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Forecasting a Large Dimensional Covariance Matrix of a Portfolio of Different Asset Classes


  • Lillie Lam

    (Research Department, Hong Kong Monetary Authority)

  • Laurence Fung

    (Research Department, Hong Kong Monetary Authority)

  • Ip-wing Yu

    (Research Department, Hong Kong Monetary Authority)


In portfolio and risk management, estimating and forecasting the volatilities and correlations of asset returns plays an important role. Recently, interest in the estimation of the covariance matrix of large dimensional portfolios has increased. Using a portfolio of 63 assets covering stocks, bonds and currencies, this paper aims to examine and compare the predictive power of different popular methods adopted by i) market practitioners (such as the sample covariance, the 250-day moving average, and the exponentially weighted moving average); ii) some sophisticated estimators recently developed in the academic literature (such as the orthogonal GARCH model and the Dynamic Conditional Correlation model); and iii) their combinations. Based on five different criteria, we show that a combined forecast of the 250-day moving average, the exponentially weighted moving average and the orthogonal GARCH model consistently outperforms the other methods in predicting the covariance matrix for both one-quarter and one-year ahead horizons.

Suggested Citation

  • Lillie Lam & Laurence Fung & Ip-wing Yu, 2009. "Forecasting a Large Dimensional Covariance Matrix of a Portfolio of Different Asset Classes," Working Papers 0901, Hong Kong Monetary Authority.
  • Handle: RePEc:hkg:wpaper:0901

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    References listed on IDEAS

    1. Diebold, Francis X & Mariano, Roberto S, 2002. "Comparing Predictive Accuracy," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 134-144, January.
    2. Engle, Robert F & Sheppard, Kevin K, 2001. "Theoretical and Empirical Properties of Dynamic Conditional Correlation Multivariate GARCH," University of California at San Diego, Economics Working Paper Series qt5s2218dp, Department of Economics, UC San Diego.
    3. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Jin Wu, 2005. "A Framework for Exploring the Macroeconomic Determinants of Systematic Risk," American Economic Review, American Economic Association, vol. 95(2), pages 398-404, May.
    4. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2003. "Modeling and Forecasting Realized Volatility," Econometrica, Econometric Society, vol. 71(2), pages 579-625, March.
    5. Hans Bystrom, 2004. "Orthogonal GARCH and covariance matrix forecasting: The Nordic stock markets during the Asian financial crisis 1997-1998," The European Journal of Finance, Taylor & Francis Journals, vol. 10(1), pages 44-67.
    6. Luc Bauwens & David Veredas & Winfried Pohlmeier, 2005. "High frequency finance," ULB Institutional Repository 2013/136220, ULB -- Universite Libre de Bruxelles.
    7. Torben G. Andersen & Luca Benzoni, 2008. "Realized volatility," Working Paper Series WP-08-14, Federal Reserve Bank of Chicago.
    8. Fleming, Jeff & Kirby, Chris & Ostdiek, Barbara, 2003. "The economic value of volatility timing using "realized" volatility," Journal of Financial Economics, Elsevier, vol. 67(3), pages 473-509, March.
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    More about this item


    Volatility forecasting; Risk management; Portfolio management; Model evaluation;

    JEL classification:

    • G17 - Financial Economics - - General Financial Markets - - - Financial Forecasting and Simulation
    • G32 - Financial Economics - - Corporate Finance and Governance - - - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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