RCM-3 The Integration of Risk and Return in Practice
- From Ratemaking to ERM
Russ Bingham
Vice President Actuarial Research
Hartford Financial Services
Ratemaking Seminar
Atlanta, GA
March 8-9, 2007
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Outline
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Corporate Objective: Financial Discipline and Operational Application
Risk / Return and the Risk Transfer Process
Risk / Return Fundamentals
Risk / Return Line
Connecting Risk and Return - RAROC and RORAC
Generic Risk Quantification Steps
Alternative Risk Metrics
Risk / Return Criteria Specifications
Risk Coverage Ratio Risk / Return Metric – Operating and Shareholder Views
Risk / Return Integration using RCR – Scenarios and Mechanics
Risk / Return Methodology in Practice – Scope and Attributes
Economic and Risk-Based Orientation and Premises
Appendix
 Example of Risk-Based Pricing
 Five Essential Structural Elements
 Historical Evolution of the Benchmark Methodology
 Ten Commandments of Insurance Financial Modeling
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Corporate Objective: Financial Discipline and Operational Application
Financial discipline is a valuation process, supported by analytical methods and
models, intended to provide timely and meaningful assessments of risk /
return performance and trends associated with underwriting, investment and
finance operations. Sound economic, risk-based analytics are used to
support strategic and operational decision making throughout company.
Apply benchmark standard financial valuation throughout entire company
 Ratemaking and product pricing
 Planning
 Performance monitoring
 Profitability studies
 Incentive compensation
 Acquisition analysis
 Capital attribution
 Risk/return assessment
 ERM
Valuation is on an Economic Basis (i.e. cash flow oriented) and Reflects Risk
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Insurance Funds Flow Schematic
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The Actuaries Role
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Uncertainty and volatility of both amount of loss and timing of payment
is typically the most significant driver of risk in P&C insurance
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This information should be used within all risk-driven activities,
particularly pricing, establishing reserve ranges and ERM
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The actuary must play a critical role in the ERM process
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However, the actuary must take a broader financial perspective
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Risk / Return and the Risk Transfer Process
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Risk Transfer Activities
 Underwriting funds flow between policyholders and company
 Investment funds flow between company and financial markets
 Finance capital funds flow between financial markets and company
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Risk Transfer Characteristics
 Transfer of cash between two parties for a future expected benefit to both
 Benefits uncertain as to amount and/or timing
 Price for the transfer of risk based on fundamental Risk / Return tradeoff
in which higher risk requires higher price
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Risk / Return Relationship
 Applies to all risk transfer activities
 Risk and Return measured from the same variable (distribution)
The same risk / return tradeoff paradigm should apply to all risk transfer activities
to the extent possible
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Risk / Return Fundamentals
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Insurance = underwriting, investing and financing
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Volatility is uncertainty of result
 Volatility characteristics of input and output variables are a key
component of risk assessment but volatility alone does not represent risk
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Risk is exposure to loss
 Risk lies in the potential for adverse outcomes, which is a function of both
the level of and volatility in important variables of interest
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Risk transfer price must consider all outcomes that can potentially result in
loss
 Frequency and severity of all adverse outcomes are relevant
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A risk-based pricing and capital attribution methodology incorporates volatility
in determining levels of outcomes in order to conform to an acceptable risk /
return relationship
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Risk / Return Line
The price (premium) that satisfies the risk criterion, by reflecting the volatility in each line
of business, places the expected total return distribution on the total risk / return line.
