How is expected loss calculated using PD, LGD and EAD in credit risk?

Question

I'm doing Risk Management in Banking and Insurance for CMA Final. In the credit risk chapter the formula Expected Loss = EAD x PD x LGD looks simple, but I don't understand how EAD is calculated for a cash credit limit that is only partly used. Also what is unexpected loss?

GradeHunt_Team · Answer

Expected Loss (EL) is the average loss a bank expects on a loan over a time horizon, usually one year.

EL = EAD x PD x LGD

1. PD (Probability of Default): the chance that the borrower defaults within the period, as a %. Banks estimate it from ratings and past default data on similar borrowers.
2. LGD (Loss Given Default): the % of the exposure the bank does not recover after default, after selling security and other recoveries. LGD = 1 - recovery rate.
3. EAD (Exposure at Default): the amount the borrower owes when the default happens. For a limit that is only partly used, EAD = amount already drawn + a percentage of the undrawn part, because borrowers tend to draw more as they get close to default. That percentage is the credit conversion factor (CCF).

Worked example:
Cash credit limit Rs 50 lakh, drawn Rs 40 lakh, undrawn Rs 10 lakh, CCF 50% (assumed for this example; the actual factor depends on the facility type and the approach the bank or regulator uses).
EAD = 40 + (50% x 10) = Rs 45 lakh
PD = 2%
Security is expected to recover 60%, so LGD = 40%
EL = 45 lakh x 0.02 x 0.40 = Rs 0.36 lakh = Rs 36,000

What the bank does with it: EL is a normal cost of lending, so it is covered through loan pricing and provisions. If the bank lends to 100 such borrowers, it expects losses of around Rs 36 lakh in total, and the interest margin should absorb that.

Unexpected Loss (UL): actual losses in a bad year can be much higher than the average. UL is the amount by which actual losses exceed expected loss, measured through the standard deviation of losses or a chosen high percentile of the loss distribution. UL is what the bank's capital is meant to absorb. So EL is priced and provided for; UL is backed by capital.

Exam tip: write the formula, compute EAD separately with its working, convert PD and LGD to decimals, and state the answer in rupees.

How is expected loss calculated using PD, LGD and EAD in credit risk?

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