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Volumn 38, Issue 6, 2010, Pages 3487-3566

High-dimensionality effects in the Markowitz problem and other quadratic programs with linear constraints: Risk underestimation

Author keywords

Concentration of measure; Convex optimization; Covariance matrices; Elliptical distributions; High dimensional inference; Markowitz problem; Multivariate statistical analysis; Quadratic programs; Random matrix theory; Wishart matrices

Indexed keywords


EID: 78650151035     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/10-AOS795     Document Type: Article
Times cited : (81)

References (43)
  • 2
    • 0347989448 scopus 로고    scopus 로고
    • Methodologies in spectral analysis of large-dimensional random matrices, a review
    • With comments by G. J. Rodgers and Jack W. Silverstein; and a rejoinder by the author, MR1711663
    • BAI, Z. D. (1999). Methodologies in spectral analysis of large-dimensional random matrices, a review. Statist. Sinica 9 611-677. With comments by G. J. Rodgers and Jack W. Silverstein; and a rejoinder by the author. MR1711663
    • (1999) Statist. Sinica , vol.9 , pp. 611-677
    • Bai, Z.D.1
  • 3
    • 72449189786 scopus 로고    scopus 로고
    • Enhancement of the applicability of Markowitz's portfolio optimization by utilizing random matrix theory
    • MR2583523
    • BAI, Z., LIU, H. and WONG, W.-K. (2009). Enhancement of the applicability of Markowitz's portfolio optimization by utilizing random matrix theory. Math. Finance 19 639-667. MR2583523
    • (2009) Math. Finance , vol.19 , pp. 639-667
    • Bai, Z.1    Liu, H.2    Wong, W.-K.3
  • 4
    • 62349112885 scopus 로고    scopus 로고
    • Covariance regularization by thresholding
    • MR2485008
    • BICKEL, P. J. and LEVINA, E. (2008a). Covariance regularization by thresholding. Ann. Statist. 36 2577-2604. MR2485008
    • (2008) Ann. Statist. , vol.36 , pp. 2577-2604
    • Bickel, P.J.1    Levina, E.2
  • 5
    • 41549106844 scopus 로고    scopus 로고
    • Regularized estimation of large covariance matrices
    • MR2387969
    • BICKEL, P. J. and LEVINA, E. (2008b). Regularized estimation of large covariance matrices. Ann. Statist. 36 199-227. MR2387969
    • (2008) Ann. Statist. , vol.36 , pp. 199-227
    • Bickel, P.J.1    Levina, E.2
  • 6
    • 38549157125 scopus 로고    scopus 로고
    • The student ensemble of correlation matrices: Eigenvalue spectrum and Kullback-Leibler entropy
    • MR2372771
    • BIROLI, G., BOUCHAUD, J.-P. and POTTERS, M. (2007). The student ensemble of correlation matrices: Eigenvalue spectrum and Kullback-Leibler entropy. Acta Phys. Polon. B 38 4009-4026. MR2372771
    • (2007) Acta Phys. Polon. B , vol.38 , pp. 4009-4026
    • Biroli, G.1    Bouchaud, J.-P.2    Potters, M.3
  • 12
    • 0012070851 scopus 로고    scopus 로고
    • Local operator theory, random matrices and Banach spaces
    • North-Holland, Amsterdam, MR1863696
    • DAVIDSON, K. R. and SZAREK, S. J. (2001). Local operator theory, random matrices and Banach spaces. In Handbook of the Geometry of Banach Spaces, Vol. I 317-366. North-Holland, Amsterdam. MR1863696
    • (2001) Handbook of the Geometry of Banach Spaces , vol.1 , pp. 317-366
    • Davidson, K.R.1    Szarek, S.J.2
  • 14
    • 46749089905 scopus 로고    scopus 로고
    • Tracy-Widom limit for the largest eigenvalue of a large class of complex sample covariance matrices
    • MR2308592
    • EL KAROUI, N. (2007). Tracy-Widom limit for the largest eigenvalue of a large class of complex sample covariance matrices. Ann. Probab. 35 663-714. MR2308592
    • (2007) Ann. Probab. , vol.35 , pp. 663-714
    • El Karoui, N.1
  • 15
    • 62349123505 scopus 로고    scopus 로고
    • Operator norm consistent estimation of large dimensional sparse covariance matrices
    • MR2485011
    • EL KAROUI, N. (2008). Operator norm consistent estimation of large dimensional sparse covariance matrices. Ann. Statist. 36 2717-2756. MR2485011
    • (2008) Ann. Statist. , vol.36 , pp. 2717-2756
    • El Karoui, N.1
  • 16
    • 73949116713 scopus 로고    scopus 로고
    • Concentration of measure and spectra of random matrices: Applications to correlation matrices, elliptical distributions and beyond
    • MR2588248
    • EL KAROUI, N. (2009a). Concentration of measure and spectra of random matrices: Applications to correlation matrices, elliptical distributions and beyond. Ann. Appl. Probab. 19 2362-2405. MR2588248
    • (2009) Ann. Appl. Probab. , vol.19 , pp. 2362-2405
    • El Karoui, N.1
  • 20
    • 0004151494 scopus 로고
    • Cambridge Univ. Press.Cambridge. Corrected reprint of the 1985 original, MR1084815
    • HORN, R. A. and JOHNSON, C. R. (1990). Matrix Analysis. Cambridge Univ. Press, Cambridge. Corrected reprint of the 1985 original. MR1084815
    • (1990) Matrix Analysis
    • Horn, R.A.1    Johnson, C.R.2
