A common goal of portfolio investors is to seek for a higher risk adjusted return. However, according to Samelson (1965) and Farma (1970), the stock market is efficient and the market prices incorporate all information, which leaves no possibility for investors to achieve abnormal returns (Hilsted, 2012). There are various factors under the real world financial market, nevertheless; prevent the market from achieving its efficiency and thus leave room for arbitrage opportunities. The superior performance comes from factors such as market timing, economic environment, stock selection, trading and etc. In our project, we are interested in exploring the effect of active portfolio management strategy on portfolio performance. we used mean-variance optimization method to construct various portfolios of nine stocks that we have chosen from five different industries. More details of these nine stocks will be demonstrated in section 2. The two main optimization method we employed were minimization of risk with and without given expected return level. Then we utilized three strategies to invest and managed our portfolio, one passive strategy and two active strategies. The passive strategy would use the weights calculated from first year historical returns and fix the number of shares of each stock for next 4 years. The active strategies enable investor change the weights invested in each stock frequently: one allowed them change every year and the other allowed changing every quarter. We would employ mean-variance optimization method on a rolling basis in active strategies. To evaluate these three management strategies, we apply them to three-month intervals from 2012 to first quarter of 2016 and compare values of these portfolios during this period. In section 2, mean-variance optimization method will be explained, including risk-return tradeoff and efficient frontier, followed by details of rolling analysis of our portfolios. In section 3, we will present our results of portfolio constructions under two different optimization restrictions. Then the performances of passive strategy and two active strategies will be compared in terms of value of portfolio. In addition, we will explain limitations of our project and demonstrate future work that could be done to improve our findings.