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Estimating correlation and covariance matrices by weighting of market similarity

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  • M.C. M�nnix
  • R. Sch�fer
  • O. Grothe

Abstract

We discuss a weighted estimation of correlation and covariance matrices from historical financial data. To this end, we introduce a weighting scheme that accounts for the similarity of previous market conditions to the present situation. The resulting estimators are less biased and show lower variance than either unweighted or exponentially weighted estimators. The weighting scheme is based on a similarity measure that compares the current correlation structure of the market to the structures at past times. Similarity is then measured by the matrix 2-norm of the difference of probe correlation matrices estimated for two different points in time. The method is validated in a simulation study and tested empirically in the context of mean-variance portfolio optimization. In the latter case we find an enhanced realized portfolio return as well as a reduced portfolio risk compared with alternative approaches based on different strategies and estimators.

Suggested Citation

  • M.C. M�nnix & R. Sch�fer & O. Grothe, 2014. "Estimating correlation and covariance matrices by weighting of market similarity," Quantitative Finance, Taylor & Francis Journals, vol. 14(5), pages 931-939, May.
    • Handle: RePEc:taf:quantf:v:14:y:2014:i:5:p:931-939
    DOI: 10.1080/14697688.2011.605075
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    1. Pafka, Szilárd & Kondor, Imre, 2004. "Estimated correlation matrices and portfolio optimization," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 343(C), pages 623-634.
    2. Stephen Lee & Simon Stevenson, 2003. "Time weighted portfolio optimisation," Journal of Property Investment & Finance, Emerald Group Publishing Limited, vol. 21(3), pages 233-249, June.
    3. Engle, Robert & Colacito, Riccardo, 2006. "Testing and Valuing Dynamic Correlations for Asset Allocation," Journal of Business & Economic Statistics, American Statistical Association, vol. 24, pages 238-253, April.
    4. Rudi Schafer & Nils Fredrik Nilsson & Thomas Guhr, 2010. "Power mapping with dynamical adjustment for improved portfolio optimization," Quantitative Finance, Taylor & Francis Journals, vol. 10(1), pages 107-119.
    5. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    6. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    7. Federico Bandi & Jeffrey Russell & Yinghua Zhu, 2008. "Using High-Frequency Data in Dynamic Portfolio Choice," Econometric Reviews, Taylor & Francis Journals, vol. 27(1-3), pages 163-198.
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    Cited by:

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    4. Francesco Lautizi, 2015. "Large Scale Covariance Estimates for Portfolio Selection," CEIS Research Paper 353, Tor Vergata University, CEIS, revised 07 Aug 2015.
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    7. Nie, Chun-Xiao & Song, Fu-Tie, 2023. "Stable versus fragile community structures in the correlation dynamics of Chinese industry indices," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).

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