Economic Capital Modeling
A Key Part of the ERM Process
Ronald T. Kuehn, FCAS, MAAA, CERA, CPCU, ARM, FCA
Consulting Actuary, Huggins Actuarial Services, Inc.
Definition of Economic Capital
• Economic Capital is defined as
– Sufficient surplus to cover adverse
outcomes or to meet a business objective
– With a given level of risk tolerance
– Over a specified period of time
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Definition of an Economic Capital
Models (ECM)
• One primary tool to assess risk in an insurance
organization
• Simulates the internal operations of the company
relative to the external environment within which it
is operating
• Indicates future levels and volatility of
profitability, and
• Estimates appropriate amounts of capital to hold
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A Brief History of ECM
1980’s
1990’s
• Life Insurance Industry
• Cash flow modeling to assess variations from
mortality assumptions used to price life
insurance and annuities
• P & C Insurance Industry – Lacks Correlations
• Dynamic Financial Analysis (DFA)
• Stochastic approach to estimating hazard
interactions impacting financial condition
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A Brief History of ECM
2000’s
Today
• Economic Capital Modeling (ECM)
• Probability-based scenario generator for future
financial results of an insurance enterprise
• Full ECM include Underwriting, Reserve,
Natural Catastrophe, Asset, and Credit Risks
• Critical factor – Correlation among Risks
• Aggregating these risks into a common model
• Producing plausible alternative financial
outcomes
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ECM Can ….
• Model
–
–
–
–
–
–
Company or Product Risk Profiles
Risk Tolerance, Constraints & Strategies
Insurance Pricing & Business strategies
Performance Measurements
Capital Adequacy & Budgeting
Incentive Compensation Investment
& Risk-Adjusted Rates of Return
– Merger & Acquisition Pricing Details
– Capital Allocation Among Business Units
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Key Risks Being Measured by a
Comprehensive Economic Capital Model
Underwriting
Market Cycles
Reinsurance
Loss Volatility
Credit Risk
Reserve Adequacy
Program Efficacy
Catastrophe
Cat Event
Loss Volatility
Reserving
Payment Patterns
Other
ECM
Investment
Key Risks
Operational
Reputational
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Benefits of an Economic Capital Model
Compliance Related
ECM
– Satisfy rating agency and regulatory
criteria/inquiries
– Aid in discussions with rating agencies
and regulators
– Capital adequacy measured against
a company’s risk profile
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Benefits of an Economic Capital Model
Compliance Related
• A.M. Best’s Supplemental Rating Questionnaire (no longer
asks the ECM question as of year-end 2013)
– Q 56: ECM – Risk Identification & Monitoring
– Q 57: Frequency of Update to ECM and Measurement of
Aggregate Risk
– Q 58: Impact of Calendar Year Inflation on Reserves
– Strong emphasis on Catastrophe Management (Updated as
of January 14th, 2014)
• Preparation of the ORSA summary report
• Essential for Solvency II Compliance
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Benefits of an Economic Capital Model
Value Beyond Compliance
More to gain from ECM than compliance
• Improves risk awareness at all levels
• Enables better risk/reward decisions making
• Facilities linking strategy with planning
• Empowers firm to improve value for stakeholders
• Provides a competitive advantage including reduced
cost of capital (University of Georgia Study 2013)
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Insurance Companies & ECM
A.M. Best 2010 ERM SRQ:
• Overall 28% of respondents use ECM to quantify
aggregate risk
• Large (55%),
• Medium (33%), and
• Small (17%)
• 8% use ECM for management compensation
NAIC moving with European regulator EIOPA ?
– Solvency II will allow companies capital relief by
use of internal ECM rather than standard model
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Insurance Companies & ECM
• Savvy Investors, media, and the financial community
speak language of risk modeling (VaR, TVaR, PML, etc.)
• Demand more disclosure of metrics from ECMs.
