# Introduction to Value At Risk (VaR)

The concept of value at risk (VaR) is closely connected with the concept of market risk mitigation. This is why the discussion about one invariably turns to a discussion about the other.

The concept of value at risk (VaR) was developed by many financial institutions as they wanted to know how volatile their portfolio was.

One way to measure this volatility was to see how much the portfolio value could change over a given period of time such as a day or a week.

The value at risk (VaR) model most commonly used has been developed by the JP Morgan group. In this article, we will understand what the concept of value at risk (VaR) is and how it is used to manage risks in business organizations.

### What is Value at Risk (VaR)?

Value at Risk (VaR) is the maximum possible amount of loss that a company is likely to face in a given period of time. For instance, if a company has a portfolio of \$ 1 million, they may apply the value at risk (VaR) formula to see what is the maximum amount they can lose on a given day.

Now, stock markets work on probabilistic phenomena. Hence, there is no one in the world who can guarantee the maximum loss on any given day. Since value at risk (VaR) relates to a probabilistic phenomenon, it is expressed in probabilistic terms.

For instance, it may be said that there is a 95% chance that the maximum loss within the next day will not exceed \$15,000 for this \$1 million portfolio. This confidence level is very important.

Oftentimes firms calculate value at risk (VaR) at different confidence levels and then plot it on a graph.

It is important to know that the value at risk (VaR) concept is forward-looking. This means the calculations are done to find out the maximum loss which may or may not become a reality in the future.

The value at risk (VaR) is time-bound. The numerical value of value at risk (VaR) changes drastically if the time limit is changed from one day to one week or one month!

However, in most cases, value at risk (VaR) is calculated for very small time periods such as a day or two. This is because there is an assumption that since these instruments are highly liquid and can be sold on the market in almost no time, there is no need to look at the long-term market risks.

The value at risk (VaR) has become extremely important in the past few years. This is because banks and other organizations nowadays hold a wide variety of shares, bonds, and other financial instruments. Since their portfolio is so large, managing it becomes difficult.

The value at risk (VaR) is a single measure that helps the management gauge the amount of risk that a company is taking. This is very useful for executive decision-making since executives do not have the time to go through all the data.

Instead, they have to make decisions quickly using data in a condensed format. That is exactly what the value at risk (VaR) allows them to do.

### Interpretations of VaR

Firstly, to interpret the value at risk (VaR) number, we must understand the confidence level.

1. A maximum confidence level means that the total losses cannot exceed that amount within that time period. For instance, 95% confidence that losses will not exceed \$15000.

2. On the other hand, a minimum confidence level means that the losses will be at least that amount. For instance, in the above case, there is a minimum 5% chance that the losses will exceed \$15000

3. The value at risk (VaR) number is immediately compared to the risk capital that the bank has earmarked for itself. For instance, the bank has earmarked \$10000 as risk capital. Hence, the \$15000 value at risk (VaR) number will worry them. Ideally, they will sell off some of their investments till this value at risk (VaR) number is reduced to \$10000 or less.

### Which Data is Used in Value at Risk (VaR) Calculations?

The value at risk (VaR) number is a representation of the maximum loss that can take place. Hence, logically the data about past losses have to be used in order to derive the answer. Ideally, market data for an extended time period is taken from the marketplace. The longer the time period for which data is taken, the more comprehensive and reliable the result is likely to be.

Once the data is collected, mathematical and statistical operations are performed in order to identify the maximum possible losses. There are several different methods to arrive at the value at risk (VaR) number. They have been discussed later in the module.

The basic concept of value at risk (VaR) is that the maximum possible losses become visible to the higher management. They can then align their risk-taking decisions to this number. In most companies, risk policies clearly define the value at risk (VaR) number which is acceptable and unacceptable keeping in mind the risk appetite of the firm.

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