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

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).

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

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).

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.

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(2004-2005), non-storable (2006-2007)

Data (2) Soybean Live cattle

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

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

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

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

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

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

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

Summary of MDM Comparison Result Horizon 2006 2004-2005 Distribution Goods Normal Student t Coffee BEKK BEKK-X wheat GJR Q Soybean X BEKK, GJR Live cattle GARCH Live hogs

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.

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.