• Developing ECM is costly as it requires:
•
•
•
•
•
Acquiring actuarial and financial expertise
Collecting of significant volume data
Analyzing data to develop risk parameters
Licensing or building ECM software platform
Validating the model and organizing the
management process for audit
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Existing Capital Adequacy Measures
• RBC (Risk-Based Capital) Ratio
– Implemented by the NAIC in the 1990’s
– Formulaic estimate of necessary surplus and comparison to
reported surplus
– Used to authorize regulatory intervention into financiallydistressed
• NAIC
ORSA (Own Risk and Solvency Assessment)
– Companies with at least $500 M WP
– Group with at least $1B WP
– Effective circa 2015
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Insurance Companies & ECM
• Rating Agency Measures: BCAR and others
– Both formulaic and simulation-based
– Used as significant input into assignment of financial
strength ratings
– Lack full transparency, as not all parameters are made
public
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Insurance Companies & ECM
• Economic Capital Models (ECM’s)
– Simulation based
– Direct calculation of Economic Capital needed
– Many other uses in addition to Economic Capital
measure
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Basic Inputs to an Economic
Capital Model
Balance Sheet Inputs:
• Assets
•
•
•
•
Cash
Bonds
Common Stock
Other Asset Classes
• Liabilities
•
•
•
•
Loss and Loss Adjust Reserves by Line / Subline
Payment patterns for Existing Reserves
Unearned Premium Reserve
Other Liabilities
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Basic Inputs to an Economic Capital
Model (Line of Business Inputs)
•
•
•
•
•
Direct Written Premium
Claim Payout Pattern for Newly Generated Loss
Underwriting Expenses
Earnings Pattern
Operational Risk – Lognormal Distribution
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Basic Inputs to an Economic
Capital Model (Cause of Loss)
• Frequency and Severity Model – Frequency of
Individual Claims with No Correlation
– Claim Frequency Distribution - Examples
• Poisson – often selected
• Negative Binomial
• Binomial
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Basic Inputs to an Economic
Capital Model (Cause of Loss)
• Frequency and Severity Model – Severity of
Individual Claims with No Correlation
– Claim Severity Distribution - Examples
•
•
•
•
•
•
•
Lognormal – often selected
Exponential
Gamma
Generalized Pareto
Normal
Uniform
Weibull
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Basic Inputs to an Economic
Capital Model (Cause of Loss)
• Aggregate Loss Model – Aggregate claims
model can incorporate copulas (i.e.,
correlation between lines of business)
• Aggregate Loss Distribution Examples
• Lognormal
• Generalized Pareto
• Normal
• Uniform
• Weibull
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Basic Inputs to an Economic
Capital Model (Cause of Loss)
• Selection of Copulas - adds correlation between
lines of business
• Normal Copula – linear correlation coefficient
• Student’s T Copula – varies weight of coefficients in
tail of distribution
• HRT Copula – more weight in right tail of
distribution
• Partial Perfect Copula – mixes perfect correlation
with uncorrelated
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Basic Inputs to an Economic
Capital Model (Reinsurance Inputs)
• Reinsurance Contract Terms
• Per Risk
• Excess
• Corridors
• Ceded Premium
• Ceded Reinsurance Attachment Point
• Ceded Reinsurance Limit
• Specific Catastrophe Reinsurance Terms
• Reinsurance Catastrophe Modeling Results (i.e.
