Tail Risk Constraints and Maximum Entropy
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 funct...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2015-06-01
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| Series: | Entropy |
| Subjects: | |
| Online Access: | http://www.mdpi.com/1099-4300/17/6/3724 |
| _version_ | 1811263309512441856 |
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| author | Donald Geman Hélyette Geman Nassim Nicholas Taleb |
| author_facet | Donald Geman Hélyette Geman Nassim Nicholas Taleb |
| author_sort | Donald Geman |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-12T19:42:24Z |
| format | Article |
| id | doaj.art-9c0d075da54b48f6aa499b12134c0e62 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-04-12T19:42:24Z |
| publishDate | 2015-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-9c0d075da54b48f6aa499b12134c0e622022-12-22T03:19:03ZengMDPI AGEntropy1099-43002015-06-011763724373710.3390/e17063724e17063724Tail Risk Constraints and Maximum EntropyDonald Geman0Hélyette Geman1Nassim Nicholas Taleb2Department of Applied Mathematics & Statistics, Johns Hopkins University, Baltimore, MD 21218-2608, USADepartment of Applied Mathematics & Statistics, Johns Hopkins University, Baltimore, MD 21218-2608, USAPolytechnic School of Engineering, New York University, New York, NY 11201, USAPortfolio 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.http://www.mdpi.com/1099-4300/17/6/3724risk managementbarbell portfolio strategymaximum entropy |
| spellingShingle | Donald Geman Hélyette Geman Nassim Nicholas Taleb Tail Risk Constraints and Maximum Entropy Entropy risk management barbell portfolio strategy maximum entropy |
| title | Tail Risk Constraints and Maximum Entropy |
| title_full | Tail Risk Constraints and Maximum Entropy |
| title_fullStr | Tail Risk Constraints and Maximum Entropy |
| title_full_unstemmed | Tail Risk Constraints and Maximum Entropy |
| title_short | Tail Risk Constraints and Maximum Entropy |
| title_sort | tail risk constraints and maximum entropy |
| topic | risk management barbell portfolio strategy maximum entropy |
| url | http://www.mdpi.com/1099-4300/17/6/3724 |
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