Explanation:
The expected loss of the portfolio is the sum of the expected losses of individual assets.
For AA-rated bonds,
\text{EA} = \`120`,000,000\text{PD} = 0.04\text{LR} = 0.35$
Thus,
\text{EL}_{\text{AA}} = 120,000,000 \times 0.04 \times 0.35 = \`$1`,680,000For BB-rated bonds,
\text{EA} = \`80`,000,000\text{PD} = 0.06\text{LR} = 0.6$
Thus,
\text{EL}_{\text{BB}} = 80,000,000 \times 0.06 \times 0.6 = \`$2`,880,000Portfolio expected loss = \`1,680,000 + \2`,880,000 = \`4`,560,000$
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Q.3684 An investor holds a portfolio of $200 million. This portfolio consists of AA-rated bonds ($120 million) and BB-rated bonds ($80 million). Assume that the one-year probabilities of default for AA-rated and BB-rated bonds are 4% and 6%, respectively, and that they are independent. In the event of default, the recovery rate for AA-rated bonds is 65%, and the recovery rate for BB-rated bonds is 40%. Determine the one-year expected loss from this portfolio:
A
$1,680,000
B
$4,560,000
C
$4,500,000
D
$2,880,000
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