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Connecting Risk and Return - Risk Adjustment Alternative 1
“Step” 1: Determine Price that satisfies specified risk criteria using uniform leverage - RAROC
perspective, Risk-Adjusted Return On Capital (varying return with uniform leverage)
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Connecting Risk and Return - Risk Adjustment Alternative 2
“Step” 2: Determine Leverage to achieve specified return - RORAC perspective, Return
On Risk-Adjusted Capital (uniform return with varying leverage)
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Generic Risk Quantification Steps
1. Select variable(s) of interest
2. Determine the statistical distribution of the variables(s)
3. Define and identify adverse outcomes
4. Determine the probability of an adverse outcome
5. Determine the average severity of an adverse outcome
6. Calculate the risk metric
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Alternative Risk Metrics
Policyholder oriented risk metrics (usually loss based)
Probability of ruin (POR)
Value at risk (VAR)
Tail Value at Risk (TVAR) - P&C
Conditional Tail Expectation (CTE) - Life
Expected policyholder deficit (EPD)
Shareholder oriented risk metrics (based on total income or return)
Variability in total return (sR)
Value at risk (VAR)
Tail Value at Risk (TVAR) - P&C
Conditional Tail Expectation (CTE) - Life
Probability of Income Ruin (POIR)
Probability of surplus drawdown deficit (PSD)
Severity of surplus drawdown deficit (SSD)
Expected surplus drawdown deficit (ESD)
Earnings at Risk
Risk / Return metrics
Sharpe Ratio
Risk Coverage Ratio (RCR)
- Metrics differ in choice of
variable used and in
definition of adverse event
(position in distribution)
- In one way or another all
risk measures address the
likelihood and/or the severity
of an adverse outcome
- Only Sharpe ratio and
RCR integrate risk and
return, others are an
expression of risk only
RBC and other Rating Agency measures
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Risk / Return Criteria Specifications in Practice
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Key variable is the distribution of Total Return (ROE or “equivalently”,
Operating Return) based on Accident period and Economic (cash flow based)
accounting.
Adverse outcome is defined as “below breakeven” return.
 For ROE; Breakeven = Risk Free return
 For Operating Return; Breakeven = Zero
These two are equivalent in that they reside at the same point of their
respective distributions and are mathematically connected to each other
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Key Return measure is the expected average return
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Key Risk measure is the expected below breakeven deficit, the product of the
frequency of result below breakeven times the severity of those outcomes
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Risk / return metric is “Risk Coverage Ratio” (RCR) which ratios the expected
return margin above breakeven to the risk measure - a Reward to Risk ratio
“All” sources of risk (cats, non-cat losses, cash flow, yield, etc.) are modeled
simultaneously to provide a distribution of possible return outcomes. Their
respective contribution to overall risk and return is identified and this forms the
basis for setting premium and assigning surplus.
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Risk Coverage Ratio Risk / Return Metric – Operating Return View
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Risk Coverage Ratio Risk / Return Metric – Shareholder Return View
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Risk Coverage Ratio Attributes
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Adverse outcome is set at breakeven where operating results turn negative
and surplus is consumed
Focus is that of an ongoing firm rather than a more extreme “ruin” risk view
(making earnings is of more frequent concern than is going out of business)
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Considers all adverse outcomes (i.e. any outcome which consumes surplus)
 Utilizes “full” information content
 Improves reliability of risk measurement
 Consistent with risk transfer pricing in which price (i.e. reward) must reflect
all potential loss scenarios
 Not biased by either excessively skewed or capped tail distributions (a
major problem with risk metrics based on tail characteristics only)
 Return and risk are measured from the same variable and distribution
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Risk is measured as a combination of frequency and severity of adverse
events (low severity, high frequency adverse outcomes can be as costly as
high severity, low frequency outcomes farther out in the tail)
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Reward to risk connection is made by pricing products in proportion to risk
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Applicable to underwriting and investing activities
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Risk / Return Integration and application of RCR
Simulation Scenarios (Low, Med, High Volatility), (Normal, Mild Skew, Heavy Skew Distribution)
Nine scenarios reflect combinations of 3 levels of volatility and 3 degrees of skewness.
Results are shown in both RAROC and RORAC perspectives.
RAROC presents risk-adjusted return on capital at fixed 3/1 leverage ratio.
RORAC presents fixed 15% return on risk-adjusted capital.
Price is set to meet Breakeven RCR reward to risk ratio of 20 to 1 in each scenario.
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Risk / Return Integration “Full” Information Breakeven RCR
- Operating Return Level (Medium Volatility, Heavy Skew Scenario Case 8)
Required Price is that which results in operating return RCR of 20.0. (Operating return is a return on asset metric.)
