Tails Curtailed: Accounting for Nonlinear Dependence in Pricing Margin Insurance for Dairy Farmers

Livestock Gross Margin Insurance for Dairy Cattle (LGM-Dairy) is a risk management tool for protecting milk income over feed cost margins. In this article, we examine the assumptions underpinning the method used to determine LGM-Dairy premiums. Analysis of the milk-feed dependence structure is conducted using copula methods, a rich set of tools that allow modelers to capture nonlinearities in dependence among variables of interest. We find a significant relationship between milk and feed prices that increases with time-to-maturity and severity of negative price shocks. Extremal, or tail, dependence is the propensity of dependence to concentrate in the tails of a distribution. A common theme in financial and actuarial applications and in agricultural crop revenue insurance is that tail dependence increases the risk to the underwriter and results in higher insurance premiums. We present, to our knowledge, the first case in which tail dependence may actually reduce actuarially fair premiums for an agricultural risk insurance product. We examine hedging effectiveness with LGM-Dairy and show that, even in the absence of basis or production risk, hedging horizon plays an important role in the ability of this tool to smooth farm income over feed cost margins over time. Rating methodology that accounts for tail dependence between milk and feed prices extends the optimal hedging horizon and increases hedging effectiveness of the LGM-Dairy program.