Tags: premium principles, agricultural insurance ratemaking, systemic risk, reweighting, weighted distribution
More from: Wenjun Zhu, Ken Seng Tan, Lysa Porth

Agricultural insurance is recognized as one of the most rapidly growing insurance markets (Swiss Re, 2013a). Over the past several decades, it has played an increasingly important role in helping to improve food productivity, achieve food security and protect economic growth (Porth and Tan, 2015; Swiss Re, 2013b). For example, the exposure of the U.S. crop insurance program was approximately USD 117 billion in 2012, with program of USD 14.1 billion (Shields, 2013). The respective figures for Canada are CAD 17.3 billion and CAD 1 billion (Agriculture and Agri-Food Canada (AAFC), 2012). The crop insurance sector has experienced rapid growth since 2005, largely due to emerging markets driven by major growth in Brazil, China and India (Swiss Re, 2013a). As agricultural insurance programs continue to grow in terms of scale and scope, actuarial foundations have become more important in order to ensure that programs are efficient and actuarially sound. Therefore, central to crop insurance programs worldwide is the ability to determine actuarially fair and sustainable premium rates (Babcock et al., 2004; Woodard, 2014).

Determining the actuarially fair premium rate can be a challenging task, especially in the case of agricultural insurance. This is attributed to a number of challenging issues including systemic risk, moral hazard, adverse selection, as well as scarcity and credibility (Chambers, 1989; Duncan and Myers, 2000; Glauber, 2004; Goodwin and Ker, 1998; Ker and Goodwin, 2000; Nelson and Loehman, 1987; Skees and Reed, 1986; Woodard and Garcia, 2008). Agriculture is a highly weather-sensitive sector that is largely exposed to increasingly adverse weather conditions (Barnett and Mahul, 2007; Brockett et al., 2009). As a result, systemic risks, such as weather risk, have become a key focus for financial regulators, given these risks can be very difficult to predict and often they have a huge impact on the insurance portfolio (Okhrin et al., 2013; Woodard and Garcia, 2008). As a result, it is imperative to incorporate systemic risk factors into the pricing framework for P&C insurance in general, and agricultural insurance specifically. As well, it is well documented in literature that information asymmetry, including adverse selection and moral hazard, makes pricing crop insurance premiums difficult (Glauber, 2004; Woodard and Garcia, 2008). While information asymmetry is present in all types of insurance, it can be particularly challenging in agriculture in part due to the fact that the experience can be quite scarce and there is often concerns over its’ credibility (Porth et al., 2015). For example, in most countries there is only one growing season per year, and hence only one observation per year. In countries with developed crop insurance programs where there is a long time series of historical records, this means that approximately 30-40 years of annual historical observations can be used for rating products (Porth et al., 2014). However, there is a concern that older experience may not be as relevant today due to program modifications, technological advancements, deviations in farming practices, changes in climate, etc. (Woodard et al., 2012a). Coupled with the fact that extreme agricultural insurance losses, such as floods and droughts, tend to occur relatively infrequently, there is a need to balance using as much of the time series as possible to capture theses significant events, versus the concern that older may not be credible and, therefore, should be discarded. For most P&C insurance lines the premium is intended to cover the expected , plus a loading charge for administration and operating, as well as uncertainty and profit, and possibly other fees, such as product research and development, of contingent capital, return on equity, etc. However, most crop insurance programs differ as they are delivered via unique partnership models involving risk-sharing arrangements between government and the private sector. This usually involves the government providing a subsidy for premiums as well as covering the full of administration and operating. Therefore, crop insurance premiums are set to cover only the expected and a relatively small loading to maintain a reasonable reserve. This means that for most crop insurance programs, such as in the U.S. and Canada, premiums do not include a charge for administration and operating and there is also no provision for profit loadings (Agriculture and Agri-Food Canada (AAFC), 2012; Coble et al., 2013). Over the past decade there has been more attention from government on making crop insurance programs actuarially sound, and this means that rates should be “actuarially fair for all insurance products, in all regions, and ideally for all producers” (Coble et al., 2013).

There is a rich body of literature that has focused on improving crop insurance pricing methods, and to-date most of this research has focused on the U.S. crop insurance system (Babcock et al., 2004; Poon and Lu, 2015; Rejesus et al., 2006; Woodard et al., 2012b; Woodard and Sherrick, 2011). Most crop insurance ratemaking approaches are based on a relatively straightforward method using the simple average of the historical ratio (LCR), which is defined as the ratio of indemnities to liabilities (Borman et al., 2013). However, the presence of systemic risks, including extreme weather events and commodity market volatility, for examples, may make the current market approach inadequate and subject to mispricing. Further, the challenges regarding scarcity and credibility may make the current market practice for pricing limited. To help overcome these problems, recent research has discussed more comprehensive approaches to pricing in agricultural insurance, including methods to scientifically reweight historical losses from different dimensions to accommodate and adjust for various risk factors. For example, Coble et al. (2011) and Borman et al. (2013) propose to improve pricing through incorporating weights into the in order to reflect program changes and weather patterns. Woodard (2014) constructs a conditional Weibull distribution model that integrates weather variables and technology evolutions into crop yields explicitly. Porth et al. (2014) propose a “liability weighted” LCR to aggregate historical and introduce a modified credibility model to weight the experiences from different geographical regions to enhance the reinsurance pricing model.

This paper contributes to the literature by formalizing the reweighing of historical losses with systemic risk factors using a new class of premium principle, known as the multivariate weighted premium principle (MWPP), in order to improve the actuarial soundness of premiums in the context of agricultural insurance. A key advantage of the MWPP is that it provides a flexible framework to incorporate the weighting of important auxiliary factors. These auxiliary factors may include variables that represent economic and market conditions, weather, soil, etc. Through considering a more comprehensive approach to pricing, it is expected that the incorporation of variables that represent systemic risk will help to overcome the problem of scarcity and credibility. This idea is motivated by empirical pricing results in agricultural insurance and reinsurance ratemaking, as well as the probability proportional to size sampling method that is widely used in statistical sampling (Patil et al., 1986; Rao, 1965). In this paper, a unique set obtained from Manitoba Agricultural Services Corporation, which corresponds to the entire crop insurance program in the province of Manitoba, Canada, is used to empirically examine the proposed MWPP, and compare it to a number of well-known insurance premium principles. The results suggest that incorporating auxiliary information into the crop insurance ratemaking approach can improve the accuracy of pricing for crop insurance. In particular, the proposed MWPP has the property of attaching increased loading to the higher risk reinsurance contract layers, ensuring the insurers and reinsurers to achieve long-term sustainability.

The complete paper is available at:
https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2835481.