BULLETIN NO.: MGR-97-015.1 TO: All Reinsured Companies All Risk Management Field Offices All Other Interested Parties FROM: Kenneth D. Ackerman Administrator SUBJECT: Federal Crop Reinsurance (FCR) Model Documentation Attached is the documentation regarding the FCR Model. There has been a change in the time and place for the briefing on the FCR model. National Crop Insurance Services, Inc. (NCIS) is holding a meeting at the Hyatt Regency Hotel in Kansas City, MO 2345 McGee Street, Phone: (816) 421-1234. NCIS has graciously provided the Risk Management Agency with two hours on its morning agenda to brief the crop insurance industry on the FCR Model. The briefing will begin at 10:00 a.m. and continue until 12:00 p.m. on Thursday, April 24, 1997. Persons attending this briefing will be responsible for their own travel and hotel arrangements. If you have any questions, please contact E. Heyward Baker, Director, Reinsurance Services Division at (202) 720-4232. Attachment REINSURANCE SIMULATION MODEL Mario J. Miranda, Joseph W. Glauber, and Keith J. Coble SRASIM is a computer simulation program designed to compute the expected rate of return of reinsured crop insurance companies under alternative quota-share provisions for the Standard Reinsurance Agreement (SRA). More specifically, SRASIM takes as input a hypothetical schedule of loss-gain share rates for each of the commercial, developmental, and assigned risk funds of the SRA. SRASIM then outputs the expected rate of return under the hypothetical SRA, either by fund and state or by fund and firm. SRASIM's analysis is limited in scope to seven major crops: wheat, corn, soybeans, grain sorghum, cotton, barley, and peanuts. SRASIM may be implemented using either a "historical" or a "structural" model of the probability distribution of loss-ratios faced by crop insurers. In the historical loss-ratio version, SRASIM assumes that the schedule of loss-ratios experienced by crop insurers between 1981 and 1994 is representative of the loss ratio distribution that will be faced by crop insurers in the future. In the structural version, SRASIM discards the historical loss ratio distribution and generates instead a loss ratio distribution from a series of structural submodels of unit-level indemnity distributions. Unlike the historical version, the structural version of SRASIM allows the user to examine the implications of structural variations in the crop insurance market not experienced during the historical 1981 to 1994 period. Such variations include, but are not limited to, the introduction of new reinsured crop insurance products such as revenue insurance, changes in the proportion of catastrophic versus buy-up coverage, and the effects of weather variability comparable to that experienced over the longer 1957 to 1994 period. Computational Procedures: "Historical" Loss-Ratios "Historical" simulations with SRASIM are based primarily on the LOSSDIST database, which contains 1981-1994 loss ratios by crop reporting district and crop, aggregated across all funds, coverages, and firms. While historical loss ratios provide useful information, several limitations of this measure should be considered when assessing actuarial soundness. First, crop insurance indemnities tend to vary widely from year to year as compared to other common insurance contracts such as automobile, health, and life insurance. As a result, most measures of crop insurance actuarial soundness aggregate across time. Generally, longer time series are expected to more accurately capture and weigh random events because more possible outcomes would be observed. Historical loss ratio measures also implicitly assume that various aspects of the program, such as coverage options and premium rates, have remained constant over time. That is, an unadjusted approach ignores the effects of alterations in rates or other characteristics of the program over time. Given changes in the program and rates, this measure may have little to do with current actuarial soundness. Recognition of these inconsistencies in the program and participants across time tends to counterbalance the desirability of long time-series to capture random events. To address the effect of changing premium rates, the model uses an adjusted loss ratio which is computed by dividing the estimated loss cost ratio for each year (indemnity divided by liability) by the current (1995) premium rates. This is done by crop reporting district for each crop in the years 1981-94. Additionally, catastrophic coverage policies are excluded because of the significantly lower coverage associated with those policies. Because insurance rates have increased for many crops and locations over time the adjusted loss ratio is generally lower than the raw historical loss ratios. A decline in 75 percent coverage policies since the early eighties is not explicitly modeled, but would act to further reduce the adjusted loss ratio. Figure 1 compares the adjusted loss ratio to the raw loss ratio for all crops in the United States for the years 1981-95. Given current rates, the adjusted loss ratio averaged 117 percent compared with 136 percent for the unadjusted historical loss ratios. SRASIM relies on three other databases to compute expected rates of returns by firm, state, and fund. All three databases are derived from data supplied by the Economic Research Service and FCIC. The BOOKCNTY database contains total liability in dollars, for 1995, by crop, county, firm, and fund, aggregated across all coverage levels. The BKRETAIN database contains the percent book of business retained in 1995, by state, firm, and fund, aggregated across all crops and coverages. The COVERPCT data base contains the percent of book of business at the 50, 65, and 75 percent coverage levels, in 1995, by district and crop, aggregated across all firms and funds. In its first phase of execution, SRASIM computes adjusted historical loss ratios for 1980-1994, by state, firm, fund, and coverage level as averages weighted by retained liability. The base loss ratios are taken from the LOSSDIST database and the weights from the BOOKCNTY, BRRETAIN, and COVERPCT databases. To compute the loss-ratios by state, firm, fund, and coverage, SRASIM makes the following assumptions: 1) The percent book of business retained is fixed at 1995 levels and is uniform across crops, coverages, and districts within a state, for a given state, firm, and fund. In other words, SRASIM observes variations in retention across states, firms, and funds, but not across crops, coverages, and districts within a state. 2) The percent distribution of book of business at the 50, 65, and 75 percent coverage levels is fixed at 1995 levels and is uniform across crops and funds, for a given district and crop. In other words, SRASIM observes variations across districts and crops in percentage business at the different coverage levels, but not across firms and funds. 