English abstract
Multivariate statistical analysis has applications in Finance, especially in portfolio
choice. A portfolio is considered as a linear combination of assets. Each asset contributes with a certain weight to the portfolio. The performance of such a portfolio
is a function of the various returns of the assets and of the weights. Portfolio selection is a critical and challenging task in financial field. The purpose of this study is
the computations of the optimal weights of the assets of interest.
Several portfolios involving different sectors including Financial, Industrial and Services, were constructed. The asset prices were collected from Muscat Stock Exchange
during the period between 2010 and 2023. Optimal weights were calculated with
their corresponding risks. The computations required, however, estimating covariance and precision matrices and testing hypotheses about the structure of those
matrices .
Three different estimators were used to estimate the covariance matrix, S , Σb and Σbb.
The inverse of the above estimators are then used to estimate the precision matrix,
Σ
−1
. Shrinkage estimation was implemented for S
−1 and Σb−1
to get better estimator
for Σ−1 under quadratic loss function.
The empirical studies on the Muscat stock exchange data revealed that direct estimation of Σ−1 using Σbb dominates S and Σ in terms of risk. Moreover, the shrinkage b
estimation for Σb−1 with a certain value of α produced smaller portfolio risk among
all other estimators. Moreover, the minimum amount of risk was obtained with the
Services portfolio. Additionally, reducing the sample size to (24 months) has an
impact on minimizing the portfolio risk.
