Production and Hedging Decisions in the Presence of Basic Risk: Note
Paroush and Wolf (1989) modeled output hedging in the presence of basis risk. They showed that (in the absence of scale shift) the optimal hedging and output fall in response to basis risk. However, they used a second-order Taylor's approximation of the utility function. Also, they did not show the impact of basis risk on the ratio of hedging to output (hedging as a fraction of output), which is a more relevant variable than the absolute change in either of the decision variables. The absence of such results constitutes a major gap in the hedging literature. Consequently, this note provides two extensions. First, it generalizes Paroush and Wolf's results (Propositions 1 and 2) by using a general utility function and general distributions. Second, it shows the impact of basis risk on the ratio of hedging to output.
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