Covariance estimation and related problems in portfolio optimization

Proceedings of the IEEE Sensor Array and Multichannel Signal Processing Workshop

Volumn , Issue , 2012, Pages 369-372

  Pollak, Ilya ^a  

^a PURDUE UNIVERSITY   (United States)

Author keywords

Covariance; estimation; finance; market; Markowitz; portfolio

Indexed keywords

CLOSED FORM SOLUTIONS; COVARIANCE; COVARIANCE ESTIMATION; EXPECTED RETURN; HISTORICAL DATA; MARKET; MARKOWITZ; OPTIMIZERS; PORTFOLIO; PORTFOLIO MANAGEMENTS; PORTFOLIO OPTIMIZATION;

COVARIANCE MATRIX; ESTIMATION; FINANCE; INVESTMENTS; SENSORS; SIGNAL PROCESSING;

FINANCIAL DATA PROCESSING;

EID: 84867196821     PISSN: None     EISSN: 2151870X     Source Type: Conference Proceeding    
DOI: 10.1109/SAM.2012.6250513     Document Type: Conference Paper

References (53)

1. M. Avellaneda and J.-H. Lee. "Statistical arbitrage in the US equities market", Quantitative Finance, 10(7):761-782, 2010.
2. C. Bengtsson and J. Holst. "On portfolio selection: Improved covariance matrix estimation for Swedish asset returns", Working paper, Lund University and Lund Institute of Technology, 2002.
3. M.J. Best and R.R. Grauer. "On the sensitivity of mean-variance-efficient portfolios to changes in asset means: Some analytical and computational results", The Review of Financial Studies, 4(2):315-342, 1991.
4. M. Broadie. "Computing efficient frontiers using estimated parameters", Annals of Operations Research, 45(1):21-58, 1993.
5. J. Brodie, I. Daubechies, C. De Mol, D. Giannone, and I. Loris. "Sparse and stable Markowitz portfolios", Proceedings of the National Academy of Sciences, 106(30):12267-12272, Jul. 2009.
6. S. Ceria and R.A. Stubbs. "Incorporating estimation errors into portfolio selection: Robust portfolio construction", Axioma Research Paper No. 003, May 2006.
7. L.K.C. Chan, J. Karceski, and J. Lakonishok. "On portfolio optimization: Forecasting covariances and choosing the risk model", The Review of Financial Studies, 12(5):937-974, Winter 1999.
8. N.F. Chen, R. Roll, and S.A. Ross. "Economic forces and the stock market", Journal of Business, 59(3):383-403, 1986.
9. V.K. Chopra andW.T. Ziemba. "The effects of error in means, variances, and covariances on optimal portfolio choice", The Journal of Portfolio Management, 19(2):6-11, 1993.
10. D.J. Disatnik and S. Benninga. "Shrinking the Covariance Matrix", Journal of Portfolio Management, 33(4):55-63, 2007.
11. V. DeMiguel, L. Garlappi, and R. Uppal. "Optimal versus naive diversification: How inefficient is the 1/N portfolio strategy?" The Review of Financial Studies, 22(5):1915-1953, 2009.
12. V. DeMiguel, L. Garlappi, F.J. Nogales, and R. Uppal. "A generalized approach to portfolio optimization: Improving performance by constraining portfolio norms", Management Science, 55(5):798-812, May 2009.
13. R. Duchin and H. Levy. "Markowitz Versus the Talmudic Portfolio Diversification Strategies", The Journal of Portfolio Management, 35(2):71-74, Winter 2009.
14. E. J. Elton and M. J. Gruber. "Estimating the dependence structure of share prices", The Journal of Finance, 28(5):1203-1232, Dec. 1973.
15. E. F. Fama and K. R. French. "Size and book-to-market factors in earnings and returns", The Journal of Finance, 50(1):131-155, Mar. 1995.
16. E. F. Fama and K. R. French. "Industry costs of equity", Journal of Financial Economics, 43(2):153-193, Feb. 1997.
17. J. Fletcher and J. Hillier. "An examination of resampled portfolio efficiency", Financial Analysts Journal, 57(5):66-74, Sep.-Oct. 2001.
18. L. Garlappi, R. Uppal, and T. Wang. "Portfolio selection with parameter and model uncertainty: A multi-prior approach", The Review of Financial Studies, 20(1):41-81, Jan. 2007.
19. D. Goldfarb and G. Iyengar. "Robust portfolio selection problems", Mathematics of Operations Research, 28(1):1-38, Feb. 2003.
20. V. Golosnoy and Y. Okhrin. "Multivariate shrinkage for optimal portfolio weights", em European Journal of Finance, 13(5):441-458, Jul. 2007.
21. J. Gotoh and A. Takeda. "On the role of norm constraints in portfolio selection", Department of Industrial and Systems Engineering Discussion Paper Series No. 09-03, Chuo University, Apr. 2010.
22. R. Jagannathan and T. Ma. "Risk reduction in large portfolios: Why imposing the wrong constraints helps", The Journal of Finance, 58(4):1651-1684, Aug. 2003.
23. R. Jansen and R. van Dijk. "Optimal benchmark tracking with small portfolios", The Journal of Portfolio Management, 28(2):33-39,Winter 2002.
24. E. Jay, P. Duvaut, S. Darolles, and A. Chretien. "Multi-factor models and signal processing techniques: survey and example", IEEE Signal Processing Magazine, 28(5):61-71, Sep. 2011.
