# Exposure, Default and Recovery Rates

In order to understand default risk, we will analyze the its key components.

**Default arrival:** As we learned earlier, a default occurs when a counterparty defaults on its obligation. In general, there are two scenarios: default or no default. The value for default arrival is taken as one if the default has occurred. Otherwise, the value is 0.

**Exposure at Default (EAD):** This refers to the total value that the bank is exposed to at the time of default. The bank will calculate the exposure at default for each obligor at the given time. Banks will use their own internal methods, using the IRB approach to calculate the exposure at default.

**Loss Given Default (LGD):** The third factor is the loss given default. This factor determines the losses incurred by the bank when an obligor defaults. The loss given defaults differs from the exposure at default because the bank is unlikely to lose all the value that they are exposed to. There will be some recovery and therefore the actual losses will be lesser. So banks will compare actual losses to the potential exposure at the time of default to calculate LGD.

LGD is not generally calculated for individual loans. Instead, it is calculated for a portfolio of loans.

**Default Loss** Using the above three factors, the bank can calculate the default loss as given below:

**Default loss: Default arrival x EAD x LGD**

The above formula assumes only the two cases where either there is a default or there is no default. In reality, banks will have to consider the probability of default to calculate the expected loss.

**Expected Loss (EL) = PD x EAD x LGD**

**Example:**

Assume that the PD is 0.25, EAD is $1 million, and LGD is 60%, then the expected loss will be calculated as follows:

**EL = 0.25 x 1,000,000 x 0.60

EL = $150,000**

The banks use various methods to calculate probability of defaults, exposures, and loss given defaults. We will look at these methods in other articles.

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