3) Adjusted historical loss ratios between 1980-1994 were uniform across funds, coverages, and firms, for a given district and crop. In other words, SRASIM observes variations in historical loss ratios across districts and crops, but not across funds, coverages, and firms. In its second phase of execution, SRASIM inputs the user's assumptions regarding quota share rates for the commercial, developmental, and assigned risk funds, for both corn belt and non corn belt states. SRASIM then computes the implied rates of return for 1981-1994 by state, fund, and firm by adjusting the historical loss ratios using the quota-share rule of the hypothetical SRA. Depending on the version of SRASIM being used, these hypothetical rates of return are either averaged across firms and over time to obtain the expected rate of return by state and fund, or are averaged across districts and over time to obtain the expected rate of return by firm and fund. SRASIM outputs the rates of return either to an ASCII file accessible to the user. The rates of returns are computed using a pretax ROCR measure, which equals net return, after adjusting for the effects of the SRA, as a percent of maximum possible underwriting loss under the SRA. Computational Procedures: "Structural" Loss-Ratios The "structural" and "historical" versions of SRASIM differ only with regard to the distribution of loss ratios assumed. Whereas the historical version of SRASIM employs an empirical distribution of historically observed loss ratios, the structural version employs loss ratio distribution generated from a series of structural submodels of unit-level indemnity distributions. Once the loss ratios have been computed from the underlying structural model of unit-level indemnities, the structural version of SRASIM computes expected rates of return just like the historical version, and in particular uses the same weighting scheme as discussed in the preceding section (with a single minor exception discussed below). In this section, we limit discussion to the method by which the structural version of SRASIM generates the loss ratio distribution. In order to appreciate the need for a structural version of SRASIM, one must understand the limitations of using historical loss ratio distributions to predict the performance of the SRA under alternative quota-share provisions. Historical distributions are adequate for analysis if one is examining only changes in the SRA structure itself. However, changes in the structure of the underlying crop insurance market, such as increased premium rates, changes in participation, a substantial shift to a new product line (e.g., revenue insurance) or significant changes in the relative incidence of the various coverage levels, will almost certainly change the distribution of loss ratios faced by crop insurers. When such structural changes have occurred, or are expected to occur, using historical loss ratios will likely render inaccurate predictions regarding the rates of return under the SRA. The structural version of SRASIM is designed to control for the effects of structural changes by employing a more disaggregate model of crop insurance indemnities that allows structural variations to be incorporated explicitly. The structural version of SRASIM relies on two major databases to generate a distribution of loss ratios. The YLDDIST database contains historical crop yields, by crop reporting district and crop, for the period 1957-94. The database also includes detrended yields, detrended using a two-piece linear spline trend function, and correcting for heteroskedasticity in the error term. The YLDDIST database was supplied by Jerry Skees of the University of Kentucky. The YLDINDV data base contains approximately 2 million individual, unit-level yield records filed in conjunction with crop insurance contracts purchased in 1995. The nearly 2 million unit-level records used in the simulations contain no less than five years and no more than 10 years of recent yields for each unit. Each record indicates the crop insurer, the policy number, and the acres in the unit, but no information on coverage level or reinsurance fund assignment. The YLDINDV data base is part of the EXPERSUM data base maintained by the Federal Crop Insurance Corporation and revised by the Economic Research Service. Consider first how SRASIM models an individual farm unit's indemnity distribution. First, the district in which the unit resides is identified. For this district, there is a record in the YLDDIST database containing the 38 district-level yields for the years 1957-94. The YLDINDV database has a record corresponding to the unit that contains five to ten unit-level yields during the 1980-1994 period. SRASIM assumes that the ratios of individual yields to the corresponding district yields of the same year constitute realizations of a random variable that is independently and identically distributed over time. (Denote these ratios r1,r2,...,rn.) Under this assumption, it is straightforward to compute a simple nonparametric estimate of the per-acre indemnity for the unit, conditional on the county yield. Take, for example, an MPCI contract with yield guarantee YBAR and price election PBAR. Then the expected per-acre indemnity for the unit, conditional on the district yield being Y is: E[Indemnity|County Yield = Y] = (1/n) * Sumi PBAR*Max(0,YBAR-Y*ri) SRASIM performs this computation for all units growing a particular crop within a district and then computes the acreage-weighted average across all such units. Repeating this process for all districts, crops, and coverage levels, and by conditioning on the detrended district-level yields between 1957 and 1994, SRASIM generates a 1994-equivalent, joint distribution of district-level per acre indemnities for all crops, districts, and coverages. By construction, the joint distribution is consistent with weather variations experienced during the 1957-94 period. The distribution of district-level per-acre indemnities is then converted into a corresponding distribution of district-level loss-ratios in one of two ways. If instructed to do so, SRASIM will impose actuarial fairness by dividing by the implied average per-acre indemnity; in this case, the loss ratios for a given district, crop, and coverage will average to one, but will vary in a manner consistent with the weather patterns of 1957-94. Alternatively, SRASIM will, by default, normalize the per-acre indemnities so that the computes loss ratio series replicates the average loss-ratios historically observed over the 1981-94 period, the period for which district-level loss ratios are available. SRASIM can be used to analyze CAT and buyup policies separately or combined in a single book of business. SRASIM can also be adapted to generate a distribution of district-level loss ratios for non-MPCI crop insurance products, such as Crop Revenue Coverage, Income Protection or Revenue Assurance. With revenue insurance policies, aggregate U.S. yields are constructed from the YLDDIST database. Market prices are then calculated using an aggregate U.S. supply and demand model.