The distribution in shifted right or left in order to place the mean return at the point which results in an RCR of 20.0
Operating return is 20 times the product of the probability of negative return times the severity of those negative returns.
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Risk / Return Integration “Full” Information Breakeven RCR
- Total Return RAROC ( Medium Volatility, Heavy Skew Scenario Case 8)
Total Return is determined by multimplying operating return by fixed leverage of 3.0 and then adding surplus yield of 5%.
Units change from return on asset to return on surplus, but RCR reward-to-risk characteristics remain the same.
Total return excess of breakeven is 20 times the product of the probability times the severity of below breakeven returns.
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Risk / Return Integration “Full” Information Breakeven RCR
- Total Return RORAC (Medium Volatility, Heavy Skew Scenario Case 8)
Total Return is scaled by adjusting leverage factor so that average return is 15%.
Return distribution shape characteristics and RCR 20 are maintained in this translation.
Total return excess of breakeven remains 20 times the product of the probability times the severity of below breakeven returns.
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Risk / Return Integration - RAROC vs. RORAC Extreme Event Tail Risk
Ruin Probability (Medium Volatility, Heavy Skew Scenario Case 8)
RORAC risk-adjusted capital attributed combined with risk-based return level ensures that ruin is unlikely.
RORAC perspective indicates greater policyholder solvency protection than does RAROC.
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Risk / Return Integration in Practice using RCR
RAROC Multiperiod Model View
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Risk / Return Integration in Practice using RCR
RORAC Multiperiod Model View
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Risk / Return Integration in Practice using RCR
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Risk measurement is a combination of the probability that returns will fall below
breakeven, together with the average severity of such outcomes
 “Loss” = Shortfall from breakeven return
 “Risk” = (Loss Frequency) x (Mean Loss Severity)
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RCR (Risk Coverage Ratio) is used to integrate risk and return
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Risk-Based Pricing - higher price dictated when volatility and risk is greater
 Establishes risk / return tradeoff whose slope is RCR
 Independent of surplus
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Two forms of risk-adjustment can be use when translating to total return (ROE)
 Risk-Adjusted Return - higher absolute total return when risk is greater,
with uniform leverage (e.g. 3/1 leverage ratio in all lines) OR
 Risk-Adjusted Leverage - lower leverage when risk is greater, with uniform
total return (e.g. 15% ROE in all lines)
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Price related to risk, leverage related to total return
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Risk / Return Integration in Practice using RCR
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RORAC Preferred Over RAROC
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Facilitates state rate regulatory dialogue
 In jurisdictions having greater underwriting risk it is easier to
discuss rate needs at modest rate of return levels that are
based on higher risk capital amounts than when risk is reflected
in a higher absolute target return alone, even though price
indication is the same
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Easier to implement internally as all business returns can be
compared to the same absolute return standard (e.g. 15%)
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By attributing greater capital when risk is greater, policyholders
appear to be better protected, since the probability of ruin is reduced
to a negligible amount
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Risk-Based Pricing in Practice
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Risk Pricing Objective is to insure that all operating activities (lines of
business in underwriting as well as alternative investments) conform to
a consistent risk / return relationship
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Pricing ideally sets all operating activities’ return/risk ratio to the
same benchmark standard, so that strategic opportunity decisions
can be made on a level playing field
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The corporate ROE goal is distributed equitably among areas
through pricing and capital allocation, in proportion to risk
contributed
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Internal Diversification and external (e.g. ratings) factors influence
this relationship
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Risk / Return Methodology in Practice – Scope and Attributes
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Primary risk orientation is that of an on-going concern meeting return
expectations in financial community
More extreme event risks (e.g. “ruin” and ratings downgrade) are indirectly
addressed since they reside within the same total return distribution although
farther out in the tail (and these can be quantified as well)
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Adequate product pricing based on product risk is viewed as the most
important risk / return lever and all adverse outcomes are considered
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Target Prices (premiums) are determined to meet specified RCR in each line of
business – gain (“reward”) per unit of risk same in all lines
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Leverage and capital attribution is determined and presented in the RORAC
risk adjustment perspective at which time capital calibration is verified
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Both policyholder (operating return level) and shareholder (total return level)
subject to same risk/return tradeoff
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Risk / Return Methodology in Practice – Scope and Attributes
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The Benchmark model provides a framework for economic measurement of riskbased underwriting performance, and is applied in virtually all areas
 Pricing, planning, tracking, incentive compensation, ERM, etc.
