Systemic Risk in U.S. Crop and Revenue Insurance Programs

The present study estimates the probability density function of the Federal Risk Management Agency’s (RMA) net income from reinsuring crop insurance for corn, wheat, and soybeans. Based on 1997 data, it is estimated that there is a 5 percent probability that RMA will need to reimburse at least $1 billion to insurance companies, and that the fair value of RMA’s reinsurance services to insurance firms equals $78.7 million. In addition, various hedging strategies are examined for their potential to reduce RMA’s reinsurance risk. The risk reduction achievable by hedging is appreciable, but use of derivative contracts alone is clearly no panacea. SYSTEMIC RISK IN U.S. CROP AND REVENUE INSURANCE PROGRAMS Insurance companies have traditionally operated in markets where risk can be pooled or diversified. Futures and options markets have traditionally operated where risk is systemic. Yields and revenues obtained by crop producers have both systemic (drought and price drops) and poolable (localized yield shortfall) risks. Farmers cannot hedge the poolable or localized source of revenue risk on speculative markets, and insurance companies will not accept risk that has a systemic component (Gardner and Kramer; Kramer; Vaughan and Vaughan). As a result, a hybrid mechanism has evolved in U.S. crop insurance markets wherein the federal government agrees to accept the systemic risk so that private insurance companies will sell crop and revenue insurance to producers. To provide incentives for insurers to offer multi-peril crop insurance, the U.S. government has designed the Standard Reinsurance Agreement (SRA). Under the SRA, insurers can transfer to the Federal Risk Management Agency (RMA) a portion of losses that can occur with widespread yield shortfalls, in exchange for ceding their right to a portion of the gains when premiums are greater than indemnities. The SRA yields an increasing proportion of the firms’ profits as positive returns increase and commits the RMA to taking responsibility for an increasing proportion of the losses as they increase. This leaves the RMA in its role as reinsurer with an uncertain level of total outlays. To date there has been no attempt to use speculative markets to hedge the systemic portion of this risk. The purpose of this study is to break down the total risk absorbed by the U.S. crop insurance industry into poolable and systemic components. We then use option pricing theory to value the reinsurance that the federal government provides when it absorbs this systemic risk. Finally, we evaluate the possibility of using speculative markets in prices and yields to hedge the systemic risk accepted by the government. The analysis considers the insurance policies that most contribute to RMA’s risk. These are Actual Production 2 / Mason, Hayes, and Lence History Buy-Up Coverage (BUP), Actual Production History Catastrophic Coverage (CAT), the Group Risk Plan (GRP), and Crop Revenue Coverage (CRC). The crops studied are corn, soybeans, and wheat, as they represent the largest of the crops insured under these programs. The research presented here is motivated in part by Miranda and Glauber, who argue that insurance companies could use derivatives markets as substitutes for government provision of reinsurance. Our work allows the individual insurance companies to pool their risk under the existing institutional structure and focuses on the systemic risk at a national level. Insurance and Reinsurance Programs Given the focus on RMA’s reinsurance activities, attention is restricted to the major insurance programs available to farmers that are reinsurable by RMA, i.e., BUP, CAT, GRP, and CRC. BUP pays indemnities when a farmer’s yields (y) fall below ψ percent of the average of the individual’s previous production (Y). In such instances, the farmer gets a payment per acre insured equal to the yield shortfall multiplied by π percent of the RMA expected price (PRMA): BUP(y; π, ψ) = max[0, π × PRMA × (ψ × Y − y)]. (1) Farmers can choose price protection levels π from the set ΠBUP ≡ {0.6, 0.65, ..., 0.95, 1.0} and yield coverage levels ψ from the set ΨBUP ≡ {0.5, 0.65, 0.75}. CAT is similar to BUP, except that the levels of price and yield protection are fixed at 60 percent and 50 percent, respectively: CAT(y) = max[0, 0.6 × PRMA × (0.5 × Y − y)]. (2) That is, CAT(y) = BUP(y; π = 0.6, ψ = 0.5). Unlike BUP and CAT policies (whose indemnities are based on the farmers’ individual yields), GRP indemnities are based on county yields. Letting Yi and yi Systemic Risk in U.S. Crop and Revenue Insurance Programs / 3 represent county i’s expected and realized yields, respectively, per-acre indemnities for GRP are calculated as GRP(yi; π, ψ) = max[0, π × PRMA × (Yi − yi/ψ)]. (3) It is clear from (1) and (3) that GRP indemnities are computed differently from BUP and CAT indemnities, even after accounting for countyrather than farm-level yields. In particular, the yield coverage level (ψ) under GRP does not define the upper limit of indemnification, as it does under BUP and CAT. Farmers can select price protection levels π ∈ ΠGRP ≡ {0.9, 0.95, ..., 1.45, 1.5} and yield coverage levels ψ ∈ ΨGRP ≡ {0.7, 0.75, 0.8, 0.85, 0.9}. CRC is a revenue-protection product and is the most recent of the four programs analyzed. CRC provides a revenue guarantee equal to the revenue the farmer would get if his actual yields were ψ percent [ψ ∈ ΨCRC ≡ {0.7, 0.75, 0.8, 0.85}] of the historical average and the actual price equaled the expected price at planting time. More specifically, per-acre CRC indemnities can be stated as CRC(y, Ph; ψ) = max[0, max(Pp, Ph) × ψ × Y − Ph × y], (4) where Pp and Ph are measures of the planting and harvest prices as defined by the CRC policy. Price Pp (Ph) is the average daily settlement price during the month prior to planting (harvest month) of the futures contract month immediately following harvest. From (4), it is clear that CRC indemnities depend crucially on market prices. This is in sharp contrast with BUP, CAT, and GRP indemnities, for which market prices are irrelevant. RMA obligations on the policies written by insurers are determined from the indemnity levels described in the SRA. At the insurer’s discretion, each of its written policies may be ceded to RMA outright (if the policy is sufficiently undesirable) or allocated to one of three different funds which determine the level of risk transferred to the RMA and the level maintained by the insurer. In this manner, the insurer may rid itself of its most undesirable policies and attenuate the risk of the portfolio of policies that it keeps. In decreasing order of risk, the RMA funds are designated Assigned Risk Fund (ARF), Development Fund (DF), and Commercial Fund (CF). The high-risk policies that the insurance company elects to keep are placed in ARF, in which the overwhelming 4 / Mason, Hayes, and Lence majority of profits and losses are yielded to the RMA. Due to their high risk for RMA, for each state there is a limit on the total value of policies that can be placed in ARF. At the opposite end of the spectrum, insurers will designate as CF only the policies perceived to pose the least amount of risk to the firm and/or those that stand to yield the greatest profits. Simulation Model Estimating the probability density function (pdf) of RMA’s net income from reinsurance is a complex modeling problem. Schematically, the procedure advocated here requires first completing the following tasks: 1. Estimating county-level yield pdfs and U.S. level price pdfs that reflect historical patterns. 2. Calibrating insurance policies and within-county yield pdfs, by using historical insurance data. 3. Assigning insurance policies to reinsurance funds, based on historical reinsurance data. Having finished the three tasks above, Monte Carlo simulations are performed to draw a large number of simulated “annual” observations on crop yields and prices. In turn, these are used to compute simulated “annual” observations on RMA’s net income from reinsurance. The histogram of the latter series provides an estimate of the unknown pdf of RMA’s net income from reinsurance. A more detailed description of the whole process is provided next. Simulation of County-Level Yields Before employing historical yields for estimation purposes, it is imperative to correct them for the significant productivity advances that occurred over the period analyzed. The large positive trends in the yields of corn, soybeans, and wheat reported in Table 1 provide strong evidence of the need for such a correction. Table 1 contains estimates of the regression: Systemic Risk in U.S. Crop and Revenue Insurance Programs / 5 TABLE 1. Ordinary least-squares regression estimates of U.S. yields against time, 1972 through 1997 Note: ** denotes significantly different from zero at the 1 percent level based on the two-tailed t-statistic. Variables with hats ( ˆ ) denote sample estimates. Numbers between parentheses below coefficient estimates are the respective standard deviations. ln(yUSt) = a0 + a1 t + et, (5) where yUSt represents U.S. yield in year t, et is an error term, a0 is the intercept, and a1 is the percentage annual change in yields (source: USDA-NASS). Following Miranda and Glauber, all of the historical yields used in the remainder of the study consist of 1997equivalent yields, obtained by detrending the original yields by means of the percentage annual yield change estimates shown in Table 1. Estimation of County-Level Yield pdf’s. Skewness in crop yields has been identified (e.g., Gallagher; Ramirez) and is particularly important for this study in which insurance payments result from lower-than-average yields. Although Just and Weninger have raised concerns regarding the methods used to reject normality in the distribution of yields, the beta pdf has been used to model the behavior of yields in various studies as a means of capturing potential skewness (e.g., Nelson and Preckel; Babcock and Hennessy). Here we adopt the beta pdf (6) because it can reflect various levels of skewness and kurtosis, and its most appropriate shape can be estimated with historical data rather than imposed in an ad hoc manner. B(y| α, β, Y, Y) ≡ ) ( ) ( ) ( β Γ α Γ β + α Γ 1 L U 1 U 1 L ) Y Y ( ) y Y ( ) Y y ( − β + α − β − α − − − for Y ≤ y ≤ Y. (6) Regression Model: ln(yUSt) = a0 + a1 t + et. Corn Soybeans Wheat 0 â a 4.5276** 3.4220** 3.4158** (0.0268) (0.0176) (0.0153) 1 â 0.01803** 0.01453** 0.00875** (0.00357) (0.00235) (0.00197) R 0.430 0.614 0.442 Number of observations 26 26 26 6 / Mason, Hayes, and Lence In (6), Y (Y) is the lower (upper) limit of the feasible range for random variable y, Γ(⋅) denotes the gamma function, and α and β are parameters which influence the shape of the pdf. Using 1997-equivalent county yields from 1972 through 1997, a separate beta pdf was fitted for each individual county i, relying upon the method of moments. This was accomplished by setting the lower bound for yields equal to zero for all counties ( L i Y = 0 ∀ i), estimating county i’s mean yield (μi) and yield variance ( 2 i σ ), plugging in such values along with county i’s maximum observed yield ( U i y ) in equations (7) through (9), and solving the latter for the numerical values of αi, βi, and U i Y .