THESIS
2013
xiv, 83 pages : illustrations ; 30 cm
Abstract
In modern portfolio theory, the accuracy and robustness of the covariance estimator plays
a critical role in defining the performance of the optimized portfolios. Traditional estimators
such as the sample covariance matrix usually perform poorly when the number of observed
daily returns is comparable to the number of assets. Moreover, the strong non-stationary
effects will further amplify estimation errors and lead to inaccurate investment decisions.
High frequency data allows one to consider a short enough history such that the covariance
matrix remains relatively unchanged, whilst still potentially offering sufficient historical
samples for accurate estimation. However, the use of sparse sampling to account for the microstructure
noise places a restriction on the maximum num...[
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In modern portfolio theory, the accuracy and robustness of the covariance estimator plays
a critical role in defining the performance of the optimized portfolios. Traditional estimators
such as the sample covariance matrix usually perform poorly when the number of observed
daily returns is comparable to the number of assets. Moreover, the strong non-stationary
effects will further amplify estimation errors and lead to inaccurate investment decisions.
High frequency data allows one to consider a short enough history such that the covariance
matrix remains relatively unchanged, whilst still potentially offering sufficient historical
samples for accurate estimation. However, the use of sparse sampling to account for the microstructure
noise places a restriction on the maximum number of intraday observations. The
well-known realized covariance estimator for high frequency data will still perform poorly
due to estimation errors, and it does not provide sufficient robustness with respect to unknown
time-variation. The limited sample and complexity in handling time-variation further make
previous works only focused on small number of assets.
To address the issues caused by limited sample and time variation effects, in this thesis,
we aim to design novel high frequency estimation techniques for optimizing large portfolios
in the presence of unknown time variation, and for practical conditions in which the number
of observed samples is of similar order to the number of assets. We focus on asset allocation
optimization under high frequency global minimum variance portfolio framework. A
key challenge is to develop suitably optimized covariance estimators for the portfolio optimization
problem. For this purpose, we propose a new method based on using the recently
developed time variation adjusted realized covariance (TVARCV) estimator in a shrinkage
structure. The shrinkage parameter is difficult to optimize when considering both the limited sample and time variation effects. For this shrinkage TVARCV estimator, we provide a deterministic
characterization of the realized portfolio risk in terms of the shrinkage parameter
and the covariance matrix. Our main result is the proposal of a novel optimized covariance
matrix estimator, designed to yield minimal realized portfolio risk, and which depends only
on the observable returns. Numerical results show that the proposed estimator is robust
to time variation and has a smaller realized portfolio risk compared with other benchmark
estimators. Superior performance based on real financial data is also demonstrated.
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