ACTUARIAL DOCUMENTATION OF 

MULTIPLE PERIL CROP INSURANCE 

RATEMAKING PROCEDURES 

Prepared for: USDA – Risk Management Agency 

Prepared by: Gary R. Josephson, F.C.A.S., M.A.A.A. 

Consulting Actuary 

Richard B. Lord, F.C.A.S., M.A.A.A. 

Consulting Actuary 

Charles W. Mitchell 

Actuarial Assistant 

Milliman & Robertson, Inc. 

Brookfield, Wisconsin 

(262) 784-2250 

August 1, 2000 

MILLIMAN & ROBERTSON, INC. 
 

ACTUARIAL DOCUMENTATION OF 

MULTIPLE PERIL CROP INSURANCE 

RATEMAKING PROCEDURES 

TABLE OF CONTENTS 

INTRODUCTION ...........................................................................................................................1 

Casualty Actuarial Society Statement Of Principles Regarding Property And 

Casualty Insurance Ratemaking 

Bibliography Of M&R Crop Insurance Reports 

RATEMAKING – ACTUARIAL CONCEPTS .............................................................................1 

DETERMINATION OF EXPOSURE, LOSS, AND PREMIUM..................................................3 

MPCI RATEMAKING OVERVIEW ............................................................................................4 

COUNTY RATING – DISCUSSION...........................................................................................6 

ADJUSTING LOSS AND EXPOSURE TO COMMON COVERAGE LEVEL ..........................7 

DERIVATION OF COUNTY UNLOADED BASE RATES ....................................................... 14 

Number of Years Used In Loss Cost Projection ................................................................... 16 

Excess Loss Adjustment....................................................................................................... 18 

Credibility ........................................................................................................................... 20 

BASE RATE LOADING............................................................................................................... 25 

Disaster Reserve Factor...................................................................................................... 25 

State Excess Load................................................................................................................ 27 

Prevented Planting Load ..................................................................................................... 29 

Unit Division Load.............................................................................................................. 29 

DETERMINING CAPPED RATE CHANGES ........................................................................... 30 

Initial Rate Changes............................................................................................................ 30 

Capped Rate Changes ......................................................................................................... 31 

TYPE / PRACTICE AND GROUP FACTORS ........................................................................... 32 

Practice Factors.................................................................................................................. 32 

Average Yield Differentials.................................................................................................. 33 

Coverage Level Differentials............................................................................................... 34 

PERFORMANCE MEASUREMENT.......................................................................................... 35 

FREQUENCY OF RATE REVIEWS .......................................................................................... 36 

ATTACHMENTS: Exhibits 1 through 4 

MILLIMAN & ROBERTSON, INC. 
ACTUARIAL DOCUMENTATION OF 

MULTIPLE PERIL CROP INSURANCE 

RATEMAKING PROCEDURES 

INTRODUCTION 

Milliman & Robertson, Inc. (M&R) was engaged by the Risk Management Agency (RMA) of 

the U.S. Department of Agriculture (USDA) to provide documentation of the current Multiple 

Peril Crop Insurance (MPCI) ratemaking procedures along with references and a discussion of 

the actuarial basis for each of the key steps in the process. Actuarial documentation helps to 

ensure the integrity of the process and provides an authoritative source of reference of 

actuarial problems. 

Our report focuses on the development of rates for the Actual Production History (APH) 

program. While many of the concepts presented herein apply also in the development of rates 

for other coverages (for example, Crop Revenue Coverage), the latter are not discussed in this 

report. This report provides a description of each key step of the rate calculation along with 

illustrative examples and a discussion of the actuarial justification for the calculation. 

RATEMAKING – ACTUARIAL CONCEPTS 

The development of rates for property and casualty insurance companies has long been the 

province of Casualty Actuaries. There is a vast body of literature that has been developed on 

ratemaking topics, much of it is incorporated into publications of the Casualty Actuarial 

Society (“CAS”). In this report, we will refer to two documents addressing actuarial 

ratemaking concepts. The first document is the Statement of Principles Regarding Property 

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and Casualty Insurance Ratemaking (“Statement of Principles”). The purpose of this 

document (which was developed by the CAS Committee on Principles of Ratemaking and 

adopted by the CAS Board of Directors in 1988) is to “identify and describe principles 

applicable to the determination and review of property and casualty insurance rates”. A copy 

of the Statement of Principles is attached. The second document is a textbook, developed by 

the CAS Textbook Steering Committee in 1989, titled Foundations of Casualty Actuarial 

Science (Foundations). The text “is intended as an introduction to casualty actuarial concepts 

and practices.” Foundations has one chapter dedicated to ratemaking. For many of the key 

steps in the MPCI ratemaking process, we will refer to these two documents to identify the 

actuarial basis for the calculation. 

It is important to understand that there is no single ratemaking approach that will apply to all 

insurance coverages. Foundations states that “...manual rates are estimates of average costs 

based upon a combination of statistical methods and professional judgment.” For MPCI, as is 

the case for most insurance coverages, the ratemaking process has evolved over time as 

information and research have become available. For each of the steps in the process, there 

may be alternative approaches that could be used and which could produce reasonable results. 

It is not our intent to try to identify all possible alternatives to the current approach. However, 

in many cases we discuss alternatives that we believe may be appropriate. 

A third reference, which provides additional background and discussion of MPCI ratemaking 

procedures, is the paper “Ratemaking Procedures for Multiple Peril Crop Insurance”, which 

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was published in the winter 2000 edition of the CAS Forum. (This paper can be downloaded 

from the CAS website, www.casact.org.) 

M&R has been providing research to the FCIC/RMA since 1983. We have attached a 

bibliography of reports that we have provided. 

DETERMINATION OF EXPOSURE, LOSS, AND PREMIUM 

Before discussing the ratemaking process, we introduce two important values that are used in 

the MPCI rate development. These values are liability and indemnity. 

Liability is a measure of the insurer’s exposure to loss for a given producer or group of 

producers. Liability represents the total insured value of the crop, calculated as: 

Liability = 

Acres planted 

x Expected Yield (called APH Yield) 

x Selected Coverage Level 

x Base Price 

x Price Election Percentage. 

Indemnity is the amount paid under MPCI coverage for a producer suffering a covered loss. 

Indemnity is paid when the value of production is less than the liability purchased. In this 

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case, the amount of indemnity paid is equal to the liability minus the value of the production 

where the latter is calculated as: 

Value of Production = 

Acres Planted 

x Actual Yield 

x Base Price 

x Price Election Percentage. 

The premium paid by a producer is derived as follows: 

Premium = 

Liability 

x Rate 

x Adjustment Factor. 

The ultimate objective of the ratemaking process is to derive the premium rate used in the 

above formula. We discuss the derivation in the next section. 

MPCI RATEMAKING OVERVIEW 

The Statement of Principles identifies a fundamental principle of insurance ratemaking as: “A 

rate is an estimate of the expected value of future costs.” Typically, the largest component of 

the rate is the provision for losses. While there are other, non-trivial considerations in rate 

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development, most of the actuarial foundations of ratemaking are intended to provide a 

framework for estimating the expected loss component of the rate. 

For MPCI rates, other expenses and capital costs are provided for in separate agreements. 

Therefore, the ratemaking procedure deals strictly with deriving the expected loss component. 

This component is represented by the Loss Cost Ratio (LCR), which is derived by dividing 

indemnity by liability. The LCR is a measure of loss per unit of exposure. Thus, one of the 

objectives of MPCI ratemaking is to derive LCR’s that are representative of the expected 

losses for a given unit of exposure. 

Because different crops are subject to different perils and therefore varying loss costs, the 

MPCI procedure establishes rates for each crop separately. It is rare that a single insured, for 

any insurance coverage, will be sufficiently large such that expected losses can be derived 

solely from the insured’s own loss history. Thus, it is common and appropriate to consider 

the aggregate experience of a group of similar risks in developing rates. For MPCI the 

aggregation is done geographically. Rates are developed by geographic area, usually county. 

Thus, for each crop, the MPCI ratemaking process typically derives LCR’s (and consequently 

rates) by county. There are other determinants used to tailor the rate to an individual 

producer, depending on utilization of certain farming practices. These will be discussed in a 

later section. 

