# Unexpected Loss and Economic Capital Buffer

In the previous articles, we have seen how we can use exposure at default (EAD), loss given default (LGD), and probability of default to calculate the value of expected losses. However, it needs to be understood that expected losses are at best a crude estimate of the amount of money that would be required to mitigate the losses.

Any organization cannot solely rely on the expected loss number. This is because the **actual losses would exceed the estimated losses roughly 50% of the time!** This is the reason that organizations also need to think about the concept of unexpected losses and how they affect the risk management processes at banks.

### What is Unexpected Loss?

Unexpected loss is the value of the loss, which may exceed the expected loss, which may occur in any particular year. Let’s understand this with the help of an example. If company A budgets $40,000 for credit losses in any particular year and in that year, the actual losses turn out to be $55,000, then the additional $15,000 are said to be "unexpected losses".

### Why Is It Important To Account For Unexpected Loss?

Unexpected loss is considered to be an important figure in order to evaluate the performance of the credit risk management function. This is because if the firm is suffering from unexpected losses every year, then obviously they are calculating expected losses in the wrong way. Also, the company has to be sure about how big their unexpected losses can be. In most scenarios, unexpected losses are covered by the equity shareholders of the company. Hence, if the unexpected loss is more than the valuation of the equity in a company, it can lead to bankruptcy within a very short period of time.

### How Is Unexpected Loss Calculated?

The calculation of unexpected losses is quite complicated. This is because it is not possible to directly calculate the unexpected loss. Instead, it can be estimated using a simulated range of expected losses. The details have been mentioned below:

**Level of Confidence:**In order to calculate the unexpected losses, the firm has to first decide the level of confidence which it seeks against unexpected losses. It needs to be understood that 100% confidence is not possible. This is because there can never be certainty in any event which is considered to be probabilistic in nature. Hence, companies choose high confidence levels such as 95% if they want to a higher level of confidence. The confidence level can be seen as the probability that a firm will not go bankrupt over a given period of time.**Normal Distribution of Expected Losses:**The next step is to use Monte Carlo simulations in order to create thousands of possible expected loss values by varying the underlying factors. The assumption here is that the expected losses always follow a normal distribution. Hence, the simulated values also follow a normal distribution.**Standard Deviation:**The standard deviation is the measure of dispersion in a normal distribution. Hence, the standard deviation can be used to calculate the value which corresponds to the confidence level selected. For instance, if the confidence level is 95%, then the value selected should be the 95th percentile of all the values.**Subtract Expected Loss:**The 95th percentile value obtained above is then used to calculate the unexpected loss. This can be easily done since the expected loss is the mean value i.e. the 50th percentile of the values calculated by the simulation. The 50th percentile value can be subtracted from the 95th percentile value in order to find the unexpected loss with 95% confidence. This means that in 95% of the cases, the unexpected loss will fall on or below this value. It is important to note that there is still a 5% chance that unexpected loss may be greater than the calculated value.**Concept of Economic Capital:**The firm does not and cannot make provisions against unexpected losses. This is because these losses are unexpected by their very nature. Hence, these losses have to be borne by the equity capital.**This part of the equity capital which is needed to bear the unexpected loss is called economic capital**.The definition of economic capital is the amount of capital that a firm needs in order to survive the various risks that it is taking. It is essential that the total capital of the company be significantly higher than the probable unexpected loss otherwise the company might be at a high risk of bankruptcy. It is common for companies to do this entire exercise for various confidence levels. The idea is to figure out how well capitalized the organization is if the confidence levels are varied.

It is important to realize that since the expected loss distribution is based over a period of time, **the unexpected loss calculation is also valid only for that period of time**. In the long run, companies may need more or less economic capital and that has to be calculated at predefined periods of time.

The fact of the matter is that it is impossible to predict with accuracy the loss that any company may have to face in the long run. However, using advanced statistical techniques, it is possible to be able to meet the solvency requirements of the firm with a high degree of certainty.

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