Review of two-constraint minimum portfolio risk: A simulation of expected return selection

The process of selecting shares used to allocate investment funds must be carried out carefully and measurably. One of the steps in portfolio formation is to minimize the risk that may occur. This research revealed portfolio formation by using minimizing risk with two constraints. The preliminary step was to find each stock's weight that minimizes risk with constraints wT p = 1 and wT r = rO. Furthermore, the simulation of the selection of rO varies was conducted and how the characteristics of λ, β, weight, and risk depended on the value of rO was seen. The results of portfolio formation showed that the highest return (mean) was in BAPB shares of 0.009538729 with a risk level (variance) of 0.006573788. In comparison, the lowest return was in LPGI shares of 0.000978691 with a risk level (variance) of 0.000411903. Then, a simulation was carried out with the selection of rO. The simulation that had been carried out showed that with the characteristic of rO closer to the maximum, the λ value decreased, and the β value increased. Meanwhile, the weight characteristics if rO was closer to the maximum for the six stocks would be 50% of the observed stocks tended to rise, 33% of the observed stocks tended to fall, and 17% of the observed stocks moved up but slowly. Finally, the measurement of the level of risk was directly proportional to the selection of rO. It meant that if you wanted the maximum return, you would get a high risk as well. © 2023 Author(s).