1. Forecasting the daily dynamic hedge ratios in agricultural futures markets: evidence from the GARCH models
Yuanyuan Zhang, School of Management,
University of Southampton
PhD conference, 11th, May, 2011

2. Introduction Hedging  reduction or transference of risk
What is hedging?
Hedging  reduction or transference of risk
Hedging in futures market: Voluminous trading is used to reduce and transfer risk by substituting for a cash market transaction (Kolb,2007).
Hedge ratio (HR) the ratio of the volume of hedged futures position to the volume of the initial cash position.
Forecast of hedge ratio is important for planning and decision- making (timing, capital preparation).

3. Research objective
We estimate and forecast OHR in agricultural futures markets.
We aim to investigate the out-of-sample forecasting ability of six GARCH models (GARCH, BEKK, GARCH- X, BEKK-X, GJR-GARCH and QGARCH ) on OHR prediction based on
1)two different distributions (normal and student’s t)
2)Forecasts over two different out-of-sample horizon: non-overlapping 1- and 2-year time horizons

4. Literature review Ederington (1979)constant OHR
Cecchetti(1988), Myers (1991), Baillie & Myers (1991) Bivariate GARCH dynamic OHR
Unequal effect of bad and good news on return (Black, 1976)
Engle and Ng (1993)GJR is the best parametric forecasting model in volatility in 7 GARCH models (Japanese)
Brooks and Henry (2002)Asymmetric BEKK-GARCH provides best OHR forecast on FTSE 100 stock index (UK).

5. Engle, Granger (1987)cointegration relationship
Literature review (2)
Engle, Granger (1987)cointegration relationship
In futures market, the cointegration measures the effect of short-term derivations for long run relationship between cash and futures prices.
Kroner & Sultan(1993) ECM-GARCH-X
Lien(1996), Ghosh (1993a) and Yang (2001) cointegration on commodity markets is necessary to ensure an optimal hedging decision.

6. Data Data is from Global financial data.
Daily data for five agricultural products: Soybean, wheat, and coffee from 01/01/1980 to 23/06/2006; Live cattle and live hogs from 01/01/1980 to 14/01/2008 in US futures markets
Storable and non-storable commodities:
storability; demand-supply; volatility of price
1-year forecast: storable (2006), non-storable(2008)
2-year forecast: storable( ), non-storable ( )

7. Data (2)
Soybean
Live cattle

8. Methodology Three steps:
Out-of-sample forecasting of OHR using six different GARCH models:
GARCH, BEKK-GARCH, GARCH-X, BEKK-X, asymmetric models (GJR-GARCH and QGARCH)
Three steps:
In-sample estimation of coefficients of parameters
Out-of-sample forecast of OHR and return
Evaluate forecast error

9. Models
Six time-varying GARCH models with bivariate diagonal specification of will be used:
1) Standard GARCH (Bollerslev(1986) )

10. Models (2)
2) BEKK-GARCH produces positive variance- covariance matrix with 7 parameters for bivariate
3) GARCH-X, BEKK-GARCH-X take into account the
effect of cointegration on conditional (co) variance

11. Models (3) APGARCH (asymmetric power GARCH models): GJR,TGARCH, QGARCH

12. Result (1) OHR forecast of Coffee-Normal distributed error
1-year forecast- BEKK,X,Q

13. Result (2) OHR forecast of Coffee-Normal distributed error
2-year forecast-BEKK

14. Summary of MAE, MSE, and Theil’ U tests on
Result (3)
Summary of MAE, MSE, and Theil’ U tests on
forecasted return of portfolio
Forecasts
Horizon
Short 1 year
Long 2 year
Distribution
Goods
Normal
Student t
Forecasted Return
Coffee
BEKK
BEKK-X
Wheat
GJR, Q Q
GJR
Soybean X
Live cattle
GJR,X
GARCH
Live hogs

15. Summary of MDM Comparison Result
Horizon
2006
Distribution
Goods
Normal
Student t
Coffee
BEKK
BEKK-X
wheat
GJR Q
Soybean X
BEKK, GJR
Live cattle
GARCH
Live hogs

16. Result (5)
For one-year forecast: both the BEKK and asymmetric GARCH models provides best prediction; asymmetric model dominates others for non-storable commodity; GARCH is the weakest one.
For two-year forecast: both the BEKK and Asymmetric GARCH are equally strong models.

17. Conclusion
Overall, the result is mixed which is consistent with Chen (2003).
Forecasting power of GARCH models somewhat depends on the commodity, the error distribution, and forecast horizon. However, the asymmetric GARCH models have great predictive power in OHR forecasting for non-storable commodity.