This research mainly discusses the linkage between the Taiwan weighted index (TAIEX) and the Philadelphia semiconductor index (SOX), the relationship of substitution, and their returns. We choose Taiwan Semiconductor Manufacturing (TSMC), the largest weighted stock in TAIEX, Intel Corporation, and Advanced Micro Devices as our representative blue-chip stocks. First, we fit each return series based on the univariate GARCH model, forecast their volatility, and compare the variation of estimated volatility respectively. In order to understand their linkage, we consider a multivariate DCC-GARCH (Dynamic Conditional Correlation) model to estimate the conditional correlation coefficient of bivariate returns. We thus investigate the relationship of the estimated result and substitution effect. In conclusion, in terms of the bivariate returns correlation, the conditional correlation coefficient range of the Intel Corporation and Advanced Micro Devices to Taiwan Semiconductor Manufacturing are 0.2~0.3, respectively. For Intel Corporation and Advanced Micro Devices, we find that their correlation coefficient is positive through the analysis, because the two companies are competitive. Their correlation coefficient is at least 0.7 in 2009, and when a new product is launched from a company, the substitution effect occurs for this new product. It eventually causes the conditional correlation coefficient to become negative in the short run, presenting. That the substitution effect appear in the counterpart stock’s return.