The MPCI ratemaking procedure can be broken into five steps: 

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1. Adjusting the Loss (Indemnity) and Exposure (Liability) to a common coverage level; 

2. Derivation of County Unloaded Base Rates; 

3. Base Rate Loading; 

4. Capping Rate Changes; and 

5. Updating the Type/Practice and Group factors. 

In the illustration and discussion that follows, we will use Adams County, Illinois actual 

production history (APH) corn data as an example for purposes of describing and performing 

actuarial calculations. We will also discuss and consider the actuarial principles underlying 

each of the significant steps. 

COUNTY RATING – DISCUSSION 

As noted above, MPCI rates are most commonly developed by county. County rating is an 

historical element of the MPCI ratemaking process; federal crop insurance evolved as a 

county based program. As will be discussed later in this report, county loss costs are often 

unstable, and the ratemaking process includes several steps intended to smooth some of the 

fluctuation. This could suggest that an alternative geographical rating unit, larger than county, 

might be considered. 

In addition to its historical basis, however, there are other reasons for maintaining the county 

as the basic ratemaking unit. In the Foundations text, chapter 5 discusses risk classification 

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and identifies several criteria for selecting rating variables. These include (pages 235-244) 

Actuarial Criteria, Operational Criteria, Social Criteria and Legal Criteria. The variability in 

county loss costs may suggest that alternative rating units might better satisfy the actuarial 

criteria. However, county rating has certain operational aspects that may be more difficult to 

achieve with other units. Foundations identifies operational criteria such as objectivity, ease 

of administration, and exclusive and exhaustive, all of which are met by the use of county. In 

addition, social criteria would also support county rating. In addition to being historically 

accepted, the county is a benchmark for many other agricultural activities. For example, farm 

programs are often administered by county and crop yields are generally reported by county 

(and used in MPCI rating for producers without an actual production history). Finally, we 

understand that fairly recent attempts to depart from county rating were not well received by 

field offices and insurance providers. 

We would note that, while the classification unit is the county, as will be illustrated in later 

sections, information from broader units are used in deriving the county rates. 

In our opinion, there are other areas of the ratemaking process that may lend themselves to 

more fruitful research than alternatives to county rating. 

ADJUSTING LOSS AND EXPOSURE TO A COMMON COVERAGE LEVEL 

MPCI is offered at various coverage levels, generally ranging from 50% to 75%. In order to 

make the greatest use of the historical data; one of the first steps in the ratemaking process is 

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to adjust the data to a common coverage level. With this adjustment, liability and indemnity 

data of producers with different coverage levels can be combined to develop the rates. For 

most crops, data is adjusted to the most commonly purchased coverage level of 65%. 

For coverage levels other than 65%, indemnity and liability are adjusted to reflect the values 

that would have been reported had the coverage been purchased at the 65% level. (As will be 

discussed below, the rates for the other coverage levels are derived from the rates developed 

at the 65% level.) 

Adjusting the liability is fairly simple. For any specific coverage level, we take the aggregate 

liability at that coverage level and multiply by the ratio of the common coverage level to that 

specific coverage level. For example, to adjust the liability from a 75% coverage level to a 

common coverage level of 65%, we would multiply all liability at the 75% coverage level by 

the ratio 0.65/0.75. Exhibit 1 shows that this produces the correct value. 

Two separate cases of adjusting indemnity need to be considered; adjusting the higher 

coverage levels down to the 65% coverage level (Case 1), or adjusting the lower coverage 

levels up to the 65% coverage level (Case 2). Indemnity amounts obtained at the 65% 

coverage level need no adjustment. 

Case 1 – Adjusting indemnity from a higher coverage level down to the 65% coverage level 

As described above, indemnity is paid when the value of production is less than the liability. 

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RMA defines production ratio as the ratio of the actual value of production to the liability. 

Thus, indemnity is paid only when the production ratio is less than the coverage level. 

Because we are adjusting to the 65% coverage level, there will be no indemnity at this 

coverage level when production ratios are greater than 65%. Therefore, for Case 1 we need 

only to consider the indemnity related to production ratios less than 65%. 

For production ratios less than the common coverage level of 65%, every dollar decrease in 

coverage (liability) would have reduced the amount indemnified by one dollar. For example, 

suppose a producer had purchased a 75% coverage level that implied $100 of liability. If this 

producer’s actual production was $60, the indemnification would be $40. If that producer had 

purchased a coverage level of 65%, the liability would have been $87 = $100 * (0.65/0.75) 

and the indemnification would be $27 = $87 - $60. In going from the 75% coverage level to 

the 65% coverage level, both the liability and indemnity went down by the same dollar 

amount, $20. 

Exhibit 2 presents a hypothetical example which illustrates that, for all production ratios less 

than 65%, the adjusted indemnity (in going from 75% coverage to 65% coverage) is equal to 

the unadjusted indemnity minus the reduction in liability. For production ratios exceeding 

65%, the adjusted indemnity will be $0. The RMA adjustment process is based on the above 

relationships. 

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Case 2 – Adjusting from a lower coverage level up to the common coverage level 

Case 2 is more difficult since we are increasing indemnity to the amount that would have 

applied had a higher coverage level been chosen. Case 2 has two components. The first is for 

indemnity related to production ratios up to the lower (50%) coverage level. This adjustment 

is relatively straightforward, and analogous to the Case 1 example above. Specifically, for 

production ratios up to 50%, the adjusted indemnity is equal to the unadjusted indemnity plus 

the increase in liability. This is illustrated on Exhibit 3. 

Exhibit 3 also displays the adjusted indemnity for production ratios above 50%. However, 

since no indemnification is made for these production ratios at the 50% coverage levels, RMA 

does not actually capture the production value information required to make this adjustment. 

In actual RMA data, the production value column of Exhibit 3 would be blank for production 

ratios above 50%. Therefore, these indemnity adjustments need to be approximated. 

RMA’s current approach to handling this problem is to develop minimum and maximum 

bounds to the adjusted indemnity and interpolating between the two. The minimum 

adjustment assumes that there are no production ratios between 50% and 65%. The minimum 

is then derived by adding the liability adjustment calculated based only on the liability related 

to production ratios less than 50% to the unadjusted indemnity. We know that we would have 

had at least this much indemnity at the higher common coverage level, the question is how 

much more would result from production ratios of 50% to 65% (for which no indemnification 

was paid and therefore no yield information collected). For these production ratios, the 

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maximum adjustment would occur if all non-indemnified production ratios were at 50%. 

Thus, to derive the maximum adjustment we would calculate the total liability adjustment 

regardless of production ratio (since we are assuming all production ratios between 50% and 

65% are at 50%). We would then add this adjustment to the unadjusted indemnity to get the 

maximum adjusted indemnity. 

In order to interpolate between the maximum and minimum indemnity, the indemnity is 

totalled over all production ratios less than or equal to the specific coverage level that we are 

adjusting from. The liability is totalled in the same way and the LCR is calculated. This ratio 

is applied to the liability that was not subject to a loss under the lower coverage level (i.e. 

liability related to production ratios greater than 50%) to determine the related additional 

indemnity at the higher coverage level. Adding this amount to the minimum indemnity 

approximates the adjusted liability. This approximation of the adjusted indemnity is then 

subject to the maximum bound as determined above. Exhibit 4 illustrates the indemnity 

adjustment using this approximation technique. 

The following table illustrates the results of the adjustments for Adams County corn. 

Columns 3 and 4 are unadjusted data. Columns 6 and 7 are adjusted data. Other columns are 

not used in the calculation, but are included for illustration. 

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TABLE 1: ADJUSTED INDEMNITY 

Adams County Illinois 

1 2 3 4 5 6 7 8 

Crop 

Year 

Net 

Acres Indemnity Liability LCR 

Average 

Cov Lvl. 

