Composition of an Optimal Portfolio in the Capital Market - Elton & Gruber Model in Portugal’s Capital Market

Abstract

In order to maximize their utility function, investors select some assets over others by choosing the ideal portfolio that will maximize their wealth. Each asset is chosen taking into account the relationship between the risk of that particular investment (usually measured by variance)- and the return it can offer, as well as the risk between this and other assets (as measured by covariance). The purpose of this work was to build an optimal portfolio using data on PSI-20's stock prices (2008-2016) where investors are aware of risk and want to minimize it. For this purpose, an optimal portfolio’s comparison in the period between 2004-2007 was conducted. This period was referred to as the financial pre-crisis, compared to the optimal portfolio obtained in the period after the financial crisis (2008-2016). The methodology used to estimate the expected profitability of each asset that makes up the PSI-20 was obtained by extracting the historical quotations from the Euronext Lisbon website. The Elton & Gruber model was used in order to determine the optimal portfolio, as well as the assets that should be part of it. In the period after the financial crisis, it can be verified in the optimal portfolio’s composition that, in the periods after the financial crisis and the financial crisis, there were no stocks to be included in the optimal portfolio, and an analysis in smaller periods was made. In the post financial crisis period actions were found with an attractiveness index superior to the cut-off point, which would lead them to be included in the optimal portfolio, and it was verified that the large distribution sector with (32.15%) has the greatest weight in the optimal portfolio, considering also the Oil and Gas (19.95%), Banking (11.84%) and Production (8.09%) sectors. While addressing shorter periods in pre financial crisis period, no asset was included in the optimal portfolio’s constitution.