Case 059Credit derivatives and counterparty riskCore

Five counterparties with exposures of Rs 40, 25, 60, 15 and 30 crore, default probabilities of 0.5%, 2%, 0.8%, 6% and 1.5%, and 60% loss given default except the fifth at 45%. Compute and rank expected loss, and say which limit you would cut first.

The situation

Ghatghar Bank's derivatives desk has uncollateralised swap and forward exposure to five corporate counterparties. The expected exposureThe average amount the counterparty would owe the bank if it defaulted, estimated from how the derivatives could move in value. to each is Rs 40 crore, Rs 25 crore, Rs 60 crore, Rs 15 crore and Rs 30 crore. The credit team's one-year default probabilities are 0.5%, 2%, 0.8%, 6% and 1.5%. Loss given default is 60% for the first four; the fifth counterparty has posted security, so its loss given default is 45%.

The head of risk wants expected loss for each name, a ranking, and a recommendation on which limit to cut first.

Your task

Compute expected loss by counterparty, rank them, state the total, and say which limit to cut first and why that is not the same as cutting the largest exposure.

Quick check

Before working it: which counterparty carries the largest expected loss?

Worked solution

Try it on paper, then open one step at a time.

30-second answerThe answer to give first

Expected loss ranks D first at Rs 0.54 crore, then B at Rs 0.30, C at Rs 0.288, E at Rs 0.2025 and A last at Rs 0.12, a total of Rs 1.45 crore a year. Cut D's limit first: it is the smallest exposure and the largest expected loss because its 6% default probability dominates. The Rs 60 crore name, C, is second-largest by exposure but only third by expected loss, which is why limits should follow expected loss, not size.

Step 1What is expected loss, and why three factors rather than one?

A shopkeeper who sells on credit to five regulars does not worry most about the one with the biggest tab; he worries about the one most likely not to pay, scaled by how much is owed and how much he could recover by sending someone round. Expected loss is exactly that product: how much is at stake, how likely the default, and how much of the stake is lost when it happens. Leave out any one factor and the ranking changes, which is the trap the question is built around.

The relationship
EL=EE×PD×LGDELD=15×0.06×0.60=0.54 crore\text{EL} = \text{EE} \times \text{PD} \times \text{LGD} \qquad \text{EL}_D = 15 \times 0.06 \times 0.60 = 0.54 \text{ crore}
EEexpected exposure, the amount the counterparty would owe on default, Rs crore
PDone-year probability of default
LGDloss given default, the share of exposure not recovered
What it says in wordsExpected loss is exposure times the chance of default times the share you lose when it happens; for D that is 15 times 6% times 60%.
CounterpartyExposure, Rs crPDLGDExpected loss, Rs crRank
A400.5%60%0.125
B252.0%60%0.32
C600.8%60%0.2883
D156.0%60%0.541
E301.5%45%0.20254
Total1701.4505
Expected loss for the five names sums to Rs 1.45 crore a year on Rs 170 crore of exposure. D, with the smallest exposure, ranks first; C, with the largest, ranks third.
The smallest exposure is the largest expected loss0.20.400.12A: Rs 40 crPD 0.5%, LGD 60%8% of total0.30B: Rs 25 crPD 2.0%, LGD 60%21% of total0.288C: Rs 60 crPD 0.8%, LGD 60%20% of total0.54D: Rs 15 crPD 6.0%, LGD 60%37% of total0.202E: Rs 30 crPD 1.5%, LGD 45%14% of totalExpected loss, Rs crore = exposure x default probability x loss given defaultTotal across the five names: Rs 1.45 crore a year
D's Rs 15 crore exposure at a 6% default probability produces the tallest expected loss bar at Rs 0.54 crore, 37% of the desk's total, while A's Rs 40 crore at 0.5% is the shortest at Rs 0.12 crore.
Step 2Which limit do you cut first, and what does cutting it achieve?

D. Every crore of exposure to D costs Rs 3.6 lakh a year in expected loss, against Rs 0.48 lakh for C and Rs 0.3 lakh for A. Halving D's limit to Rs 7.5 crore removes Rs 0.27 crore of expected loss; halving C's much larger limit to Rs 30 crore removes only Rs 0.144 crore. The desk gives up less business for more risk reduction by cutting D. The same arithmetic says E is less dangerous than its Rs 30 crore suggests, because the security it posted lowers the loss given default; the next conversation with D should be about collateral for the same reason.

Step 3Where does expected loss stop being the right measure?

Expected loss is an average, the cost of doing business, and it is what a bank prices into its spreads and provisions. It says nothing about the worst case. If C defaults the desk loses Rs 36 crore in one event, while D's worst case is Rs 9 crore, so a limit framework that only follows expected loss would let C grow until a single default could hurt the quarter. A complete answer cuts D first on expected loss and watches C on concentration, and names the limitation of the inputs: a 6% default probability is an estimate, and expected exposure is a model output that grows when markets move against the counterparty, which is often when the counterparty is also weakest.

Where candidates lose it

Candidates rank by exposure and name C, or they notice D's 6% and stop there without multiplying. The interviewer wants the three-factor product written out for all five, then the ranking read off it.

The second miss is treating the secured name's 45% as a default probability rather than a loss given default. Keep PD and LGD in separate columns and the arithmetic stays honest.

What the interviewer asks next

  • D offers to post Rs 5 crore of cash collateral. Redo its expected loss and say whether that changes the ranking.
  • How does expected exposure differ from current exposure, and why might C's expected exposure of Rs 60 crore be understated in a stress?
  • The bank charges a credit valuation adjustment on each trade. How does expected loss feed into it?

Company names and figures are illustrative.