July 17-18, 2000John W. Rollins, FCAS, MAAA2 A Public Vehicle for Securitizing Cat Risks: The...

July 17-18, 2000 John W. Rollins, FCAS, MAAA 2

A Public Vehicle for Securitizing Cat Risks:The Florida Hurricane Catastrophe Fund

The Floridian public has funded a large part of its The Floridian public has funded a large part of its catastrophe exposure through an indirect “line of credit” catastrophe exposure through an indirect “line of credit” with the capital markets, which defers part of the cost of with the capital markets, which defers part of the cost of catastrophes until after an event.catastrophes until after an event.

The FHCF (Cat Fund), a reinsurer, acts as a tax-exempt The FHCF (Cat Fund), a reinsurer, acts as a tax-exempt cash accumulation vehicle, as well as the interface cash accumulation vehicle, as well as the interface between insurers and the bond market after a storm.between insurers and the bond market after a storm.

Insurers Insurers andand citizens are exposed to market risks because citizens are exposed to market risks because the Cat Fund relies on issuing post-event bonds to pay its the Cat Fund relies on issuing post-event bonds to pay its obligations - serviced by future assessment (tax) revenue. obligations - serviced by future assessment (tax) revenue.


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 Cat Fund promises several times its cash to insurers. The promise is supported by:The promise is supported by: The authority to issue tax-exempt debt after a stormThe authority to issue tax-exempt debt after a storm The authority to assess all insurance-buying citizens to The authority to assess all insurance-buying citizens to

service this debt as it matures.service this debt as it matures.


How it Works: Before the Storm

Private Reinsurers

Citizens

Insurers


How It Works – Cat Fund Essential Details

Cat Fund capacity is capped at $11 billion/season, Cat Fund capacity is capped at $11 billion/season, subject subject to its ability to fund losses through cash and bonds.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 Assessments are capped at 4%/season, 6% overall, of all

non-WC property/casualty premium.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 company’s Cat Fund retention and amount of coverage A company’s Cat Fund retention and amount of coverage

are a function of its premium paid to the Cat Fund.are a function of its premium paid to the Cat Fund.


How it Works: After the Storm

At season’s end, the Cat Fund pays losses from:At season’s 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 The cash balance is replenished in the next season solely by (fixed) reinsurance premiums and investment income by (fixed) reinsurance premiums and investment income (if any investable cash is left).(if any investable cash is left).

To service the debt, assessments are levied on all Florida To service the debt, assessments are levied on all Florida policyholders. policyholders. The FHCF and insurers just act as The FHCF and insurers just act as “collection agent” for the bondholders“collection agent” for the bondholders. Assessment . Assessment authority is reduced by law for future seasons.authority is reduced by law for future seasons.


How It Works: After the Storm

Capital Markets

Cash Balance


Coverage Risks to Insurers:First and “Second Season”

Season aggregate coverage could be threatened by two Season aggregate coverage could be threatened by two types of securitization problems:types of securitization problems: Reduction in bonding capacity due to an unexpected Reduction in bonding capacity due to an unexpected

rise in market interest rates (rise in market interest rates (in any seasonin any season)) Reduction in bonding capacity due to inability to Reduction in bonding capacity due to inability to

service debt – limits on assessments (service debt – limits on assessments (in a “second in a “second season”season”))

Florida insurers using the Cat Fund as a cornerstone of Florida insurers using the Cat Fund as a cornerstone of their reinsurance program need to assess the impact of their reinsurance program need to assess the impact of uncertainty in coverage uncertainty in coverage over a multi-season horizonover a multi-season horizon..


A Plan for Measuring Second Season Coverage Risk

1.1. Obtain a databaseObtain a database of simulated hurricane experience for the company of simulated hurricane experience for the company from cat modeling partners.from cat modeling partners.

2.2. Augment databaseAugment database with fields representing simulated losses with fields representing simulated losses subject to subject to Cat Fund coverageCat Fund coverage, for the , for the insurance industry as a wholeinsurance industry as a whole, by storm., by storm.

3.3. Build an engine to Build an engine to randomly samplerandomly sample a portion of the experience over a a portion of the experience over a user-defined time horizon and number of trials.user-defined time horizon and number of trials.

4.4. Build a Build a dynamic modeldynamic model of the financial position of the Cat Fund at the of the financial position of the Cat Fund at the end of every season in the horizon, modeling both end of every season in the horizon, modeling both cash flowscash flows and and debt debt burdenburden for each season. for each season.

5.5. Run simulationRun simulation to generate relevant statistics for each year of horizon. to generate relevant statistics for each year of horizon. Analyze empirical distributions of these statistics. Analyze empirical distributions of these statistics.


Database Preparation

Converting direct losses to “subject to Cat Fund losses” Converting direct losses to “subject to Cat Fund losses” may require several steps, for example:may require several steps, for example: Remove commercial property lossesRemove commercial property losses Remove Additional Living Expense lossesRemove Additional Living Expense losses

A A market sharemarket share approach can be used to estimate approach can be used to estimate industry-wide subject losses from company losses. Scale industry-wide subject losses from company losses. Scale up company losses using exposure market share tables by:up company losses using exposure market share tables by: Line of businessLine of business County or territoryCounty or territory


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 FundIndustry-wide losses subject to Cat Fund

Other preparatory steps:Other preparatory steps: RandomizeRandomize data before simulation by “shuffling” data before simulation by “shuffling”

seasons like a deck of cards. Keep storm records seasons like a deck of cards. Keep storm records together and in order within each season.together and in order within each season.

Determine Determine probability of a storm-free yearprobability of a storm-free year from from dividing the number of distinct year indices in the data dividing the number of distinct year indices in the data by the number of simulated seasons.by the number of simulated seasons.


