Abstract
Markowitz's portfolio model laid the foundation of the modern portfolio theory (MPT). As an intuitive and effective quantitative method, the Markowitz model has long been considered one of the most successful approaches in financial modeling. This paper tries to illustrate the process of Markowitz modeling and demonstrate the usefulness of the Markowitz theory empirically. Three high-tech companies, Apple Inc. (AAPL), Alphabet Inc. (GOOG), and Microsoft Corporation (MSFT) investigated to build the Markowitz model. We first retrieve the dataset from the website of yahoo finance and provide the descriptive statistics for the three companies, respectively. Then, the global minimum variance (GMV) portfolio is constructed to identify the boundary point of the efficient frontier. The optimized portfolio model at the given risk level is constructed according to the Markowitz theory. Also, the random portfolio weights under the budget constraint are generated for comparison. To evaluate the performance, we provide the Sharpe ratio for the constructed Markowitz portfolio.
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