AIR, EQECAT, RMS)
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Basic Inputs to an Economic Capital
Model (Economic Scenarios)
• Leading edge economic models, providing full market risk
and asset class coverage
• Estimates inflationary changes, wage & CPI
• Estimates of investment returns and default risk:
• US Treasury bonds
• US, United Kingdom, and Euro stock markets
• Emerging Markets stocks
• Blue Chip Stocks
• Corporate and Municipal bonds of varying quality
• Master Limited Partnerships
• Real Estate Investment Trusts (REITs)
• Mortgage Backed Securities
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Basic Outputs from an
Economic Capital Model
Outputs include but are not limited to:
• Over 180 customizable reports
• Cumulative Probability Density Functions
• Compare results from differing assumptions
• Include effect of catastrophe losses
• Calculates Value at Risk (VaR) & Tail Value at
Risk (TVaR)
• Pro Forma Financial Statements
• Balance Sheet
• Income Statement
• Number of projected years is flexible
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ECM - Key Risk Metrics
• Value at Risk (VAR) – Maximum loss at no more than
one minus the confidence level
•
Tail Value at Risk (TVaR) – Expected loss in worst X
percentage of distribution; also called CTE
•
Risk Adjusted Performance – Measure risk adjusted
returns on some established capital amount
•
Return on Equity – Simple accounting
performance metric
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Happy Valley Insurance Company
Case Study
Line of Businesses:
General Liability
Workers’ Compensation
Property
Miscellaneous
Write Businesses in 13
States on the East Coast
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Happy Valley Insurance Company
Base Case - Liabilities & Surplus
As of 12/31/2014
Liabilities
Values
Net L&LAE Reserve
$ 22.75 M
Net UEPR
$ 23.10 M
Other Liabilities
$
4.72 M
Total Liabilities
$ 50.57 M
Capital & Surplus
$ 20.87 M
Liabilities & Surplus
$ 71.44 M
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Happy Valley Insurance Company
Base Case - Assets by Class
As of 12/31/2014
Assets
Bonds
Stocks
Cash
Other Invested
Total Invested
Uncollected Premium
Other Assets
Total Assets
Values
$ 43.40 M
$ 1.25 M
$ 5.50 M
$ 0.30 M
$ 50.45 M
$ 17.00 M
$ 4.00 M
$ 71.45 M
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Happy Valley Insurance Company
Base Case - Earned Premium 2015
As of 12/31/2014
Lines of Business
Gross EP
Ceded EP
Net EP
$ 6.40 M
$ 0.60 M
$ 5.80 M
Workers’ Compensation $ 3.70 M
$ 1.00 M
$ 2.70 M
Property
$ 35.90 M
$ 11.00 M
$ 24.90 M
Total All Lines
$ 46.00 M
$ 12.60 M
$ 33.40 M
General Liability
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Happy Valley Insurance Company
Base Case - Reinsurance Program
Reinsurance For All Years 2015 - 2019
Line of
Base Case
Business
Retention
General Liability
Workers' Comp
Property Per Risk
$1.10 M
$0.50 M
$0.50 M
Line of
Business
Catastrophe
Layers
Property Cat
$ 4.00 M X/S $ 6.00 M
$10.00 M X/S $10.00 M
$20.00 M X/S $20.00 M
$40.00 M X/S $40.00 M
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Happy Valley Insurance Company
Base Case ECM Results
Surplus at Various Confidence Intervals
Probability
2015 VaR 2019 VaR
Solvency II
Standard
0.010%
$ (7.49) M
0.079%
$
0M
0.491%
$ 7.16 M
0.500%
$ 7.21 M
50.000%
$ 23.53 M
75.000%
$ 24.57 M
99.000%
$ 26.39 M
99.500%
$ 26.62 M
Mean
$ 22.58 M
Year - End 2014 Surplus
$ (27.03) M
$ (14.46) M
$
0M
$ 0.09 M
$ 32.29 M
$ 36.60 M
$ 43.68 M
$ 44.49 M
$ 30.81 M
$ 20.87 M
*Results of 100,000 Monte Carlo Simulations
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Happy Valley Insurance Company
Alternative Investment Scenario
• In the Base Case scenario, Happy Valley invests in:
