This paper investigates portfolio optimization using robust covariance estimators and Conditional Value-at-Risk (CVaR) constraints to address the instability and tail risk issues of traditional Markowitz mean-variance optimization. The study compares several covariance estimation methods: exponentially weighted sample covariance, Ledoit-Wolf shrinkage, and the Gerber robust covariance, which uses a threshold-based co-movement measure to reduce sensitivity to outliers. Additionally, Nested Clustering Optimization (NCO) with K-means clustering is employed to mitigate numerical instability by grouping assets before optimization. The empirical analysis uses large-cap U.S. stocks from 2012 to 2022, with monthly rebalancing and a minimum-variance objective. Results show that robust covariance estimators, particularly Gerber with Mean-Absolute-Deviation (MAD), outperform the market-cap weighted benchmark during bull markets but fail to manage tail risk during extreme events like the COVID-19 crash. To address this, the paper incorporates CVaR constraints, which effectively limit extreme losses and improve risk-adjusted performance. The NCO method also reduces drawdowns and enhances stability. Overall, the study demonstrates that combining robust covariance estimation with CVaR constraints and clustering techniques can significantly improve portfolio performance and risk management.