Taming Large Events: Optimal Portfolio Theory for Strongly Fluctuating Assets

J. Bouchaud, D. Sornette, Christian Walter () and J. Aguilar
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J. Bouchaud: CFM - Capital Fund Management
D. Sornette: IGPP - Institute of Geophysics and Planetary Physics [Los Angeles] - UCLA - University of California [Los Angeles] - UC - University of California, LPMC - Laboratoire de physique de la matière condensée - UNS - Université Nice Sophia Antipolis (1965 - 2019) - CNRS - Centre National de la Recherche Scientifique

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Abstract: We propose a method of optimization of asset allocation in the case where the stock price variations are supposed to have "fat" tails represented by power laws. Generalizing over previous works using stable Lévy distributions, we distinguish three distinct components of risk described by three different parts of the distributions of price variations: unexpected gains (to be kept), harmless noise inherent to financial activity, and unpleasant losses, which is the only component one would like to minimize. The independent treatment of the tails of distributions for positive and negative variations and the generalization to large events of the notion of covariance of two random variables provide explicit formulae for the optimal portfolio. The use of the probability of loss (or equivalently the Value-at-Risk), as the key quantity to study and minimize, provides a simple solution to the problem of optimization of asset allocations in the general case where the characteristic exponents are different for each asset.

Date: 2011-11-21
Note: View the original document on HAL open archive server: https://hal.science/hal-04566694v1
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Published in International Journal of Theoretical and Applied Finance, 2011, 01 (01), pp.25-41. ⟨10.1142/S0219024998000035⟩

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Journal Article: Taming Large Events: Optimal Portfolio Theory for Strongly Fluctuating Assets (1998)
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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-04566694

DOI: 10.1142/S0219024998000035

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