• Government bonds,
• Blue chip stocks
• Cash
• Miscellaneous other assets
• In the Alternative Investment Scenario, Happy Valley
increases its investment in:
• Blue chip stocks and
• Adds a substantial investment in master limited
partnerships (MLP’s)
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Happy Valley Insurance Company
Comparison of Investment Distribution
Investment Percentage
Assets
Bonds
Stocks
MLP's
Cash
Other
Total
Yield
2.50%
0.00%
6.00%
0.10%
0.00%
Base Case
60.70%
1.70%
0.00%
7.70%
29.90%
100.00%
Alternative
45.00%
3.50%
14.00%
7.70%
29.80%
100.00%
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Happy
ValleyInsurance
Insurance Company
Happy
Valley
Company
Alternative Investment Scenario ECM Results
Alternative Investments
Surplus at Various Confidence Intervals
Probability
2015 VaR 2019 VaR
Solvency II
Standard
0.010%
$ (6.91) M
0.080%
$
0M
0.340%
$
6.27 M
0.500%
$
7.45 M
50.000%
$ 23.75 M
75.000%
$ 25.10 M
99.000%
$ 28.08 M
99.500%
$ 28.56 M
Mean
$ 22.99 M
Year - End 2014 Surplus
$ (27.15) M
$ (13.01) M
$
0M
$
2.41 M
$ 34.78 M
$ 39.69 M
$ 49.75 M
$ 51.15 M
$ 33.64 M
$ 20.87 M
*Results of 100,000 Monte Carlo Simulations
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Happy Valley Insurance Company
Case Study - Buys Small Auto Insurer
• In the Base Case scenario, Happy Valley invests in:
• Government bonds
• Blue chip stocks
• Cash
• Miscellaneous other assets
• In the second alternative, Happy Valley uses excess
surplus, to buy small, profitable personal auto insurer
• Costs $2.3 million over book value
• Assumes $5.0 million in net loss & loss adjustment
reserves
• Assumes $3.5 million in unearned premium reserves
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Happy Valley Insurance Company
Buy Auto Insurer - Liabilities & Surplus
As of 12/31/2014
Liabilities
Values
Net L&LAE Reserve
$ 27.75 M
Net UEPR
$ 26.60 M
Other Liabilities
$
4.72 M
Total Liabilities
$ 59.07 M
Capital & Surplus
$ 18.53 M
Liabilities & Surplus
$ 77.61 M
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Happy Valley Insurance Company
Buy Auto Insurer - Assets by Class
As of 12/31/2014
As of 12/31/2014
Assets
Values
Assets
Values
$49.60
M M
BondsBonds
$ 49.56
$1.25
M M
StocksStocks
$ 1.25
Cash
$5.50 M
Cash
$ 5.50 M
Other Invested
$0.30 M
Other
Invested
$ 0.30
Total
Invested
$56.65
M M
Total Invested
$ 56.61 M
Uncollected
Premium $17.00
M M
Uncollected
Premium
$ 17.00
$4.00
M M
Other Other
AssetsAssets
$ 4.00
Total Assets
$77.65 M
Total Assets
$ 77.61 M
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Happy Valley Insurance Company
Buy Auto Insurer - Earned Premium 2015
As of 12/31/2014
Lines of Business
Gross EP Ceded EP
Personal Auto
$ 7.20 M $ 2.00 M
General Liability
$ 6.40 M $ 0.60 M
Workers’ Compensation $ 3.70 M $ 1.00 M
Property
$ 35.90 M $ 11.00 M
Total All Lines
$ 53.20 M $ 14.60 M
Net EP
$ 5.20 M
$ 5.80 M
$ 2.70 M
$ 24.90 M
$ 38.60 M
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Happy Valley Insurance Company
Buy Auto Insurer - ECM Results
Surplus at Various Confidence Intervals
Probability
2015 VaR
2019 VaR
Solvency II
Standard
0.010%
$ (9.48) M
0.100%
$
0M
0.480%
$
5.13 M
0.500%
$
5.22 M
50.000%
$ 21.53 M
75.000%
$ 22.60 M
99.000%
$ 24.47 M
99.500%
$ 24.71 M
Mean
$ 20.59 M
Year - End 2014 Surplus
$ (27.17) M
$ (10.75) M
$
0M
$
0.15 M
$ 31.90 M
$ 36.22 M
$ 43.42 M
$ 44.19 M
$ 30.47 M
$ 18.53 M
*Results of 100,000 Monte Carlo Simulations
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Happy Valley Insurance Company
Case Study – Alternative Reinsurance
• In the third alternative scenario, Happy Valley reduces its
reliance on reinsurance by:
• Doubling retention on General Liability
• Doubling retention on Property Per Risk
