Robust portfolio optimization with risk measures under distributional uncertainty

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buir.advisorPınar, Mustafa Ƈ.
dc.contributor.authorPaƧ, A. Burak
dc.date.accessioned2016-08-26T10:00:39Z
dc.date.available2016-08-26T10:00:39Z
dc.date.copyright2016-07
dc.date.issued2016-07
dc.date.submitted2016-08-12
dc.departmentDepartment of Industrial Engineeringen_US
dc.descriptionCataloged from PDF version of article.en_US
dc.descriptionThesis (Ph.D.): Bilkent University, Department of Industrial Engineering, İhsan Doğramacı Bilkent University, 2016.en_US
dc.descriptionIncludes bibliographical references (leaves 115-121).en_US
dc.description.abstractIn this study, we consider the portfolio selection problem with different risk measures and different perspectives regarding distributional uncertainty. First, we consider the problem of optimal portfolio choice using the first and second lower partial moment risk measures, for a market consisting of n risky assets and a riskless asset, with short positions allowed. We derive closed-form robust portfolio rules minimizing the worst case risk measure under uncertainty of the return distribution given the mean/covariance information. A criticism levelled against distributionally robust portfolios is sensitivity to uncertainties or estimation errors in the mean return data, i.e., Mean Return Ambiguity. Modeling ambiguity in mean return via an ellipsoidal set, we derive results for a setting with mean return and distributional uncertainty combined. Using the adjustable robustness paradigm we extend the single period results to multiple periods in discrete time, and derive closed-form dynamic portfolio policies. Next, we consider the problem of optimal portfolio choice minimizing the Conditional Value-at-Risk (CVaR) and Value-at-Risk (VaR) measures under the minimum expected return constraint. We derive the optimal portfolio rules for the ellipsoidal mean return vector and distributional ambiguity setting. In the presence of a riskless asset, the robust CVaR and VaR measures, coupled with a minimum mean return constraint, yield simple, mean-variance efficient optimal portfolio rules. In a market without the riskless asset, we obtain a closed-form portfolio rule that generalizes earlier results, without a minimum mean return restriction. In the final problem, we have a change of perspective regarding uncertainty. Rather than the information on first and second moments, knowledge of a nominal distribution of asset returns is assumed, and the actual distribution is considered to be within a ball around this nominal distribution. The metric choice on the probability space is the Kantorovich distance. We investigate convergence of the risky investment to uniform portfolio when a riskless asset is available. While uniform investment to risky assets becomes optimal, it is shown that as the uncertainty radius increases, the total allocation to risky assets diminishes. Hence, as uncertainty increases, the risk averse investor is driven out of the risky market.en_US
dc.description.degreePh.D.en_US
dc.description.statementofresponsibilityby A. Burak PaƧ.en_US
dc.embargo.release2017-09-01
dc.format.extentxii, 121 leaves : charts.en_US
dc.identifier.itemidB153766
dc.identifier.urihttp://hdl.handle.net/11693/32164
dc.language.isoEnglishen_US
dc.publisherBilkent Universityen_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.subjectRobust Portfolio Choiceen_US
dc.subjectDistributional Robustnessen_US
dc.subjectAdjustable Robustnessen_US
dc.subjectLower Partial Momentsen_US
dc.subjectDynamic Portfolio Rulesen_US
dc.subjectEllipsoidal Uncertaintyen_US
dc.subjectConditional Value-at-Risken_US
dc.titleRobust portfolio optimization with risk measures under distributional uncertaintyen_US
dc.title.alternativeDağılım belirsizliği altındaki risk ƶlĆ§Ć¼leri iƧin gĆ¼rbĆ¼z portfolyo optimizasyonuen_US
dc.typeThesisen_US

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