Expected Loss (EL) Calculation

Lending institutions need to understand the loss that can be incurred as a result of lending to a company that may default; this is known as expected loss (EL).  EL can be expressed as a simple formula:

EL = PD * LGD * EAD

The total exposure to credit risk is the amount that the borrower owes to the lending institution at the time of default; the exposure at default (EAD). Generally, EAD will not be larger than the borrowing facility.

PD & LGD are risk metrics employed in the measurement and management of credit risk. The metrics are used to calculate EL.

The probability of default (PD) is the likelihood that a loan will not be repaid and will fall into default. It must be calculated for each borrower. The credit history of the borrower and the nature of the investment must be taken into consideration when calculating PD. External ratings agencies such as Standard and Poors or Moody’s may be used to get a PD; however, banks can also use internal rating methods.  PD can range from 0% to 100%. If a borrower has 50% PD it is considered a less risky company vs. a company with an 80% PD.  For example:

A borrower (Company X) takes out a loan from Bank ABC for $10 million (EAD). Company X pledges $3 million collateral against this loan (for simplicity, let’s say the collateral is cash). The Company’s PD is determined by analyzing their credit risk aspects (evaluate the financial health of the borrower, taking into account economic trends, borrower relationship with the bank, etc.) For Company X, let’s say the PD is 0.99. This means that the Company is extremely risky; the probability of them defaulting on the loan is 99%.

Loss given default (LGD) is the fractional loss due to default. Continuing from the previous example:

If Company X defaults (is unable to pay back the $10 million to Bank ABC), the Bank will be able to recover $3 million (this is the cash-secured collateral).

So, how do we calculate the actual loss given default (LGD)?

LGD = 1 – Recovery Rate (RR)

The Recovery Rate (RR) is defined as the proportion of a bad debt that can be recovered. It is calculated as:

RR = Value of Collateral/Value of the Loan

Back to our example, the recovery rate for Bank ABC = $3 million/ $10 million = 30%

So % LGD= 1- 0.30 = 0.70 or 70%.

$ LGD= 70% of a $10 million (EAD) loan is equal to $7 million.

$ LGD = $7 million

Expected Loss (EL) is what a bank can expect to lose in the case that their borrower defaults. It is calculated below:

EL = PD * LGD * EAD

EL= 0.99* 70% * $10 million

EL = $6.93 million

Bank ABC can expect to lose $6.93 million.

Sources:

Financial Risk Manager Handbook: (Fifth Edition) Philippe Jorion Introduction to Credit Risk (pg 434)

Wharton: What Do We Know About Loss Given Default?  Til Schuermann

http://fic.wharton.upenn.edu/fic/papers/04/0401.pdf