July 17-18, 2000John W. Rollins, FCAS, MAAA2 A Public Vehicle for Securitizing Cat Risks: The Florida Hurricane Catastrophe Fund The Floridian public has funded a large part of its catastrophe exposure through an indirect line of credit with the capital markets, which defers part of the cost of catastrophes until after an event. The Floridian public has funded a large part of its catastrophe exposure through an indirect line of credit with the capital markets, which defers part of the cost of catastrophes until after an event. The FHCF (Cat Fund), a reinsurer, acts as a tax-exempt cash accumulation vehicle, as well as the interface between insurers and the bond market after a storm. The FHCF (Cat Fund), a reinsurer, acts as a tax-exempt cash accumulation vehicle, as well as the interface between insurers and the bond market after a storm. Insurers and citizens are exposed to market risks because the Cat Fund relies on issuing post-event bonds to pay its obligations - serviced by future assessment (tax) revenue. Insurers and citizens are exposed to market risks because the Cat Fund relies on issuing post-event bonds to pay its obligations - serviced by future assessment (tax) revenue.

July 17-18, 2000John W. Rollins, FCAS, MAAA3 How it Works: Before the Storm Citizens buy traditional coverage from insurers. Citizens buy traditional coverage from insurers. Insurers buy reinsurance from: Insurers buy reinsurance from: Private sources (at risk-adjusted market rates) Private sources (at risk-adjusted market rates) The Cat Fund (at prescribed sub-market rates) The Cat Fund (at prescribed sub-market rates) The Cat Fund promises several times its cash to insurers. The promise is supported by: The Cat Fund promises several times its cash to insurers. The promise is supported by: The authority to issue tax-exempt debt after a storm The authority to issue tax-exempt debt after a storm The authority to assess all insurance-buying citizens to service this debt as it matures. The authority to assess all insurance-buying citizens to service this debt as it matures.

July 17-18, 2000John W. Rollins, FCAS, MAAA4 How it Works: Before the Storm Private Reinsurers Citizens Insurers

July 17-18, 2000John W. Rollins, FCAS, MAAA5 How It Works – Cat Fund Essential Details Cat Fund capacity is capped at $11 billion/season, subject to its ability to fund losses through cash and bonds. Cat Fund capacity is capped at $11 billion/season, subject to its ability to fund losses through cash and bonds. Cat Fund capacity fluctuates over time with loss history. Cat Fund capacity fluctuates over time with loss history. Assessments are capped at 4%/season, 6% overall, of all non-WC property/casualty premium. Assessments are capped at 4%/season, 6% overall, of all non-WC property/casualty premium. Cat Fund rates are set independently of: Cat Fund rates are set independently of: Primary company rates and reinsurance coverage. Primary company rates and reinsurance coverage. Cat Fund capacity (price set, capacity changes). Cat Fund capacity (price set, capacity changes). Cat Fund rates contain no risk load. Cat Fund rates contain no risk load. A companys Cat Fund retention and amount of coverage are a function of its premium paid to the Cat Fund. A companys Cat Fund retention and amount of coverage are a function of its premium paid to the Cat Fund.

July 17-18, 2000John W. Rollins, FCAS, MAAA6

July 17-18, 2000John W. Rollins, FCAS, MAAA7 How it Works: After the Storm At seasons end, the Cat Fund pays losses from: At seasons end, the Cat Fund pays losses from: Its cash balance (first) Its cash balance (first) The proceeds of issuing bonds (second) The proceeds of issuing bonds (second) The cash balance is replenished in the next season solely by (fixed) reinsurance premiums and investment income (if any investable cash is left). The cash balance is replenished in the next season solely by (fixed) reinsurance premiums and investment income (if any investable cash is left). To service the debt, assessments are levied on all Florida policyholders. The FHCF and insurers just act as collection agent for the bondholders. Assessment authority is reduced by law for future seasons. To service the debt, assessments are levied on all Florida policyholders. The FHCF and insurers just act as collection agent for the bondholders. Assessment authority is reduced by law for future seasons.

