  In portfolio risk minimization, the inverse covariance matrix of returns is
often unknown and has to be estimated in practice. This inverse covariance
matrix also prescribes the hedge trades in which a stock is hedged by all the
other stocks in the portfolio. In practice with finite samples, however,
multicollinearity gives rise to considerable estimation errors, making the
hedge trades too unstable and unreliable for use. By adopting ideas from
current methodologies in the existing literature, we propose 2 new estimators
of the inverse covariance matrix, one which relies only on the l2 norm while
the other utilizes both the l1 and l2 norms. These 2 new estimators are
classified as shrinkage estimators in the literature. Comparing favorably with
other methods (sample-based estimation, equal-weighting, estimation based on
Principal Component Analysis), a portfolio formed on the proposed estimators
achieves substantial out-of-sample risk reduction and improves the
out-of-sample risk-adjusted returns of the portfolio, particularly in
high-dimensional settings. Furthermore, the proposed estimators can still be
computed even in instances where the sample covariance matrix is
ill-conditioned or singular