Adjusted 

Indemnity 

Adjusted 

Liability 

1975 11,508.00 25,867 954,368 0.0271 0.6500 25,867 954,368 

1976 11,664.00 83,230 1,133,267 0.0734 0.6500 83,230 1,133,267 

1977 10,822.00 196,559 1,104,678 0.1779 0.6500 196,559 1,104,678 

1978 7,853.00 1,516 776,273 0.0020 0.6500 1,516 776,273 

1979 7,270.00 1,503 825,168 0.0018 0.6500 1,503 825,168 

1980 8,179.78 71,952 979,716 0.0734 0.6778 57,361 933,501 

1981 9,569.74 44,635 1,368,243 0.0326 0.7171 36,610 1,232,335 

1982 8,247.01 29,686 1,193,112 0.0249 0.7140 21,332 1,084,981 

1983 5,121.45 440,321 795,481 0.5535 0.7230 370,530 712,218 

1984 20,536.93 307,177 3,941,985 0.0779 0.7341 189,261 3,490,799 

1985 23,360.27 22,324 4,317,435 0.0052 0.7192 13,674 3,897,513 

1986 27,753.28 31,743 4,330,324 0.0073 0.7065 19,193 3,979,198 

1987 24,854.77 22,045 3,460,542 0.0064 0.6917 15,407 3,250,849 

1988 25,027.35 458,200 3,547,678 0.1292 0.6882 361,489 3,350,736 

1989 44,661.30 944,430 7,555,038 0.1250 0.6927 742,506 7,054,559 

1990 41,182.34 84,176 6,192,243 0.0136 0.6885 64,990 5,809,174 

1991 32,770.97 112,740 5,115,210 0.0220 0.6893 90,655 4,819,363 

1992 37,440.26 54,667 6,066,375 0.0090 0.6905 28,889 5,714,961 

1993 32,300.36 687,775 5,452,763 0.1261 0.6852 658,436 5,177,813 

1994 42,541.45 5,944 7,599,101 0.0008 0.6698 4,508 7,352,287 

1995 42,110.51 531,576 6,460,633 0.0823 0.6603 526,503 6,362,352 

1996 54,397.36 100,447 11,457,322 0.0088 0.6551 105,439 11,372,363 

1997 39,719.70 27,304 7,741,718 0.0035 0.6472 23,266 7,778,276 

Summary 568,891.83 4,285,817 92,368,673 0.0689 0.6826 3,638,724 88,167,032 

Actuarial Justification 

The concept of adjusting exposures and losses to a common coverage level is valid and 

appropriate. Without adjustment, combining the data for different coverage levels would 

produce rates that were not representative of any single coverage level. Rates would reflect 

the past mixture of the various coverage levels and would not be appropriate in the future if 

the distribution of coverage levels changes. 

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An alternative would be to treat each coverage level separately, and develop rates for each. 

This may be appropriate if there are differences in loss experience for producers who select 

different coverage levels. For example, if producers who have better experience insure with 

lower coverage levels in order to save on premiums, and producers with poor experience 

insure to higher levels of coverage in order to protect against persistent losses, loss cost ratios 

may vary by coverage level. On the other hand, segregating the data by coverage level can 

result in less stability and predictability of expected losses due to the greater statistical 

variation. In addition, the consideration of differences in expected losses between coverage 

levels is considered in the coverage level relativities, which are discussed later in this report. 

There are two actuarial concepts involved here: homogeneity and credibility. Homogeneity 

refers to the degree to which data has been segregated into similar groupings. The Statement 

of Principles discusses homogeneity as follows: “Ratemaking accuracy often is improved by 

subdividing experience into groups exhibiting similar characteristics... subdividing or 

combining the data so as to minimize the distorting effects of operational or procedural 

changes should be fully explored” (page 7). 

Credibility is discussed as follows, “Credibility is a measure of the predictive value that the 

actuary attaches to a particular body of data. Credibility is increased by making groupings 

more homogeneous or by increasing the size of the group analyzed.” (page 8). 

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The two criteria for increasing credibility often conflict. Generally, the data can be refined 

into increasingly homogeneous groups, but as it is refined there is less data in each separate 

group. This results in greater statistical variation, and hence a lesser degree of confidence in 

the predictive value of the data. 

Adjusting the data to a common coverage level allows the Risk Management Agency (RMA) 

to utilize as large a base as possible while also maintaining the homogeneity of the data. In 

our opinion, the concept utilized by RMA is actuarially sound. 

The Indemnity Coverage Level Adjustment was discussed in the M&R report titled “Federal 

Crop Insurance Corporation Ratemaking Overview” dated June 14, 1996. In that report we 

discussed possible alternatives to that adjustment approach. The current RMA approach 

differs from that used at the time of the earlier study. However, it still requires a fairly 

significant approximation in going from a lower to higher coverage level. Although we 

believe this approximation to be reasonable given the current availability of data, we continue 

to recommend additional analysis to determine feasible alternatives. As stated in the June 14, 

1996 report, two possible approaches would be to convert all data to a 50% coverage level or 

to examine a distribution of yield data to evaluate an approximation approach. 

DERIVATION OF COUNTY UNLOADED BASE RATES 

After adjusting the data to a common coverage level, the next step is to derive the LCR for 

each county. In the table below, Columns 2 and 3 display the adjusted indemnity and liability 

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data from the previous section. 

TABLE 2: LOSS COST RATIOS 

Adams County Illinois 

1 2 3 4 

Crop Year Adjusted Indemnity Adjusted Liability Adjusted LCR 

1975 25,867 954,368 0.0271 

1976 83,230 1,133,267 0.0734 

1977 196,559 1,104,678 0.1779 

1978 1,516 776,273 0.0020 

1979 1,503 825,168 0.0018 

1980 57,361 933,501 0.0614 

1981 36,610 1,232,335 0.0297 

1982 21,332 1,084,981 0.0197 

1983 370,530 712,218 0.5202 

1984 189,261 3,490,799 0.0542 

1985 13,674 3,897,513 0.0035 

1986 19,193 3,979,198 0.0048 

1987 15,407 3,250,849 0.0047 

1988 361,489 3,350,736 0.1079 

1989 742,506 7,054,559 0.1053 

1990 64,990 5,809,174 0.0112 

1991 90,655 4,819,363 0.0188 

1992 28,889 5,714,961 0.0051 

1993 658,436 5,177,813 0.1272 

1994 4,508 7,352,287 0.0006 

1995 526,503 6,362,352 0.0828 

1996 105,439 11,372,363 0.0093 

1997 23,266 7,778,276 0.0030 

Summary 3,638,724 88,167,032 0.0631 

Column 4 (Adjusted LCR) is the ratio of the adjusted indemnity to adjusted liability. For each 

year, this ratio reflects the percentage of liability that would have been paid to producers had 

they all purchased 65% coverage. 

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A. Number Of Years Used In Loss Cost Projection 

One of the first steps in any ratemaking process is to specify the number of years that will be 

used in deriving the rates. The MPCI process uses years 1975 and subsequent. 

Actuarial Justification 

Two of the more significant considerations in the determination of number of years are: 

1) Year-to-year variability in loss costs; 

2) Long term trends, or changes in the underlying exposures or costs. 

The Foundations text discusses the length of the experience period as follows. “The 

determination of the loss experience period to be used in the manual ratemaking process 

involves a combination of statistical and judgmental elements. There is a natural preference 

for using the most recent incurred loss experience since it is generally the most representative 

of the current situation... Where the business involved is subject to catastrophe losses...the 

experience period must be representative of the average catastrophe incidence. Finally, the 

experience period must have sufficient loss experience that the resulting indications will have 

statistical significance or credibility.”(Page 41). In more general terms, the Statement of 

Principles asserts, “This experience is relevant if it provides a basis for developing a 

reasonable indication of the future.” (page 7). 

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In examining Table 2, we observe that the loss costs exhibit considerable variability over the 

history presented. In addition, we observe that the loss costs do not appear to exhibit a longterm trend. This may be expected since the general inflation component of loss (indemnity) is 

directly related to the exposure base (liability). Because they are directly related, their dollar 

cost trends should be the same and should therefore produce LCR’s with no dollar cost trend. 

Any residual trend would relate to changes in farming procedures or other changes that affect 

yield variability. 

In considering the MPCI exposure and coverage, we believe it is important to consider that 

weather patterns and crop conditions tend to be cyclical, such that several good years of 

experience can be followed by several poor years. As such, a long-term average may be 

needed to adequately capture the loss history. In a 1983 study, performed for the FCIC, M&R 

evaluated the length of the experience period. That study concluded “.... the FCIC should 

continue to use all available past history in the ratemaking process with possibly greater 

weight given to the more recent years.” At the time of the 1983 study, each year was given 

equal weight in the determination of the county average. The suggestion of greater weight to 

more recent years was made because of concerns about the impact of amendments to the 

FCIC Act of 1980, and the possibility that the pre-1980 experience may not be relevant. 

