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Estimation of Time-Varying Hedge Ratios for Corn and Soybeans: BGARCH and Random Coefficient Approaches


  • Anil K. Bera

    (University of Illinois at Urbana-Champaign)

  • Philip Garcia

    (University of Illinois at Urbana-Champaign)

  • Jae-Sun Roh

    (Seoul National University)


This paper deals with the estimation of optimal hedge ratios. A number of recent papers have demonstrated that the ordinary least squares (OLS) method which gives constant hedge ratio is inappropriate and recommended the use of bivariate autoregressive conditional heteroskedastic (BGARCH) model. In this paper we introduce the use of a random coefficient autoregressive (RCAR) model to estimate time varying hedge ratios. Using daily data of spot and futures prices of corn and soybeans we find substantial presence of conditional heteroskedasticity, and also of random coefficients in the regressions of return from the spot market on the return from the futures markets. Hedging performance in terms of variance reduction of returns from alternative models are also conducted. For our data set diagonal vech presentation of BGARCH model provides the largest reduction in the variance of the return portfolio.

Suggested Citation

  • Anil K. Bera & Philip Garcia & Jae-Sun Roh, 1997. "Estimation of Time-Varying Hedge Ratios for Corn and Soybeans: BGARCH and Random Coefficient Approaches," Finance 9712007, EconWPA.
  • Handle: RePEc:wpa:wuwpfi:9712007
    Note: Type of Document - pdf; prepared on PC; to print on HP Laserjet; pages: 35; figures: included. Office for Futures and Options Research (OFOR) at the University of Illinois at Urbana-Champaign. Working Paper 97-06. For a complete list of OFOR working papers see

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    References listed on IDEAS

    1. Pagan, Adrian, 1980. "Some identification and estimation results for regression models with stochastically varying coefficients," Journal of Econometrics, Elsevier, vol. 13(3), pages 341-363, August.
    2. Engle, Robert F. & Kroner, Kenneth F., 1995. "Multivariate Simultaneous Generalized ARCH," Econometric Theory, Cambridge University Press, vol. 11(01), pages 122-150, February.
    3. Baillie, Richard T. & Bollerslev, Tim, 1990. "A multivariate generalized ARCH approach to modeling risk premia in forward foreign exchange rate markets," Journal of International Money and Finance, Elsevier, vol. 9(3), pages 309-324, September.
    4. Anderson, Ronald W & Danthine, Jean-Pierre, 1980. " Hedging and Joint Production: Theory and Illustrations," Journal of Finance, American Finance Association, vol. 35(2), pages 487-498, May.
    5. Kroner, Kenneth F. & Sultan, Jahangir, 1993. "Time-Varying Distributions and Dynamic Hedging with Foreign Currency Futures," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 28(04), pages 535-551, December.
    6. Tong, Wilson H. S., 1996. "An examination of dynamic hedging," Journal of International Money and Finance, Elsevier, vol. 15(1), pages 19-35, February.
    7. Ernst R. Berndt & Bronwyn H. Hall & Robert E. Hall & Jerry A. Hausman, 1974. "Estimation and Inference in Nonlinear Structural Models," NBER Chapters,in: Annals of Economic and Social Measurement, Volume 3, number 4, pages 653-665 National Bureau of Economic Research, Inc.
    8. Tae H. Park & Lorne N. Switzer, 1995. "Bivariate GARCH estimation of the optimal hedge ratios for stock index futures: A note," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 15(1), pages 61-67, February.
    9. Baillie, Richard T & Myers, Robert J, 1991. "Bivariate GARCH Estimation of the Optimal Commodity Futures Hedge," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 6(2), pages 109-124, April-Jun.
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    11. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    12. Bera, A.K. & Higgins, M.L., 1990. "A Test For Conditional Heterskedasticity In Time Series Midels," University of Western Ontario, The Centre for the Study of International Economic Relations Working Papers 9003, University of Western Ontario, The Centre for the Study of International Economic Relations.
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    More about this item


    Optimal Hedge Ratios; Conditional Heteroskedasticity; BGARCH;

    JEL classification:

    • C3 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables
    • Q - Agricultural and Natural Resource Economics; Environmental and Ecological Economics
    • Q13 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Agriculture - - - Agricultural Markets and Marketing; Cooperatives; Agribusiness


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