Sheng-Syan ChenCheng Few LeeFu-Lai LinKeshab Shrestha2024-11-112024-11-112024-04-0897898112699369789811269943https://www.scopus.com/record/display.uri?eid=2-s2.0-85201485572&origin=resultslisthttps://scholars.lib.ntu.edu.tw/handle/123456789/722953This chapter first presents a review of various theoretical models and six estimation methods to the optimal futures hedge ratios. Then we use data to show how some of the hedge ratios can be applied to estimate hedge ratio in terms of S&P 500 future. We also show the estimation procedure on how to apply OLS, GARCH, and CECM models to estimate optimal hedge ratios through R language. These approaches are theoretically derived in terms of minimum variance, mean-variance, expected utility, and Value-at-Risk. Various ways of estimating these hedge ratios are also discussed, ranging from simple ordinary least squares to complicated heteroskedastic cointegration methods. Under martingale, jointnormality conditions, and some other conditions, different hedge ratios can be shown that this different ratio can be converted to the minimum variance hedge ratio. Otherwise, the optimal hedge ratios based on the different approaches are in general different. Finally, our empirical findings suggest the importance of capturing the heteroskedastic error structures including the long-run equilibrium error term in conventional regression model.enfalseGARCH methodHedge ratioMinimum variance hedge ratioOptimum mean variance hedge ratioR languageSharpe hedge ratiobook part10.1142/9789811269943_00382-s2.0-85201485572