An alternative to equal weighting would be a liability weighted LCR. In periods of increased 

participation (as in recent years), this would have the effect of giving more weight to recent 

years, as the M&R study suggested. However, an argument could be made that each year’s 

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results (i.e., LCR) reflects a sample value which is used to estimate the mean value. In this 

context, the sample value might not be influenced by the participation volume, and therefore 

equal weighting is appropriate. The issue was addressed again by M&R in 1995 (“Multiple 

Peril Crop Insurance Ratemaking Experience Period”, dated August 25, 1995), and in 1996 

(“Federal Crop Insurance Company Ratemaking Overview”, referred to above). In the latter 

report we recommended no changes to equal weighting of all years. 

B. Excess Loss Adjustment 

While the long-term average (shown in the column 4 summary row of Table 2) is 0.0631, the 

average is adversely affected by a few years with much higher than average LCRs. RMA has 

developed a procedure that is intended to reduce the impact that a single year will have on the 

average loss cost of each county. Under this procedure, the adjusted average LCR for any 

single year is capped at the 80th percentile LCR of all years. The following table shows the 

uncapped and the capped LCR’s. 

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TABLE 3: CAPPED LCRs AND CAT INDEMNITY 

Adams County Illinois 

1 2 3 4 

Crop Year Adjusted LCR Capped LCR Excess Indemnity 

1975 0.0271 0.0271 0 

1976 0.0734 0.0734 0 

1977 0.1779 0.0918 95,113 

1978 0.0020 0.0020 0 

1979 0.0018 0.0018 0 

1980 0.0614 0.0614 0 

1981 0.0297 0.0297 0 

1982 0.0197 0.0197 0 

1983 0.5202 0.0918 305,114 

1984 0.0542 0.0542 0 

1985 0.0035 0.0035 0 

1986 0.0048 0.0048 0 

1987 0.0047 0.0047 0 

1988 0.1079 0.0918 53,947 

1989 0.1053 0.0918 95,237 

1990 0.0112 0.0112 0 

1991 0.0188 0.0188 0 

1992 0.0051 0.0051 0 

1993 0.1272 0.0918 183,295 

1994 0.0006 0.0006 0 

1995 0.0828 0.0828 0 

1996 0.0093 0.0093 0 

1997 0.0030 0.0030 0 

Summary 0.0631 0.0379 732,706 

In Table 3, the Capped LCR (Column 3) is calculated by linear interpolation to the 80th 

percentile of the Adjusted LCR. In this case there are 23 years of data, so we need to 

interpolate between the 18th and 19th highest Adjusted LCR’s. The interpolated value (80th 

percentile) is 0.0918. For each year, the Capped LCR is the minimum of the Adjusted LCR 

and the 80th percentile (or 0.0918). Column 4, identified as Excess Indemnity, is the amount 

of indemnity that is excluded from the capped LCR. For example, Crop Year 1977 Excess 

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Indemnity = (0.1779 – 0.0918) x 1,104,676 = 95,113. This will be used later in the 

ratemaking process. 

Actuarial Justification 

The adverse affect of a single year, or several years, is not uncommon for a property 

coverage, in particular one in which weather can affect loss experience. The Statement of 

Principles states, “Consideration should be given to the impact of catastrophes on the 

experience and procedures should be developed to include an allowance for the catastrophe 

exposure in the rate” (page 8). This step removes those losses that are identified as excess 

from the county experience. It will be seen later that the excess losses are built back into the 

rates by spreading them over a broader base. This is an appropriate concept. 

The 80th percentile originated with M&R’s 1983 report to the FCIC (Task 3, “Analysis of 

Catastrophe Provisions”). The MPCI catastrophe procedure was revisited by M&R in 

September, 1995 (“Analysis and Recommendations for FCIC Catastrophe Procedure”). In 

that study, we supported the general concept of the excess losses procedure, including the use 

of a percentile threshold for identifying excess losses. We recommended, however, that the 

80% threshold may be too invasive for some crops/states, and that a threshold that varies by 

state and crop should be considered. 

C. Credibility 

As discussed above, credibility is a measure of the predictive value of the loss experience. 

MILLIMAN & ROBERTSON, INC. 
 

 

 

 

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Generally, the greater the volume and homogeneity of the data, the greater the credibility. 

MPCI has a process whereby each county’s capped LCR is assigned credibility based on the 

number of policies indemnified in the experience period. Credibility values range from 0% to 

60% based on the following formula: 

0.60

271 

1 ,( 271)

x 

Min P Z o 

where P1 = Policies indemnified 

(A county with 271 or more policies indemnified will receive the maximum credibility of 

60%). The remaining amount (100% minus county credibility) is assigned to what is referred 

to as the simple circle LCR. 

The Simple Circle LCR is a weighted average of surrounding counties’ Simple County LCR’s 

(weighted by each county’s Total Adjusted Liability). In other words, it is the sum of the 

product of Total Adjusted Liability and Simple County LCR divided by the sum of Total 

Adjusted Liability. In mathematical notation: 

å (County _ Total _ Adjusted _ Liability)*(Simple _ County _ LCR )

Surrouding _ Counties 

å (County _ Total _ Adjusted _ Liability) Surrounding _ Counties 

The following displays an example of the calculation of the Simple Circle LCR for Adams 

County Illinois: 

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TABLE 4: SIMPLE CIRCLE LCR 

Adams County Illinois 

1 2 3 4 

Surrounding 

County Name 

Adjusted 

Liability 

Simple 

County LCR 

(2) x (3) 

Brown 33,087,483 0.0336 1,111,596 

Hancock 121,904,576 0.0236 2,882,778 

Pike 35,882,331 0.0251 902,051 

Schuyler 23,459,717 0.0459 1,077,311 

Totals 214,334,107 5,973,735 

Simple Circle LCR [Total Column (4) / Total Column (2)]: 0.0279 

The County Unloaded Rate is calculated as Z% of the Simple County LCR plus (100%-Z) of 

the Simple Circle LCR. For Adams County, this is as follows: 

TABLE 5: CALCULATION OF COUNTY UNLOADED RATE 

1 2 3 4 

LCR Weight (2) * (3) 

Simple County 0.0379 60% 0.0227 

Simple Circle 0.0279 40% 0.0112 

County Unloaded Rate 0.0339 

Actuarial Justification 

Credibility is one of the most complex actuarial concepts. It is sufficiently important to 

command a full chapter in the Foundations text. As noted earlier, credibility is a measure of 

predictive value attaching to a specific item (in this case, the county LCR). The credibility 

process is the weighting together of different estimates to come up with a combined estimate. 

The credibility formula, in general, is: 

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I = Z x I1 + (100% - Z) x I2 

In the above formula : I is the item being estimated (e.g., county LCR); 

I1 is an indication from that item’s own experience (e.g., 

Simple County Average LCR); 

Z is the credibility attached to I(1) 

I2 is an alternative indication (e.g., Simple Circle LCR) 

Credibility (Z) can range from 100% (full credibility; full weight) to 0% (no credibility; no 

weight). For an item with credibility less than 100%, it is important to identify an appropriate 

item to receive the remaining weight. The Foundations text states that “The complement of 

credibility (100% - Z) should be applied to an indication which can be expected to reflect 

consistent trends in the same general way as the underlying data.” 

As noted above, the MPCI procedure assigns maximum credibility if a county has 271 claims 

(policies indemnified). The threshold of 271 claims was developed by a former Assistant 

Manager for the Actuarial and Underwriting Services division of the USDA Economic 

Research Service (ERS). As of this writing, the specific documentation for the 271 claim 

threshold is not available, however it appears to be taken from one of the seminal papers on 

credibility theory in the Casualty Actuarial Society literature (An Introduction to Credibility 

Theory). 

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The number of claims is a common measure of credibility for property/casualty insurance 

ratemaking. Number of claims may be considered analogous to number of observations of 

data in a sample in estimating a particular statistic (e.g., LCR). However, there are certain 

characteristics of multiple peril crop insurance that suggest that number of claims may not be 

the best measure of credibility. For example, the credibility formula will result in greater 

credibility being assigned to a county in a state with high average loss costs (and consequently 

a greater claim frequency) than in a state with low average loss costs. At a minimum, the 

threshold for maximum credibility (271 claims) may need to vary, by state or region, to reflect 

the expected claim frequency. 

