Pricing Strategies for Multi-Line Multi-Year

(MLMY) Policies

April 12, 1999

CAS Financial Risk Management Seminar

Denver, Colorado

Nathan J. Babcock, ACAS, MAAADeloitte & Touche LLP

Agenda

I. MLMY Advantages, Disadvantages

II. Pricing Example

III. MLMY Pricing Considerations

IV. Risk Loads

V. Business Dynamics

Insurer/Seller

Extended duration of premium receipts Enhanced market share Relief from market cycles Higher “implied” renewal rates generating a more

“seasoned” book Development of long-term relationships

MLMY Advantages

Insured/Buyers

Lower, more stable premium Lower commission Simplified administration Relief from market cycles Enhanced Corporate Risk Management focus Coverage for traditionally uninsurable risks Guaranteed renewal Customized program

MLMY Advantages

MLMY DisadvantagesInsurer/Seller

Limited ability to react to poor experience by increasing rates

Complex pricing Complex profitability measures Allocation issues (WP, UPR, capital)

MLMY DisadvantagesInsured/Buyer

Possibility of an aberrant line or loss impacting overall coverage for all lines

Opportunity cost of locking-in Lack of focus on traditional risk management “All eggs in one basket”

Pricing Example

Burning cost On-level historical loss ratios Exposure rating Monte Carlo simulation

Traditional Pricing Approaches

Pricing of a layer excess of a self-insured retention SIR applies per occurrence to all lines, with

annual and term aggregates Lines considered: WC, GL, EQ, FX Model output = losses and premiums by layer

Policy ExampleBaseline Assumptions

ExampleLoss Metrics

WCMean = $12 MMStd dev = $1.5 MMCV = 0.125

GLMean = $4 MMStd dev = $1 MMCV = 0.250

EQMean = $2 MMStd dev = $25 MMCV = 12.500

FXMean = $3 MMStd dev = $5 MMCV = 1.667

Scenario I

$25 mm per occ. and ann. agg. SIR

$100 mm annualaggregate limit

Year 1

WC sublimit - $500k per occ. SIR

Scenarios II & III

Prog: $25 mmWC: $500K

Prog: $25 mmWC: $500K

Prog: $25 mmWC: $500K

(implicit $300 mm term aggregate)

Year 1 Year 2 Year 3

$100 mmann aggregate

$100 mmann aggregate

$100 mmann aggregate

Scenario IV

Prog: $25 mmWC: $500K

Prog: $25 mmWC: $500K

Prog: $25 mmWC: $500K

$100 mm term aggregate limit

Year 1 Year 2 Year 3

$100 mmann agg.

$100 mmann agg.

$100 mmann agg.

Scenario I (1 one-year policy) $5 mm

Scenario II (3 one-year policies) $15 mm

Scenario III (1 three-year policy) $12.5 mm

Scenario IV (3-year policy with a term limit) $12 mm

Modeled Premiums

Multi-Line / Multi-YearPricing Considerations

Distribution of Aggregate Losses, Relative to Expected Value

One Two Three Four

Number of Years in Policy Term

5%-50% 50%-75% 75%-95%

Portfolio Effect

Correlation

Among lines of business

Among multiple years

More or less risk?

Impact of Correlation on Risk Loads

-0.50 0.00 0.50

Line of Business Correlation

Pre

miu

m

Loss & Expense Risk Load

Discount Rate Implied risk margin

Paying the “last losses” on aggregate

Appropriate patterns of premium and loss payments

Reinstatements Use Monte Carlo simulation output to determine likelihood of limits

“blown” Or, model likelihood of limits “blown” once a significant loss has

occurred. When would limits be reinstated Very judgmental -- adjust insured’s assumed loss distribution for large

loss that has occurred?

Additional MLMYPricing Considerations

Exposure growth Sublimits/Towers Knockout features Residual Retentions

“THE INSURANCE PREMIUM FORMULA”

P = (expected losses) + (risk load) 1 - (expense ratio)

Risk Loads

Risk Load Considerations

Insured-Specific Attributes Loss distribution - standard deviation Loss distribution - coefficient of variation Confidence level desired

Risk Load Considerations

Insurer-Specific Attributes Return on equity/surplus Expected policyholder deficit Limitations on probability of ruin Probability of surplus declining by xx% Value of RBC or AM Best ratings

Risk Load Considerations

Categories of risk load factors Insured-specific = process risk Insurer-specific = parameter risk

Risk Load as a Percentage of Premium

0.0%

4.0%

8.0%

12.0%

WC WC + EQ WC + GL + EQ WC + GL + EQ + FX

Variance Standard Deviation Coefficient of Variation

Business Dynamics

Opportunity cost of locking in Market cycle Renewal retention pressures Hedges in other areas of insurer’s operations Can risk loads be achieved?

– One risk vs. entire book

– As a cost of liquidity

Ensure no big hits early on in program Dynamic modifications to program Expense allocation/UPR Accounting issues (FAS113)

Business Dynamics