Abstract: The objective of this study is to investigate the possible existence and stability of the day of the week effect and measures the mean and conditional volatility in testing the degree of market efficiency in the BSE Sensitivity Index and S&P CNX Nifty Index over the period spanning from July 1, 1997 to March 31, 2012 by using asymmetric TGARCH Model and introduced dummy variables into the mean equation and conditional variance equation the assess the distributional properties between Monday to Friday. Unit Root test, Augmented Dickey Fuller (ADF) test, Phillips-Peron (PP) test, Ljung Box Q were applied. The result of the study indicates the return and volatility for both the index are scattered over a period of time. Apart from that the risk averse investors are willing to commit huge amount of transaction with higher risk appetite because the market digest the information and react immediately towards news shocks. Therefore, the seasonality changes and interexchange arbitrage opportunity in emerging markets makes the investors to create various trading strategies in both the market. Overall, the professionals market watchers who are aware of the daily return pattern should adjust the timing of their buying and selling to take advantage of the effect.