  The only input to attain the portfolio weights of global minimum variance
portfolio (GMVP) is the covariance matrix of returns of assets being considered
for investment. Since the population covariance matrix is not known, investors
use historical data to estimate it. Even though sample covariance matrix is an
unbiased estimator of the population covariance matrix, it includes a great
amount of estimation error especially when the number of observed data is not
much bigger than number of assets. As it is difficult to estimate the
covariance matrix with high dimensionality all at once, clustering stocks is
proposed to come up with covariance matrix in two steps: firstly, within a
cluster and secondly, between clusters. It decreases the estimation error by
reducing the number of features in the data matrix. The motivation of this
dissertation is that the estimation error can still remain high even after
clustering, if a large amount of stocks is clustered together in a single
group. This research proposes to utilize a bounded clustering method in order
to limit the maximum cluster size. The result of experiments shows that not
only the gap between in-sample volatility and out-of-sample volatility
decreases, but also the out-of-sample volatility gets reduced. It implies that
we need a bounded clustering algorithm so that maximum clustering size can be
precisely controlled to find the best portfolio performance.
