# Loss Given Default Formula

Default risk represents the chance that a borrower does not repay their debt obligation. Almost every loan or debt obligation comes with default risk. The higher the default risk is, the more unlikely it is for lenders to recover their loaned amount. Default risks can be crucial for lenders when deciding on whether to provide a loan or not.

There are various precautions that lenders or investors may take to mitigate default risks on their loans. While these steps may decrease the default chances, they do no eliminate those risks. Therefore, defaults on loans are always possible and cause losses for the lender. A term often associated with these losses is the loss given default.

## What is Loss Given Default?

Loss given default (LGD) refers to the amount of money that financial institutions lose when a borrower fails to repay a loan. Usually, they calculate it as a percentage of the total exposure at the time of default. Loan given default is a common metric used for calculating a lender’s expected losses when making decisions about loan provision.

There are several factors that may dictate the chances of defaults by borrowers. Usually, the borrower’s credit rating can indicate whether they will repay the loan or not. Similarly, any ongoing financial crisis may significantly increase the probability of defaults by borrowers. When these chances are high, the loss given default of the lender will also be high.

## What is the Loss Given Default formula?

Measuring the loss given default for a particular loan is crucial for lenders. They can calculate the LGD in one of two ways. Firstly, they can use the loss given default formula below.

Loss Given Default = Total Loss / Total Loan Value x 100

In the above formula, the total loss represents the loan value after deducting the amount recovered. Similarly, the total loan value represents the amount of loan that the lender provided.

The loss given default of debt also depends on its recovery rate. The higher the recovery rate of a loan is, the lower its loss given default will be and vice versa. Since both of these are a percentage of the total amount of loan provided, lenders can also use the recovery rate to calculate the loss given default. They can use the following formula to do so.

Loss Given Default = 1 – Recovery Rate

## Example

An investor provides a loan of \$100,000 to a company. The company repays \$80,000 of the debt. However, it fails to repay the remaining amount and defaults on the payment. Therefore, the loss given default for the investor will be as follows.

Loss Given Default = Total Loss / Total Loan Value x 100

Loss Given Default = (\$100,000 – \$80,000) / \$100,000 x 100

Loss Given Default = 20%

Similarly, the loan’s recovery rate will be 80% as the investor only lost 20% of the loan due to default.

## What is the importance of Loss Given Default?

Loss given default is crucial for lenders for several reasons. Firstly, it is useful in the calculation of expected loss, economic capital, and regulatory capital. Lenders can also use the LGD in various models, such as the Basel Model. If used properly, LGD can help lenders forecast any possible defaults and work towards maximizing recoverability.

## Conclusion

Loss given default is a term used to describe the amount of money that lenders lose in case of a default from the borrower. Lenders can calculate the LGD as a percentage of the total value of the loan they provide. There are two loss given default formulas that they can use to do so, both of which are easy to use.

## Further questions

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