Fuzzy Portfolio Selection Problem with Different Borrowing and Lending Rates

Wei Chen,Yiping Yang,Hui Ma

doi:10.1155/2011/263240

Abstract

As we know, borrowing and lending risk‐free assets arise extensively in the theory and practice of finance. However, little study has ever investigated them in fuzzy portfolio problem. In this paper, the returns of each assets are assumed to be fuzzy variables, then following the mean‐variance approach, a new possibilistic portfolio selection model with different interest rates for borrowing and lending is proposed, in which the possibilistic semiabsolute deviation of the return is used to measure investment risk. The conventional probabilistic mean variance model can be transformed to a linear programming problem under possibility distributions. Finally, a numerical example is given to illustrate the modeling idea and the impact of borrowing and lending on optimal decision making.

Highlights

Portfolio selection is concerned with selecting a combination of securities among portfolios containing large numbers of securities to reach the investment goal
Analogous to Markowitz’s mean-variance methodology for the portfolio selection problem, the crisp possibilistic mean value corresponds to the return while the possibilistic semi-absolute deviation corresponds to the risk
In order to illustrate our proposed effective approaches for the portfolio selection problem in this paper, we give a numerical example introduced by Markowitz in 1959 3

Summary

Introduction

Portfolio selection is concerned with selecting a combination of securities among portfolios containing large numbers of securities to reach the investment goal. Bhattacharyya et al proposed a mean-variance-skewness model with transaction costs for portfolio selection with interval coefficients under the consideration of constraints on short- and long-term returns with transaction costs, liquidity, dividends, the number of assets in the portfolio, and the maximum and the minimum allowable capital invested in selected stocks. Zhang et al extended traditional Markowitz model to case of different interest rates for borrowing and lending, and solve the proposed problems by the Kuhn-Tucker condition. The focus of the research is to incorporate the possibility theory into a semi-absolute deviation portfolio selection model for investors’ taking into account different interest rates for borrowing and lending in fuzzy environment.

Formulation of the Possibilistic Portfolio Model

Numerical Example

Findings

Conclusion