Encyclopedia of Finance

2013 Edition
| Editors: Cheng-Few Lee, Alice C. Lee

Futures Hedge Ratios: A Review

  • Sheng-Syan Chen
  • Cheng-Few Lee
  • Keshab Shrestha
Reference work entry
DOI: https://doi.org/10.1007/978-1-4614-5360-4_74

Abstract

This paper presents a review of different theoretical approaches to the optimal futures hedge ratios. These approaches are based on minimum variance, mean-variance, expected utility, mean extended-Gini coefficient, semivariance and Value-at-Risk. Various ways of estimating these hedge ratios are also discussed, ranging from simple ordinary least squares to complicated heteroscedastic cointegration methods. Under martingale and joint-normality conditions, different hedge ratios are the same as the minimum variance hedge ratio. Otherwise, the optimal hedge ratios based on the different approaches are in general different and there is no single optimal hedge ratio that is distinctly superior to the remaining ones.

Keywords

Cointegration Gini coefficient Hedge ratio Minimum variance Semi variance 
This is a preview of subscription content, log in to check access.

References

  1. Baillie, R.T., & Myers, R.J. (1991). Bivariate Garch estimation of the optimal commodity futures hedge. Journal of Applied Econometrics, 6, 109–124.CrossRefGoogle Scholar
  2. Bawa, V.S. (1978). Safety-first, stochastic dominance, and optimal portfolio choice. Journal of Financial and Quantitative Analysis, 13, 255–271.CrossRefGoogle Scholar
  3. Benet, B.A. (1992). Hedge period length and ex-ante futures hedging effectiveness: the case of foreign-exchange risk cross hedges. Journal of Futures Markets, 12, 163–175.CrossRefGoogle Scholar
  4. Cecchetti, S.G., Cumby, R.E., & Figlewski, S. (1988). Estimation of the optimal futures hedge. Review of Economics and Statistics, 70, 623–630.CrossRefGoogle Scholar
  5. Chen, S.S., Lee, C.F., & Shrestha, K. (2001). On a mean-generalized semivariance approach to determining the hedge ratio. Journal of Futures Markets, 21, 581–598.CrossRefGoogle Scholar
  6. Cheung, C.S., Kwan, C.C.Y., & Yip, P.C.Y. (1990). The hedging effectiveness of options and futures: a mean-Gini approach. Journal of Futures Markets, 10, 61–74.CrossRefGoogle Scholar
  7. Chou, W.L., Fan, K.K., & Lee, C.F. (1996). Hedging with the Nikkei index futures: the conventional model versus the error correction model. Quarterly Review of Economics and Finance, 36, 495–505.CrossRefGoogle Scholar
  8. Crum, R.L., Laughhunn, D.L., & Payne, J.W. (1981). Risk-seeking behavior and its implications for financial models. Financial Management, 10, 20–27.CrossRefGoogle Scholar
  9. D’Agostino, R.B. (1971). An omnibus test of normality for moderate and large size samples. Biometrika, 58, 341–348.CrossRefGoogle Scholar
  10. De Jong, A., De Roon, F., & Veld, C. (1997). Out-of-sample hedging effectiveness of currency futures for alternative models and hedging strategies. Journal of Futures Markets, 17, 817–837.CrossRefGoogle Scholar
  11. Dickey, D.A., & Fuller, W.A. (1981). Likelihood ratio statistics for autoregressive time series with a unit root. Econometrica, 49, 1057–1072.CrossRefGoogle Scholar
  12. Ederington, L.H. (1979). The hedging performance of the new futures markets. Journal of Finance, 34, 157–170.CrossRefGoogle Scholar
  13. Engle, R.F., & Granger, C.W. (1987). Co-integration and error correction: representation, estimation and testing. Econometrica, 55, 251–276.CrossRefGoogle Scholar
  14. Fishburn, P.C. (1977). Mean-risk analysis with risk associated with below-target returns. American Economic Review, 67, 116–126.Google Scholar
  15. Geppert, J.M. (1995). A statistical model for the relationship between futures contract hedging effectiveness and investment horizon length. Journal of Futures Markets, 15, 507–536.CrossRefGoogle Scholar
  16. Ghosh, A. (1993). Hedging with stock index futures: estimation and forecasting with error correction model. Journal of Futures Markets, 13, 743–752.CrossRefGoogle Scholar
  17. Grammatikos, T., & Saunders, A. (1983). Stability and the hedging performance of foreign currency futures. Journal of Futures Markets, 3, 295–305.CrossRefGoogle Scholar
  18. Howard, C.T., & D’Antonio, L.J. (1984). A risk-return measure of hedging effectiveness. Journal of Financial and Quantitative Analysis, 19, 101–112.CrossRefGoogle Scholar
  19. Hsin, C.W., Kuo, J., & Lee, C.F. (1994). A new measure to compare the hedging effectiveness of foreign currency futures versus options. Journal of Futures Markets, 14, 685–707.CrossRefGoogle Scholar
  20. Hung, J.C., Chiu, C.L. & Lee, M.C. (2006). Hedging with zero-value at risk hedge ratio, Applied Financial Economics, 16, 259–269.CrossRefGoogle Scholar
  21. Hylleberg, S., & Mizon, G.E. (1989). Cointegration and error correction mechanisms. Economic Journal, 99, 113–125.CrossRefGoogle Scholar
  22. Jarque, C.M., & Bera, A.K. (1987). A test for normality of observations and regression residuals. International Statistical Review, 55, 163–172.CrossRefGoogle Scholar
