Tail Risk Constraints and Maximum Entropy
Abstract
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: risktaking 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 realworld lefttail constraints and other expectations. Two consequences are (i) the lefttail 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.
 Publication:

Entropy
 Pub Date:
 June 2015
 DOI:
 10.3390/e17063724
 arXiv:
 arXiv:1412.7647
 Bibcode:
 2015Entrp..17.3724G
 Keywords:

 Quantitative Finance  Risk Management
 EPrint:
 Entropy 17 (6), 37243737, 2015