Federal Crop Insurance Ratemaking
and Profitability Projections
October 25, 2010
Richard Bill, FCAS, MAAA
R. A. Bill Consulting
Bill.consulting@frontier.com
Overview
•
•
•
•
•
•
•
•
Coverage
Perils Insured
Federal/Private Partnership
Coverage Examples
Ratemaking Considerations
Profitability Considerations
Standard Reinsurance Contract (SRA)
Projected Profitability
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Coverage Provided
• The policy Guarantees the yield of the crop or
the revenue from the crop
• Loss is not one event but is based on crop
production (and price for Revenue Insurance)
at the end of the season
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Perils Insured
•
•
•
•
•
•
•
Too Dry (Large Area)
Too Wet
Hail
Insects
Prevented Planting
All other Risks except poor farming practices
Price (Revenue products only)
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Seven Prerequisites of Insurable Risk
#7-”Unlikely to produce loss to a
great many insured units at the same
time”
Mehr & Cammack; Principles of Insurance; 1972
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Federal/Private Partnership
• Began strictly as a Govt Program in 30’s
• Small program until Private Industry began
participating in the early 80’s
• Private Companies took over all delivery in the
90’s
• Safety Net for Nation’s Farmers
• Intended to replace Free Ad Hoc Disaster
Payments
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Growth of Crop Program
1981
Acres Insured
Premium
Average Premium Subsidy
Expense Reimbursement
# Private Companies
~ 50 M
377 M
<30%
32%
30
2009
265 M
8.9 B
61%
~18%
16
Note: Includes Business Produced by Govt Agents
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Federal Government Role
• Programs and Policy language
• Rates (All companies charge same rates)
• A&O Expense reimbursement to the companies
(Expenses are not built into the rate)
• Pays a portion of the Farmer’s premium (about 60%
in addition to the expense reimbursement)
• Oversight
• Provides Reinsurance to Private Companies
• Program administered thru the Risk Management
Agency (RMA) which is part of the United States
Dept. of Ag (www.rma.usda.gov)
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Private Industry Role
• Provides distribution system through their
agents
• Issues policies on their paper
• Adjusts Claims
• Retains risk after Government Reinsurance
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Two Types of Plans
• Individual Farmer Plan
• Guarantee based on Farmer’s actual production
• Up to 10 years of individual farmer yield history
used to establish the guarantee
• Group Plan
• Guarantee based on yield history of a larger
area or an index
• Basis Risk
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Individual Farmer Guarantee
Yield Product Guarantee
• Yield Guarantee=Actual Production History
(APH) X Coverage Level
• Example-200 Bushels per acre X 75% Coverage
Level = 150 Bushels per acre
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Revenue product Guarantee
• Revenue Guarantee=APH X Anticipated Price
Per Bushel X Coverage Level
• Example-200 Bushels per acre X $4 per Bushel
X 75% = $600 per acre
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Coverage Level
• Generally from 50% to 85%
• Acts like a deductible
• Example – 75% coverage level is really a 25%
Deductible.
• A 25% loss is needed before any payment is
made
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Corn Example
(1) Yield Bushels Per Acre
(2) Acres
(3) Production in Bushels (1) X (2)
Expected Value
Spring
200
100
20,000
(4) Price Per Bushel
(5) Revenue per Acre (1) X (4)
(6) Revenue (3) X (4)
$
$
$
4.00
800
80,000
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Actual
Harvest
160
100
16,000
$2.50
$400
$40,000
%
of Expected
80%
80%
50%
50%
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Expected Yield
Bushels Per Acre
• Minimum of 4 years of average yield for
individual Farmer
• Building up to 10 years of history
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Expected Price – CBOT Corn Futures
Feb 2011
Corn Futures-CBOT
o|
Open Outcry Futures
Market Data is delayed at least 10 minutes
View Spread Quotes
About this ReportTurn Auto-refresh
Month
Charts
Last
|
Change
Prior
Settle
Open
High
Low
Volume
Mar 2011
504'2
-8'2
512'4
512'2
514'4
490'0
13,776
May 2011
509'0
-9'2
518'2
518'0
520'0
503'4
4,872
Jul 2011
512'4
-8'6
521'2
521'0
522'6
506'4
8,224
Sep 2011
486'4
-8'2
494'6
494'6
495'4
483'0
1,427
Dec 2011
400'0
-7'6
477'6
476'0
478'6
463'6
10,907
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Hi /
Lo Limit
542'4
482'4
548'2
488'2
551'2
491'2
524'6
464'6
507'6
447'6
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Corn Example
(1) Yield Bushels Per Acre
(2) Acres
(3) Production in Bushels (1) X (2)
(4) Price Per Bushel
(5) Revenue per Acre (1) X (4)
(6) Revenue (3) X (4)
Expected Value
Spring
200
100
20,000
$4.00
$800
$80,000
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Actual
Harvest
160
100
16,000
$2.50
$400
$40,000
%
of Expected
80%
80%
50%
50%
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Corn Example
(1) Yield Bushels Per Acre
(2) Acres
(3) Production in Bushels (1) X (2)
Expected Value
Spring
200
100
20,000
(4) Price Per Bushel
(5) Revenue per Acre (1) X (4)
(6) Revenue (3) X (4)
$
$
$
75% Cov Lvl
Guarantee
150
4.00
800 $
80,000 $
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14,000
Actual
Harvest
160
100
16,000 $
600.00
60,000
$2.50
$400
$40,000 $
Loss
-
20,000
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MPCI Ratemaking
• Simplified in the interest of time.
