evaluation of capital needs in insurance
DESCRIPTION
Presentation on capital adequacy analysis for property casualty insurance companies, as presented to Milliman\'s 2008 Casualty Consultants Forum in DenverTRANSCRIPT
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Evaluation of Capital Needs
Jeff Courchene, FCAS, MAAAKyle Mrotek, FCAS, MAAA
Joy Schwartzman, FCAS, MAAA
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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
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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
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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
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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
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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
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Solvency II
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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
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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
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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!
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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
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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.
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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
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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
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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
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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
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Rating Agencies
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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
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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
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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
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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.
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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
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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
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Quantifying Risk and Capital Adjustments Example
Source: Moody’s
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Quantifying Risk and Capital Adjustments Example
Source: Moody’s
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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
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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
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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
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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
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Relating VAR/TVAR to Rating
Source: Fitch
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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
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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
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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