[en] This paper introduces a new optimization heuristic for the robustification of critical inputs under consideration in many problems. It is shown that it allows to improve significantly the quality and the stability of the results for two classical financial problems, i.e. the Markowitz' portfolio selection problem and the computation of the financial beta.
Focus here is on the robust Minimum Covariance Determinant (MCD) estimator which can easily be substituted to the classical estimators of location and scatter. By definition, the computation of this estimator gives rise to a combinatorial optimization problem. We present a new heuristic, called 'RelaxMCD', which is based on a relaxation of the problem to the continuous space. The utility of this approach and the performance of our heuristic, with respect to other competitors, are illustrated through extensive simulations.
Research Center/Unit :
QuantOM
Disciplines :
Quantitative methods in economics & management
Author, co-author :
Schyns, Michael ; Université de Liège - ULiège > HEC - École de gestion de l'ULiège > Informatique de gestion
Language :
English
Title :
A robust heuristic for the optimal selection of a portfolio of stocks
scite shows how a scientific paper has been cited by providing the context of the citation, a classification describing whether it supports, mentions, or contrasts the cited claim, and a label indicating in which section the citation was made.
Bibliography
Agullò, J. (1998) 'Computing the minimum covariance determinant estimator', Technical paper, Universidad de Alicante.
Atkinson, A.C. (2007) 'Econometric applications of the forward search in regression: robustness, diagnostics and graphics', Econometric Reviews, Vol. 28, Nos. 1-3, pp.21-39.
Bailer, H. and Martin, R.D. (2007) 'Fama MacBeth 1973: reproduction, extension, robustification', Journal of Economic and Social Measurement, Vol. 32, No. 1, pp.41-63. (Pubitemid 47039825)
Bernholt, T. and Fisher, P. (2004) 'The complexity of computing the MCD-estimator', Theoretical Computer Science, Vol. 326, Nos. 1-3, pp.383-398.
Brealey, R.A. and Myers, S.C. (2002) Principles of Corporate Finance (7th ed.). International Edition: McGraw-Hill.
Butler, R.W., Davies, P.L. and Jhun, M. (1993) 'Asymptotics for the minimum covariance determinant estimator', The Annals of Statistics, Vol. 21, pp.1385-1400.
Chen, C. and Liu, L-M. (1993) 'Joint estimation of model parameters and outlier effects in time series', Journal of the American Statistical Association, Vol. 88, No. 421, pp.284-297, March.
Chen, Z-P. and Zhao, C-E. (2002) 'Is the MV efficient portfolio really that sensitive to estimation errors?', Asia-Pacific Journal of Operational Research, Vol. 19, No. 2, pp.149-168.
Chopra, V.K. and Ziemba, W.T. (1993) 'The effect of erros in means, variances, and covariances on optimal portfolio choice', The Journal of Portfolio Management, Vol. 19, No. 2, pp.6-11.
Costanzo, S. (2003) Robust Estimation of Multivariate Location and Scatter with Application to Financial Portfolio Selection, PhD Thesis. Department of Statistics, London School of Economics, London.
Critchley, F., Schyns, M., Haesbroeck, G., Fauconnier, C., Lu, G., Atkinson, R.A. and Wang, D.Q. (forthcoming) 'A relaxed approach to combinatorial problems in robustness and diagnostics', Statistics and Computing, Available online (DOI:10.1007/s11222-009-9119-x).
Delage, E. and Ye, Y. (forthcoming) 'Distributionally robust optimization under moment uncertainty with application to data-driven problems', Operations Research.
DeMiguel, V. and Nogales, F.J. (forthcoming) 'Portfolio selection with robust estimation', Operations Research, May-June 2009, Vol. 57, No. 3, pp.560-577, Available online (DOI:10.1287/ opre.1080.0566).
Donoho, D.L. and Huber, P.J. (1983) 'The notion of breakdown point', In P.J. Bickel, K.A. Doksum and J.L. Hodges, Jr. (Eds.), A Festschrift for Erich L. Lehmann, (pp.157-184), Wadsworth, California.
Elton, E.J. and Gruber, M.J. (1991) Modern Portfolio Theory and Investment Analysis (4th ed.). New York, London: John Wiley.
Fabozzi, F.J., Huang, D. and Zhou, G. (forthcoming) 'Robust portfolios: contributions fromoperations research and finance', Annals of Operations Research, Available online (DOI:10.1007/s10479009-0515-6).
Fabozzi, F.J., Kolm, P.N., Pachamanova, D. and Focardi, S.M. (2007) Robust Portfolio Optimization and Management. Hoboken: Wiley.
Garlappi, L., Uppal, R. andWang, T. (2007) 'Portfolio selection with parameter and model uncertainty: a multi-prior approach', Review of Financial Studies, Vol. 20, No. 1, pp.41-81. (Pubitemid 44968266)
Goldfarb, D. and Iyengar,G. (2003) 'Robust portfolio selection problems', Mathematics of Operations Research, Vol. 28, No. 1, pp.1-38.
Hawkins, D.M. (1994) 'The feasible solution algorithm for the minimum covariance determinant estimator in multivariate data', Computational Statistics and Data Analysis, Vol. 17, No. 2, pp.197-210.
Hawkins, D.M. and Olive, D.J. (1999) 'Improved feasible solution algorithms for high breakdown estimators', Computational Statistics and Data Analysis, Vol. 30, No. 1, pp.1-11.
