Resolving multi objective stock portfolio optimization problem using genetic algorithm

Abstract

Portfolio optimization is an important research field in modern finance. The most important characteristic within this optimization problem is the risk and the returns. Modern portfolio theory provides a well-developed paradigm to form a portfolio with the highest expected return for a given level of risk tolerance. Multi objective portfolio optimization problem is the portfolio selection process that result highest expected return and smallest identified risk among the various financial assets. In this paper, we propose to identify expected return (mean profit) and risk using historical data of stock prices. The downside values of the variance of each stock are considered to be the identified risk in first case. The value at risk of each stock that we obtained using parametric and historical simulation methodology are considered to be the identified risk in second case. One of method being widely used lately for optimization need is Genetic Algorithm or GA. This method adapted the mechanism of biology mechanism involving natural selection. With many advantages it has, numerical process of a portfolio optimization in both case are attempted to be coupled with Genetic Algorithm. The values of expected return and risk of each stock will be used as inputs into a fitness function in Genetic Algorithm. Performance evaluation is done by examining the parameters of GA, such as population size, stall generation and number of elitism.

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