Risks of Large Portfolios
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.
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- Gary Chamberlain & Michael Rothschild, 1982.
"Arbitrage, Factor Structure, and Mean-Variance Analysis on Large Asset Markets,"
NBER Working Papers
0996, National Bureau of Economic Research, Inc.
- Chamberlain, Gary & Rothschild, Michael, 1983. "Arbitrage, Factor Structure, and Mean-Variance Analysis on Large Asset Markets," Econometrica, Econometric Society, vol. 51(5), pages 1281-304, September.
- Chamberlain, Gary & Rothschild, Michael, 1982. "Arbitrage, Factor Structure, and Mean-Variance Analysis on Large Asset Markets," Scholarly Articles 3230355, Harvard University Department of Economics.
- Brodie, Joshua & Daubechies, Ingrid & De Mol, Christine & Giannone, Domenico, 2007.
"Sparse and Stable Markowitz Portfolios,"
CEPR Discussion Papers
6474, C.E.P.R. Discussion Papers.
- Joshua Brodie & Ingrid Daubechies & Christine De Mol & Domenico Giannone & Ignace Loris, 2007. "Sparse and stable Markowitz portfolios," Papers 0708.0046, arXiv.org, revised May 2008.
- Brodie, Joshua & Daubechies, Ingrid & De Mol, Christine & Giannone, Domenico & Loris, Ignace, 2008. "Sparse and stable Markowitz portfolios," Working Paper Series 0936, European Central Bank.
- Fama, Eugene F & French, Kenneth R, 1992. " The Cross-Section of Expected Stock Returns," Journal of Finance, American Finance Association, vol. 47(2), pages 427-65, June.
- Pesaran, M.H. & Zaffaroni, P., 2008.
"Optimal Asset Allocation with Factor Models for Large Portfolios,"
Cambridge Working Papers in Economics
0813, Faculty of Economics, University of Cambridge.
- M. Hashem Pesaran & Paolo Zaffaroni, 2008. "Optimal Asset Allocation with Factor Models for Large Portfolios," CESifo Working Paper Series 2326, CESifo Group Munich.
- Bertille Antoine, 2010. "Portfolio Selection with Estimation Risk: A Test-Based Approach," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 10(1), pages 164-197, 2012 10 1.
- Victor DeMiguel & Lorenzo Garlappi & Francisco J. Nogales & Raman Uppal, 2009. "A Generalized Approach to Portfolio Optimization: Improving Performance by Constraining Portfolio Norms," Management Science, INFORMS, vol. 55(5), pages 798-812, May.
- Jianqing Fan & Yuan Liao & Martina Mincheva, 2013.
"Large covariance estimation by thresholding principal orthogonal complements,"
Journal of the Royal Statistical Society Series B,
Royal Statistical Society, vol. 75(4), pages 603-680, 09.
- Fan, Jianqing & Liao, Yuan & Mincheva, Martina, 2011. "Large covariance estimation by thresholding principal orthogonal complements," MPRA Paper 38697, University Library of Munich, Germany.
- Olivier Ledoit & Michael Wolf, 2001.
"Improved estimation of the covariance matrix of stock returns with an application to portofolio selection,"
Economics Working Papers
586, Department of Economics and Business, Universitat Pompeu Fabra.
- Ledoit, Olivier & Wolf, Michael, 2003. "Improved estimation of the covariance matrix of stock returns with an application to portfolio selection," Journal of Empirical Finance, Elsevier, vol. 10(5), pages 603-621, December.
- Bannouh, K. & Martens, M.P.E. & Oomen, R.C.A. & van Dijk, D.J.C., 2012. "Realized mixed-frequency factor models for vast dimensional covariance estimation," ERIM Report Series Research in Management ERS-2012-017-F&A, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
- Rothman, Adam J. & Levina, Elizaveta & Zhu, Ji, 2009. "Generalized Thresholding of Large Covariance Matrices," Journal of the American Statistical Association, American Statistical Association, vol. 104(485), pages 177-186.
- repec:oup:jfinec:v:10:y:2012:i:1:p:164-197 is not listed on IDEAS
- Stock J.H. & Watson M.W., 2002. "Forecasting Using Principal Components From a Large Number of Predictors," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 1167-1179, December.
- Tze Leung Lai & Haipeng Xing & Zehao Chen, 2011. "Mean--variance portfolio optimization when means and covariances are unknown," Papers 1108.0996, arXiv.org.
- Connor, Gregory & Korajczyk, Robert A, 1993. " A Test for the Number of Factors in an Approximate Factor Model," Journal of Finance, American Finance Association, vol. 48(4), pages 1263-91, September.
- Cai, Tony & Liu, Weidong, 2011. "Adaptive Thresholding for Sparse Covariance Matrix Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 106(494), pages 672-684.
- Fan, Jianqing & Fan, Yingying & Lv, Jinchi, 2008. "High dimensional covariance matrix estimation using a factor model," Journal of Econometrics, Elsevier, vol. 147(1), pages 186-197, November.
- Fama, Eugene F. & French, Kenneth R., 1993. "Common risk factors in the returns on stocks and bonds," Journal of Financial Economics, Elsevier, vol. 33(1), pages 3-56, February.
- Jushan Bai, 2003. "Inferential Theory for Factor Models of Large Dimensions," Econometrica, Econometric Society, vol. 71(1), pages 135-171, January.
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