evaluation of capital needs in insurance

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1 Evaluation of Capital Needs Jeff Courchene, FCAS, MAAA Kyle Mrotek, FCAS, MAAA Joy Schwartzman, FCAS, MAAA

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Presentation on capital adequacy analysis for property casualty insurance companies, as presented to Milliman\'s 2008 Casualty Consultants Forum in Denver

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Page 1: Evaluation of Capital Needs in Insurance

1

Evaluation of Capital Needs

Jeff Courchene, FCAS, MAAAKyle Mrotek, FCAS, MAAA

Joy Schwartzman, FCAS, MAAA

Page 2: Evaluation of Capital Needs in Insurance

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Capital Capital is amount needed to meet future obligations arising from

business with a high “degree of certainty” over a defined time horizon

Method used to calculate capital depends on the “desired use” of that capital and/or the “customer” being served

Varying views on “degree of certainty” and the time frame over which to make the assessment

Degree of certainty often tied to a “financial” rating

Degree of Certainty Financial Rating

99.9 AAA

99.7 AA

99.4 A

96.9 BBB

Page 3: Evaluation of Capital Needs in Insurance

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Selection of Method to Quantify Capital Needs What question are you trying to answer? Who will use the results?

– Investors– Regulators– Rating agencies– Policyholders– Management

Page 4: Evaluation of Capital Needs in Insurance

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Perspectives/Methods to be Discussed

Static financial projections using a multiple of indicated regulatory RBC Dynamic financial projections simulating a distribution of outcomes to achieve a defined

percentile outcome of capital Regulatory regimes – Solvency II for European Union Perspectives of and requirements for rating agencies

Page 5: Evaluation of Capital Needs in Insurance

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Static Financial Projections

1) Develop financial projections over a multi year period

2) Develop indicated RBC using regulatory “factor based method”

3) Select desired multiple of RBC; consider industry averages either for subsets of companies in same business sector, or other characteristic

4) Develop required capital at each year end using the selected target multiple of indicated RBC

5) Review sources of capital - - what will be contributed from retained earnings versus paid in capital

6) Consider impact of Changes in key forecasting assumptions Alternate reinsurance structures Other business changes

Page 6: Evaluation of Capital Needs in Insurance

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DFA Analysis Evaluating capital needs as the “Tail” of the distribution of outcomes

over a defined period Tail definition

– Two common definitions of the “tail”:• VAR = value at risk: rank results and select result for desired confidence level

(percentile outcome)• TVAR = tail value at risk: rank results and average all scenarios at and beyond the

desired confidence level

Confidence Level– Often linked to companies desired rating– TVAR targets lower confidence level than VAR for comparable level of

certainty

Time Horizon– Often between 1 and 10 years

Page 7: Evaluation of Capital Needs in Insurance

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Solvency II

Page 8: Evaluation of Capital Needs in Insurance

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8

Regulatory Minimum Capital

Assets Ma

rket C

on

sisten

t (fo

r he

dg

ea

ble

)

Be

st Estim

ate

Risk

Margin

MCR

Technical Provisions

Solvency Capital Requirement – SCR Assets covering

Technical Provisions, MCR and SCR

Page 9: Evaluation of Capital Needs in Insurance

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Technical Provisions

Hedgeable insurance obligations

Non-hedgeable insurance obligations

Replication using financial instruments

Sum of discounted best estimate and risk margin

Page 10: Evaluation of Capital Needs in Insurance

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Best Estimate Principles

The Amended Solvency II Framework Directive (article 76, paragraph 2), released in February 2008, states “The best estimate shall be equal to the probability-weighted average of future cash-flows, taking account of the time value of money (expected present value of future cash-flows), using the relevant risk-free interest rate term structure.”

This sentence appears to have been drafted in the spirit of the anticipated IFRS Phase II principles. At face value it may be interpreted as meaning that stochastic reserving will be a requirement for all portfolios. While this approach appears to be inconsistent with QIS4, whose guidance is segregated by level of uncertainty, we are aware that the FSA is presently interpreting article 76 as meaning stochastic reserving will be a requirement for all portfolios! 

Page 11: Evaluation of Capital Needs in Insurance

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Market Value Risk Margin

n

i

ii vSCRfactorCoCRM

1

_

Project SCR

Apply CoC factor (6%) and discount

Need to project future SCRs

Reported at segment level

t=0 is included Market and

premium risk excluded

Page 12: Evaluation of Capital Needs in Insurance

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SCR Principles The Amended Solvency II Framework Directive defines the SCR

(recital 37), as the amount of capital to ensure “that ruin occurs no more often than once in every 200 cases or, alternatively, that those undertakings will still be in a position, with a probability of at least 99.5%, to meet their obligations to policyholders and beneficiaries over the forthcoming 12 months”.

