Spatial Aggregation and Weather Risk Management

in the case that a tail event does occur, and thus is a preference free measure of tail-risk.¹⁴
The expected shortfall measure is used rather than the Value-at-Risk (VaR), which
provides an estimate of the worst loss that one might expect given a tail event does not
occur, because it is subadditive making it less likely to produce puzzling and inconsistent
findings in hedging applications (Dowd and Blake 2006).

Data

The data used are Illinois CRD corn yields for 1971-2002. Illinois consists of nine
CRD’s. Temperature data were collected for a location within each CRD. An attempt
was made to select the most centralized location in each district (Table 1). Yield data
were obtained from the National Agricultural Statistics Service website, and weather data
from United States Historical Climatology Network (USHCN) website. The state level
(i.e. aggregated) yield and ACDD index measures were calculated as a simple average of
the individual district yields and ACDD indexes.¹⁵

Results and Discussion

The results of the hedging analysis appear in Tables 2 and 3. All estimates are obtained
by minimizing SV as outlined above assuming a constant price of $2.50/bu.¹⁶ Results are
presented for the full-sample (Table 2), and then for the 2^nd half (Table 3) sub-sample
period which provides an out-of-sample dimension to the analysis. Out-of-sample
estimates in Table 3 are obtained by applying the in-sample solution for the 1^st half of the
sample to the 2^nd half of the sample.

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