Explanation:
The joint default probability and the default correlation are nugatory as far as the expected credit loss of the portfolio is concerned. In other words, they do not matter.
The expected loss of the portfolio is simply the sum of the expected losses of individual assets.
For the first bond,
EA = `$500`,000,
PD = 0.05, and
LR = 0.5
Thus,
\text{EL}_{\text{AA}} = 500,000 \times 0.05 \times 0.5 = \`$12`,500For the second bond,
EA = `$300`,000,
PD = 0.03, and
LR = 0.7
Thus,
\text{EL}_{\text{BB}} = 300,000 \times 0.03 \times 0.7 = \`$6`,300Portfolio credit loss = `12`,500 + \`6,300 = \$18`,800
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Q.3685 A portfolio consists of two bonds. The credit VaR – as defined by the bondholder – is the maximum loss due to defaults at a confidence level of 99%, over a period of one year. The probability that the two bonds jointly default is 2%, with a default correlation of 25%. The bond value, default probability, and recovery rate are USD 500,000, 5%, and 50% for one bond, and USD 300,000, 3%, and 30% for the other. Determine the expected credit loss of the portfolio:
A
USD 18,800
B
USD 12,500
C
USD 18,424
D
USD 12,424