The objective of this study is to create optimal two-asset portfolios consisting of stocks from Western Europe, the United States, and the BRICS (Brazil, China, India, Russia, and South Africa), as well as sixteen commodity types during the BREXIT period. We utilized dynamic variances and covariances from the GARCH model to derive weights for the two-asset portfolios, with each portfolio consisting of one equity factor and one commodity factor. Subsequently, hedge ratios were calculated for these various assets. Our findings indicate that portfolios consisting of European stocks do not require the inclusion of commodities, whereas the other equities do.

Traditional hedge of bond duration and convexity are incorrect. We derive correct hedge ratios by capturing the neglected volatility linkage between Treasury futures and cheapest-to-deliver Treasuries. Our hedge-ratio equations specify each hedge instrument’s contribution against short-term spot and forward rate exposures. Our numerical analysis indicates that traditional hedge substantially overhedges. The relative overhedge is especially large in hedging high coupon bond when the hedge horizon is long, the term structure is steep, or the cheapest-to-deliver is a high coupon Treasury. The results are robust to various maturity of bond and the cheapest-to-deliver Treasuries.

This study estimates optimal hedge ratios using various econometric models. These models are evaluated based on the in- and out-of-sample optimal hedge ratio forecasts. Using daily data of spot and futures 1-month, 3-month, 6-month prices of aluminum and copper in the Shanghai Futures Exchange, the optimal hedge ratios are calculated from the OLS regression model, the VAR with error correction model, the bivariate GARCH model and the Exponential GARCH (EGARCH) Model. Hedging performance in terms of variance reduction of returns from four different models are also conducted. It is found that the EGARCH hedge ratio provides the largest reduction in the variance of the return portfolio, but they do not perform better than the alternatives over the out-of-sample period.