# Sensitivity analysis of Mixed Tempered Stable parameters with implications in portfolio optimization

## Abstract

This paper investigates the use, in practical financial problems, of the Mixed Tempered Stable distribution both in its univariate and multivariate formulation. In the univariate context, we study the dependence of a given coherent risk measure on the distribution parameters. The latter allows to identify the parameters that seem to have a greater influence on the given measure of risk. The multivariate Mixed Tempered Stable distribution enters in a portfolio optimization problem built considering a real market dataset of seventeen hedge fund indexes. We combine the flexibility of the multivariate Mixed Tempered Stable distribution, in capturing different tail behaviors, with the ability of the ARMA-GARCH model in capturing the time dependence observed in the data.

## Keywords

Mixed Tempered Stable distribution Sensitivity analysis Portfolio optimization## Notes

### Acknowledgements

The authors would like to thank the Editor and three anonymous Referees for their helpful comments. All remaining errors are responsibility of the authors. This research is part of the project “Advanced Methods for Portfolio Optimization” (Number 35364), which is financially supported by the “MIUR-DAAD Joint Mobility Program (2nd Edition)”.

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