Directional Variance Adjustment: improving covariance estimates for high-dimensional portfolio optimization
Robust and reliable covariance estimates play a decisive role in financial and many other applications. An important class of estimators is based on Factor models. Here, we show by extensive Monte Carlo simulations that covariance matrices derived from the statistical Factor Analysis model exhibit a systematic error, which is similar to the well-known systematic error of the spectrum of the sample covariance matrix. Moreover, we introduce the Directional Variance Adjustment (DVA) algorithm, which diminishes the systematic error. In a thorough empirical study for the US, European, and Hong Kong market we show that our proposed method leads to improved portfolio allocation.
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Shanken, Jay, 1992. "On the Estimation of Beta-Pricing Models," Review of Financial Studies, Society for Financial Studies, vol. 5(1), pages 1-33.
- Schäfer Juliane & Strimmer Korbinian, 2005. "A Shrinkage Approach to Large-Scale Covariance Matrix Estimation and Implications for Functional Genomics," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 4(1), pages 1-32, November.
- Michael E. Tipping & Christopher M. Bishop, 1999. "Probabilistic Principal Component Analysis," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(3), pages 611-622.
- Loretan, Mico & Phillips, Peter C. B., 1994.
"Testing the covariance stationarity of heavy-tailed time series: An overview of the theory with applications to several financial datasets,"
Journal of Empirical Finance,
Elsevier, vol. 1(2), pages 211-248, January.
- Loretan, M. & Phillips, P.C.B., 1992. "Testing the Covariance Stationarity of Heavy-Tailed Time Series: An Overview of the Theory with Applications to Several Financial Datasets," Working papers 9208, Wisconsin Madison - Social Systems.
- Gregory Connor & Lisa R. Goldberg & Robert A. Korajczyk, 2010. "Portfolio Risk Analysis," Economics Books, Princeton University Press, edition 1, number 9224, 01-2013.
- Ravi Jagannathan & Tongshu Ma, 2003.
"Risk Reduction in Large Portfolios: Why Imposing the Wrong Constraints Helps,"
Journal of Finance,
American Finance Association, vol. 58(4), pages 1651-1684, 08.
- Ravi Jagannathan & Tongshu Ma, 2002. "Risk Reduction in Large Portfolios: Why Imposing the Wrong Constraints Helps," NBER Working Papers 8922, National Bureau of Economic Research, Inc.
- 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.
- Ledoit, Olivier & Wolf, Michael, 2000. "Improved estimation of the covariance matrix of stock returns with an application to portfolio selection," DES - Working Papers. Statistics and Econometrics. WS 10089, Universidad Carlos III de Madrid. Departamento de Estadística.
- Roll, Richard & Ross, Stephen A, 1980. " An Empirical Investigation of the Arbitrage Pricing Theory," Journal of Finance, American Finance Association, vol. 35(5), pages 1073-1103, December.
- 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.
- K. Jöreskog, 1967. "Some contributions to maximum likelihood factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 32(4), pages 443-482, December.
- Campbell, Rachel A.J. & Forbes, Catherine S. & Koedijk, Kees G. & Kofman, Paul, 2008. "Increasing correlations or just fat tails?," Journal of Empirical Finance, Elsevier, vol. 15(2), pages 287-309, March.
- 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.
- Longin, Francois, 2005. "The choice of the distribution of asset returns: How extreme value theory can help?," Journal of Banking & Finance, Elsevier, vol. 29(4), pages 1017-1035, April.
- Donald Rubin & Dorothy Thayer, 1982. "EM algorithms for ML factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 47(1), pages 69-76, March.
- Pagan, Adrian R. & Schwert, G. William, 1990. "Testing for covariance stationarity in stock market data," Economics Letters, Elsevier, vol. 33(2), pages 165-170, June.
When requesting a correction, please mention this item's handle: RePEc:arx:papers:1109.3069. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (arXiv administrators)
If references are entirely missing, you can add them using this form.