The research observed that equity portfolio and investment managers were facing challenges in determining the optimum portfolio, especially during the turbulent times. As a result, they needed to implement portfolio management strategies to overcome the risk associated with stock return volatility in turbulence periods. This research focused on selecting stocks from the LQ-45 index during 2005-2011 using The Markowitz theory combining the Solver Linear Programming. The portfolio selection method which has been introduced by Markowitz (1952) used variance or standard deviation as a risk measurement. The result of this research proves that the composition of the portfolio is not the same in the different period. In the bearish period, the composition of the optimum portfolio is dominated by the banking sector and manufacture sector. In the bullish period, the optimum portfolio is dominated by the commodity stocks.