• Eliminating first Catastrophe layer
Graphic: RadientSkies/123RF.com
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Happy Valley Insurance Company
Alternative Reinsurance – Liabilities & Surplus
As of 12/31/2014 - Same as Base Case
Liabilities
Values
Net L&LAE Reserve
$ 22.75 M
Net UEPR
$ 23.10 M
Other Liabilities
$
4.72 M
Total Liabilities
$ 50.57 M
Capital & Surplus
$ 20.87 M
Liabilities & Surplus
$ 71.44 M
Graphic: RadientSkies/123RF.com
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Happy Valley Insurance Company
Alternative Reinsurance - Assets by Class
As of 12/31/2014 – Same as Base Case
Assets
Values
Bonds
$ 43.40 M
Stocks
$ 1.25 M
Cash
$ 5.50 M
Other Invested
$ 0.30 M
Total Invested
$ 50.45 M
Uncollected Premium
$ 17.00 M
Other Assets
$ 4.00 M
Total Assets
$ 71.45 M
Graphic: RadientSkies/123RF.com
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Happy Valley Insurance Company
Comparison of Reinsurance Program
Reinsurance For All Years 2015 - 2019
Line of
Base Case
Alternative
Business
Retention
Retention
General Liability
Workers' Comp
Property Per Risk
$1.10 M
$0.50 M
$0.50 M
$2.20 M
$0.50 M
$1.00 M
Line of
Business
Catastrophe
Original Layers
Catastrophe
Alternative Layers
Property Cat
$ 4.00 M X/S $ 6.00 M
$10.00 M X/S $10.00 M
$20.00 M X/S $20.00 M
$40.00 M X/S $40.00 M
$10.00 M Retention
$10.00 M X/S $10.00 M
$20.00 M X/S $20.00 M
$40.00 M X/S $40.00 M
Graphic: RadientSkies/123RF.com
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Happy Valley Insurance Company
Alternative Reinsurance - ECM Results
Surplus at Various Confidence Intervals
Probability
2015 VaR
2019 VaR
Solvency II
Standard
0.010% $
(11.81) M
0.166% $
0M
0.500% $
4.65 M
0.588% $
5.31 M
50.000% $
24.48 M
75.000% $
25.53 M
99.000% $
27.35 M
99.500% $
27.58 M
Mean $
23.32 M
Year - End 2014 Surplus
$ (31.88) M
$ (9.60) M
$ (1.04) M
$
0M
$ 37.19 M
$ 42.23 M
$ 50.48 M
$ 51.41 M
$ 35.43 M
$ 20.87 M
*Results of 100,000 Monte Carlo Simulations
Graphic: RadientSkies/123RF.com
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Happy Valley Insurance Company
Case Study – $1.8 M Dividend Per Year
• In the Base Case scenario, Happy Valley invests in:
• Government bonds
• Blue chip stocks
• Cash
• Miscellaneous other assets
• In the fourth alternative scenario, Happy Valley begins to
pay its shareholders $1.8 million of dividends per year
beginning in 2015 to reduce under-utilized surplus.
Graphic: CSA Images / B&W Engrave Ink Collection / Getty Images
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Happy Valley Insurance Company
$1.8 M Dividend Per Year – Liabilities & Surplus
As of 12/31/2014 - Same as Base Case
Liabilities
Values
Net L&LAE Reserve
$ 22.75 M
Net UEPR
$ 23.10 M
Other Liabilities
$
4.72 M
Total Liabilities
$ 50.57 M
Capital & Surplus
$ 20.87 M
Liabilities & Surplus
$ 71.44 M
Graphic: CSA Images / B&W Engrave Ink Collection / Getty Images
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Happy Valley Insurance Company
$1.8 M Dividend Per Year - Assets by Class
As of 12/31/2014 – Same as Base Case
Assets
Values
Bonds
$ 43.40 M
Stocks
$ 1.25 M
Cash
$ 5.50 M
Other Invested
$ 0.30 M
Total Invested
$ 50.45 M
Uncollected Premium
$ 17.00 M
Other Assets
$ 4.00 M
Total Assets
$ 71.45 M
Graphic: CSA Images / B&W Engrave Ink Collection / Getty Images
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Happy Valley Insurance Company
$1.8 M Dividend Per Year - Same as Base Case
Reinsurance Program
Reinsurance For All Years 2015 - 2019
Line of
Base Case
Business
Retention
General Liability
Workers' Comp
Property Per Risk
$1.10 M
$0.50 M
$0.50 M
Line of
Business
Catastrophe
Original Layers
Property Cat
$ 4.00 M X/S $ 6.00 M
$10.00 M X/S $10.00 M
$20.00 M X/S $20.00 M
$40.00 M X/S $40.00 M
