Constructing the Optimal Portfolio Using the Simple Sharpe Gradient Method

An Application to Companies Listed on the Bahrain Islamic Index (BIX)

Abstract

This study aimed to identify the optimal investment portfolio using the Simple Stepwise Method, also known as the Single Index Model (Sharpe), under the constraint of no short selling. The analysis was applied to a group of securities listed on the Bahrain Islamic Index (BIX), using published monthly data covering the period from August 1, 2023, to August 1, 2024. Microsoft Excel was employed to carry out the analysis and determine the optimal portfolio. The results indicated the possibility of constructing an efficient portfolio consisting of a specific combination of stocks with defined relative importance that align with the investor's objectives. The optimal portfolio was composed of five stocks: ABMTB (8.567%), SALAM (21.870%), GFHB (5.229%), SOLLD (61.742%), and INOV (2.592%). The findings also confirmed that the Single Index Model can serve as a reliable tool for guiding investors in selecting well-performing stocks, while excluding those with poor performance, thereby achieving a better balance between return and risk compared to the benchmark portfolio represented by the Bahrain Islamic Index.