July 17-18, 2000John W. Rollins, FCAS, MAAA8 How It Works: After the Storm Capital Markets Cash Balance

July 17-18, 2000John W. Rollins, FCAS, MAAA9 Coverage Risks to Insurers: First and Second Season Season aggregate coverage could be threatened by two types of securitization problems: Season aggregate coverage could be threatened by two types of securitization problems: Reduction in bonding capacity due to an unexpected rise in market interest rates (in any season) Reduction in bonding capacity due to an unexpected rise in market interest rates (in any season) Reduction in bonding capacity due to inability to service debt – limits on assessments (in a second season) Reduction in bonding capacity due to inability to service debt – limits on assessments (in a second season) Florida insurers using the Cat Fund as a cornerstone of their reinsurance program need to assess the impact of uncertainty in coverage over a multi-season horizon. Florida insurers using the Cat Fund as a cornerstone of their reinsurance program need to assess the impact of uncertainty in coverage over a multi-season horizon.

July 17-18, 2000John W. Rollins, FCAS, MAAA10 A Plan for Measuring Second Season Coverage Risk 1. Obtain a database of simulated hurricane experience for the company from cat modeling partners. 2. Augment database with fields representing simulated losses subject to Cat Fund coverage, for the insurance industry as a whole, by storm. 3. Build an engine to randomly sample a portion of the experience over a user-defined time horizon and number of trials. 4. Build a dynamic model of the financial position of the Cat Fund at the end of every season in the horizon, modeling both cash flows and debt burden for each season. 5. Run simulation to generate relevant statistics for each year of horizon. Analyze empirical distributions of these statistics.

July 17-18, 2000John W. Rollins, FCAS, MAAA11 Database Preparation Converting direct losses to subject to Cat Fund losses may require several steps, for example: Converting direct losses to subject to Cat Fund losses may require several steps, for example: Remove commercial property losses Remove commercial property losses Remove Additional Living Expense losses Remove Additional Living Expense losses A market share approach can be used to estimate industry- wide subject losses from company losses. Scale up company losses using exposure market share tables by: A market share approach can be used to estimate industry- wide subject losses from company losses. Scale up company losses using exposure market share tables by: Line of business Line of business County or territory County or territory

July 17-18, 2000John W. Rollins, FCAS, MAAA12 Database Preparation (continued) The final database contains these important fields: The final database contains these important fields: Year index (1-50,000) Year index (1-50,000) Storm index (within year) Storm index (within year) Industry-wide losses subject to Cat Fund Industry-wide losses subject to Cat Fund Other preparatory steps: Other preparatory steps: Randomize data before simulation by shuffling seasons like a deck of cards. Keep storm records together and in order within each season. Randomize data before simulation by shuffling seasons like a deck of cards. Keep storm records together and in order within each season. Determine probability of a storm-free year from dividing the number of distinct year indices in the data by the number of simulated seasons. Determine probability of a storm-free year from dividing the number of distinct year indices in the data by the number of simulated seasons.

July 17-18, 2000John W. Rollins, FCAS, MAAA13 Excerpt from Augmented Database Season Event Order Industry Subject Loss 21$2,500,000,000 41$800,000,000 42$6,500,000,000 71$15,000,000,000 72$3,500,000,000 81$5,000,000,000

July 17-18, 2000John W. Rollins, FCAS, MAAA14 Simulation Logic 1. Ask user for desired number of trials (T) and number of seasons (N) in horizon. 2. For each season within each trial, randomly determine whether year is storm-free. If it is, no losses occur. 3. If not storm-free, draw one years experience (which may include several storms) from the top of the deck and assign to the season. 4. Once experience is assigned to every year within every trial, run analysis of Cat Fund financial position at end of successive seasons 1-N, one trial at a time.

July 17-18, 2000John W. Rollins, FCAS, MAAA15 Cat Fund Financial Model: Cash Position Difference equation describing cash position: Difference equation describing cash position: End balance = Begin balance +Premium income +Investment income --Operating expenses --Losses paid from cash Investment income assumes conservative portfolio yield. Investment income assumes conservative portfolio yield. Losses paid from cash determined by simulated Cat Fund incurred losses. Incurred losses are subject losses net of: Losses paid from cash determined by simulated Cat Fund incurred losses. Incurred losses are subject losses net of: Estimated industry aggregate retention Estimated industry aggregate retention Estimated industry average co-participation Estimated industry average co-participation