Graphic: CSA Images / B&W Engrave Ink Collection / Getty Images
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Happy Valley Insurance Company
$1.8 M Dividend Per Year - ECM Results
Surplus at Various Confidence Intervals
Probability
2015 VaR
2019 VaR
Solvency II
Standard
0.010% $
(9.29) M
0.100% $
0M
0.500% $
5.41 M
2.480% $
11.08 M
50.000% $
21.73 M
75.000% $
22.77 M
99.000% $
24.59 M
99.500% $
24.82 M
Mean $
20.78 M
Year - End 2014 Surplus
$ (38.10) M
$ (22.44) M
$ (10.74) M
$
0M
$ 23.06 M
$ 27.39 M
$ 34.45 M
$ 35.25 M
$ 21.44 M
$ 20.87 M
*Results of 100,000 Monte Carlo Simulations
Graphic: CSA Images / B&W Engrave Ink Collection / Getty Images
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Happy Valley Insurance Company
Comparison of Key Metrics for Scenarios
Scenarios
1
2
3
4
5
Key Metrics
2015 BCAR
Base
Alternative Buy Auto Alternative Pay $1.8 M
Case Investment Insurer Reinsurance Dividends
257.13%
262.53% 211.44%
255.82%
234.02%
2019 BCAR
271.77%
287.90% 241.83%
283.02%
199.51%
1 Yr Prob. of Ruin
0.08%
0.08%
0.10%
0.17%
0.10%
5 Yr Prob. of Ruin
0.49%
0.34%
0.48%
0.59%
2.48%
12/31/2014 Surplus (M)
$20.87
$20.87
$18.53
$20.87
$20.87
12/31/2019 Surplus (M)
$30.81
$33.64
$30.47
$35.43
$21.44
8.10%
10.02%
10.45%
11.16%
7.84%
5 Yr Annual Adj. ROE
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Happy Valley Insurance Company
Initial Capital Allocation Using Net 99% VaR
Initial Allocation of Year-End 2014 Surplus at 99% VaR
Percent
Capital
LOB
99% VaR
of Total
Allocation
Casualty
$ 4.221 M
13.69% $ 2.857 M
Workers' Compensation
$ 1.900 M
6.16%
$ 1.286 M
All Other
$ 2.551 M
8.27%
$ 1.727 M
Property
$ 22.165 M
71.88%
$ 15.003 M
Total
$ 30.837 M
100.00%
$ 20.873 M
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Happy Valley Insurance Company
Initial Capital Allocation Using Net 50% VaR
Initial Allocation of Year-End 2014 Surplus at 50% VaR
Percent
Capital
LOB
50% VaR
of Total
Allocation
Casualty
$ 2.335 M
12.83% $ 2.679 M
Workers' Compensation
$ 1.504 M
8.27%
$ 1.726 M
All Other
$ 0.905 M
4.97%
$ 1.038 M
Property
$ 13.452 M
73.93%
$ 15.431 M
Total
$ 18.197 M
100.00%
$ 20.873 M
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Ronald T. (Rusty) Kuehn , FCAS, MAAA, CERA, CPCU,
ARM, FCA
Mr. Kuehn is a consulting actuary with Huggins Actuarial Services,
Inc. In his consulting practice he specializes in medical malpractice,
private passenger automobile, workers’ compensation and
commercial lines coverage working for insurance carriers, selfinsured healthcare systems, self-insured corporations, brokers,
municipal bond and mortgage insurance experience, and other types
of clients.
Mr. Kuehn is professionally active; he served as the chairman of the Casualty Loss Reserve
Seminar (CLRS). He has also served on the on the Casualty Practice Council of the
American Academy of Actuaries, the CAS Examination Committee and Committee for
Consultants’ Interests, and as past President, Education Chairman and Board Member of the
Casualty Actuaries of the Mid-Atlantic Region (CAMAR).
He currently serves on the Board of the Insurance Society of Philadelphia (ISOP), and he is
a member of the ORSA subgroup of the ERM Committee of the Risk Management and
Financial Reporting Council of the American Academy of Actuaries.
His over forty three years in business have given him a thorough knowledge of the propertycasualty business both from a company and consulting viewpoint.
Contact Information:
E-mail: [email protected]
Cell Phone: 610-892-1823
www.hugginsactuarial.com
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Economic Capital Modeling
A Key Part of the ERM Process
Ronald T. Kuehn, FCAS, MAAA, CERA, CPCU, ARM, FCA
Consulting Actuary, Huggins Actuarial Services, Inc.