Calculated using standard formulae or via an approved internal model.

Entity specific parameters are being tested in QIS4 for the standard formula approach.

Partial internal models may be permitted, e.g. insurance risk calculated via an approved internal model and other capital charges via standard formulae. The FSA are currently quite keen to promote this approach.

Page 13: Evaluation of Capital Needs in Insurance

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MarketNon-Life Health Default

OperationalBSCR

SCR

Life

Premium & Reserve FX

Cat

Equity

Lapse

Property

Spread

Interest

Expense

Disability

Mortality

Long

Cat

Concentration Revision

Factors

Scenarios with simplified alternative

Health LT

Accident & Health ST

Workers Comp.

= adjustment for risk mitigating effect of future

profit sharing

SCR – (Standard Formula) Structure

Page 14: Evaluation of Capital Needs in Insurance

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Aggregate risk capital for: LifeNon-lifeHealthMarketCounterparty

Adj FDBBasic SCR Adj DT SCR OP

SCR = BSCR - Adj FDB - Adj DT + SCR OP

Adjustment for the risk absorbing effect of future profit sharing

Adjustment for the risk absorbing effect of deferred taxes

Capital charge for operational risk (which does not benefit explicitly from diversification)

SCR Calculation Structure

Page 15: Evaluation of Capital Needs in Insurance

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Market Default Life Health Non-life

Market 1 - - - -

Default 0.25 1 - - -

Life 0.25 0.25 1 - -

Health 0.25 0.25 0.25 1 -

Non-life 0.25 0.5 0 0.25 1

Aggregation of Capital Charges using Correlation Matrix in Standard Formulae.

Calculation of Basic SCR

Page 16: Evaluation of Capital Needs in Insurance

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QIS4 has an extensive information request on internal models:

– Collecting quantitative data to help assess the standard approach calibration and its likely impact on Solvency II

– How companies use, calibrate, document and validate their models in order to help develop the approval criteria

– Current and future development plans for internal models to assess their likely future importance

Internal Models

Page 17: Evaluation of Capital Needs in Insurance

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Rating Agencies

Page 18: Evaluation of Capital Needs in Insurance

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Capital Models A Cog in the Rating Process Key Rating Factors (Moody’s)

– Business profile• Market position, brand and distribution (weighting 25%)• Product risk and diversification (10%)

– Financial profile• Asset risk (5%)• Capital adequacy (15%)• Profitability (15%)• Reserve adequacy (10%)• Financial flexibility (20%)

Key Rating Factors (AM Best)– Balance sheet strength– Operating performance– Business profile

Balance sheet strength

Page 19: Evaluation of Capital Needs in Insurance

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Insurer’s Internal Capital Models More weight assigned if:

– A high degree of transparency to the agency– A proven track record– A suitable level of sophistication– Appropriate testing and controls over use– Suitable expertise to control and run the model

Regulatory Requirements Not a model, however regulations may cast constraints on

capital requirements, especially for weak insurers

Rating Agency Model More weight goes toward the rating agency’s model if the

above factors are lacking

Rating Agency Model

Rating Agency Capital Models A Cog in the Rating Process

Page 20: Evaluation of Capital Needs in Insurance

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Model Outputs

Relating model results to ratings – Ratio mapping

• Relate adjusted capital to required capital– Adjusted capital-amount of capital available– Required capital-modelled capital

• Rating agencies have their own twists– Moody’s – Moody’s Risk Adjusted Capital (MRAC) Ratio– Fitch - PrismScore– AM Best – Best’s Capital Adequacy Ratio (BCAR)– S&P – Standard and Poor’s Capital Adequacy Ratio (S&P CAR)

– VAR– TVAR

Page 21: Evaluation of Capital Needs in Insurance

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MRAC Ratio

Adjusted capital / Required capital

Source: Moody’s

Adjusted capital– From financial statements

Required capital– Derived using models. The modeling

assumptions are determined based on the key risk drivers.