 Supports internal line of business risk-versus-return-oriented decision-making
 Accident / Calendar triangle structure demonstrates flow into conventional
calendar period reported financials
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Economic and risk-based rules are used to control flow of risk capital and to
distribute profits generated by the individual businesses over time internally
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Incorporates all sources of risk that can be “distributionalized” – Loss,
Catastrophe Loss, Investment Yield, Cash Flow, etc.
Provides all critical performance metrics – Total Risk-Adjusted Return, Economic
Value Added, Benchmark Surplus, Embedded Value, etc.
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Economic and Risk-Based Orientation and Premises
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Internal line of business decisions are made based on financials that reflect the
“purest” view of financial performance possible
 Accident period oriented, not Calendar period, and revised to include latest
estimates of ultimate values
 Economically based accounting, not Conventional (statutory or GAAP)
 Forward looking (includes future cash flow expectations)
 Investment risk beyond low-risk cash flow matched strategy considered as
separate investment activity, not part of underwriting
 Risk-adjustment (and capital attribution) based on independent view of risk
(using benchmark accident year, economic, cash flow, and low risk
investment structure as noted above), not the rating agency view
 Consistent with fair value accounting and economic capital principles
External total company “constraints” must be met based on
 Calendar period (e.g. reported earnings), static where revised estimates
can only be included in accounting period when revisions are made
 Conventional accounting (Stat for rating agency and regulatory, GAAP for
financial reporting)
 Backward looking (reported historical financials)
 Combined underwriting and investment results
 Rating agency capital (e.g. S&P)
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Appendix: Example of Risk-Based Pricing – Operating Level Risk
Und
Line
Ratio
Return on Inv Assets (APR) Below ‘0’ Breakeven Oper Return Risk
Und
Inv
Total Oper
Prob
U
r
O
P
-T
3%
14%
5%
14%
Homeowners
90
11%
Automobile
98
1
3
4
10
104
(1)
3
2
10
Workers Comp
Severity
Risk
P(-T)
RCR
O/{P(-T)}
0.7%
20
2
0.2
20
1
0.1
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Underwriting, Investment and Operating Return are shown as an annual percentage rate on invested
insurance assets.
Risk is the expected average adverse outcome, the product of the probability and average severity
of adverse outcomes.
Price per Unit of Risk (RCR reward to risk ratio) is the same in each line.
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Translation from Operating Return to Total Return
Operating return is converted to total return by introducing surplus and investment income
on surplus as follows:
Operating Income (I) = Income from insurance (policyholder) operations, the sum of
underwriting income and the investment income on policyholder asset float
Insurance Asset Float (A) = Invested assets supporting policyholder liabilities generated
from insurance funds flows
Underwriting Return (U) = Underwriting Income / A
Investment Return (r) = Investment Income of Policyholder Asset Float / A
Operating Return (O) = I / A = U + r
Insurance Operating Leverage (L) = A / S
Surplus (S)
Investment Return on Surplus = r
Total Return on Surplus (R) = O x L + r
All items are based on net present value across policy / accident period lifetime
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Example of Risk-Based Pricing – Total Return Level Risk
Risk-Adjusted
Return on Capital
Line
Return on Risk-Adjusted Capital
Und Oper
Levg Total
Levg Total
Below Breakeven Total Return Risk
Ratio Return
Ratio Return
Ratio Return
Prob
O
L
R
L
R
Severity
Risk
P
(r-T)
P(r-T) (R-r)/{P(r-T)}
5%
12%
Homeowners
90
14%
3.0
45%
0.86
15%
Automobile
98
4
3.0
15
3.0
15
10
Workers Comp 104
2
3.0
9
6.0
15
10
RCR
0.6%
20
6
0.6
20
6
0.6
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Operating Leverage is the ratio of Insurance Assets to Surplus (Equity or Capital).
