# Value at risk (VaR)

Value at risk, commonly known as VaR ( Value at Risk ), is a statistical technique to measure the financial risk of an investment. Indicates the probability (usually 1% or 5%) of suffering a certain loss over a period of time (usually 1 day, 1 week or 1 month).

In other words, the VaR establishes the maximum loss that an investment can experience within a time horizon, given a confidence level (1- α), normally 95% or 99%. For example, the maximum loss will be for a month with a 95% probability equal to or less than 5 million euros. Or what is the same, there is a 5% probability that the loss will be at least 5 million euros in a month. Therefore, it also measures the minimum loss that an investment will suffer for a significance level (α).

Although it seems a complicated technique, it is really only measured with three variables, which makes it very easy to understand and apply. The three variables are the amount of loss, the probability of loss, and time. Continuing with the previous example, a company could estimate that it has a 5% probability of losing in a month more than 5 million euros. This means that there is a 5% probability that the company will lose more than 5 million euros some month and a 95% probability that the loss will be less. Therefore, the company will have to take into account that one in every 100 months will lose at least 5 million euros.

VaR measures the financial risk of an investment , so it has a wide application in the world of finance. The maximum loss can be calculated for both a single financial asset and a portfolio of financial assets. It is widely used in risk analysis to measure and control the level of risk that a company is capable of bearing. The risk manager is to ensure that no greater risks are incurred than the company could face.

Companies can estimate the benefits of each investment compared to their VaR and thus invest more money where there are higher returns for each unit of risk. Of course, at the same time it is important to maintain investment in different business units to achieve greater risk diversification , which is one of the advantages observed when using VaR.

## Ways to calculate VaR

There are three main ways to calculate VaR:

1. Parametric VaR: Uses estimated profitability data and assumes a normal distribution of profitability.
2. Historical VaR– Uses historical data.
3. VaR for Monte Carlo :uses computer software to generate hundreds or thousands of possible results based on initial data entered by the user.

• Adds all the risk of an investment in a single number, making it very easy to assess risk
• It is a highly standardized measure of risk and therefore can be compared as it is widely calculated.
• When the correlation between different investments is less than 1, the VaR set will be less than the sum of the VaRs.

• VaR is as useful as good are the results that have been used to calculate it. If the included data is not correct, the VaR will not be useful.
• VaR does not consider all the worst possible scenarios. To solve this, the VaR is complemented by stress tests, which consider extreme scenarios not covered by the VaR.
• Some methods to calculate it are expensive and difficult to apply (Monte Carlo).
• The results obtained by different methods may be different.
• It generates a false sense of security, when it is just a probability. It doesn’t have to be taken for granted.
• It does not calculate the amount of the expected loss that remains in the probability percentage, that is, if there is 1% of losing more than 5 million euros, what will be the amount of expected loss? For that, the technique of waiting loss or Tail VaR is used.
• Sometimes the diversification that VaR provides is not intuitive. We can think that it is better to invest only in the sectors that have higher returns for each risk unit, but in this way we do not diversify the risk.

## Importance of VaR

After the outbreak of the crisis in 2008, the VaR takes on special importance, especially in the treasury rooms of banks. The increasing capital demand ( Basel III ) towards the banking sector and consequently greater risk control, make risk departments assign (lower amounts of VaR consumption), a daily, weekly and monthly VaR to the different tables of interest rate, bonds, trading, volatility or other negotiable instruments in the markets. However, it is also particularly important in the world of asset management, portfolio management or other sectors in contact with the  financial markets.

## Example of VaR at 95% confidence

Imagine a company that has a 5% probability of losing 5 million euros in a month, or what is the same a VaR 5 million at 5%. This means that there is a 5% chance that the company will lose more than 5 million euros in a month and 95% that the loss will be less. For this reason, the company will have to take into account that five out of every 100 months will lose at least 5 million euros, or that one out of every 20 months will lose at least 5 million euros.

In the distribution of frequencies we can see how the 5% tail determines that, for every 100 months, 5 of them will suffer losses greater than or equal to VaR: