Portfolio optimization using higher moments in an uncertain random environment
In this paper, a multi-objective portfolio optimization problem is studied in an uncertain random environment using higher moments. We consider a scenario involving an asset universe wherein some assets have sufficient historical return data for modelling as random variables, and others, listed rela...
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| Vydané v: | Information sciences Ročník 567; s. 348 - 374 |
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| Hlavní autori: | , , |
| Médium: | Journal Article |
| Jazyk: | English |
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Elsevier Inc
01.08.2021
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| ISSN: | 0020-0255, 1872-6291 |
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| Abstract | In this paper, a multi-objective portfolio optimization problem is studied in an uncertain random environment using higher moments. We consider a scenario involving an asset universe wherein some assets have sufficient historical return data for modelling as random variables, and others, listed relatively recently, lack historical data. The asset returns of such assets are modelled as uncertain variables. Thus, a hybrid environment involving both uncertain and random variables is considered. We use mean absolute semi-deviation as a risk measure and employ skewness (i.e., third moment) in the portfolio optimization model. The expressions for the mean absolute semi-deviation and skewness of an uncertain random variable have been derived. We show that the derivation of mean absolute semi-deviation is not based on any stipulation and thus is an accurate measure of risk (unlike the variance of an uncertain random variable, which uses stipulation). We propose a hybrid genetic algorithm as a solution methodology and provide empirical proofs to illustrate its advantages. The proposed methodology has been applied to a case study involving 100 assets listed in the NASDAQ-100 index of the U.S. stock market. We do an ex-post analysis to track the performance of our model out-of-sample and illustrate its advantages. |
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| AbstractList | In this paper, a multi-objective portfolio optimization problem is studied in an uncertain random environment using higher moments. We consider a scenario involving an asset universe wherein some assets have sufficient historical return data for modelling as random variables, and others, listed relatively recently, lack historical data. The asset returns of such assets are modelled as uncertain variables. Thus, a hybrid environment involving both uncertain and random variables is considered. We use mean absolute semi-deviation as a risk measure and employ skewness (i.e., third moment) in the portfolio optimization model. The expressions for the mean absolute semi-deviation and skewness of an uncertain random variable have been derived. We show that the derivation of mean absolute semi-deviation is not based on any stipulation and thus is an accurate measure of risk (unlike the variance of an uncertain random variable, which uses stipulation). We propose a hybrid genetic algorithm as a solution methodology and provide empirical proofs to illustrate its advantages. The proposed methodology has been applied to a case study involving 100 assets listed in the NASDAQ-100 index of the U.S. stock market. We do an ex-post analysis to track the performance of our model out-of-sample and illustrate its advantages. |
| Author | Mehlawat, Mukesh Kumar Khan, Ahmad Zaman Gupta, Pankaj |
| Author_xml | – sequence: 1 givenname: Mukesh Kumar surname: Mehlawat fullname: Mehlawat, Mukesh Kumar – sequence: 2 givenname: Pankaj surname: Gupta fullname: Gupta, Pankaj email: pankajgupta@gmail.com – sequence: 3 givenname: Ahmad Zaman surname: Khan fullname: Khan, Ahmad Zaman |
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| Keywords | Portfolio optimization Chance distribution Multi-objective programming Uncertain random variable Real-coded genetic algorithm Uncertain measure |
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| SubjectTerms | Chance distribution Multi-objective programming Portfolio optimization Real-coded genetic algorithm Uncertain measure Uncertain random variable |
| Title | Portfolio optimization using higher moments in an uncertain random environment |
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