From an underwriting point of view, few lines of business are as complex and challenging as crop insurance. Contrary to commercial and residential exposures—which are relatively static over time—crop losses are much more complex to analyze.

Every year, farmers alter the crop exposure landscape by choosing to plant more or less of a particular crop—a choice that is guided, for the most part, by an expectation of the highest profit they can obtain at harvest time. Technological improvements have increased the ability of crops to recover and produce average yields, even after a growing season that got off to a bad start. The accumulated effect of adverse weather during the growing season will not be known with certainty until harvest time—once the crop is harvested, weighed, and marketed and insured losses have been reported. Overall, in non-irrigated agricultural systems in the United States, near-term weather variability and long-term climate change are the major influences of production variability (Lobell and Asner 2003; and North 2008). Because losses in agricultural production areas are spatially correlated, catastrophic weather events such as droughts or floods will trigger widespread insured losses in a company's crop insurance portfolio. Eventually, if the pervasive weather conditions persist (i.e., the 1988 summer-long drought and the 1993 and 2008 floods that affected the Midwest states), crops will fail entirely and insurance companies will be liable for billions of dollars in insured losses (U.S. Department of Commerce 2008).

This article discusses ways in which catastrophe risk modeling can be used in agriculture as a planning tool to anticipate the likelihood and severity of potential future weather-based catastrophic events, ultimately permitting crop insurance companies and policy makers to better prepare for the financial impact of natural disasters. Using the crop insurance industry exposure information for 2007, we model the probability of weather-related catastrophic losses for different return periods and draw conclusions for the overall profitability of the program. We anticipate increased interest and participation from the global reinsurance market serving the U.S. crop insurance program as well as the development and use of novel risk management instruments that will complement traditional reinsurance.

## Inside a Catastrophe Risk Model for Agriculture

Following a schematic framework developed by AIR (Vergara 2007), figure 1 shows the principal components of a catastrophe risk model for agriculture.

Figure 1

Components of a catastrophe risk model for agricultural insurance

Figure 1

Components of a catastrophe risk model for agricultural insurance

### Hazard Component

The hazard component involves quantifying the impact that weather risk has on the historical crop yield data using an Agricultural Weather Index (AWI) model. The AWI model is crop and county specific and uses a high-resolution grid of daily temperature and precipitation data available from the National Center for Environmental Prediction (NCEP). The spatial resolution of the gridded data is 50 kilometers for temperature and 25 kilometers for precipitation. The AWI model also uses a high-resolution (1 kilometer) soil characterization of water holding capacity database available from the U.S. Geological Survey This information is combined with crop-specific data to produce a water balance model that correlates water availability to crops during the growing season with the crop requirements based on phenological information from experimental stations. The end result is a single-index value that condenses all the weather effects experienced by a crop in the field into a single-index number that is a quantifierof how good (or detrimental) the entire growing season has been to crops and its influence on the yield outcome. There is one AWI value per county and crop for each one of the last thirty-four years in our database. Because direct use of observed yields is inappropriate (Goodwin and Ker 1998), a previous detrending step is always involved when utilizing crop yield time series information. In this case, the AWI value is later used as a weather correction to properly detrend the historical yield time series. After detrending, crop yield distributions are fitted to the historical yield data to be used in the crop insurance portfolio risk analysis (Zuba, Vergara, and Doggett 2005). A potential advantage of the AWI-based yield distributions over other types of models proposed by the agricultural economics literature (Ker and Goodwin 2000; Ramirez, Misra, and Field 2003; and Sherrick et al. 2004) is that by construction, they should be more suitable to assess weather-derived crop yield losses.

### Yield/Price Component

In addition to yield modeling, a price modeling component is necessary in response to the increasing share of revenue-based policies and decreasing share of yield-based policies in today's crop insurance program. This is particularly important due to the high degree of commodity price volatility currently observed in the futures markets. Generally speaking, a simple price model will look at the historical relationship between the planting and harvesting prices and the nationwide crop yields. The yield and price distributions are jointly combined to construct a stochastic event catalog of 10,000 loss event scenarios using Monte Carlo techniques. The county loss event scenarios are aggregated at the state and nationwide levels to provide 10,000 stochastic yield and price scenarios that are equally likely to occur next year. When compiling the nationwide stochastic event catalog, it is critical to make sure that the natural crop yield correlation between neighboring counties and between crops within a county is maintained.

