Minimizing volatility increases large risks

Details Minimizing volatility increases large risks Minimizing volatility increases large risks

1998-11-19

arxiv.org/abs/cond-mat/9811292v1

International Journal of Theoretical and Applied Finance 3 (3), 523-535 (2000)

Physics

Condensed Matter

Statistical Mechanics

13 pages, 6 figures

Scientific paper

We introduce a faithful representation of the heavy tail multivariate distribution of asset returns, as parsimonous as the Gaussian framework. Using calculation techniques of functional integration and Feynman diagrams borrowed from particle physics, we characterize precisely, through its cumulants of high order, the distribution of wealth variations of a portfolio composed of an arbitrary mixture of assets. The portfolio which minimizes the variance, i.e. the relatively small risks, often increases larger risks as measured by higher normalized cumulants and by the Value-at-risk.

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