Abstract
Time variability of the expected returns as well as the volatility of asset returns can be caused by changes in the fundamental factors; for example, changes in commodity prices, macroeconomic policy, market trading activity, technological development, governmental policies, and so on. This leads to the deviation of a selected optimal portfolio from the Markowitz efficient frontier that consists of all portfolios with the highest expected return for the given level of risk or with the smallest risk for a preselected profit and, thus, is fully defined by the first two moments of asset returns (Markowitz, 1952). Changes in these characteristics are subject to structural breaks of the efficient frontier location in the mean-variance space and the optimal portfolios allocated on it.
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References
Alt, F.B. and Smith, N.D. (1988) “Multivariate Process Control”, in P.R. Krishnaiah and C.R. Rao (eds), Handbook of Statistics, Vol. 7 (Amsterdam: North-Holland).
Andersen, T.G., Bollerslev, T., Diebold, F.X. and Ebens, H. (2001) “The Distribution of Realized Exchange Rate Volatility”, Journal of the American Statistical Association, 96 (453): 42–55.
Andersson, E., Bock, B. and Frisen, M. (2003) “Detection of Turning Points in Business Cycles”, Journal of Business Cycle Measurement and Analysis, 1: 93–108.
Andersson, E., Bock, B. and Frisen, M. (2005) “Statistical Surveillance of Cyclical Processes with Application to Turns in Business Cycles”, Journal of Forecasting, 24 (2): 465–90.
Bamdorff-Nielsen, O.E. and Shephard, N. (2002) “Econometric Analysis of Realized Volatility and Its Use in Estimating Stochastic Volatility Models”, Journal of the Royal Statistical Society, Ser. B, 64(2): 253–80.
Barndorff-Nielsen, O.E. and Shephard, N. (2004) “Econometric Analysis of Realized Covariation: High Frequency Based Covariance, Regression and Correlation in Financial Economics”, Econometrica, 72 (3): 885–925.
Bodnar, O. (2005) “Control Charts for Multivariate Financial Time Series”, PhD thesis, Frankfurt (Oder), Germany.
Bodnar, O. and Schmid, W. (2006) “CUSUM Control Schemes for Multivariate Time Series”, in H.-J. Lenz and P.-Th. Wilrich (eds), Frontiers of Statistical Process Control, vol. 8 (Heidelberg: Physica).
Bodnar, T. (2004) “Optimal Portfolios in an Elliptical Model — Statistical Analysis and Tests for Efficiency”, PhD thesis, Europa University Viadrina, Frankfurt (Oder), Germany.
Bodnar, T. and Schmid, W. (2004) “A Test for the Weights of the Global Minimum Variance Portfolio in an Elliptical Model”, EUV Working Paper 2, Europa University Viadrina, Frankfurt (Oder), Germany.
Britten-Jones, M. (1999) “The Sampling Error in Estimates of Mean—Variance Efficient Portfolio Weights”, Journal of Finance, 54 (2): 655–71.
Crosier, R.B. (1986) “A New Two-Sided Cumulative Sum Quality Control Scheme”, Technometrics, 28 (3): 187–94.
Crosier, R.B. (1988) “Multivariate Generalizations of Cumulative Sum Quality Control Schemes”, Technometrics, 30 (3): 291–303.
Fang, K.T. and Zhang, Y.T. (1990) Generalized Multivariate Analysis (Berlin, Germany: Springer-Verlag and Beijing, China: Science Press).
Frisen, M. (2003) “Statistical Surveillance: Optimality and Methods”, International Statistical Review, 71 (2): 403–34.
Gibbons, M.R., Ross, S.A. and Shanken, J. (1989) “A Test of the Efficiency of a Given Portfolio”, Econometrica, 57 (5): 1121–52.
Healy, J.D. (1987) “A Note on Multivariate CUSUM Procedure”, Technometrics, 29 (4): 409–12.
Hotelling, H. (1947) “Multivariate Quality Control — Illustrated by the Air Testing of Sample Bombsights”, in C. Eisenhart, M.W. Hastay and W.A. Wallis (eds), Techniques of Statistical Analysis (New York, NY: McGraw-Hill).
Jobson, J.D. and Korkie, B. (1989) “A Performance Interpretation of Multivariate Tests of Asset Set Intersection, Spanning, and Mean—Variance Efficiency”, Journal of Financial and Quantitative Analysis, 24 (2): 185–204.
Kan, R. and Zhou, G. (2001) “Tests of Mean—Variance Spanning”, Working paper, Washington University.
