Applications of robust statistics in Markowitz portfolio theory

Bartosz Kaszuba

Abstract

The purpose of this dissertation is to assess whether correct application of robust estimators in construction of efficient portfolios allows to achieve better investment results in comparison with the portfolios created using classical MLE estimators. This dissertation makes performance comparison between classical portfolios and portfolios constructed with robust methods: affine equivariant robust estimators of mean and covariance matrix (S, MM, MVE, MCD, SDE), pairwise covariance matrix (QC, OGK, I2D), as well as robust portfolio estimators (M, S, LAD, LTS, LMS). Apart from robust portfolios, portfolios created using other non-classical methods are compared as well. The assessment of portfolio properties is carried out on the basis of return rates of out-of-sample portfolios. The research utilizes historical returns from Warsaw Stock Exchange. The dissertation describes the aforementioned methods in details and compares their theoretical properties. The fundamental definitions and their interpretation in the context of applications in the portfolio theory are described as well. It has been revealed that only selected robust portfolios performs better than classical portfolios. The increase of portfolio transaction costs during the increase of its robustness has been also revealed. The empirical results also show that application of Markowitz portfolio theory in practice is justified only for minimum variance portfolios.
Diploma typeDoctor of Philosophy
Author Bartosz Kaszuba
Bartosz Kaszuba,,
-
Title in EnglishApplications of robust statistics in Markowitz portfolio theory
Languagepl polski
Certifying UnitFaculty of Management, Information Systems and Finance (MISaF)
Disciplineekonomia / nauki ekonomiczne(nauki ekonomiczne) / nauki społeczne()
Defense Date17-10-2012
End date15-11-2012
Supervisor Krzysztof Jajuga (MISaF / IZF / KIFiZR)
Krzysztof Jajuga,,
- Katedra Inwestycji Finansowych i Zarządzania Ryzykiem

Internal reviewers Wanda Ronka-Chmielowiec (MISaF / IZF / KU)
Wanda Ronka-Chmielowiec,,
- Katedra Ubezpieczeń
External reviewers Mirosław Szreder
Mirosław Szreder,,
-
Pages216
Keywords in EnglishRobust statistics, robust portfolios, portfolio theory, robust estimation, asset allocation
Abstract in EnglishThe purpose of this dissertation is to assess whether correct application of robust estimators in construction of efficient portfolios allows to achieve better investment results in comparison with the portfolios created using classical MLE estimators. This dissertation makes performance comparison between classical portfolios and portfolios constructed with robust methods: affine equivariant robust estimators of mean and covariance matrix (S, MM, MVE, MCD, SDE), pairwise covariance matrix (QC, OGK, I2D), as well as robust portfolio estimators (M, S, LAD, LTS, LMS). Apart from robust portfolios, portfolios created using other non-classical methods are compared as well. The assessment of portfolio properties is carried out on the basis of return rates of out-of-sample portfolios. The research utilizes historical returns from Warsaw Stock Exchange. The dissertation describes the aforementioned methods in details and compares their theoretical properties. The fundamental definitions and their interpretation in the context of applications in the portfolio theory are described as well. It has been revealed that only selected robust portfolios performs better than classical portfolios. The increase of portfolio transaction costs during the increase of its robustness has been also revealed. The empirical results also show that application of Markowitz portfolio theory in practice is justified only for minimum variance portfolios.
KBN classificationekonomia
Thesis file
Kaszuba_B_Zastosowanie_Wielowymiarowych_Metod_Statystyki_Odpornej.pdf 1,32 MB

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