Within the tables, the “Average of Districts” column statistics are calculated as
the average of the individual district statistics, and are presented as a basis of comparison
to the “State (aggregated)” portfolio statistics which are obtained by averaging the data
across districts (i.e. aggregating) and then performing the analysis. Notice, if the weather
effects captured by an ACCD index across districts are relatively uncorrelated and/or the
other factors affecting yields are strongly correlated then the “State (Aggregated)” results
will closely mirror the “Average of Districts” results. Thus, substantial differences in the
risk-reducing effectiveness of WDs for the “State (Aggregated)” portfolio compared to
the “Average of Districts” portfolio indicates that the risk reduction offered by WDs at
the aggregate level is stronger than what would be implied by evaluating the hedging
effectiveness of the individual districts separately.
Statistics measuring changes in RMSL and ES are calculated relative to the
unhedged yield exposures. If the change in RMSL resulting from the addition of a WD is
negative (positive) then the WD is risk-reducing (risk-enhancing), whereas for the ES a
positive (negative) change implies risk-reduction (risk-enhancement).
The results for the full sample are presented in Table 2. The return is the same for
all hedged and unhedged portfolios in-sample, a direct result of fair option pricing.
Hedging effectiveness varied widely across districts, with reductions in RMSL (change in
ES 6%) ranging from 11.45% ($15.58) in the Southwest D80 (East Southeast D70)
region when hedging with swaps, to 41.76% ($67.76) for Southeast D90
(Southeast 90) when hedging with call options. The large variability indicates that at low
levels of aggregation there is a high degree of idiosyncratic risk present in crop yields.
Hedging with options was consistently more effective than hedging with swaps
17
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