Huber, P.J. and Ronchetti, E.M. (2009) Robust Statistics, (2nd ed.). Hoboken, New Jersey: Wiley. Hubert, M., Rousseeuw, P.J. and Van Aelst, S. (2008) 'High breakdown multivariate methods', Statistical Science, Vol. 23, No. 1, pp.92-119.
Hubert, M., Rousseeuw, P.J. and Verdonck, T. (2009) 'Robust PCA for skewed data and its outlier map', Computational Statistics and Data Analysis, Vol. 53, No. 6, pp.2264-2274.
Kan, R. and Zhou, G. (2007) 'Optimal portfolio choice with parameter uncertainty', Journal of Financial and Quantitative Analysis, Vol. 42, No. 3, pp.621-656.
Luenberger, D.G. (1998) Investment Science, New York, USA: Oxford University Press.
Lutgens, F., Sturm, J. and Kolen, A. (2006) 'Robust one-period option hedging', Operations Research, Vol. 54, No. 6, November-December, pp.1051-1062.
Mahaney, J.K., Goeke, R.J. and Booth, D.E. (2007) 'Out of control (outlier) detection in business data using the ARMA(1,1) model', Int. J. Operational Research, Vol. 2, No. 2, pp.115-134.
Maronna, R., Martin, D. and Yohai, V. (2006) Robust Statistics: Theory and Methods. John Wiley & Sons Ltd, Tha Atrium, Southern Gate, Chichester, West Sussex, England: Wiley.
Natarajan, K., Pachamanova, D. and Sim, M. (forthcoming) 'Constructing risk measures from uncertainty sets', Operations Research. Available online: (DOI:10.1287/opre.1080.0683).
Perret-Gentil, C. andVictoria-Feser, M.P. (2003) 'Robust mean-variance portfolio selection', Cahiers du département d'économétrie, no 2003.02, Faculté des sciences économiques et sociales, Université de Genève, Available at: SSRN:http://ssrn.com/abstract= 721509.
Ronchetti, E. (2006) 'The historical development of robust statistics', In Proceedings of the 7th International Conference On Teaching Statistics, Salvador, Bahia, Brazil.
Rousseeuw, P.J. (1985) 'Multivariate estimation with high breakdown point', In W. Grossmann, G. Pflug, I. Vincze and W. Wertz (Eds.), Mathematical Statistics and Applications, Vol. B, Dordrecht: Reidel, pp.283-297.
Rousseeuw, P.J. and Van Driessen, K. (1999) 'A fast algorithm for the minimum covariance determinant estimator', Technometrics, Vol. 41, No. 3, pp.212-223.
Scherer, B. and Martin, R.D. (2005) Introduction to Modern Portfolio Optimization with NuOPT, S-PLUS and S+Bayes. New York: Springer Sciences+Business.
Schyns, M., Haesbroeck, G. and Critchley, F. (2008) 'RelaxMCD: smooth optimization for the minimum covariance determinant estimator', Working Paper, HEC-Management School, University of Liège. Available in the Open Repository http://hdl.handle.net/2268/12074.
Shen, R. and Zhang, S. (2008) 'Robust portfolio selection based on a multi-stage scenario tree', European Journal of Operational Research, Vol. 191, No. 3, pp.864-887. (Pubitemid 351778620)
Todorov, V. (1992) 'Computing the minimum covariance determinant estimator (MCD) by simulated annealing', Computational Statistics and Data Analysis, Vol. 14, No. 4, November, pp.515-525.
TÜtÜncÜ, R. and Koenig, M. (2004) 'Robust asset allocation', Annals of Operations Research, Vol. 132, Nos. 1-4, pp.157-187. (Pubitemid 39393467)
Vaz de Melo Mendes, B. and Pereira Cmara Leal, R. (2005) 'Robust multivariate modeling in finance', Int. J. Managerial Finance, Vol. 1, No. 2, pp.95-106.
Welsch, R.E. and Zhou, X. (2007) 'Application of robust statistics to asset allocation models', Statistical Journal, Vol. 5, No. 1, pp.97-114, March.
Woodruff, D.L. (1996) 'Ghost image processing for minimum covariance determinants', ORSA Journal on Computing, Vol. 7, No. 4, Fall, pp.468-473.
Zaman, A., Rousseeuw, P.J. and Orhan, M. (2001) 'Econometric applications of high-breakdown robust regression techniques', Economics Letters, Vol. 71, No. 1, pp.1-8.
This website uses cookies to improve user experience. Read more
Save & Close
Accept all
Decline all
Show detailsHide details
Cookie declaration
About cookies
Strictly necessary
Performance
Strictly necessary cookies allow core website functionality such as user login and account management. The website cannot be used properly without strictly necessary cookies.
This cookie is used by Cookie-Script.com service to remember visitor cookie consent preferences. It is necessary for Cookie-Script.com cookie banner to work properly.
Performance cookies are used to see how visitors use the website, eg. analytics cookies. Those cookies cannot be used to directly identify a certain visitor.
Used to store the attribution information, the referrer initially used to visit the website
Cookies are small text files that are placed on your computer by websites that you visit. Websites use cookies to help users navigate efficiently and perform certain functions. Cookies that are required for the website to operate properly are allowed to be set without your permission. All other cookies need to be approved before they can be set in the browser.
You can change your consent to cookie usage at any time on our Privacy Policy page.
