Farm/crop portfolio simulations under variable risk: a case study from Italy

Important sources of risk in agriculture are yield and price fluctuations caused by unpredictable and uncontrollable events, inducing income volatility and adding considerable complexity to farmers’ decisions. The literature suggests that these events could affect farmers’ risk aversion in decision making and justify their preferences for risk minimizing and safety-first survival, rather than a profit maximization strategy. The aim of this study is to test this hypothesis by using a quadratic programming in linearized version and the sumex utility function, which is representable as sum of products of polynomials and exponential (or “polynex”) functions to simulate risk aversion for specific traits of the E-V frontier (Nakamura, Mathematical Soc Sci 31:39–47, 1996). The linear approximation of the utility function is obtained with the MOTAD approach, consisting in the minimization of errors generated by total absolute deviations of gross income from the expected value (Hardaker et al. Rev Mark Agric Econ 59:9–22, 1991). This method allows different portfolio simulations to be run of selected cereal and oilseed crops as risky prospects, by varying the risk parametrically. The results obtained confirm the hypothesis that risk affects farmers’ decisions and that crop diversification is a viable strategy as a hedge against risk.