Bai, Zhidong and Li, Hua and Wong, WingKeung (2013): The best estimation for highdimensional Markowitz meanvariance optimization.

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Abstract
The traditional(plugin) return for the Markowitz meanvariance (MV) optimization has been demonstrated to seriously overestimate the theoretical optimal return, especially when the dimension to sample size ratio $p/n$ is large. The newly developed bootstrapcorrected estimator corrects the overestimation, but it incurs the "underprediction problem," it does not do well on the estimation of the corresponding allocation, and it has bigger risk. To circumvent these limitations and to improve the optimal return estimation further, this paper develops the theory of spectralcorrected estimation. We first establish a theorem to explain why the plugin return greatly overestimates the theoretical optimal return. We prove that under some situations the plugin return is $\sqrt{\gamma}\ $\ times bigger than the theoretical optimal return, while under other situations, the plugin return is bigger than but may not be $\sqrt{\gamma}\ $\ times larger than its theoretic counterpart where $\gamma = \frac 1{1y}$ with $y$ being the limit of the ratio $p/n$.
Thereafter, we develop the spectralcorrected estimation for the Markowitz MV model which performs much better than both the plugin estimation and the bootstrapcorrected estimation not only in terms of the return but also in terms of the allocation and the risk. We further develop properties for our proposed estimation and conduct a simulation to examine the performance of our proposed estimation. Our simulation shows that our proposed estimation not only overcomes the problem of "overprediction," but also circumvents the "underprediction," "allocation estimation," and "risk" problems. Our simulation also shows that our proposed spectralcorrected estimation is stable for different values of sample size $n$, dimension $p$, and their ratio $p/n$. In addition, we relax the normality assumption in our proposed estimation so that our proposed spectralcorrected estimators could be obtained when the returns of the assets being studied could follow any distribution under the condition of the existence of the fourth moments.
Item Type:  MPRA Paper 

Original Title:  The best estimation for highdimensional Markowitz meanvariance optimization 
Language:  English 
Keywords:  Markowitz meanvariance optimization, Optimal Return, Optimal Portfolio Allocation, Large Random Matrix, Bootstrap Method 
Subjects:  G  Financial Economics > G1  General Financial Markets > G11  Portfolio Choice ; Investment Decisions C  Mathematical and Quantitative Methods > C3  Multiple or Simultaneous Equation Models ; Multiple Variables 
Item ID:  43862 
Depositing User:  WingKeung Wong 
Date Deposited:  18 Jan 2013 11:56 
Last Modified:  01 Oct 2019 04:44 
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URI:  https://mpra.ub.unimuenchen.de/id/eprint/43862 