Optimization of Risk and Return Using Fuzzy Multiobjective Linear Programming

Darsha Panwar,Manoj Jha,Namita Srivastava

doi:10.1155/2018/4279236

Abstract

Stock selection poses a challenge for both the investor and the finance researcher. In this paper, a hybrid approach is proposed for asset allocation, offering a combination of several methodologies for portfolio selection, such as investor topology, cluster analysis, and the analytical hierarchy process (AHP) to facilitate ranking the assets and fuzzy multiobjective linear programming (FMOLP). This paper considers some important factors of stock, like relative strength index (RSI), coefficient of variation (CV), earnings yield (EY), and price to earnings growth ratio (PEG ratio), apart from the risk and return and stocks which are included within these same factors. Employing fuzzy multiobjective linear programming, optimization is performed using seven objective functions viz., return, risk, relative strength index (RSI), coefficient of variation (CV), earnings yield (EY), price to earnings growth ratio (PEG ratio), and AHP weighted score. The FMOLP transforms the multiobjective problem to a single objective problem using the “weighted adaptive approach” in which the weights are calculated by AHP or choices by the investors. The FMOLP model permits choices in solution.

Highlights

Due to the uncertainty of return it is not easy to select the stocks
This paper is organized in four sections as follows: Section 2 includes an account of the research methodology, the fuzzy multiobjective linear programming (FMOLP) algorithm, and its working process with reference to each of the seven objectives, viz., return, risk, relative strength index, coefficient of variation, earning yield, price to earnings growth ratio, and analytical hierarchy process (AHP) weighted score
The multiobjective portfolio selection problem with seven objective functions such as return, risk, relative strength index, coefficient of variation, earning yield, price to earnings growth ratio, and AHP weight and some notations are introduced as follows: ri: return of the ith stock, xi: the proportion of the total fund invested in the ith stock, bi: the binary variable indicating whether the ith stock is contained in the portfolio or not, i.e., bi = {1, if ithstock contained in portfolio, 0, if not containing in portfolio}

Summary

Introduction

Due to the uncertainty of return it is not easy to select the stocks. The main aim of portfolio selection is to obtain an accurate ratio of the assets to ensure that the investor gets the maximum return with minimum risk. Some new features for stock selection have been included, such as relative strength index (RSI), coefficient of variation (CV), earnings yield (EY), and price to earnings growth ratio (PEG ratio), which have not been used earlier in the AHP. Optimization is done using fuzzy multiobjective linear programming with seven objective functions viz., return, risk, relative strength index (RSI), coefficient of variation (CV), earnings yield (EY), price to earnings growth ratio (PEG ratio), and AHP weighted score. This paper is organized in four sections as follows: Section 2 includes an account of the research methodology, the FMOLP algorithm, and its working process with reference to each of the seven objectives, viz., return, risk, relative strength index, coefficient of variation, earning yield, price to earnings growth ratio, and AHP weighted score.

Methodology

Numerical Illustration

Assets Allocation

Conclusion