A simulation optimization model for portfolio selection problem with quadratic programming technique.

Portfolio investment is one of the important topics in financial management. Its aim of having the wealth in a period of time with maximum return and minimum risk has been well-defined in the literature. Specifically, the portfolio selection is arisen to be an interesting investment issue. Since the risk is defined as the probability of losses relative to the expected return in the portfolio investment, the existing risk would influence the rate of return and affect the investment decision. In this paper, the portfolio selection problem is discussed. The aim is to provide an effective quantitative study in managing the portfolio. In the beginning, the rates of return are calculated and it is followed by computing the expected rates of return and the related covariance matrix. Accordingly, the mean-variance optimization model, which is the quadratic programming model, is formulated and solved by the quadratic programming technique. Here, the objective function to be minimized represents the risk of the portfolio selection, while the weights of the portfolio selection, which are defined as the decision variables, are normalized with the total amount of investment, and the expected return is assigned to a certain targeted return. For illustration, a set of historical data on the stock prices in the Financial Times Stock Exchange (FTSE) Bursa Malaysia Kuala Lumpur Composite Index (KLCI) is considered. Through simulation and optimization of the mean-variance portfolio model, the result shows the relationship between risk and return with the various targeted returns. Moreover, by applying the Sharpe ratio, the optimal weight of the portfolio selection, which is the optimal portfolio decision, is properly suggested. In conclusion, the simulation optimization model for the portfolio selection problem is highly recommended. [ABSTRACT FROM AUTHOR]