• Rates controlled by RMA
• Paper in the Winter 2000 Forum by Schnapp, Driscoll,
Zacharias, and Josephson which describes ratemaking in detail
• Also see RMA website www.rma.usda.gov– “A Comprehensive
Review of RMA APH and COMBO Rating”
Ratemaking (Cont.)
• Losses and Liability are converted to common
coverage level
• Basic ratemaking unit is County. A Loss Cost
per $100 of Liability is Calculated for each
County by year
• Catastrophe procedure
Ratemaking (Cont.)
• A maximum of 60% credibility is assigned to
the County Loss Cost
• The remainder of the credibility is assigned to
“Simple circle Loss Cost “ which is a weighted
average of the surrounding Counties Loss Cost
• Loading for Unforeseen Losses
Ratemaking (Cont.)
• Pure premium method of ratemaking (also known as loss cost
or loss cost ratio method).
• Experience period is much longer due to volatility (introduces
problems if current experience is different than older years).
• Expenses are not loaded into the premium.
• Revenue guarantees – every farmer could have a loss the
same year
• Basic unit of ratemaking is county.
Pure Premium Method
• Does not employ actual premiums charged to policyholder.
• Pure Premium = Losses / Exposure
• Exposure in crop insurance is the amount of coverage which is
referred to as liability.
• Example – if losses were $1.5M and liability were $100M, the
pure premium would be .015 or 1.5%.
First Steps-APH Rate
• Loss experience by county for 1975 forward.
• Losses and liability are adjusted to common level of coverage
(65% Level).
• Catastrophe procedure.
Next Steps
• Adjust for Credibility – surrounding counties pure premium is
weighted with the pure premium determined in the last slide.
The higher the volume, the more weight given to the county’s
own pure premium.
• Base Rate Loadings.
Coverage Level Differentials
• The rates derived above are for the 65% coverage level.
• Rates for other coverage levels are derived from these rates
using coverage level differentials.
•
The differentials are based on the historical experience of the
various coverage levels.
Example of Coverage Level Factors
Average Yield Differentials
The county rates developed to this point reflect rates for
producers with APH yields at or near the county average yield.
RMA research has demonstrated that, on average, the
probability of a loss is greater for producers with a yield lower
than the average for an area and vice versa. Thus, rates based
on the average LCR for a county may be too low for producers
with a lower APH and too high for producers with a higher
APH. To address this, the RMA has developed a formula to
adjust the base rate for yield differentials.
Revenue Ratemaking
• All farmers can have a loss the same year if prices are low
enough.
• Difficult to insure Price
• Adverse selection if Product is not Rated Correctly
Basic Approach
• Yield Risk
– APH rates at 65% coverage level.
• Price Risk
– Commodity Markets options based volatility measureBlack Scholes Model
• Yield Risk x Price Risk = Revenue Risk
– Distributions of yield and revenue risk by county must be
developed in order to model revenue risk.
Simulated Revenue Risk
• Yield Distribution x Price Distribution = Revenue Distribution
• Assumes negative price-yield correlation.
• Losses are simulated from the theoretical revenue
distribution.
• Loss costs are calculated from the simulated losses.
Simulation Example
Private Industry
Profitability Considerations
Standard Reinsurance Contract (SRA)
• Standard Contract for all of the Private
Companies that specifies all the Terms
of the Govt/Private Sector Partnership
• New Contact Just negotiated that
went into effect July 1, 2010 for 2011
Crop Year
• Savings to Govt of $6 B over 10 years
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Federal Crop Loss Ratios
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Aggregate Loss Ratio, 1981 - 2002
Less than 1
1 - 1.5
Greater than 1.5
Source: Joe Glauber’s Presentation
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Projected Profitability
• 1981-2009 Average Loss Ratio was 115%
• Much better recently (improvement in
experience or weather cycle?)
