Optimal Portfolios with Skewed and Heavy-Tailed Distributions

S. Keel, F. Herzog, H.P. Geering, and N. Mirjolet (Switzerland)


Risk, Management, Optimal Portfolio, Generalized Hyper bolic, Currency Index


The effects of skewed and heavy-tailed return distri butions for optimal portfolio construction are investigated. Therefore, the class of generalized hyperbolic (GH) distri butions 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 as set 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 port folio optimization problems are stated. Finally, the port folio 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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