Optimal portfolio analysis using power and natural logarithm utility functions with e-commerce data

Determining the optimal portfolio is important in the investment process because it includes the selection of appropriate fund allocation to manage financial risk effectively. Although risk cannot be entirely eliminated, it is managed through strategic allocation based on investor preferences. Therefore, this research aimed to use mathematical models, including the power utility function, the natural logarithm utility function, and a combination of both, to capture varying degrees of risk aversion. The optimal allocation was obtained by analytically maximizing the expected end-of-period wealth utility under each specification, where the investor level of risk aversion was derived by determining the constant. The utility function that failed to produce closed-form solutions was solved through the use of a numerical method to approximate the optimal portfolio weight. Furthermore, numerical simulations were performed using data from two stocks in the e-commerce sector to prove the impact of parameter changes on investment decisions. The result showed explicit analytical values for each utility function, providing investors with a structured framework for determining optimal portfolio weights consistent with their risk profile.