The expected distribution associated with participation in the deficiency-payment
program (NRDL) is scaled considerably higher than the others, resulting in a mean of about
$170. The probability of falling below $95 is 2.3%.
An important point when comparing the free market distributions to either of the
distributions involving government programs involves the "stability" of the results across
regions. The underlying basis risk of price hedges and particularly yield hedges may vary
considerably from region to region, presumably causing the comparative results between non-
program and program distributions to be sensitive to location.
Finally, one perspective on the impact of changing the yield distribution assumption from
lognormality to beta is offered by comparing the HE results under beta to those under
lognormality. Tables 8 and 9 show the results using the beta assumption. The pure price-hedge
results are similar to those of Tables 6 and 7 because lognormality in prices is used in all cases,
although they are not exactly the same because “revenue,# not “price,” is being hedged. For the
pure yield hedges, the results under lognormality indicated that a small amount of variance
reduction could be obtained by hedging at the 0.4 level. Under beta, pure yield hedges at any
level increase the revenue variance. When using both the price and yield contracts, the “optimal
hedge” for corn is at the hedge ratios of 1.0 for price and 0.6 for yield (versus 0.7 and 0.5 under
lognormality), causing the HE measure to increase to about 39%. For soybeans, the optimal
hedge ratios are 1.0 in price and 0.9 in yield (versus 0.9 and 0.8 under lognormality), causing HE
to increase to 85%.
Regardless of whether yields are lognormal or beta, the HE measure increases
considerably by using both yield and price contracts as opposed to using just one of the contracts.
However, care should be taken in the comparison of HE levels across the different distributional
scenarios because the initial variance that is being reduced has different meanings and because
they are at different levels. Nonetheless, the general results are the same in that (1) there is little
to be gained in revenue hedges from using just the yield contract, (2) price hedges provide much
more revenue protection than yield hedges, (3) combining the two contracts increases hedging
effectiveness considerably, and (4) the optimal hedging ratios for the combined contract use are
“in the same ballpark,” regardless of whether lognormality or beta is assumed.
Conclusions
We draw four major conclusions from the results. First, hedging effectiveness using the
new crop yield contract depends critically on yield basis risk which presumably can be reduced
considerably by covering large geographical areas. Second, crop yield futures can be used in
conjunction with price futures to derive risk management benefits significantly higher than using
either of the two alone. Third, hedging using price and crop yield futures has a potential to offer
benefits larger than those from the simulated revenue assurance program. However, the
robustness of the findings depends largely on whether yield basis risk varies significantly across
regions. Finally, the qualitative results described by the above three conclusions do not change
depending on whether yields are distributed according to the beta or lognormal distribution.