It is clear that the MPCI procedure utilizes the formula above for Z, with all counties assigned 

credibility (Z) of up to 60%. The complement of credibility (100%-Z) is assigned to the 

Simple Circle LCR. We would expect the surrounding counties to have consistent trends with 

those of the central county, so this measure meets the general requirement presented in the 

Foundations discussion above. Thus, in general the approach used in the MPCI process is 

actuarially supported. Refinements might consider varying the weights of surrounding 

counties based on comparative soil or climatological characteristics. 

Based on the above discussion, we believe that credibility is an area that may warrant 

additional study by RMA. 

MILLIMAN & ROBERTSON, INC. 
 

 

 

 

 

 

 

 

 

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BASE RATE LOADING 

The LCR derived above for Adams County (0.0339) represents an estimate of the expected 

capped loss cost ratio for the forthcoming year. Several adjustments are required to derive the 

base rate. These include: Disaster Reserve Factor 

State Excess Load 

Prevented Planting Load 

Unit Division Load 

An example is given in the following table for a sample of Illinois counties: 

TABLE 6: IMPLIED BASE RATES 

1 2 3 4 5 6 7 8 

State County 

Simple 

County 

LCR 

Simple 

Circle 

LCR 

County 

Unloaded 

Rate 

State 

Excess 

Load 

Prevented 

Planting 

Load 

Implied Base 

Rate 

[(5)/.88+(6)+(7 

)]/.9 

Illinois Adams 0.0379 0.0279 0.0339 0.0127 0.0040 0.0614 

Illinois Alexander 0.1436 0.0569 0.1089 0.0127 0.0060 0.1583 

Illinois Bond 0.0479 0.0268 0.0395 0.0127 0.0040 0.0684 

Illinois Boone 0.0161 0.0131 0.0149 0.0127 0.0060 0.0396 

Illinois Brown 0.0336 0.0299 0.0321 0.0127 0.0040 0.0591 

Illinois Bureau 0.0055 0.0098 0.0072 0.0127 0.0040 0.0276 

Illinois Calhoun 0.0426 0.0211 0.0340 0.0127 0.0040 0.0615 

Each of these adjustments will be discussed in more detail below. 

A. Disaster Reserve Factor 

The first step in going from the County Unloaded Rate to the Implied Base Rate is to divide 

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the unloaded rate by the Disaster Reserve Factor (0.88). This reserve factor is intended to 

meet the Congressional requirement that rates be adequate to pay expected losses and to build 

a reasonable reserve. 

Actuarial Justification 

Actuarial procedures often incorporate a risk load or contingency load in order to build in an 

additional margin of protection against future adverse experience. The Statement of 

Principles states, “The rate should include a charge for the risk of random variation from the 

expected costs.” In Table 3 it can be seen that even after removing the extreme portions of 

the historical loss cost ratios, the annual LCR’s may vary significantly from the long-term 

average of 0.0379. There is no single approach that will produce an appropriate risk margin 

in all circumstances. Factors that need to be considered include: variability in loss costs from 

year to year, accumulated funds that have been earmarked to pay claims if indemnified losses 

exceed premium revenues, and availability of funds from other sources to pay claims should 

the accumulated funds be depleted. 

While we have not evaluated the reserve factor, we understand that it was based on 

assumptions relating to the probability distribution of national crop insurance losses. RMA 

management has attributed the reserve factor to a former Assistant Manager for Actuarial and 

Underwriting Services, but appropriate documentation does not currently exist. 

MILLIMAN & ROBERTSON, INC. 
 

 

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In light of the variability of MPCI losses, we believe it is prudent and appropriate to include a 

risk load. 

B. State Excess Load 

The next step in loading the base rates consists of calculating the state excess. The State 

Excess Load adds a provision for the Excess Indemnity excluded from the loss cost in the 

unloaded rate calculation. The following table summarizes the state excess calculation 

for Illinois: 

TABLE 7: STATE EXCESS 

1 2 3 4 5 

State 

Adjusted 

Liability 

Excess 

Indemnity 

Implied State 

Excess 

(3) / (2) 

State Excess 

Min{Max 

[(4),0.01],0.05} 

Illinois 7,575,001,361 96,286,560 0.0127 0.0127 

Adjusted liability and cat indemnity amounts are totaled by state by summing across all 

counties (e.g., the adjusted liability for IL includes 88,167,032 from Adams county; the 

Excess Indemnity includes 732,706 from Adams County), “Implied State Excess” is 

calculated as Excess Indemnity divided by Adjusted Liability. “State Excess” is then 

calculated by limiting the state excess ratio to a maximum of 5% (capping) or a minimum of 

1% (cupping). Any state excess above the 5% cap is distributed back to each county from 

which the excess came. 

MILLIMAN & ROBERTSON, INC. 
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Actuarial Justification 

The Excess Indemnity for each county is essentially pooled for the entire state and then spread 

back evenly to each county. As noted earlier, the actuarial justification for the capping 

process is that extreme LCR’s are generally due to catastrophic events and as such are 

infrequent, lack statistical credibility, and may not be reflective of the county’s expected 

value. Since they have been removed from the county experience, it is appropriate to add 

them in at a broader level. The State Excess calculation accomplishes this. 

The imposition of capping on the excess factor is somewhat inconsistent with the general 

premise that excess losses are random and not predictable at the county level. The capping 

process essentially takes the most extreme amounts (i.e., those causing the state factor to 

exceed 5%) and “gives” them back to the county. It isn’t clear that this step is necessary. 

In M&R’s 1995 analysis of the Catastrophe Procedure, we discussed the additive approach 

used by the FCIC, that is, the state excess is added to each county’s LCR. This can result in a 

large disparity in the percentage of the rate that represents the catastrophe component, and 

possibly an inequitable shift of catastrophe exposure to lower loss cost areas. In that report, 

we recommended a blended approach to reflect the state excess, with a portion added directly 

to the loss cost (present approach) and the remainder incorporated proportionately. 

We also suggested consideration be given to pooling a portion of the catastrophe loss on a 

nationwide level. We recognize that there may be public policy implications that 

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preclude this. 

C. Prevented Planting Load 

The Prevented Planting Load adds a provision for losses due to crops never planted because 

of external factors “which are not directly related to yield loss.” 

Actuarial Justification 

The prevented planting loss data is not included in the data underlying the rates. 

Nevertheless, since prevented planting is an indemnifiable event, the rates should include a 

provision for this type of loss, so the concept of the adjustment is appropriate. 

The prevented planting load is based on RMA studies of the effect of prevented planting. We 

have not reviewed the underlying calculations. 

D. Unit Division Load 

The Unit Division Load takes into account the fact that indemnity is not computed for an 

entire farm, but rather for each division of a farm. For example, if a farm is divided into four 

equal segments where one segment had zero percent production and the other three had 100% 

production, the producer would receive indemnity for the unproductive segment at a 75% 

coverage level, whereas, if the farm was insured as a whole, there would be no indemnity at 

the 75% coverage level. 

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Actuarial Justification 

Maintaining the indemnity data separately by unit or field, as would be necessary to avoid the 

Unit Division Load correction factor, would probably be more accurate but also more 

cumbersome and less cost efficient. It is often necessary to balance the benefits of more 

accurate results and the costs of obtaining those results. We believe the procedure of deriving 

rate indications based on data at the field level instead of the field unit level is a reasonable 

simplification as long as the adequacy of the Unit Division load is monitored. 

DETERMINING CAPPED RATE CHANGES 

A. Initial Rate Changes 

The implied base rates calculated above are compared to the current base rates to get initial 

rate changes by county. An example of these rate changes is displayed in the table below for 

a sample of Illinois counties: 

TABLE 8: RATE CHANGES 

1 2 3 4 5 6 

State County 

Implied Base 

Rate 

(From above) 

Current Base 

Rate 

Initial Rate 

Change 

[(3)/(4)-1] 

Capped 

and 

Cupped 

Illinois Adams 0.0614 0.0730 -15.9% -5.0% 

Illinois Alexander 0.1583 0.1100 43.9% 10.0% 

Illinois Bond 0.0684 0.0620 10.3% 10.0% 

Illinois Boone 0.0396 0.0480 -17.5% -5.0% 

Illinois Brown 0.0591 0.0680 -13.0% -5.0% 

Illinois Bureau 0.0276 0.0370 -25.3% -5.0% 

Illinois Calhoun 0.0615 0.0690 -10.9% -5.0% 

MILLIMAN & ROBERTSON, INC. 
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B. Capped Rate Changes 

Although rate increases are limited to 20% by federal law, in recent years the initial rate 

changes, as shown, have been capped at 10% and cupped at 5%. 

