Developing Efficient Frontier for Investment Portfolio: A Fuzzy Model Approach

Abstract

AbstractInvestment in financial securities is a compound process involving decision concerning possible expected rates of return and risk. As a rule, decision maker often deals with insufficient data while selecting investment portfolio, due to uncertain business environment.Markowitz’s portfolio theory is a methodology in financial world that aims to maximize investment portfolio expected return for a given level of risk or minimize the risk of investment for a certain level of expected return. The classic mean-variance approach to portfolio selection is performed in this paper under the assumption that the returns and risk of financial securities are fuzzy values, which can successfully integrate the experts’ knowledge and the managers’ subjective opinion. The real financial world is very sensitive and influenced by changes in political-economic environment. Therefore, classical approach based only on historical data may lead to inaccurate results. The methodology performed in this paper considers fuzzy environment which contributes to actuality of this study. The aim of this paper is to develop fuzzy efficient frontier for portfolio consisting of eight assets. Modeling of sample investment portfolio is provided by using statistical data provided by Yahoo Finance web-platform and expert opinion. The software based on C# programming language is developed for determining efficient portfolios and constructing fuzzy efficient frontier. Obtained results of this study completely elucidate the efficiency of the proposed approach.KeywordsMean-variance modelFuzzy setsPortfolio selectionEfficient frontier