Performance analysis and optimal selection of large mean-variance portfolios under estimation risk
We 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.
References listed on IDEAS
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.:
- Luenberger, David G., 1997. "Investment Science," OUP Catalogue, Oxford University Press, number 9780195108095, December.
- Campbell, John Y. & Viceira, Luis M., 2002. "Strategic Asset Allocation: Portfolio Choice for Long-Term Investors," OUP Catalogue, Oxford University Press, number 9780198296942, December.
- 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.
- BAUWENS, Luc & LAURENT, Sébastien & ROMBOUTS, Jeroen, 2003.
"Multivariate GARCH models: a survey,"
CORE Discussion Papers
2003031, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- 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.
- 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 Département d'Econométrie et d'Economie politique (DEEP)
04.10, Université de Lausanne, Faculté des HEC, DEEP.
- 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.
- Gabriel Frahm & Christoph Memmel, 2010.
"Dominating Estimators for Minimum-Variance Portfolios,"
- Frahm, Gabriel & Memmel, Christoph, 2010. "Dominating estimators for minimum-variance portfolios," Journal of Econometrics, Elsevier, vol. 159(2), pages 289-302, December.
- 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.
- Isabelle Huault & V. Perret & S. Charreire-Petit, 2007. "Management," Post-Print halshs-00337676, HAL.
When requesting a correction, please mention this item's handle: RePEc:arx:papers:1110.3460. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (arXiv administrators)
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.