  23. Johansen, S., & Juselius, K. (1990). Maximum likelihood estimation and inference on cointegration—with applications to the demand for money. Oxford Bulletin of Economics and Statistics, 52, 169–210.CrossRefGoogle Scholar
  24. Johnson, L.L. (1960). The theory of hedging and speculation in commodity futures. Review of Economic Studies, 27, 139–151.CrossRefGoogle Scholar
  25. Junkus, J.C., & Lee, C.F. (1985). Use of three index futures in hedging decisions. Journal of Futures Markets, 5, 201–222.CrossRefGoogle Scholar
  26. Kolb, R.W., & Okunev, J. (1992). An empirical evaluation of the extended mean-Gini coefficient for futures hedging. Journal of Futures Markets, 12, 177–186.CrossRefGoogle Scholar
  27. Kolb, R.W., & Okunev, J. (1993). Utility maximizing hedge ratios in the extended mean Gini framework. Journal of Futures Markets, 13, 597–609.CrossRefGoogle Scholar
  28. Kroner, K.F., & Sultan, J. (1993). Time-varying distributions and dynamic hedging with foreign currency futures. Journal of Financial and Quantitative Analysis, 28, 535–551.CrossRefGoogle Scholar
  29. Lee, C.F., Bubnys, E.L., & Lin, Y. (1987). Stock index futures hedge ratios: test on horizon effects and functional form. Advances in Futures and Options Research, 2, 291–311.Google Scholar
  30. Lee, H.T. & Yoder J. (2007). Optimal hedging with a regime-switching time-varying correlation GARCH model. Journal of Futures Markets, 27, 495–516.CrossRefGoogle Scholar
  31. Lence, S. H. (1995). The economic value of minimum-variance hedges. American Journal of Agricultural Economics, 77, 353–364.CrossRefGoogle Scholar
  32. Lence, S. H. (1996). Relaxing the assumptions of minimum variance hedging. Journal of Agricultural and Resource Economics, 21, 39–55.Google Scholar
  33. Lien, D., & Luo, X. (1993a). Estimating the extended mean-Gini coefficient for futures hedging. Journal of Futures Markets, 13, 665–676.CrossRefGoogle Scholar
  34. Lien, D., & Luo, X. (1993b). Estimating multiperiod hedge ratios in cointegrated markets. Journal of Futures Markets, 13, 909–920.CrossRefGoogle Scholar
  35. Lien, D., & Shaffer, D.R. (1999). Note on estimating the minimum extended Gini hedge ratio. Journal of Futures Markets, 19, 101–113.CrossRefGoogle Scholar
  36. Lien, D. & Shrestha, K. (2007). An empirical analysis of the relationship between hedge ratio and hedging horizon using wavelet analysis. Journal of Futures Markets, 27, 127–150.CrossRefGoogle Scholar
  37. Lien, D. & Shrestha, K. (2010). Estimating optimal hedge ratio: a multivariate skew-normal distribution. Applied Financial Economics, 20, 627–636.CrossRefGoogle Scholar
  38. Lien, D., & Tse, Y.K. (1998). Hedging time-varying downside risk. Journal of Futures Markets, 18, 705–722.CrossRefGoogle Scholar
  39. Lien, D., & Tse, Y.K. (2000). Hedging downside risk with futures contracts. Applied Financial Economics, 10, 163–170.CrossRefGoogle Scholar
  40. Malliaris, A.G., & Urrutia, J.L. (1991). The impact of the lengths of estimation periods and hedging horizons on the effectiveness of a hedge: evidence from foreign currency futures. Journal of Futures Markets, 3, 271–289.CrossRefGoogle Scholar
  41. Myers, R.J., & Thompson, S.R. (1989) Generalized optimal hedge ratio estimation. American Journal of Agricultural Economics, 71, 858–868.CrossRefGoogle Scholar
  42. Osterwald-Lenum, M. (1992). A note with quantiles of the asymptotic distribution of the maximum likelihood cointegration rank test statistics. Oxford Bulletin of Economics and Statistics, 54, 461–471.CrossRefGoogle Scholar
  43. Phillips, P.C.B., & Perron, P. (1988). Testing unit roots in time series regression. Biometrika, 75, 335–46.CrossRefGoogle Scholar
  44. Rutledge, D.J.S. (1972). Hedgers’ demand for futures contracts: a theoretical framework with applications to the United States soybean complex. Food Research Institute Studies, 11, 237–256.Google Scholar
  45. Sephton, P.S. (1993a). Hedging wheat and canola at the Winnipeg commodity exchange. Applied Financial Economics, 3, 67–72.CrossRefGoogle Scholar
  46. Sephton, P.S. (1993b). Optimal hedge ratios at the Winnipeg commodity exchange. Canadian Journal of Economics, 26, 175–193.CrossRefGoogle Scholar
  47. Shalit, H. (1995). Mean-Gini hedging in futures markets. Journal of Futures Markets, 15, 617–635.CrossRefGoogle Scholar
  48. Stock, J.H., & Watson, M.W. (1988). Testing for common trends. Journal of the American Statistical Association, 83, 1097–1107.CrossRefGoogle Scholar
  49. Working, H. (1953). Hedging reconsidered. Journal of Farm Economics, 35, 544–561.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Sheng-Syan Chen
    • 1
  • Cheng-Few Lee
    • 2
    • 3
  • Keshab Shrestha
    • 4
  1. 1.Department of Finance, College of ManagementNational Taiwan UniversityTaipeiChina
  2. 2.Rutgers Business SchoolRutgers UniversityNew BrunswickUSA
  3. 3.Graduate Institute of FinanceNational Chiao Tung UniversityHsinchuChina
  4. 4.Risk Management InstituteNational University of SingaporeSingaporeSingapore