Hedging with a new risk-aversion concept.
In this note, we apply a new definition of risk aversion to the standard hedging model where the firm (producer) is concerned with the negative impact of the shocks. From the perspective of the risk-averse producer, shocks can only have an adverse (or at best neutral) effect (a reduction in output, etc.). Consequently, risk-aversion can be defined in terms of the concerns and outlook of the agent and not the derivatives of a utility function. Contrary to the traditional concept of risk-aversion, a major advantage of this framework is that the attitude toward risk is not synonymous with the attitude toward wealth.
This formulation will significantly affect the standard hedging results obtained by Holthausen (D. Holthausen, American Economic Review, 1979), among others. In this note, contrary to the traditional models, we show the hedge position is independent of the forward price market structure.
Profit is specified by [PI] = p(Y - h) + bh - c(Y), where c is a regular cost function, Yis output, p is the random output price and p = Ep + [sigma][epsilon]. As usual, the firm maximizes its expected utility from profit by:
where U is the utility function (U' > 0). The firm is risk-averse if it specifies output and price as q [less than or equal to] Y and p [less than or equal to] Ep ([epsilon] < 0).
The first-order conditions are
EU'([PI])(p - c'(Y)) = 0 (1)
EU'([PI])(b - p) = (b - Ep)EU' - [sigma]EU'[epsilon] = 0 (2)
Clearly, Ep>b since EU'[epsilon] < 0, even in the case of over-hedging (h>Y). The firm always sets its subjective expected price above the forward price. Thus, the hedge position is independent of the market structure of the forward price b-Ep. Alternatively, risk aversion can be defined as Ep>b, since [epsilon] [less than or equal to] 0 implies Ep>b.
Published online: 3 August 2008
M. Alghalith ([mail])
Econ. Department, University of the West Indies, St. Augustine, Trinidad & Tobago
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|Publication:||Atlantic Economic Journal|
|Article Type:||Brief article|
|Date:||Dec 1, 2008|
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