| Abstract [eng] |
This Master's thesis examines the principles behind the construction of two types of investment portfolios: the minimum variance (also known as the minimum standard deviation) (Min-STD) and the mean absolute deviation (MAD) and compares them with the performance of the S&P 500 index. Using the fundamentals of Modern Portfolio Theory (MPT) and based on historical data of the S&P 500 components from three different 3-year periods, the portfolios were optimized using quadratic and linear programming algorithms. The results showed that Min-STD portfolios tend to be more diversified but require more computational resources, while MAD portfolios are more concentrated and faster to compute. The returns and risk indicators achieved in the test periods show that the Min-STD and MAD portfolios, although underperforming the S&P 500 in some months, can offer similar investment results and can be used as an alternative to a market index. The analysis of the efficient frontiers also shows that, despite their different risk measures, the two approaches are able to form similar sets of efficient portfolios. |
