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Answer: The correlation between each pair of Ui distributions is equal to a².
## Explanation **D is correct.** The correlation between each pair of Ui distributions is indeed equal to a² in this model structure. **A is incorrect** because values in the extreme left tail (not right tail) represent default in this standard normal distribution mapping. **B is incorrect** because high values of F indicate a strong economy (not weak), and low values of F indicate a weak economy (not strong). **C is incorrect** because F is a common factor that is equal for all loans in the portfolio (not unique to each loan). The model described uses a common factor F that affects all loans, with individual loan-specific factors Ui. The correlation structure is determined by the parameter a, where the correlation between each pair of Ui distributions equals a².
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The correlation between each pair of Ui distributions is equal to a². Which of the following statements is correct about the default probabilities and the common factor F in the context of the model described?
A
The default probabilities are each mapped to the standard normally distributed variable Ui, and values in the extreme right tail represent default.
B
High values of F indicate a weak economy, and low values of F indicate a strong economy.
C
F is a unique factor that varies for each loan in the portfolio.
D
The correlation between each pair of Ui distributions is equal to a².
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