Explanation:
To calculate the Economic Capital (EC) for exposures 2 and 3, we first need to determine their risk contributions (RC). The risk contribution formula is provided in the example:
For Exposure #2:
,000 \times [\840`,000 + (\`597,000 \times 0.40) + (\1`,023,500 \times 0.40)] / \`1`,920,250$,000 \times [\840`,000 + \`238,800 + \409`,400] / \`1`,920,250$,000 \times \1`,488,200 / \`1,920,250 = \Economic Capital for Exposure #2:
,003.77 \times 5.50 = \3`,580,520.73 \approx \`3.6` \text{ million}$For Exposure #3:
,023,500 \times [\1`,023,500 + (\`597,000 \times 0.40) + (\840`,000 \times 0.40)] / \`1`,920,250$,023,500 \times [\1`,023,500 + \`238,800 + \336`,000] / \`1`,920,250$,023,500 \times \1`,598,300 / \`1,920,250 = \Economic Capital for Exposure #3:
,899.25 \times 5.50 = \4`,685,445.88 \approx \`4.7` \text{ million}$Therefore, the required economic capitals are nearest to $3.6 million and $4.7 million.
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922.1. Consider a credit portfolio that contains three positions. The exposure (EAD) of each position is $10.0 million. Further, our model assumes the shape of the loss distribution (aka, the credit risk of each exposure) is identical for each exposure, although their means vary as follows:
$597,000$840,000$1,023,500The pairwise default correlation is 0.40 among each exposure pair, such that the portfolio’s unexpected loss is $1,920,250. In regard to Exposure #1, its risk contribution is given by
$597,000 * [$597,000 + ($840,000 * 0.40) + ($1,023,500 * 0.40)] / $1,920,250 = $417,348.
Because the capital multiplier, CM, is set at 5.50 to reflect a specified confidence level, the economic capital for Exposure #1, EC(#1) = $417,348 * 5.50 = $2,295,415, or about $2.30 million. Which of the following is NEAREST, respectively, to the required economic capital for the second and third exposures, EC(#2) and EC(#3)?
A
$434,000 and $568,000
B
$651,000 and $852,000
C
$3.6 and $4.7 million
D
$5.9 and $7.7 million