  Minimum-variance portfolio optimizations rely on accurate covariance
estimator to obtain optimal portfolios. However, it usually suffers from large
error from sample covariance matrix when the sample size $n$ is not
significantly larger than the number of assets $p$. We analyze the random
matrix aspects of portfolio optimization and identify the order of errors in
sample optimal portfolio weight and show portfolio risk are underestimated when
using samples. We also provide LoCoV (low dimension covariance voting)
algorithm to reduce error inherited from random samples. From various
experiments, LoCoV is shown to outperform the classical method by a large
margin.