### Financial Component

Here, the crop insurance policy conditions are applied to the modeled yield and price scenarios on a county-by-county basis in the stochastic event catalog to calculate the potential indemnities. These are aggregated at the state level in order to quantify the gross insured losses from all the company's underwritten policies (also known as the “company's book of business”). Because the reinsurance market is mostly interested in the retained company losses, the portfolio losses are also reported on a post-Standard Reinsurance Agreement (SRA) basis once the reinsurance protection offered to the industry by the SRA has been accounted for (Glauber 2004). The insured loss calculation output provides risk managers with a range of potential losses on their crop insurance portfolio and the corresponding probability that each level of loss will occur. This information is presented in the form of exceedance probability curves and as average annual losses.

## Different Uses of Catastrophe Risk Modeling Output

The primary purpose of catastrophe risk modeling in agriculture is to estimate—for a company or government agency—the portfolio loss potential due to adverse weather events. This estimation provides a critical tool for optimizing risk management strategies, such as those described below.

### Quantifying Reinsurance Coverage Needs

For a crop insurance company interested in protecting its agricultural portfolio, catastrophe risk modeling represents the best way to determine the necessary reinsurance coverage limits. Simulating thousands of potential outcomes of yield and price event scenarios, models compute loss distributions and produce loss exceedance probability curves that allow risk managers to align their reinsurance buying more closely with their companies' risk tolerance levels.

### Optimizing Premium Cession/Retention to the SRA Funds

Crop insurance risk managers must decide on the policies and corresponding premiums allocated to the different SRA funds, as well as the premium retention within each SRA fund that will optimize the profitability of their book of business (Vedenov et al. 2006; Coble, Dismukes, and Glauber 2007). Models can help crop insurance companies to do side-by-side comparison of various policy allocation and retention scenarios, including the probable gains and losses of each approach.

### Managing Exposures

Catastrophe risk modeling can provide a crop insurance company with insight into more effective ways to manage its risk exposure. Currently, this is a topic that has garnered significant attention from policy makers: a recent report by the U.S. Government Accountability Office (2007a) on the impact of climate change recommended the use of catastrophe models by the U.S. Department of Agriculture Risk Management Agency (RMA) to develop “realistic scenarios of future losses under anticipated climatic conditions and expected exposure levels.” A major advantage of using a weather-based modeling approach is that the yield distributions used in the portfolio loss calculations are detrended for both technology and climate change.

### Negotiating Insurance Coverage in Even Terms

The acceptance and use of catastrophe risk modeling among insurance and reinsurance companies is widespread. Today, most global reinsurers and reinsurance brokers use models to rate and price crop insurance deals. Therefore, the use of catastrophe risk models by crop insurance companies works in their favor by leveling the information playing field. Also, sharing modeling results with reinsurance underwriters, particularly when the analysis includes levels of detail to which the underwriter would not normally have access, can be a powerful tool when negotiating renewal of the company's annual reinsurance contracts such as quota shares (in which the reinsurer participates in the actual gains and losses of the company) or excess of loss agreements (in which the reinsurer is liable for any company loss in excess of a specified retention).

### Communicating with Management and Rating Agencies

As risk managers continue to become more visible under the current wave of mergers and acquisitions affecting the crop insurance industry (for example the recent acquisitions of ARMTech by Endurance Specialty Holdings and Agro National by Renaissance Re), they will also be increasingly held accountable for their decisions, such as what portion of their book of business should be ceded for reinsurance or retained for self-insurance. When dealing with management and rating agencies, decisions that have an economic impact on the company's profitability should be justified, and catastrophe risk models provide an explicit source of justification.

## Modeling the Profitability of the Crop Insurance Industry Portfolio

One of the most controversial points of disagreement among politicians involves budgetary cuts to the federal crop insurance program to fund the new five-year Farm Bill. On one hand some policy makers argue that these cuts have merit given the abnormally high levels of return observed by the industry in the past years (U.S. Government Accountability Office 2007b). Conversely, the industry argues that profitability is important in order to maintain a high level of service to farmers as well as to build capital reserves against the likelihood of widespread liabilities in the future (Grant Thornton LLP 2007). What is the most likely level of profitability for the industry in any given year given multiple potential yields, prices, and environmental outcomes? What are the maximum probable losses that the industry can sustain, and what are the return periods of such losses? Catastrophe risk models can help address these challenging questions.

The data used in the crop insurance industry portfolio analysis consisted of the 2007 gross and retained premium information (per state and SRA fund). This information was retrieved from the RMA Summary of Business online application. The modeled exposure consisted of a total of $6.54 billion in gross premiums and$5.15 billion in retained premiums distributed among the seven SRA funds, for a total of premiums retained of 79%.

