Banking
Credit risk and expected loss
Expected loss is probability of default times loss given default times exposure at default, and it has to be priced into every loan.
Definition
Credit risk is the risk that a borrower does not pay as promised. It is measured as an expected loss rather than a single worst case, so that the average cost of default is built into the interest rate the lender charges.
Three estimates drive the number: how likely a default is, how much is lost when it happens, and how much is owed at that moment.
Intuition
Lending is a portfolio business. A small expected loss on every loan is affordable; the danger is a loss larger than you assumed, all at once, in the same corner of the book.
When to use it
- Setting the interest rate on a loan or a portfolio of loans.
- Comparing lending opportunities with different default and recovery profiles.
- Explaining the difference between expected loss and the capital held against uncertainty.
When not to use it
- As a substitute for stress testing, which asks what happens if the estimates are wrong together.
- Assuming PD and LGD are stable through a cycle.
Formula
Expected loss
EL = PD × LGD × EAD
Probability of default times loss given default times exposure at default.
- PD
- Probability of default
- LGD
- Loss given default, as a share of exposure
- EAD
- Exposure at default
Formula
Expected loss rate
Expected loss rate = PD × LGD
The loss expected per unit of exposure, used to set the loan price.
Worked example
Pricing a portfolio
A ৳10,00,000 portfolio has a 3% probability of default and, when a borrower defaults, 60% of the exposure is lost.
- 1
Loss rate
PD × LGD = 3% × 60% = 1.8% of exposure.
- 2
Expected loss
1.8% × ৳10,00,000 = ৳18,000.
- 3
Price it in
The book must earn more than 1.8% in spread to be worthwhile.
Expected loss is ৳18,000. Capital is held on top of this for the losses that exceed the average.
Common mistakes
- Using a probability of default from a benign period to price loans in a downturn.
- Ignoring concentration: many small loans to the same industry are not diversified.
- Confusing expected loss, an average, with unexpected loss, the tail that capital covers.
How it connects
is measured by
The target is the metric or diagnostic for the source.
- Ratio analysis: Coverage and leverage ratios are the first read on credit quality.
relates to
Useful to study together, in either order.
requires
Learn the source first; the target assumes it.