Extension of the random matrix theory to the L-moments for robust portfolio selection

References

• Black, F., Jensen, M.C. and Scholes, M., The CAPM: some empirical tests. In Jensen Studies in the Theory of Capital Markets, pp. 79–121, 1972 (Praeger: New York).
   Google Scholar
• Chopra , V.K. 1993 . Improving optimization . J. Invest. , 8 : 51 – 59 .
   Google Scholar
• Conlon, T., Ruskin, H.J. and Crane, M., Random matrix theory and fund of funds portfolio optimization. Working Paper, Dublin City University, 2008.
   Google Scholar
• David , H.A. and Nagaraja , H.N. 2003 . Order Statistics , 3rd ed. , New York : Wiley .
   Google Scholar
• DeMiguel , V. , Garlappi , L. , Nogales , F.J. and Uppal , R. 2009 . A generalized approach to portfolio optimization: improving performance by constraining portfolio norms . Mgmt Sci. , 55 ( 5 ) : 798 – 812 .
   Web of Science ®Google Scholar
• DeMiguel , V. and Nogales , F.J. 2009 . Portfolio selection with robust estimation of risk . Oper. Res. , 57 ( 3 ) : 560 – 577 .
   Web of Science ®Google Scholar
• Dyson , F.J. 1962 . Statistical theory of the energy levels of complex systems I . J. Math. Phys. , 3 : 140 – 156 .
   Web of Science ®Google Scholar
• Dyson , F.J. 1971 . Distribution of eigenvalues for a class of real symmetric matrices . Revista Mexicana de Fisica , 20 : 231 – 237 .
   Google Scholar
• Dyson , F.J. and Metha , M.L. 1963 . Statistical theory of the energy levels of complex systems V . J. Math. Phys. , 4 : 713 – 719 .
   Web of Science ®Google Scholar
• Edelman, A., Eigenvalues and condition numbers of random matrices. PhD thesis, Department of Mathematics, Massachussetts Institute of Technology, 1989.
   Google Scholar
• Fan , J. , Fan , Y. and Jiang , J. 2007 . Dynamic integration of time- and state-domain methods for volatility estimation . J. Am. Statist. Assoc. , 102 : 618 – 631 .
   Web of Science ®Google Scholar
• Frost , P. and Savarino , J. 1988 . For better performance constraint portfolio weights . J. Portfol. Mgmt , 15 : 29 – 34 .
   Web of Science ®Google Scholar
• Guhr , T. , Muller-Groeling , A. and Weidenmuuller , H.A. 1998 . Random matrix theories in quantum physics: common concept . Phys. Rep. , 299 : 189 – 425 .
   Google Scholar
• Haugen , R. 1999 . Inefficient Market , Englewood Cliffs , NJ : Prentice Hall .
   Google Scholar
• Hosking, J., The theory of probability weighted moments. Research Report RC12210, IBM Research Division, 1986.
   Google Scholar
• Hosking, J., Some theoretical results concerning L-moments. Research Report RC14492, IBM Research Division, 1989.
   Google Scholar
• Hosking , J. 1990 . L-moments: analysis and estimation . J. R. Statist. Soc. Ser. B , 52 : 105 – 124 .
   Google Scholar
• Hosking , J. and Wallis , J. 1987 . Parameter and quantile estimation for the generalized Pareto distribution . Technometrics , 29 : 339 – 349 .
   Web of Science ®Google Scholar
• Hosking , J. , Wallis , J. and Wood , J. 1985 . Estimation of the generalized extreme-value distribution by the method of probability-weighted moments . Technometrics , 27 : 251 – 261 .
   Web of Science ®Google Scholar
• Laloux , L. , Cizeau , P. , Bouchaud , J.P. and Potters , M. 1999 . Noise dressing of financial correlation matrices . Phys. Rev. Lett. , 83 : 1467 – 1470 .
   Web of Science ®Google Scholar
• Ledoit , O. and Wolf , M. 2003 . Improved estimation of the covariance matrix of stock returns with an application to portfolio selection . J. Empir. Finance , 10 : 603 – 621 .
   Google Scholar
• Ledoit , O. and Wolf , M. 2004 . A well-conditioned estimator for large dimensional covariance matrices . J. Multivar. Anal. , 88 : 365 – 411 .
   Web of Science ®Google Scholar
• Marcenko , V. and Pastur , L. 1967 . Distribution of eigenvalues for some sets of random matrices . Maths USSR Sborni , 1 : 457 – 483 .
   Google Scholar
• Markowitz , H. 1952 . Mean–variance analysis in portfolio choice and capital markets . J. Finance , 7 : 77 – 91 .
   Web of Science ®Google Scholar
• Mehta , M.L. 1991 . Random Matrices , Boston : Academic Press .
   Google Scholar
• Merton , R. 1980 . On estimating the expected return on the market: an exploratory investigation . J. Financ. Econ. , 8 ( 4 ) : 323 – 361 .
   Web of Science ®Google Scholar
• Michaud , R. 1989 . The Markowitz optimization enigma: is ʻoptimized’ optimal? . Financ. Anal. J. , 45 : 31 – 42 .
   Google Scholar
• Pafka , S. and Kondor , I. 2004 . Estimated correlation matrices and portfolio optimization . Physica A , 343 : 623 – 634 .
   Web of Science ®Google Scholar
• Plerou, V., Gopikrishnan, P., Rosenow, B., Amaral, L.A.N., Guhr, T. and Stanley, H.E., A random matrix approach to cross-correlations in financial data. Phys. Rev. E, 2002, 65.
   Google Scholar
• Potters , M. , Bouchaud , J.P. and Laloux , L. 2005 . Financial applications of random matrix theory: old laces and new pieces . Acta Phys. Pol. B , 36 ( 9 ) : 2767 – 2784 .
   Google Scholar
• Sengupta , A.M. and Mitra , P.P. 1999 . Distributions of singular values for some random matrices . Phys. Rev. E , 60 : 3389 – 3392 .
   PubMed Web of Science ®Google Scholar
• Serfling , R. and Xiao , P. 2007 . A contribution to multivariate L-moments: L-comoment matrices . J. Multivar. Anal. , 98 : 1765 – 1781 .
   Web of Science ®Google Scholar
• Sharpe , W. 1963 . A simplified model for portfolio analysis . J. Mgmt Sci. , 9 : 277 – 293 .
   Web of Science ®Google Scholar
• Sillito , G. 1951 . Interrelations between certain linear systematic statistics of sample from any continuous population . Biometrika , 38 : 377 – 382 .
   Web of Science ®Google Scholar
• Stein, C., Inadmissibility of the usual estimator for the mean of a multivariate normal distribution. In Proceedings of the Third Berkeley Symposium on Mathematical and Statistical Probability, University of California, Berkeley 1, 1956, pp. 197–206.
   Google Scholar
• Wigner , E.P. 1956 . Results and Theory of Resonance Absorption , Oak Ridge National Laboratories Press .
   Google Scholar
• Wishart , J. 1928 . The generalized product moment distribution in samples from a normal multivariate population . Biometrika , 20 : 32 – 52 .
   Google Scholar
• Yang , S. 1977 . General distribution theory of the concomitants of order statistics . Ann. Statist. , 5 : 996 – 1002 .
   Web of Science ®Google Scholar