Ratemaking for Multi-Peril
Crop Insurance
CAS Seminar on Ratemaking
Concurrent Session COM-7
Philadelphia, PA
March 21-22, 2004
Thomas Worth, Ph.D.
Senior Actuary
Research and Development
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
Liability
Year
Acres
2003
2002
2001
2000
1999
1998
1997
1996
1995
1994
1993
1992
1991
1990
1989
$ Billions
$45
$40
$35
$30
$25
$20
$15
$10
$5
$0
200
150
100
50
0
Millions of Acres
Industry Liability
250
Industry Liability
2003 Total Liability All Crops
Liability
in Millions
0 to 1
1 to 10
10 to 40
40 to 100
100 to 451
(723)
(973)
(850)
(229)
(29)
Industry Liability
Total Liability by Commodity, 2003
All Other
Commodities
(100+)
32%
Corn,
Soybeans,
Wheat,
Cotton,
Sorghum,
Rice
68%
Insured Perils
Cause of Loss: Indemnity 1998-2002
Drought
45%
Other
13%
Plant Disease
3%
Heat
5%
Hail
8%
Excess
Moisture
26%
Crop Insurance Indemnity
2001 Loss Ratios
2001 Loss Ratios
2002 Loss Ratios
2002 Loss Ratios
Loss Ratios
0 to 0.5 (1310)
0.5 to 1
(636)
1 to 2
(559)
2 to 4
(264)
4 to 20.5
(49)
Loss Ratios
0 to 0.5
0.5 to 1
1 to 2
2 to 4
4 to 17.5
(835)
(534)
(633)
(601)
(208)
Crop Insurance Indemnity
2002 Loss Ratios
2002 Loss Ratios
Loss Ratios
0 to 0.5
0.5 to 1
1 to 2
2 to 4
4 to 17.5
(835)
(534)
(633)
(601)
(208)
Source: US Drought Monitor
http://drought.unl.edu/dm
Map issued July 23, 2002
Crop Insurance Indemnity
Gross Loss Ratios for the Crop Insurance Program
2.50
Loss Ratio
2.00
1.50
1.00
0.50
0.00
1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002
Year
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 80th
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
Relative Yield Adjustment
Adjustment Factor
County Average Yield = 100, Exponent = -1.8
4
3.5
3
2.5
2
1.5
1
0.5
0
50
60
70
80
90
100 110 120 130 140 150
Grower's Average 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
Coverage Level Differential
Coverage Level Differentials for Corn
2.50
85%
2.00
80%
1.50
75%
70%
1.00
65%
0.50
0.00
0.01
60%
55%
0.04
0.07
0.10
0.13
County Base Rate
0.16
0.19
50%
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
40%
20%
0%
-20%
-40%
-60%
-80%
-100%
Commercial Fund
Developmental Fund
Assigned Risk Fund
0.
00
0.
50
1.
00
1.
50
2.
00
2.
50
3.
00
3.
50
4.
00
4.
50
5.
00
Gain/Loss
Underwriting Gain/Loss on Retained
Premium
Loss Ratio
Standard Reinsurance Agreement
Loss Ratios by Reinsurance Fund
2.00
Commercial Fund
1.50
Assigned Risk and
Developmental Funds
1.00
0.50
Year
02
20
00
20
98
19
96
19
94
19
92
0.00
19
Loss Ratio
2.50
Standard Reinsurance Agreement
30%
20%
10%
0%
-10%
-20%
Year
02
20
01
20
00
20
99
19
98
19
97
19
96
19
95
19
94
19
93
19
92
-30%
19
Percent of Retained
Premium
Post-Reinsurance Underwriting Gains
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.
Thank You
 Visit the RMA website for more
information:
www.rma.usda.gov