In investment transactions, such as stocks and commodities, risk is always involved. The link between investment returns and risk factors is often discussed. Many academics have attempted to develop models under any expected rate of return. The primary purpose of this paper is to demonstrate the application of modern portfolio theory in optimizing investment portfolios. The paper mainly analyzes the viewpoint through the use of historical financial data. The study constructs and examines portfolios using the Full Markowitz Model (MM) and the Index Model (IM) through five constraint conditions. By incorporating various constraints, the study aims to understand how regulatory, industry- specific, and client-driven limitations impact portfolio construction and performance.