IDEAS home Printed from https://ideas.repec.org/a/ebl/ecbull/eb-22-00684.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.accessecon.com/Pubs/EB/2023/Volume43/EB-23-V43-I2-P61.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Atanu Saha & C. Richard Shumway & Hovav Talpaz, 1994. "Joint Estimation of Risk Preference Structure and Technology Using Expo-Power Utility," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 76(2), pages 173-184.
    2. Smith, William T. & Zhang, Qiang, 2007. "Asset pricing with multiplicative habit and power-expo preferences," Economics Letters, Elsevier, vol. 94(3), pages 319-325, March.
    3. Eaton, Jonathan, 1985. "Optimal and time consistent exchange-rate management in an overlapping-generations economy," Journal of International Money and Finance, Elsevier, vol. 4(1), pages 83-100, March.
    4. Ederington, Louis H, 1979. "The Hedging Performance of the New Futures Markets," Journal of Finance, American Finance Association, vol. 34(1), pages 157-170, March.
    5. Thomas B. Wiens, 1976. "Peasant Risk Aversion and Allocative Behavior: A Quadratic Programming Experiment," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 58(4_Part_1), pages 629-635.
    6. Leland L. Johnson, 1960. "The Theory of Hedging and Speculation in Commodity Futures," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 27(3), pages 139-151.
    7. Rolfo, Jacques, 1980. "Optimal Hedging under Price and Quantity Uncertainty: The Case of a Cocoa Producer," Journal of Political Economy, University of Chicago Press, vol. 88(1), pages 100-116, February.
    8. Friend, Irwin & Blume, Marshall E, 1975. "The Demand for Risky Assets," American Economic Review, American Economic Association, vol. 65(5), pages 900-922, December.
    9. Charles A. Holt & Susan K. Laury, 2002. "Risk Aversion and Incentive Effects," American Economic Review, American Economic Association, vol. 92(5), pages 1644-1655, December.
    10. Paul A. Samuelson, 1970. "The Fundamental Approximation Theorem of Portfolio Analysis in terms of Means, Variances and Higher Moments," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 37(4), pages 537-542.
    11. Willy Kamdem & Jules Sadefo Kamdem & David Kamdem & Louis aimé Fono, 2020. "Risk Aversion and Optimal Hedge Ratio in Commodities Futures Markets," Economics Bulletin, AccessEcon, vol. 40(1), pages 587-600.
    12. John Heaney & Geoffrey Poitras, 1991. "Estimation of the optimal hedge ratio, expected utility, and ordinary least squares regression," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 11(5), pages 603-612, October.
    13. Carl H. Nelson, 2004. "Toward exploring the location-scale condition: a constant relative risk aversion location-scale objective function," European Review of Agricultural Economics, Oxford University Press and the European Agricultural and Applied Economics Publications Foundation, vol. 31(3), pages 273-287, September.
    14. Buccola, Steven T., 1982. "Portfolio Selection Under Exponential And Quadratic Utility," Western Journal of Agricultural Economics, Western Agricultural Economics Association, vol. 7(1), pages 1-10, July.
    15. Hansen, Lars Peter & Singleton, Kenneth J, 1983. "Stochastic Consumption, Risk Aversion, and the Temporal Behavior of Asset Returns," Journal of Political Economy, University of Chicago Press, vol. 91(2), pages 249-265, April.
    16. Mankiw, N Gregory & Shapiro, Matthew D, 1986. "Risk and Return: Consumption Beta versus Market Beta," The Review of Economics and Statistics, MIT Press, vol. 68(3), pages 452-459, August.
    17. Atanu Saha, 1993. "Expo-Power Utility: A ‘Flexible’ Form for Absolute and Relative Risk Aversion," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 75(4), pages 905-913.
    18. Smith, William T., 1991. "Forward exchange rates in general equilibrium," Journal of International Money and Finance, Elsevier, vol. 10(4), pages 497-511, December.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. William T. Smith, 2022. "The optimal hedge ratio: A solution, a conjecture, and a challenge," Economics Bulletin, AccessEcon, vol. 42(2), pages 877-888.
    2. Barbi, Massimiliano & Romagnoli, Silvia, 2018. "Skewness, basis risk, and optimal futures demand," International Review of Economics & Finance, Elsevier, vol. 58(C), pages 14-29.
    3. Masako Ikefuji & Roger Laeven & Jan Magnus & Chris Muris, 2013. "Pareto utility," Theory and Decision, Springer, vol. 75(1), pages 43-57, July.
