Fan, Jianqing and Liao, Yuan and Shi, Xiaofeng (2013): Risks of large portfolios.

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Abstract
Estimating and assessing the risk of a large portfolio is an important topic in financial econometrics and risk management. The risk is often estimated by a substitution of a good estimator of the volatility matrix. However, the accuracy of such a risk estimator for large portfolios is largely unknown, and a simple inequality in the previous literature gives an infeasible upper bound for the estimation error. In addition, numerical studies illustrate that this upper bound is very crude. In this paper, we propose factorbased risk estimators under a large amount of assets, and introduce a highconfidence level upper bound (HCLUB) to assess the accuracy of the risk estimation. The HCLUB is constructed based on three different estimates of the volatility matrix: sample covariance, approximate factor model with known factors, and unknown factors (POET, Fan, Liao and Mincheva, 2013). For the first time in the literature, we derive the limiting distribution of the estimated risks in high dimensionality. Our numerical results demonstrate that the proposed upper bounds significantly outperform the traditional crude bounds, and provide insightful assessment of the estimation of the portfolio risks. In addition, our simulated results quantify the relative error in the risk estimation, which is usually negligible using 3month daily data. Finally, the proposed methods are applied to an empirical study.
Item Type:  MPRA Paper 

Original Title:  Risks of large portfolios 
Language:  English 
Keywords:  High dimensionality; approximate factor model; unknown factors; principal components; sparse matrix; thresholding; risk management; volatility 
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 > C38  Classification Methods ; Cluster Analysis ; Principal Components ; Factor Models G  Financial Economics > G3  Corporate Finance and Governance > G32  Financing Policy ; Financial Risk and Risk Management ; Capital and Ownership Structure ; Value of Firms ; Goodwill C  Mathematical and Quantitative Methods > C5  Econometric Modeling > C58  Financial Econometrics 
Item ID:  44206 
Depositing User:  Yuan Liao 
Date Deposited:  05 Feb 2013 03:33 
Last Modified:  28 Sep 2019 16:02 
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URI:  https://mpra.ub.unimuenchen.de/id/eprint/44206 