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Explanation:
First, we determine the portfolio's unexpected loss (). The formula for a two-asset portfolio's unexpected loss is:
Where:
Since the two loans are identical in terms of exposure, PD, LR, and standard deviation, their risk contributions to the portfolio's unexpected loss must be equal. Therefore, the risk contribution of each asset is simply half of the portfolio's total unexpected loss: RC = \frac{UL_p}{2} = \frac{8.80}{2} = \`$4.40` \text{ million}
Alternatively, using the exact risk contribution formula: RC_1 = UL_1 \times \frac{UL_1 + \rho \times UL_2}{UL_p} = 5.5 \times \frac{5.5 + 0.28 \times 5.5}{8.80} = 5.5 \times \frac{7.04}{8.80} = \`$4.40` \text{ million}
Both methods yield $4.40 million.
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506.3. A bank has extended two loans to customers in the same industry. Both loans have an exposure amount (EA) of $50.0 million, default probability (PD) of 2.0%, loss rate (LR) of 50.0%, and standard deviation of loss rate of 60.0%, such that each loan has an expected loss of $500,000 and an unexpected loss of $5.5 million. In this way, the bank's credit portfolio consists of these two credit assets; and the default correlation between the two loans is 28.0%.
Which is nearest to the risk contribution of each asset to the portfolio's unexpected loss?
A
$3.33 million
B
$4.40 million
C
$5.37 million
D
$5.50 million