  The measure of portfolio risk is an important input of the Markowitz
framework. In this study, we explored various methods to obtain a robust
covariance estimators that are less susceptible to financial data noise. We
evaluated the performance of large-cap portfolio using various forms of Ledoit
Shrinkage Covariance and Robust Gerber Covariance matrix during the period of
2012 to 2022. Out-of-sample performance indicates that robust covariance
estimators can outperform the market capitalization-weighted benchmark
portfolio, particularly during bull markets. The Gerber covariance with
Mean-Absolute-Deviation (MAD) emerged as the top performer. However, robust
estimators do not manage tail risk well under extreme market conditions, for
example, Covid-19 period. When we aim to control for tail risk, we should add
constraint on Conditional Value-at-Risk (CVaR) to make more conservative
decision on risk exposure. Additionally, we incorporated unsupervised
clustering algorithm K-means to the optimization algorithm (i.e. Nested
Clustering Optimization, NCO). It not only helps mitigate numerical instability
of the optimization algorithm, but also contributes to lower drawdown as well.
