This paper proposes a twist to the classical Markowitz approach to build efficient portfolios of risky assets that improves their risk-return performance. The originality of our approach consists in the utilization of a covariance matrix from a member of the Generalized Hyperbolic (GH) Family distribution, instead of the sample covariance matrix described in Markowitz's (1959) seminal contribution. We test the approach with the daily returns of stocks traded in MILA (Mercado Integrado Latino Americano) markets: Chile, Colombia, Mexico and Peru, from January 1st, 2010, to December 31st, 2015. The GH based portfolios are benchmarked with an equally weighted portfolio and a historical covariance based Markowitz portfolio using the coefficient of variation of returns. The results confirm the GH based portfolio's dominance over the other two benchmarks.
