Abstract
Standard methods for optimal allocation of shares in a financial portfolio are determined by second-order conditions which are very sensitive to outliers. The well-known Markowitz approach, which is based on the input of a mean vector and a covariance matrix, seems to provide questionable results in financial management, since small changes of inputs might lead to irrelevant portfolio allocations. However, existing robust estimators often suffer from masking of multiple influential observations, so we propose a new robust estimator which suitably weights data using a forward search approach. A Monte Carlo simulation study and an application to real data show some advantages of the proposed approach.
Similar content being viewed by others
References
Alexander GJ, Baptista AM (2002) Economic implication of using a mean-VaR model for portfolio selection: a comparison with mean-variance analysis. J Econ Dyn Control 26: 1159–1193
Atkinson AC (1994) Fast very robust methods for the detection of multiple outliers. J Am Stat Assoc 89: 1329–1339
Atkinson AC, Riani M (2000) Robust diagnostic regression analysis. Springer-Verlag, New York
Atkinson AC, Riani M, Cerioli A (2004) Exploring multivariate data with the forward search. Springer-Verlag, New York
Atkinson AC, Riani M, Cerioli A (2010) The forward search: theory and data analysis. J Korean Stat Soc 39: 117–134
Broadie M (1993) Computing efficient frontiers using estimated parameters. Ann Oper Res 45: 21–58
DeMiguel V, Nogales FJ (2009) Portfolio selection with robust estimation. Oper Res 57(3): 560–577
Fabozzi FJ, Kolm PN, Pachamanova DA, Focardi SM (2007) Robust portfolio optimization management. Wiley, New York
Grossi L, Laurini F (2009) A robust forward weighted Lagrange multiplier test for conditional heteroscedasticity. Comput Stat Data Anal 53(6): 2251–2263
Huang D, Zhu SS, Fabozzi FJ, Fukushima M (2008) Portfolio selection with uncertain exit time: a robust CVaR approach. J Econ Dyn Control 32: 594–623
Lauprete GJ, Samarov AM, Welsch RE (2002) Robust portfolio optimization. Metrika 55: 139–149
Marazzi A (1993) Algorithms, routines and S functions for robust statistics. Chapman and Hall, New York
Markowitz H (1959) Portfolio selection: efficient diversification of investments. Wiley, New York
Maronna RA, Martin RD, Yohai VJ (2006) Robust statistics. Wiley, New York
McNeil AJ, Frey R, Embrechts P (2005) Quantitative risk management: concepts, techniques and tools. Princeton University Press, Princeton
Michaud R (1989) The Markowitz optimization enigma: is optimized optimal?. Financ Anal J 45: 31–42
Riani M, Atkinson AC, Cerioli A (2009) Finding an unknown number of multivariate outliers. J R Stat Soci Ser B 71(2): 447–466
Rousseeuw PJ, Van Driessen K (1999) A fast algorithm for the minimum covariance determinant estimator. Technometrics 41: 212–223
Rousseeuw PJ, Leroy AM (1987) Robust regression and outlier detection. Wiley, New York
Welsch RE, Zhou X (2007) Application of robust statistics to asset allocation models. Revstat Stat J 5(1): 97–114
Zani S, Riani M, Corbellini A (1998) Robust bivariate boxplots and multiple outlier detection. Comput Stat Data Anal 28: 257–270
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Grossi, L., Laurini, F. Robust estimation of efficient mean–variance frontiers. Adv Data Anal Classif 5, 3–22 (2011). https://doi.org/10.1007/s11634-010-0082-3
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11634-010-0082-3