  • 21
    • 0003952516 scopus 로고
    • Cambridge Univ. Press.Cambridge. Corrected reprint of the 1991 original, MR1288752
    • HORN, R. A. and JOHNSON, C. R. (1994). Topics in Matrix Analysis. Cambridge Univ. Press, Cambridge. Corrected reprint of the 1991 original. MR1288752
    • (1994) Topics in Matrix Analysis
    • Horn, R.A.1    Johnson, C.R.2
  • 22
    • 0000893636 scopus 로고
    • Estimation for Markowitz efficient portfolios
    • MR0590686
    • JOBSON, J. D. and KORKIE, B. (1980). Estimation for Markowitz efficient portfolios. J. Amer. Statist. Assoc. 75 544-554. MR0590686
    • (1980) J. Amer. Statist. Assoc. , vol.75 , pp. 544-554
    • Jobson, J.D.1    Korkie, B.2
  • 23
    • 0035641726 scopus 로고    scopus 로고
    • On the distribution of the largest eigenvalue in principal component analysis
    • MR1863961
    • JOHNSTONE, I. (2001). On the distribution of the largest eigenvalue in principal component analysis. Ann. Statist. 29 295-327. MR1863961
    • (2001) Ann. Statist. , vol.29 , pp. 295-327
    • Johnstone, I.1
  • 24
    • 61849182089 scopus 로고    scopus 로고
    • The distribution of the sample minimum-variance frontier
    • KAN, R. and SMITH, D. R. (2008). The distribution of the sample minimum-variance frontier. Management Science 54 1364-1380.
    • (2008) Management Science , vol.54 , pp. 1364-1380
    • Kan, R.1    Smith, D.R.2
  • 27
    • 0346961488 scopus 로고    scopus 로고
    • A well-conditioned estimator for large-dimensional covariance matrices
    • MR2026339
    • LEDOIT, O. and WOLF, M. (2004). A well-conditioned estimator for large-dimensional covariance matrices. J. Multivariate Anal. 88 365-411. MR2026339
    • (2004) J. Multivariate Anal. , vol.88 , pp. 365-411
    • Ledoit, O.1    Wolf, M.2
  • 30
    • 0000263239 scopus 로고
    • Distribution of eigenvalues in certain sets of random matrices
    • MR0208649
    • MARČENKO, V. A. and PASTUR, L. A. (1967). Distribution of eigenvalues in certain sets of random matrices. Mat. Sb. (N.S.) 72 507-536. MR0208649
    • (1967) Mat. Sb. (N.S.) , vol.72 , pp. 507-536
    • Marčenko, V.A.1    Pastur, L.A.2
  • 32
    • 84995186518 scopus 로고
    • Portfolio selection
    • MARKOWITZ, H. (1952). Portfolio selection. J. Finance 7 77-91.
    • (1952) J. Finance , vol.7 , pp. 77-91
    • Markowitz, H.1
  • 34
    • 34547855081 scopus 로고    scopus 로고
    • Springer Finance. Springer, Berlin, MR2155219
    • MEUCCI, A. (2005). Risk and Asset Allocation. Springer Finance. Springer, Berlin. MR2155219
    • (2005) Risk and Asset Allocation
    • Meucci, A.1
  • 37
    • 0037364017 scopus 로고    scopus 로고
    • Noisy covariance matrices and portfolio optimization. II
    • MR1965597
    • PAFKA, S. and KONDOR, I. (2003). Noisy covariance matrices and portfolio optimization. II. Phys. A 319 487-494. MR1965597
    • (2003) Phys. A , vol.319 , pp. 487-494
    • Pafka, S.1    Kondor, I.2
  • 38
    • 62349119614 scopus 로고    scopus 로고
    • Sparse permutation invariant covariance estimation
    • (electronic), MR2417391
    • ROTHMAN, A. J., BICKEL, P. J., LEVINA, E. and ZHU, J. (2008). Sparse permutation invariant covariance estimation. Electron. J. Statist. 2 494-515 (electronic). MR2417391
    • (2008) Electron. J. Statist. , vol.2 , pp. 494-515
    • Rothman, A.J.1    Bickel, P.J.2    Levina, E.3    Zhu, J.4
  • 39
    • 43149087649 scopus 로고    scopus 로고
    • Springer, New York. Corrected second printing of the 2004 original, MR2060918
    • RUPPERT, D. (2006). Statistics and Finance: An Introduction. Springer, New York. Corrected second printing of the 2004 original. MR2060918
    • (2006) Statistics and Finance: An Introduction
    • Ruppert, D.1
  • 40
    • 0002627253 scopus 로고
    • Strong convergence of the empirical distribution of eigenvalues of largedimensional random matrices
    • MR1370408
    • SILVERSTEIN, J. W. (1995). Strong convergence of the empirical distribution of eigenvalues of largedimensional random matrices. J. Multivariate Anal. 55 331-339. MR1370408
    • (1995) J. Multivariate Anal. , vol.55 , pp. 331-339
    • Silverstein, J.W.1
  • 41
    • 0000342767 scopus 로고
    • A distribution-free M-estimator of multivariate scatter
    • MR0885734
    • TYLER, D. E. (1987). A distribution-free M-estimator of multivariate scatter. Ann. Statist. 15 234-251. MR0885734
    • (1987) Ann. Statist. , vol.15 , pp. 234-251
    • Tyler, D.E.1
  • 43
    • 0002247902 scopus 로고
    • The strong limits of random matrix spectra for sample matrices of independent elements
    • MR0467894
    • WACHTER, K. W. (1978). The strong limits of random matrix spectra for sample matrices of independent elements. Ann. Probab. 6 1-18. MR0467894
    • (1978) Ann. Probab. , vol.6 , pp. 1-18
    • Wachter, K.W.1


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