Actuarial Justification 

It is not uncommon for rates to be limited to specified increases or decreases. This is 

addressed in the Foundations text, as follows: “Occasionally, due to regulatory requirements 

or marketing considerations, it is necessary that individual rate changes be limited to a 

maximum increase or decrease.” For MPCI, the imposition of a limit (cap or cup) may be a 

public policy consideration, to stabilize premiums for producers from year to year. It may 

also be a reflection of the fact that ratemaking is an imprecise process; even with the longterm averaging, and the application of catastrophe and credibility procedures, rates can vary 

significantly from one valuation to the next. The use of limitation procedures is an accepted 

approach. 

However, when rates for individual classes (e.g., county) are limited to a specified increase or 

decrease, there is a potential that the resulting overall rate level (e.g., state) may be too low or 

too high. It is common for a final step in the process to be the incorporation of an “offbalance” factor, to adjust for the effects of capping. The process is similar to that used in 

building back the catastrophe losses. We would recommend that RMA incorporate a final 

off-balance adjustment in the rates. 

MILLIMAN & ROBERTSON, INC. 
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TYPE / PRACTICE AND GROUP FACTORS 

The rates developed to this point have used data aggregated for all types of farming practices. 

In addition, as noted above the rates reflect the 65% coverage level. Finally, the rates reflect 

those for producers with a long-term average yield similar to the average yield for Adams 

County. Each of these items (practice type, coverage level, and average yield) can affect a 

producer’s expected indemnification and, consequently, needs to be reflected in the individual 

producer’s rates. 

A. Practice Factors 

Practice factors reflect the fact that different farming practices increase or reduce the risk of 

loss. For example, irrigation reduces the risk of loss due to inadequate moisture. For each 

practice, the rate is multiplied by a factor representing the relative risk. Type/Practice factors 

are derived from MPCI data that is aggregated at a level greater than the county level. This is 

appropriate, since the county data would likely lack sufficient credibility. In addition, we 

would not expect that the relative impact of specific practices would vary significantly from 

one county to the next (although the impact could vary across broader regions). Finally, we 

note that this approach – subdividing data, and aggregating at a broader level, is commonly 

used in insurance ratemaking. 

Actuarial Justification 

The practice factors are derived by dividing the practice specific LCR by the combined LCR 

where the combined LCR is calculated over all practices in the rating area. This is a 

MILLIMAN & ROBERTSON, INC. 
 

 

 

 

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reasonable approach. We would recommend that RMA monitor the practice factors over time 

to determine whether there are any trends emerging in the factors. 

B. 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 

Exponential County Unloaded Rate  ́ (Yield Span) 

+ Catastrophe Rate 

Reserve Factor Base Rate = 

Unit Division Factor 

Yield span is the ratio of the producer’s expected yield to the county average. In practice, 

spans are divided into nine categories. The exponential is a factor varying from –1 to –1.5. 

Actuarial Justification 

The use of the exponential factor dates back to the time when yield guarantees were based on 

average yields established for all farmers in a specific area. Thus, the rates would vary 

inversely with average yield (this is equivalent to an exponent of –1). M&R’s analysis in 1983 

(“Analysis of Area Average Yield and Individual Yield Coverage Programs” concluded that a 

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lower exponent (which would result in a lower premium per acre as yields increase) was 

indicated by the data. 

The exponentials were revisited in M&R’s report, Federal Crop Insurance Corporation 

Ratemaking Overview, dated June 14, 1996. In that report, we supported the general 

approach, but suggested possible alternatives to the above formula to reduce some of the 

discontinuities that exist in rates in adjacent yield intervals. We also noted that it is very 

important to periodically evaluate the formula, particularly the exponential, to reflect current 

experience. 

C. 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. Presently, a common set of differentials 

is used for most crops and states. 

Actuarial Justification 

Coverage level differentials have been the subject of several M&R analyses. The first study 

was “Analysis of Coverage Level Rate Relativities” dated September 9, 1993. Subsequent 

analyses were conducted in “Analysis and Recommendation for the FCIC Coverage Level 

Rate Relativities” dated June 23, 1995, and in the report “Federal Crop Insurance 

Corporation Ratemaking Overview”, dated June 14, 1996. In addition to these analyses, 

MILLIMAN & ROBERTSON, INC. 
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RMA has conducted research into the coverage level relativity factors. 

The most recent M&R work suggests that relativities differ by crop and area. In addition 

there were indications that the relativities among coverage levels vary with yield span (yield 

spans were discussed in the previous section). 

It is appropriate to adjust rates to reflect different levels of indemnification under the various 

coverage levels. We believe this is an area where continued analysis is warranted, in order to 

identify and reflect the appropriate rate relationships for the different crops and classes. 

PERFORMANCE MEASUREMENT 

One item that appears to be absent in the MPCI ratemaking process, is a final test or 

calculation to determine whether the target rate level has been achieved. Most property and 

casualty rates are developed using a “top down” approach. With this approach, an average 

rate, or percentage rate change, is developed at an aggregate level (e.g., State). The rates for 

lower levels (e.g., county) may then be derived separately, but in the end balanced to the 

aggregate target. 

This final balancing seems appropriate for the MPCI rates, since many of the steps along the 

way involve limiting the data, applying caps/cups, and otherwise causing potential departures 

from the aggregate rate requirement. We would encourage RMA to develop a process for 

measuring the ultimate rate schedules against some aggregate target. 

MILLIMAN & ROBERTSON, INC. 
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FREQUENCY OF RATE REVIEWS 

One final issue that we were asked to address was how often MPCI rate reviews should take 

place. Presently rates are reviewed and revised annually for most major crops. 

There is no “right answer” to this question. Less frequent reviews would reduce 

administrative costs, or allow more resources to be used for research on improving the 

ratemaking process. Less frequent rate changes may or may not provide more stability in 

rates (i.e., rates would not change between rate reviews). 

However, less frequent reviews would likely cause more significant rate changes from one 

review to the next. The present caps (+10%) and cups (-5%) may need to increase to reflect 

the longer time period between reviews. For example, for a three-year rate cycle, an 

equivalent cap would be about 30%. RMA will want to consider the affect on procedures and 

participation of such large increases. 

If the overall rate indication performance measure discussed in the previous section can be 

developed, one option would be to only modify rates if the overall indicated change is greater 

than a specified threshold (±5%), with perhaps an automatic review every 3rd year. 

* * * * * 

MILLIMAN & ROBERTSON, INC. 
 

 

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We would like to acknowledge and thank Jim Driscoll and LeWayne Jansonius, of RMA, for 

their assistance in providing information and responding to our many questions as we 

prepared this report. We appreciate the opportunity to be of service to RMA and will be 

happy to respond to any questions. 

Sincerely, 

Gary R. Josephson, F.C.A.S., M.A.A.A. 

Consulting Actuary 

Richard B. Lord, F.C.A.S., M.A.A.A. 

Consulting Actuary 

Charles W. Mitchell 

Actuarial Assistant 

GRJ/RBL/CWM/sbs 

August 1, 2000 

H:\CLIENT\Rma\Jul.00\Report.doc 

MILLIMAN & ROBERTSON, INC. 
 

