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The optimal hedge ratio: A closed-form solution, a conjecture, and a challenge

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  • William T. Smith

    (University of Memphis)

Abstract

Calculating the Optimal Hedge Ratio (OHR) is challenging for agricultural exporting countries. The alternatives have been either to rely upon closed-form solutions for the OHR that require unpalatable assumptions (quadratic utility, or CARA utility with Gaussian distributions) or to employ complicated numerical methods. This paper derives an approximate closed-form solution for “compact” distributions with “small” risks. Given empirical distributions of prices and quantities it requires simple calculations to arrive at the OHR for any desired class and calibration of risk preferences. To the extent that futures markets are unbiased, the solution also suggests that a simple minimum-variance calculation be sufficient to calculate the OHR.

Suggested Citation

  • William T. Smith, 2023. "The optimal hedge ratio: A closed-form solution, a conjecture, and a challenge," Economics Bulletin, AccessEcon, vol. 43(2), pages 748-758.
    • Handle: RePEc:ebl:ecbull:eb-22-00684
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    References listed on IDEAS

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    More about this item

    Keywords

    futures markets; optimal hedge ratio;

    JEL classification:

    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • G1 - Financial Economics - - General Financial Markets

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