Backtesting Value at Risk (VaR)

Merely creating a model which calculates the value at risk (VaR) i.e. the greatest possible loss that a company can face in a particular time period is not enough. In order for risk management to be effective, the results provided by the model should actually correlate with reality.

Otherwise, the model will make predictions that will never come true. This might end up impacting the business in a negative manner.

In this article, we will have a look at the process called backtesting. The purpose of backtesting, as well as its advantages, will be enumerated in this article.

What is Backtesting?

The purpose of backtesting is to evaluate the accuracy of the results provided by the model. This is the reason why backtesting is a backward-looking activity (as opposed to VaR calculation which is forward-looking).

Backtesting is done by collecting actual loss data in a timely manner. This loss data is then compared with the predictions made by the value at risk (VaR) model for that particular day. The confidence level is also taken into account during this comparison.

For instance, if the model predicted with 99% confidence that the losses will remain less than $1 million and the actual results also correspond to this, then the model is said to be efficient. 99% confidence means that the losses should lie within the prescribed limit 99% of the time.

The results given by the value at risk (VaR) model are absolutely critical. They are used by senior management to make key decisions.

Hence, it is extremely important for the company to make sure that the model stays current and gives accurate results. This is why companies are willing to spend considerable time and resources to ensure that the model is accurate.

The Process of Backtesting

The process of backtesting is quite simple. Each time, the actual losses exceed the expected losses, the event is called an exception or an exceedance.

The percentage of these exceptions is calculated over a period of time. The model will be considered to be successful if the actual results actually correspond to the confidence level.

This means that if the confidence level is 95%, then the exceptions should be close to 5%. If the exceptions are 25% in a model with 95% confidence, then the model is not reliable and should not be used to make decisions.

The opposite of this is also true, if only 0.5% exceptions occur, this means that the risk has been overstated and the company is being unnecessarily conservative in conducting its operations.

This exercise is done periodically since it is possible that a model which worked accurately in the past does not give accurate results anymore.

Conditional and Unconditional Backtesting

Unconditional backtesting is when the time factor is not taken into account. This means that each day is considered to be a different day and hence the results of each day are not considered to be correlated to each other.

However, this is not how the financial markets really work. It is common for losses to be centered around a major event. It is also common for uncorrelated losses to happen during the same time period. In such cases, unconditional testing will provide faulty results.

This can be corrected by using conditional backtesting. Conditional backtesting is like conditional probability. It calculates the accuracy of the model given that an event has already taken place in the past.

Backtesting and Regulations

Financial services organizations are subject to regulations made by the Basel Committee. The Basel Committee has mandated that organizations conduct backtesting of the value at risk models that they develop. This is because the value-at-risk models are organization-specific. This means that there are no set industrywide standards that need to be followed.

Hence, it is always possible that management in an organization may deliberately or inadvertently underestimate the risk. This could have potentially catastrophic ramifications on the investors of the organization.

In order to avoid this, the Bank of International Settlements has made backtesting mandatory.

Limitations of Backtesting

Backtesting a value at risk model seems like a simple idea prima-facie. However, there are several complications that are commonly faced by organizations.

For instance, the backtesting process assumes that the underlying portfolio will remain static. However, in large organizations, there is constant trading.

Hence, the value of the portfolio keeps on changing every minute. However, the model predicts results for a longer period of time such as a day.

It is quite possible that the portfolio which was used to make the value at risk (VaR) prediction ends up being quite different than the one on which the actual loss was incurred. Hence, the comparison may not be an apples-to-apples comparison.

In many cases, the entire portfolio is too large, and hence data collection may become difficult. In such cases, a sample may be collected from the entire data in order to conduct backtesting.

It is quite possible that the sample may not truly be representative of the larger group.

Hence, it would be fair to say that backtesting is as important (if not more important) as creating the value at risk (VaR) model.

In the absence of backtesting, the reliability of the VaR models will be limited. As such companies will not be able to make decisions based on this model. The backtesting really puts the confidence in the confidence level used in value at risk models!