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A closed-form solution of the multi-period portfolio choice problem for a quadratic utility function
Stockholm University, Faculty of Science, Department of Mathematics.
Number of Authors: 3
2015 (English)In: Annals of Operations Research, ISSN 0254-5330, E-ISSN 1572-9338, Vol. 229, no 1, 121-158 p.Article in journal (Refereed) Published
Abstract [en]

In the present paper, we derive a closed-form solution of the multi-period portfolio choice problem for a quadratic utility function with and without a riskless asset. All results are derived under weak conditions on the asset returns. No assumption on the correlation structure between different time points is needed and no assumption on the distribution is imposed. All expressions are presented in terms of the conditional mean vectors and the conditional covariance matrices. If the multivariate process of the asset returns is independent, it is shown that in the case without a riskless asset the solution is presented as a sequence of optimal portfolio weights obtained by solving the single-period Markowitz optimization problem. The process dynamics are included only in the shape parameter of the utility function. If a riskless asset is present, then the multi-period optimal portfolio weights are proportional to the single-period solutions multiplied by time-varying constants which are dependent on the process dynamics. Remarkably, in the case of a portfolio selection with the tangency portfolio the multi-period solution coincides with the sequence of the single-period solutions. Finally, we compare the suggested strategies with existing multi-period portfolio allocation methods on real data.

Place, publisher, year, edition, pages
2015. Vol. 229, no 1, 121-158 p.
Keyword [en]
Multi-period asset allocation, Quadratic utility function, Closed-form solution, Tangency portfolio
National Category
Mathematics Economics and Business
URN: urn:nbn:se:su:diva-118345DOI: 10.1007/s10479-015-1802-zISI: 000354387600007OAI: diva2:823344
Available from: 2015-06-18 Created: 2015-06-15 Last updated: 2015-06-18Bibliographically approved

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Bodnar, Taras
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