Pricing Strategies for Multi-Line Multi-Year (MLMY) Policies April 12, 1999 CAS Financial Risk Management Seminar Denver, Colorado Nathan J. Babcock, ACAS, MAAA Deloitte & Touche LLP

Agenda I.MLMY Advantages, Disadvantages II.Pricing Example III.MLMY Pricing Considerations IV.Risk Loads V.Business Dynamics

Insurer/Seller l Extended duration of premium receipts l Enhanced market share l Relief from market cycles l Higher “implied” renewal rates generating a more “seasoned” book l Development of long-term relationships MLMY Advantages

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

MLMY Disadvantages Insurer/Seller l Limited ability to react to poor experience by increasing rates l Complex pricing l Complex profitability measures l Allocation issues (WP, UPR, capital)

MLMY Disadvantages Insured/Buyer l Possibility of an aberrant line or loss impacting overall coverage for all lines l Opportunity cost of locking-in l Lack of focus on traditional risk management l “All eggs in one basket”

Pricing Example

l Burning cost l On-level historical loss ratios l Exposure rating l Monte Carlo simulation Traditional Pricing Approaches

l Pricing of a layer excess of a self-insured retention l SIR applies per occurrence to all lines, with annual and term aggregates l Lines considered: WC, GL, EQ, FX l Model output = losses and premiums by layer Policy Example Baseline Assumptions

Example Loss Metrics WC Mean = $12 MM Std dev = $1.5 MM CV = GL Mean = $4 MM Std dev = $1 MM CV = EQ Mean = $2 MM Std dev = $25 MM CV = FX Mean = $3 MM Std dev = $5 MM CV = 1.667

Scenario I $25 mm per occ. and ann. agg. SIR $100 mm annual aggregate limit Year 1 WC sublimit - $500k per occ. SIR

Scenarios II & III Prog: $25 mm WC: $500K (implicit $300 mm term aggregate) Year 1Year 2Year 3 $100 mm ann aggregate $100 mm ann aggregate $100 mm ann aggregate

Scenario IV Prog: $25 mm WC: $500K $100 mm term aggregate limit Year 1Year 2Year 3 $100 mm ann agg. $100 mm ann agg. $100 mm ann agg.

l Scenario I (1 one-year policy) $5 mm l Scenario II (3 one-year policies) $15 mm l Scenario III (1 three-year policy) $12.5 mm l Scenario IV (3-year policy with a term limit) $12 mm Modeled Premiums

Multi-Line / Multi-Year Pricing Considerations

Portfolio Effect

Correlation l Among lines of business l Among multiple years l More or less risk?

Discount Rate l Implied risk margin l Paying the “last losses” on aggregate l Appropriate patterns of premium and loss payments

Reinstatements l Use Monte Carlo simulation output to determine likelihood of limits “blown” l Or, model likelihood of limits “blown” once a significant loss has occurred. l When would limits be reinstated l Very judgmental -- adjust insured’s assumed loss distribution for large loss that has occurred?

Additional MLMY Pricing Considerations l Exposure growth l Sublimits/Towers l Knockout features l Residual Retentions

“THE INSURANCE PREMIUM FORMULA” P = (expected losses) + (risk load) 1 - (expense ratio)

Risk Loads

Risk Load Considerations Insured-Specific Attributes l Loss distribution - standard deviation l Loss distribution - coefficient of variation l Confidence level desired

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

Risk Load Considerations Categories of risk load factors l Insured-specific = process risk l Insurer-specific = parameter risk

Business Dynamics l Opportunity cost of locking in l Market cycle l Renewal retention pressures l Hedges in other areas of insurer’s operations l Can risk loads be achieved? –One risk vs. entire book –As a cost of liquidity

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