The effects of skewed and heavy-tailed return distributions for optimal portfolio construction are investigated.Therefore, the class of generalized hyperbolic (GH) distributions is considered. Important distributions in finance such as the normal distribution also belong to the GH class of distributions. In the first part of the paper, models for asset returns are discussed and the class of GH distributions is introduced. Important limiting cases of the class of GH distributions are described. Next, the terms coherent and convex risk measures are introduced and the resulting portfolio optimization problems are stated. Finally, the portfolio optimization problem is solved with real-world data. Thereby, the efficient frontier is compared with the efficient frontier generated by a Markowitz model. It is shown that the normal assumption severely underestimates the extreme risks of the portfolio. Special attention is given to the effect of a currency index in a portfolio. The currency index has, on its own, no superior risk/return properties. However, in a portfolio context, the currency index greatly improves the risk/return profile of a portfolio.
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