• Little or no investment income
• Highly catastrophe line requiring higher
risk charge
• Low expense reimbursement (A&O)
• Can Companies make Money???
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Categories of Funds
Assigned Risk
Commerical Fund
Policies that are
significantly under
priced with the risk
being primarily
born by the Federal
Govt
Policies that the
companies chose
to take the
maximum amount
of risk
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Terms-Commercial Fund
SRA Differences by State
• Each State stands on its own
• States with favorable past loss ratios have different
Reinsurance terms than all other States i.e., IL, IN,
IA, MN, NE (State group #1 representing 34% of the
2009 Premium
• State Group 3 States are underserved States
• All remaining States are Group 2
• Stop loss Terms for Groups 2 & 3 are the same and
are much more favorable than Group 1
• Companies retain minimal risk for Assigned Risk
policies
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2010 Final SRA Commercial Fund Gain or (Loss)
Applies to each State Separately
LOSS
RATIO
550%
500%
400%
250%
200%
160%
145%
130%
110%
100%
90%
80%
70%
50%
0%
State Group 1
Profit (Loss)
-94.0%
-94.0%
-84.0%
-69.0%
-57.0%
-39.0%
-29.3%
-19.5%
-6.5%
0.0%
7.5%
15.0%
22.5%
32.3%
34.8%
State Groups 2&3
Profit (Loss)
-51.5%
-51.5%
-46.5%
-39.0%
-33.5%
-25.5%
-19.1%
-12.8%
-4.3%
0.0%
9.8%
19.5%
29.3%
40.1%
42.6%
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Modeling Profitability
• Most states appear to have Lognormal
Distribution with Original Coefficient of
Variation of between 50% and 125%
• I used Lognormal Distribution for illustration
purposes
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State XYZ-Commercial Fund
Lognormal Loss Ratio Distribution
Mean = 110%; Median = 88%
Coefficient Of Variation = 75%
Log Normal
0%
25%
50%
75%
100%
125%
150%
Median
175%
200%
Mean
225%
250%
275%
300%
Loss Ratio
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Calculation of Expected Profitibility
State XYZ-Commerical Fund-State Group 2
Expected Loss Ratio = 110%; COV = 75%
(1)
(2)
(3)
Cumulative
Distribution Incremental
F(X)
Area
Loss Ratio
From
To
0%
50%
65%
100%
160%
220%
500%
50%
65%
100%
160%
220%
500%
Plus
19.9%
32.5%
57.6%
81.5%
91.5%
99.5%
100.0%
(5)
Company
Avg Loss
Retained
Ratio
Gain (Loss)*
19.9%
12.6%
25.1%
23.9%
10.0%
8.0%
0.5%
(4)
36.0%
57.5%
81.5%
125.8%
185.7%
292.9%
629.9%
Weighted Average of Col (3) and Col (5) = Expected Gain =
40.8%
37.1%
18.1%
-11.0%
-30.6%
-41.1%
-51.5%
8.1%
*Based on 2011 Crop Year Reinsurance Contract (SRA)
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Long Term Expected Underwriting Gain based on Log Normal Distribution
State Group 2 and 3
Long Term
Loss Ratio
50%
75%
Coefficient of Variation
90%
100%
110%
120%
80%
90%
100%
110%
120%
130%
140%
19.6%
14.2%
9.1%
4.3%
-0.2%
-4.3%
-8.0%
20.1%
15.9%
11.9%
8.1%
4.5%
1.1%
-2.0%
20.6%
16.9%
13.3%
9.9%
6.7%
3.7%
0.8%
21.0%
17.5%
14.2%
11.0%
8.0%
5.1%
2.5%
21.4%
18.1%
15.0%
12.0%
9.1%
6.5%
3.9%
21.8%
18.7%
15.7%
12.9%
10.2%
7.7%
5.3%
150%
-11.4%
-4.9%
-1.8%
-0.1%
1.5%
3.0%
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Other Considerations
• The Profit on the previous pages only
applies to the Commercial Fund.
• Underwriting Gain Dollars reduced by:
• Assigned Risk Fund cession
• 6.5% Mandatory Quota Share
• Does not consider any shortfall of the
A&O Expense Allowance
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Final Considerations
• Profitability varies considerably from state to
state
• Complex models are available to help decide
which fund each policy should be assigned
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