July 17-18, 2000John W. Rollins, FCAS, MAAA16 Cat Fund Financial Model: Debt Burden Debt burden starts at zero (no outstanding bond) in first season of each trial. Debt burden starts at zero (no outstanding bond) in first season of each trial. If incurred losses during any season exceed available cash, debt is issued for the difference – subject to statutory cap on total paid losses ($11 billion). If incurred losses during any season exceed available cash, debt is issued for the difference – subject to statutory cap on total paid losses ($11 billion). The bond term and the market interest rate for the season, together with the amount borrowed, determine the size of the required assessment. This debt service is applied against the capacity of future seasons. The bond term and the market interest rate for the season, together with the amount borrowed, determine the size of the required assessment. This debt service is applied against the capacity of future seasons.

July 17-18, 2000John W. Rollins, FCAS, MAAA17 Cat Fund Financial Model: Debt Burden (cont.) In a second season, if incurred losses exceed available cash, additional debt is issued if possible. In a second season, if incurred losses exceed available cash, additional debt is issued if possible. Model must keep track of total outstanding assessments from prior seasons to determine maximum assessment. Model must keep track of total outstanding assessments from prior seasons to determine maximum assessment. If the assessment cannot support the amount the Cat Fund needs to borrow, the industry recovers less than its promised $11 billion. The complement of the ratio of total actual to promised recovery is the deficit ratio. Pro-rata sharing means ratio is the same for all insurers. If the assessment cannot support the amount the Cat Fund needs to borrow, the industry recovers less than its promised $11 billion. The complement of the ratio of total actual to promised recovery is the deficit ratio. Pro-rata sharing means ratio is the same for all insurers.

July 17-18, 2000John W. Rollins, FCAS, MAAA18 Analyzing the Model Results The distribution of any season-indexed statistic can be empirically tabulated from this simulation, e.g.: The distribution of any season-indexed statistic can be empirically tabulated from this simulation, e.g.: Coverage deficit ratio (for insurers) Coverage deficit ratio (for insurers) Required assessment or amount of debt (for public policy makers) Required assessment or amount of debt (for public policy makers) Excess (over $11 billion) industry incurred losses Excess (over $11 billion) industry incurred losses Expectations, dispersion measures, and tail probabilities can be derived and compared against stakeholder risk tolerances: I want no more than a 1% chance that the coverage deficit ratio will exceed 10% within 5 years Expectations, dispersion measures, and tail probabilities can be derived and compared against stakeholder risk tolerances: I want no more than a 1% chance that the coverage deficit ratio will exceed 10% within 5 years

July 17-18, 2000John W. Rollins, FCAS, MAAA19 Applications of Empirical Analysis of Cat Fund Design and pricing of innovative reinsurance products (second season/wrap-around covers) to plug gaps. Design and pricing of innovative reinsurance products (second season/wrap-around covers) to plug gaps. Determination of optimal vertical and horizontal coverage structure for private reinsurance program. Determination of optimal vertical and horizontal coverage structure for private reinsurance program. Integration of public reinsurance risk module into the corporate Dynamic Financial Analysis model: Integration of public reinsurance risk module into the corporate Dynamic Financial Analysis model: The event-level cat data is a powerful information set for analyzing both public and private reinsurance. The event-level cat data is a powerful information set for analyzing both public and private reinsurance. The simulation model can be plugged into the enterprise DFA model, passing important statistics which greatly influence corporate financial results. The simulation model can be plugged into the enterprise DFA model, passing important statistics which greatly influence corporate financial results.

July 17-18, 2000John W. Rollins, FCAS, MAAA20 Whats Missing: Other Real-World Risks No inflation or trends have been assumed in: No inflation or trends have been assumed in: Exposure base (raw event losses) Exposure base (raw event losses) Assessment base (for debt service, based on premium) Assessment base (for debt service, based on premium) No forecast module for (borrowing or lending) interest rates has been included. Interest rates and investment yields would vary over seasons in horizon. No forecast module for (borrowing or lending) interest rates has been included. Interest rates and investment yields would vary over seasons in horizon. There may be a significant lag between payment of claims and receipt of cash/bond proceeds from Cat Fund. Timing risk has been ignored (but of practical importance). There may be a significant lag between payment of claims and receipt of cash/bond proceeds from Cat Fund. Timing risk has been ignored (but of practical importance).