Livestock Gross Margin Insurance for Dairy: Designing Margin Insurance Contracts to Account for Tail Dependence Risk

Livestock Gross Margin Insurance for Dairy Cattle (LGM-Dairy) is a recently introduced tool for protecting average income over feed cost margins in milk production. In this paper we examine the assumptions underpinning the rating method used to determine premiums charged for LGM-Dairy insurance contracts. The first test relates to the assumption of lognormality in terminal futures prices. Using high-frequency futures and options data for milk, corn and soybean meal we estimate implied densities with flexible higher moments. Simulations indicate there is no strong evidence that imposing lognormality introduces bias in LGM-Dairy premiums. The remainder of the paper is dedicated to examining dependency between milk and feed marginal distributions. The current LGM-Dairy rating method imposes the restriction of zero conditional correlation between milk and corn, as well as milk and soybean meal futures prices. Using futures data from 1998-2011 we find that allowing for non-zero milk-feed correlations considerably reduces LGM-Dairy premiums for insurance contracts with substantial declared feed amounts. Further examination of the nature of milk-feed dependencies reveals that Spearman’s correlation coefficient is mostly reflecting tail dependence. Using the empirical copula approach we find that non-parametric method of modeling milk-feed dependence decreases LGM-Dairy premiums more than a method that allows only for linear correlation. Unlike other situations in portfolio risk assessment where extremal dependence increases risk, in agricultural margins, tail dependence between feed and the Class III milk price may actually decrease insurance risk, and reduce actuarially fair premiums.