Performance analysis and optimal selection of large mean-variance portfolios under estimation risk
AbstractWe study the consistency of sample mean-variance portfolios of arbitrarily high dimension that are based on Bayesian or shrinkage estimation of the input parameters as well as weighted sampling. In an asymptotic setting where the number of assets remains comparable in magnitude to the sample size, we provide a characterization of the estimation risk by providing deterministic equivalents of the portfolio out-of-sample performance in terms of the underlying investment scenario. The previous estimates represent a means of quantifying the amount of risk underestimation and return overestimation of improved portfolio constructions beyond standard ones. Well-known for the latter, if not corrected, these deviations lead to inaccurate and overly optimistic Sharpe-based investment decisions. Our results are based on recent contributions in the field of random matrix theory. Along with the asymptotic analysis, the analytical framework allows us to find bias corrections improving on the achieved out-of-sample performance of typical portfolio constructions. Some numerical simulations validate our theoretical findings.
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 arXiv.org in its series Papers with number 1110.3460.
Date of creation: Oct 2011
Date of revision:
Contact details of provider:
Web page: http://arxiv.org/
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.:
- Hlouskova, Jaroslava & Schmidheiny, Kurt & Wagner, Martin, 2009.
"Multistep predictions for multivariate GARCH models: Closed form solution and the value for portfolio management,"
Journal of Empirical Finance,
Elsevier, vol. 16(2), pages 330-336, March.
- Jaroslava HLOUSKOVA & Kurt SCHMIDHEINY & Martin WAGNER, 2004. "Multistep Predictions for Multivariate GARCH Models: Closed Form Solution and the Value for Portfolio Management," Cahiers de Recherches Economiques du DÃ©partement d'EconomÃ©trie et d'Economie politique (DEEP) 04.10, Université de Lausanne, Faculté des HEC, DEEP.
- Kan, Raymond & Zhou, Guofu, 2007. "Optimal Portfolio Choice with Parameter Uncertainty," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 42(03), pages 621-656, September.
- Laurent Laloux & Pierre Cizeau & Jean-Philippe Bouchaud & Marc Potters, 1999. "Random matrix theory," Science & Finance (CFM) working paper archive 500052, Science & Finance, Capital Fund Management.
- BAUWENS, Luc & LAURENT, Sébastien & ROMBOUTS, Jeroen VK, .
"Multivariate GARCH models: a survey,"
CORE Discussion Papers RP
-1847, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Frahm, Gabriel & Memmel, Christoph, 2010.
"Dominating estimators for minimum-variance portfolios,"
Journal of Econometrics,
Elsevier, vol. 159(2), pages 289-302, December.
- Gabriel Frahm & Christoph Memmel, 2010. "Dominating Estimators for Minimum-Variance Portfolios," Post-Print peer-00741629, HAL.
- Laurent Laloux & Pierre Cizeau & Jean-Philippe Bouchaud & Marc Potters, 1998. "Noise dressing of financial correlation matrices," Science & Finance (CFM) working paper archive 500051, Science & Finance, Capital Fund Management.
- Okhrin, Yarema & Schmid, Wolfgang, 2006. "Distributional properties of portfolio weights," Journal of Econometrics, Elsevier, vol. 134(1), pages 235-256, September.
- Campbell, John Y. & Viceira, Luis M., 2002. "Strategic Asset Allocation: Portfolio Choice for Long-Term Investors," OUP Catalogue, Oxford University Press, number 9780198296942.
- Luenberger, David G., 1997. "Investment Science," OUP Catalogue, Oxford University Press, number 9780195108095.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (arXiv administrators).
If references are entirely missing, you can add them using this form.