Table 1 presents a breakdown of the post-SRA loss ratios and average annual gains and losses per SRA reinsurance fund based on the 2007 crop insurance exposure data. The agricultural loss model uses the information provided on gross premium and retained premium to calculate the average annual retained loss ratios post-SRA by applying the state-specific SRA rules and regulations to the retained losses/gains and premiums. Finally, the 2007 crop insurance industry average annual gains and losses are calculated from the average annual retained loss ratios post-SRA applied to the retained premiums. Based on the fund allocation and retention (79% of the premiums) proportions used by the industry for the 2007 crop year, the average loss ratio post-SRA for the whole industry book of business is 80%. The average annual program gains and losses for the industry fund designation in 2007 is a gain of $1 billion (before applying the 5% mandatory quota share with the RMA), which represents an average return on retained premiums of 20%. Table 1 Industry Loss Ratios and Losses from 2007 Fund Allocation  SRA Fund Allocation (Percent) Retention (Percent) Gross Premium (Millions) Retained Premium (Millions) Loss Ratios Post-SRA (Percent) Losses Post-SRA (Millions) A. Risk fund 22 18 1,451.3 265.8 103 −7.9 D. Fund-buy up 2 74 158.7 117.4 94 7.1 D. Fund-CAT < 1 89 5.7 5.1 129 −1.5 D. Fund-revenue 9 78 602.8 471.8 94 28.3 C. Fund-buy up 10 98 679.4 666.9 77 153.3 C. Fund-CAT 4 100 255.5 255.5 89 28.1 C. Fund-revenue 52 100 3,381.7 3,365.2 75 841.3 Total 100 79 6,535.1 5,147.7 80 1,048.7  SRA Fund Allocation (Percent) Retention (Percent) Gross Premium (Millions) Retained Premium (Millions) Loss Ratios Post-SRA (Percent) Losses Post-SRA (Millions) A. Risk fund 22 18 1,451.3 265.8 103 −7.9 D. Fund-buy up 2 74 158.7 117.4 94 7.1 D. Fund-CAT < 1 89 5.7 5.1 129 −1.5 D. Fund-revenue 9 78 602.8 471.8 94 28.3 C. Fund-buy up 10 98 679.4 666.9 77 153.3 C. Fund-CAT 4 100 255.5 255.5 89 28.1 C. Fund-revenue 52 100 3,381.7 3,365.2 75 841.3 Total 100 79 6,535.1 5,147.7 80 1,048.7 Table 2 shows the estimated probability distribution of annual losses for the 2007 crop insurance exposure data. In table 2 probabilities of exceedance are expressed as return periods. The industry ten-year occurrence return period mean loss is$201 million, which corresponds to a loss ratio post-SRA of 104%. In other words the probability of losses being equal to or exceeding $201 million on any given year is 10%. There are no modeled losses for the five-year return period and below. The industry 1,000-year occurrence return period mean loss is$1.9 billion, which corresponds to a loss ratio post-SRA of 138% . Extreme occurrence losses in excess of the 1,000-year return period (which is equivalent to a 0.1% probability of occurrence) are still possible. They have, however, a very low probability of occurrence.

Table 2

Industry Loss Ratios and Losses from 2007 Fund Allocation for Different Return Periods

 Return Period (Years) Gross Losses (Millions) Gross Loss Ratios (Percent) Losses Post-SRA (Millions) Loss Ratios Post-SRA (Percent) 5 550.7 108 −454.3 91 10 2,060.8 132 200.8 104 20 3,451.6 153 649.8 113 50 5,566.9 185 1,195.2 123 100 6,732.1 203 1,461.4 128 500 8,643.1 232 1,785.8 135 1,000 9,274.6 242 1,936.6 138
 Return Period (Years) Gross Losses (Millions) Gross Loss Ratios (Percent) Losses Post-SRA (Millions) Loss Ratios Post-SRA (Percent) 5 550.7 108 −454.3 91 10 2,060.8 132 200.8 104 20 3,451.6 153 649.8 113 50 5,566.9 185 1,195.2 123 100 6,732.1 203 1,461.4 128 500 8,643.1 232 1,785.8 135 1,000 9,274.6 242 1,936.6 138