Page 22: Evaluation of Capital Needs in Insurance

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Getting to Adjusted Capital

Varies by rating agency Moody’s as an example…

– Investments• Book to market adjustments• One year expected return on invested assets (returns vary by asset class)

– Reinsurance-• Assess collectibility of reinsurance recoverables• Collectibility measured by reinsurer rating (eg, A95%, Baa 90%)

– Reserves• True-up (complete traditional actuarial reserving exercise, split between core lines and A&E)• Discount (consider LOB and AY)

– Underwriting-calculate expected P/L for full year of business• Written but not earned• New business for one year

Page 23: Evaluation of Capital Needs in Insurance

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Getting to Required Capital

Use capital model-both stochastic and static Risks

– Investments• Bonds and stocks stochastic-generally normal• Other assets static (eg, mortgages)

– Reinsurance• Varies by reinsurer rating, offset for collateral• Normally distributed• 50% correlation across reinsurer rating categories

– Reserves• Ultimate losses by LOB by AY lognormal• Correlation across LOB and AY

– Underwriting– Catastrophes– Operating-15% of sum of risk type charges– Aggregate

• Sum of risk types• Tax adjustment

Page 24: Evaluation of Capital Needs in Insurance

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Quantifying Risk and Capital Adjustments Example

Source: Moody’s

Page 25: Evaluation of Capital Needs in Insurance

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Quantifying Risk and Capital Adjustments Example

Source: Moody’s

Page 26: Evaluation of Capital Needs in Insurance

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Fitch’s PrismScore

Available capital/Required capital

Available capital– The amount of capital available in a controlled run-off during stressed economic and/or insurance

conditions– Balance sheet inputs that are specifically adjusted to align with Fitch’s definition of required capital

Required capital– Stochastically derived by modeling various risks

• Asset/Liability mismatch risk• Investment risk• Reserve risk• Underwriting risk• Catastrophe risk• Uncollectible reinsurance risk• Operational risk (not yet modeled, instead it’s qualitatively measured)

Source: Fitch

Page 27: Evaluation of Capital Needs in Insurance

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AM Best’s BCAR

Adjusted surplus/Net required capital Adjusted surplus

– Reported surplus– Equity adjustments

• Unearned premium• Assets• Loss reserves• Reinsurance

– Debt adjustments• Surplus notes• Debt service requirements

– Other adjustments• Potential catastrophe losses• Future operating losses

Net required capital– Fixed-income securities– Equity securities– Interest rate– Credit– Loss and LAE reserves– Net written premium– Off balance sheet

Source: AM Best

Page 28: Evaluation of Capital Needs in Insurance

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S&P’s CAR

Total adjusted capital - Asset-related risk charges - Credit-related risk charges

Underwriting risk + Reserve risk + Other business risk

Total adjusted capital– Statutory surplus – +/- Loss reserve deficiency – + Time value of money – +/- Other

Asset-related risk– Bonds– Mortgages– Real estate– Stocks

Credit-related risk– Reinsurance recoverables– Other recoverables

Underwriting risk– Risk that company’s present

and future business will be unprofitable

Reserve risk– Risk that past business will be

less profitable than expected

Other business risk– Exposure to guarantee fund

assessments

Source: S&P

Page 29: Evaluation of Capital Needs in Insurance

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Ratio Mapping (AC/RC)

S&PStatus Min S&P CAR

Superior 175

Excellent 150

Good 125

Adequate 100

Vulnerable Below 100

Source: AM Best and S&P

AM Best

Rating Min BCAR

A++ 175

A+ 160

A 145

A- 130

B++ 115

B+ 100

B 90

B- 80

C++ 70

C+ 60

C 50

C- 40

D 0

Page 30: Evaluation of Capital Needs in Insurance

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Relating VAR/TVAR to Rating

Source: Fitch

Page 31: Evaluation of Capital Needs in Insurance

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Ratings From VARValue at Risk

0

10

20

30

40

50

60

70

80

90

100

Years

Val

ue

at R

isk

(%)

‘AAA’

‘AA’

‘A’

‘BBB’

‘BB’

‘B’

‘CCC+’

Source: Fitch

Page 32: Evaluation of Capital Needs in Insurance

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Ratings From TVARTail-Value at Risk

0

10

20

30

40

50

60

70

80

90

100

Years

Tai

l-V

alu

e at

Ris

k (%

) ‘AAA’

‘AA’

‘A’

‘BBB’

‘BB’

‘B’

‘CCC+’

Source: Fitch

Page 33: Evaluation of Capital Needs in Insurance

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Rating Agency Closing Thoughts

To learn more– Rating agency websites– Recommended reading– Rating agency models and public domain models available

Opportunities– Ratings consulting– Model assistance

• Develop internal capital models• Validate internal capital models