Generalized hyperbolic distribution and portfolio efficiency in energy and stock markets of BRIC countries

Oil, also called black gold, is considered as the commodity which has the greatest impact on the world's economy, and it has been studied in terms of its relationship and effects on macroeconomic variables such as Gross Domestic Product (GDP), inflation, trade balance, exchange rate and some others. Likewise, the relationship of oil with the financial market has been deepened and is very interesting in the case of emergent economies such as Brazil, Russia, India and China (BRIC) countries. There are many studies and approaches to this topic, but few of them focus on seeking investment opportunities through the diversification of these variables and therefore creating efficient portfolios using other distribution from the norm. This research proposes the construction of diversified portfolios with the returns of the indexes and oil mixes of the BRIC countries modeled under a Normal Inverse Gaussian (NIG) distribution, which is a notable member of the Generalized Hyperbolic (GH) family, and analyzing the effect on investment, by the inclusion of each variable into the portfolio. An important property of the GH family is that the correlations matrix of the returns is obtained from estimation of the parameters of empirical distribution through maximum likelihood. The results show in an optimal configuration, that each instrument of India, China and Brazil, contributes to the portfolio efficiency, in contrast to the index and oil mix of Russia, that do not contribute significantly.