Ratemaking for Multi-Peril Crop Insurance CAS Seminar on RatemakingThomas Worth, Ph.D. Concurrent Session COM-7Senior Actuary Philadelphia, PA Research and Development March 21-22, 2004 Risk Management Agency U.S. Dept. of Agriculture

Mission of the Federal Crop Insurance Program “to promote the national welfare... through a sound system of crop insurance” “provide the means for the research and experience helpful in devising and establishing such insurance.” FCIC Act, section 502(a), Feb. 16, 1938

Industry Structure A Public-Private Partnership Federal Government (RMA) –Determines or approves policy terms and premium rates –Subsidizes premium for growers –Provides Program Oversight –Reinsures approved insurance providers (AIP’s) –Reimburses AIP’s administrative and operating expenses

Industry Structure Approved Insurance Providers (AIP’s) –Market and issue policies –Policyholder underwriting –Adjust claims –Retain a portion of underwriting risk

Industry Liability

Insured Perils

Crop Insurance Indemnity

Source: US Drought Monitor Map issued July 23, 2002

Crop Insurance Indemnity Gross Loss Ratios for the Crop Insurance Program

Insurance Guarantee Yield Insurance Yield Guarantee = Actual Production History (APH) x Coverage Level Indemnity = Max[Yield Guarantee – Realized Production, 0] x Established Price Per Unit APH based on historical average yield Coverage Level varies from 50% to 85% –Deductible = 1- Coverage Level

Insurance Guarantee Yield Insurance Example –Yield Guarantee = 100 bushels per acre x 65% or 65 bushels per acre –Assume realized production is 50 bushels per acre and the establish price is $2.00 per bushel. –Indemnity = (65 – 50) x $2.00 or $30 per acre

Insurance Guarantee Revenue Insurance Revenue Guarantee = Actual Production History (APH) x Expected Price x Coverage Level Indemnity = Max[Revenue Guarantee – (Realized Yield x Realized Price), 0] Expected and Realized Prices are determined by futures contracts on a commodities exchange.

Insurance Guarantee Revenue Insurance Example –Revenue Guarantee = 100 bushels per acre x $2.00 per bushel x 65% or $130 per acre –Assume realized production is 50 bushels per acre and the Realized Price is $2.50 per bushel. –Indemnity = ($130 – $125) or $5 per acre

Ratemaking Method Pure Premium (Loss Cost) Method –Average loss per unit of exposure Premium is not loaded for program expenses. –AIP administrative and operating costs are paid for separately

Assumptions The average loss cost is a reasonable estimate of future losses –Historic series covers a reasonable length of time –Data is comparable over time –Data can be adjusted to a common unit of measure

Rate Basis County/Crop Annual loss-cost ratios (LCR’s) from 1975 to present.

Rating Process Adjusting Loss and Exposure to a Common Unit Historic data is adjusted to a common coverage level -- 65%. –Most business is around this coverage level. The liability and indemnity of all growers in a county are adjusted to reflect the values that would have been reported had the coverage been purchased at the 65% level. Adjusting lower coverage levels up to 65% requires estimation.

Rating Process Develop Unloaded County Base Rates Adjusted data is used to derive historic annual LCR’s for each crop and county. Each county’s LCR is capped at the 80 th percentile. –Losses above the cap are pooled at the state level Each county’s capped LCR is averaged with those of surrounding counties. –The amount of weight given to surrounding county LCR’s is determined by a credibility measure

Rating Process Develop Loaded County Base Rate Several loads are applied to the unloaded county base rate. –Disaster Reserve Factor –State Excess Load – Prevented Planting Load –Unit Division Factor

Rating Process Calculate Individual Rate – Relative Yield The county rate reflects rates for growers whose average yield is at the county average yield. Probability of loss is correlated with grower’s average yield relative to the county average yield. –The probability of loss is lower for growers with an average yield that is above the county average. –Vice-versa. [Grower Yield/County Avg Yield] Exponent

Rating Process Calculate Individual Rate – Relative Yield

Rating Process Calculate Individual Rate – Coverage Level County base rate is for the 65% coverage level. Rate is adjusted by a coverage level differential (factor) to derive a rate for other coverage levels. The differential varies by county base rate.

Rating Process Calculate Individual Rate – Coverage Level

Rating Process Summary The final rate is the county base rate with cumulative adjustments. –Relative Yield –Coverage Level –Unit Division Factor –Type Practice Factors

Standard Reinsurance Agreement Reimbursement for Administrative and Operating expenses. –22% of premium on average. Risk sharing with AIP’s –AIP’s must accept all eligible producers. –Large systemic risk. –AIP’s may place policies in one of 3 reinsurance funds. –Commercial (greatest risk/gain), Assigned Risk (least risk/gain), or Developmental (in between) funds

Standard Reinsurance Agreement

Agricultural Risk Protection Act of 2000: –Government “may renegotiate the Standard Reinsurance Agreement once during the 2001 through 2005 reinsurance years.” –Negotiations are under way. –An initial draft of the new SRA is available on RMA’s website.

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