Which characteristics of a portfolio are important, how can we select an optimal portfolio and which portfolio a risk-averse investor should avoid? Pioneering theory about portfolio selection methods introduced by Harry Markowitz in the 1950’s has helped to solve some of these issues in financial world. His mean-variance portfolio theory has yielded tools for the selection of efficient portfolios and is a backbone of all contemporary optimization methods. Although Markowitz’s portfolio theory has faced many challenges in practice, due to some assumptions that are not mirroring the real world, it is a still basic model that underlies modern portfolio theory. The model has also been criticized because it is suitable for elliptical distributions and if returns are not elliptical, analysis can yield wrong conclusions. Due these drawbacks many risk measures have been introduced since. One of them is Value at Risk, however its sub-additivity property issues and ignorance of the worst losses in the far tail has been overcome with another risk measure Expected Shortfall or also called Conditional Value at Risk (CVaR). This paper explores the performance of two portfolio optimization methods, Conditional Value at Risk and Mean-Variance portfolio optimization during two different periods, one before and other during the corona crisis. This approach is tested in R on a portfolio composed of four NASDAQ index stocks (Alphabet.inc (GOOGL), Tesla.inc (TSLA), Facebook.inc (FB) and Amazon.inc (AMZN)) to demonstrate whether there is a difference in portfolio performance under two different risk measures and different market conditions.