Agency Capital Models

57 Pages·2006·0.26 MB·English

Casualty Actuarial Society
Review and Comparison of Rating
Agency Capital Models

Joseph R. Lebens, FCAS, MAAA
François Morin, FCAS, MAAA, CFA

November 2006

© Towers Perrin

Reprinted and distributed by the
Casualty Actuarial Society with permission
Table of Contents
1. EXECUTIVE SUMMARY...................................................................................................1
Approach................................................................................................................................1
Areas of Research..................................................................................................................2
Conclusions............................................................................................................................3
2. OVERALL APPROACHES................................................................................................5
Determination of Adjusted Capital..........................................................................................6
Required Capital – Risk Categories........................................................................................8
Required Capital – Investment Risk........................................................................................8
Required Capital – Underwriting Risk...................................................................................18
Required Capital – Other Risks............................................................................................27
Results and Interpretation.....................................................................................................32
Relative Contribution of Risk Categories..............................................................................39
3. LOSS RESERVE ADEQUACY........................................................................................40
4. QUALITATIVE FACTORS................................................................................................44
5. ENTERPRISE RISK MANAGEMENT DEVELOPMENTS..............................................46
6. REFERENCES.................................................................................................................49
APPENDIX I – HISTORICAL AM BEST RATINGS.............................................................50
APPENDIX II – HISTORICAL BCAR SCORES...................................................................51
APPENDIX III – HISTORICAL S&P RATINGS....................................................................52
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APPENDIX IV – HISTORICAL MOODY’S RATINGS..........................................................53

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1. EXECUTIVE SUMMARY
The Tillinghast business of Towers Perrin was asked by the Dynamic Risk Modeling
Committee (DRM) of the Casualty Actuarial Society (CAS) to undertake a research project
to review and compare the various capital adequacy models currently employed by rating
agencies.
This research project is not intended to opine on the reasonableness of the methods and
assumptions used by each of the models. Rather, it is intended to provide professionals
interested in the financial strength of property/casualty insurance companies with a reference
guide to compare the various models and reconcile the results between them.
Approach
As a starting point, we identified the various models currently in use in the property/casualty
insurance industry. While there are more models in use, we limited our review to the
following capital adequacy models:
RATING AGENCY CAPITAL ADEQUACY MODELS
List of Models Reviewed
Rating Agency Model Name
National Association of Insurance Commissioners (NAIC) Risk-Based Capital (RBC)
A.M. Best Company (A.M. Best) Best’s Capital Adequacy Ratio (BCAR)
Standard and Poor’s (S&P) Standard and Poor’s Capital Adequacy Ratio (CAR)
Moody’s Investor Service (Moody’s) Moody’s P&C Risk Adjusted Capital Model (MRAC)

While the NAIC is not in itself a rating agency, the RBC model introduced in December
1993, effective for the 1994 and subsequent Annual Statements, is generally considered the
ancestor of most rating agency models, and as such, provides a good foundation to
understand how the models have evolved to their current state.
FitchRatings (Fitch) also provides ratings and research on property/casualty insurance
companies worldwide. Their rating process is similar to the other agencies, although they
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have not provided details through publicly available documents on how they perform their
quantitative analysis. At the time of this writing, it is our understanding that Fitch is
currently developing a multi-line capital adequacy model designed to upgrade their current
capabilities.
Regulators and rating agencies alike are primarily concerned with insurance company
solvency, although the rating agencies’ mission is slightly different. A.M. Best’s [3]
objective is to “provide an opinion of an insurer’s financial strength and ability to meet
ongoing obligations to policyholders.” Hence, while rating agencies may set a higher bar to
attain a certain rating, all models are concerned with the evaluation of all sources of risk
potentially affecting an insurer.
In order to perform the comparison, we relied on public information as well as proprietary
documents that describe in significant detail the various models in use.
Areas of Research
All capital adequacy models attempt to capture the various sources of risk affecting an
insurer. In order to perform a meaningful comparison, we developed the following list of
items to guide us through this research project:
(cid:132) Insurance Product Segmentation
(cid:132) Asset Type Segmentation
(cid:132) Risk Categories
(cid:132) Risk Charges (Underwriting, Catastrophe, Credit, etc.)
(cid:132) Time Horizon
(cid:132) Risk Metrics
(cid:132) Risk Tolerance Level
(cid:132) Data Used in Parameterization
(cid:132) Diversification of Risk
(cid:132) Calibration of Results to Rating Levels
(cid:132) Output and Results

