Value at Risk (V@R) is one of the most popular risk assessment tools in the world of investment and risk management. Conditional value at risk (CV@R) or Expected Shortfall (ES) is a technique often used to reduce the probability that a portfolio will incur large losses and is performed by assessing the likelihood (at a specific confidence level) that a specific loss will exceed the V@R. This thesis studies the ES notion and compares its estimation methods. The goal of the thesis is to analyze the techniques of V@R and ES estimations and apply the techniques of 1) Historical and 2) Monte Carlo simulation method. The empirical study concerns the assessment of alternatives ES methods in a real mixed portfolio and the comparison of their results. We used a portfolio with historical data and estimated the one-day 99% V@R, one-day 95% V@R such as one-day 99% ES and one-day 95% ES in order to compare their results. Using different ways of estimation for two portfolios, we came to a conclusion in which, Historical Simulation is this simulation in which we have the underestimation of V@R and ES contrary to Monte Carlo Simulation.