25. J.D. Jobson and B. Korkie. "Putting Markowitz theory to work", The Journal of Portfolio Management, 7(4):70-74, Summer 1981.
26. P. Jorion. "International portfolio diversification with estimation risk", The Journal of Business, 58(3):259-278, Jul. 1985.
27. P. Jorion. "Bayes-Stein estimation for portfolio analysis", The Journal of Financial and Quantitative Analysis, 21(3):279-292, Sep. 1986.
28. P. Jorion. "Portfolio optimization in practice", Financial Analysts Journal, 48(1):68-74, Jan.-Feb. 1992.
29. R. Kan and G. Zhou. "Optimal portfolio choice with parameter uncertainty", Journal of Financial and Quantitative Analysis, 42(3):621-656, Sep. 2007.
30. N. El Karoui. "High-dimensionality effects in the Markowitz problem and other quadratic programs with linear equality constraints: Risk underestimation", Preprint, 2009.
31. N. El Karoui. "On the realized risk of Markowitz portfolios", Preprint, 2009.
32. L. Laloux, P. Cizeau, J.-P. Bouchaud, and M. Potters. "Noise dressing of financial correlation matrices", Physical Review Letters, 83(7):1467-1470, 1999.
33. L. Laloux, P. Cizeau, J.-P. Bouchaud, and M. Potters. "Random matrix theory and financial correlations", International Journal of Theoretical and Applied Finance, 3(3):391-398, 2000.
34. O. Ledoit and M. Wolf. "Improved estimation of the covariance matrix of stock returns with an application to portfolio selection", Journal of Empirical Finance, 10(5):603-621, Dec. 2003.
35. O. Ledoit and M. Wolf. "A well-conditioned estimator for large-dimensional covariance matrices", Journal of Multivariate Analysis, 88(2):365-411, Feb. 2004.
36. H. Levy and R. Duchin. "Markowitz's Mean-Variance Rule and the Talmudic Diversification Recommendation", In The Handbook of Portfolio Construction: Contemporary Applications of Markowitz Techniques, J.B. Guerard, Jr., Ed., Springer, 2009.
37. H. M. Markowitz. "Portfolio selection", The Journal of Finance, 7(1):77-91, 1952.
38. D.S. Matteson and D. Ruppert. "GARCH Models of Dynamic Volatility and Correlation", IEEE Signal Processing Magazine, 28(5):72-82, Sep. 2011.
39. R.O. Michaud. "The Markowitz optimization enigma: Is 'optimized' optimal?" Financial Analysts Journal, 45(1):31-42, Jan.-Feb. 1989.
40. R.O. Michaud and R.O. Michaud. Efficient Asset Management: A Practical Guide to Stock Portfolio Optimization and Asset Allocation, 2nd Edition. Oxford University Press, 2008.
41. K.K. Ng, P. Agarwal, N. Mullen, D. Du, and I. Pollak. "Comparison of several covariance matrix estimators for portfolio optimization", In Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, May 22-27, 2011, Prague, Czech Republic.
42. V. Plerou, P. Gopikrishnan, B. Rosenow, L.A.N. Amaral, and H.E. Stanley. "Universal and non-universal properties of cross-correlations in financial time series", Physical Review Letters, 83(7):1471-1474, 1999.
43. V. Plerou, P. Gopikrishnan, B. Rosenow, L.A.N. Amaral, T. Guhr, and H.E. Stanley. "Random matrix approach to cross correlations in financial data", Physical Review E, 65:066126-1-066126-18, Jun. 2002.
44. I. Pollak. "Weight shrinkage for portfolio optimization", In Proceedings of the Fourth International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, December 13-16, 2011, San Juan, Puerto Rico.
45. D. Ruppert. Statistics and Data Analysis for Financial Engineering. Springer, 2010.
46. J. Schäfer and K. Strimmer. "A Shrinkage Approach to Large-Scale Covariance Matrix Estimation and Implications for Functional Genomics", Statistical Applications in Genetics and Molecular Biology, Volume 4, Issue 1, Article 32, 2005.
47. B. Scherer. "Portfolio resampling: Review and critique", Financial Analysts Journal, 58(6):98-109, Nov.-Dec. 2002.
48. W. F. Sharpe. "A simplified model for portfolio analysis", Management Science, 9(2):277-293, Jan. 1963.
49. W. F. Sharpe. "Mutual fund performance", Journal of Business, 39(1):119-138, 1966.
50. M.U. Torun, A.N. Akansu, and M. Avellaneda. "Portfolio Risk in Multiple Freqiencies", IEEE Signal Processing Magazine, 28(5):61-71, Sep. 2011.
51. J. Tu and G. Zhou. "Markowitz meets Talmud: A combination of sophisticated and naive diversification strategies", Journal of Financial Econometrics, 99:204-215, 2011.
52. R.H. Tütüncü and M. Koenig. "Robust asset allocation", Annals of Operations Research, 132:157-187, 2004.
53. J.-H. Won, J. Lim, S.-J. Kim, and B. Rajaratnam. "Maximum likelihood covariance estimation with a condition number constraint", Technical Report No. 2009-10, Department of Statistics, Stanford University, Aug. 2009.