Excerpt from Augmented Database

SeasonSeason Event OrderEvent Order Industry Subject LossIndustry Subject Loss

22 11 $2,500,000,000$2,500,000,000

44 11 $800,000,000$800,000,000

44 22 $6,500,000,000$6,500,000,000

77 11 $15,000,000,000$15,000,000,000

77 22 $3,500,000,000$3,500,000,000

88 11 $5,000,000,000$5,000,000,000


Simulation Logic

1.1. Ask user for desired number of trials (T) and number of Ask user for desired number of trials (T) and number of seasons (N) in horizon.seasons (N) in horizon.

2.2. For each season within each trial, randomly determine For each season within each trial, randomly determine whether year is storm-free. If it is, no losses occur.whether year is storm-free. If it is, no losses occur.

3.3. If not storm-free, draw one year’s experience (which may If not storm-free, draw one year’s experience (which may include several storms) from the “top of the deck” and include several storms) from the “top of the deck” and assign to the season.assign to the season.

4.4. Once experience is assigned to every year within every Once experience is assigned to every year within every trial, run analysis of Cat Fund financial position at end of trial, run analysis of Cat Fund financial position at end of successive seasons 1-N, one trial at a time.successive seasons 1-N, one trial at a time.


Cat Fund Financial Model: Cash Position

Difference equation describing cash position:Difference equation describing cash position:

End balance = Begin balanceEnd balance = Begin balance

++Premium incomePremium income

++Investment incomeInvestment income

---- Operating expensesOperating expenses

---- Losses paid from cashLosses paid from cash Investment income assumes conservative portfolio yield.Investment income assumes conservative portfolio yield. Losses paid from cash determined by simulated Cat Fund Losses paid from cash determined by simulated Cat Fund

incurred losses. Incurred losses are subject losses net of:incurred losses. Incurred losses are subject losses net of: Estimated industry aggregate retentionEstimated industry aggregate retention Estimated industry average co-participation Estimated industry average co-participation


Cat Fund Financial Model: Debt Burden

Debt burden starts at zero (no outstanding bond) in first Debt burden starts at zero (no outstanding bond) in first season of each trial.season of each trial.

If incurred losses during any season exceed available cash, If incurred losses during any season exceed available cash, debt is issued for the difference – subject to statutory cap debt is issued for the difference – subject to statutory cap on total paid losses ($11 billion).on total paid losses ($11 billion).

The bond term and the market interest rate for the season, The bond term and the market interest rate for the season, together with the amount borrowed, determine the size of together with the amount borrowed, determine the size of the required assessment. This debt service is applied the required assessment. This debt service is applied against the capacity of future seasons.against the capacity of future seasons.


Cat Fund Financial Model: Debt Burden (cont.)

In a “second season”, if incurred losses exceed available In a “second season”, if incurred losses exceed available cash, additional debt is issued if possible.cash, additional debt is issued if possible.

Model must keep track of Model must keep track of total outstanding assessments total outstanding assessments from prior seasonsfrom prior seasons to determine maximum assessment. to determine maximum assessment.

If the assessment cannot support the amount the Cat Fund If the assessment cannot support the amount the Cat Fund needs to borrow, the industry recovers less than its needs to borrow, the industry recovers less than its promised $11 billion. The complement of the ratio of promised $11 billion. The complement of the ratio of totaltotal actual to promised recovery is the “actual to promised recovery is the “deficit ratiodeficit ratio”. Pro-rata ”. Pro-rata sharing means ratio is the same for all insurers.sharing means ratio is the same for all insurers.


Analyzing the Model Results

The distribution of any season-indexed statistic can be The distribution of any season-indexed statistic can be empirically tabulated from this simulation, e.g.: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 Required assessment or amount of debt (for public

policy makers)policy makers) Excess (over $11 billion) industry incurred lossesExcess (over $11 billion) industry incurred losses

Expectations, dispersion measures, and tail probabilities Expectations, dispersion measures, and tail probabilities can be derived and compared against stakeholder risk can be derived and compared against stakeholder risk tolerances: “tolerances: “I want no more than a 1% chance that the I want no more than a 1% chance that the coverage deficit ratio will exceed 10% within 5 yearscoverage deficit ratio will exceed 10% within 5 years””


Applications of Empirical Analysis of Cat Fund

Design and pricing of innovative reinsurance products Design and pricing of innovative reinsurance products (second season/wrap-around covers) to plug gaps.(second season/wrap-around covers) to plug gaps.

Determination of optimal vertical and horizontal coverage Determination of optimal vertical and horizontal coverage structure for private reinsurance program.structure for private reinsurance program.

Integration of public reinsurance risk module into the Integration of public reinsurance risk module into the corporate Dynamic Financial Analysis model:corporate Dynamic Financial Analysis model: The event-level cat data is a powerful information set The event-level cat data is a powerful information set

for analyzing both public and private reinsurance.for analyzing both public and private reinsurance. The simulation model can be “plugged into” the The simulation model can be “plugged into” the

enterprise DFA model, passing important statistics enterprise DFA model, passing important statistics which greatly influence corporate financial results.which greatly influence corporate financial results.


What’s 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 No forecast module for (borrowing or lending) interest rates has been included. Interest rates and investment rates has been included. Interest rates and investment yields would vary over seasons in horizon.yields would vary over seasons in horizon.

There may be a significant lag between payment of claims There may be a significant lag between payment of claims and receipt of cash/bond proceeds from Cat Fund. Timing and receipt of cash/bond proceeds from Cat Fund. Timing risk has been ignored (but of practical importance).risk has been ignored (but of practical importance).

.JRollins@sfbcic com.JRollins@sfbcic com

July 17-18, 2000John W. Rollins, FCAS, MAAA2 A Public Vehicle for Securitizing Cat Risks: The...

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