ThetaBank has extended substantial financing to two mortgage companies, which these mortgage lenders use to finance their own lending. Individually, each of the mortgage companies have an exposure at default (EAD) of $20 million, with a loss given default (LGD) of 100%, and a probability of default of 10%. ThetaBank’s risk department predicts the joint probability of default at 5%.

ThetaBank has extended substantial financing to two mortgage companies, which these mortgage lenders use to finance their own lending. Individually, each of the mortgage companies have an exposure at default (EAD) of $20 million, with a loss given default (LGD) of 100%, and a probability of default of 10%. ThetaBank’s risk department predicts the joint probability of default at 5%.

If the default risk of these mortgage companies were modeled as independent risks, the actual probability would be underestimated by:
A . 1%
B . 2%
C . 3%
D . 4%

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Answer: D