The paper derives the shape of portfolio distributions that have maximum entropy subject to real-world left-tail constraints and other expectations.

This is a factual claim about the content of the paper (Geman, Geman & Taleb, 'Tail Risk Constraints and Maximum Entropy', c. 2014-12). True: the paper derives the form of the maximum-entropy portfolio distribution under left-tail constraints (e.g. value-at-risk/CVaR) and other moment or expectation constraints. Mostly true: it derives this under tail constraints, with only minor differences in which other expectations are used. Mixed: it derives a maximum-entropy distribution, but not under left-tail constraints, or the reverse. Mostly false: the derivation is only sketched or asserted. False: the paper contains no such derivation.

Set before the research began.

1. E1 BIROn - Birkbeck Institutional Research Online Birkbeck, University of London (repository copy of Entropy 2015, 17, 3724-3737) · 5 June 2015 Own record

   “In a nutshell, we hardwire the curtailments on loss but otherwise assume maximal uncertainty about the returns. More precisely, we equate the return distribution with the maximum entropy extension of constraints expressed as statistical expectations on the left-tail behavior as well as on the expectation of the return or log-return in the non-danger zone.”

2. E2 BIROn - Birkbeck Institutional Research Online Birkbeck, University of London (repository copy of Entropy 2015, 17, 3724-3737) · 5 June 2015 Own record

   “Our strategy is to generalize the second scenario by replacing the variance σ2 by two left-tail value-at-risk constraints and to model the portfolio return as the maximum entropy extension of these constraints together with a constraint on the overall performance or on the growth of the portfolio in the non-danger zone.”

3. E3 Taleb, the Barbell Portfolio and Safety-First Financial Planning Advisor Perspectives · 13 February 2017

   “The basic idea is to anchor a portfolio to a hard, downside-only risk constraint – i.e., not standard deviation – and then to split the portfolio into two elements that meet two very different objectives: a hedged element that strictly meets the downside risk constraint and an aggressive element in which you maximize the uncertainty of the result.”

The paper's own text [E1][E2] shows that it models the portfolio return as the maximum-entropy extension of left-tail value-at-risk constraints and a constraint on performance or growth. However, none of the evidence shows the derived distribution itself, and the independent source [E4] does not address the derivation. So the evidence cannot tell a full derivation apart from one that is only sketched, which is the line the criteria draw between true and mostly false.