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    Tail risk constraints and maximal entropy

    Geman, Hélyette and Geman, D. and Taleb, N. (2015) Tail risk constraints and maximal entropy. Entropy 17 (6), pp. 3724-3737. ISSN 1099-4300.

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    Abstract

    Portfolio selection in the financial literature has essentially been analyzed under two central assumptions: full knowledge of the joint probability distribution of the returns of the securities that will comprise the target portfolio; and investors’ preferences are expressed through a utility function. In the real world, operators build portfolios under risk constraints which are expressed both by their clients and regulators and which bear on the maximal loss that may be generated over a given time period at a given confidence level (the so-called Value at Risk of the position). Interestingly, in the finance literature, a serious discussion of how much or little is known from a probabilistic standpoint about the multi-dimensional density of the assets’ returns seems to be of limited relevance. Our approach in contrast is to highlight these issues and then adopt throughout a framework of entropy maximization to represent the real world ignorance of the “true” probability distributions, both univariate and multivariate, of traded securities’ returns. In this setting, we identify the optimal portfolio under a number of downside risk constraints. Two interesting results are exhibited: (i) the left- tail constraints are sufficiently powerful to override all other considerations in the conventional theory; (ii) the “barbell portfolio” (maximal certainty/ low risk in one set of holdings, maximal uncertainty in another), which is quite familiar to traders, naturally emerges in our construction.

    Metadata

    Item Type: Article
    Keyword(s) / Subject(s): risk management, barbell portfolio strategy, maximum entropy
    School: Birkbeck Schools and Departments > School of Business, Economics & Informatics > Economics, Mathematics and Statistics
    Research Centre: Commodities Finance Centre
    Depositing User: Helyette Geman
    Date Deposited: 26 May 2016 13:19
    Last Modified: 26 Jul 2019 16:05
    URI: http://eprints.bbk.ac.uk/id/eprint/15329

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