No. 53 (2020)
Artículos

Optimal Hedge Ratios for the Mexican Stock Market Index Futures Contract: A Multivariate GARCH Approach

Roberto J. Santillán-Salgado
Tecnológico de Monterrey, Campus Monterrey
Bio
Luis Jacob Escobar
Tecnológico de Monterrey, Campus Monterrey
Bio
Francisco López-Herrera
Universidad Nacional Autónoma de México
Bio
Published July 31, 2020

Abstract

This work compares different hedging strategies that use the Mexican Stock Exchange (MSE) Index futures contract traded at the Mercado Mexicano de Derivados – (Mexican Derivatives Market or MexDer), to minimize the impact of stock price fluctuations on the value of a well-diversified portfolio (the Mexican Stock Exchange Index, or IPC). We study the ex-post empirical performance of each using the daily closing contract’s price and the MSE Index for a period from December 30th, 1999, through December 30th, 2016. The set of hedging strategies we compare includes: a) a No-hedge strategy; b) a Naive hedge ratio (1 to 1); c) a constant hedge ratio, (obtained from an OLS); and d) a dynamic hedge ratio, obtained using a Constant Conditional Correlation Bivariate GARCH model, with Asymmetric Responses.  Moreover, the sample period has four structural breaks, so the analysis is divided in five subperiods. The different strategies are compared using different risk measures: Value at Risk, Expected Shortfall and LAQ. In all cases, hedging effectively reduces the volatility of the portfolio, but the dynamic hedge ratio produces the best possible results, while the constant hedge ratio is a close second.

