Heuristic Optimization of Portfolio Considering Sharpe's Single Index Model: An Analytical Approach

Introduction

Investment in securities confronts with the problems of selection of assets in the portfolio. Inclusion of more than one asset in the portfolio increases the chances of risk reduction. Therefore, for diversification inclusion of more than one asset is desirable in the portfolio. Portfolio management faces another problem related to the selection of weight or the proportion of investment of the selected assets in the portfolio. Extant literature proposes noble approaches to solve the problems in portfolio optimization. The pioneering work was proposed by Noble Laureate Markowitz (1956) proposing the optimization of portfolio by Mean-Variance (M-V) model. The Markowitz mean-variance model has assumed that the investors are risk averse in nature. The investors are always looking for the high risk premium without taking much risk. Therefore, they penalize the return for involvement of certain amount of risk. According to the model, a rational investor either maximizes his return subject to a certain level of risk or minimizes his risk subject to a certain level of return. Starting from the seminal work of mean-variance model of Markowitz, portfolio optimization has assumed many variations and interventions mostly to address the evolving financial landscape and the new issues of financial modeling. After his pioneering work, W. Sharpe (1962) introduced another optimization model to address the data requirement of the previous model. He simplified the mean-variance model. Researchers are focusing in the field of portfolio optimization to make it simpler or statistically more appealing. As the classical models of portfolio optimisation are difficult to understand and require expert knowledge. Heuristic optimisation can give an easy, near accurate and faster solution which can be comprehensible without having to be expert in the subject. Therefore, the dynamism of heuristic portfolio optimisation has an appeal to the researchers.

The purpose of the work is to construct an optimum portfolio based on the Sharpe’s Single Index Model and to offer a heuristic portfolio which can help the general investors having less technical knowledge about complex mathematics or statistics.