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William T. Smith
 
''The optimal hedge ratio: A closed-form solution, a conjecture, and a challenge''
( 2023, Vol. 43 No.2 )
 
 
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.
 
 
Keywords: futures markets, optimal hedge ratio
JEL: C6 - Mathematical Methods and Programming: General
G1 - General Financial Markets
 
Manuscript Received : Sep 14 2022 Manuscript Accepted : Jun 30 2023

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