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Assessment of the uncertainty in small and large dimensional portfolio allocation
Stockholm University, Faculty of Science, Department of Mathematics.
2019 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

Portfolio theory is a large subject with many branches. In this thesis we concern ourselves with one of these, the precense of uncertainty in the portfolio allocation problem and in turn, what it leads to. There are many forms of uncertainty, we consider two of these. The first being the optimization problem itself and optimizing what might be the wrong objective. In the classical mean-variance portfolio problem we aim to provide a portfolio with the smallest risk while we constrain the mean. However, in practice we might not assign a fixed portfolio goal but assign probabilities to the amount of return a portfolio might give and its relation to benchmarks. That is, we assign quantiles of the portfolio return distribution. In this scenario, the use of the portfolio mean as a return measure could be misleading. It does not take any quantile into account! In the first paper, we exchange the portfolio moments to quantile-based measures in the portfolio selection problem. The properties of the quantilebased portfolio selection problem is thereafter investigated with two different (quantile-based) measures of risk. We also present a closed form solution under the assumption that the returns follow an elliptical distribution. In this specific case the portfolio is shown to be mean-variance efficient.

The second paper takes on a different type of uncertainty which is classic to statistics, the problem of estimation uncertainty. We consider the sample estimators of the mean vector and of the covariance matrix of the asset returns and integrate the uncertainty these provide into a large class of optimal portfolios. We derive the sampling distribution, of the estimated optimal portfolio weights, which are obtained in both small and large dimensions. This consists of deriving the joint distribution of several quantities and thereafter specifying their high dimensional asymptotic distribution.

Place, publisher, year, edition, pages
Stockholm: Department of Mathematics, Stockholm University , 2019. , p. 18
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:su:diva-176095OAI: oai:DiVA.org:su-176095DiVA, id: diva2:1371723
Presentation
2019-12-11, 306, Kräftriket 6A, Stockholm, 15:15 (English)
Opponent
Supervisors
Available from: 2019-11-22 Created: 2019-11-20 Last updated: 2019-11-22Bibliographically approved
List of papers
1. Quantile-based optimal portfolio selection
Open this publication in new window or tab >>Quantile-based optimal portfolio selection
(English)Manuscript (preprint) (Other academic)
National Category
Probability Theory and Statistics
Identifiers
urn:nbn:se:su:diva-176093 (URN)
Available from: 2019-11-20 Created: 2019-11-20 Last updated: 2019-11-22Bibliographically approved
2. Sampling Distributions of Optimal Portfolio Weights and Characteristics in Small and Large Dimensions
Open this publication in new window or tab >>Sampling Distributions of Optimal Portfolio Weights and Characteristics in Small and Large Dimensions
(English)Manuscript (preprint) (Other academic)
National Category
Probability Theory and Statistics
Identifiers
urn:nbn:se:su:diva-176094 (URN)
Available from: 2019-11-20 Created: 2019-11-20 Last updated: 2019-11-22Bibliographically approved

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2829303132333431 of 67
CiteExportLink to record
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Citation style
  • apa
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Output format
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