## Modeling the Profitability of the Crop Insurance Industry Portfolio in Selected Corn Belt States

According to RMA data, a major portion of the 2007 crop insurance industry gross premiums ($2.8 billion) are concentrated in the seven Corn Belt states of Illinois ($620.4 million), Iowa ($600.4 million), Nebraska ($447.4 million), Kansas ($442.4 million), Indiana ($300.9 million), Ohio ($193 million), and Missouri ($187.8 million). The high concentration of retained premium in this region makes it of special significance to evaluate the potential impact to the industry from weather-related catastrophe losses that have occurred in the past and could occur again in the future. Table 3 presents a breakdown of the industry 2007 post-SRA loss ratios as well as average annual gains and losses per SRA reinsurance fund for the seven Corn Belt states. Based on the fund allocation and retention (88% of the premiums) proportions used by the industry for the 2007 crop year in these seven Corn Belt states, the average loss ratio post-SRA for the whole industry book of business is now 76%. The average annual program gains and losses for the industry fund designation in 2007 is a gain of $572 million (before applying the 5% mandatory quota share with the RMA), which represents an average return on retained premiums of 24%. Table 3 Loss Ratios and Average Gains and Losses from 2007 Fund Allocation in Selected States  SRA Fund Allocation (Percent) Retention (Percent) Gross Premium (Millions) Retained Premium (Millions) Loss Ratios Post-SRA (Percent) Losses Post-SRA (Millions) A. Risk fund 13 22 376.2 84.4 102 −1.6 D. Fund-buy up 1 78 14.8 11.6 89 1.2 D. Fund-CAT < 1 92 0.3 0.3 125 −0.1 D. Fund-revenue 11 83 300.7 250.4 92 20 C. Fund-buy up 6 100 155.1 155.1 70 46.5 C. Fund-CAT 1 100 31.7 31.7 72 8.8 C. Fund-revenue 69 100 1,913.4 1,913.4 74 497.4 Total 100 88 2,792.2 2,446.9 76 572.2  SRA Fund Allocation (Percent) Retention (Percent) Gross Premium (Millions) Retained Premium (Millions) Loss Ratios Post-SRA (Percent) Losses Post-SRA (Millions) A. Risk fund 13 22 376.2 84.4 102 −1.6 D. Fund-buy up 1 78 14.8 11.6 89 1.2 D. Fund-CAT < 1 92 0.3 0.3 125 −0.1 D. Fund-revenue 11 83 300.7 250.4 92 20 C. Fund-buy up 6 100 155.1 155.1 70 46.5 C. Fund-CAT 1 100 31.7 31.7 72 8.8 C. Fund-revenue 69 100 1,913.4 1,913.4 74 497.4 Total 100 88 2,792.2 2,446.9 76 572.2 Table 4 shows the estimated probability distribution of annual losses for the 2007 crop insurance exposure data in these seven Corn Belt states. Table 4 Losses and Loss Ratios from 2007 Fund Allocation for Different Return Periods in Selected States  Return Period (Years) Gross Losses (Millions) Gross Loss Ratios (Percent) Losses Post-SRA (Millions) Loss Ratios Post-SRA (Percent) 5 121.1 104 −191.9 92 10 1,070.1 138 213.4 109 20 2,115.7 176 578.6 124 50 3,564.8 228 871.7 136 100 4,258.1 252 1,011.6 141 500 5,625.5 301 1,170.2 148 1,000 5,939.4 313 1,226.0 150  Return Period (Years) Gross Losses (Millions) Gross Loss Ratios (Percent) Losses Post-SRA (Millions) Loss Ratios Post-SRA (Percent) 5 121.1 104 −191.9 92 10 1,070.1 138 213.4 109 20 2,115.7 176 578.6 124 50 3,564.8 228 871.7 136 100 4,258.1 252 1,011.6 141 500 5,625.5 301 1,170.2 148 1,000 5,939.4 313 1,226.0 150 The industry ten-year occurrence return period mean loss is$213 million, which now corresponds to a loss ratio post-SRA of 109%. Still, there are no modeled losses for the five-year return period and below. The industry 1,000-year occurrence return period mean loss is \$1.2 billion, which now corresponds to a loss ratio post-SRA of 150%. A marked risk/reward relationship results from the analysis: a more localized portfolio composed of several Corn Belt states with a high percentage of premium retention (88%) will yield a higher average return on retained premium (24%) but will face the risk of a loss ratio of 141% on a 100-year catastrophe event. On the other hand a well-diversified portfolio with less premium retention (79%) is also less profitable (20%) but less risky at the same time since the exceedance probability curve is less steep for higher return periods: the 100-year catastrophe event loss ratio is 128%.

## Assessing the Potential Losses to the Crop Insurance Industry Portfolio from Past Catastrophic Weather Events under Current Program Conditions

How severe would a reoccurrence of significant past catastrophe loss events, such as the drought of 1988 or the flood of 1993, be to the crop insurance industry? According to the U.S. Department of Agriculture (2007), the 239% loss ratio of 1988 is the highest one that the program has experienced since its inception. Similarly, the 219% program loss ratio of 1993 is the second largest one in the last twenty-five years. There have been other notable loss events of a more localized nature, such as the drought event of 2002 that affected Nebraska and Kansas and contributed to the failure of American Growers Insurance Company, one of the largest crop insurance companies at that time, or the most recent localized drought event that affected northern Illinois in 2005.

