A risk dashboard with different meanings
Series XXI-B case study · set 2, case 4 of 6 · 5 questions · 2 marks each
Question 1 of 5Case practice
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The case · stays here for all 5 questions
A portfolio’s observed values, with no external flows, are ₹100 lakh, ₹120 lakh, ₹90 lakh and ₹108 lakh in chronological order. Its risk report also shows a one-day 95% value at risk of ₹4 lakh, based on the manager’s specified model. A separate credit exposure has ₹20 lakh outstanding, a one-year default probability of 3% and a loss-given-default estimate of 40%. The report’s assumptions may fail, so model outputs are not guarantees. The committee wants to distinguish historical drawdown, recovery, a modelled loss quantile and expected credit loss. Use expected credit loss = exposure × probability of default × loss given default.
All amounts and contract terms in this case are hypothetical.
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The case and its answers
Every question of this case, with its answer and why each other option is wrong.
A portfolio’s observed values, with no external flows, are ₹100 lakh, ₹120 lakh, ₹90 lakh and ₹108 lakh in chronological order. Its risk report also shows a one-day 95% value at risk of ₹4 lakh, based on the manager’s specified model. A separate credit exposure has ₹20 lakh outstanding, a one-year default probability of 3% and a loss-given-default estimate of 40%. The report’s assumptions may fail, so model outputs are not guarantees. The committee wants to distinguish historical drawdown, recovery, a modelled loss quantile and expected credit loss. Use expected credit loss = exposure × probability of default × loss given default.
All amounts and contract terms in this case are hypothetical.
Q1What is the largest observed peak-to-trough drawdown in the value sequence?
Option A. 10%
Why it is wrong: This compares the initial value with the trough rather than the prior peak.
Option B. 20%
Why it is wrong: This is the later rise from ₹90 lakh to ₹108 lakh.
Option C. 30%
Why it is wrong: This divides the ₹30 lakh fall by the initial ₹100 lakh instead of the ₹120 lakh peak.
Option D. 25% — Correct answer
Answer: D. (₹120 lakh − ₹90 lakh)/₹120 lakh = 25%. Remember: Drawdown is measured from a prior peak to a subsequent trough.
Hint, shown before you answer in practice mode: Use the preceding peak as the denominator.
XXIB-S2-C04-Q1mediumnumerical
Q2What gain would have been needed at ₹90 lakh to regain the ₹120 lakh peak?
Option A. 33.33% — Correct answer
Option B. 30%
Why it is wrong: This uses ₹100 lakh as the denominator.
Option C. 25%
Why it is wrong: A fall and its recovery use different bases.
Option D. 20%
Why it is wrong: That gain reaches only ₹108 lakh.
Answer: A. ₹30 lakh/₹90 lakh × 100 = 33.3333%. Remember: A percentage recovery needed after a loss is larger than the loss percentage.
Hint, shown before you answer in practice mode: Divide the ₹30 lakh recovery requirement by the trough value.
XXIB-S2-C04-Q2mediumnumerical
Q3At the latest ₹108 lakh value, how far below the old peak is the portfolio?
Option A. 25%
Why it is wrong: This was the earlier maximum drawdown.
Option B. 12%
Why it is wrong: This divides the ₹12 lakh gap by the initial value.
Option C. 10% — Correct answer
Option D. 20%
Why it is wrong: This is the rise from the trough.
Answer: C. (₹120 lakh − ₹108 lakh)/₹120 lakh = 10%. Remember: Distinguish current drawdown from maximum observed drawdown.
Hint, shown before you answer in practice mode: Compare current value with the ₹120 lakh peak.
XXIB-S2-C04-Q3easynumerical
Q4Which reading of the one-day 95% VaR is most appropriate?
Option A. The model estimates a 5% chance of a one-day loss exceeding ₹4 lakh — Correct answer
Option B. The portfolio will lose ₹4 lakh every twentieth day
Why it is wrong: A probability does not create a fixed calendar pattern.
Option C. The average loss on the worst 5% of days is exactly ₹4 lakh
Why it is wrong: That describes a tail-average concept, not VaR itself.
Option D. A loss can never exceed ₹4 lakh
Why it is wrong: VaR is not a maximum-loss guarantee.
Answer: A. At the stated confidence level, the model assigns 5% probability to losses beyond the threshold. Model error and changing conditions can alter realised outcomes. Remember: Keep model confidence levels separate from guarantees.
Hint, shown before you answer in practice mode: VaR identifies a modelled quantile, not the size of every tail loss.
XXIB-S2-C04-Q4hardapplication
Q5What is the separate exposure’s one-year expected credit loss?
Option A. ₹2.40 lakh
Why it is wrong: This overstates the result by ten times.
Option B. ₹60,000
Why it is wrong: This ignores the loss-given-default fraction.
Option C. ₹8 lakh
Why it is wrong: This is loss given default in rupees without weighting by default probability.
Option D. ₹24,000 — Correct answer
Answer: D. ₹20,00,000 × 3% × 40% = ₹24,000. This probability-weighted expectation is not a forecast of the actual realised loss. Remember: Expected credit loss combines exposure, probability and severity.
Hint, shown before you answer in practice mode: Multiply exposure by both probability and severity.
XXIB-S2-C04-Q5mediumnumerical
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