Ratemaking: An ERM Function

CAS Ratemaking Seminar

March 13 & 14, 2006

Russ Bingham, Hartford

Curt Parker, Grange Mutual

John Kollar, ISO

CAS ERM Definition• Process

– Assess,– Control,– Exploit,– Finance,– Monitor risk

• Holistic treatment of risk

• Senior management function

• Upside and downside

ERM “Drivers”• Improved corporate governance

– Sarbanes Oxley Act

• Consolidation • Financial services convergence• Globalization – International Association of

Insurance Supervisors (IAIS)• International insurance accounting standards

– Solvency II – International Accounting Standards Board (IASB)

• Risk management evolution

Some OTHER Ratemaking Questions(Outline)

• Adequacy of reserve estimates?

• Capital adequacy?

• Risk measurement by line, state, etc.?

• Reinsurance? Amount? Cost? Risk transfer?

• Marketing program?

• Underwriting guidelines?

• Underwriting cycle position?

• Predictive modeling? Adverse selection?

Loss Reserve AdequacyShort-Tailed vs. Long-Tailed Lines

Short-Tailed Lines

Release most capital at the end of 1st year.

Long-Tailed Lines

Release a portion of capital at the end of each year.

Year 1 Year 2 Year 3 Year 4 Y1 Y2 Y3 Y4

Reserve Risk:Average Size and Volatility of GL

Open Claims Increases Over TimeBig Claims Settle Slowly

0 1 2 3 4 5 6

Open After n Years

Cla

im A

mo

un

t

95th %Mean

Capital RequirementsLoss Volatility

} }Less Capital

More Capital

Expected costs

Insurer A Insurer B

Years Years

Correlation = More Volatility

LineA

LineB

LineC

LineD

Total

{Capital}Capital

Low Correlation

HighCorrelation

Total

Insurer A Insurer B

Correlation increases with volume

Correlation and Risk Size

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

0.20

Size of Risk

Co

rre

lati

on

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

Cumulative Probability

Lo

ss A

mo

un

t

Aggregate Loss Distribution& Implied Economic Capital

Value at Risk

TVaR

Different measures of risk imply different amounts of economic capital

Implied Capital

2xStd. Dev. VaR@99% TVaR@99%

Am

ou

nt

CapitalLiabilities

Risk Measurement & (Cost of) Capital Allocation by Line, etc.

CMP HO Auto Cat Multiline

Am

ou

nt

Diversification Benefit

Standalone

Note capital isallocated to loss reserves

Cost of Financing Risk = Cost of Capital + Net Cost of Reinsurance • Cost of capital reflects:

– Release of capital as claims are resolved– Discounted at the target rate of return on capital– Rate of return on invested assets

• Net cost of reinsurance is the difference of the ceded premium and the expected reinsurance recovery after it has been reduced for:– Discounted cash flows– Federal income taxes

• Minimize the cost of financing risk.

Optimize reinsurance by minimizing the cost of financing

Cost of Financing Insurance

No Re Cat Re All Re

Am

ou

nt

Net Cost of ReinsCost of Capital

Reinsurance Risk Transfer Testing

Aggregate Loss Reserve Distribution

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1,000 1,100 1,200 1,300 1,400 1,500 1,600 1,700 1,800

Loss Reserves ($Millions)

Cu

mu

lati

ve

Pro

ba

bil

ity

Expected losses

Marketing/Underwriting StrategyReflect Risk in Planning Change

Growing the Business

Standalone Standalone Standalone Total Total

Req

uir

ed C

apit

al

Prospect 1Prospect 2Existing

RatemakingSetting Combined Ratio

Targets by Line

• Expected losses

• Expected expenses

• Investment income

• Cost of financing– Cost of reinsurance– Cost of capital (risk)

Standard RatemakingExhibit Scroll to end –>

Cost of Financing

Target Combined

Ratio

Set combined ratio targets by line and overall

Target Combined Ratios

96%

98%

100%

102%

104%

106%

108%

CMP HO Auto Cats Total

Underwriting CyclePricing Risk

• Develop a number of pricing scenarios reflecting marketplace conditions (cycle).

• For each pricing scenario:– Adjust premiums.– Calculate (projected) combined ratio.– Calculate (projected) return on capital.

Predictive ModelingRisk of Adverse Selection

• Use of other information (beyond rating variables) to more accurately rate a policy– Increased profits– Reduced risk– Lower economic capital

• Inability to select better policies and compete with other insurers results in adverse selection– Losses or reduced profits– Increased downside risk– Higher economic capital

Confidence Interval Around the Target Combined Ratio

0

0.2

0.4

0.6

0.8

1

0 20 40 60 80 100 120 140 160 180

Combined Ratio (%)

Cu

mu

lati

ve

Pro

ba

bili

ty

CDFTarget Combined

Ratio (104%)

Robust Analysis of an Enterprise’s Risks (ERM) is

Essential to Sound Ratemaking!