Return and Risk Model for Optimal Portfolio: Applied Case Study Cairo Stock Exchange

Modern financial theory, commonly known as portfolio theory, provides an analytical framework for the investment decision to be made under uncertainty. It is a well-established proposition in portfolio theory that whenever there is an imperfect correlation between returns risk is reduced by maintaining only a portion of wealth in any asset, or by selecting a portfolio according to expected returns and correlations between returns.

The major improvement of the portfolio approaches over prior received theory is the incorporation of (a) the riskiness of an asset, and (b) the addition from investing in any asset.

Building an investment portfolio is a problem that numerous researchers have addressed for many years. The theme of this paper is to discuss how to propose a new mathematical model like that provided by Markowitz, which helps in choosing a nearly perfect portfolio and an efficient input /output. Besides applying this model to reality, the researcher uses game theory, stochastic and linear programming to provide the model proposed and then uses this model to select a perfect portfolio in the Cairo stock exchange. Game theory is a mathematical framework that is used to study decision-making in situations of strategic interaction. The results are fruitful and the researcher considers this model a new contribution to previous models. The target of this proposed model is achieved, as the risks increase by expanding the size of the portfolio because of the positive direct relationship between risks and returns.