Template-type: ReDIF-Paper 1.0
Author-Name: Zhidong Bai
Author-Workplace-Name: KLASMOE and School of Mathematics and Statistics, Northeast Normal University, China.
Author-Name:
 Hua Li
Author-Workplace-Name: School of Sciences, Chang Chun University, China.
Author-Name:
 Michael McAleer
Author-Workplace-Name: Department of Quantitative Finance National Tsing Hua University, Taiwan and Econometric Institute Erasmus School of 
	Economics Erasmus University Rotterdam, The Netherlands and Department of Quantitative Economics Complutense University of 
	Madrid, Spain And Institute of Advanced Sciences Yokohama National University, Japan.
Author-Name: 
Wing-Keung Wong
Author-Workplace-Name: Department of Economics, Hong Kong Baptist University, China. Research Grants Council of Hong Kong, Hong Kong.
Title: Spectrally-corrected estimation for high-dimensional markowitz mean-variance optimization
Abstract: This paper considers the portfolio problem for high dimensional data when the dimension and size are both large. We analyze 
	the traditional Markowitz mean-variance (MV) portfolio by large dimension matrix theory, and find the spectral distribution of 
	the sample covariance is the main factor to make the expected return of the traditional MV portfolio overestimate the 
	theoretical MV portfolio. A correction is suggested to the spectral construction of the sample covariance to be the sample 
	spectrally corrected covariance, and to improve the traditional MV portfolio to be spectrally corrected. In the expressions of 
	the expected return and risk on the MV portfolio, the population covariance matrix is always a quadratic form, which will 
	direct MV portfolio estimation. We provide the limiting behavior of the quadratic form with the sample spectrally-corrected 
	covariance matrix, and explain the superior performance to the sample covariance as the dimension increases to infinity 
	proportionally with the sample size. Moreover, this paper deduces the limiting behavior of the expected return and risk on the 
	spectrally-corrected MV portfolio, and illustrates the superior properties of the spectrally-corrected MV portfolio. In 
	simulations, we compare the spectrally-corrected estimates with the traditional and bootstrap-corrected estimates, and show 
	the performance of the spectrally-corrected estimates are the best in portfolio returns and portfolio risk. We also compare 
	the performance of the new proposed estimation with deferent optimal portfolio estimates for real data from S&P 500. The 
	empirical findings are consistent with the theory developed in the paper.
Classification-JEL: G11, C13, C61.
Keywords: Markowitz mean-variance optimization, Optimal return, Optimal portfolio allocation, Large random matrix, Bootstrap method, 
	Spectrally-corrected covariance matrix.
Length: 48 pages 
Creation-Date: 2016-12
Number: 2017-05
X-File-Ref: http://america.sim.ucm.es/repec/ucm/ref/doicae1705.txt
File-URL: https://eprints.ucm.es/id/eprint/40905/1/1705.pdf
File-Format: Application/pdf
Handle: RePEc:ucm:doicae:1705