Abstract
This paper examines the behavior of a competitive firm that faces joint price and inflation risk. Given that the price risk is negatively correlated with the inflation risk in the sense of expectation dependence, we show that the firm optimally opts for an over-hedge (under-hedge) if the firm’s coefficient of relative risk aversion is everywhere no greater (no smaller) than unity. We show further that banning the firm from forward trading may induce the firm to produce more or less, depending on whether the price risk premium is positive or negative, respectively. While the price risk premium is unambiguously negative in the absence of the inflation risk, it is not the case when the inflation risk prevails. In contrast to the conventional wisdom, forward hedging needs not always promote production should firms take inflation seriously.
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Notes
The strict convexity of C(Q) is driven by the firm’s production technology that exhibits decreasing returns to scale.
Throughout the paper, random variables have a tilde (∼) while their realizations do not.
The less likely case wherein \(\tilde {P}\) and \(\tilde {Z}\) are positively expectation dependent can be analogously analyzed.
For any two random variables, \(\tilde {X}\) and \(\tilde {Y}\), it is true that \(\text {Cov}(\tilde {X},\tilde {Y})=\mathrm {E}(\tilde {X}\tilde {Y}) -\mathrm {E}(\tilde {X})\mathrm {E}(\tilde {Y})\).
If R(Π) = 1 for all Π > 0, i.e, the firm has a logarithmic utility function, the firm’s optimal forward position is a full-hedge, i.e., X ∗ = Q ∗.
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Acknowledgments
The authors thank an anonymous referee and Odd Rune Straume (co-editor) for their very helpful comments and suggestion.
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Broll, U., Wong, K.P. The impact of inflation risk on forward trading and production. Port Econ J 14, 65–73 (2015). https://doi.org/10.1007/s10258-015-0109-y
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DOI: https://doi.org/10.1007/s10258-015-0109-y