The Integration of Risk and Return in Practice
- Ratemaking, Reserving and ERM
Russ Bingham
Vice President Actuarial Research
Hartford Financial Services
CLRS
Atlanta, GA
Sept 11-12, 2006
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Outline
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Corporate Objective: To Instill Financial Discipline
Reserving and The Actuaries Role
Risk / Return Fundamentals
 Risk / Return Line
 Connecting Risk and Return - RAROC and RORAC
Risk Quantification
 Generic Steps
 Alternative Risk Metrics
 Risk / Return Criteria Specifications
Risk Coverage Ratio Risk Metric
 Policyholder and Shareholder levels
 Attributes
 Risk / Return Integration using RCR
Risk / Return Methodology in Practice – Summary
Appendix
 Economic and Risk-Based Orientation and Premises
 Five Essential Structural Elements
 Ten Commandments of Insurance Financial Modeling
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Corporate Objective: To Instill Financial Discipline
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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The Actuaries Role
Uncertainty and volatility of both amount of loss and timing of payment is
typically the most significant driver of risk in P&C insurance
Establishing reserve ranges requires that this be quantified
This information should be used within all risk-driven activities,
particularly pricing and ERM
The actuary must play a critical role in the ERM process
However, the actuary must take a broader financial perspective
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Risk / Return Fundamentals
Insurance = underwriting, investment and financial leverage
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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 financial 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, particulary loss
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Risk transfer price must consider all outcomes that can potentially result in
financial 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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Risk Quantification: Generic 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 severity of an adverse outcome
6. Calculate the risk metric
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Risk Quantification: Alternative Risk Metrics
Policyholder
oriented risk metrics
Probability of ruin (POR)
Expected policyholder deficit (EPD)
Shareholder oriented risk metrics
Variability in total return (sR)
Sharpe Ratio
Value at risk (VAR)
Tail Value at Risk (TVAR)
Tail Conditional Expectation (TCE)
Probability of Income Ruin (POIR)
Probability of surplus drawdown deficit (PSD)
Severity of surplus drawdown deficit (SSD)
Expected surplus drawdown deficit (ESD)
Risk Coverage Ratio (RCR)
RBC and other Rating Agency measures
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
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Risk Quantification: Risk / Return Criteria Specifications
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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
Risk metric is “Risk Coverage Ratio” (RCR) which reflects the expected
return margin above breakeven in ratio to the risk as measured by the
expected frequency of result below breakeven times the severity of those
outcomes – this is a Reward to Risk ratio.
“All” sources of risk (cats, non-cat losses, cash flow, yield, etc.) are
modeled simultaneously. Their respective contributions 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 Metric – Policyholder Operating Return Level
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Risk Coverage Ratio Risk Metric – Shareholder Total Return Level
RCR reward / risk relationship is maintained in transition from operating to total return
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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 one 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)
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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 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 Methodology in Practice – Summary
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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
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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 – Summary
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The Benchmark model provides a framework for economic measurement of
risk-based 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 decisionmaking
 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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Appendix: 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
 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 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
External total company “constraints” must be met based on
 Calendar period (e.g. meet reported earnings expectations)
 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: Five Essential Structural Elements
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Financial Model Completeness and Integrity: Cash Flow,
Balance Sheet and Income Statements that tie to each other
without adjustments
Development Triangles of Marketing / Policy / Accident Period
into Calendar Period (see next slide)
Accounting Valuations: Conventional (statutory or GAAP) and
Economic (present value)
Functional Delineation (Underwriting, Investment and Finance)
Risk / Return Decision Framework
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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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