The value at risk is a statistical risk management technique that monitors and quantifies the risk level associated with an investment portfolio. The value at risk measures the maximum amount of loss over a specified time horizon with a given confidence level. Backtesting measures the accuracy of the value at risk calculations. The loss forecast calculated by the value at risk is compared with actual losses at the end of the specified time horizon.

Backtesting is a technique for simulating a model or strategy on past data to gauge its accuracy and effectiveness. Backtesting in value at risk is used to compare the predicted losses from the calculated value at risk with the actual losses realized at the end of the specified time horizon. This comparison identifies the periods where the value at risk is underestimated or where the portfolio losses are greater than the original expected value at risk. Value at risk predictions can be recalculated if the backtesting values are not accurate, thereby reducing the risk of unexpected losses.

### Potential Maximum Loss

Value at risk calculates the potential maximum losses over a specified time horizon with a certain degree of confidence. For example, the one-year value at risk of an investment portfolio is $10 million with a confidence level of 95%. The value at risk indicates that there is a 5% chance of having losses that exceed $10 million at the end of the year. With 95% confidence, the worst expected portfolio loss over one trading year will not exceed $10 million.

If the value at risk is simulated over the past yearly data and the actual portfolio losses have not exceeded the expected value at risk losses, then the calculated value at risk is an appropriate measure. On the other hand, if the actual portfolio losses exceed the calculated value at risk losses, then the expected value at risk calculation may not be accurate.

When the actual portfolio losses are greater than the calculated value at risk estimated loss, it is known as a breach of value at risk. However, if the actual portfolio loss is above the estimated value at risk only a few times, it doesn't mean that the estimated value at risk has failed. The frequency of breaches needs to be determined.

For example, the daily value at risk of an investment portfolio is $500,000 with a 95% confidence level for 250 days. At the 95% confidence level, the actual losses are expected to breach $500,000 approximately 13 days out of 250 days. There is only a problem with the value at risk estimates when breaches occur more than 13 days out of 250 days; this signals the value at risk estimate is inaccurate and needs to be re-evaluated.