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Of the following statements, select the one(s) that is (are) most likely true with regards to a loan portfolio:
i) Lowering the recovery rate + Increasing the default probability = an increase expected loss
ii) Increasing the recovery rate + Increasing the default probability = an increase expected loss
iii) Lowering the recovery rate + Lowering the default probability = an increase expected loss
(Do not include the answer options.)
A
i only
B
ii only
C
iii only
D
i and ii only
E
i and iii only
F
i, ii and iii
Explanation:
Expected loss (EL) for a loan portfolio is typically given by EL = PD * LGD * EAD (where PD = probability of default, LGD = loss given default = 1 - recovery rate, and EAD = exposure at default). Consider effects:
Statement (i): Lowering the recovery rate raises LGD; increasing PD raises PD. Both changes push EL higher (product of PD and LGD increases), so EL increases. This statement is true.
Statement (ii): Increasing the recovery rate lowers LGD (which reduces EL) while increasing PD raises EL. The net effect is ambiguous without magnitudes — EL may increase or decrease depending on which effect dominates. Therefore the statement that it "= an increase expected loss" is not generally true.
Statement (iii): Lowering the recovery rate (raises LGD → increases EL) but lowering PD (reduces EL). Again the net effect is ambiguous and not necessarily an increase. So (iii) is not generally true.
Thus only (i) is most likely true in general; the correct choice is A. This question falls under Credit Risk Measurement and Management because it concerns PD, recovery/LGD and expected loss.