The recasted loss ratios reflect what the industry losses would be (based in current 2007 premium volume, prices, and program conditions) if past events would repeat again this year. Table 5 shows a recast of the industry losses (gross and post-SRA) between 1988 and 2005. For comparison purposes the historical loss ratios published by the RMA are presented as well. For example the catastrophic year of 1988, which produced a loss ratio of 239%, would not be as detrimental for the industry today, given the amount of premium volume that is currently collected as compared to 1988. Also, a repeat of 1988 in today's market conditions would not be as damaging to the industry because the expected price increases due to weather-related crop failures (once factored-in the revenue products) would offset part of the crop yield losses. As a result, if similar weather conditions that triggered the drought of 1988 were to confront the crop insurance industry today, the modeled loss ratios would be approximately 191% (on a gross basis) and 124% (on a post-SRA basis). On a less diversified portfolio composed of seven Corn Belt states, today's losses from an event similar to the 1988 drought would be somewhat more severe (236% on a gross basis and 134% on a post-SRA basis). According to tables 2 and 4, these levels of loss on a post-SRA basis would correspond approximately to the fifty-year return period in the exceedance probability curves. It is important to mention that although losses are dependent on historical yields and prices, more research is needed to fully understand how current price volatilities are affecting the modeled yield-price relationships as well as any possible implications for the crop insurance products in general and the crop insurance industry losses in particular.

Table 5

Modeled and Historical Loss Ratios for the U.S. Crop Insurance 1988–2005

 Entire Industry Corn Belt States RMA Loss Ratios (Gross) Year Loss Ratios (Gross) Loss Ratios (Post-SRA) Loss Ratios (Gross) Loss Ratios (Post-SRA) 2005 58 67 47 65 59 2004 71 72 53 62 76 2003 72 71 67 70 95 2002 90 80 88 81 139 2001 74 70 43 60 99 2000 77 74 68 72 102 1999 71 72 59 69 105 1998 80 76 67 71 89 1997 42 62 26 57 56 1996 59 68 39 61 81 1995 86 77 79 75 101 1994 57 66 34 58 63 1993 113 100 99 93 219 1992 64 69 35 58 121 1991 79 75 87 81 129 1990 64 68 37 59 116 1989 95 84 87 82 149 1988 191 124 236 134 239
 Entire Industry Corn Belt States RMA Loss Ratios (Gross) Year Loss Ratios (Gross) Loss Ratios (Post-SRA) Loss Ratios (Gross) Loss Ratios (Post-SRA) 2005 58 67 47 65 59 2004 71 72 53 62 76 2003 72 71 67 70 95 2002 90 80 88 81 139 2001 74 70 43 60 99 2000 77 74 68 72 102 1999 71 72 59 69 105 1998 80 76 67 71 89 1997 42 62 26 57 56 1996 59 68 39 61 81 1995 86 77 79 75 101 1994 57 66 34 58 63 1993 113 100 99 93 219 1992 64 69 35 58 121 1991 79 75 87 81 129 1990 64 68 37 59 116 1989 95 84 87 82 149 1988 191 124 236 134 239

## Conclusions

The global reinsurance market serving the U.S. crop insurance program has showed ample capacity. Every renewal season, an increasing number of reinsurance companies compete aggressively to obtain a portion of the premiums offered by the crop insurance companies to the marketplace via traditional quota share or excess of loss programs. Nevertheless, the trend in the reinsurance market is toward an increased use of financial market instruments, such as insurance-linked securities (ILS) and industry loss warranties (ILW). Particularly among the ILS products, there is a growing interest in agricultural catastrophe bonds (Vedenov, Epperson, and Barnett 2006). This push toward an increased level of sophistication in the reinsurance marketplace will eventually result in an increased use of models by risk managers. Leading crop insurance companies adopting models will be able to better communicate with securities investors and rating agencies overseeing a new generation of reinsurance transactions in the marketplace.

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AIR is the leading risk modeling and technology firm specializing in risks associated with natural and man-made disasters. AIR is a wholly owned subsidiary of Insurance Services Office (ISO). The authors gratefully acknowledge the editorial assistance of Meagan White.
This article was presented in a principal paper session at the 2008 AAEA annual meeting in Orlando, FL. The articles in these sessions are not subjected to the journal's standard refereeing process.