The application of genetic algorithm optimization on quadratic investment portfolio without a risk-free asset under Value-at-Risk

In this paper, we performed the Genetic Algorithm within problems of quadratic investment portfolio without a risk-free asset under Value-at-Risk. The limitation of this study is that the risk of an investment portfolio measured by Value-at-Risk, and each investor has the nature of risk aversion. To solve these problems: First, we established the mean vector and covariance matrix. The second step was to define the vector mean and covariance matrices for the formulation of Value-at-Risk of the investment portfolio. Third, using the mean vector and Value-at-Risk established the model. To complete the optimization problem, we performed the Genetic Algorithm. The results show that the trade-off between risk and expected return does not only depend on the type of investor but also on the size of the investment. The Genetic Algorithm certifies us the robust solution in the optimization problem because of its natural ability to locate the global minimal. Moreover, genetic algorithm can be used as an effective way in numerical completion of the optimization of quadratic investment portfolio. In a realistic investment situation, it has likely more constraints. For example, the restriction on short-selling, is need to be considered.