Exhibit 1 

ADJUSTING LIABILITY TO COMMON COVERAGE LEVEL 

1) Liability (L)= Acres x APH x Price x Coverage Level 

2) Define : Value = Acres x APH x Price 

3) Then : L = Value x Coverage Level 

4) At 75% Coverage Level : L75 = Value x .75 

5) At 65% Coverage Level : L65 = Value x .65 

6) Therefore : L65 = Value x .75 x (.65/.75) 

L65 = L75 x (.65/.75) 

MILLIMAN & ROBERTSON, INC. 
Exhibit 2 

ADJUSTING INDEMNITY FROM A HIGHER

 TO A LOWER COVERAGE LEVEL 

Coverage Level 75% 65% Difference 

Liability* $9,000 $7,800 $1,200 

Indemnity* 

Yield per 

Acre 

Production 

Ratio 

Production 

Value 

Coverage Level 

75% 65% Difference 

0 0.0% $0 $9,000 $7,800 $1,200 

15 12.5 1,500 7,500 6,300 1,200 

30 25.0 3,000 6,000 4,800 1,200 

45 37.5 4,500 4,500 3,300 1,200 

60 50.0 6,000 3,000 1,800 1,200 

75 62.5 7,500 1,500 300 1,200 

78 65.0 7,800 1,200 - 1,200 

85 70.8 8,500 500 - -

90 75.0 9,000 - - -

105 87.5 10,500 - - -

* Acres = 100 

APH = 120 

Price = $1.00 

MILLIMAN & ROBERTSON, INC. 
Exhibit 3 

ADJUSTING INDEMNITY FROM A HIGHER

 TO A LOWER COVERAGE LEVEL 

Coverage Level 50% 65% Difference 

Liability* $6,000 $7,800 $1,800 

Indemnity* 

Yield per 

Acre 

Production 

Ratio 

Production 

Value 

Coverage Level 

50% 65% Difference 

0 0.0% $0 $6,000 $7,800 $1,800 

15 12.5 1,500 4,500 6,300 1,800 

30 25.0 3,000 3,000 4,800 1,800 

45 37.5 4,500 1,500 3,300 1,800 

50 41.7 5,000 1,000 2,800 1,800 

55 45.8 5,500 500 2,300 1,800 

60 50.0 6,000 - 1,800 1,800 

65 54.2 6,500 - 1,300 1,300 

70 58.3 7,000 - 800 800 

75 62.5 7,500 - 300 300 

78 65.0 7,800 - - -

85 70.8 8,500 - - -

90 75.0 9,000 - - -

105 87.5 10,500 - - -

* Acres = 100 

APH = 120 

Price = $1.00 

MILLIMAN & ROBERTSON, INC. 
Exhibit 4 

ADJUSTING INDEMNITY FROM A HIGHER

 TO A LOWER COVERAGE LEVEL 

(APPROXIMATION TECHNIQUE)1 

Adjusting Indemnity to Higher Coverage Level (50% to 65%) 

Production Ratios Liability Indemnity Adjusted Liability2 

<50% $150,000 $30,000 $195,000 

>=50% 400,000 0 520,000 

1) The above values are created to illustrate the calculation. They are not true RMA data. 

2) Liability x (.65/.50) 

Adjusted Indemnity Calculation 

The minimum adjusted indemnity is equal to the unadjusted indemnity plus the liability 

adjustment for production ratios less than 50%. 

Minimum Adjusted Indemnity = $30,000 + ($195,000 - $150,000) = $75,000 

The maximum adjusted indemnity is equal to the unadjusted indemnity plus the liability 

adjustment for all production ratios. 

Maximum Adjusted Indemnity = 

$30,000 + ($195,000 - $150,000) + ($520,000 - $400,000) = $195,000 

The loss cost ratio used in the interpolation is based on the liability and indemnity for production 

ratios less than 50%. 

Loss Cost Ratio = $30,000 / $150,000 = 20% 

The interpolated adjusted indemnity is then the minimum indemnity 20% of the liability 

adjustment for production ratios greater than or equal to 50%. 

Interpolated Adjusted Indemnity = $75,000 + .20 * ($520,000 – $400,000) = $99,000 

If necessary, the interpolated adjusted indemnity would be subject to the maximum adjusted 

indemnity. 

H:\CLIENT\Rma\Jul.00\Exhibits 1-4.doc 

MILLIMAN & ROBERTSON, INC. 
Statement of Principles Regarding 

Property and Casualty Insurance Ratemaking 

(Adopted by the Board of Directors of the CAS May 1988) 

The purpose of this Statement is to identify and describe principles applicable to the determination 

and review of property and casualty insurance rates. The principles in this Statement are limited to 

that portion of the ratemaking process involving the estimation of costs associated with the 

transfer of risk. This Statement consists of four parts: 

I. DEFINITIONS 

II. PRINCIPLES 

III. CONSIDERATIONS 

IV. CONCLUSION 

The principles contained in this Statement provide the foundation for the development of actuarial 

procedures and standards of practice. It is important that proper actuarial procedures be 

employed to derive rates that protect the insurance system's financial soundness and promote 

equity and availability for insurance consumers. 

Although this Statement addresses property and casualty insurance ratemaking, the principles 

contained in this Statement apply to other risk transfer mechanisms. 

I. DEFINITIONS 

Ratemaking is the process of establishing rates used in insurance or other risk transfer 

mechanisms. This process involves a number of considerations including marketing goals, 

competition and legal restrictions to the extent they affect the estimation of future costs 

associated with the transfer of risk. This Statement is limited to principles applicable to the 

estimation of these costs. Such costs include claims, claim settlement expenses, operational and 

administrative expenses, and the cost of capital. Summary descriptions of these costs are as 

follows: 

—Incurred losses are the cost of claims insured. 

—Allocated loss adjustment expenses are claims settlement costs directly assignable to specific 

claims. 

—Unallocated loss adjustment expenses are all costs associated with the claim settlement 

function not directly assignable to specific claims. 
—Commission and brokerage expenses are compensation to agents and brokers. 

—Other acquisition expenses are all costs, except commission and brokerage, associated with the 

acquisition of business. 

—Taxes, licenses and fees are all taxes and miscellaneous fees except federal income taxes. 

—Policyholder dividends are a non-guaranteed return of premium charged to operations as an 

expense. 

—General administrative expenses are all other operational and administrative costs. 

—The underwriting profit and contingency provisions are the amounts that, when considered 

with net investment and other income, provide an appropriate total after-tax return. 

II. PRINCIPLES 

Ratemaking is prospective because the property and casualty insurance rate must be developed 

prior to the transfer of risk. 

Principle 1: A rate is an estimate of the expected value of future costs. 

Ratemaking should provide for all costs so that the insurance system is financially sound. 

Principle 2: A rate provides for all costs associated with the transfer of risk. 

Ratemaking should provide for the costs of an individual risk transfer so that equity among 

insureds is maintained. When the experience of an individual risk does not provide a credible 

basis for estimating these costs, it is appropriate to consider the aggregate experience of similar 

risks. A rate estimated from such experience is an estimate of the costs of the risk transfer for 

each individual in the class. 

Principle 3: A rate provides for the costs associated with an individual risk transfer. 

Ratemaking produces cost estimates that are actuarially sound if the estimation is based on 

Principles 1, 2, and 3. Such rates comply with four criteria commonly used by actuaries: 

reasonable, not excessive, not inadequate, and not unfairly discriminatory. 

Principle 4: A rate is reasonable and not excessive, inadequate, or unfairly discriminatory 

if it is an actuarially sound estimate of the expected value of all future costs associated 

with an individual risk transfer. 

III. CONSIDERATIONS 

A number of ratemaking methodologies have been established by precedent or common usage 
within the actuarial profession. Since it is desirable to encourage experimentation and innovation 

in ratemaking, the actuary need not be completely bound by these precedents. Regardless of the 

ratemaking methodology utilized, the material assumptions should be documented and available 

for disclosure. While no ratemaking methodology is appropriate in all cases, a number of 

considerations commonly apply. Some of these considerations are listed below with summary 

descriptions. These considerations are intended to provide a foundation for the development of 

actuarial procedures and standards of practice. 

Exposure Unit—The determination of an appropriate exposure unit or premium basis is 

essential. It is desirable that the exposure unit vary with the hazard and be practical and verifiable. 

Data—Historical premium, exposure, loss and expense experience is usually the starting 

point of ratemaking. This experience is relevant if it provides a basis for developing a reasonable 

indication of the future. Other relevant data may supplement historical experience. These other 

data may be external to the company or to the insurance industry and may indicate the general 

direction of trends in insurance claim costs, claim frequencies, expenses and premiums. 