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.
  2. Bai, J. (1997). Estimating Multiple Breaks One at a Time. Econometric Theory. 13, 315–352.
  3. Bai, J., & Perron, P. (1998). Estimating and Testing Linear Models with Multiple Structural
  4. Changes. Econometrica, 66, 47–78.
  5. Bai, J., & Perron, P. (2003a). Computation and Analysis of Multiple Structural Change Models. Journal of Applied Econometrics. 18 (1): 1–22.
  6. Bai, J., & Perron, P. (2003b). Critical Values for Multiple Structural Change Tests. Econometrics Journal, 6, 72–78.
  7. Bollerslev, T. (1986). Generalized autoregressive conditional heteroskedasticity. Journal of Econometrics, 31. 307-327.
  8. Bollerslev, T. (1990). Modelling the coherence in short-run nominal exchange rates: A multivariate generalized ARCH model. Review of Economics and Statistics, 498-505.
  9. Bollerslev, T., Engle, R. F., & Wooldridge, J. M. (1988). A Capital Asset Pricing model with Time-varying Covariances. Journal of Political Economy, 116-131.
  10. Bollerslev, T. & Wooldridge, J. M. (1992). Quasi-maximum likelihood estimation and inference in dynamic models with time-varying covariances. Econometric Reviews, 11(2), 147-172
  11. Brooks, C., Henry, Ó. T., & Persand, G. (2002). The effects of asymmetries on optimal hedge ratios. The Journal of Business, 75(2), 333–352. http://doi.org/10.1086/338484
  12. Campbell, S. D. (2005). A Review of Backtesting and Backtesting Procedures. Finance and Economics Discussion Series; Division of Research & Statistics and Monetary Affairs; Federal Reserve Board, Washington, D.C.
  13. Chang, C. L., González-Serrano, L., & Jimenez-Martin, J. A. (2013). Currency hedging strategies using dynamic multivariate GARCH. Mathematics and Computers in Simulation. http://doi.org/10.1016/j.matcom.2012.02.008
  14. Christoffersen, P. F. (1998). Evaluating Interval Forecasts. International Economic Review, 39(4), 841–862. http://doi.org/10.2307/2527341
  15. Efron, B. (1982). The jackknife, the bootstrap, and other resampling plans. Standford University Technical Report No. 63.
  16. Engle, R. F. (1982). Autoregressive conditional heteroskedasticity with estimates of the variance of U.K. inflation. Econometrics, 50: 987-1008.
  17. Engel, R.F. (2002) “Dynamic conditional correlation: A simple class of multivariate generalized autoregressive conditional heteroskedasticity models.” Journal of Business & Economic Statistics 20: 339-350.
  18. Fama, E. F. (1970). Efficient Capital Markets: a Review of Theory and Empirical Work. Journal of Finance, 25(2): 383-417
  19. Fama, E. F. (1991). Efficient Capital Markets: II. Journal of Finance, 45(5): 1575-1617
  20. Ghosh. (1986). Cointegration and Error Correction Models: Intertemporal Causality. The Journal of Futures Markets Apr, 13(2)
  21. Glosten, L.R., Jagannathan, R., & Runkle, D. E. (1993), On the Relation Between the Expected Value and the Volatility of the Nominal Excess Returns in Stocks. Federal Reserve Bank of Minneapolis, Research Department Staff Report #157.
  22. González-Rivera, G., Lee, T., & Mishra, S. (2004). Forecasting volatility: A reality check based on option pricing, utility function, value-at-risk, and predictive likelihood. International Journal of Forecasting, 20: 629-645
  23. Hsieh, D. A. (1993). Implications of Nonlinear Dynamics for Financial Risk Management. Journal of Financial and Quantitative Analysis, 28(1).
  24. Johansen, S., & Mosconi, R. (2000). Cointegration analysis in the presence of structural breaks in the deterministic trend. Econometrics Journal, 3, 216–249. Retrieved from http://www.iue.it/Personal/Johansen
  25. Kupiec, P. H. (1995). Techniques for Verifying the Accuracy of Risk Measurement Models. The Journal of Derivatives. http://doi.org/10.3905/jod.1995.407942
  26. Lien, D. (2005). A Note on Asymmetric Stochastic Volatility and Futures Hedging. Journal of Futures Markets, 25(6), 607–612. http://doi.org/10.1002/fut.20158
  27. Lien, D., & Wilson, B. K. (2001). Multiperiod hedging in the presence of stochastic volatility. International Review of Financial Analysis. http://doi.org/10.1016/S1057-5219(01)00060-6
  28. Lien, Donald and Yang, Li. (2008). Asymmetric effect of basis on dynamic futures hedging: Empirical evidence from commodity markets. Journal of Banking and Finance, Elsevier, vol. 32(2), pages 187-198, February.
  29. Tse, Yiu Kuen; Lien, Donald; and Tsui, Albert K. C. (2002). Evaluating the Hedging Performance of the Constant-Correlation GARCH Model. Applied Financial Economics, 12(11), 791.
  30. Lopez, J., & Walter, C. (2001). Evaluating covariance matrix forecasts in a value-at-risk framework. Journal of Risk, 3(3), 69–97. http://doi.org/10.2139/ssrn.305279
  31. McAleer, M., & Da Veiga, B. (2008). Forecasting Value-at-Risk with a Parsimonious Portfolio Spillover GARCH (PS-GARCH) Model. Journal of Forecasting, 27: 1-19
  32. Newey, Whitney K., West, Kenneth D., Econometrica. (1986). A Simple Positive Semi-Definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix, Econometrica, 55 (3), 703-708.
  33. Park, S. Y., & Jei, S. Y. (2010). Estimation and Hedging Effectiveness of Time varying Hedge Ratio: Flexible Bivariate Garch Approches. The Journal of Futures Markets, 30(1), 71–99. http://doi.org/10.1002/fut.20401
  34. Sheu, H. J., & Lee, H. T. (2014). Optimal Futures Hedging Under Multichain Markov Regime Switching. Journal of Futures Markets. 34(2), 173-202. http://doi.org/10.1002/fut.21583
  35. Venegas Martínez, F., Díaz-Tinoco, J. & González-Aréchiga , B. (2002). Cobertura con Futuros de Títulos de Capital. Momento Económico, 120. 14-34
  36. Zivot, E., & Andrews, D. W. (1992). Further Evidence on the Great Crash, the Oil-Price Shock, and the Unit-Root Hypothesis. Journal of Business & Economic Statistics, 251-270.