Value at risk (VaR) is the statistical calculation that estimates the future risk of loss that may be realized on a financial instrument or portfolio in the observed period with a defined level of reliability. It is expressed with one number and is valid only for normal market conditions. The VaR appeared in the latest 80s of the last century and is popular until today. Many investors and also financial regulators use it as well. Including numerous advantages of VaR, it also has got certain disadvantages, so, therefore, it is considered a necessary, but not a sufficient way of measuring market risk. Since the appearance of the first model until today there are a lot of different models of the valuation of risk. The three most often used approaches in the valuation of risk values are: historical method, variance-covariance and Monte Carlo simulation. In this graduate thesis the basics of historical methods are presented, variance-covariance method and Monte Carlo methods, describing their theoretical side, the advantages and disadvantages of the various methods, and steps you need to follow to make a calculation. As an attempt to improve VaR a Conditional value of risk (CVaR) was created and is defined as the average loss value greater than VaR. It is important in situations where distribution of yield is not normal so CVaR and VaR can be significantly different and, unlike the VaR, it fulfills the principle of subaditability. In the research part of the work, the Var and CVaR method was applied on 24 shares divided into 7 sectors in the observed period until 21st July 2015 – 21st July 2017 and by the backtesting both methods it comes to the conclusion that CVaR gives more representative results than the Var methods, as it is supposed by the working hypothesis. Accordingly, a decision is made to accept the hypothesis that reads: “ CVaR” gives more precise and more reliable estimates of the risk of particular sector than VaR, (because the CVaR has better theoretical characteristics than VaR, and it can be supposed that it will give us better and more accurate results”.