    4. Emmanuel Jurczenko & Bertrand Maillet & Paul Merlin, 2008. "Efficient Frontier for Robust Higher-order Moment Portfolio Selection," Post-Print halshs-00336475, HAL.
    5. J. François Outreville, 2015. "The Relationship Between Relative Risk Aversion And The Level Of Education: A Survey And Implications For The Demand For Life Insurance," Journal of Economic Surveys, Wiley Blackwell, vol. 29(1), pages 97-111, February.
    6. Troncoso Sepúlveda, Ricardo & Cabas Monje, Juan, 2019. "Factibilidad del uso de contratos de futuros del Chicago Mercantile Exchange para la cobertura del riesgo de precio en el ganado bovino chileno," Revista Lecturas de Economía, Universidad de Antioquia, CIE, issue 90, pages 9-44, January.
    7. Smith, William T. & Zhang, Qiang, 2007. "Asset pricing with multiplicative habit and power-expo preferences," Economics Letters, Elsevier, vol. 94(3), pages 319-325, March.
    8. Hardouvelis, Gikas A. & Kim, Dongcheol & Wizman, Thierry A., 1996. "Asset pricing models with and without consumption data: An empirical evaluation," Journal of Empirical Finance, Elsevier, vol. 3(3), pages 267-301, September.
    9. Inmaculada Rodríguez-Puerta & Alberto A. Álvarez-López, 2016. "Optimal allocation of a fixed production under price uncertainty," Annals of Operations Research, Springer, vol. 237(1), pages 121-142, February.
    10. Pandey, Ajay, 2008. "Hedging Effectiveness of Constant and Time Varying Hedge Ratio in Indian Stock and Commodity Futures Markets," IIMA Working Papers WP2008-06-01, Indian Institute of Management Ahmedabad, Research and Publication Department.
    11. Benninga, Simon & Eldor, Rafael & Zilcha, Itzhak, 1983. "Optimal hedging in the futures market under price uncertainty," Economics Letters, Elsevier, vol. 13(2-3), pages 141-145.
    12. Campbell, John Y, 1993. "Intertemporal Asset Pricing without Consumption Data," American Economic Review, American Economic Association, vol. 83(3), pages 487-512, June.
    13. Wenming Shi & Kevin X. Li & Zhongzhi Yang & Ganggang Wang, 2017. "Time-varying copula models in the shipping derivatives market," Empirical Economics, Springer, vol. 53(3), pages 1039-1058, November.
    14. Peterson, Jeffrey M. & Boisvert, Richard N., 1998. "Optimal Voluntary "Green" Payment Programs To Limit Nitrate Contamination Under Price and Yield Risk," Research Bulletins 122687, Cornell University, Department of Applied Economics and Management.
    15. Ismael Pérez-Franco & Esteban Otto Thomasz & Gonzalo Rondinone & Agustín García-García, 2022. "Feed price risk management for sheep production in Spain: a composite future cross-hedging strategy," Risk Management, Palgrave Macmillan, vol. 24(2), pages 137-163, June.
    16. Benjamin L. Collier & Daniel Schwartz & Howard C. Kunreuther & Erwann O. Michel-Kerjan, 2017. "Risk Preferences in Small and Large Stakes: Evidence from Insurance Contract Decisions," NBER Working Papers 23579, National Bureau of Economic Research, Inc.
    17. Nakashima, Takahiro, 2006. "Linear Structural Models of Production under Price Uncertainty: A Mean-Standard Deviation Approach," Japanese Journal of Agricultural Economics (formerly Japanese Journal of Rural Economics), Agricultural Economics Society of Japan (AESJ), vol. 8, pages 1-11.
    18. Gandelman, Néstor & Hernández-Murillo, Rubén, 2013. "What do happiness and health satisfaction data tell us about relative risk aversion?," Journal of Economic Psychology, Elsevier, vol. 39(C), pages 301-312.
    19. Jakusch, Sven Thorsten, 2017. "On the applicability of maximum likelihood methods: From experimental to financial data," SAFE Working Paper Series 148, Leibniz Institute for Financial Research SAFE, revised 2017.
    20. Inmaculada Rodríguez-Puerta & Alberto Álvarez-López, 2016. "Optimal allocation of a fixed production under price uncertainty," Annals of Operations Research, Springer, vol. 237(1), pages 121-142, February.

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:ebl:ecbull:eb-22-00684. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: John P. Conley (email available below). General contact details of provider: .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.