In today‟s global financial market, risk plays high fragile role in investment. Investors are looking to overcome this financial risk at any cost, with the global crisis arises day by day, investors have concern to diversify their portfolios effectively. The aim of this study is to construct an efficient portfolio of domestic level stocks using optimal hedge ratio which will minimize the overall variance of the portfolio. The study uses DBEKK model of MGARCH family for estimation of hedge ratio and uses minimum variance approach for the efficiency of portfolio selection. A sample of total 30 firms was used for portfolio construction which represents the six sectors of Pakistan stock exchange. Daily data from January 2014 to December 2019 were taken which make a total 1485 observations for each stock. The normality and stationarity of return series has been checked using Skewness, kurtosis and Jarque-bera test and KPSS test, while to know ARCH effect LM-ARCH test is used. Q-stat test is used to know serial correlation. After calculation of return of the actual series, variance and covariance of each return series has been calculated using DBEKK model, which were further used in calculation of portfolio return and portfolio variance. As we have used minimum variance approach in this study, so for minimum variance we have used reduction in variance formula for each 40 randomly constructed portfolios. Each portfolio is ranked on the basis of reduction in variance, the best portfolio is one which gives maximum reduction in portfolio variance. The finding of this study shows that it is possible to minimize variance or risk of a portfolio. The current method of estimation helps in reduction in variance of portfolios with three securities and have suggested best portfolio having minimum variance, and hence gives investors an opportunity to minimize their portfolio variance using current method of estimation and portfolio diversification. Supervisor:- Dr. Attiya Yasmin Javid Co-Supervisor:- Dr. Saud Ahmed Khan