Kim, D. and Kon, S. (1999) “Structural Change and Time Dependence in Models of Stock Returns”, Journal of Empirical Finance, 6 (3): 283–308.
Ledoit, O. and Wolf, M. (2003) “Improved Estimation of the Covariance Matrix of Stock Returns with an Application to Portfolio Selection”, Journal of Empirical Finance, 10 (5): 603–21.
Ledoit, O. and Wolf, M. (2004) “A Well-Conditioned Estimator for Large-Dimensional Covariance Matrices”, Journal of Multivariate Analysis, 88 (2): 365–411.
Lowry, C.A., Woodall, W.H., Champ, C.W. and Rigdon, S.E. (1992) “A Multivariate Exponentially Weighted Moving Average Control Charts”, Technometrics, 34(1): 46–53.
Markowitz, H. (1952) “Portfolio Selection”, Journal of Finance, 7 (1): 77–91.
Moustakides, G.V. (2004) “Optimality of the CUSUM Procedure in Continuous Time”, Annals of Statistics, 32 (1): 302–15.
Muirhead, R.J. (1982) Aspects of Multivariate Statistical Theory (New York, NY: John Wiley & Sons).
Ngai, H.-M. and Zhang, J. (2001) “Multivariate Cumulative Sum Control Charts Based on Projection Pursuit”, Statistica Sinica, 11 (3): 747–66.
Pignatiello, Jr., J.J. and Runger, G.C. (1990) “Comparison of Multivariate CUSUM Charts”, Journal of Quality Technology, 22 (2): 173–86.
Pollak, M. (1985) “Optimal Detection of a Change in Distribution”, Annals of Statistics, 13 (1): 206–27.
Prahbu, S.S. and Runger, G.C. (1997) “Designing a Multivariate EWMA Control Chart”, Journal of Quality Technology, 29 (1): 8–15.
Roberts, S.W. (1959) “Control Charts Tests Based on Geometric Moving Averages”, Technometrics, 1 (3): 239–50.
Runger, G., Alt, F.B. and Montgomery, D. (1996) “Contributors to a Multivariate Statistical Process Control Chart Signal”, Communications in Statistics —Theory and Methods, 25 (10): 2203–13.
Schipper, S. and Schmid, W. (2001) “Sequential Methods for Detecting Changes in the Variance of Economic Time Series”, Sequential Analysis, 20 (4): 235–62.
Schmid, W. and Tzotchev, D. (2004) “Sequential Monitoring of the Parameters of a One Factor Cox—Ingersoll—Ross Model”, Sequential Analysis, 23 (1): 1–40.
Schwert, G.W. (1989) “Why Does Stock Market Volatility Change Over Time?”, Journal of Finance, 44 (5): 1115–53.
Sliwa, P., and Schmid, W. (2005) “Monitoring the Cross-Covariances of a Multivariate Time Series”, Metrika, 61 (1): 89–115.
Srivastava, M.S. and Wu, Y.H. (1997) “Evaluation of Optimum Weights and Average Run Lengths in EWMA Control Schemes”, Communications in Statistics —Theory and Methods, 26 (6): 1253–67.
Theodossiou, P.T. (1993) “Predicting Shifts in the Mean of a Multivariate Time Series Process: An Application in Predicting Business Failures”, Journal of the American Statistical Association, 88 (422): 441–9.
Tu, J. and Zhou, G. (2004) “Data-Generating Process Uncertainty: What Difference Does It Make in Portfolio Decisions?”, Journal of Financial Economics, 72 (2): 385–421.
Wald, A. (1947) Sequential Analysis (New York, NY: John Wiley & Sons).
Woodall, W.H. and Mahmoud, M.A. (2005) “The Inertial Properties of Quality Control Charts”, Technometrics, 47 (4): 425–36.
Yakir, B. (1997) “A Note on Optimal Detection of a Change in Distribution”, Annals of Statistics, 25 (5): 2117–26.
Yashchin, E., Steinand, D. and Philips, T. (1997) “Monitoring Active Portfolios Using Statistical Process Control”, in H. Amman et al. (eds), Computational Approaches to Economic Problems (Norwell, MA: Kluwer).
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© 2007 Olha Bodnar
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Bodnar, O. (2007). Sequential Procedures for Monitoring Covariances of Asset Returns. In: Gregoriou, G.N. (eds) Advances in Risk Management. Finance and Capital Markets Series. Palgrave Macmillan, London. https://doi.org/10.1057/9780230625846_13
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DOI: https://doi.org/10.1057/9780230625846_13
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