A General Framework for Portfolio Theory. Part II: Drawdown Risk Measures

Stanislaus Maier-Paape and Qiji Jim Zhu
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Stanislaus Maier-Paape: Institut für Mathematik, RWTH Aachen University, 52062 Aachen, Germany
Qiji Jim Zhu: Department of Mathematics, Western Michigan University, Kalamazoo, MI 49008, USA

Risks, 2018, vol. 6, issue 3, 1-31

Abstract: 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.

Keywords: admissible convex risk measures; current drawdown; efficient frontier; portfolio theory; fractional Kelly allocation, growth optimal portfolio; financial mathematics (search for similar items in EconPapers)
JEL-codes: C G0 G1 G2 G3 K2 M2 M4 (search for similar items in EconPapers)
Date: 2018
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (6)

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