the beta distribution. In other words, among the 25 alternative distributions considered, the beta
distribution was found to be the best fit for the sample data.
The hedging analyses were conducted under the assumption that an Iowa corn yield
contract and an Illinois soybean yield contract can be used. This assumption was made last year,
and reflects our (incorrect) prediction about the type of contracts that would be available to
Illinois producers in 1996.
Results
Gross revenue realizations are computed for each of the marketing strategies described
above. A fixed level of cost, representing all production costs except land costs, is subtracted
from each gross revenue realization to compute net revenue realizations. The parameter values
used for the simulation analysis are described in Table 3. The resulting distributions are analyzed
in two contexts -- hedging effectiveness (HE) and the frequency distribution of net revenue
realizations. HE indicates the level of variance reduction achieved through the use of a risk
management tool, and is measured here in a way that requires explicit incorporation of basis risk.
HE is computed as: [1- (VAR(HR)∕VAR(UHR))] where VAR is the variance operator, HR is the
hedged revenue and UHR is the unhedged revenue3.
We first illustrate the impact of yield basis risk. Recall that basis risk is reflected in the
simulations through 'cp, 'cy, 'sp, and 'sy; i.e., the correlation coefficients between the intra-year
changes in the Wiener processes associated with the cash and futures processes of corn prices
and yields, and of soybean prices and yields. It is expected that the largest source of basis
uncertainty for a Champaign county cash grain farm pertains to corn yield basis. We compute
revenue realizations following equation (2) using a range of values for 'cy (0.2 to 1.0) but holding
the values of 'cp , 'sp and 'sy constant at 0.973, 0.995 and 0.876. The resulting frequency
distributions and the corresponding HE measures are reported in Table 4. As 'cy increases the
resulting revenue distribution tightens. Correspondingly, HE increases from 0.23 to 0.92 as 'cy
increases from 0.2 to 1.0, indicating that hedging effectiveness for a producer using crop yield
futures depends critically on the yield basis risk. It is important to emphasize in this context that,
unlike cash and futures prices which tend to be highly correlated, farm yields are not necessarily
correlated highly with the state average yield (Iowa for corn and Illinois for soybeans). This
implies that even though price basis risk does not vary widely across the Midwest, yield basis
risk may vary substantially and thus the effectiveness of the yield hedge for individual producers
may vary by location even within the Midwest. The ability to widen the geographical area to
reduce basis risk may prove particularly useful when using yield futures. For example, large
grain companies or insurers may be able to reduce basis risk considerably by covering large
areas, and then offer secondary contracts to producers that reflect this decreased basis risk. In the
subsequent analysis, 'cy is fixed at 0.621 which is the estimated correlation coefficient between
the changes in corn yields for Champaign county and Iowa.
Above, the hedge ratios for both price and yield contracts are assumed to be one,
implying a full hedge. We search for “optimal hedge ratios# for the price and yield contracts by
parametrically varying the hedge ratios associated with price and yield for corn and soybeans
3See Hauser, Garcia and Tumblin for a detailed discussion on HE.