**Value at risk (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 during 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 probability of 5% that the loss is 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 the loss, the probability of the loss, and the time.

Continuing with the previous example, a company could estimate that it has a 5% probability of losing more than 5 million euros in a month. 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 out of 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 able to bear.

Companies can estimate the benefits of each investment compared to its 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.

**How to Calculate Value at Risk (VAR)**

There are three main ways to calculate **VaR**:

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

**Advantages of Value at Risk (VAR)**

Among the advantages of **Value at risk** are:

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

**Disadvantages of Value at Risk (VaR)**

Likewise, among the disadvantages of **Value at risk** we have:

**Value at Risk**is only as useful as the results that have been used to calculate it are good. If the data included is not correct, the VaR will not be useful.**VaR**does not consider all worst possible scenarios. To solve this, the VaR is complemented with the stress tests, which consider extreme scenarios not contemplated 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 only a probability. It does not 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 a 1% probability of losing more than 5 million euros, what will be the expected amount of loss? For that the technique of waiting loss or Tail VaR is used.
- Sometimes the diversification that
**VaR**provides is not intuitive. We may think that it is better to invest only in the sectors that have higher returns for each unit of risk, but in this way we do not diversify the risk.

**Importance of Value at Risk (VAR)**

After the outbreak of the crisis in 2008, the **VaR** took on special importance, especially in the treasury rooms of banks. The increasing capital requirement (Basel III) towards the banking sector, and consequently greater risk control, make the risk departments assign a daily, weekly and monthly **VaR** to the different interest rate, bond, trading, etc. tables. volatility or other instruments negotiable in the markets.

However, it is also particularly important in the world of asset management, portfolio management or in other sectors in contact with financial markets.

**Example of Value at Risk at 95% confidence**

Let’s imagine a company that has a 5% probability of losing 5 million euros in a month, or what is the same, a 5 million VaR at 5%. This means that there is a 5% probability that the company will lose more than 5 million euros some month and a 95% that the loss is less. Therefore, 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 frequency distribution we can see how the 5% tail determines that, out of every 100 months, 5 of them will suffer losses greater than or equal to VaR: