The Integration of Risk and Return in Practice
- From Ratemaking to ERM
Russ Bingham
Vice President Actuarial Research
Hartford Financial Services
CAS Spring Meeting
San Juan, Puerto Rico
May 8-10, 2006
1
Outline














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 Metric – Policyholder and Shareholder levels
Risk / Return Integration using RCR
Risk-Based Pricing
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
 Ten Commandments of Insurance Financial Modeling
2
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
3
Insurance Funds Flow Schematic
4
Risk / Return and the Risk Transfer Process

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

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

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
5
Risk / Return Fundamentals
Insurance = underwriting, investment and financial leverage

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

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

Risk transfer price must consider all outcomes that can potentially result in loss
 Frequency and severity of all adverse outcomes are relevant

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
6
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.
7
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)
8
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)
9
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 severity of an adverse outcome
6. Calculate the risk metric
10
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
11
Risk / Return Criteria Specifications in Practice




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.
12
Risk Coverage Ratio Risk Metric – Policyholder Operating Return Level
13
Risk Coverage Ratio Risk Metric – Shareholder Total Return Level
RCR reward / risk relationship is maintained in transition from operating to total return
14
Risk Coverage Ratio Attributes


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)

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)

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)

Reward to risk connection is made by pricing products in proportion to risk

Applicable to underwriting and investing activities
15
Risk / Return Integration “Full” Information Breakeven RCR vs VAR/TVAR
Simulation Scenarios (Low, High Volatility), (Normal, Skewed Distribution), and (5%,10% VAR)
Four scenarios reflect combinations of volatility (low std dev, high std dev), distribution (normal, skewed)
Risk metrics are shown at breakeven and with VAR at 5% and 10%.
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 / risk ratio of 20 / 1 in each scenario.
A single Breakeven based reward/risk RCR pricing line responds to all combinations of volatility and skewness.
The VAR/TVAR based reward/risk relationship varies with VAR and responds to changes in volatility, but NOT to
changes in skewness. VAR/TVAR is distribution location and distribution shape dependent.
16
Risk / Return Integration “Full” Information Breakeven RCR vs VAR/TVAR
High Volatility, Skewed Distribution Scenario (Case 4)
17
Risk / Return Integration “Full” Information Breakeven RCR vs VAR/TVAR
A single Breakeven based reward/risk RCR pricing line responds to all combinations of volatility and skewness.
The VAR/TVAR based reward/risk relationship varies with VAR and responds to changes in volatility, but NOT to
changes in skewness. VAR/TVAR is distribution location and distribution shape dependent.
18
Risk / Return Integration in Practice using RCR





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)
RCR (Risk Coverage Ratio) is used to integrate risk and return
Risk-Based Pricing - higher price dictated when volatility and risk is
greater
 Establishes risk / return tradeoff whose slope is RCR
 Independent of surplus
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)
Price related to risk, leverage related to total return
19
Risk-Based Pricing in Practice

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
 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
 The corporate ROE goal is distributed equitably among areas through
pricing and capital allocation, in proportion to risk contributed
 Internal Diversification and external (e.g. ratings) factors influence this
relationship
20
Risk / Return Methodology in Practice – Scope and Attributes


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

Adequate product pricing based on product risk is viewed as the most
important risk / return lever and all adverse outcomes are considered

Target Prices (premiums) are determined to meet specified RCR in each
line of business – gain (“reward”) per unit of risk same in all lines

Leverage and capital attribution is determined and presented in the
RORAC risk adjustment perspective at which time capital calibration is
verified

Both policyholder (operating return level) and shareholder (total return
level) subject to same risk/return tradeoff
21
Risk / Return Methodology in Practice – Scope and Attributes

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

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


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.
22
Economic and Risk-Based Orientation and Premises


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)
23
Appendix: Example of Risk-Based Pricing – Operating Level Risk
Und
Line
Ratio
Return on Inv Assets
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
20
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.
24
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
Reward / Risk relationship is maintained in translation from Operating to Total Return
All items are based on net present value across policy / accident period lifetime
25
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
20
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”.
26
Appendix: Five Essential Structural Elements





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
27
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
28