separately from 0.0 to 1.0 in discrete intervals of 0.1. Values of HE under alternatives parametric
assumptions of hedge ratios are presented in Tables 5 and 6. The first column in both tables
represents hedging effectiveness using a pure price hedge, and the first row represents hedging
effectiveness using a pure yield hedge. For corn, the “optimal# hedge ratios for pure price and
yield hedges are 0.6 and 0.4 respectively, resulting in a HE of only 28 percent and 11 percent
respectively. For soybeans, the “optimal# hedge ratios for pure price and yield hedges are 0.7 and
0.4 respectively, resulting in a HE of 53 percent and 10 percent respectively. However, if both
crop yield and price futures are used, HE increases considerably. In the case of corn, HE
increases to about 50 percent using a combination of price (0.7 hedge ratio) and crop yield (0.5
hedge ratio) futures contracts. Similarly, for soybeans, HE increases to 86 percent using a
combination of price (0.9 hedge ratio) and crop yield (0.8 hedge ratio) futures contracts. Thus
these results suggest that price and crop yield futures can be used together to achieve significant
improvements in risk management benefits.
Expected net revenue distributions from cash marketing and various hedging strategies
using “optimal hedge ratios# are compared to those resulting from government programs in
Table 7 in terms of discrete probability densities. The probabilities associated with the scenario
where revenue is determined by just realized price and realized yield (i.e., no hedging or
government program participation) are presented in the NMR column. NHR1, NHR2 and NHR3
represent hedging results using both price and yield futures (NHR1), a pure price hedge (NHR2),
and a pure yield hedge (NHR3). NRDL and NRA represent the expected distribution associated
with a deficiency and loan program (NRDL) and with a revenue assurance program (NRA).
When no hedging strategies are used (NMR), the probability of receiving a net revenue of
$45 to $70 is 7.5%. When hedging with both price and yield contracts, the probability falls to
0.1%. Examination of Table 7 provides perspective on how the use of price and yield contracts
causes the market revenue distribution to collapse. The mean remains at about $134 while, as
expected, the distribution becomes progressively tighter with the use of yield contracts (NHR3),
price contracts (NHR2), and then yield and price contracts (NHR1).
In a safety-first context where, say, $95 is the threshold level, the probability of receiving
less than the threshold level is 24.2% in the no-hedge scenario, NMR. Hedging with the yield
contract reduces the probability to 22.3%. The use of just price contracts reduces it to 17.7%,
and the use of both contracts reduces it to 8%.
Under 70% revenue assurance, the mean increases slightly from about $134 to $135.5 and
the probability of revenue at the lower end of the distribution goes to zero. The probability of
receiving revenue less than the $95 threshold is quite high, as much as 24.2%. The overall risk-
reduction effect seems minimal. Note that the expected average gross revenue is about $262 per
acre and thus the 70% revenue assurance level is about $183. After accounting for non-land
costs, the assured net revenue is about $60. Consequently, because of the relatively low
threshold levels and because of the offsetting effects of corn and soybeans, the truncating effect
on the net revenue distribution is not large.4
4The present analysis ignores any market price effect of programs. It might be argued, for
example, that a revenue-assurance program would cause commodity prices in general to increase
because replacing the deficiency-payment program with a revenue-assurance program would
presumably lead to a decrease in production and an increase in price.