A general framework for portfolio theory. Part II: Drawdown risk measures

The aim of this paper is to provide several examples of convex risk measures necessary for the application of the general framework for portfolio theory of Maier-Paape and Zhu (2018), presented in Part I of this series. As an alternative to classical portfolio risk measures such as the standard devi...

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Bibliographic Details
Published in:Risks (Basel) 2018-09, Vol.6 (3), p.1-31
Main Authors: Maier-Paape, Stanislaus, Zhu, Qiji Jim
Format: Article
Language:English
Subjects:
admissible convex risk measures
Asset allocation
Capital assets
CAPM
current drawdown
Economic models
efficient frontier
financial mathematics
fractional Kelly allocation
fractional Kelly allocation, growth optimal portfolio
growth optimal portfolio
Investment policy
Mathematics
Portfolio management
portfolio theory
Securities markets
Standard deviation
Theory
Utility functions
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Summary:The aim of this paper is to provide several examples of convex risk measures necessary for the application of the general framework for portfolio theory of Maier-Paape and Zhu (2018), presented in Part I of this series. As an alternative to classical portfolio risk measures such as the standard deviation, we, in particular, construct risk measures related to the 'current' drawdown of the portfolio equity. In contrast to references Chekhlov, Uryasev, and Zabarankin (2003, 2005), Goldberg and Mahmoud (2017), and Zabarankin, Pavlikov, and Uryasev (2014), who used the absolute drawdown, our risk measure is based on the relative drawdown process. Combined with the results of Part I, Maier-Paape and Zhu (2018), this allows us to calculate efficient portfolios based on a drawdown risk measure constraint.
ISSN:2227-9091
2227-9091
DOI:10.3390/risks6030076