Optimization of Risk and Return Using Fuzzy Multiobjective Linear Programming

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.

Comparison Analysis of “Safe Investment”

“…The higher the standard deviation value, the higher the risk experienced and vice versa. According to Hartono (2018), risk can be measured using the following formula: According to (Panwar, Jha, & Srivastava, 2018;Sorros, 2003;Brigham & Houston, 2010), if we have to choose between two investments that have the same returns, but with different standard deviations, most people will choose investments with lower standard deviations and therefore less risk. Likewise, if faced with a choice between two investments with the same risk, but with different, investors will generally choose the investment with the higher return.…”

“…From a risk perspective, money market mutual funds are the right investment instruments because they have a low level of risk. The calculation of the coefficient of variation can compare return and risk so that it can determine the best investment instrument (Panwar, Jha, & Srivastava, 2018;Sorros, 2003;Brigham & Houston, 2010). Based on the calculation of the coefficient of variation, government bond is the best and most profitable investment instruments compared to money market mutual funds and gold.…”

“…To obtain an accurate analysis, investors also need to pay attention to the coefficient of variation of each investment product. If the return and risk of the investment instrument are at different levels, then the calculation that needs to be done is to compare the coefficient of variation (Panwar, Jha, & Srivastava, 2018;Sorros, 2003;Brigham & Houston, 2010, Fahmi, 2015.…”

An Experimental Study with Objectives Functions for Portfolio Optimization Problem

“…The selected 146 stocks are divided into three clusters as the investors focus only on the three points, namely, return, risk, and liquidity. The result of cluster analysis for both the techniques are given in [10,11].…”

“…With the help of a membership function, a multi-objective function can be converted into a single objective function. The complete methodology and data analysis are given in [11].…”