Risks of large portfolios

Jianqing Fan, Yuan Liao and Xiaofeng Shi

MPRA Paper from University Library of Munich, Germany

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 factor-based risk estimators under a large amount of assets, and introduce a high-confidence level upper bound (H-CLUB) to assess the accuracy of the risk estimation. The H-CLUB 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 3-month daily data. Finally, the proposed methods are applied to an empirical study.

Keywords: High dimensionality; approximate factor model; unknown factors; principal components; sparse matrix; thresholding; risk management; volatility (search for similar items in EconPapers)
JEL-codes: C38 C58 G11 G32 (search for similar items in EconPapers)
Date: 2013-02
New Economics Papers: this item is included in nep-ecm and nep-rmg
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (8)

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Related works:
Journal Article: Risks of large portfolios (2015)
Working Paper: Risks of Large Portfolios (2013)
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Persistent link: https://EconPapers.repec.org/RePEc:pra:mprapa:44206

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