CHAPTER 13
Sequential Procedures
for Monitoring
Covariances of Asset
Returns
Olha Bodnar
13.1 INTRODUCTION
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 activ-
ity, 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.
For a long time financial studies have been concentrated on the proper
estimation of the covariance matrix of asset returns. To reduce the estimation
error in the covariance matrix of asset returns when the sample portfolio is
constructed, Ledoit and Wolf (2003, 2004) proposed the shrinkage estimator
of the covariances. In another branch of studies (Andersen, Bollerslev,
Diebold and Ebens, 2001; Barndorff-Nielsen and Shephard, 2002, 2004) the
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