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Conclusions
All models share the same basic concepts in determining the amount of required capital. The
models differ in their actual implementation of the concepts, either:
(cid:132) in the underlying factors used to calculate the required capital (e.g., the risk charges
applied to the different bond categories), or
(cid:132) through application of the concept (e.g., calculation of their respective capital adequacy
ratios)

With the exception of the MRAC model, all of the models use a factor-based approach; the
MRAC model combines the results from a Monte Carlo simulation with a factor-based
approach.
All models generally rely on the NAIC Annual Statement for most of the model inputs1.
The rating agency capital models reviewed are nearly identical in a few aspects:
(cid:132) Insurance Product Segmentation – Schedule P lines of business are generally used as the
basis to segment the business underwritten by the company
(cid:132) Risk Categories – all models capture the same risk categories, some in slightly greater
detail
(cid:132) Time Horizon – with the exception of the MRAC model, the models measure capital at a
point in time (usually as of December 31st )
(cid:132) Data Used in Parameterization – many of the factors are based on work performed by the
American Academy of Actuaries Property/Casualty Risk-Based Capital Task Force in
1993

1 Throughout this paper, we will describe the models relative to a U.S.-domiciled property and casualty
insurance company filing a statutory property and casualty Annual Statement. It is our understanding that the
rating agency models have been adapted to meet different data reporting requirements in other countries.
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The asset type segmentations defined by the capital adequacy models are also generally
consistent with each other, except for slight variations in the segmentations of the bond/fixed
income category.
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2. OVERALL APPROACHES
The basic concept underlying all models is the same: each model is designed to measure the
capital adequacy of a company as of a certain point in time by comparing the calculated risk-
based required capital to the company’s actual capital. The company’s actual capital is
generally based on the company’s reported policyholders’ surplus, after adjustment for
factors such as the equity in loss reserves. These adjustments are designed to level-out the
playing field between companies.
The RBC, BCAR and S&P models determine the required capital by applying risk charge
factors to annual statement values. All the models rely on the NAIC Statutory Annual
Statement for most of the model inputs. In many cases the factors used are very consistent or
identical. The source of the factors depends on the risk category; proprietary factors for
some risk categories make each model unique. Individual risk charges are calculated for the
different risk categories and are then aggregated. The RBC and BCAR models use a square
root rule to reflect the diversification benefits of combining the different risk category
charges; S&P’s model does not explicitly reflect diversification benefits.
The approach underlying the MRAC model is to simulate a one year total profit or loss of the
company. Their model produces 60,000 trials and the 99.9% confidence interval is defined
to be the company’s required capital. While most risk categories in the MRAC model use
this stochastic approach, others use a factor-based approach similar to the other models.
Their model automatically captures risk diversification.
The models calculate ratios of the company’s adjusted capital to the aggregated risk-based
capital (post any diversification benefit). The rating agencies have calibrated their models so
that ranges of results produced by the models correspond to predetermined ratings under
their proprietary rating system. For example, the results of the BCAR model are calibrated
such that a result of 175% implies a balance sheet strength rating of A++. Of course, other
qualitative factors are considered before making a final determination of the company’s
rating. Some of the additional qualitative considerations are discussed in more detail in a
subsequent section of this report.
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Determination of Adjusted Capital
All capital adequacy models, while generally focused on absolute results for a given
company (i.e. how much capital do I need to achieve a certain rating?), are calibrated to
provide the rating agencies a measurement stick to compare different companies to each
other. As such, policyholders’ surplus as reported in the annual statement is generally
adjusted in order to put companies on a level playing field.
RBC
The RBC formula computes the Total Adjusted Capital (Post-Deferred Tax) by adjusting
actual policyholders’ surplus for the following items:
(cid:132) Non-tabular discounts are moved from surplus to reserves
(cid:132) If the insurer owns a life subsidiary, the following may also be added to surplus:
 Asset valuation reserve
 Reserves for voluntary investments
 50% of the liability for policyholder dividends
(cid:132) Capital notes are also added to surplus

BCAR
A.M. Best calculates Adjusted Surplus (APHS) by adjusting a company’s reported surplus
for the following:
(cid:132) Unearned Premium Reserve Equity (Net of Tax)
(cid:132) Loss Reserve Equity (Net of Tax)
(cid:132) Fixed Income Equity (Net of Tax)

In addition, they make adjustments for the following items:
(cid:132) Surplus Notes
(cid:132) Off-Balance Sheet Losses
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