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Answer: 8.9%
D is correct. The standard deviation of losses for each individual loan is: α = Vp = p2 [L(1 - R)] = /0.04 - 0.042 [500,000 * (1 0.3)] =68,585.71 where p represents probability of default, Li represents exposure at default (amount borrowed), and Ri represents recovery rate. The standard deviation of losses on the portfolio of n loans as a percentage of its size is then calculated as: α/1 + (n - 1)p α= LVn 68,585.71V1 + (30 1) *0.4 500,000/30 = 0.08890 or 8.9%
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A risk analyst at a financial institution is evaluating the potential distribution of credit losses associated with a portfolio of 30 identical loans. The analyst assumes that the credit losses follow a binomial distribution. The details for each individual loan are specified as follows:
Using this information, calculate the standard deviation of the total losses for the entire loan portfolio, expressed as a percentage of the portfolio's aggregate amount.
A
3.8%
B
5.8%
C
7.8%
D
8.9%
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