Construction of uncertainty sets for portfolio selection problems
AbstractWhile modern portfolio theory grounds on the trade-off between portfolio return and portfolio variance to determine the optimal investment decision, postmodern portfolio theory uses downside risk measures instead of the variance. Prominent examples are given by the risk measures Value-at-Risk and its coherent extension, Conditional Value-at-Risk. When avoiding distributional assumptions on the process that generates the risky assets' returns, historical return data or expert knowledge remain the only data available to the investor. His problem is then to maximize the return of his portfolio given the risk constraint that his portfolio does not fall short of some threshold return. For the Conditional Value-at-Risk, the solution is known to be achievable by a linear program. This paper extends the solution to the investor's problem whenever his risk preferences are given by any coherent distortion risk measure. More precisely, it is shown that whenever the risk constraint is given by a coherent distortion risk measure, a linear program leads to the solution. A geometric interpretation of this solution is immediate, which is related to the non-parametric description of data by socalled weighted-mean trimmed regions. The connections of the solution to robust optimization and decision theory are illustrated. --
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by University of Cologne, Department for Economic and Social Statistics in its series Discussion Papers in Statistics and Econometrics with number 4/11.
Date of creation: 2011
Date of revision:
Contact details of provider:
Postal: Albertus Magnus Platz, 50923 Köln
Phone: 0221 / 470 5607
Fax: 0221 / 470 5179
Web page: http://www.wisostat.uni-koeln.de/Englisch/index_en.html
More information through EDIRC
Portfolio Optimization; Risk Constraints; Coherent Distortion Risk Measures; Uncertainty Sets;
Find related papers by JEL classification:
- C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
- C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General
- C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
- G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
- G32 - Financial Economics - - Corporate Finance and Governance - - - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill
This paper has been announced in the following NEP Reports:
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Ogryczak, Wlodzimierz & Ruszczynski, Andrzej, 1999.
"From stochastic dominance to mean-risk models: Semideviations as risk measures,"
European Journal of Operational Research, Elsevier,
Elsevier, vol. 116(1), pages 33-50, July.
- W. Ogryczak & A. Ruszczynski, 1997. "From Stochastic Dominance to Mean-Risk Models: Semideviations as Risk Measures," Working Papers ir97027, International Institute for Applied Systems Analysis.
- Gordon J. Alexander & Alexandre M. Baptista, 2004. "A Comparison of VaR and CVaR Constraints on Portfolio Selection with the Mean-Variance Model," Management Science, INFORMS, INFORMS, vol. 50(9), pages 1261-1273, September.
- Dyckerhoff, Rainer & Mosler, Karl, 2012. "Weighted-mean regions of a probability distribution," Statistics & Probability Letters, Elsevier, Elsevier, vol. 82(2), pages 318-325.
- Bazovkin, Pavel & Mosler, Karl, 2010. "An exact algorithm for weighted-mean trimmed regions in any dimension," Discussion Papers in Statistics and Econometrics 6/10, University of Cologne, Department for Economic and Social Statistics.
- Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 9(3), pages 203-228.
- Mosler, Karl & Lange, Tatjana & Bazovkin, Pavel, 2009. "Computing zonoid trimmed regions of dimension d>2," Computational Statistics & Data Analysis, Elsevier, Elsevier, vol. 53(7), pages 2500-2510, May.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (ZBW - German National Library of Economics).
If references are entirely missing, you can add them using this form.