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The purpose of this study is to discuss the asymmetric volatility, basis and conditional fat-tail or skewed distribution which can improve the futures hedging effectiveness of SIMEX MSCI Taiwan Stock Index Futures. This study utilizes the four conditional distributions which are normal distribution, Student t distribution, the generalized error distribution (GED) and the skewed generalized t distribution (SGT), in addition to symmetric and asymmetric basis, also GARCH and GJR models to estimate the assessment of different models to the hedging effectiveness. We perform Hansen (2005) superior predictive ability to test for predictive superiority of our methods over the benchmark model, and find that there is no influence of asymmetric, fat-tail, basis upon the hedging period one day. The findings also find the asymmetric volatility, basis and conditional fat-tail distribution especially the student t distribution and GARCH models of asymmetric basis can improve the hedging effectiveness of stock index futures