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

Maier-Paape, Stanislaus; Zhu, Qiji Jim

doi:10.3390/risks6030076

Cited by 11 publications

(7 citation statements)

References 21 publications

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“…For example, when the risk measure is a deviation measure [20], which happens e.g. when an approximation of the current drawdown is considered (see [14]), and the expected return is used to gauge the performance we show that the affine structure of the efficient solution in the classical capital market pricing model is preserved (cf. Theorem 5.1), recovering in particular the results in [20].…”

Section: Introductionmentioning

confidence: 94%

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A General Framework for Portfolio Theory—Part I: Theory and Various Models

Maier-Paape

Zhu

2018

Risks

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Utility and risk are two often competing measurements on the investment success. We show that efficient trade-off between these two measurements for investment portfolios happens, in general, on a convex curve in the two-dimensional space of utility and risk. This is a rather general pattern. The modern portfolio theory of Markowitz (1959) and the capital market pricing model Sharpe (1964), are special cases of our general framework when the risk measure is taken to be the standard deviation and the utility function is the identity mapping. Using our general framework, we also recover and extend the results in Rockafellar et al. (2006), which were already an extension of the capital market pricing model to allow for the use of more general deviation measures. This generalized capital asset pricing model also applies to e.g., when an approximation of the maximum drawdown is considered as a risk measure. Furthermore, the consideration of a general utility function allows for going beyond the "additive" performance measure to a "multiplicative" one of cumulative returns by using the log utility. As a result, the growth optimal portfolio theory Lintner (1965) and the leverage space portfolio theory Vince (2009) can also be understood and enhanced under our general framework. Thus, this general framework allows a unification of several important existing portfolio theories and goes far beyond. For simplicity of presentation, we phrase all for a finite underlying probability space and a one period market model, but generalizations to more complex structures are straightforward.

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Section: Introductionmentioning

confidence: 94%

“…In this first installment of the paper, we layout the framework, derive the theoretical results of crucial importance and illustrate them with a few examples. More new applications will appear in the subsequent papers [3,14]. We arrange the paper as follows: First we discuss necessary preliminaries in the next section.…”

Section: Introductionmentioning

confidence: 99%

A General Framework for Portfolio Theory—Part I: Theory and Various Models

Maier-Paape

Zhu

2018

Risks

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“…However, one assumption draws more reaction than the others is that risk can be measured as the dispersion of dataset of returns relative to its mean value, in other words, standard deviation. Maier-Paape and Zhu [7,8] reviewed the definition of the risk within the context of modern portfolio theory, its limitations, objections and some alternative risk measures.…”

Section: Introductionmentioning

confidence: 99%

Optimal Life Extension Management of Offshore Wind Farms Based on the Modern Portfolio Theory

Yeter

Garbatov

2021

Oceans

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The present study aims to develop a risk-based approach to finding optimal solutions for life extension management for offshore wind farms based on Markowitz’s modern portfolio theory, adapted from finance. The developed risk-based approach assumes that the offshore wind turbines (OWT) can be considered as cash-producing tangible assets providing a positive return from the initial investment (capital) with a given risk attaining the targeted (expected) return. In this regard, the present study performs a techno-economic life extension analysis within the scope of the multi-objective optimisation problem. The first objective is to maximise the return from the overall wind assets and the second objective is to minimise the risk associated with obtaining the return. In formulating the multi-dimensional optimisation problem, the life extension assessment considers the results of a detailed structural integrity analysis, a free-cash-flow analysis, the probability of project failure, and local and global economic constraints. Further, the risk is identified as the variance from the expected mean of return on investment. The risk–return diagram is utilised to classify the OWTs of different classes using an unsupervised machine learning algorithm. The optimal portfolios for the various required rates of return are recommended for different stages of life extension.

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“…However, one assumption draws more reaction than the others: risk can be measured as the dispersion of dataset of returns relative to its mean value, in other words, standard deviation. Maier-Paape and Zhu [7,8] reviewed the definition of the risk within the context of modern portfolio theory, its limitations, objections and some alternative risk measures.…”

Section: Introductionmentioning

confidence: 99%

Optimal Life Extension Management of Offshore Wind Farms Based on the Modern Portfolio Theory

Yeter¹,

Garbatov²

2021

Preprint

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The present study aims to develop a risk-based approach to find optimal solutions for life extension management for offshore wind farms based on Markowitz’s modern portfolio theory, adapted from finance. The developed risk-based approach assumes that the offshore wind turbines (OWT) can be considered as cash-producing tangible assets providing positive return from the initial investment (capital) with a given risk attaining the targeted (expected) return. In this regard, the present study performs a techno-economic life extension analysis within the scope of the multi-objective optimisation problem. The first objective is to maximise the return from the overall wind assets, while the latter aims to minimise the risk associated with obtaining the return. In formulating the multi-dimensional optimisation problem, the life-extension assessment considers the results of a detailed structural integrity analysis, free-cash-flow analysis, and probability of project failure, local and global economic constraints. Further, the risk is identified as the variance from the expected mean of return on investment. The risk-return diagram is utilised to classify the OWTs of different classes using an unsupervised machine learning algorithm. The optimal portfolios for the various required rate of return are recommended for different stages of life extension.

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

Cited by 11 publications

References 21 publications

A General Framework for Portfolio Theory—Part I: Theory and Various Models

A General Framework for Portfolio Theory—Part I: Theory and Various Models

Optimal Life Extension Management of Offshore Wind Farms Based on the Modern Portfolio Theory

Optimal Life Extension Management of Offshore Wind Farms Based on the Modern Portfolio Theory

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