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Tail Risk Constraints and Maximum Entropy


  • Donald Geman
  • H'elyette Geman
  • Nassim Nicholas Taleb


In the world of modern financial theory, portfolio construction has traditionally operated under at least one of two central assumptions: the constraints are derived from a utility function and/or the multivariate probability distribution of the underlying asset returns is fully known. In practice, both the performance criteria and the informational structure are markedly different: risk-taking agents are mandated to build portfolios by primarily constraining the tails of the portfolio return to satisfy VaR, stress testing, or expected shortfall (CVaR) conditions, and are largely ignorant about the remaining properties of the probability distributions. As an alternative, we derive the shape of portfolio distributions which have maximum entropy subject to real-world left-tail constraints and other expectations. Two consequences are (i) the left-tail constraints are sufficiently powerful to overide other considerations in the conventional theory, rendering individual portfolio components of limited relevance; and (ii) the "barbell" payoff (maximal certainty/low risk on one side, maximum uncertainty on the other) emerges naturally from this construction.

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  • Donald Geman & H'elyette Geman & Nassim Nicholas Taleb, 2014. "Tail Risk Constraints and Maximum Entropy," Papers 1412.7647,
  • Handle: RePEc:arx:papers:1412.7647

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    References listed on IDEAS

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    Cited by:

    1. Aleksander Schiffers & Marcin Chlebus, 2021. "The effectiveness of Value-at-Risk models in various volatility regimes," Working Papers 2021-28, Faculty of Economic Sciences, University of Warsaw.
    2. Farzad Alavi Fard & Firmin Doko Tchatoka & Sivagowry Sriananthakumar, 2021. "Maximum Entropy Evaluation of Asymptotic Hedging Error under a Generalised Jump-Diffusion Model," JRFM, MDPI, vol. 14(3), pages 1-19, February.

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