Total Return is as an annual percentage rate on Surplus.
In the RAROC perspective Risk-Adjustment is thru a varying Total Return. Operating Leverage is constant.
In the RORAC perspective Risk-Adjustment is thru a varying Operating Leverage. Total Return is constant.
Each line’s return reflects the relative risk of the line, with a uniform risk/return tradeoff across all lines.
RCR (Gain per Unit of Risk) is the same as at the Operating Level.
Under RORAC, Risk (expected surplus drawdown) is a constant (% points of return) along with constant
return.
Finance literature refers to risk measure as “the mean lower partial moment”.
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Appendix: Five Essential Structural Elements
Key Structural Model Elements
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Financial Model Completeness and Integrity: Cash Flow,
Balance Sheet and Income Statements that tie to each other
without adjustments
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Development Triangles of Marketing / Policy / Accident Period
into Calendar Period (see next slide)
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Accounting Valuations: Conventional (statutory or GAAP) and
Economic (present value)
Key Structural Decision Making Elements
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Functional Delineation (Underwriting, Investment and Finance)
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Risk / Return Decision Framework
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Appendix: Historical Evolution of the The Hartford’s Benchmark Methodology
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1986: Benchmark ROE DCF/NPV model is adopted for monitoring returns by line of business in P&C.
1987: National actuarial consulting firm validates methodology for AARP.
1988: Risk-based liability leverage ratio methodology implemented (probability of ruin).
1989: The Hartford publicly advocates use of the Benchmark ROE methodology in testimony at California’s
Proposition 103 hearings and institutes Benchmark ROE methodology in company ratemaking activities.
1990: Benchmark Discounted Cash Flow Methodology Paper is published in the Proceedings of the
Casualty Actuarial Society.
1992: Benchmark ROE introduced into incentive compensation.
1993: Rate of Return and Surplus Flow Papers are published in the Proceedings of the Casualty Actuarial
Society.
1992-1996: Multi-discipline team reviews concepts and promotes integration into conventional business
segment accounting exhibits. Benchmark leverage factors introduced into conventional accounting
exhibits.
1996-1999: Leverage methodology modified to reflect catastrophe distributions, interest rate risk and the
probability of surplus drawdown (return below breakeven) replaces the probability of ruin as primary risk
criterion.
2000: Risk/return paper published in the Proceedings of the Casualty Actuarial Society.
2001: The Multi-Period Model (MPM) is created to reflect cash flows and income statements over time.
2001: Risk Coverage Ratio (RCR) article published in ASTIN.
2002: The MPM is adopted as the standard financial tool to be used across the P&C organization. All
accident year financial plans are based on MPM.
2003: Leverage methodology modified to reflect severity of adverse outcomes.
2004: Value Creation paper published in the Proceedings of the Casualty Actuarial Society.
2004: Risk metrics introduced and published as part of target underwriting ratio and leverage factor
process.
2005: RCR risk/return metric adopted in ERM throughout entire company - P&C, Life and Investment.
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Appendix: Ten Commandments of Insurance Financial Modeling
1. Thou shalt build only models that have an integrated set of balance sheet,
income and cash flow statements
2. Thou shalt remain rooted in a policy period orientation and develop calendar
period results from this base
3. Thou shalt reflect both conventional and economic accounting perspectives guided by economics, constrained by conventions
4. Thou shalt recognize the separate contributions from each of underwriting,
investment and finance activities
5. Thou shalt be guided by the risk / return relationship in all aspects
6. Thou shalt include all sources of company, policyholder and shareholder
revenue and expense embodied in the insurance process
7. Thou shalt reflect all risk transfer activities
8. Thou shalt not separate risk from return
9. Thou shalt not omit any perspective or financial metric that adds understanding
10. Thou shalt allow differences in result only from clearly identified differences in
assumption, and not from model omission
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