
Explanation:
First, determine the Exposure at Default (EAD):
EAD = Outstanding + (Drawdown \times Undrawn) = \`80,000 + (0.70 \times \20`,000) = \`94`,000$
Calculate Expected Loss (EL):
EL = EAD \times PD \times LGD = \`94,000 \times 0.02 \times 0.40 = \
Calculate Unexpected Loss (UL) given that only PD and LGD have variation:
Where .
UL = \`94,000 \times \sqrt{0.02(0.30^2) + 0.40^2(0.0196)}$ $UL = \94`,000 \times \sqrt{0.0018 + 0.003136} = \`94,000 \times \sqrt{0.004936}$ $UL = \94`,000 \times 0.07025667 \approx \`6`,604$
Option C is exactly correct.
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Q.39 A bank has booked a loan with a total commitment amounting to $100,000. 80% of this amount is currently outstanding. The default probability of the loan is assumed to be 2% for the next year, and the loss given default (LGD) stands at 40%. The standard deviation of LGD is 30%. The drawdown on default (i.e., the fraction of the undrawn loan) is assumed to be 70%. Determine the expected and unexpected losses for the bank.
A
Expected loss = USD 640; unexpected loss = USD 5,621.
B
Expected loss = USD 640; unexpected loss = USD 6,604.
C
Expected loss = USD 752; unexpected loss = USD 6,604.
D
Expected loss = USD 752; unexpected loss = USD 5,621.
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