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# Loss Given Default (LGD): Two Ways to Calculate, Plus an Example

## What Is Loss Given Default (LGD)?

Loss given default (LGD) is the estimated amount of money a bank or other financial institution loses when a borrower defaults on a loan. LGD is depicted as a percentage of total exposure at the time of default or a single dollar value of potential loss. A financial institution’s total LGD is calculated after a review of all outstanding loans using cumulative losses and exposure.

### Key Takeaways

• The loss given default (LGD) is an important calculation for financial institutions projecting out their expected losses due to borrowers defaulting on loans.
• The expected loss of a given loan is calculated as the LGD multiplied by both the probability of default and the exposure at default.
• Exposure at default is the total value of the loan at the time a borrower defaults.
• An important figure for any financial institution is the cumulative amount of expected losses on all outstanding loans.
• LGD is an essential component of the Basel Model (Basel II), a set of international banking regulations.

## Understanding Loss Given Default (LGD)

Banks and other financial institutions determine credit losses by analyzing actual loan defaults. Quantifying losses can be complex and require an analysis of several variables. How credit losses are accounted for on a company’s financial statements include determining both an allowance for credit losses and an allowance for doubtful accounts.

Consider if Bank A lends \$2 million to Company XYZ, and the company defaults. Bank A’s loss is not necessarily \$2 million. Other factors must be considered such as the amount of collateral, whether installment payments have been made, and whether the bank makes use of the court system for reparations from Company XYZ. With these and other factors considered, Bank A may, in reality, have sustained a far smaller loss than the initial \$2 million loan.

Determining the amount of loss is an important and fairly common parameter in most risk models. LGD is an essential component of the Basel Model (Basel II), a set of international banking regulations, as it is used in the calculation of economic capital, expected loss, and regulatory capital. The expected loss is calculated as a loan’s LGD multiplied by both its probability of default (PD) and the financial institution’s exposure at default (EAD).

Loans with collateral, known as secured debt, greatly benefit the lender and can benefit the borrower through lower interest rates.

## How to Calculate LGD

There are a number of different ways to calculate LGD.

A common variation considers the exposure at risk and recovery rate. Exposure at default is an estimated value that predicts the amount of loss a bank may experience when a debtor defaults on a loan. The recovery rate is a risk-adjusted measure to right-size the default based on the likelihood of the outcome.

LGD (in dollars) = Exposure at Risk (EAD) * (1 - Recovery Rate)

Another basic variation compares the potential net collectible proceeds to the outstanding debt. This formula provides a general ratio of what portion of debt is expected to be lost:

LGD (as percentage) = 1 - (Potential Sale Proceeds / Outstanding Debt)

Of these two methods, it is more common to see the first formula be used as it is more conservative approach to reflect the maximum potential loss. It can often be difficult to assess what the potential sale proceeds are especially considering multiple collateral assets, disposition costs, timing of payments, and liquidity of each asset.

## Loss Given Default (LGD) vs. Exposure at Default (EAD)

Exposure at default is the total value of a loan that a bank is exposed to when a borrower defaults. For example, if a borrower takes out a loan for \$100,000 and two years later the amount left on the loan is \$75,000, and the borrower defaults, the exposure at default is \$75,000.

When analyzing default risk, banks will often calculate the EAD on a loan as it aims to predict the amount the bank will be exposed to when a borrower defaults. Exposure at default constantly changes as a borrower pays down their loan.

Depending on the loan, such as a mortgage or student loan, there are a different number of days passed without payment that counts as a default. Make sure you are aware of the figure for your specific loan.

The main difference between LGD and EAD is that LGD takes into consideration any recovery on the default. For this reason, EAD is the more conservative measurement as it is the higher figure. LGD is more often the best case scenario that relies on multiple assumptions.

For example, if a borrower defaults on their remaining car loan, the EAD is the amount of the loan left they defaulted on. Now, if a bank can then sell that car and recover a certain amount of the EAD, that will be taken into consideration to calculate LGD.

## Example of Loss Given Default (LGD)

Imagine a borrower takes out a \$400,000 loan for a condo. After making installment payments on the loan for a few years, the borrower begins to face financial difficulties. It is estimated that the borrower has an 80% of default. The outstanding loan balance is \$300,000, and the bank will be able to sell the condo for \$200,000 upon foreclosure.

To calculate the LGD in dollars, compare the amount at risk to the likelihood of default. In this situation, the lender interprets \$240,000 at risk of default.

LGD (in dollars omitting collateral) = \$300,000 * (1 - 80%) = \$240,000

Alternatively, LGD can be calculated as a percentage that typically incorporates the value of the collateral. Although the formula above is easier to calculate, it did not factor in the disposition proceeds of the condo in the event of default. Using the second variation, the lender should anticipate losing 33% of their capital should the condo owner default when considering the collateral value.

LGD (as percentage including collateral) = 1 - (\$200,000 / \$300,000) = 33.33%

## What Does Loss Given Default Mean?

Loss given default (LGD) is the amount of money a financial institution loses when a borrower defaults on a loan, after taking into consideration any recovery, represented as a percentage of total exposure at the time of loss.

## What Are PD and LGD?

LGD is loss given default and refers to the amount of money a bank loses when a borrower defaults on a loan. PD is the probability of default, which measures the probability, or likelihood that a borrower will default on their loan.

## What Is the Difference Between EAD and LGD?

EAD is exposure at default and represents the value of a loan that a bank is at risk of losing at the time a borrower defaults on their loan. Loss given default is the value of a loan that a bank is at the risk of losing, after taking into proceeds from the sale of the asset, represented as a percentage of total exposure.

## Can Loss Given Default Be Zero?

Loss given default can theoretically be zero when a financial institution is modeling LGD. If the model believes that a full recovery on the loan is possible then the LGD can be zero. This is usually not the case, however.

## What Is Usage Given Default?

Usage given default is another term for exposure at default, which is the total value left on a loan when the borrower defaults.

## The Bottom Line

When making loans, banks tend to reduce their risk as much as they can. They evaluate a borrower and determine the risk factors of lending to that borrower, including the probability of them defaulting on the loan and how much the bank stands to lose if they do default. Loss given default (LGD), probability of default (PD), and exposure at default (EAD) are calculations that help banks quantify their potential losses.

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