Ratemaking for Multi-Peril Crop Insurance

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Ratemaking for Multi-Peril Crop Insurance

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

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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

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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 (AIPs)
• Reimburses AIPs administrative and operating
  expenses

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Industry Structure

• Approved Insurance Providers (AIPs)
• Market and issue policies
• Policyholder underwriting
• Adjust claims
• Retain a portion of underwriting risk

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Industry Liability
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Industry Liability
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Industry Liability
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Insured Perils
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Crop Insurance Indemnity
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Crop Insurance Indemnity
Source US Drought Monitor http//drought.unl.edu/
dm Map issued July 23, 2002
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Crop Insurance IndemnityGross Loss Ratios for
the Crop Insurance Program
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Insurance GuaranteeYield Insurance

• Yield Guarantee Actual Production History (APH)
  x Coverage Level
• Indemnity MaxYield 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

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Insurance GuaranteeYield 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

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Insurance GuaranteeRevenue Insurance

• Revenue Guarantee Actual Production History
  (APH) x Expected Price x Coverage Level
• Indemnity MaxRevenue Guarantee (Realized
  Yield x Realized Price), 0
• Expected and Realized Prices are determined by
  futures contracts on a commodities exchange.

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Insurance GuaranteeRevenue 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

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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

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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

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Rate Basis

• County/Crop
• Annual loss-cost ratios (LCRs) from 1975 to
  present.

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Rating ProcessAdjusting 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.

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Rating ProcessDevelop Unloaded County Base Rates

• Adjusted data is used to derive historic annual
  LCRs for each crop and county.
• Each countys LCR is capped at the 80th
  percentile.
• Losses above the cap are pooled at the state
  level
• Each countys capped LCR is averaged with those
  of surrounding counties.
• The amount of weight given to surrounding county
  LCRs is determined by a credibility measure

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Rating ProcessDevelop 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

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Rating ProcessCalculate 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 growers
  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 YieldExponent

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Rating ProcessCalculate Individual Rate
Relative Yield
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Rating ProcessCalculate 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.

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Rating ProcessCalculate Individual Rate
Coverage Level
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Rating ProcessSummary

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

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Standard Reinsurance Agreement

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

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Standard Reinsurance Agreement
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Standard Reinsurance Agreement
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Standard Reinsurance Agreement
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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
  RMAs website.

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Thank You

• Visit the RMA website for more information
  www.rma.usda.gov