Organization of Data—There are several acceptable methods of organizing data including 

calendar year, accident year, report year and policy year. Each presents certain advantages and 

disadvantages; but, if handled properly, each may be used to produce rates. Data availability, 

clarity, simplicity, and the nature of the insurance coverage affect the choice. 

Homogeneity—Ratemaking accuracy often is improved by subdividing experience into 

groups exhibiting similar characteristics. For a heterogeneous product, consideration should be 

given to segregating the experience into more homogeneous groupings. Additionally, subdividing 

or combining the data so as to minimize the distorting effects of operational or procedural 

changes should be fully explored. 

Credibility—Credibility is a measure of the predictive value that the actuary attaches to a 

particular body of data. Credibility is increased by making groupings more homogeneous or by 

increasing the size of the group analyzed. A group should be large enough to be statistically 

reliable. Obtaining homogeneous groupings requires refinement and partitioning of the data. 

There is a point at which partitioning divides data into groups too small to provide credible 

patterns. Each situation requires balancing homogeneity and the volume of data. 

Loss Development—When incurred losses and loss adjustment expenses are estimated, the 

development of each should be considered. The determination of the expected loss development 

is subject to the principles set forth in the Casualty Actuarial Society's Statement of Principles 

Regarding Property and Casualty Loss and Loss Adjustment Expense Reserves. 

Trends—Consideration should be given to past and prospective changes in claim costs, 

claim frequencies, exposures, expenses and premiums. 

Catastrophes—Consideration should be given to the impact of catastrophes on the 

experience and procedures should be developed to include an allowance for the catastrophe 
exposure in the rate. 

Policy Provisions—Consideration should be given to the effect of salvage and 

subrogation, coinsurance, coverage limits, deductibles, coordination of benefits, second injury 

fund recoveries and other policy provisions. 

Mix of Business—Consideration should be given to distributional changes in deductibles, 

coverage limitations or type of risks that may affect the frequency or severity of claims. 

Reinsurance—Consideration should be given to the effect of reinsurance arrangements. 

Operational Changes—Consideration should be given to operational changes such as 

changes in the underwriting process, claim handling, case reserving and marketing practices that 

affect the continuity of the experience. 

Other Influences—The impact of external influences on the expected future experience 

should be considered. Considerations include the judicial environment, regulatory and legislative 

changes, guaranty funds, economic variable, and residual market mechanisms including subsidies 

of residual market rate deficiencies. 

Classification Plans—A properly defined classification plan enables the development of 

actuarially sound rates. 

Individual Risk Rating—When an individual risk's experience is sufficiently credible, the 

premium for that risk should be modified to reflect the individual experience. Consideration 

should be given to the impact of individual risk rating plans on the overall experience. 

Risk—The rate should include a charge for the risk of random variation from the expected 

costs. This risk charge should be reflected in the determination of the appropriate total return 

consistent with the cost of capital and, therefore, influences the underwriting profit provision. 

The rate should also include a charge for any systematic variation of the estimated costs from the 

expected costs. This charge should be reflected in the determination of the contingency provision. 

Investment and Other Income—The contribution of net investment and other income 

should be considered. 

Actuarial Judgment—Informed actuarial judgments can be used effectively in ratemaking. 

Such judgments may be applied throughout the ratemaking process and should be documented 

and available for disclosure. 

IV. CONCLUSION 

The actuary, by applying the ratemaking principles in this Statement, will derive an estimation of 

the future costs associated with the transfer of risk. Other business considerations are also a part 

of ratemaking. By interacting with professionals from various fields including underwriting, 
marketing, law, claims, and finance, the actuary has a key role in the ratemaking process. 
 

BIBLIOGRAPHY OF MILLIMAN & ROBERTSON, INC. 

CROP INSURANCE REPORTS 

Date Sent Title Signed by: 

July 28, 1983 

Milliman & Robertson, Inc. 

Analysis of the Experience Rating Table 

for the 1984 Crop Year Proposed 

for Cotton and Rice 

James R. Berquist 

Michael A. McMurray 

September 9, 1983 Milliman & Robertson, Inc. 

Analysis of Coverage Level Rate Relativities Michael A. McMurray 

September 9, 1983 Milliman & Robertson, Inc. 

Analysis of Catastrophe Provisions Michael A. McMurray 

September 14, 1983 

Milliman & Robertson, Inc. 

Analysis of Area Average Yield 

And Individual Yield Coverage Programs 

Daniel J. Flaherty 

Gary R. Josephson 

September 23, 1983 

Milliman & Robertson, Inc. 

Analysis of Procedrues to Determine 

Rating Areas and Classifications 

David R. Bickerstaff 

October 21, 1983 

Milliman & Robertson, Inc. 

Analysis of Experience Rating 

For Crop Insurance 

James R. Berquist 

Michael A. McMurray 

November 2, 1983 Milliman & Robertson, Inc. 

Analysis of Late Planting Dates 

James R. Berquist 

Michael A. McMurray 

November 30, 1983 

Milliman & Robertson, Inc. 

Analysis of the Effects 

Of Unitizing on Loss Costs 

And Related Issues 

David R. Bickerstaff 

November 30, 1983 

Milliman & Robertson, Inc. 

Evaluation of the Ratemaking Formula and 

Procedures for Multiple Peril Crop Insurance 

James R. Berquist 

Michael A. McMurray 

December 1, 1983 Milliman & Robertson, Inc. 

Specification of an Actuarial Data Base 

James R. Berquist 

Michael A. McMurray 

June 21, 1984 

Analysis of 

The Federal Crop Insurance Corporation 

Standard Reinsurance Agreement 

Michael A. McMurray 

January 30, 1995 FCIC Catastrophe Procedure 

White Paper Michael A. McMurray 

February 14, 1995 Analysis and Recommendation for 

The FCIC Catastrophe Procedure Michael A. McMurray 

March 20, 1995 Analysis and Recommendations for 

The FCIC Catastrophe Procedure Michael A. McMurray 

June 23, 1995 

Analysis and Recommendation 

For the FCIC Coverage Level Rate 

Relativities 

Michael A. McMurray 

September 27, 1995 Analysis and Recommendations for the 

FCIC Catastrophe Procedure 

Richard B. Lord 

Michael A. McMurray 

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MILLIMAN & ROBERTSON, INC. 
BIBLIOGRAPHY OF MILLIMAN & ROBERTSON, INC. 

REPORTS FOR ECONOMIC RESEARCH SERVICE 

Date Sent Title Signed by: 

October 31, 1995 FCIC Pricing Procedures 

For Unrated Areas 

Richard B. Lord 

Michael A. McMurray 

November 21, 1995 FCIC Coverage Level Rate Relativities Michael A. McMurray 

November 28, 1995 

FCIC Coverage Level 

Rate Relativities 

Winter Wheat 

Michael A. McMurray 

January 30, 1996 Federal Crop Insurance Corporation 

County Rate Smoothing Procedure 

Richard B. Lord 

Michael A. McMurray 

January 30, 1996 Analysis of FCIC Hail and Fire 

Peril Exclusion Credit 

Richard B. Lord 

Michael A. McMurray 

April 26, 1996 

Analysis of FCIC Hail and Fire 

Peril Exclusion Credit 

Apples & Peaches 

Richard B. Lord 

Michael A. McMurray 

June 14, 1996 Federal Crop Insurance Company 

Ratemaking Overview 

Richard B. Lord 

Michael A. McMurray 

December 17, 1996 An Analysis of 

Crop Revenue Insurance Products 

Richard B. Lord 

Michael A. McMurray 

December 19, 1996 

Federal Crop Insurance Company 

Analysis of 

Rate Expansion Factors for Corn 

Richard B. Lord 

Michael A. McMurray 

March 31, 1997 1998 Standard Reinsurance 

Agreement Review 

Richard B. Lord 

Michael A. McMurray 

September 18, 1998 

Federal Crop Insurance Corporation 

Standard Reinsurance Agreement 

Rate of Return Methodology 

Richard B. Lord 

Michael A. McMurray 

September 22, 1998 

Federal Crop Insurance Corporation 

1999 Nursery Crop Insurance 

Rate Level Analysis 

Richard B. Lord 

Michael A. McMurray 

H:\CLIENT\Rma\Jul.00\BIBLIOGRAPHY OF REPORTS.doc 

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MILLIMAN & ROBERTSON, INC.