VaR for Monte Carlo
Monte Carlo VaR is a method to estimate VaR (Value at Risk) that uses computer software to generate hundreds or thousands of possible results based on initial data entered by the user.
The results obtained are ordered from the highest to the lowest profitability as in the calculation of VaR by the historical method. Next, we identify the 5% of data with the lowest returns, and the highest of that 5% lowest returns will be the VaR. The data are usually presented graphically to have a better visualization of the results and their frequency.
The main advantage of estimating VaR by the Monte Carlo method is in turn its main disadvantage, since depending on the initial data entered, a series of assumptions will be generated that will guide the results (path dependency or dependent on the path chosen). Given the complexity of Monte Carlo, you can have a false sense of reliability, but if the data entered (inputs) are not correct, the information will not be reliable. Despite this, it is usually more accurate than the parametric VaR method.
Monte Carlo simulation
Example of VaR by the Monte Carlo method
Imagine that after having generated 100 different results by the computer program (normally more are used, but we will use 100 to facilitate the example), and ordering the values obtained from highest to lowest, we obtain that the five worst are the following:
-15,25%, -12,75%, -10,85%, -10,05%, -8,75%
If we want to calculate the VaR at 95% confidence, we must choose the 5% with the worst results. We then choose the fifth worst result (5% of 100) of the entire period, which is -8.75%. If we assume that the investment in this asset is 1 million euros, the 5% VaR will be 87,500 euros, that is, there is a 5% probability of losing at least 87,500 euros and a 95% probability that this loss is less. Therefore, the company will have to take into account that five out of every 100 months will lose at least 87,500 euros, or that one out of every 20 months will lose at least 87,500 euros.