How to combine the Serbian stock index with precious metals in a multivariate Markowitz portfolio?

Abstract

This paper aims to determine how to combine the Serbian stock index, BELEXline, with four precious metals - gold, silver, platinum and palladium, in order to minimize risk. In the process of portfolio construction, we use the theoretical concept of Markowitz. In particular, we first determine a portfolio of five assets, then exclude an asset with the lowest share and repeat the procedure till we reach a portfolio of two assets. In this way, we construct four portfolios of five, four, three and two assets. In the five-asset portfolio, the portfolio optimization process determines a zero share of silver, because silver bears the highest risk of all other portfolio instruments. This, also, means that five and four-asset portfolios have the same characteristics. On the other hand, in the three-asset portfolio, which contains the Serbian index, gold and platinum, we find a higher share of platinum, compared to the five-asset portfolio, because platinum has a higher negative correlation with BELEXline, vis-à-vis gold-BELEXline pair. Two-asset portfolio, which includes only the index and gold, has a higher risk in the amount of 5% and 4%, in relation to the four and three-asset counterparts. The general conclusion is that a three-asset portfolio is the best one, since it has slightly higher risk than a five or four-asset portfolio, but it has lower transaction cost because it includes only three instruments.